<p>You want to basically assume that the supernova is a &quot;standard candle,&quot; i.e., if we know with confidence how bright it <span class="math-container">$\it{should}$</span> be, then we can estimate the distance after measuring it's luminosity.</p>
<p>In a simple, crude approach, one can just use the good 'ole <a href="https://en.wikipedia.org/wiki/Luminosity#Luminosity_formulae" rel="nofollow noreferrer">luminosity formula</a>: assuming the source radiates with constant luminosity, its brightness will decrease with the inverse square law, and you invert the formula to get the luminosity distance,
<span class="math-container">$$ D_{\rm L} = \sqrt{\frac{L}{4\pi F}}$$</span>
where <span class="math-container">$L$</span> is the luminosity and <span class="math-container">$F$</span> is the <a href="https://en.wikipedia.org/wiki/Radiant_flux" rel="nofollow noreferrer">flux</a>.</p>
<p>Here's a <a href="http://astro.unl.edu/naap/distance/animations/snCurveExplorer.html" rel="nofollow noreferrer">GUI</a> you may or may not find useful (ie see item 13 <a href="https://www.physics.unlv.edu/%7Ejeffery/astro/applet/naap_supernovae.html" rel="nofollow noreferrer">here</a>).</p>
<p>Lots of helpful info <a href="https://www.physics.unlv.edu/%7Ejeffery/astro/applet/naap_supernovae.html" rel="nofollow noreferrer">here</a>, and they also have an applet that you can download and play around with which uses the <a href="https://en.wikipedia.org/wiki/Distance_modulus" rel="nofollow noreferrer">distance modulus</a> (as answered <a href="https://astronomy.stackexchange.com/questions/48365/how-to-calculate-distance-to-other-galaxies-using-type-1a-supernova">here</a>).</p>
<p>Note this is only a (crude) approximation, since it assumes zero extinction due to dust and doesn't account for cosmology. If this is for a research project, you'll likely need to do something more sophisticated and should consult your advisor and the literature, i.e., see <a href="https://notebook.community/banneker-aztlan/python-week-2/Part%204/Supernova%20Cosmology" rel="nofollow noreferrer">this</a> nice python notebook, or <a href="https://github.com/sncosmo/sncosmo" rel="nofollow noreferrer">this</a> python module.</p>
<p>I hope this helps!</p>

CC BY-SA 4.0
2023-02-24T08:28:42.817Z
2023-02-24T08:28:42.817Z
Daddy Kropotkin
<p>I have some light curve data of a SN Ia from which I want to find the luminosity distance <span class="math-container">$D_L$</span>.</p>
<p>How can I do it mathematically?</p>
<p>I'll then try to implement the answer using Python.</p>

CC BY-SA 4.0
2023-02-24T00:17:51.197Z
The references here might be of help: https://en.m.wikipedia.org/wiki/Phillips_relationship
Greg Miller
<observational-astronomy><distances><supernova><light-curve>
How to obtain luminosity distance from a light curve
Abdullah
# How to obtain luminosity distance from a light curve

(Asked by: username_0 on 2023-02-23)

I have some light curve data of a SN Ia from which I want to find the luminosity distance $D\_L$.

How can I do it mathematically?

I'll then try to implement the answer using Python.

**Tags:** observational-astronomy, distances, supernova, light-curve

> **Comments:**
> **username_1**: The references here might be of help: https://en.m.wikipedia.org/wiki/Phillips_relationship  

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## 1 answers

### Answer by username_2 on 2023-02-24. Score: 2 | Accepted answer

You want to basically assume that the supernova is a "standard candle," i.e., if we know with confidence how bright it $\it{should}$ be, then we can estimate the distance after measuring it's luminosity.

In a simple, crude approach, one can just use the good 'ole [luminosity formula](https://en.wikipedia.org/wiki/Luminosity#Luminosity_formulae): assuming the source radiates with constant luminosity, its brightness will decrease with the inverse square law, and you invert the formula to get the luminosity distance,
$$ D\_{\rm L} = \sqrt{\frac{L}{4\pi F}}$$
where $L$ is the luminosity and $F$ is the [flux](https://en.wikipedia.org/wiki/Radiant_flux).

Here's a [GUI](http://astro.unl.edu/naap/distance/animations/snCurveExplorer.html) you may or may not find useful (ie see item 13 [here](https://www.physics.unlv.edu/%7Ejeffery/astro/applet/naap_supernovae.html)).

Lots of helpful info [here](https://www.physics.unlv.edu/%7Ejeffery/astro/applet/naap_supernovae.html), and they also have an applet that you can download and play around with which uses the [distance modulus](https://en.wikipedia.org/wiki/Distance_modulus) (as answered [here](https://astronomy.stackexchange.com/questions/48365/how-to-calculate-distance-to-other-galaxies-using-type-1a-supernova)).

Note this is only a (crude) approximation, since it assumes zero extinction due to dust and doesn't account for cosmology. If this is for a research project, you'll likely need to do something more sophisticated and should consult your advisor and the literature, i.e., see [this](https://notebook.community/banneker-aztlan/python-week-2/Part%204/Supernova%20Cosmology) nice python notebook, or [this](https://github.com/sncosmo/sncosmo) python module.

I hope this helps!


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