<ul>
<li>This is just a unitless number by which the flux is multiplied. The conversion from magnitudes to a factor is handled by the <span class="math-container">$10^{-0.4}$</span> bit. Note you should be using <span class="math-container">$A'(\lambda)$</span> in the exponent.</li>
<li>Yes, I think that is the right way around. The corrected flux should be higher than the observed flux.</li>
<li>The factor of 3.1 is a good average for interstellar dust. It was likely assumed when modelling the spectra to derive <span class="math-container">$A_0$</span>. It is there because of the way <span class="math-container">$A'(\Lambda)$</span> is scaled to be 3.1 at 541 nm.</li>
<li>Why would you want to convolve with a kernel? (And what do you mean by &quot;e.g. hydrogen alpha emission&quot;? A filtering kernel is some function of wavelength, like a Gaussian.)</li>
</ul>

CC BY-SA 4.0
2024-10-25T16:57:48.413Z
Thank you so much! For the filtering, it's just because I'm still researching how to apply an H-alpha filter for a spectra. I assumed (perhaps incorrectly) that I would model the delta peak as a gaussian kernel, then convolve over the xp spectra. If this approach is incorrect, what is the proper way to make a filter or a pass band? I probably need to ask in a separate post
RRR
CC BY-SA 4.0
2024-10-25T16:47:19.063Z
2024-10-25T16:47:19.063Z
ProfRob
<p>I am working on the GAIA XP sampled spectral data and want to implement XP spectrum correction for extinction. I would like to check if my approach is correct as I am not an astronomer. I followed the gaia documentation <a href="https://gea.esac.esa.int/archive/documentation/GDR3/Data_analysis/chap_cu8par/sec_cu8par_data/ssec_cu8par_data_xp.html#SSS1.P4" rel="nofollow noreferrer">here</a></p>
<p>assuming that the XP spectra <span class="math-container">$f(\lambda)$</span> is the observed flux, the corrected <span class="math-container">$F(\lambda)$</span> can be computed by
<span class="math-container">$$
F(\lambda)=f(\lambda)⋅10^{0.4A_0 A(\lambda)/3.1}
$$</span></p>
<p>Where <span class="math-container">$A_0$</span> is <code>azero_gspphot</code> from <a href="https://gea.esac.esa.int/archive/documentation/GDR3/Gaia_archive/chap_datamodel/sec_dm_main_source_catalogue/ssec_dm_gaia_source.html" rel="nofollow noreferrer">here</a>. <span class="math-container">$A(\lambda)$</span> is the extinction curve for <span class="math-container">$\lambda$</span> in the same range as the sampled XP spectra, but converted to <span class="math-container">$Å$</span>.</p>
<p>This is my code in python</p>
<pre><code># wavelengths for xp spectra range in nm
wavelengths  = np.arange(336, 1021, 2)

# extinction curve using fitzpatrick99
# convert nm to angstrom
ext_curve = extinction.fitzpatrick99(wavelengths * 10, 1., 3.1)

# get star info. eg source id 2080220238201704832
star = {
flux: np.array([...]), # array of size 343 representing the sampled xp spectra from
azero: 0.1336,
}

# extinction factor
extinguish = 10** (0.4 * star.azero * ext_curve / 3.1)
corrected_flux = star.flux * extinguish 

# plot
plt.plot(wavelengths, star.flux, label=&quot;observed&quot;)
plt.plot(wavelengths, corrected_flux)
</code></pre>
<p>my questions:</p>
<ul>
<li><p>According to the documentation <a href="https://gea.esac.esa.int/archive/documentation/GDR3/Gaia_archive/chap_datamodel/sec_dm_spectroscopic_tables/ssec_dm_xp_sampled_mean_spectrum.html" rel="nofollow noreferrer">here</a> the XP spectra flux is given in <span class="math-container">$W m^{−2} nm^{−1}$</span> and <span class="math-container">$A_0$</span> is a magnitude quantity. Is there any units conversion I should be doing?</p>
</li>
<li><p>Is my assumption that <span class="math-container">$f(\lambda)$</span> is the XP spectra? therefore using <span class="math-container">$0.4$</span> instead of <span class="math-container">$-0.4$</span> in the extinction factor exponent?</p>
</li>
<li><p>Is the extinction factor exponent correct? particularly the division by 3.1? I saw a few <a href="https://github.com/krislars/GaiaExtinctionTutorial/blob/main/GaiaExtinctionTutorial.ipynb" rel="nofollow noreferrer">other tutorials</a> that do not include it. I am not sure if that means it is implicitly there in the library they used or if they're using a different approach.</p>
</li>
<li><p>Should convoluting with a filtering kernel (e.g., hydrogen alpha emission) be applied to the XP spectra after the extinction correction?</p>
</li>
</ul>
<p>Thank you</p>

<photometry><gaia><extinction>
How to compute extinction for XP GAIA spectra?
RRR
# How to compute extinction for XP GAIA spectra?

(Asked by: username_0 on 2024-10-25)

I am working on the GAIA XP sampled spectral data and want to implement XP spectrum correction for extinction. I would like to check if my approach is correct as I am not an astronomer. I followed the gaia documentation here
assuming that the XP spectra $f(\lambda)$ is the observed flux, the corrected $F(\lambda)$ can be computed by
$$
F(\lambda)=f(\lambda)⋅10^{0.4A_0 A(\lambda)/3.1}
$$
Where $A_0$ is azero_gspphot from here. $A(\lambda)$ is the extinction curve for $\lambda$ in the same range as the sampled XP spectra, but converted to $Å$.
This is my code in python
# wavelengths for xp spectra range in nm
wavelengths  = np.arange(336, 1021, 2)

# extinction curve using fitzpatrick99
# convert nm to angstrom
ext_curve = extinction.fitzpatrick99(wavelengths * 10, 1., 3.1)

# get star info. eg source id 2080220238201704832
star = {
flux: np.array([...]), # array of size 343 representing the sampled xp spectra from
azero: 0.1336,
}

# extinction factor
extinguish = 10** (0.4 * star.azero * ext_curve / 3.1)
corrected_flux = star.flux * extinguish 

# plot
plt.plot(wavelengths, star.flux, label="observed")
plt.plot(wavelengths, corrected_flux)

my questions:

According to the documentation here the XP spectra flux is given in $W m^{−2} nm^{−1}$ and $A_0$ is a magnitude quantity. Is there any units conversion I should be doing?

Is my assumption that $f(\lambda)$ is the XP spectra? therefore using $0.4$ instead of $-0.4$ in the extinction factor exponent?

Is the extinction factor exponent correct? particularly the division by 3.1? I saw a few other tutorials that do not include it. I am not sure if that means it is implicitly there in the library they used or if they're using a different approach.

Should convoluting with a filtering kernel (e.g., hydrogen alpha emission) be applied to the XP spectra after the extinction correction?


Thank you

**Tags:** photometry, gaia, extinction

---

## 1 answers

### Answer by username_1 on 2024-10-25. Score: 1 | Accepted answer

* This is just a unitless number by which the flux is multiplied. The conversion from magnitudes to a factor is handled by the $10^{-0.4}$ bit. Note you should be using $A'(\lambda)$ in the exponent.
* Yes, I think that is the right way around. The corrected flux should be higher than the observed flux.
* The factor of 3.1 is a good average for interstellar dust. It was likely assumed when modelling the spectra to derive $A\_0$. It is there because of the way $A'(\Lambda)$ is scaled to be 3.1 at 541 nm.
* Why would you want to convolve with a kernel? (And what do you mean by "e.g. hydrogen alpha emission"? A filtering kernel is some function of wavelength, like a Gaussian.)

> **Comments:**
> **username_0**: Thank you so much! For the filtering, it's just because I'm still researching how to apply an H-alpha filter for a spectra. I assumed (perhaps incorrectly) that I would model the delta peak as a gaussian kernel, then convolve over the xp spectra. If this approach is incorrect, what is the proper way to make a filter or a pass band? I probably need to ask in a separate post  

---

