<p>I'm looking for a function which gives the typical <em>isotropic</em> spectral power of light emitted by an entire galaxy on the whole electromagnetic spectrum (in watts per frequency unit), as a function of frequency:
$$\tag{1}
\mathrm{d}\mathcal{P} = \mathcal{Q}(\omega) \, \mathrm{d}\omega = \; ?
$$
The total bolometric power emitted (in watts) is then
$$\tag{2}
\mathcal{P}_{\text{tot}} = \int_0^{\infty} \mathcal{Q}(\omega) \, \mathrm{d}\omega.
$$
What would be the function $\mathcal{Q}(\omega)$, for an "ideal" (theoretical) spherical galaxy?</p>

<p>As a candidate, how can we justify a function like the following one, where $\alpha$ and $\omega_0$ are two adjustable positive parameters, and $\mathcal{P}$ is a constant (the total bolometric power)?
$$\tag{3}
\mathcal{Q}(\omega) = \frac{\mathcal{P}}{\Gamma(\alpha + 1)} \; \Big( \, \frac{\alpha \, \omega}{\omega_0} \, \Big)^{\alpha} \; e^{-\, \alpha \, \omega / \omega_0} \; \frac{\alpha}{\omega_0}.
$$</p>

CC BY-SA 3.0
2016-11-02T00:52:53.563Z
I found an old paper which gives something very similar to equation (3), with $\alpha = 2$.  See page 687 : http://thesis.library.caltech.edu/3219/1/Shectman_sa_1974.pdf
Cham
CC BY-SA 3.0
2016-11-02T13:16:37.200Z
I can't say I have a definitive answer for you, but why does Planck's law not work for you? That is literally exactly the isotropic spectral power of light of a black body. You can modify the function to apply to an entire galaxy with some simple changes. I think its also worth pointing out that you equation 3 is basically just a scaled version of Wien's approximation to Planck's law, when $\alpha = 3$.
zephyr
CC BY-SA 3.0
2016-11-02T13:47:37.230Z
@zephyr, yes, I knew that the function (3) is a generalisation of Wien's law (when $\alpha = 3$).  But I don't think that a galaxy could be modelized as a blackbody.  There are lots of absorption and diffusion caused by dust and gaz.  And you have a mix of many kind of stars inside (i.e. a mix of small blackbodies, each with different temperatures).  Actually, this is the sense of my question :  what should be the best representation of the spectral power output of a galaxy ?
Cham
CC BY-SA 3.0
2016-11-03T13:13:21.377Z
I found a detailled paper about this subject.  The spectral luminosity of galaxies is extremely complex, and is so far away from the Planck's distribution, it's not even funny anymore !  Equation (3) above is not even close !  :-( https://arxiv.org/pdf/1008.0395v1.pdf
Cham
CC BY-SA 3.0
2016-11-03T13:38:13.690Z
Great! Feel free to post an answer to your own question.
zephyr
<galaxy><cosmology><astrophysics><luminosity><radiation>
What is the spectral power output of a typical galaxy?
Cham
# What is the spectral power output of a typical galaxy?

(Asked by: username_0 on 2016-11-01)

I'm looking for a function which gives the typical *isotropic* spectral power of light emitted by an entire galaxy on the whole electromagnetic spectrum (in watts per frequency unit), as a function of frequency:
$$\tag{1}
\mathrm{d}\mathcal{P} = \mathcal{Q}(\omega) \, \mathrm{d}\omega = \; ?
$$
The total bolometric power emitted (in watts) is then
$$\tag{2}
\mathcal{P}\_{\text{tot}} = \int\_0^{\infty} \mathcal{Q}(\omega) \, \mathrm{d}\omega.
$$
What would be the function $\mathcal{Q}(\omega)$, for an "ideal" (theoretical) spherical galaxy?

As a candidate, how can we justify a function like the following one, where $\alpha$ and $\omega\_0$ are two adjustable positive parameters, and $\mathcal{P}$ is a constant (the total bolometric power)?
$$\tag{3}
\mathcal{Q}(\omega) = \frac{\mathcal{P}}{\Gamma(\alpha + 1)} \; \Big( \, \frac{\alpha \, \omega}{\omega\_0} \, \Big)^{\alpha} \; e^{-\, \alpha \, \omega / \omega\_0} \; \frac{\alpha}{\omega\_0}.
$$

**Tags:** galaxy, cosmology, astrophysics, luminosity, radiation
> **Comments:**
> **username_0**: I found an old paper which gives something very similar to equation (3), with $\alpha = 2$.  See page 687 : http://thesis.library.caltech.edu/3219/1/Shectman_sa_1974.pdf  
> **username_1**: I can't say I have a definitive answer for you, but why does Planck's law not work for you? That is literally exactly the isotropic spectral power of light of a black body. You can modify the function to apply to an entire galaxy with some simple changes. I think its also worth pointing out that you equation 3 is basically just a scaled version of Wien's approximation to Planck's law, when $\alpha = 3$.  
> **username_0**: @zephyr, yes, I knew that the function (3) is a generalisation of Wien's law (when $\alpha = 3$).  But I don't think that a galaxy could be modelized as a blackbody.  There are lots of absorption and diffusion caused by dust and gaz.  And you have a mix of many kind of stars inside (i.e. a mix of small blackbodies, each with different temperatures).  Actually, this is the sense of my question :  what should be the best representation of the spectral power output of a galaxy ?  
> **username_0**: I found a detailled paper about this subject.  The spectral luminosity of galaxies is extremely complex, and is so far away from the Planck's distribution, it's not even funny anymore !  Equation (3) above is not even close !  :-( https://arxiv.org/pdf/1008.0395v1.pdf  
> **username_1**: Great! Feel free to post an answer to your own question.  

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## 0 answers

