mirror of
https://asciireactor.com/otho/as-500.git
synced 2024-11-24 04:25:05 +00:00
41 lines
1.2 KiB
Plaintext
41 lines
1.2 KiB
Plaintext
|
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.
|