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.
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$\begingroup$ Where did you see it used? $\endgroup$– HDE 226868 ♦Nov 30, 2014 at 19:48
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$\begingroup$ Related. $\endgroup$– HDE 226868 ♦Dec 1, 2014 at 0:25
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$\begingroup$ @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? $\endgroup$– GuestDec 1, 2014 at 4:33
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$\begingroup$ 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. $\endgroup$– WarrickDec 1, 2014 at 16:54
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$\begingroup$ @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! $\endgroup$– GuestDec 1, 2014 at 20:38
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just check what 'median' means. the median stellar mass is such that half of all stars have lower and the other half hihger mass. it has nothing to do with the logarithm. I havn't seen the term (median stellar mass) in the scientific literature.
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.
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$\begingroup$ Thank you, however in this paper, I was confused by this statement: "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? (arxiv.org/pdf/1309.5972v2.pdf ) $\endgroup$– GuestDec 1, 2014 at 4:34