Homework 1: The Main Sequence Mass – Luminosity relation

Due in class on Monday, February 18^th, 2008

The two files Astrometric_Binaries.txt and Eclipsing_Binaries.txt contain data from astrometric binaries and double line eclipsing binaries, respectively. The 1^st column contains the name of the star, the 2^nd column contains the absolute bolometric magnitude, M_Bol, and the 3^rd column contains the mass in units of solar mass ( ).

(a)    Use the relation

                                                                              

to convert M_Bol to luminosity in units of solar luminosity ( ).

(b)   For each data set plot against .

(c)    By fitting a straight line to the combined data sets, determine the slope of the Mass-Luminosity relation, i.e. find α where the fitted line is

                                                                                

(d)   Identify the two stars in the astrometric binaries data set that deviate most from the straight line fit. What kind of stars are they?

[This homework is most easily done using software.  I have had success with the graphing software AXUM and the spread sheet software EXCEL.]