# What is “Median Stellar Mass”?

Could someone explain what is "median stellar mass" and how is it calculated? I have seen it written as:

$$\log(M)$$

or as:

$$\log\left(\frac{M_*}{M_{\text{Sun}}}\right)$$

but I do not understand what it means.

• Where did you see it used? – HDE 226868 Nov 30 '14 at 19:48
• Related. – HDE 226868 Dec 1 '14 at 0:25
• @HDE 226868 In the abstract in this paper: arxiv.org/pdf/1309.5972v2.pdf They say "The characteristic mass (M*) and slope at the lowest masses (alpha) of a double-Schechter function fit to the SMF stay roughly constant at Log(M*/M)~10.65..." Why do they use the log there? – Guest Dec 1 '14 at 4:33
• Is it "median" stellar mass you don't understand? That's a fundamental statistical concept (see e.g. Wikipedia). Or is it "characteristic" mass you don't understand? Or the reason they use logarithms? Your question asks a different question to your comments. – Warrick Dec 1 '14 at 16:54
• @Warrick Yes, I was confused by what is "characteristic" mass and also the reason logarithms were used. I'm sorry for my lack of clarity! – Guest Dec 1 '14 at 20:38

Looking at the paper you're referring to, they never use the expression "median stellar mass". Moreover, this study is not concerned about the masses of individual stars, but with the total stellar mass of a galaxy, which they donote by $M$. They then consider the typical or characteristic value for $M$ (as obtained by fitting a Schechter function to the observed distribution of $M$), and denote it by $M^\ast$. Since this is a rather large number, of the order of $\sim10^{10}$M$_\odot$, they prefer to use its logarithm to base ten: $$\log\left(\frac{M^\ast}{\mathrm{M}_\odot}\right).$$ I think the paper explains all that quite clearly and am puzzled by your difficulty.