<p>I see the SED being referred to as several different things and now I am confused about what it actually is and what are its units. In particular, I find the <a href="https://en.wikipedia.org/wiki/Spectral_energy_distribution" rel="nofollow noreferrer">SED Wikipedia page</a> not understandable.</p>

<p>The Flux <span class="math-container">$F$</span> of a star/galaxy is related to its luminosity <span class="math-container">$L$</span> by
<span class="math-container">$$F=\dfrac{L}{4\pi d_L^2}\,,$$</span> where <span class="math-container">$d_L$</span> is the luminosity distance.
If we differentiate the quantities and remembering that the emitted wavelength <span class="math-container">$\lambda_{em}$</span> is related to the observed one by <span class="math-container">$\lambda_{obs}=(1+z)\lambda_{em}$</span>, where <span class="math-container">$z$</span> is the redshift, we can have two quantities:</p>

<ul>
<li><span class="math-container">$\dfrac{dF}{d\lambda_{obs}}\equiv f_{\lambda}$</span></li>
<li><span class="math-container">$\dfrac{dL}{d\lambda_{em}}\equiv l_{\lambda}$</span></li>
</ul>

<p>I <strong>think</strong> <span class="math-container">$f_{\lambda}$</span> is the specta (units of [Energy][Time]<span class="math-container">$^{-1}$</span>[Lenght]<span class="math-container">$^{-3}$</span>) and <span class="math-container">$l_{\lambda}$</span> is the SED (and therefore has units of [Energy][Time]<span class="math-container">$^{-1}$</span>[Lenght]<span class="math-container">$^{-1}$</span>). Is this correct? Can you give me some resources (eg. papers or books) where this is written down? Thank you.</p>

CC BY-SA 4.0
2020-03-02T14:24:41.950Z
SED = Spectral Energy Distribution. It can be in flux units or in luminosity units, but is quoted as flux per unit wavelength (or sometimes flux per unit frequency).
ProfRob
CC BY-SA 4.0
2020-03-02T15:01:04.547Z
@RobJeffries, I am sorry but I didn't understand it. Since it is "distribution", I assumed it is always per unit of wavelength (or frequency). Additionally, it has a name and $l_{\lambda}$ and $f_{\lambda}$ are two intrinsically different things, so how can we call the same to both?
Catarina Alves
CC BY-SA 4.0
2020-03-02T15:04:16.177Z
Because one is just the other multiplied by $4\pi d^2$. We call a spectrum a spectrum, but that can mean a lot of different things. I guess you might distinguish between an observed SED (always flux) and an intrinsic SED.
ProfRob
CC BY-SA 4.0
2020-03-02T17:14:08.227Z
The most important thing is: both show exactly the same frequency (or wavelength) dependence - multiplied by a constant factor (the distance to the source does not change in this regard; its distance is only important when you need the overall luminosity)
planetmaker
CC BY-SA 4.0
2020-03-02T20:37:35.347Z
The important thing to remember is that spectral energy is radically different from the spectral photon count (because photons have different energy depending on wavelength)
Carl Witthoft
CC BY-SA 4.0
2020-03-02T23:57:59.623Z
@CarlWitthoft, when would we use spectral photon count?
Catarina Alves
CC BY-SA 4.0
2020-03-03T00:00:55.377Z
@planetmaker, it is not true that both $f_{\lambda}$ and $f_{\lambda}$ only differ by a multiplicative constant. In fact, 
$$f_{\lambda}(\lambda_{obs})\propto l_{\lambda}(\lambda_{em})=l_{\lambda}((1+z)\lambda_{obs})$$
Catarina Alves
CC BY-SA 4.0
2020-03-03T00:05:31.727Z
@RobJeffries, do you simply ignore the different scaling that goes into the function then? (The scaling I posted in my previous message)
Catarina Alves
CC BY-SA 4.0
2020-03-03T00:28:20.613Z
I am not an extragalactic astronomer, so the redshift complication is unfamiliar. I would call $f_\lambda$ the observed SED. Then $l_\lambda$ would be an intrinsic SED. If you want them both to be in the same units, just divide $l_\lambda$ by $4\pi d_L^2$. However you will see all sorts of axes $\nu f_\nu$, $\lambda f_\lambda$, $f_\lambda$, $\lambda L_\lambda$ and they can all be called SEDs because they just indicate how much energy is emerging at what wavelengths (or frequencies).
ProfRob
CC BY-SA 4.0
2020-03-03T01:19:54.050Z
@CatarinaAlves yes... I'm dealing with more local stuff where cosmic redshift is negligible :)
planetmaker
CC BY-SA 4.0
2020-03-03T10:55:57.993Z
Thank you. I wonder if once we go to higher redshifts, people start to distinguish more the names, but I understand what @RobJeffries said about all of those quantities indicating the energy at those wavelengths (or frequencies).
Just to add that in I put the formula wrong on the comment above. It should be
$$f_{\lambda}(\lambda_{obs})\propto l_{\lambda}(\lambda_{em})=l_{\lambda}\left(\dfrac{\lambda_{obs}}{1+z}\right)$$
Catarina Alves
CC BY-SA 4.0
2020-03-03T12:56:39.490Z
@CatarinaAlves the photon count matters when you are dealing with a quantum sensor, such as a CCD or the human retina.  These things detect photons, not "wave energy"
Carl Witthoft
<spectra><luminosity>
What is the spectral energy distribution (SED)?
Catarina Alves
# What is the spectral energy distribution (SED)?

(Asked by: username_0 on 2020-03-02)

I see the SED being referred to as several different things and now I am confused about what it actually is and what are its units. In particular, I find the [SED Wikipedia page](https://en.wikipedia.org/wiki/Spectral_energy_distribution) not understandable.

The Flux $F$ of a star/galaxy is related to its luminosity $L$ by
$$F=\dfrac{L}{4\pi d\_L^2}\,,$$ where $d\_L$ is the luminosity distance.
If we differentiate the quantities and remembering that the emitted wavelength $\lambda\_{em}$ is related to the observed one by $\lambda\_{obs}=(1+z)\lambda\_{em}$, where $z$ is the redshift, we can have two quantities:

* $\dfrac{dF}{d\lambda\_{obs}}\equiv f\_{\lambda}$
* $\dfrac{dL}{d\lambda\_{em}}\equiv l\_{\lambda}$

I **think** $f\_{\lambda}$ is the specta (units of [Energy][Time]$^{-1}$[Lenght]$^{-3}$) and $l\_{\lambda}$ is the SED (and therefore has units of [Energy][Time]$^{-1}$[Lenght]$^{-1}$). Is this correct? Can you give me some resources (eg. papers or books) where this is written down? Thank you.

**Tags:** spectra, luminosity

> **Comments:**
> **username_1**: SED = Spectral Energy Distribution. It can be in flux units or in luminosity units, but is quoted as flux per unit wavelength (or sometimes flux per unit frequency).  
> **username_0**: @RobJeffries, I am sorry but I didn't understand it. Since it is "distribution", I assumed it is always per unit of wavelength (or frequency). Additionally, it has a name and $l_{\lambda}$ and $f_{\lambda}$ are two intrinsically different things, so how can we call the same to both?  
> **username_1**: Because one is just the other multiplied by $4\pi d^2$. We call a spectrum a spectrum, but that can mean a lot of different things. I guess you might distinguish between an observed SED (always flux) and an intrinsic SED.  
> **username_2**: The most important thing is: both show exactly the same frequency (or wavelength) dependence - multiplied by a constant factor (the distance to the source does not change in this regard; its distance is only important when you need the overall luminosity)  
> **username_3**: The important thing to remember is that spectral energy is radically different from the spectral photon count (because photons have different energy depending on wavelength)  
> **username_0**: @username_3, when would we use spectral photon count?  
> **username_0**: @username_2, it is not true that both $f_{\lambda}$ and $f_{\lambda}$ only differ by a multiplicative constant. In fact,  $$f_{\lambda}(\lambda_{obs})\propto l_{\lambda}(\lambda_{em})=l_{\lambda}((1+z)\lambda_{obs})$$  
> **username_0**: @RobJeffries, do you simply ignore the different scaling that goes into the function then? (The scaling I posted in my previous message)  
> **username_1**: I am not an extragalactic astronomer, so the redshift complication is unfamiliar. I would call $f_\lambda$ the observed SED. Then $l_\lambda$ would be an intrinsic SED. If you want them both to be in the same units, just divide $l_\lambda$ by $4\pi d_L^2$. However you will see all sorts of axes $\nu f_\nu$, $\lambda f_\lambda$, $f_\lambda$, $\lambda L_\lambda$ and they can all be called SEDs because they just indicate how much energy is emerging at what wavelengths (or frequencies).  
> **username_2**: @username_0 yes... I'm dealing with more local stuff where cosmic redshift is negligible :)  
> **username_0**: Thank you. I wonder if once we go to higher redshifts, people start to distinguish more the names, but I understand what @RobJeffries said about all of those quantities indicating the energy at those wavelengths (or frequencies). Just to add that in I put the formula wrong on the comment above. It should be $$f_{\lambda}(\lambda_{obs})\propto l_{\lambda}(\lambda_{em})=l_{\lambda}\left(\dfrac{\lambda_{obs}}{1+z}\right)$$  
> **username_3**: @username_0 the photon count matters when you are dealing with a quantum sensor, such as a CCD or the human retina.  These things detect photons, not "wave energy"  

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## 0 answers

