# Galactic mass estimation from apparent magnitude and distance

Can we estimate the order of the total mass of any galaxy from the apparent magnitude and its distance to us? Just like $$\begin{equation} M_{galaxy}=c\times 10^{8}M_{\odot }, \end{equation}$$ where $$c$$ is a constant (can be arbitrary or ignored, the order is important). For example mass of the Tucana Dwarf of the Local group isn't known. But its apparent magnitude is 15.7 and average distance is $$8.8\times10^{5}pc$$. How can I estimate its approximate total mass?

## 2 Answers

First you must estimate the luminosity. That may be difficult unless the magnitude you have is a bolometric magnitude.

Then you assume some mass to light ratio (actually mass to luminosity ratio, where in solar units the M/L of the Sun is 1).

The M/L ratios of galaxies depend on galaxy type (and age, metallicity, star forming history) and vary from about 2-10. However, this is just the stellar mass. In most cases these ratios would need to be increased by a factor of 10 to give the total mass of a galaxy, which may be dominated by dark matter. The total M/L ratio of dwarf spheroidals like Tucana is likely to be $$\sim 100$$.

In conclusion, there is no single value of $$c$$ that can convert from a magnitude (luminosity) to a mass. Further reading: https://courses.lumenlearning.com/astronomy/chapter/properties-of-galaxies/

• Thank you for your answer. I just want to ask one more thing. One equation about the absolute magnitude with respect to apparent magnitude and the distance is $M_{abs}=M_{app}-5(logD-1)$. $D$ is the distance in parsecs. After calculating the absolute magnitude may I use $L_{galaxy}=L_{0}10^{-0.4{M_{abs}}}$ ($L_{0}$ is the zero point luminosity) for the galactic luminosity? – Haliki Dec 26 '18 at 12:57

As Rob Jeffries said, you typically assume a value of $$M/L$$ to find the mass from luminosity. I want to share a nice problem which guides you through the calculation for NGC1052 in the problem T8 here. Solutions are available here