<p>Yes, for any spherical-overdensity mass definition, halo mass and halo radius are uniquely related at fixed time.</p>

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2024-04-18T21:05:31.537Z
2024-04-18T21:05:31.537Z
Sten
<p>I was studying about the definitions of virial mass and virial radius of a dark matter halo and it is basically defined as</p>
<p><span class="math-container">$$M_{vir}= \frac{4}{3}\pi R_{vir}^3\Delta_{c}\rho_{crit} $$</span>n where <span class="math-container">$\rho_{crit} $</span> is the critical density at a fixed redshift, and overdensity or  <span class="math-container">$\Delta_{c}$</span> is usually 200, but dependent on cosmology. This is derived assuming a spherical collapse, but does this mean that if we know the <span class="math-container">$M_{vir}$</span> of a halo at a specific redshift z, we can calculate <span class="math-container">$R_{vir}$</span>, ie all halos of mass <span class="math-container">$M_{vir}$</span> have a virial radii of <span class="math-container">$R_{vir}$</span> ?</p>

<dark-matter>
Relating virial radius to virial mass of a dark matter halo
Esanmouli Ghosh
# Relating virial radius to virial mass of a dark matter halo

(Asked by: username_0 on 2024-04-18)

I was studying about the definitions of virial mass and virial radius of a dark matter halo and it is basically defined as

$$M\_{vir}= \frac{4}{3}\pi R\_{vir}^3\Delta\_{c}\rho\_{crit} $$n where $\rho\_{crit} $ is the critical density at a fixed redshift, and overdensity or $\Delta\_{c}$ is usually 200, but dependent on cosmology. This is derived assuming a spherical collapse, but does this mean that if we know the $M\_{vir}$ of a halo at a specific redshift z, we can calculate $R\_{vir}$, ie all halos of mass $M\_{vir}$ have a virial radii of $R\_{vir}$ ?

**Tags:** dark-matter

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## 1 answers

### Answer by username_1 on 2024-04-18. Score: 2

Yes, for any spherical-overdensity mass definition, halo mass and halo radius are uniquely related at fixed time.


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