Estimating Physical Quantitites

Observations do not give the kind of physical quantities that we can directly pull from simulations. There is usually no direct way to measure masses, densities, temperatures, etc. Instead we must rely on (often uncertain) conversions between observable quantities and physical ones.

Stellar Mass

In a perfect world, we would have a simple mass-to-light ration ${{\rm Y}}_{\ast }$ that would let us simply observe the luminosity of a galaxy $L$ and obtain the stellar mass as $M_{\ast }={{\rm Y}}_{\ast }L$ . Unfortunately, ${\rm Y}$ depends on the age and metallicity of a stellar population, and most visible/UV wavelengths are susceptible to extinction.

The closest we have to the perfect conversion factor is in the near infrared (NIR), at $3.6\mu m$, where ${{\rm Y}}_{\ast }\simeq 0.2-0.7{\mathrm{M}}_{\odot }/{\mathrm{L}}_{\odot }$ Lelli et al. 2016.

Working in the optical is much more contentious. For example, if we take equation 9 from Nazarova et al. 2025, we can estimate the stellar mass of a galaxy with $B$ and $V$ [Filtered magnitudes, we can estimate the stellar mass as:

$\log (M_{\ast }/M_{\odot })=11.27+2\log (D)+1.45(B-V)-0.4B$

Gas Mass

Atomic Hydrogen (HI)

HI is relatively easy to measure, as it has an optically thin radio line at 21 cm (1421 MHz). Radio observations are also handy because they are inherently spectra: every radio telescope is also an IFU. If we measure a peak 21cm flux $S_{peak}$ in Janskys, and a velocity width of $W$ in km/s, the HI mass for an object $D$ Mpc away is given in equation 2 of Giovanelli et al. 2005 as:

$M_{HI}\simeq 2.4\times 10^5{D}^2{S}_{peak}W{\mathrm{M}}_{\odot }$

Molecular Hydrogen ($H_2$)

This one is much tougher, because molecular hydrogen isn’t very bright.