=================================================================

**Edit:** I moved this topic here, since it concerns a recent development feature in

**celestia.Sci**. In irregular time intervals, members of the celestia.Sci dev team will report here about topical research underlying some important new code development.

This material will often be addressed to people with some background in Astrophysics/ Mathematics, who want to know in more concise terms about the theoretical concepts and astrophysical/astronomical data on which new celestia.Sci code will be based.

Throughout it is encouraged to present links to used scientific papers..

=================================================================

I needed a smooth function fit of the best available Luminosity Function (LF) data for nearby MilkyWay stars (< 25 pc). After proper normalization, its purpose is to serve as probability distribution for statistically generating

**realistic** populations of faint stars in the ~ spherical halos around galaxies in

**celestia.Sci**. Perhaps my analysis results are of some interest to others.

The best LF data (including Hipparcos stars!) are tabulated (with statistical errors) in this paper

http://adsabs.harvard.edu/abs/1997ESASP.402..675Jby H. Jahreiß and R. Wielen (1997).

Here I have done a plot of these data with Maple 17:

[Click on image for a bigger display]

Attachment:

LF_data_nearbystars.jpg [ 36.36 KiB | Viewed 4661 times ]
On the x-axis you have the

**absolute visual magnitude M_V** while on the y-axis you see the corresponding star counts per unit volume [pc^3].

Note the conspicuous peak around M_V~ 12 -14 and the shoulder around M_V~ 5.6. In this region left of the main peak, the errors are pretty small and the least-square fit should be very good here.

It should be quite obvious that a very good ansatz is in terms of a sum of two Gaussians, one multiplied with another factor of M_V^2. Each Gaussian brings 3 parameters along like so

G1(x) = a[1] *x^2*exp(-(x-x0)^2/a[2]^2);

G2(x) = a[3] * exp(-(x-x0)^2/a[4]^2);

LF = G1(M_V) + G2(M_V)

with parameters a[1]..a[4] and x0, x1 to be determined by a least square optimization algorithm in Maple. In the paper also the errors were given, so these can be accounted for as usual in the fit.

**Note**: Gaussian fit functions have the big advantage over

**polynomial-based** fits that outside the proper fitting range they quickly tend towards zero, while (high-order) polynomials VERY quickly run out of control by adopting non-sensical values!

Here is the beautiful result, with all parameters determined:

[Click on image for a bigger display]

Attachment:

LF_data_nearbystars_fit.jpg [ 38.96 KiB | Viewed 4661 times ]
Here is the link to my well-commented Maple17 worksheet from where all determined parameters etc may be copied.

http://www.celestialmatters.org/users/t00fri/files/luminosityfunction_HIP_PMSU4_fit.pdf Interested readers may also get a concise idea about the typical working steps in such type of scientific analysis...

For your convenience, here is a summary of the used function and its determined parameters

[Click on image for a bigger display]

Attachment:

pars.jpg [ 24.15 KiB | Viewed 4658 times ]
Fridger