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41 lines
1.2 KiB
Plaintext
41 lines
1.2 KiB
Plaintext
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1) Estimate the temperature of the warm dust emission.
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Read the wavelength at the peak of the blackbody region.
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λₚₑₐₖ = 10¹³ Hz.
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Using Wien Law,
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λₚₑₐₖ = 2.90 × 10⁻³ m K / T.
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T = 2.90 × 10⁻³ m K / 10¹³ Hz.
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T = 96.7 K.
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2) What is the turnover frequency of the brems emission?
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This is just gleaned from the SED.
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1.5 GHz = 1.5 × 10⁹ Hz.
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3) Assume that the brems comes from ionized hydrogen at 10 4 K and
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a density of 10 4 cm -3 . What is the thickness of NGC 7027 in cm?
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In parsecs?
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κʹₛ = 0.0178 Z² g ν⁻² T^(-3/2) nₑ nₗ.
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g = 10.6 + 1.9*log(T) - 1.26*log(Z*ν)
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= 6.63.
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κʹₛ = 0.0178 × 1 × (3.32) × (1.5 × 10⁹ Hz)⁻² × (10⁴ K)^(-3/2) × (10⁴ cm⁻³)².
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κʹₛ = 5.25 × 10⁻¹⁸ cm⁻¹.
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For turnover frequency,
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1 = τ = κʹₛ l.
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l = τ / κʹₛ = κʹₛ⁻¹.
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l = 1.90 × 10¹⁷ cm
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= 0.0617 parsecs.
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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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