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Day 01 homework, due Aug 29
Briefly (one paragraph) describe why you are taking this course and what you hope to get out of it.
My research interest is in learning and working with Cloudy. You are the originator of the software, so I want to learn what you know. The story I have in my head is that Cloudy grew around solving and explaining problems in astrophysics related to spectroscopy. I never asked directly, but it seems reasonable to assume that many of those problems are going to be described and practiced in this course. More generally, I want to learn about as many astrophysical phenomena as I can. Within the limit of taking required courses, the topical course requirement allows for only one astrophysics course. Given the nature of the course, I suspect (or hope?) this class surveys a wide breadth of phenomena. With these two important criteria satisfied by the course, attending it is a no-brainer.
Did you see the solar eclipse? Briefly describe what you saw if you did.
Yes! I was surprised that, visually, I barely noticed the eclipse even past 75% coverage, unless I looked directly at the sun's disk with glasses. After something around 75%, it became noticeably dimmer, and eventually I saw earthly things in a color I don't remember seeing before. It was something like a dark blue. At some point, the moon became visible as part of a black disk across the sun, and it looked like a hole in the sky, which eventually gobbled up the last bit of bright light from the sun. After that, surrounding this hole, I could see the dimmer shine of the sun's corona, with a few outward streams of light-emitting gases converging to tips at a distance about 2 solar disk radii from the center. I expected them to be longer. For about 2.5 minutes, I sat back and watched the streams as I pondered the magnetohydrodynamics of the beast. When the sun's disk peered its brighter light around the back edge of the moon's obscuring disk, it was strikingly bright, like a laser shining in my direction, and that was the last I saw.
Why kind of laptop (Linux, Mac, Windows) do you have?
Linux
What experience have you had with Linux utilities such as ssh or ftp? “None” is a perfectly fine answer.
Very experienced

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"Species" "Ionization Potential"
0 9.46E+04
1 1.90E+05
2 3.89E+05
3 5.24E+05
4 1.94E+06
5 2.38E+06
6 2.86E+06
7 3.52E+06
8 4.07E+06
9 4.66E+06
10 5.53E+06
11 6.07E+06
12 2.83E+07
13 3.10E+07

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Homework 10, due Sept 28
Ionization Potential T₀ = E₀ / kᵦ.
kᵦ = 8.62×10⁻⁵ eV K⁻¹.
1) What is the ionization potential of H 0 in K?
T₀ = 158000 K.
2) What are the ionization potentials, in K, of the all 14 atoms and ions of
Si? (Si 0 , Si + , Si 2+ , Si 3+ , Si 4+ , ... Si 13+ ?)
T₀[Si I] = 9.46E+04 K. (M)
T₀[Si II] = 1.90E+05 K. (M)
T₀[Si III] = 3.89E+05 K. (M)
T₀[Si IV] = 5.24E+05 K. (M)
T₀[Si V] = 1.94E+06 K. (L)
T₀[Si VI] = 2.38E+06K. (L)
T₀[Si VII] = 2.86E+06 K. (L)
T₀[Si IIX] = 3.52E+06 K. (L)
T₀[Si IX] = 4.07E+06 K. (L)
T₀[Si X] = 4.66E+06 K. (L)
T₀[Si XI] = 5.53E+06 K. (L)
T₀[Si XII] = 6.07E+06 K. (L)
T₀[Si XIII] = 2.83E+07 K. (K)
T₀[Si XIV] = 3.10E+07 K. (K)
3) On the table you make of ionization potentials, indicate whether the
outermost electrons are in the K, L, or M shell.
Above.
4) Make a plot with the x axis the ion number (0 for Si 0 , 1 for Si + , etc), the y
axis the ionization potential in eV
a. First linear y axis
b. Second log y axis
Plots uploaded sparately.

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data = read.table("coronal.cut",header=T)
names(data)
count(data)
length(datA)
length(data)
length(data[,2])
length(data[,1])
length(data[,0])
plot(data[,1],data[,2])
plot(data)
plot(data)
plot(data,log="x")
plot(data,log="x",type="b")
plot(data,log="x",type="l")
plot(data,log="x",type="l",ylab="erg/s",xlab="micrometers")
plot(data,log="x",type="l",ylab="erg/s",xlab="micrometer")
plot(data,log="x",type="l",ylab="erg/s",xlab="micrometer wavelength")
plot(data,log="x",type="l",ylab="erg/s flux",xlab="micrometer wavelength")
pdf("coronal.pdf")
plot(data,log="x",type="l",ylab="erg/s flux",xlab="micrometer wavelength")
dev.off()
plot(data,log="x",type="l",ylab="erg/s flux",xlab="micrometer wavelength",xlim=c(1e-4,1e4))
plot(data,log="x",type="l",ylab="erg/s flux",xlab="micrometer wavelength",xlim=c(1e-4,1e0))
plot(data,log="x",type="l",ylab="erg/s flux",xlab="micrometer wavelength",xlim=c(1e-4,1e4))
pdf("coronal.pdf")
plot(data,log="x",type="l",ylab="erg/s flux",xlab="micrometer wavelength",xlim=c(1e-4,1e4))
dev.off()
quit()
pdf("coronal.pdf")
plot(data,log="x",type="l",ylab="erg/s/cm^2 flux",xlab="micrometer wavelength",xlim=c(1e-4,1e4))
dev.off()
quit()

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Homework 12, due Oct 5
1) For the kinetic temperatures of a cluster of galaxies, T=3x10⁷ K, and for the Orion H II region, T=10⁴ K, what energy in eV does it correspond to?
T 3x10⁷ K 10⁴ K
Eₖₜ 2585.2 eV 0.86173 eV
2) What is the closest ionization stage of the six most common elements for those two temperatures, considering just the ionization energy?
Cluster Orion
Thermal Average Energy
────────────────────────
2585.2 eV 0.86173 eV
Near Ionization Stage
────────────────────────
H I H I
He II He I
O VIII O I
C VI C I
Ne X Ne I
Fe XXIV Fe I
We expect all of the elements to be ionized in the cluster, except iron.
3) Consider the very important case of H 2 , H 0 , and H + . What is the temperature needed to dissociate H 2 and form H 0 , and then to ionize H 0 ?
H₂[zero point] = -4.5 eV.
4.5 eV / kᵦ = 5.2×10⁴ K.
H⁰[zero point] = 13.6 eV.
13.6 / kᵦ = 1.58×10⁶ K.

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Homework 13, due Oct 10
1) Use the simple form of the NIST transition probabilities for H I. What is the transition probability for Lyman alpha? Lyman gamma?
Just reading Aₖᵢ values from the table.
6.27×10⁸ s⁻¹
1.278×10⁷ s⁻¹
2) What is the transition probability for Balmer alpha? Balmer beta?
4.410×10⁷ s⁻¹
8.419×10⁶ s⁻¹
3) What is the lifetime for the n=2 and n=4 levels of hydrogen?
This is the inverse of the sum ∑ₗAᵤ﹐ₗ where l = {1..u}.
n=2:
Lifetime T = (∑ₗA₂﹐ₗ)⁻¹
= (6.27×10⁸ s⁻¹)⁻¹
= 1.60×10⁻⁹ s.
n=4:
T = (∑ₗA₄﹐ₗ)⁻¹
= (1.278×10⁷ s⁻¹ + 8.419×10⁶ s⁻¹ + 8.986×10⁶ s⁻¹)⁻¹
= 3.313×10⁻⁸ s.

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ls()
data = read.table("partition.tab")
plot(data,type"b")
plot(data,type="b")
data
plot(x=data.V1)
data.V1
data["partition.tab"]
ls(data)
data[,"V1"]
data = read.table("partition.tab",header=T)
plot(data,type="b")
plot(data,type="b",log="xy")
plot(data,type="b",log="xy",xlab="Temperature (K)",ylab="Partition Function (n.u.)")
pdf("partition.pdf")
plot(data,type="b",log="xy",xlab="Temperature (K)",ylab="Partition Function (n.u.)")
dev.off()
quit()
lyman = read.table("lyman.tab")
plot(lyman,ylab="Emissivity (erg /s /cm^3)",xlab="Temperature (K)",log="xy",type="b")
plot(lyman,ylab="Emissivity (erg /s /cm^3)",xlab="Temperature (K)",log="xy",type="b")
lyman
plot(lyman[,V1],lyman[,V3],,ylab="Emissivity (erg /s /cm^3)",xlab="Temperature (K)",log="xy",type="b")
plot(lyman[,V1],lyman[,V3],ylab="Emissivity (erg /s /cm^3)",xlab="Temperature (K)",log="xy",type="b")
plot(lyman[,"V1"],lyman[,"V3"],ylab="Emissivity (erg /s /cm^3)",xlab="Temperature (K)",log="xy",type="b")
pdf("lyman.pdf")
plot(lyman[,"V1"],lyman[,"V3"],ylab="Emissivity (erg /s /cm^3)",xlab="Temperature (K)",log="xy",type="b")
dev.off()
exit
quit()

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10 0 0
100 0 0
1000 1.9e-40 1.3e-42
10000 2199661 22548
100000 1402819 14380
1000000 983798 10084
10000000 949502 9733

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T U
10 2
100 2
1000 2
10000 2.095
100000 139606
1000000 577892
10000000 666102

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Homework 14, due Oct 12
1) The partition function of H, given in lecture.
T U
10 2
100 2
1000 2
10000 2.095
100000 139606
1000000 577892
10000000 666102
Plot submitted as pdf.
2) The emissivity of Lyman alpha given in the lecture
T Density (first excited) Emissivity (erg s⁻¹ cm⁻³)
10 0 0
100 0 0
1000 1.9e-40 1.3e-42
10000 2199661 22548
100000 1402819 14380
1000000 983798 10084
10000000 949502 9733

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curve()
curve(
?curve
curve(0.00308105*exp(-4241.3*x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)")
curve(0.00308105*exp(-4241.3*x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",ylim=c(0,0.004))
curve(0.00308105*exp(-4241.3*x)*x,xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",ylim=c(0,0.004))
curve(0.00308105*exp(-4241.3*x)*x,xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",ylim=c(0,0.0004))
curve(0.00308105*exp(-4241.3*x)*x,xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",ylim=c(0,0.000004))
curve(0.00308105*exp(-4241.3*x)*x,xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",ylim=c(0,0.0000000004))
q
curve(0.00308105*exp(-4241.3/x),xlim=c(5000,50000))
curve(0.00308105*exp(-4241.3/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)"))
curve(0.00308105*exp(-4241.3/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)"))
curve(0.00308105*exp(-4241.3/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)")
curve(0.00308105*exp(-4241.3/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",log="x")
curve(0.00308105*exp(-4241.3/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",log="y")
pdf("lineratio.pdf")
curve(0.00308105*exp(-4241.3/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",log="y")
dev.off()
ln(0.0048/0.00308105)/-4241.3
log(0.0048/0.00308105)/-4241.3
log10(0.0048/0.00308105)/-4241.3
?log
log(0.0048/0.00308105)/-4241.3
quit()
pdf("lineratio.pdf")
curve(0.00308105*exp(-4241.3/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",log="y")
pdf("lineratio.pdf")
dev.off()
curve(0.00308105*exp(-4241.3/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",log="y")
dev.off()
pdf("lineratio.pdf")
curve(0.0040569*exp(-4241.3/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",log="y")
dev.off()
exit()
exit
quit()
curve(36.070*exp(-32976/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",log="y")
pdf("lineratio.pdf")
curve(36.070*exp(-32976/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="Line Ratio (n.u.)",log="y")
dev.off()
curve(36.070*exp(-32976/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="I[4262A]/I[5007A] (n.u.)",log="y")
pdf("lineratio.pdf")
curve(36.070*exp(-32976/x),xlim=c(5000,50000),xlab="Temperature (K)",ylab="I[4262A]/I[5007A] (n.u.)",log="y")
dev.off()
quit()

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Homework 15, due Oct 17
1) Find the ratio of emission in the [O III] 4363 to 5007 lines as a function of temperature assuming LTE. Use the energies and TPs from NIST and assume LTE. Give this as an equation as a function of temperature.
A₁﹐ᵦ
j₁/j₂ = g₁/g₂ A₁/A₂ hν₁/hν₂ exp(-E₁₂/kT).
j₁/j₂ = g₁/g₂ A₁/A₂ λ₂/λ₁ exp(-E₁₂/kT).
g₁/g₂ = 1/3.
A₁/A₂ = 94.292.
λ₂/λ₁ = 1.1476.
E₁₂ = 2.84 eV.
exp(-E₁₂/kT) = exp(-2.84 eV/k × T) = exp(-32976 K⁻¹ × T).
j₁/j₂ = 1/3 × 94.292 × 1.1476 × exp(-32976 K⁻¹ × T).
j₁/j₂ = 36.070 × exp(-32976 K⁻¹ × T).
─────────────
2) Plot the line ratio as a function of temperature between 5000 K and 50 000 K. Make the y-axis a log.
Attached.
─────────────
3) The line ratio is observed to be I(4363)/I(5007) = 0.0048 in Orion. What would be the LTE temperature? (Orion is not in LTE).
*
0.0048 = 36.070 × exp(-32976 K⁻¹ × T).
0.0048/36.070 = exp(-32976 K⁻¹ × T).
ln(0.0048/36.070) = -32976 K⁻¹ × T.
(ln(0.0048/36.070)/-32976) K = T.
T = 0.0027064 K.
Way too small! Something wrong.
─────────────
4) What is the coefficient
the Saha equation, in CGS units?
⎛2 π mₑ k T ⎞3/2
⎜---------- ⎟ = 2.41468×10¹⁵ g/(K erg s²) T^(3/2).
⎝ h² ⎠
─────────────
5) Assume a hydrogen density of 1e15 cm-3. What is the hydrogen ionization fraction H+/H0 at 6000 K, 10 000 K, and 20 000 K?
n[ion]/n[atom] = 1/nₑ
× U[ion]/U[atom]
× gₑ
× (coefficient)
× T^(3/2)
× exp(-E[ion]/kT).
nₑ = 10¹⁵ cm⁻³.
U[ion] = 1.
U[atom] = 10^0.3 ≈ 2.
gₑ = 2.
coefficient = 2.41468×10¹⁵ g/(K erg s²).
Temperature Ion Fraction
6000 K 4.196×10⁻⁶
10000 K 3.365×10⁻¹
20000 K 2.552×10³
─────────────
6) Use the Boltzmann equation to find the n=2 population at these three temperatures and give the Lya emissivity.
Just following the process from hw14.
4 π j = n₂ Aᵤₗ hν.
hν = 1.63403 × 10⁻¹¹ ergs.
n₂ differs by temperature: ~1.1×10⁷, ~3.9×10⁷, ~6.3×10⁷.
Aᵤₗ = 6.27×10⁸ s⁻¹.
Temperature Emissivity
6000 K 1.136×10⁵ ergs
10000 K 4.024×10⁵ ergs
20000 K 6.525×10⁵ ergs

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1) What is the partition function for O III at 10 4 K?
The partition function for O III is approximately independent of temperature, provided the density is not very small, and can be read from table 3-2B in Stellar Atmospheres.
U[O III] = 10^0.95 ≈ 8.9.
I computed this by taking the sum in an excel spreadsheet.. I get ~9.009. Like this:
Config.  Term J  "Level (eV)" gᵢ E₁ᵢ Weight
       
2s22p2   3P  0 0 1 0 1
    1 0.0140323 3 0.0140323 2.951544
    2 0.0379607 5 0.0379607 4.784523
2s22p2   1D  2 2.513565 5 2.513565 0.270513
2s22p2   1S  0 5.354349 1 5.354349 0.002002
2s2p3   5S°  2 7.479321 5 7.479321 0.000850
2s2p3   3D°  3 14.88123 7 14.88123 2.214550E-07
  2 14.88472 5 14.88472 1.575428E-07
    1 14.88532 3 14.88532 9.445992E-08
2s2p3   3P°  2 17.65299 5 17.65299 6.342369E-09
...
Temperature 1.00E+04 U 9.00943346
2) What is the density of the 1 S level if the total O III density is 1e10 cm -3 ?
nₜₒₜ/nₛ = g₁ₛ/U.
gᵢ = 2*Jᵢ+1, g₁ₛ = 1.
n₁ₛ/nₜₒₜ = g₁ₛ*exp(-E₁﹐₁ₛ/kT)/8.9 = 0.000222.
n₁ₛ = 2.22×10⁶ cm⁻³.
3) Assume a temperature of 10 4 K, about that of a typical A star like Vega or Sirius.
What is the hydrogen ionization fraction H + /H total at hydrogen densities of 10 10 ,
10 15 and 10 20 cm -3 ?
I'm actually stuck on how to solve this. I can get the algebraic manipulation to
nₕ/(nₕ₊)² = 1/nₕ₊ + 1/saha,
but I can't figure out how to solve for nₕ/(nₕ₊). Once I get that, then I just plug the saha equation in the appropriate place and get the density. Most people are saying that they just are not putting the square in and getting about the right answer anyway, so I would appreciate my credit being considered within that context.
At least for partial credit, the saha equation evaluates to
6.948×10²². I have the densities, so once this is solved I'll have the density of nₕ₊.
***Late Finish:
This is a quadratic equation that reads
(nₕ₊)² + nₕ₊*saha - nₕ*saha = 0, which has positive solution
nₕ₊ = 1/2 (√(saha)*√(4*nₕ+saha) - saha)
This gives solutions
nₕ₊ = {1.00×10¹⁰, 4.35×10¹⁴, 1.83×10¹⁷}, so
nₕ₊/nₕ = {1.00, 43.5, 1.83×10³}.
This is not right, however. I know these should be different by about 5 orders of magnitude. I am not sure what is wrong. I am copying in my spreadsheet values, because maybe you can help identify where my values went wrong. Thanks.
2*pi*me*k/h/h = 17998640157.
(2*pi*me*k/h/h)^3/2 = 2.41×10¹⁵.
nH 1.00E+10 1.00E+15 1.00E+20
UH 2 2 2
UH+ 1 1 1
ge 2 2 2
Eion 13.605693 13.605693 13.605693009
T 1.00E+04 1.00E+04 1.00E+04
kT 0.86173303 0.86173303 0.86173303
saha 3.3565×10¹⁴ 3.3565×10¹⁴ 3.3565×10¹⁴
nH+ 1.00E+10 4.35E+14 1.83E+17
nH+/nH 1.00E+00 4.35E-01 1.83E-03

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λ(obs) = λ(rest) (1 + z)
z = (λ(obs) - λ(rest)) λ(rest)⁻¹
adiabatic process
─────────────
P^(1-γ) T^γ = constant
VT^(f/2) = constant
TV^(γ-1) = constant

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Day 17 homework
─────────────
Assume the following very approximate scaling relations for the temperature, density, and age of the universe, as a function of redshift z.
◆ T kinetic = 2.7 (1+z) K
◆ n(H) ≈ 2.51×10⁻⁷ (1+z)³ cm ⁻³
◆ Age ≈ 1.3×10¹⁰ (1+z)\^-1.5 yr
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Find the H + , H 0 , n e density vs z. Neglect all elements other than H, and assume that H + is the only source of free electrons. Use the Saha equation for the kinetic temperature given. Make a plot showing the H + /H and H 0 /H ionization fractions as a function of redshift, for 0.1 < z < 10 6 . Make both axes a base 10 log.
I use the approximate total hydrogen number density as a function of z.
n(H) ≈ 2.51×10⁻⁷ (1+z)³ cm ⁻³
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Find the brems opacity at 0.5 microns vs z. Plot this opacity vs redshift with both axes logs.
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Find the photon mean free path vs z and plot this. Add the visible diameter of the universe, c × Age, to this plot.
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
At what redshift does the photon mean free path equal the visible diameter of the universe? The universe is transparent with the mean free path is larger than the diameter, and a foggy photosphere when the mean free path is less.
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
What is the temperature at this redshift?
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Assuming Wein’s Law, λₚₑₐₖ ∝ T⁻¹ , what would be the temperature of this blackbody today? How does this compare with the observed CMB temperature of 2.7K?

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@ -0,0 +1,237 @@
data = read.table("h+.tab")
plot(data)
data = read.table("h+.tab")
plot(data[,1])
plot(data)
data
data = read.table("h+.tab")
plot(data[,1])
plot(data[,1],data[,9])
plot(data[,1],data[,9],type="b")
plot(data[,1],data[,9],type="b",log="x")
plot(data[,1],data[,9],type="b",log="xy")
plot(data[,1],data[,9],type="b")
plot(data[,1],data[,9],type="b",log="x")
plot(data[,1],data[,9]/data[,3],type="b",log="x")
.125/2
data = read.table("h+.tab")
data = read.table("h+.tab")
plot(data[,1],data[,11],type="b",log="x")
plot(data[,1],data[,13],type="b",log="x")
line(data[,1],data[,13],type="b")
line(data[,1],data[,13])
?line
?lines
lines(data[,1],data[,13],type="b")
lines(data[,1],data[,11],type="b")
pdf("saha.pdf")
plot(data[,1],data[,13],type="b",log="x")
lines(data[,1],data[,11],type="b")
dev.off()
plot(data[,1],data[,13],type="b",log="x")
lines(data[,1],data[,11],type="b",pch="□")
plot(data[,1],data[,13],type="b",log="x")
lines(data[,1],data[,11],type="b",pch="x")
lines(data[,1],data[,11],type="l",pch="x")
plot(data[,1],data[,13],type="l",log="x")
lines(data[,1],data[,11],type="l",pch="x")
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift")
?plot
tick
ticks
label
lab
par
?par
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",xaxp=c(1,10,100,1000,10000))
?xaxp
plot
?plot
?par
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",lab=c(5,5,20))
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",lab=c(7,5,20))
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",lab=c(7,5,5))
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",lab=c(7,5,3))
?par
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",xaxp=c(1,10000,5))
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",xaxp=c(1,1000,5))
?par
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",xaxp=c(0,5,1))
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",xaxp=c(0,5,1:1))
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",xaxp=c(1,5,1))
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",xaxp=c(-1,5,1))
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",xaxp=c(1,5,1))
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",xaxp=c(1,5,1),type="b")
plot(data[,1],data[,13],type="b",log="x",xlab="Redshift",xaxp=c(1,5,1))
lines(data[,1],data[,11],type="l",pch="x")
lines(data[,1],data[,11],type="b",pch="x")
plot(data[,1],data[,13],type="b",log="x",xlab="Redshift",xaxp=c(1,5,1).pch="-")
plot(data[,1],data[,13],type="b",log="x",xlab="Redshift",xaxp=c(1,5,1),pch="-")
lines(data[,1],data[,11],type="b",pch="|")
plot(data[,1],data[,13],type="b",log="x",xlab="Redshift",xaxp=c(1,5,1),pch="-")
lines(data[,1],data[,11],type="b",pch="=")
plot(data[,1],data[,13],type="b",log="x",xlab="Redshift",xaxp=c(1,5,1),pch="-")
lines(data[,1],data[,11],type="b",pch="x")
plot(data[,1],data[,13],type="b",log="x",xlab="Redshift",xaxp=c(1,5,1),pch="-")
lines(data[,1],data[,11],type="b",pch=".")
lines(data[,1],data[,11],type="b",pch="█")
plot(data[,1],data[,13],type="b",log="x",xlab="Redshift",xaxp=c(1,5,1),pch="-")
lines(data[,1],data[,11],type="b",pch="◎")
?lines
lines(data[,1],data[,11],type="b",lty = 1)
plot(data[,1],data[,13],type="b",log="x",xlab="Redshift",xaxp=c(1,5,1),pch="-")
lines(data[,1],data[,11],type="b",lty = 1)
lines(data[,1],data[,11],type="l",lty = 1)
plot(data[,1],data[,13],type="b",log="x",xlab="Redshift",xaxp=c(1,5,1),pch="-")
lines(data[,1],data[,11],type="l",lty = 1)
lines(data[,1],data[,11],type="l",lty = 2)
plot(data[,1],data[,13],type="b",log="x",xlab="Redshift",xaxp=c(1,5,1),pch="-")
lines(data[,1],data[,11],type="l",lty = 2)
plot(data[,1],data[,13],type="b",log="x",xlab="Redshift",xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],type="b",lty=2)
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],type="l",lty=2)
?legend
legend( x="left",
legend=c("Red line, blue points","Green line, purple points"),
col=c("red","green"), lwd=1, lty=c(1,2), pch=c(15,17), merge=FALSE )
> plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",xaxp=c(1,5,1),lty=3)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )
plot(data[,1],data[,13],type="l",log="x",xlab="Redshift",xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],type="l",lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )
plot(data[,1],data[,13],
type="l",
log="x",
xlab="Redshift",
xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],
type="l",
lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )
plot(data[,1],data[,13],
type="l",
log="x",
xlab="Redshift",
ylab="n/nₜₒₜ"
xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],
type="l",
lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )
plot(data[,1],data[,13],
type="l",
log="x",
xlab="Redshift",
ylab="n/nₜₒₜ"
xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],
type="l",
lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )
plot(data[,1],data[,13],
type="l",
log="x",
xlab="Redshift",
ylab="n/n[tot] (n.u.)"
xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],
type="l",
lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )
plot(data[,1],data[,13],
type="l",
log="x",
xlab="Redshift",
ylab="n/n[tot] (n.u.)"
xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],
type="l",
lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )
plot(data[,1],data[,13],
type="l",
log="x",
xlab="Redshift",
ylab="n/nₜₒₜ",
xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],
type="l",
lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )
plot(data[,1],data[,13],
type="l",
log="x",
xlab="Redshift",
ylab="n/nₜₒₜ",
xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],
type="l",
lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )plot(data[,1],data[,13],
type="l",
log="x",
xlab="Redshift",
ylab="n/nₜₒₜ",
xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],
type="l",
lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )
plot(data[,1],data[,13],
type="l",
log="x",
xlab="Redshift",
ylab="n/nₜₒₜ",
xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],
type="l",
lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )
plot(data[,1],data[,13],
type="l",
log="x",
xlab="Redshift",
ylab="n/nₜₒₜ [n.u.]",
xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],
type="l",
lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )
plot(data[,1],data[,13],
type="l",
log="x",
xlab="Redshift [n.u.]",
ylab="n/nₜₒₜ [n.u.]",
xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],
type="l",
lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )
quit()

92
hw18/h+.tab Normal file
View File

@ -0,0 +1,92 @@
1.00E+00 5.40E+00 2.01E-06 4.60E+09 3.03E+16 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.01E-06 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
1.15E+00 5.82E+00 2.51E-06 4.11E+09 3.39E+16 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.51E-06 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
1.33E+00 6.30E+00 3.19E-06 3.65E+09 3.82E+16 0.00E+00 0.00E+00 0.00E+00 0.00E+00 3.19E-06 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
1.54E+00 6.86E+00 4.11E-06 3.21E+09 4.34E+16 0.00E+00 0.00E+00 0.00E+00 0.00E+00 4.11E-06 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
1.78E+00 7.50E+00 5.38E-06 2.81E+09 4.96E+16 0.00E+00 0.00E+00 0.00E+00 0.00E+00 5.38E-06 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
2.05E+00 8.24E+00 7.15E-06 2.44E+09 5.72E+16 0.00E+00 0.00E+00 0.00E+00 0.00E+00 7.15E-06 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
2.37E+00 9.10E+00 9.62E-06 2.10E+09 6.63E+16 0.00E+00 0.00E+00 0.00E+00 0.00E+00 9.62E-06 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
2.74E+00 1.01E+01 1.31E-05 1.80E+09 7.74E+16 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.31E-05 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
3.16E+00 1.12E+01 1.81E-05 1.53E+09 9.10E+16 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.81E-05 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
3.65E+00 1.26E+01 2.53E-05 1.30E+09 1.07E+17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.53E-05 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
4.22E+00 1.41E+01 3.56E-05 1.09E+09 1.28E+17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 3.56E-05 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
4.87E+00 1.58E+01 5.08E-05 9.14E+08 1.52E+17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 5.08E-05 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
5.62E+00 1.79E+01 7.29E-05 7.63E+08 1.83E+17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 7.29E-05 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
6.49E+00 2.02E+01 1.06E-04 6.34E+08 2.20E+17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.06E-04 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
7.50E+00 2.29E+01 1.54E-04 5.25E+08 2.65E+17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.54E-04 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
8.66E+00 2.61E+01 2.26E-04 4.33E+08 3.22E+17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.26E-04 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
1.00E+01 2.97E+01 3.34E-04 3.56E+08 3.91E+17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 3.34E-04 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
1.15E+01 3.39E+01 4.96E-04 2.92E+08 4.76E+17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 4.96E-04 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
1.33E+01 3.87E+01 7.39E-04 2.40E+08 5.81E+17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 7.39E-04 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
1.54E+01 4.43E+01 1.11E-03 1.96E+08 7.11E+17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.11E-03 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
1.78E+01 5.07E+01 1.66E-03 1.60E+08 8.72E+17 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.66E-03 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
2.05E+01 5.81E+01 2.51E-03 1.30E+08 1.07E+18 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.51E-03 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
2.37E+01 6.67E+01 3.79E-03 1.06E+08 1.32E+18 0.00E+00 0.00E+00 0.00E+00 0.00E+00 3.79E-03 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
2.74E+01 7.66E+01 5.74E-03 8.60E+07 1.62E+18 0.00E+00 0.00E+00 0.00E+00 0.00E+00 5.74E-03 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
3.16E+01 8.81E+01 8.71E-03 6.98E+07 2.00E+18 0.00E+00 0.00E+00 0.00E+00 0.00E+00 8.71E-03 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
3.65E+01 1.01E+02 1.33E-02 5.66E+07 2.46E+18 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.33E-02 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
4.22E+01 1.17E+02 2.02E-02 4.58E+07 3.04E+18 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.02E-02 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
4.87E+01 1.34E+02 3.08E-02 3.71E+07 3.75E+18 0.00E+00 0.00E+00 0.00E+00 0.00E+00 3.08E-02 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
5.62E+01 1.55E+02 4.71E-02 3.00E+07 4.64E+18 0.00E+00 0.00E+00 0.00E+00 0.00E+00 4.71E-02 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
6.49E+01 1.78E+02 7.20E-02 2.43E+07 5.74E+18 0.00E+00 0.00E+00 0.00E+00 0.00E+00 7.20E-02 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
7.50E+01 2.05E+02 1.10E-01 1.96E+07 7.10E+18 0.00E+00 0.00E+00 0.00E+00 0.00E+00 1.10E-01 1.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
8.66E+01 2.37E+02 1.69E-01 1.59E+07 8.78E+18 1.20E-290 1.05E-271 2.66E-136 2.66E-136 1.69E-01 1.00E+00 1.33E-136 7.89E-136 -1.33E-136 7.89E-136
1.00E+02 2.73E+02 2.59E-01 1.28E+07 1.09E+19 3.57E-252 3.88E-233 6.34E-117 6.34E-117 2.59E-01 1.00E+00 3.17E-117 1.23E-116 -3.17E-117 1.23E-116
1.15E+02 3.14E+02 3.97E-01 1.03E+07 1.35E+19 9.25E-219 1.25E-199 4.45E-100 4.45E-100 3.97E-01 1.00E+00 2.22E-100 5.60E-100 -2.22E-100 5.60E-100
1.33E+02 3.63E+02 6.09E-01 8.35E+06 1.67E+19 9.40E-190 1.57E-170 1.95E-85 1.95E-85 6.09E-01 1.00E+00 9.77E-86 1.60E-85 -9.77E-86 1.60E-85
1.54E+02 4.18E+02 9.35E-01 6.74E+06 2.07E+19 1.40E-164 2.89E-145 1.04E-72 1.04E-72 9.35E-01 1.00E+00 5.20E-73 5.56E-73 -5.20E-73 5.56E-73
1.78E+02 4.83E+02 1.44E+00 5.44E+06 2.56E+19 9.67E-143 2.48E-123 1.19E-61 1.19E-61 1.44E+00 1.00E+00 5.96E-62 4.15E-62 -5.96E-62 4.15E-62
2.05E+02 5.57E+02 2.21E+00 4.39E+06 3.18E+19 8.48E-124 2.69E-104 4.87E-52 4.87E-52 2.21E+00 1.00E+00 2.44E-52 1.10E-52 -2.44E-52 1.10E-52
2.37E+02 6.43E+02 3.39E+00 3.54E+06 3.94E+19 2.26E-107 8.91E-88 1.10E-43 1.10E-43 3.39E+00 1.00E+00 5.50E-44 1.62E-44 -5.50E-44 1.62E-44
2.74E+02 7.42E+02 5.21E+00 2.85E+06 4.88E+19 3.95E-93 1.93E-73 2.01E-36 2.01E-36 5.21E+00 1.00E+00 1.00E-36 1.92E-37 -1.00E-36 1.92E-37
3.16E+02 8.57E+02 8.01E+00 2.30E+06 6.05E+19 8.78E-81 5.31E-61 4.13E-30 4.13E-30 8.01E+00 1.00E+00 2.06E-30 2.57E-31 -2.06E-30 2.57E-31
3.65E+02 9.89E+02 1.23E+01 1.86E+06 7.51E+19 4.41E-70 3.31E-50 1.28E-24 1.28E-24 1.23E+01 1.00E+00 6.39E-25 5.18E-26 -6.39E-25 5.18E-26
4.22E+02 1.14E+03 1.90E+01 1.50E+06 9.31E+19 8.29E-61 7.72E-41 7.65E-20 7.65E-20 1.90E+01 1.00E+00 3.83E-20 2.02E-21 -3.83E-20 2.02E-21
4.87E+02 1.32E+03 2.92E+01 1.21E+06 1.15E+20 9.02E-53 1.04E-32 1.10E-15 1.10E-15 2.92E+01 1.00E+00 5.51E-16 1.89E-17 -5.51E-16 1.89E-17
5.62E+02 1.52E+03 4.49E+01 9.72E+05 1.43E+20 8.29E-46 1.19E-25 4.62E-12 4.62E-12 4.49E+01 1.00E+00 2.31E-12 5.14E-14 6.40E-16 5.14E-14
6.49E+02 1.76E+03 6.91E+01 7.84E+05 1.78E+20 8.95E-40 1.59E-19 6.63E-09 6.63E-09 6.91E+01 1.00E+00 3.31E-09 4.80E-11 -1.46E-15 4.80E-11
7.50E+02 2.03E+03 1.06E+02 6.32E+05 2.20E+20 1.51E-34 3.33E-14 3.76E-06 3.76E-06 1.06E+02 1.00E+00 1.88E-06 1.77E-08 -6.29E-15 1.77E-08
8.66E+02 2.34E+03 1.64E+02 5.09E+05 2.73E+20 5.09E-30 1.39E-09 9.54E-04 9.54E-04 1.64E+02 1.00E+00 4.77E-04 2.92E-06 2.37E-15 2.92E-06
1.00E+03 2.70E+03 2.52E+02 4.10E+05 3.39E+20 4.26E-26 1.44E-05 1.21E-01 1.21E-01 2.52E+02 1.00E+00 6.03E-02 2.40E-04 5.71E-15 2.40E-04
1.15E+03 3.12E+03 3.88E+02 3.31E+05 4.21E+20 1.06E-22 4.48E-02 8.33E+00 8.29E+00 3.83E+02 9.89E-01 4.14E+00 1.07E-02 -2.22E-14 1.08E-02
1.33E+03 3.60E+03 5.97E+02 2.67E+05 5.22E+20 9.33E-20 4.87E+01 3.44E+02 2.96E+02 4.49E+02 7.52E-01 1.48E+02 2.48E-01 0.00E+00 3.30E-01
1.54E+03 4.16E+03 9.18E+02 2.15E+05 6.48E+20 3.30E-17 2.14E+04 2.32E+04 1.76E+03 3.63E+01 3.96E-02 8.82E+02 9.60E-01 0.00E+00 2.43E+01
1.78E+03 4.80E+03 1.41E+03 1.73E+05 8.04E+20 5.33E-15 4.29E+06 4.29E+06 2.83E+03 4.66E-01 3.30E-04 1.41E+03 1.00E+00 0.00E+00 3.03E+03
2.05E+03 5.55E+03 2.18E+03 1.40E+05 9.98E+20 4.35E-13 4.34E+08 4.34E+08 4.35E+03 1.09E-02 5.01E-06 2.18E+03 1.00E+00 0.00E+00 2.00E+05
2.37E+03 6.41E+03 3.35E+03 1.13E+05 1.24E+21 1.97E-11 2.44E+10 2.44E+10 6.70E+03 4.59E-04 1.37E-07 3.35E+03 1.00E+00 0.00E+00 7.30E+06
2.74E+03 7.40E+03 5.16E+03 9.07E+04 1.54E+21 5.36E-10 8.24E+11 8.24E+11 1.03E+04 5.34E-08 1.04E-11 5.16E+03 1.00E+00 0.00E+00 9.65E+10
3.16E+03 8.54E+03 7.94E+03 7.31E+04 1.91E+21 9.37E-09 1.79E+13 1.79E+13 1.59E+04 -3.01E-04 -3.79E-08 7.94E+03 1.00E+00 0.00E+00 -2.64E+07
3.65E+03 9.86E+03 1.22E+04 5.89E+04 2.37E+21 1.12E-07 2.64E+14 2.64E+14 2.45E+04 -8.45E-03 -6.91E-07 1.22E+04 1.00E+00 0.00E+00 -1.45E+06
4.22E+03 1.14E+04 1.88E+04 4.75E+04 2.93E+21 9.53E-07 2.80E+15 2.80E+15 3.77E+04 -1.17E-02 -6.23E-07 1.88E+04 1.00E+00 0.00E+00 -1.61E+06
4.87E+03 1.32E+04 2.90E+04 3.82E+04 3.64E+21 6.11E-06 2.22E+16 2.22E+16 5.80E+04 -1.11E+00 -3.83E-05 2.90E+04 1.00E+00 0.00E+00 -2.61E+04
5.62E+03 1.52E+04 4.47E+04 3.08E+04 4.52E+21 3.05E-05 1.38E+17 1.38E+17 8.93E+04 2.63E+00 5.89E-05 4.47E+04 1.00E+00 0.00E+00 1.70E+04
6.49E+03 1.75E+04 6.88E+04 2.48E+04 5.61E+21 1.23E-04 6.89E+17 6.89E+17 1.38E+05 -3.39E+01 -4.93E-04 6.88E+04 1.00E+00 0.00E+00 -2.03E+03
7.50E+03 2.02E+04 1.06E+05 2.00E+04 6.96E+21 4.11E-04 2.86E+18 2.86E+18 2.12E+05 -9.58E+01 -9.05E-04 1.06E+05 1.00E+00 0.00E+00 -1.11E+03
8.66E+03 2.34E+04 1.63E+05 1.61E+04 8.63E+21 1.17E-03 1.01E+19 1.01E+19 3.24E+05 1.26E+03 7.72E-03 1.62E+05 9.92E-01 0.00E+00 1.28E+02
1.00E+04 2.70E+04 2.51E+05 1.30E+04 1.07E+22 2.89E-03 3.09E+19 3.09E+19 5.00E+05 1.22E+03 4.86E-03 2.50E+05 9.95E-01 0.00E+00 2.05E+02
1.15E+04 3.12E+04 3.87E+05 1.05E+04 1.33E+22 6.32E-03 8.41E+19 8.41E+19 7.70E+05 1.60E+03 4.13E-03 3.85E+05 9.96E-01 0.00E+00 2.41E+02
1.33E+04 3.60E+04 5.95E+05 8.44E+03 1.65E+22 1.25E-02 2.06E+20 2.06E+20 1.21E+06 -1.09E+04 -1.82E-02 6.06E+05 1.02E+00 0.00E+00 -5.58E+01
1.54E+04 4.16E+04 9.17E+05 6.80E+03 2.05E+22 2.24E-02 4.59E+20 4.59E+20 1.84E+06 -7.38E+02 -8.05E-04 9.18E+05 1.00E+00 0.00E+00 -1.24E+03
1.78E+04 4.80E+04 1.41E+06 5.48E+03 2.54E+22 3.73E-02 9.48E+20 9.48E+20 2.75E+06 3.55E+04 2.51E-02 1.38E+06 9.75E-01 0.00E+00 3.88E+01
2.05E+04 5.54E+04 2.17E+06 4.42E+03 3.15E+22 5.80E-02 1.83E+21 1.83E+21 4.19E+06 7.67E+04 3.53E-02 2.10E+06 9.65E-01 0.00E+00 2.73E+01
2.37E+04 6.40E+04 3.35E+06 3.56E+03 3.91E+22 8.49E-02 3.32E+21 3.32E+21 6.82E+06 -6.03E+04 -1.80E-02 3.41E+06 1.02E+00 0.00E+00 -5.65E+01
2.74E+04 7.39E+04 5.15E+06 2.87E+03 4.85E+22 1.18E-01 5.74E+21 5.74E+21 1.05E+07 -8.80E+04 -1.71E-02 5.24E+06 1.02E+00 0.00E+00 -5.96E+01
3.16E+04 8.54E+04 7.94E+06 2.31E+03 6.02E+22 1.57E-01 9.48E+21 9.48E+21 1.68E+07 -4.51E+05 -5.68E-02 8.39E+06 1.06E+00 0.00E+00 -1.86E+01
3.65E+04 9.86E+04 1.22E+07 1.86E+03 7.48E+22 2.02E-01 1.51E+22 1.51E+22 2.52E+07 -3.59E+05 -2.94E-02 1.26E+07 1.03E+00 0.00E+00 -3.50E+01
4.22E+04 1.14E+05 1.88E+07 1.50E+03 9.28E+22 2.50E-01 2.32E+22 2.32E+22 3.36E+07 2.05E+06 1.09E-01 1.68E+07 8.91E-01 0.00E+00 8.20E+00
4.87E+04 1.31E+05 2.90E+07 1.21E+03 1.15E+23 3.01E-01 3.46E+22 3.46E+22 5.87E+07 -3.73E+05 -1.29E-02 2.94E+07 1.01E+00 0.00E+00 -7.86E+01
5.62E+04 1.52E+05 4.46E+07 9.75E+02 1.43E+23 3.54E-01 5.05E+22 5.05E+22 9.23E+07 -1.50E+06 -3.36E-02 4.61E+07 1.03E+00 0.00E+00 -3.08E+01
6.49E+04 1.75E+05 6.87E+07 7.86E+02 1.77E+23 4.06E-01 7.20E+22 7.20E+22 1.43E+08 -2.57E+06 -3.73E-02 7.13E+07 1.04E+00 0.00E+00 -2.78E+01
7.50E+04 2.02E+05 1.06E+08 6.33E+02 2.20E+23 4.59E-01 1.01E+23 1.01E+23 2.01E+08 5.19E+06 4.90E-02 1.01E+08 9.51E-01 0.00E+00 1.94E+01
8.66E+04 2.34E+05 1.63E+08 5.10E+02 2.73E+23 5.09E-01 1.39E+23 1.39E+23 3.19E+08 3.62E+06 2.22E-02 1.59E+08 9.78E-01 0.00E+00 4.41E+01
1.00E+05 2.70E+05 2.51E+08 4.11E+02 3.39E+23 5.57E-01 1.89E+23 1.89E+23 4.70E+08 1.61E+07 6.42E-02 2.35E+08 9.36E-01 0.00E+00 1.46E+01
1.15E+05 3.12E+05 3.87E+08 3.31E+02 4.20E+23 6.03E-01 2.53E+23 2.53E+23 7.72E+08 6.56E+05 1.70E-03 3.86E+08 9.98E-01 0.00E+00 5.89E+02
1.33E+05 3.60E+05 5.95E+08 2.67E+02 5.22E+23 6.45E-01 3.36E+23 3.36E+23 1.14E+09 2.48E+07 4.17E-02 5.70E+08 9.58E-01 0.00E+00 2.30E+01
1.54E+05 4.16E+05 9.17E+08 2.15E+02 6.47E+23 6.84E-01 4.43E+23 4.43E+23 1.88E+09 -2.29E+07 -2.50E-02 9.40E+08 1.03E+00 0.00E+00 -4.10E+01
1.78E+05 4.80E+05 1.41E+09 1.73E+02 8.03E+23 7.20E-01 5.78E+23 5.78E+23 2.75E+09 3.58E+07 2.53E-02 1.38E+09 9.75E-01 0.00E+00 3.85E+01
2.05E+05 5.54E+05 2.17E+09 1.40E+02 9.97E+23 7.52E-01 7.50E+23 7.50E+23 4.29E+09 2.61E+07 1.20E-02 2.15E+09 9.88E-01 0.00E+00 8.22E+01
2.37E+05 6.40E+05 3.35E+09 1.13E+02 1.24E+24 7.81E-01 9.67E+23 9.67E+23 6.71E+09 -8.26E+06 -2.47E-03 3.36E+09 1.00E+00 0.00E+00 -4.06E+02
2.74E+05 7.39E+05 5.15E+09 9.07E+01 1.54E+24 8.08E-01 1.24E+24 1.24E+24 1.05E+10 -8.01E+07 -1.55E-02 5.23E+09 1.02E+00 0.00E+00 -6.54E+01
3.16E+05 8.54E+05 7.94E+09 7.31E+01 1.91E+24 8.31E-01 1.58E+24 1.58E+24 1.61E+10 -1.16E+08 -1.46E-02 8.05E+09 1.01E+00 0.00E+00 -6.96E+01
3.65E+05 9.86E+05 1.22E+10 5.89E+01 2.36E+24 8.52E-01 2.01E+24 2.01E+24 2.44E+10 9.17E+06 7.50E-04 1.22E+10 9.99E-01 0.00E+00 1.33E+03
4.22E+05 1.14E+06 1.88E+10 4.75E+01 2.93E+24 8.71E-01 2.55E+24 2.55E+24 3.76E+10 3.20E+07 1.70E-03 1.88E+10 9.98E-01 0.00E+00 5.87E+02
4.87E+05 1.31E+06 2.90E+10 3.83E+01 3.64E+24 8.87E-01 3.23E+24 3.23E+24 5.80E+10 -5.82E+06 -2.01E-04 2.90E+10 1.00E+00 0.00E+00 -4.98E+03

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hw18/plots.R Normal file
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@ -0,0 +1,12 @@
plot(data[,1],data[,13],
type="l",
log="x",
xlab="Redshift [n.u.]",
ylab="n/nₜₒₜ [n.u.]",
xaxp=c(1,5,1),lty=3)
lines(data[,1],data[,11],
type="l",
lty=2)
legend( x="left",
legend=c("H⁺/H","H⁰/H"),
col=c("black","black"), lwd=1, lty=c(3,2), merge=FALSE )

170
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Homework 18, due Nov 1
The N II spectrum forms from N + , which is iso-electronic with O III / O 2+. This means that they have the same number of orbiting electrons although the nuclear charge is different. The structure of the energy levels of N II will be similar to O III although the energies and As will bedifferent. In homework 15 did O III. For this we will do N II. Go to NIST and look at the energy levels given there. 1 The lowest terms of O III are 3 P, 1 D, and 1 S, as shown in Lecture 15, top left slide of page 3. The energies of the levels are also given on that slide. How does the energies of the levels in N II compare with O III? What is the net nuclear charge of an orbiting valence electron in N II? What is the net nuclear charge for O III? For both, the net charge is the nuclear charge minus the number of inner electrons that screen the nuclear charge.
The energy levels have the same ratios, so the absolute value of each level for one ion is a scalar multiple of the absolute value of the energy of the level of the other ion.
For N II, Z[N II] = 7. For O III, Z[O III] = 8.
Net nuclear charge Q[N II] = 7 - 1 = 6, and Q[O III] = 8 - 2 = 6.
─────────────
2. Use these energies to write out the Boltzmann factor, exp −E/kT, for the 1 D and 1 S levels.
@ 10000 K, kT = 0.6333621 Rydberg
Boltzmann Factor β = exp(-E/kt) = exp(-E/(0.6333621 R))
1D 1S
E 1.396e-1 2.979e-1
β 4.0111 6.2480e-1
─────────────
3. For O III the 1 S – 1 D transition has a wavelength of 4363A. The wavelength of the 1 D – 3 P 2 level is 5007A. Use NIST and air wavelengths to find the wavelength of these two transitions for N II.
E = hf = hc/λ, λ = hc/E, where E = E₁ - E₂ (a transition from higher energy E₂ to lower energy E₁).
N II E1 (R) E2 (R) wavelength (A)
1S → 1D 2.9788E-01 1.3957E-01 5755.9878991494
1D → 3P2 1.3957E-01 1.1920E-03 6585.0757723516
─────────────
4. Use NIST to find the total Einstein A for the 1 S – 1 D and 1 D – 3 P 2 lines. How do they compare with the As for O III?
Just looking them up in the table by wavelength,
N II wavelength (A) A (1/s)
1S → 1D 5755.9878991494 1.14
1D → 3P2 6585.0757723516 8.65e-06
By the way, I see that my wavelengths are off a bit. Maybe difference between air and vacuum?
─────────────
5. What is the Boltzmann factor that predicts the LTE population ratio of the 1 D and 1 S levels? Assume LTE to predict the ratio of the 5755 to 6584 lines.
I realize now as I inspect homework 15 more closely that I should be doing these things as a function of T. Alright,
exp(-E₁₂/kT) = exp(-(E₁ᴅ - E₁ꜱ)/kT)
exp(((E₁ᴅ - E₁ꜱ)/k)/T)
= exp((0.1384 R - 0.1583)/(6.334e-6 R K⁻¹)/T)
= exp((-3147 K)/T).
Assuming LTE, the line ratio is given by g₁/g₂ A₁/A₂ λ₂/λ₁ exp((-3147 K)/T).
g₁/g₂ A₁/A₂ λ₂/λ₁ = 3.316e-5.
Seems small just based on that we'd be studying something in class that has a lot of action, but I think this should be expected considering the disparity in the einstein probabilities. I guess this just slides the action up or down the temperature scale, anyway.
─────────────
6. The ratio observed in the Orion Nebula is 0.02 ±0.003. What is the kinetic temperature, including the uncertainty? (This assumes LTE – that is not correct for the Orion Nebula.)
3.316e-5 exp((3147 K)/T) = 0.02 ±0.003.
Note: I've gone back and forth about this, because I would think this exp() factor should be negative, but from
g₁/g₂ nₜₒₜ/U U/nₜₒₜ exp(-(E₁ - E₀))/exp(-(E₂ - E₀)),
I get g₁/g₂ exp(E₂ - E₁).
3.316e-5 exp((3147 K)/T) = 0.02 ±0.003.
ln(3.316e-5) (3147 K)/T = ln(0.02 ±0.003).
T = ln(3.316e-5)/ln(0.02 ±0.003) (3147 K) = 7.966e3 K
≈ 8000 K.
This is quite high, like the photosphere of a star a bit hotter than Sol. I expected to get something more like 4000K, because of a previous assignment. I'm thinking there's an error here, but not an egregious one.
─────────────
We have demonstrated that Mathmatica cannot solve HW 17. Redo this with a spreadsheet. First derive and show the equations that will go in each column of the spreadsheet. In the spreadsheet make the first columns a log10 range in z with 10 < z < 1e5. Makecolumns giving the kinetic temperature, total hydrogen density, and age of the universe. Next use the Saha equation and electron conservation to write down the expression for the H + and H 0 density in terms of the temperature, by solving the quadratic.
Approximate relationship of redshift z to thermodynamic properties:
◆ T kinetic = 2.7 (1+z) K
◆ n(H) ≈ 2.51×10⁻⁷ (1+z)³ cm ⁻³
◆ Age ≈ 1.3×10¹⁰ (1+z)\^-1.5 yr
The Saha equation for ionized hydrogen is
nᵢₒₙ nₑ/nₐₜₒₘ = Uᵢₒₙgₑ/Uₐₜₒₘ (2πmₑkT/h²)^(3/2) exp(-Eᵢₒₙ/kT).
Checking units:
2πmₑkT/h² → g R (R*s)⁻²
→ g R⁻¹ s⁻²
→ g (g cm² s⁻²)⁻¹ s⁻²
→ cm⁻²
(2πmₑkT/h²)^3/2 → cm⁻³
Of course, nᵢₒₙ = nₑ, for ionized hydrogen.
(2πmₑkT/h²)^(3/2) = 2.415e15 cm⁻³ K^-(3/2) T^(3/2).
Established in previous assignments.
Eᵢₒₙ = 1 R.
gₑ = 2.
Uᵢₒₙ = 1.
Uₐₜₒₘ = 2.
So,
nᵢₒₙ²/nₐₜₒₘ = (2.415e15 cm⁻³ K^-(3/2) T^(3/2)) exp(-(1 R)/kT).
Set
α(T) = 2.415e15 cm⁻³ K^-(3/2) T^(3/2), and
β(T) = exp(-(1 R)/kT) = exp(-157900 K T⁻¹), and
γ(T) = α β.
Then, nᵢₒₙ²/nₐₜₒₘ = γ.
Particle conservation gives nₜₒₜ - nᵢₒₙ = nₐₜₒₘ.
To find an expression for the ionized hydrogen fraction, substitute for
nᵢₒₙ²/(nₜₒₜ - nᵢₒₙ) = γ.
nᵢₒₙ² + γ nᵢₒₙ - γ nₜₒₜ = 0.
Quadratic formula gives
nᵢₒₙ(nₜₒₜ,T) = 1/2 (-√γ √(γ + 4nₜₒₜ) - γ) and
nᵢₒₙ(nₜₒₜ,T) = 1/2 (√γ √(γ + 4nₜₒₜ) - γ).
For neutral hydrogen fraction,
(nₜₒₜ - nₐₜₒₘ)²/nₐₜₒₘ = γ.
(nₜₒₜ - nₐₜₒₘ)(nₜₒₜ - nₐₜₒₘ) = γ nₐₜₒₘ.
nₜₒₜ² - 2 nₐₜₒₘ nₜₒₜ + nₐₜₒₘ² = γ nₐₜₒₘ.
nₐₜₒₘ² + nₜₒₜ² - 2 nₐₜₒₘ nₜₒₜ - γ nₐₜₒₘ = 0.
nₐₜₒₘ² - nₐₜₒₘ(2 nₜₒₜ + γ) + nₜₒₜ² = 0.
Quadratic formula gives
nₐₜₒₘ(nₜₒₜ,T) = 1/2 (± √γ √(γ + 4 nₜₒₜ) + γ + 2 nₜₒₜ).
Reminder: α(T) = 2.415e15 cm⁻³ K^-(3/2) T^(3/2), and
β(T) = exp(-157900 K⁻¹ T).
So, I have
nᵢₒₙ(nₜₒₜ,T) = 1/2 (√γ √(γ + 4nₜₒₜ) - γ), and
nₐₜₒₘ(nₜₒₜ,T) = 1/2 (√γ √(γ + 4 nₜₒₜ) + γ + 2 nₜₒₜ), with
γ(T) = 2.415e15 cm⁻³ K^-(3/2) T^(3/2) exp(-157900 K T⁻¹).
─────────────
Make columns giving the H + and H 0 density at each redshift. Do not take the difference to two nearly identical numbers! Use different solutions for the quadratic to get the H + and H 0 densities. Plot each over the z range 10 to 1e5. The universe recombined at roughly z≈1000.
OK. I was stuck on this for a long time. I used the above equations, but I have what seems like numerical instability at high redshift. Perhaps I've used an unstable expression, but I think what I'm seeing here is a problem with librecalc when it computes √γ √(γ + 4nₜₒₜ) - γ. It seems that it's leaving out the nₜₒₜ factor where γ is very large, because of the disparity in order, I suppose. This is unfortunate, but I can't see how to fix it at the moment. However, the graph at least shows the general characteristics I'm looking for, with the ionization front at z≃1000. Plot attached.
─────────────
Find the brems opacity, recalling that the units are cm -1 . Make columns giving the photon mean free path (the inverse of the opacity) and the visible diameter of the universe. At what z do they cross? What is the temperature at that redshift? That is the photosphere we observe. Use the Wien displacement theorem to find the temperature of the blackbody we observe today.
Plot axes must be labeled with a font that can be read on a screen. Do not use a tiny font. Clearly label all lines on the plot. Especially clear and well-done examples may be posted as the solution. There will be extra credit if I use yours.

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1.0000E-03 6.0100E-18 4.1000E-09
1.0000E-02 6.0100E-16 4.1000E-08
1.0000E-01 6.0100E-14 4.1000E-07
1.0000E+00 6.0100E-12 4.1000E-06
1.0000E+01 6.0099E-10 4.1000E-05
1.0000E+02 6.0091E-08 4.1000E-04
1.0000E+03 6.0011E-06 4.1000E-03
1.0000E+04 5.9223E-04 4.1000E-02
1.0000E+05 5.2352E-02 4.1000E-01
1.0000E+06 2.4234E+00 4.1000E+00
1.0000E+07 3.8038E+01 4.1000E+01
1.0000E+08 4.0336E+02 4.1000E+02
1.0000E+09 4.0581E+03 4.1000E+03
1.0000E+10 4.0605E+04 4.1000E+04
1.0000E+11 4.0608E+05 4.1000E+05
1.0000E+12 4.0608E+06 4.1000E+06
1.0000E+13 4.0608E+07 4.1000E+07
1.0000E+14 4.0608E+08 4.1000E+08

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data = read.table("data.tab")
png("plot.png")
plot(
data[,1],
data[,2],
type="l",
lty=1,
log="xy",
xlim=c(1e-2,1e10),
xlab="Hydrogen Density [cm⁻³]",
ylab="Level Population 1D [cm⁻³]"
)
lines(data[,1],data[,3],lty=2)
abline(v=6.78e5,lty=3)
legend(
.5,
1e6,
legend = c("NLTE Steady State","LTE","Critical Density"),
lty=c(1,2,3)
# col=c("blue","green","red")
)
dev.off()

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Homework 19 (marked homework 21 on the pdf)
1. Solve the NLTE balance equation (equation 3.24 in AGN3, also given on page 6, side 2, of the lecture notes) for the population of the ¹D level of O III, n(¹D), cm⁻³. That equation gives the dimensionless population ratio n(¹D) / n(3P) we want the population. Assume that the total density of O²⁺ is 10⁻⁴ of the hydrogen density, and that the electron density is equal to the hydrogen density. Vary the hydrogen density n(H) between 10⁻² to 10¹⁰ cm⁻³ in 1 dex steps. Plot log n(¹D) as the x-axis and log n(H) as the y-axis.
NTLE balance is given by
n₂/n₁ = nₑ q₁₂/A₂₁ (1 + nₑ q₂₁/A₂₁)⁻¹.
I model a two level O-III atom.
I assume density n[O²⁺]/n[H] = 10⁻⁴.
I assume hydrogen is completely ionized, i.e.,
nₑ = n[H].
I will vary n[H], so I need only find the coefficients q and A, which can be pulled from AGN3,
From combining the 3P levels,
A₂₁(1D→3P) = [6.8e-3 + 2.0e-2 + 1.7e-6] s⁻¹
= 0.0268 [s⁻¹].
The collision strengths are also given in AGN3,
γ₁₂ = 2.29
q₂₁ = 8.629e-6 γ₁₂ Tₑ^(-1/2) g₂⁻¹ [cm³/s]
= 1.98e-5 Tₑ^(-1/2) g₂⁻¹ [cm³/s].
Assuming electron temperature
Tₑ = 1e4 K.
g₁ = 9,
combining all the states of the 3P levels.
g₂ = 2*J + 1,
with J = 2 for 1D, so
g₂ = 5,
q₂₁ = 1.98e-5 * 1e-2 K^(-1/2) 1/5
= 3.96e-08 [cm³/s].
q₁₂ = q₂₁ g₂/g₁ exp(-Eₜₒₜ/kT).
Eₜₒₜ = 26169 K.
q₁₂ = 2.20e-8 exp(-26169/1e4) [cm³/s].
= 2.20e-8 * 0.073 [cm³/s]
= 1.61e-9 [cm³/s].
So, the population ratio is
n₂/n₁ = nₑ q₁₂/A₂₁ (1 + nₑ q₂₁/A₂₁)⁻¹
= nₑ (1.61e-9 [cm³/s])/(0.0268 [s⁻¹])
× (1 + nₑ (3.96e-08 [cm³/s])/(0.0268 [s⁻¹]))⁻¹
= nₑ (1.61e-9/0.0268 [cm³])
× (1 + nₑ (3.96e-08/0.0268) [cm³])⁻¹
= nₑ (6.01e-8 [cm³]) (1 + nₑ (1.48e-6) [cm³])⁻¹.
This can now be computed across the n[H] density spectrum.
Plot attached.
2. Solve for this population using the Boltzmann equation, assuming U=9. Add this to the plot.
From the boltzmann equation
n₂/n₁ = g₂/g₁ exp(-Eₜₒₜ/kt)
= 5/9 * 0.073
= 0.041.
3. Find the critical density and indicate that on the plot. How does this compare with the density where the ¹D level has come into LTE?
Critical density can be predicted as
n[crit] = A₂₁/q₂₁ = 6.78e5 [cm⁻³].
This line is drawn on the plot, and shows where the level populations predicted by the NLTE solution agrees with LTE predictions.

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(1)
Solar Luminosity, according to this page, is 3.828 × 10²⁶ W.
The conversion from W to erg/s is (1 W)/(10⁷ erg/s).
3.828 × 10²⁶ W × (10⁷ erg/s) / (1 W) = 3.828 × 10³³ erg/s.
(2)
It quotes the most powerful quasars exceeding 10⁴¹ W.
10⁴¹ W × (10⁷ erg/s) / (1 W) = 10⁴⁸ erg/s.
The article claims that 3C 273 is about 4 trillion times as bright as our sun (intrinsically).
3.828 × 10³³ erg/s × 4 × 10¹² = 1.531 × 10⁴⁶ erg/s.
(3)
Flux F observed by some distant observer is related to intrinsic luminosity L by the inverse square law and the encompassing solid angle 4 π. We use 1 AU as the distance light travels from the sun to the top of earth's atmosphere, but of course in reality the light travels from the sun's photosphere (essentially the outer edge of the sun) and strikes the earth's atmosphere at essentially the edge of the earth's sphere. To compute this more accurately, we could subtract the radii of the earth and sun from the distance. Again, we'll just use 1 AU for these calculations, as indicated by the problem.
F = L/(4 π d²) = (3.828 × 10³³ erg/s) / ( 12.566 × (1 AU)² )
F = (3.046 × 10³² erg/s) / (1 AU)²
= (3.046 × 10³² erg/s) / (1.4960 × 10¹³ cm)²
= (3.046 × 10³² erg/s) / 3.3480 × 10²⁶
= 9.098 × 1⁵ erg/s/cm²
(4)
I note some useful conversions and constants here, then convert the wavelength to cm. To convert from wavelength λ to energy E or frequency ν, I use the DeBroglie relationships and the definition of wave velocity. I also note that one Rydberg is 13.606 eV, the energy needed to ionize hydrogen with an electron in the ground state.
1 Å = 10⁻⁸ cm.
h = 4.13567 × 10⁻¹⁵ eV s.
c = 29979245800 cm / s.
λ = 5000 Å × (10⁻⁸ cm/1 Å)
= 5 × 10⁻⁵ cm.
E = h ν.
λ ν = v = c (for a photon).
∴ E = h c / λ.
E = (4.13567 × 10⁻¹⁵ eV s) × (29979245800 cm / s) / (5000 Å) × (1 Å/10⁻⁸ cm).
= 2.479686 × 10⁷ × 10⁻¹⁵ × 10⁸ eV s cm Å /s / Å / cm
= 2.480 eV.
1 Rydberg = 13.606 eV.
E = 2.480 eV × (1 Rydberg/13.606 eV)
= 0.1823 rydberg.

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Homework 20, Day 22, Due Nov 9
Solve HW17 for the case of non-equilibrium time dependent ionization.
Plot H+/H and H0/H as a function of redshift, for 100 < z < 1e5. Include the equilibrium solution from HW17 or HW18 on the same plot, but with different line styles.
Find the recombination and ionization timescales. Make a plot showing these timescales together with the age of the universe.

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fe = read.table("shock.fe")
fe
plot(fe)
plot(fe[1,])
fe[1.]
fe[1,]
fe[1,]
fe[1,1]
fe[1,2]
fe[1,,]
fe[2,]
fe[0,]
fe[1,]
plot,x=c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28),y=fe[1,])
plot(x=c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28),y=fe[1,])
1..28
1...28
?seq
seq(1..28)
seq(1,28)
plot(seq(1,28),fe[1,])
plot(seq(1,27),fe[1,2..28])
plot(seq(1,27),fe[1,2..27])
plot(seq(1,27),fe[1,2...27])
plot(seq(1,27),fe[1,])
plot(seq(1,28),fe[1,])
plot(seq(1,28),fe[1,2])
plot(seq(1,28),fe[1,0])
plot(seq(1,28),fe[1,])
plot(seq(1,28),fe[1,>1])
plot(seq(1,28),subset(fe[1,],>1)
?subset
fe[c(seq(2,28)]
fe[c(seq(2,28))]
fe[c(seq(1,28))]
fe[c(seq(2,28)]
plot(seq(1,28),fe[1,c(seq(2,28))])
plot(seq(2,28),fe[1,c(seq(2,28))])
plot(seq(2,28),fe[1,c(seq(2,28))],type="b")
pdf("fe_stages.pdf")
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction")
dv.off()
dev.off()
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction")
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(seq(1,28)))
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(1,28,1))
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(1,1,28))
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(1,28,28))
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(1,28,27))
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(1,28,27))
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(1,28,27))
fe
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(1,28,0))
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(1,28,0))
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,0))
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
?for
?
for
?for
for
axis(1,"yo")
?axis
axis(1,at=1,"yo"0
axis(1,at=1,"yo)
axis(1,at=1,"yo")
axis(1,at=1,label="yo")
fe[1,1]
fe[0,1]
fe[0,2]
fe[1,1]
fe[1,0]
fe[1,]
fe[1,1]
fe[2,1]
fe[2,2]
fe[2,3]
fe[1,3]
fe[0,3]
fe[0,5]
fe[1,5]
fe[1,1]
name(fe[1,1])
names(fe[1,1])
names(fe[1,2])
names(fe[1,3])
fe
fe[1,]
fe[1,1]
fe[1,2]
fe[1,0]
fe[1,1]
fe[1,2]
fe
title
title(fe[1,1])
fe[1]
fe[2]
fe[3]
names(fe[3])
names(fe[4])
names(fe[5])
names(fe[6])
names(fe[1])
names(fe[2])
fe
names(fe[3])
names(fe[4])
axis(1,at=2,label="Fe")
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
axis(1,at=2,label="Fe")
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Iron Stages.")
axis(1,at=2,label="Fe")
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Iron Stages, AGN Shock Winds")
subtitle("v=10,000 km/s, T = 2e9 K")
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K")
?title
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(3,28),axis(1,at=coord,label=paste("FE+",coord-2)))
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(3,28)){axis(1,at=coord,label=paste("FE+",coord-2))}
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(3,28,2)){axis(1,at=coord,label=paste("FE+",coord-2))}
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=paste("FE+",coord-2))}
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=paste("FE-",coord-2))}
?paste
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=paste0("FE-",coord-2))}
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=paste0("FE^+",coord-2))}
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=paste0("FE",^+,coord-2))}
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=paste0("FE",^"+",coord-2))}
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=paste0("FE","^+",coord-2))}
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=paste0("FE",parse("^+"),coord-2))}
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=paste0("FE",parse(text="^+"),coord-2))}
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=parse(text=paste0("FE","^+",coord-2)))
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=parse(text=paste0("FE","^+",coord-2))}
for(coord in seq(4,28,2)){axis(1,at=coord,label=parse(text=paste0("FE","^+",coord-2)))}
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=parse(text=paste0("FE","^+",coord-2)))}
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
#title("Ionization Fraction for Iron Stages, AGN Shock Winds\rv=10,000 km/s, T = 2e9 K",main="")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=parse(text=paste0("Fe","^+",coord-2)))}
pdf("fe_ion.pdf")
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Iron Stages, AGN Shock Winds (v=10,000 km/s, T = 2e9 K)")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=parse(text=paste0("Fe","^+",coord-2)))}
pdf("fe_ion.pdf")
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Iron Stages, AGN Shock Winds (v=10,000 km/s, T = 2e9 K)")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=parse(text=paste0("Fe","^+",coord-2)))}
pdf("fe_ion.pdf")
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Iron Stages, AGN Shock Winds (v=10,000 km/s, T = 2e9 K)")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=parse(text=paste0("Fe","^+",coord-2)))}
dev.off()
pdf("fe_ion.pdf")
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Iron Stages, AGN Shock Winds (v=10,000 km/s, T = 2e9 K)")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=parse(text=paste0("Fe","^+",coord-2)))}
dev.off()
oxy= read.table("shock.oxy",header=T)
oxy
pdf("oxy_ion.pdf")
oxy= read.table("shock.oxy",header=T)
plot(seq(2,12),oxy[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Oxygen Stages, AGN Shock Winds (v=10,000 km/s, T = 2e9 K)")
axis(1,at=2,label="O")
for(coord in seq(4,12,2)){axis(1,at=coord,label=parse(text=paste0("O","^+",coord-2)))}
dev.off()
oxy= read.table("shock.oxy",header=T)
plot(seq(2,12),oxy[1,c(seq(2,12))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
xy[1,c(seq(2,12))]
oxy[1,c(seq(2,12))]
pdf("oxy_ion.pdf")
oxy= read.table("shock.oxy",header=T)
plot(seq(2,12),oxy[1,c(seq(2,12))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Oxygen Stages, AGN Shock Winds (v=10,000 km/s, T = 2e9 K)")
axis(1,at=2,label="O")
for(coord in seq(4,12,2)){axis(1,at=coord,label=parse(text=paste0("O","^+",coord-2)))}
dev.off()
pdf("oxy_ion.pdf")
oxy= read.table("shock.oxy",header=T)
plot(seq(2,10),oxy[1,c(seq(2,10))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Oxygen Stages, AGN Shock Winds (v=10,000 km/s, T = 2e9 K)")
axis(1,at=2,label="O")
for(coord in seq(4,10,2)){axis(1,at=coord,label=parse(text=paste0("O","^+",coord-2)))}
dev.off()
pdf("fe_ion.pdf")
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Iron Stages, AGN Shock Winds (v=10,000 km/s)")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=parse(text=paste0("Fe","^+",coord-2)))}
dev.off()
pdf("oxy_ion.pdf")
oxy= read.table("shock.oxy",header=T)
plot(seq(2,10),oxy[1,c(seq(2,10))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Oxygen Stages, AGN Shock Winds (v=10,000 km/s)")
axis(1,at=2,label="O")
for(coord in seq(4,10,2)){axis(1,at=coord,label=parse(text=paste0("O","^+",coord-2)))}
dev.off()
pdf("fe_ion.pdf")
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Fe Stages, AGN Shock Winds (v=10,000 km/s)")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=parse(text=paste0("Fe","^+",coord-2)))}
dev.off()
pdf("oxy_ion.pdf")
oxy= read.table("shock.oxy",header=T)
plot(seq(2,10),oxy[1,c(seq(2,10))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for O Stages, AGN Shock Winds (v=10,000 km/s)")
axis(1,at=2,label="O")
for(coord in seq(4,10,2)){axis(1,at=coord,label=parse(text=paste0("O","^+",coord-2)))}
dev.off()
pdf("cont.pdf")
cont = read.table("shock.con")
plot(cont[,1],cont[,7])
cont
pdf("cont.pdf")
cont = read.table("shock.con")
plot(cont[,1],cont[,7])
dev.off()
?plot
?Read
?read
?read
?read.table
pdf("cont.pdf")
cont = read.table("shock.con",fill=T)
plot(cont[,1],cont[,7])
dev.off()
cont
pdf("cont.pdf")
cont = read.table("shock.con",fill=T)
plot(cont[,1],cont[,4])
dev.off()
pdf("cont.pdf")
cont = read.table("shock.con",fill=T)
plot(cont[,1],cont[,4],log="xy")
dev.off()
pdf("cont.pdf")
cont = read.table("shock.con",fill=T)
plot(cont[,1],cont[,4],log="x")
dev.off()
plot(cont)
plot(cont)
plot(cont)
plot(cont[,1],cont[,4],log="x")
pdf("cont.pdf")
cont = read.table("shock.con",fill=T)
plot(cont[,1],cont[,4],log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab="Intensity (ergs/cm/cm/s)")
dev.off()
pdf("cont.pdf")
cont = read.table("shock.con",fill=T)
plot(cont[,1],cont[,4],log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab="Flux (ergs/cm/cm/s)")
dev.off()
pdf("cont.pdf")
cont = read.table("shock.con",fill=T)
plot(cont[,1],cont[,4],log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab="Flux (ergs/cm^2/s)")
dev.off()
pdf("cont.pdf")
cont = read.table("shock.con",fill=T)
plot(cont[,1],cont[,4],log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab=parse(text="Flux (ergs/cm^2/s)"))
dev.off()
pdf("cont.pdf")
cont = read.table("shock.con",fill=T)
plot(cont[,1],cont[,4],log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab=parse(text=paste("Flux,(ergs/cm^2/s)")))
dev.off()
pdf("cont.pdf")
cont = read.table("shock.con",fill=T)
plot(cont[,1],cont[,4],log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab=parse(text=paste("Flux","(ergs/cm^2/s)")))
dev.off()
cont[,1]
cont[,4]
cont[,3]
cont[,2]
cont = read.table("cont.preplot")
plot(cont)
plot(cont)
cont
cont[1]
cont[2]
plot(cont[1],cont[2])
cont[1,]
cont[,1]
cont[,2]
pdf("cont.pdf")
cont = read.table("cont.preplot",fill=T)
plot(cont[,1],cont[,2],log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab=parse(text=paste("Flux","(ergs/cm^2/s)")))
dev.off()
pdf("cont.pdf")
cont = read.table("cont.preplot",fill=T)
plot(cont[,1],cont[,2],type="l",log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab=parse(text=paste("Flux","(ergs/cm^2/s)")))
dev.off()
pdf("cont.pdf")
cont = read.table("cont.preplot",fill=T)
plot(cont[,1],cont[,2],type="l",log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab=parse(text=paste("Flux","(ergs/cm^2/s)")))
title("Emitted Continuum, AGN Shock Winds (v=10,000 km/s, T=2e9 K) ")
dev.off()pdf("cont.pdf")
cont = read.table("cont.preplot",fill=T)
plot(cont[,1],cont[,2],type="l",log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab=parse(text=paste("Flux","(ergs/cm^2/s)")))
title("Emitted Continuum, AGN Shock Winds (v=10,000 km/s, T=2e9 K) ")
dev.off()
pdf("cont.pdf")
cont = read.table("cont.preplot",fill=T)
plot(cont[,1],cont[,2],type="l",log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab=parse(text=paste("Flux","(ergs/cm^2/s)")))
title("Emitted Continuum, AGN Shock Winds (v=10,000 km/s, T=2e9 K) ")
dev.off()
pdf("cont.pdf")
cont = read.table("cont.preplot",fill=T)
plot(cont[,1],cont[,2],type="l",log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab=parse(text=paste("Flux","(ergs/cm^2/s)")))
title("Emitted Continuum, AGN Shock Winds (v=10,000 km/s, T=2e9 K) ")
dev.off()
exit
quit()

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pdf("fe_ion.pdf")
fe = read.table("shock.fe",header=T)
plot(seq(2,28),fe[1,c(seq(2,28))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for Fe Stages, AGN Shock Winds (v=10,000 km/s)")
axis(1,at=2,label="Fe")
for(coord in seq(4,28,2)){axis(1,at=coord,label=parse(text=paste0("Fe","^+",coord-2)))}
dev.off()
pdf("oxy_ion.pdf")
oxy= read.table("shock.oxy",header=T)
plot(seq(2,10),oxy[1,c(seq(2,10))],type="b",xlab="Ionization Stage",ylab="Ionization Fraction",xaxp=c(0,0,1))
title("Ionization Fraction for O Stages, AGN Shock Winds (v=10,000 km/s)")
axis(1,at=2,label="O")
for(coord in seq(4,10,2)){axis(1,at=coord,label=parse(text=paste0("O","^+",coord-2)))}
dev.off()
pdf("cont.pdf")
cont = read.table("cont.preplot",fill=T)
plot(cont[,1],cont[,2],type="l",log="x",xlim=c(1e-5,1e4),xlab="Wavelength (microns)",ylab=parse(text=paste("Flux","(ergs/cm^2/s)")))
title("Emitted Continuum, AGN Shock Winds (v=10,000 km/s, T=2e9 K) ")
dev.off()

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depth Fe Fe+ Fe+2 Fe+3 Fe+4 Fe+5 Fe+6 Fe+7 Fe+8 Fe+9 Fe+10 Fe+11 Fe+12 Fe+13 Fe+14 Fe+15 Fe+16 Fe+17 Fe+18 Fe+19 Fe+20 Fe+21 Fe+22 Fe+23 Fe+24 Fe+25 Fe+26
5.00000e-01 0.00e+00 1.92e-82 1.47e-78 8.50e-75 5.52e-72 3.48e-69 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 4.31e-36 1.71e-31 1.50e-27 7.57e-24 2.96e-20 1.09e-16 2.94e-13 3.65e-10 4.33e-07 2.34e-04 2.82e-02 9.72e-01

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# Shock temperature T = 20 v^2 = 20 * (10000)^2 = 2000000000
coronal 2e9
hden 0
stop zone 1
set dr 0
save emitted contiuum units microns "shock.con"
save element iron "shock.fe"
save element oxygen "shock.oxy"
cosmic ray background -3

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depth O O+ O+2 O+3 O+4 O+5 O+6 O+7 O+8 O[1] O[2] O[3]
5.00000e-01 0.00e+00 1.14e-44 2.40e-36 6.77e-29 7.17e-22 2.36e-15 2.35e-10 1.87e-05 1.00e+00 0.00e+00 0.00e+00 0.00e+00

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1.
∫[ν₁,∞] ϕ[ν] a[ν] dν = Γ, the photoionization rate, in s⁻¹ under the units used below.
ϕ[ν] = 10¹³ (ν/ν₀)⁻³ [photons cm⁻² s⁻¹ Ryd⁻¹].
a[ν] = A₀/Z² (ν₁/ν)⁴ exp(4 - (4 tan⁻¹(ε)/ε)) (1 - exp(-2π/ε))⁻¹ [cm²],
with A₀ = 6.30 × 10¹⁸ [cm²] and ε = √(ν/ν₁ - 1) and Z = 1,
but, above the ionization threshold, this is approximately a power law, so
a[ν] ≈ 6.30 × 10¹⁸ (ν/ν₀)⁻³ [cm²],
with ν₀ = 3.288 × 10¹⁵ [s⁻¹].
ϕ[ν] a[ν] dν
= 10¹³ (ν/ν₀)⁻³ [cm⁻² s⁻¹ Ryd⁻¹] ×
6.30 × 10¹⁸ (ν/ν₀)⁻³ [cm²]
= 6.30 ×10³¹ (ν/ν₀)⁻⁶ [s⁻¹ Ryd⁻¹].
∫[ν₀,∞] ϕ[ν] a[ν] dν
= ∫[ν₀,∞] dν (6.30 ×10³¹ (ν/ν₀)⁻⁶ [s⁻¹ Ryd⁻¹])
= 6.30 ×10³¹ (1/ν₀)⁻⁶ [s⁻¹ Ryd⁻¹] ∫[ν₀,∞] ν⁻⁶ dν
= 6.30 ×10³¹ (3.288 × 10¹⁵)⁶ [s⁻⁶ Ryd⁻¹] [∞⁻⁵/(-5) - ((3.288× 10¹⁵ Ryd s⁻¹)⁻⁵/(-5)]
= (1/5) 6.30 × 10³¹ (3.288 × 10¹⁵)⁶ [s⁻⁶ Ryd⁻¹] (3.288× 10¹⁵)⁻⁵ [Ryd s⁵].
*** = 4.14288 × 10⁴⁶ s⁻¹.
Seems really high... maybe I goofed something up, because 10¹³ hydrogen ionizing flux density seems sort of middle of the road. When we did AGN simulations, we went to around 10²⁴. Moving on for now, though...
─────────────
2.
L = ϕ / (nₑ nₚ αᵦ(T))
αᵦ(T) = 2.59 ×10⁻¹³
n[H] = 10³ cm⁻³ = nₑ nₚ.
ϕ = 10¹⁴ cm⁻² s⁻¹
L = 10¹⁴ / (10³)² / 2.59 ×10⁻¹³ [cm]
*** L = 3.861 × 10²⁰ cm.

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Homework 23, day 25, due Nov 28
Form a number by taking your birth month as a string and concatenating your birth day after it. For instance, my birth month is May, “05”, and birth day is 10, so I get 0510. Next multiply this by 5.5. In my case I get 2805. Finally, look through the Kaler catalogue to find a nebula with an NGC number as close as possible to your number. (Do not worry about precision – this is just so that we pick different nebulae).
─────────────
1) Which one did you pick?
0530 * 5.5 = 2915.
NGC 2899
─────────────
2) What type of nebula is it? H II region, planetary nebula, supernova remnant, other??
NGC 2899 is a Planetary Nebula.
─────────────
3) Find your nebula on the web and post its image.
Posted to discussion board. That's what this means, right?
─────────────
4) Measure the gas kinetic temperature in your nebula by choosing the [O III] lines discussed in class, forming the ratio, and looking up the temperature on the plot in AGN3.
Looking at the ratio from:
[O III]
─────────── ⟵ 1 S₀
│
│
│ λ = 4363 Å
│
│
↓
─────────── ⟵ 1 D₂
│
│
│ λ = 5007 Å, λ = 4959 Å
│
│
↓
─────────── ⟵ 3 P (3 combined levels)
Where j is the emissivity at a wavelength.
line ratio = j(5007 + 4959)/j(4363).
For NGC 2899,
j(5007) = 94.77,
j(4959) = 33.76, and
j(4363) = 2.86.
I didn't check what units the table is using. They will cancel. Oh, you know what, this appears to be a relative intensity to H-β, at any rate.
Line ratio = (94.77 + 33.76)/2.86 = 44.94.
Log₁₀(line ratio) = 1.65.
Extrcting the value from the plot, gives a temperature
*** T ≈ 18500K.
─────────────
5) Measure the electron density in your nebula by finding either the [O II] or [S II] lines and using the plot in AGN3.
I will use S II, since it's readily available in front of me in the table.
Line ratio = j(6731)/j(6717) = 6.55/6.57 = 1.00.
Extracting from the table. this gives an electron density
*** nₑ ≈ 550 cm⁻³.
─────────────
6) What is the gas pressure in dynes/cm 2 ? How does this compare with the pressure in the Earth’s atmosphere?
Treating this as an ideal gas (of course these are charged particles, so not ideal), P = n R[O III] T, with R the specific gas constant.
I have
T = 18500K, and
nₑ = n[H⁺] = 550 cm⁻³.
I can find n[O III]/n[H II], assuming case B, where
j(5006)/j(H-β)
= n[O III]/(nₚ nₑ) × (atomic physics factor = α)
= α/(550 cm⁻³) n[O III]/n[H II].
j(5006) = 94.77, and
j(4861) = 10.00, so
j(5006)/j(H-β) = 9.477.
n[O III]/n[H II] = 9.477 (550 cm⁻³)/α = 5212.35 α⁻¹
I'm not sure what atomic physics factor to use, here, and neither are my colleagues. We can check this out later, but Gary's door is closed at the moment. For now, I will leave it... should have asked on the discussions, but I am too late. If it's a similar factor from the earlier assignments, at least we know it had units cm⁻³, which is consistent with the following expression.
n[O III] = 5212.35 n[H II] α⁻¹
= (5212.35) (550 cm⁻³) α⁻¹
= 2.867 × 10⁶ α⁻¹.
P = n R[O III] T
= (2.867 × 10⁶ α⁻¹) (259.8 Joules/(kg K)) (18500 K)
= (2.867 × 10⁶) (259.8 Joules/(kg K)) (18500 K) α⁻¹
= 1.378 × 10¹³ α⁻¹ Joules/kg.
I'm having trouble converting this... should be obvious. I'm out of time, though, so I'll hav eto come back to this. Thanks.

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#include <iostream>
#include <iomanip>
#include <math.h>
int main(int argc, char const *argv[])
{
double hnu = 4.138e-10; // ergs
for (double logn_e = -10; logn_e <= 10; logn_e = logn_e + 0.0625) {
double n_e = pow(10,logn_e);
double net_cooling = hnu *
(1e-13)*pow(n_e,2) *
(
(2.19)*pow(1.47e-7*n_e+1,-1) -
(3.95)*pow(1-(1.47e-7*(n_e)),-1)
);
std::cout << std::setprecision(4) << std::fixed
<< std::scientific
<< std::setw(10) << n_e << '\t'
<< std::setw(10) << net_cooling << '\n';
}
return 0;
}

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1.0000e-10 -7.2829e-43
1.1548e-10 -9.7119e-43
1.3335e-10 -1.2951e-42
1.5399e-10 -1.7270e-42
1.7783e-10 -2.3030e-42
2.0535e-10 -3.0712e-42
2.3714e-10 -4.0955e-42
2.7384e-10 -5.4614e-42
3.1623e-10 -7.2829e-42
3.6517e-10 -9.7119e-42
4.2170e-10 -1.2951e-41
4.8697e-10 -1.7270e-41
5.6234e-10 -2.3030e-41
6.4938e-10 -3.0712e-41
7.4989e-10 -4.0955e-41
8.6596e-10 -5.4614e-41
1.0000e-09 -7.2829e-41
1.1548e-09 -9.7119e-41
1.3335e-09 -1.2951e-40
1.5399e-09 -1.7270e-40
1.7783e-09 -2.3030e-40
2.0535e-09 -3.0712e-40
2.3714e-09 -4.0955e-40
2.7384e-09 -5.4614e-40
3.1623e-09 -7.2829e-40
3.6517e-09 -9.7119e-40
4.2170e-09 -1.2951e-39
4.8697e-09 -1.7270e-39
5.6234e-09 -2.3030e-39
6.4938e-09 -3.0712e-39
7.4989e-09 -4.0955e-39
8.6596e-09 -5.4614e-39
1.0000e-08 -7.2829e-39
1.1548e-08 -9.7119e-39
1.3335e-08 -1.2951e-38
1.5399e-08 -1.7270e-38
1.7783e-08 -2.3030e-38
2.0535e-08 -3.0712e-38
2.3714e-08 -4.0955e-38
2.7384e-08 -5.4614e-38
3.1623e-08 -7.2829e-38
3.6517e-08 -9.7119e-38
4.2170e-08 -1.2951e-37
4.8697e-08 -1.7270e-37
5.6234e-08 -2.3030e-37
6.4938e-08 -3.0712e-37
7.4989e-08 -4.0955e-37
8.6596e-08 -5.4614e-37
1.0000e-07 -7.2829e-37
1.1548e-07 -9.7119e-37
1.3335e-07 -1.2951e-36
1.5399e-07 -1.7270e-36
1.7783e-07 -2.3030e-36
2.0535e-07 -3.0712e-36
2.3714e-07 -4.0955e-36
2.7384e-07 -5.4614e-36
3.1623e-07 -7.2829e-36
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data = read.table("data.tab")
png("othoulrich_net_cooling.png")
plot(data,type="l",xlab="Electron Density [cm⁻³]",ylab="Net Cooling [ergs cm⁻³ s⁻¹]")
dev.off()

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2.0535e+04 4.4958e-18
2.3714e+04 4.3821e-18
2.7384e+04 4.2448e-18
3.1623e+04 4.0898e-18
3.6517e+04 3.9222e-18
4.2170e+04 3.7462e-18
4.8697e+04 3.5657e-18
5.6234e+04 3.3836e-18
6.4938e+04 3.2024e-18
7.4989e+04 3.0241e-18
8.6596e+04 2.8501e-18
1.0000e+05 2.6815e-18
1.1548e+05 2.5192e-18
1.3335e+05 2.3637e-18
1.5399e+05 2.2153e-18
1.7783e+05 2.0743e-18
2.0535e+05 1.9407e-18
2.3714e+05 1.8143e-18
2.7384e+05 1.6951e-18
3.1623e+05 1.5829e-18
3.6517e+05 1.4775e-18
4.2170e+05 1.3785e-18
4.8697e+05 1.2857e-18
5.6234e+05 1.1988e-18
6.4938e+05 1.1174e-18
7.4989e+05 1.0414e-18
8.6596e+05 9.7029e-19
1.0000e+06 9.0392e-19
1.1548e+06 8.4196e-19
1.3335e+06 7.8415e-19
1.5399e+06 7.3023e-19
1.7783e+06 6.7995e-19
2.0535e+06 6.3308e-19
2.3714e+06 5.8940e-19
2.7384e+06 5.4870e-19
3.1623e+06 5.1078e-19
3.6517e+06 4.7547e-19
4.2170e+06 4.4257e-19
4.8697e+06 4.1194e-19
5.6234e+06 3.8341e-19
6.4938e+06 3.5685e-19
7.4989e+06 3.3213e-19
8.6596e+06 3.0911e-19
1.0000e+07 2.8768e-19
1.1548e+07 2.6773e-19
1.3335e+07 2.4916e-19
1.5399e+07 2.3188e-19
1.7783e+07 2.1579e-19
2.0535e+07 2.0082e-19
2.3714e+07 1.8689e-19
2.7384e+07 1.7392e-19
3.1623e+07 1.6185e-19
3.6517e+07 1.5062e-19
4.2170e+07 1.4017e-19
4.8697e+07 1.3044e-19
5.6234e+07 1.2138e-19
6.4938e+07 1.1296e-19
7.4989e+07 1.0512e-19
8.6596e+07 9.7820e-20
1.0000e+08 9.1030e-20
1.1548e+08 8.4710e-20
1.3335e+08 7.8830e-20
1.5399e+08 7.3357e-20
1.7783e+08 6.8265e-20
2.0535e+08 6.3526e-20
2.3714e+08 5.9115e-20
2.7384e+08 5.5011e-20
3.1623e+08 5.1192e-20
3.6517e+08 4.7638e-20
4.2170e+08 4.4331e-20
4.8697e+08 4.1253e-20
5.6234e+08 3.8389e-20
6.4938e+08 3.5724e-20
7.4989e+08 3.3244e-20
8.6596e+08 3.0936e-20
1.0000e+09 2.8788e-20
1.1548e+09 2.6789e-20
1.3335e+09 2.4929e-20
1.5399e+09 2.3199e-20
1.7783e+09 2.1588e-20
2.0535e+09 2.0089e-20
2.3714e+09 1.8694e-20
2.7384e+09 1.7397e-20
3.1623e+09 1.6189e-20
3.6517e+09 1.5065e-20
4.2170e+09 1.4019e-20
4.8697e+09 1.3046e-20
5.6234e+09 1.2140e-20
6.4938e+09 1.1297e-20
7.4989e+09 1.0513e-20
8.6596e+09 9.7828e-21
1.0000e+10 9.1036e-21

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#include <iostream>
#include <iomanip>
#include <math.h>
int main(int argc, char const *argv[])
{
double hnu = 4.138e-10; // ergs
double A = 2.20e-6;
double alpha = 7.10e3;
double EinK = 29168;
for (double logT = -10; logT <= 10; logT = logT + 0.0625) {
double T = pow(10,logT);
double cooling = hnu * A * pow(T,-0.5) * exp(-1*EinK/T);
std::cout << std::setprecision(4) << std::fixed
<< std::scientific
<< std::setw(10) << T << '\t'
<< std::setw(10) << cooling << '\n';
}
return 0;
}

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data = read.table("cooling.data")
png("plot.png")
hnu = 4.138e-10;
A = 2.20e-6;
alpha = 7.10e5;
hnu_T = 1.4E4;
EinK = 29168;
plot(data,
log="xy",
xlim=c(1e3,1e5),
ylim=c(1e-18,1e-17),
type="l",
xlab="Temperature [K]",
ylab=" [Cooling Rate ergs cm⁻³ s⁻¹]"
)
abline(v=hnu_T)
dev.off()
hnu_T

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Old approach:
4πj(u,l) = nᵤ (Aᵤₗ + qᵤₗ nₑ) hν.
Let's ignore collisional excitement, making
4πj(u,l) = n₂ Aᵤₗ hν.
From Allen, Table 4.11,
A[Hβ] = 8.419 × 10⁶ s⁻¹
If H was totally ionized this would be 0, right? Thought I could maybe find a recombination balance to determine a better ratio, but assuming H is not ionized seems to be the approach other students are taking.
From the Boltzman factors computed for hydrogen in hw14, I just reused my spreadsheet to find n₂ = (Z₂/∑Zᵢ * nₜₒₜ) at T=1e4 K:
n₂ = 0.275 [cm⁻³].
hν = 4.09 × 10⁻¹² [ergs].
4πj(u,l) = n₂ Aᵤₗ hν
= 0.275 [cm⁻³] 8.419 × 10⁶ [s⁻¹] 4.09 × 10⁻¹² [ergs]
*** = 9.47 × 10⁻⁶ [ergs cm⁻³ s⁻¹].

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Homework 26, day 29, due Dec 7
Let’s compute the radio brems to Balmer beta emissivity ratio for the Orion Nebula! As mentioned in class this is a great way to measure the interstellar reddening, since dust extinguishes visible light but not the radio. Let’s assume T=10⁴ K, n(H) = 10⁴ cm⁻³ , only consider H, and assume that it is fully ionized.
─────────────
1. What is the brems emissivity 4πνj[ν], erg cm⁻³ s⁻¹, at 21 cm?
Conditions:
T = 10⁴ K
n(H) = 10⁴ cm⁻³
H fully ionized.
From Brandt, the emissivity j[ν] at is given by (note: n in m⁻³.)
j[ν](ν) dν = (6.8 × 10⁻⁵¹ [J m³ K^(1/2)]) g(ν,T,Z) Z² nₑ nᵢ
× exp(-hν/kT) T^(-1/2).
The gaunt correction factor is approximated from the contour for
log(T) = 4 [log(K)] and log(λ) = 5.32 [log(μm)].
g[ν,T,Z] ≈ 5.
nₑ = nᵢ = nₕ = 10⁴ [cm⁻³] = 10⁴ [cm⁻³] (100 [cm/m])³ = 10¹⁰ [m⁻³].
For 21 cm,
hν/k = 0.0685 [K].
T = 10⁴ [K].
j[ν](ν) dν = (6.8 × 10⁻⁵¹ [J m³ K^(1/2)])
× g(ν,T,Z) Z² nₑ nᵢ exp(-hν/kT) T^(-1/2).
= (6.8 × 10⁻⁵¹ [J m³ K^(1/2)])
× (5) (10¹⁰ [m⁻³])²
× exp(-0.0685 [K]/(10⁴ [K])) (10⁴ [K])^(-1/2)
= (6.8e-51) * (5) * (1e20)
* exp(-0.0685 [K]/(1e4 [K])) * (1e4)^(-1/2)
[J m³ m⁻³ m⁻³]
= (6.8e-51) * (5) * (1e20)
* math.exp(-0.0685/1e4) * math.pow((1e4),(-1/2))
[J m⁻³]
= 3.4e-32 [J m⁻³].
ν[21 cm] = 1.48 × 10⁹ s⁻¹.
j[ν](ν) ν = 3.4e-32 [J m⁻³] * 1.48e9 [s⁻¹]
= 3.4e-32 * 1.48e9 [J m⁻³ s⁻¹]
= 5.03e-23 [J m⁻³ s⁻¹].
j[ν](ν) ν = 5.03e-23 [J m⁻³ s⁻¹] × [10⁷ ergs/J] × [1/100 m/cm]³.
*** = 5.02e-22 [ergs cm⁻³ s⁻¹].
─────────────
2. What is the emissivity in the Balmer beta line, the n=4-2 transition at 4861Å? The units of 4pj, are also erg cm -3 s -1 .
The Balmer emission here is from recombination. From the table 4.4,
4π j[Hβ] = 1.24 × 10⁻²⁵ [ergs cm³ s⁻¹] nₑ nᵢ
= 1.24e-25 [ergs cm³ s⁻¹] 1e8 [cm⁻⁶]
= 1.24e-17 [ergs cm⁻³ s⁻¹].
─────────────
3. What is the dimensionless ratio of the Balmer beta to radio brems emissivities? This is very nearly equal to the ratio of emission from the Orion Nebula. (I get roughly 2e4 but did this quickly).
(1.24e-17 [ergs cm⁻³ s⁻¹])/(5.02e-22 [ergs cm⁻³ s⁻¹])
= 1.24e-17 / 5.02e-22
*** = 2.47e4.
─────────────
4. If the ratio measured with Space Telescope and the VLA is 2e3, find the optical depth due to dust at Balmer beta.
Assuming dust is the only source of absorption and scattering,
τ = ∫ (κ) dl ⟶ I = I₀ exp(-τ).
exp(-τ) = I/I₀ = 2e3/2.47e4 * I₀﹐ᵦᵣ/Iᵦᵣ
From ISM opacity,
τᵦᵣ = ∫ 1e-24 [cm⁻¹] dl
= 1e-24 [cm⁻¹] * 1344 [ly]
= 1e-24 [cm⁻¹] * 1.27e21 [cm]
= 0.0013.
I₀﹐ᵦᵣ/Iᵦᵣ = exp(-0.0013) ≈ 1.
-τ = ln(2e3/2.47e4)
= -2.51.
*** τ = 2.51.

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axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
plot(lambda,lfl_T1,main="Planck's Law for a Blackbody",log="xy",xlab=expression(paste("Wavelength (",mu,"m)")),ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),type="l",col="red",xlim=c(0.01,10),xaxt='n',yaxt='n')
lines(lambda,lfl_T2,col="green")
lines(lambda,lfl_T3,col="blue")
legend(0.1,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("red","green","blue"))
axis(1,at=0.01,label="0.01")
axis(1,at=0.02,label="0.02")
axis(1,at=0.05,label="0.05")
axis(1,at=0.1,label="0.1")
axis(1,at=0.2,label="0.2")
axis(1,at=0.5,label="0.5")
axis(1,at=1,label="1")
axis(1,at=2,label="2")
axis(1,at=5,label="5")
axis(1,at=10,label="10")
axis(2,at=10^15,label=expression("10"^15))
axis(2,at=10^14,label=expression("10"^14))
axis(2,at=10^13,label=expression("10"^13))
axis(2,at=10^12,label=expression("10"^12))
axis(2,at=10^11,label=expression("10"^11))
axis(2,at=10^10,label=expression("10"^10))
axis(2,at=10^9,label=expression("10"^9))
axis(2,at=10^8,label=expression("10"^8))
axis(2,at=10^7,label=expression("10"^7))
axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
axis(2,at=1,label=expression("1"))
line(v=1)
?line
line(h=1)
?line
abline(h=1)
abline(v=1)
plot(lambda,lfl_T1,
main="Planck's Law for a Blackbody",
log="xy",
xlab=expression(paste("Wavelength (",mu,"m)")),
ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),
type="l",
col="red",
xlim=c(0.01,10),
ylim=c(1e5,1e15),
xaxt='n',
yaxt='n'
)
lines(lambda,lfl_T2,col="green")
lines(lambda,lfl_T3,col="blue")
legend(0.1,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("red","green","blue"))
axis(1,at=0.01,label="0.01")
axis(1,at=0.02,label="0.02")
axis(1,at=0.05,label="0.05")
axis(1,at=0.1,label="0.1")
axis(1,at=0.2,label="0.2")
axis(1,at=0.5,label="0.5")
axis(1,at=1,label="1")
axis(1,at=2,label="2")
axis(1,at=5,label="5")
axis(1,at=10,label="10")
axis(2,at=10^15,label=expression("10"^15))
axis(2,at=10^14,label=expression("10"^14))
axis(2,at=10^13,label=expression("10"^13))
axis(2,at=10^12,label=expression("10"^12))
axis(2,at=10^11,label=expression("10"^11))
axis(2,at=10^10,label=expression("10"^10))
axis(2,at=10^9,label=expression("10"^9))
axis(2,at=10^8,label=expression("10"^8))
axis(2,at=10^7,label=expression("10"^7))
axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
axis(2,at=1,label=expression("1"))
line(h=1)
plot(lambda,lfl_T1,
main="Planck's Law for a Blackbody",
log="xy",
xlab=expression(paste("Wavelength (",mu,"m)")),
ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),
type="l",
col="red",
xlim=c(0.01,10),
ylim=c(1e6,1e16),
xaxt='n',
yaxt='n'
)
lines(lambda,lfl_T2,col="green")
lines(lambda,lfl_T3,col="blue")
legend(0.1,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("red","green","blue"))
axis(1,at=0.01,label="0.01")
axis(1,at=0.02,label="0.02")
axis(1,at=0.05,label="0.05")
axis(1,at=0.1,label="0.1")
axis(1,at=0.2,label="0.2")
axis(1,at=0.5,label="0.5")
axis(1,at=1,label="1")
axis(1,at=2,label="2")
axis(1,at=5,label="5")
axis(1,at=10,label="10")
axis(2,at=10^15,label=expression("10"^15))
axis(2,at=10^14,label=expression("10"^14))
axis(2,at=10^13,label=expression("10"^13))
axis(2,at=10^12,label=expression("10"^12))
axis(2,at=10^11,label=expression("10"^11))
axis(2,at=10^10,label=expression("10"^10))
axis(2,at=10^9,label=expression("10"^9))
axis(2,at=10^8,label=expression("10"^8))
axis(2,at=10^7,label=expression("10"^7))
axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
axis(2,at=1,label=expression("1"))
plot(lambda,lfl_T1,
main="Planck's Law for a Blackbody",
log="xy",
xlab=expression(paste("Wavelength (",mu,"m)")),
ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),
type="l",
col="red",
xlim=c(0.01,10),
ylim=c(1e6,1e16),
xaxt='n',
yaxt='n'
)
lines(lambda,lfl_T2,col="green")
lines(lambda,lfl_T3,col="blue")
legend(0.1,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("red","green","blue"))
axis(1,at=0.01,label="0.01")
axis(1,at=0.02,label="0.02")
axis(1,at=0.05,label="0.05")
axis(1,at=0.1,label="0.1")
axis(1,at=0.2,label="0.2")
axis(1,at=0.5,label="0.5")
axis(1,at=1,label="1")
axis(1,at=2,label="2")
axis(1,at=5,label="5")
axis(1,at=10,label="10")
axis(2,at=10^15,label=expression("10"^16))
axis(2,at=10^15,label=expression("10"^15))
axis(2,at=10^14,label=expression("10"^14))
axis(2,at=10^13,label=expression("10"^13))
axis(2,at=10^12,label=expression("10"^12))
axis(2,at=10^11,label=expression("10"^11))
axis(2,at=10^10,label=expression("10"^10))
axis(2,at=10^9,label=expression("10"^9))
axis(2,at=10^8,label=expression("10"^8))
axis(2,at=10^7,label=expression("10"^7))
axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
axis(2,at=1,label=expression("1"))
plot(lambda,lfl_T1,
main="Planck's Law for a Blackbody",
log="xy",
xlab=expression(paste("Wavelength (",mu,"m)")),
ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),
type="l",
col="red",
xlim=c(0.01,10),
ylim=c(1e6,1e16),
xaxt='n',
yaxt='n'
)
lines(lambda,lfl_T2,col="green")
lines(lambda,lfl_T3,col="blue")
legend(0.1,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("red","green","blue"))
axis(1,at=0.01,label="0.01")
axis(1,at=0.02,label="0.02")
axis(1,at=0.05,label="0.05")
axis(1,at=0.1,label="0.1")
axis(1,at=0.2,label="0.2")
axis(1,at=0.5,label="0.5")
axis(1,at=1,label="1")
axis(1,at=2,label="2")
axis(1,at=5,label="5")
axis(1,at=10,label="10")
axis(2,at=10^16,label=expression("10"^16))
axis(2,at=10^15,label=expression("10"^15))
axis(2,at=10^14,label=expression("10"^14))
axis(2,at=10^13,label=expression("10"^13))
axis(2,at=10^12,label=expression("10"^12))
axis(2,at=10^11,label=expression("10"^11))
axis(2,at=10^10,label=expression("10"^10))
axis(2,at=10^9,label=expression("10"^9))
axis(2,at=10^8,label=expression("10"^8))
axis(2,at=10^7,label=expression("10"^7))
axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
axis(2,at=1,label=expression("1"))
plot(lambda,lfl_T1,
main="Planck's Law for a Blackbody",
log="xy",
xlab=expression(paste("Wavelength (",mu,"m)")),
ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),
type="l",
col="blue",
xlim=c(0.01,10),
ylim=c(1e6,1e16),
xaxt='n',
yaxt='n'
)
lines(lambda,lfl_T2,col="green")
lines(lambda,lfl_T3,col="red")
legend(0.1,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red"))
axis(1,at=0.01,label="0.01")
axis(1,at=0.02,label="0.02")
axis(1,at=0.05,label="0.05")
axis(1,at=0.1,label="0.1")
axis(1,at=0.2,label="0.2")
axis(1,at=0.5,label="0.5")
axis(1,at=1,label="1")
axis(1,at=2,label="2")
axis(1,at=5,label="5")
axis(1,at=10,label="10")
axis(2,at=10^16,label=expression("10"^16))
axis(2,at=10^15,label=expression("10"^15))
axis(2,at=10^14,label=expression("10"^14))
axis(2,at=10^13,label=expression("10"^13))
axis(2,at=10^12,label=expression("10"^12))
axis(2,at=10^11,label=expression("10"^11))
axis(2,at=10^10,label=expression("10"^10))
axis(2,at=10^9,label=expression("10"^9))
axis(2,at=10^8,label=expression("10"^8))
axis(2,at=10^7,label=expression("10"^7))
axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
axis(2,at=1,label=expression("1"))
plot(lambda,lfl_T1,
main="Planck's Law for a Blackbody",
log="xy",
xlab=expression(paste("Wavelength (",mu,"m)")),
ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),
type="l",
col="blue",
xlim=c(0.01,10),
ylim=c(1e6,1e16),
xaxt='n',
yaxt='n'
)
lines(lambda,lfl_T2,col="green")
lines(lambda,lfl_T3,col="red")
legend(0.1,1e8,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red"))
axis(1,at=0.01,label="0.01")
axis(1,at=0.02,label="0.02")
axis(1,at=0.05,label="0.05")
axis(1,at=0.1,label="0.1")
axis(1,at=0.2,label="0.2")
axis(1,at=0.5,label="0.5")
axis(1,at=1,label="1")
axis(1,at=2,label="2")
axis(1,at=5,label="5")
axis(1,at=10,label="10")
axis(2,at=10^16,label=expression("10"^16))
axis(2,at=10^15,label=expression("10"^15))
axis(2,at=10^14,label=expression("10"^14))
axis(2,at=10^13,label=expression("10"^13))
axis(2,at=10^12,label=expression("10"^12))
axis(2,at=10^11,label=expression("10"^11))
axis(2,at=10^10,label=expression("10"^10))
axis(2,at=10^9,label=expression("10"^9))
axis(2,at=10^8,label=expression("10"^8))
axis(2,at=10^7,label=expression("10"^7))
axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
axis(2,at=1,label=expression("1"))
plot(lambda,lfl_T1,
main="Planck's Law for a Blackbody",
log="xy",
xlab=expression(paste("Wavelength (",mu,"m)")),
ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),
type="l",
col="blue",
xlim=c(0.01,10),
ylim=c(1e6,1e16),
xaxt='n',
yaxt='n'
)
lines(lambda,lfl_T2,col="green")
lines(lambda,lfl_T3,col="red")
legend(1,1e8,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red"))
axis(1,at=0.01,label="0.01")
axis(1,at=0.02,label="0.02")
axis(1,at=0.05,label="0.05")
axis(1,at=0.1,label="0.1")
axis(1,at=0.2,label="0.2")
axis(1,at=0.5,label="0.5")
axis(1,at=1,label="1")
axis(1,at=2,label="2")
axis(1,at=5,label="5")
axis(1,at=10,label="10")
axis(2,at=10^16,label=expression("10"^16))
axis(2,at=10^15,label=expression("10"^15))
axis(2,at=10^14,label=expression("10"^14))
axis(2,at=10^13,label=expression("10"^13))
axis(2,at=10^12,label=expression("10"^12))
axis(2,at=10^11,label=expression("10"^11))
axis(2,at=10^10,label=expression("10"^10))
axis(2,at=10^9,label=expression("10"^9))
axis(2,at=10^8,label=expression("10"^8))
axis(2,at=10^7,label=expression("10"^7))
axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
axis(2,at=1,label=expression("1"))
?pdf
pdf("planck.pdf")
plot(lambda,lfl_T1,
main="Planck's Law for a Blackbody",
log="xy",
xlab=expression(paste("Wavelength (",mu,"m)")),
ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),
type="l",
col="blue",
xlim=c(0.01,10),
ylim=c(1e6,1e16),
xaxt='n',
yaxt='n'
)
lines(lambda,lfl_T2,col="green")
lines(lambda,lfl_T3,col="red")
legend(1,1e8,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red"))
axis(1,at=0.01,label="0.01")
axis(1,at=0.02,label="0.02")
axis(1,at=0.05,label="0.05")
axis(1,at=0.1,label="0.1")
axis(1,at=0.2,label="0.2")
axis(1,at=0.5,label="0.5")
axis(1,at=1,label="1")
axis(1,at=2,label="2")
axis(1,at=5,label="5")
axis(1,at=10,label="10")
axis(2,at=10^16,label=expression("10"^16))
axis(2,at=10^15,label=expression("10"^15))
axis(2,at=10^14,label=expression("10"^14))
axis(2,at=10^13,label=expression("10"^13))
axis(2,at=10^12,label=expression("10"^12))
axis(2,at=10^11,label=expression("10"^11))
axis(2,at=10^10,label=expression("10"^10))
axis(2,at=10^9,label=expression("10"^9))
axis(2,at=10^8,label=expression("10"^8))
axis(2,at=10^7,label=expression("10"^7))
axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
axis(2,at=1,label=expression("1"))
dev.off()
pdf("planck.pdf")
plot(lambda,lfl_T1,
main="Planck's Law for a Blackbody",
log="xy",
xlab=expression(paste("Wavelength (",mu,"m)")),
ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),
type="l",
col="blue",
xlim=c(0.01,10),
ylim=c(1e6,1e16),
xaxt='n',
yaxt='n'
)
lines(lambda,lfl_T2,col="green")
lines(lambda,lfl_T3,col="red")
legend(.65,1e8,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red"))
axis(1,at=0.01,label="0.01")
axis(1,at=0.02,label="0.02")
axis(1,at=0.05,label="0.05")
axis(1,at=0.1,label="0.1")
axis(1,at=0.2,label="0.2")
axis(1,at=0.5,label="0.5")
axis(1,at=1,label="1")
axis(1,at=2,label="2")
axis(1,at=5,label="5")
axis(1,at=10,label="10")
axis(2,at=10^16,label=expression("10"^16))
axis(2,at=10^15,label=expression("10"^15))
axis(2,at=10^14,label=expression("10"^14))
axis(2,at=10^13,label=expression("10"^13))
axis(2,at=10^12,label=expression("10"^12))
axis(2,at=10^11,label=expression("10"^11))
axis(2,at=10^10,label=expression("10"^10))
axis(2,at=10^9,label=expression("10"^9))
axis(2,at=10^8,label=expression("10"^8))
axis(2,at=10^7,label=expression("10"^7))
axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
axis(2,at=1,label=expression("1"))
dev.off()
pdf("planck.pdf")
plot(lambda,lfl_T1,
main="Planck's Law for a Blackbody",
log="xy",
xlab=expression(paste("Wavelength (",mu,"m)")),
ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),
type="l",
col="blue",
xlim=c(0.01,10),
ylim=c(1e6,1e16),
xaxt='n',
yaxt='n'
)
lines(lambda,lfl_T2,col="green")
lines(lambda,lfl_T3,col="red")
legend(.5,1e8,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red"))
axis(1,at=0.01,label="0.01")
axis(1,at=0.02,label="0.02")
axis(1,at=0.05,label="0.05")
axis(1,at=0.1,label="0.1")
axis(1,at=0.2,label="0.2")
axis(1,at=0.5,label="0.5")
axis(1,at=1,label="1")
axis(1,at=2,label="2")
axis(1,at=5,label="5")
axis(1,at=10,label="10")
axis(2,at=10^16,label=expression("10"^16))
axis(2,at=10^15,label=expression("10"^15))
axis(2,at=10^14,label=expression("10"^14))
axis(2,at=10^13,label=expression("10"^13))
axis(2,at=10^12,label=expression("10"^12))
axis(2,at=10^11,label=expression("10"^11))
axis(2,at=10^10,label=expression("10"^10))
axis(2,at=10^9,label=expression("10"^9))
axis(2,at=10^8,label=expression("10"^8))
axis(2,at=10^7,label=expression("10"^7))
axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
axis(2,at=1,label=expression("1"))
dev.off()
3.828/6.417
4*pi()
pi()
%pi
pi
4*pi
5.965e22
5.965e22/12.5664
sqrt(5.965e22/12.5664)
14959790000000*14959790000000
3.828/12.5664/2.2380/1e26*1e33
1.361e6 / 29979245800
(4.54e-5 * 29979245800)/(5.6704e-5)
(4.54e-5 * 29979245800)/(5.6704e-5)^(-4)
(4.54e-5 * 29979245800)/(5.6704e-5)^(1/4)
1.568e7^4
(1.568e7)^4
(4.54e-5 * 29979245800)
(4.54e-5 * 29979245800)/(5.6704e-5)
pow((4.54e-5 * 29979245800)/(5.6704e-5),1/4)
power
power((4.54e-5 * 29979245800)/(5.6704e-5),1/4)
?power
?exp
?pow
power((4.54e-5 * 29979245800)/(5.6704e-5),1/4)
(4.54e-5 * 29979245800)/(5.6704e-5)
((4.54e-5 * 29979245800)/(5.6704e-5))^(1/4)
393^4
393.6 - 289.15
0.28979/5800
quit()

BIN
hw3/blackbody.ods Normal file
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Binary file not shown.

88
hw3/planck.tab Normal file
View File

@ -0,0 +1,88 @@
0.0036517413 10541756.5038332 2.41192771918153E-23 1.1221546329846E-261
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0.0048696753 1654430654.18458 9.80331015279875E-14 1.85076974272241E-192
0.0056234133 11272272034.9956 6.36771460910216E-10 1.08482138651403E-164
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0.0273841963 7310954324154.95 815348687.530744 1.34653866777397E-23
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0.1539926526 111096051032.966 22019651646.4572 49097.6465535706
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0.4869675252 1661375743.9912 995852704.721293 16253799.707507
0.5623413252 957858801.983046 614923677.416754 17423482.4479495
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0.7498942093 315360362.513779 226186801.74534 15626664.9426197
0.8659643234 180236301.016314 135160287.958063 13360111.5375667
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1.1547819847 58507304.283737 47149646.7761832 8313913.44733848
1.3335214322 33249000.3058469 27581020.5236935 6137004.61576915
1.5399265261 18868386.0301689 16048924.5433182 4367882.61380698
1.77827941 10694503.9991308 9295934.15103023 3012115.85577442
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4.8696752517 196431.746164089 186631.26573568 123668.866749526
5.6234132519 110737.582993933 105936.839543701 74178.5580659845
6.4938163158 62406.9838934647 60057.2010790581 44110.3984143153
7.4989420933 35159.7356664838 34010.3903650947 26034.6366448071
8.6596432336 19803.8267037132 19241.9818903867 15266.7255773598
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15.3992652606 1989.4744499063 1957.5347675547 1718.6679829013
17.7827941004 1119.646573791 1104.0638613264 986.3977159549
20.5352502646 630.0537861333 622.4532056907 564.5787966018
23.7137370566 354.514931452 350.8084976788 322.3804372025
27.3841963426 199.4605456576 197.6534376352 183.7055374817
31.6227766017 112.2146747419 111.3337449694 104.4971947421
36.5174127255 63.1271939297 62.6978184616 59.349791677
42.1696503429 35.5108406642 35.3015835988 33.6632048586
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56.234132519 11.2355515005 11.1858654729 10.7942563907
64.9381631576 6.3195799147 6.2953720213 6.1040627394
74.9894209332 3.5544257859 3.5426320913 3.4492132267
86.596432336 1.9991243197 1.9933789641 1.9477781096
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115.4781984689 0.6323441144 0.6309808289 0.6201252781
133.3521432163 0.3556306354 0.3549665938 0.3496720699
153.992652606 0.2000040211 0.1996805845 0.1970988496
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237.1373705662 0.0355736431 0.0355362749 0.0352372298
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316.2277660168 0.011250449 0.0112415856 0.0111705705
365.1741272548 0.0063268354 0.0063225189 0.0062879171
421.6965034286 0.0035579594 0.0035558572 0.003538999
486.9675251659 0.0020008452 0.0019998215 0.0019916086
562.3413251904 0.001125186 0.0011246875 0.0011206866
649.3816315762 0.0006327523 0.0006325095 0.0006305605
749.8942093325 0.0003558294 0.0003557112 0.0003547618
865.9643233601 0.0002001008 0.0002000432 0.0001995808
1000 0.0001125265 0.0001124985 0.0001122733

88
hw3/planck_l Normal file
View File

@ -0,0 +1,88 @@
0.0036517413
0.004216965
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1
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17.7827941004
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27.3841963426
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36.5174127255
42.1696503429
48.6967525166
56.234132519
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100
115.4781984689
133.3521432163
153.992652606
177.8279410039
205.3525026457
237.1373705662
273.8419634264
316.2277660168
365.1741272548
421.6965034286
486.9675251659
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1000

88
hw3/planck_lfl_150000 Normal file
View File

@ -0,0 +1,88 @@
10541756.5038332
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2.41192771918153E-23
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pdf("planck.pdf")
plot(lambda,lfl_T1,
main="Planck's Law for a Blackbody",
log="xy",
xlab=expression(paste("Wavelength (",mu,"m)")),
ylab=expression(paste(lambda,'F'[lambda]," (erg cm"^-2," s"^-1,")")),
type="l",
col="blue",
xlim=c(0.01,10),
ylim=c(1e6,1e16),
xaxt='n',
yaxt='n'
)
lines(lambda,lfl_T2,col="green")
lines(lambda,lfl_T3,col="red")
legend(.5,1e8,legend = c("T = 150000 K","T = 40000 K","T = 5800 K"),lty=c(1,1,1),col=c("blue","green","red"))
axis(1,at=0.01,label="0.01")
axis(1,at=0.02,label="0.02")
axis(1,at=0.05,label="0.05")
axis(1,at=0.1,label="0.1")
axis(1,at=0.2,label="0.2")
axis(1,at=0.5,label="0.5")
axis(1,at=1,label="1")
axis(1,at=2,label="2")
axis(1,at=5,label="5")
axis(1,at=10,label="10")
axis(2,at=10^16,label=expression("10"^16))
axis(2,at=10^15,label=expression("10"^15))
axis(2,at=10^14,label=expression("10"^14))
axis(2,at=10^13,label=expression("10"^13))
axis(2,at=10^12,label=expression("10"^12))
axis(2,at=10^11,label=expression("10"^11))
axis(2,at=10^10,label=expression("10"^10))
axis(2,at=10^9,label=expression("10"^9))
axis(2,at=10^8,label=expression("10"^8))
axis(2,at=10^7,label=expression("10"^7))
axis(2,at=10^6,label=expression("10"^6))
axis(2,at=10^5,label=expression("10"^5))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^4,label=expression("10"^4))
axis(2,at=10^3,label=expression("10"^3))
axis(2,at=10^2,label=expression("10"^2))
axis(2,at=10^1,label=expression("10"^1))
axis(2,at=1,label=expression("1"))
dev.off()

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(1) Submitted separately
(2)
The Stefan-Boltzmann Law gives the surface brightness B of an object as a function of its temperature T, with dimension energy over distance-squared over time.
B = σ T⁴, with σ the Stefan-Boltzmann constant.
σ ≈ 5.6704 × 10⁻⁵ erg cm⁻² s⁻¹ K⁻⁴.
B = 5.6704 × 10⁻⁵ × T⁴ erg cm⁻² s⁻¹, with T in kelvin.
For a spherical body, this surface brightness can be related to the total luminosity L by,
L = 4 π r² B, with r the radius of the sphere.
The radius is therefore,
________
r = / __L__
√ 4 π B .
Assuming the solar luminosity L* = 3.828×10³³ erg/s and the solar surface temperature T* = 5800 K, the solar radius can be determined.
B* = σ × 5800⁴ K⁴ = 6.417 × 10¹⁰ erg cm⁻² s⁻¹.
L*/B* = 3.828×10³³ erg s⁻¹ / 6.417 × 10¹⁰ erg cm⁻² s⁻¹
= 5.965 × 10²² cm².
_____________
r* = √ L*/B*/(4 π)
_____________________________
= √ 5.965 × 10²² cm² / (12.5664)
_________________
= √ 4.747 × 10²¹ cm²
= 6.890 × 10¹⁰ cm.
(3)
Given the luminosity of a body, one can determined the energy flux Φ at a shell of arbitrary distance D, because this flux reduces with distance by an inverse square law. This is seen in the expression in (2), as well.
Φ = L / (4 π D²), compare with the expression in (2) where Φ = B and D = r at the surface of the emitter.
The distance from the Earth to the Sun D* is one AU, or in cm,
D* = 14959790000000 cm.
Φ* = L* / (12.5664 × 2.2380 ×10²⁶ cm²)
= 3.828 × 10³³ erg s⁻¹ / (12.5664 × 2.2380 × 10²⁶ cm²)
= 1.361 × 10⁶ erg cm⁻² s⁻¹.
The energy density ρ is related to the energy flux Φ by
ρ = Φ / v, and for electromagnetic energy,
ρ = Φ / c.
The energy density at Earth's orbit ρ* is therefore,
ρ* = Φ* / c
= 1.361 × 10⁶ erg cm⁻² s⁻¹ / (29979245800 cm s⁻¹)
= 4.540 × 10⁻⁵ erg cm⁻³.
This relationship is also associated to the Stefan-Boltzman Law, hinted at with the comparison to the expression in (2).
ρ = σ T⁴ / c = Φ / c, or
₄________
T = √ ρ c / σ
The temperature T` related to the energy density at Earth's orbital radius is therefore,
₄_________
T` = √ ρ* c / σ
⎛ 4.540 × 10⁻⁵ erg cm⁻³ × 29979245800 cm s⁻¹ ⎞1/4
= ⎜ ------------------------------------------ ⎟
⎝ 5.6704 × 10⁻⁵ erg cm⁻² s⁻¹ K⁻⁴ ⎠
= 3.936 × 10² K.
The average temperature at the Earth's surface is approximate 289.15 K.
393.6 K - 289.15 K = 104.45 K.
So, the temperature associated with the electromagnetic energy density at the Earth's orbital radius is sigificantly (>100 K) greater than the temperature at the Earth's surface. Is this due to reflection and other scattering?
(4)
Wien's Law allows one to calculate the peak of emission of a blackbody for a given temperature. Using the assumed surface temperature of the Sun T*, this peak wavelength λ* can be found.
λ[peak] T = 0.28979 cm K; this is Wien's Law in cm and K.
λ* = 0.28979 cm K / T*
= 0.28979 cm K / (5800 K)
= 4.996 × 10⁻⁵ cm.

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(1)
The approximate distances D[feature] and paths from the Solar System of the following features are relevant.
1 cm = 1.057001 × 10⁻¹⁸ ly.
D[Proxima Centauri] = D[PC] = 4.25 ly = 4.02 × 10¹⁸ cm.
D[Orion Nebula] = D[ON] = 1,344 ± 2 ly ≈ 1.272 × 10²¹ cm.
D[Center of Galaxy] = D[CG] = 24–28.4 kly ≈ 2.48 × 10²² cm.
I'll assume the following interstellar number densities n[species], and assume isotropic densities across the paths.
n[H⁺] = 1 cm⁻³.
n[e-] = 1 cm⁻³.
n[H⁰] = 0.1 cm⁻³.
n[H⁻] = 10⁻¹¹ cm⁻³.
n[H₂] = 10⁻³ cm⁻³.
n[H⁰ + H⁺ +H⁻] = 1 + 0.1 + 10⁻¹¹ cm⁻³ ≈ 1.100 cm⁻³.
(2)
To find column densities N[species,feature] from Sol to these features, I integrate the (constant) number densities across the path lengths D[feature].
N[species,feature] = n[species] × D[feature].
N[H⁰,feature] = n[H⁰] × D[feature]
= 0.1 cm⁻³ × D[feature].
N[H⁺,feature] = n[H⁺] × D[feature]
= 1 cm⁻³ × D[feature].
N[H⁻,feature] = n[H⁻] × D[feature]
= 10⁻¹¹ cm⁻³ × D[feature].
N[H⁰ + H⁺ +H⁻,feature] = n[H⁰ + H⁺ +H⁻] × D[feature]
≈ 1.100 cm⁻³ × D[feature].
N[e⁻,feature] = n[e⁻] × D[feature]
= 1 cm⁻³ × D[feature].
N[H⁰,PC] = 0.1 cm⁻³ × 4.02 × 10¹⁸ cm
= 4.02 × 10¹⁷ cm⁻².
N[H⁺,PC] = 1 cm⁻³ × 4.02 × 10¹⁸ cm
= 4.02 × 10¹⁸ cm⁻².
N[H⁻,PC] = 10⁻¹¹ cm⁻³ × 4.02 × 10¹⁸ cm
= 4.02 × 10⁷ cm⁻².
N[H⁰ + H⁺ +H⁻,PC] = 1.100 cm⁻³ × 4.02 × 10¹⁸ cm
= 4.42 × 10¹⁸ cm⁻².
N[e⁻,PC] = 1 cm⁻³ × 4.02 × 10¹⁸ cm
= 4.02 × 10¹⁸ cm⁻².
N[H⁰,ON] = 0.1 cm⁻³ × 1.272 × 10²¹ cm
= 1.272 × 10²⁰ cm⁻².
N[H⁺,ON] = 1 cm⁻³ × 1.272 × 10²¹ cm
= 1.272 × 10²¹ cm⁻².
N[H⁻,ON] = 10⁻¹¹ cm⁻³ × 1.272 × 10²¹ cm
= 1.272 × 10¹⁰ cm⁻².
N[H⁰ + H⁺ +H⁻,ON] = 1.100 cm⁻³ × 1.272 × 10²¹ cm
= 1.399 × 10²¹ cm⁻².
N[e⁻,ON] = 1 cm⁻³ × 1.272 × 10²¹ cm
= 1.272 × 10²¹ cm⁻².
N[H⁰,CG] = 0.1 cm⁻³ × 2.48 × 10²² cm
= 2.48 × 10²¹ cm⁻².
N[H⁺,CG] = 1 cm⁻³ × 2.48 × 10²² cm
= 2.48 × 10²² cm⁻².
N[H⁻,CG] = 10⁻¹¹ cm⁻³ × 2.48 × 10²² cm
= 2.48 × 10¹¹ cm⁻².
N[H⁰ + H⁺ +H⁻,CG] = 1.100 cm⁻³ × 2.48 × 10²² cm
= 2.79 × 10²² cm⁻².
N[e⁻,CG] = 1 cm⁻³ × 2.48 × 10²² cm
= 2.48 × 10²² cm⁻².
(3)
Assuming an appropriate choice of wavelength and process, the column density N is related to the optical depth τ by the opacity κ for a process, with κ defined in terms of the cross section of interaction σ and the number density n of the target species of that interaction. I compute κ[target] and then find the optical depth between Sol and the features of interest for each process.
κ[process] = n[target] σ[process].
κ[Thomson Scattering] = n[e⁻] × σ[e⁻]
= 1 cm⁻³ × 6 × 10⁻²⁵ cm²
= 6 × 10⁻²⁵ cm⁻¹.
κ[Grain Absorption] = n[H⁰ + H⁺ +H⁻] × σ[Grain Absorption]
= 1.100 cm⁻³ × 10⁻²¹ cm²
= 1.100 × 10⁻²¹ cm⁻¹.
κ[H⁰ Photoionization] = n[H⁰] × σ[H⁰ Photoionization]
= 0.1 cm⁻³ × 6 × 10⁻¹⁸ cm²
= 6 × 10⁻¹⁹ cm⁻¹.
κ[Lyα Scattering] = n[H⁰] × σ[Lyα Scattering]
= 0.1 cm⁻³ × 10⁻¹² cm²
= 10⁻¹³ cm⁻¹.
κ[H⁻ Absorption] = n[H⁻] × σ[H⁻ Absorption]
= 10⁻¹¹ cm⁻³ × 3 × 10⁻¹⁷ cm²
= 3 × 10⁻²⁸ cm⁻¹.
τ[process,feature] = κ[process] × N[target,feature].
τ[Thomson Scattering,PC] = 6 × 10⁻²⁵ cm⁻¹ × 4.02 × 10¹⁸ cm⁻²
= 2.41 × 10⁻⁶ cm⁻³.
τ[Thomson Scattering,ON] = 6 × 10⁻²⁵ cm⁻¹ × 1.272 × 10²¹ cm⁻²
= 7.632 × 10⁻⁴ cm⁻³.
τ[Thomson Scattering,GC] = 6 × 10⁻²⁵ cm⁻¹ × 2.48 × 10²² cm⁻²
= 1.49 × 10⁻² cm⁻³.
(4)
τ[Grain Absorption,PC] = 1.100 × 10⁻²¹ cm⁻¹ × 4.42 × 10¹⁸ cm⁻²
= 4.86 × 10⁻³ cm⁻³.
τ[Grain Absorption,ON] = 1.100 × 10⁻²¹ cm⁻¹ × 1.399 × 10²¹ cm⁻²¹
= 0.1539 × cm⁻³.
τ[Grain Absorption,GC] = 1.100 × 10⁻²¹ cm⁻¹ × 2.79 × 10²² cm⁻²
= 3.07 cm⁻³.
(5)
τ[H⁰ Photoionization,PC] = 6 × 10⁻¹⁹ cm⁻¹ × 4.02 × 10¹⁷ cm⁻²
= 0.241 cm⁻³.
τ[H⁰ Photoionization,ON] = 6 × 10⁻¹⁹ cm⁻¹ × 1.272 × 10²⁰ cm⁻²
= 76.32 × 10² cm⁻³.
τ[H⁰ Photoionization,GC] = 6 × 10⁻¹⁹ cm⁻¹ × 2.48 × 10²¹ cm⁻²
= 1.49 × 10³ cm⁻³.
(6)
τ[Lyα Scattering,PC] = 10⁻¹³ cm⁻¹ × 4.02 × 10¹⁷ cm⁻²
= 4.02 × 10⁴ cm⁻³.
τ[Lyα Scattering,ON] = 10⁻¹³ cm⁻¹ × 1.272 × 10²⁰ cm⁻²
= 1.272 × 10⁷ cm⁻³.
τ[Lyα Scattering,GC] = 10⁻¹³ cm⁻¹ × 2.48 × 10²¹ cm⁻²
= 2.48 × 10⁸ cm⁻³.
(7)
τ[H⁻ Absorption,PC] = 3 × 10⁻²⁸ cm⁻¹ × 4.02 × 10⁷ cm⁻²
= 1.21 × 10⁻²⁰ cm⁻³.
τ[H⁻ Absorption,ON] = 3 × 10⁻²⁸ cm⁻¹ × 1.272 × 10¹⁰ cm⁻²
= 3.816 × 10⁻¹⁸ cm⁻³.
τ[H⁻ Absorption,GC] = 3 × 10⁻²⁸ cm⁻¹ × 2.48 × 10¹¹ cm⁻²
= 7.44 × 10⁻¹⁷ cm⁻³.
(8)
The density of Earth's atmosphere is obviously not isotropic, but to a first approximation I will assume it has a particle number density ρ and thickness T. The column density is then computed.
ρ = 5 × 10¹⁹ cm⁻³.
T = 10 km = 10⁶ cm.
N[Earth's Atmosphere] = ρ × T
= 5 × 10¹⁹ cm⁻³ × 10⁶ cm⁻³
= 5 × 10²⁵ cm⁻².
The greatest number density I see in the ISM is that of the sum of hydrogen species. Even given that sum of species, the column density to the center of the galaxy is on the order of 10²², whereas the column density seen across 10km of the Earth's atmosphere is on the order of 10²⁵. So, we see ~1000 times the optical thickness across the Earth's atmosphere than across a quarter of the galaxy!

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(1)
Light is visible to approximately an optical depth τ = 1.
τ = ∫ κ dL, with κ the opacity and ∫ dL the integral over some path with length L.
κ is wavelength dependent and known for the spectrum, so to find where on the spectrum I expect to be able to see across 100 PC of the ISM, I substitute the following and compute. κ is considered constant, per wavelength, across a region where only scattering from the ISM is considered.
1 = ∫ κ dL = κ ∫ dL = κ (100 PC).
κ = 10⁻² PC⁻¹ = 3.1 × 10⁻²⁰ cm ≈ 10⁻²⁰.
I've made this very approximate, since we're just looking for understanding.
This is the limiting value of κ, so any wavelengths with greater κ will not be visible to the observer.
κ < 3.1 × 10⁻²⁰ cm.
Consider both the cross-section of absorption and scattering. The opacity of absorption is significantly greater through most of the spectrum than that of scattering. The scattering opacity does not reach strength sufficient to "tip" the opacity above the threshold when summed with that of absorption. Therefore, I only consider opacity of absorption.
The regions of interest are:
κ[λ → 0 μm] → 0
κ[10⁻² μm < λ < 10⁻¹ μm] > 10⁻²⁰ cm⁻¹
κ[10⁻¹ μm < λ < 10⁷ μm] < 10⁻²⁰ cm⁻¹
κ[λ → ∞] → ∞
The opacity is sufficiently weak through the regions
λ = {0 .. 10⁻² μm } and λ = { 10⁻¹ .. 10⁷ μm }.
(2)
(a)
n[e⁻] = n[H⁺] = 10⁹ cm⁻³.
(b)
R[sol] = 6.957 × 10¹⁰ cm.
L = R[sol]/4 = 1.740 × 10¹⁰ cm.
N = n[e⁻] × L
= 10⁹ cm⁻³ × 1.740 × 10¹⁰ cm
= 1.740 × 10¹⁹ cm⁻².
(c)
τ = ∫ κ dL = κ × L.
κ = n[e⁻] × σ[e⁻]
= 10⁹ cm⁻³ × 6 × 10⁻²⁵ cm²
= 6 × 10⁻¹⁶ cm⁻¹.
τ = 6 × 10⁻¹⁶ cm⁻¹ × 1.740 × 10¹⁰ cm
= 1.05 × 10⁻⁵.
(d)
L[sol] = 3.848 × 10³³ erg s⁻¹.
τ < 1, so this cloud is optically thin.
L[scattered] ≈ L[sol] × τ
= 3.848 × 10³³ erg s⁻¹ × 10⁻⁵
= 3.848 × 10²⁸ erg s⁻¹.
(3)
All good here. I can login, but I haven't compiled cloudy or anything.

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(1) pi
(2)
(a)
Solar Mass = 1.99 × 10³⁰ kg.
Solar Radius = 6.96 × 10¹⁰ cm.
Solar Volume = 4/3 π R³
= 1.410 × 10³³ cm³.
H⁺ mass = 1.67 × 10²⁷ kg.
H⁺ density = Solar Mass/Solar Volume/H⁺ Mass
= 8.435 × 10²³ cm⁻³.
e⁻ density = H⁺ density.
(b)
mean free path = l = κ⁻¹.
κ = n[e⁻] × σ[thompson]
= 0.506 cm⁻¹.
l = 1.98 cm.
(c)
For average κ,
τ = κ × Solar Radius
= 3.52 × 10¹⁰.
(d)
AGN3 gives an approximation for luminosity from bremsstrahlung as, assuming H⁺ is the only ion, in erg cm⁻³ s⁻¹,
L[ff] = 1.42 × 10⁻²⁷ Z² T⁰˙⁵ g[ff] nₑ H⁺.
The gaunt correction factor
g[ff] = 1.3.
T = 106 K.
L[ff] = 1.42 × 10⁻²⁷
= 1.35 × 10²² erg cm⁻³ s⁻¹.
This is the luminosity from Brems. radiation per unit volume, but has to be integrated while considering the optical depth to find the total emission from Brems. radiation. We will assume the sun is optically thin, and by our derivation in the lecture, the optical depth then is no longer important.
The luminosity from the emissivity is, for optically thin conditions and constant emissivity j = L[ff]/4π,
L = ∫ 4 π j dV
= L[ff] × V.
Note L[ff] includes the solid angle 4π across which each unit volume emits.
Integrating over the sun's volume, then
L[total,ff] = L[ff] × V
= 1.91 × 10⁵⁵ ergs s⁻¹.
(e)
This number is way too huge. The total luminosity of the sun is on the order of 10³³ erg s⁻¹, 22 orders of magnitude smaller. I think this means I have a conceptual problem, somewhere. I don't think optically thin is a good assumption for the sun.

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1) Estimate the temperature of the warm dust emission.
Read the wavelength at the peak of the blackbody region.
λₚₑₐₖ = 10¹³ Hz.
Using Wien Law,
λₚₑₐₖ = 2.90 × 10⁻³ m K / T.
T = 2.90 × 10⁻³ m K / 10¹³ Hz.
T = 96.7 K.
2) What is the turnover frequency of the brems emission?
This is just gleaned from the SED.
1.5 GHz = 1.5 × 10⁹ Hz.
3) Assume that the brems comes from ionized hydrogen at 10 4 K and
a density of 10 4 cm -3 . What is the thickness of NGC 7027 in cm?
In parsecs?
κʹₛ = 0.0178 Z² g ν⁻² T^(-3/2) nₑ nₗ.
g = 10.6 + 1.9*log(T) - 1.26*log(Z*ν)
= 6.63.
κʹₛ = 0.0178 × 1 × (3.32) × (1.5 × 10⁹ Hz)⁻² × (10⁴ K)^(-3/2) × (10⁴ cm⁻³)².
κʹₛ = 5.25 × 10⁻¹⁸ cm⁻¹.
For turnover frequency,
1 = τ = κʹₛ l.
l = τ / κʹₛ = κʹₛ⁻¹.
l = 1.90 × 10¹⁷ cm
= 0.0617 parsecs.
After fixing the typo from the Allen text, this seems to be a much more reasonable result. The actual radius (from wikipedia) is approximately .068 parsec for this object, so this is very close to that answer.

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Homework Day 8, Sept 21
1) NGC 7027 has a distance of about 920 pc and diameter of about 14
seconds of arc
a. How does its diameter compare with its thickness (from previous
homework)?
Diameter D = θ(radians) × Distance d
= 6.7787×10⁻⁵ radians × 920 pc
= 0.0624 pc.
This is very comparable to the result from HW7 (0.617). Well within 10%.
b. Its shell is expanding at about 20km/s. How old is it? (how long
ago was the shell ejected?)
age t = (0.0624 pc) / (20 km s⁻¹ × 3.24×10⁻¹⁷ pc / 10⁻³ km)
× (3.17×10⁻⁸ years / 1.00 s)
= 4.50×10⁷ years.
2) The Orion nebula is about 400 pc distant and has an apparent diameter of about 60 minutes of arc.
a. What is its physical diameter?
D = 6.98 pc.
b. The gas density is about 10 4 cm -3 and its temperature is about 10 4 K. The turnover frequency is obvious on Wilson’s SED plot. How thick is the H + layer along our line of sight?
turnover ν = 500 MHz.
At turnover, τ = 1.
Gaunt factor g = 10.6 + 1.9 log(T) - 1.26 log(Z ν)
= 7.24.
κ′ₛ = 0.178 Z² g ν⁻² T^(-3/2) nₑ nₕ
= 5.15×10⁻¹⁶ cm⁻¹.
Thickness l = τ / κ′ₛ.
3) The Perseus cluster of galaxies is about 73.6 Mpc distant and has an angular diameter of 860 arc minutes. The total mass in stars is about 2×10 13 M sun and the virial mass is about 10 15 M sun . It is one of the strongest x-ray sources in the sky, with L x = 4x10 45 erg/s. X-rays come from 5 million Kelvin brems.
a. Use total luminosity to find the emission measure.
L = 4π j V.
4π j = (From AGN3) 1.42×10⁻²⁷ Z² √T g[ff] n².
I will adopt an average g[ff] = 1.3.
Emission measure n² V = L / (4π 1.42×10⁻²⁷ Z² √T g[ff])
= 7.71×10⁶⁷ cm⁻³.
b. Use diameter to find V
Spherical V = 4/3 π r³
= 4/3 π (2.84×10²⁵ cm)³
= 9.61×10⁷⁶ cm³.
c. Solve for the density
n² = 7.71×10⁶⁷ cm⁻³ / 9.61×10⁷⁶ cm³
= 8.03×10⁻¹⁰.
n = √n² = 2.83×10⁻⁵ cm⁻³.
d. What is the total mass in hot gas?
M = μ n V
μₕ = 1.67×10⁻²⁷ kg × 2.83×10⁻⁵ cm⁻³ × 9.61×10⁷⁶ cm³
= 2.29×10¹⁵ Mₛₒₗ.

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_________
v = √ k T / m
1) 2.50 × 10⁵ cm/s
2) 1.17 × 10⁹ cm/s
3) 4665

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