# Homework Help: Stellar physics (number crunching)

1. Jan 2, 2012

### Lavabug

Decided to have a go at an extra credit assignment:

1. The problem statement, all variables and given/known data
I am given some data for ~9000 stars of 21 known spectral types along with their:
• measured parallax & uncertainty
• proper movements in right ascension & declination per year
• (B-V) color & relative mag (V).
I am asked to compute the following:

a) HR diagram
b) Show that the luminosity function can be approximated to Gaussian distributions of a given form.

^^Working on these, good so far.

c) Construct the frequency histograms with respect to the absolute magnitude, grouped into different intervals of Mv. These will provide the stellar luminosity function for a given spectral type.
d) Calculate the spatial density of stars in the Sun's neighborhood and show that its density it is approximately constant (function of radial position from the Sun)
e) Show how the measurement errors($\Delta m_v \approx 0.2$) affect the calculated absolute magnitude. If the parallax measurements follow a Gaussian distribution, will Mv's error also follow a Gaussian curve?

3. The attempt at a solution

On (c), I'm not exactly sure what is meant by frequency histogram, nor how large of an interval should I pick for Mv? I think I better ask my prof for this one.

(d) How would I go about doing this? I've got enough to find the distance in parsec for all the stars, but what kind of function should I try to fit them to? 3rd degree polynomial?
I could plot density = 3*(N stars)/4*pi*r^3, which I expect will taper off to a flat slope if the density really is constant, but how far should I consider the "Solar neighborhood" to be (in parsec)?
Or is my approach totally wrong?

(e) My expression for error propagation looks like this (see attachment), I pray that I have not offended the Calculus gods. Is it correct? Not sure how to respond to the other part of the question, what specifically should I plot to test this?