Is the interval of the M_r prior dependent on [FeH]?

[HWRix]

p(M_r) -- after Equation 5 -- states M_r_min_obs, and M_r_max_obs,
outside of which p(M_r)==0; this is important for the normalization.
But it doesn't say what these limiting values are.
In particular, the "tip" and the "base" of the giant branch depends on metallicity
(see plot below from the data in the X14 paper).
It the tip there is only little variation for -1.4>FeH>-2.5, which is where most of the sample is.
But the minimal luminosity of the sample depends quite significantly on [FeH].
Should then not p( M_r | [Fe/H] ), simply because M_r_min_obs([FeH]) and
M_r_max_obs([FeH]).
Did you include this?

[xiangxiangxue]

Sorry, I can not upload the figures on github.

I include the dependence of the fiducials’ tips on the metallicities in S(m(DM,Mr),c(Mr,[Fe/H])). When doing the interpolation, I set all colors where Mr<Mr_tip as -9999, which means no value. The attached interpolated fiducials show that we have considered the tip problem. I also make a plot of [Fe/H] vs. Mr for SEGUE-2 l-color K giants, which shows the tips of the Mr changed for stars with [Fe/H]>-2. The dependence of the maximum Mr (faint tail) on the [Fe/H] is caused by the cutting of HB/RC stars. I did not include the effect of HB/RC cutting in p(Mr|[Fe/H]).

Best regards
Xiangxiang

Max-Planck-Institut fuer Astronomie, Koenigstuhl 17, D-69117, Heidelberg
Email: [e-mail] mailto:[e-mail]

On 14 Jan 2015, at 10:02, HWRix [e-mail] wrote:

p(M_r) -- after Equation 5 -- states M_r_min_obs, and M_r_max_obs --,
but doesn't say what theses values are.
In particular, the "tip of the giant branch" depends on metallicity;
that seems to be a small effect for -1.4>FeH>-2.5, which is where pst of the sample is.
But the minimal luminosity of the sample depends very much on [FeH].
Should then not p(M_r | [Fe/H] )
Did you include this?

https://cloud.githubusercontent.com/assets/5234830/5732834/68b20e22-9b56-11e4-86a5-a3522fefa3a4.png
—
Reply to this email directly or view it on GitHub #9.

[xuexx]

I include the dependence of the fiducials’ tips on the metallicities in S(m(DM,Mr),c(Mr,[Fe/H])). When doing the interpolation, I set all colors where Mr<Mr_tip as -9999, which means no value. The attached interpolated fiducials show that we have considered the tip problem. I also make a plot of [Fe/H] vs. Mr for SEGUE-2 l-color K giants, which shows the tips of the Mr changed for stars with [Fe/H]>-2. The dependence of the maximum Mr on the [Fe/H] is caused by the cutting of HB/RC stars. I did not include the effect of HB/RC cutting in p(Mr|[Fe/H]).

[HWRix]

XX: I can see the plot and also can see where to upload the plot, but I can not upload it because of the internet speed. So I have to reply to you directly if I want to show you some plots.
I will multiply a function p(Mr,[Fe/H])=1 if Mr<=f([Fe/H]) or p(Mr,[Fe/H])=0 if Mr>f([Fe/H]) to Eqn(5). f([Fe/H]) is the blue line on your figure.

That sounds right, and needs to be done in addition to an analogous "cut" at the tip of the giant branch

[xuexx]

Ok, I wil do it. But I want to explain to you.
Actually, I think I have included the cut at the tip of the giant branch in fiducial interpolation. For example, given an M_r<M_r_tip for [Fe/H]=-2, the color g-r predicted by M_r and [Fe/H]=-2 is -9999, then S(m,c) in Equation 5 is 0. Though p(M_r)=1, Equation 5 is still 0, because the S(m,c)=0.