This code generate a Hertzsprung-Rusell diagram from a stellar astrophysics homework based in the text An Introduction to Modern Astrophysics (2nd Edition) - Bradley W. Carroll & Dale A. Ostile.
The homework's taks were:
The main sequence present an aproximate mass-luminosity relation as
and a radius-mass relation as
.
- With the before relations you can graph the main sequence in an Hertzsprung-Rusell theoretical diagram (HRD). Your HRD should cover the range 3.5 - 4.5 for
and a appropiate range for
. Hint: Derivate first a expresion for
in
terms for stars in main sequences.
We now that the relation between the luminosity and the effective temperature for a star is:
where is the Stefan-Boltzmann constant and
is the star's radius.
if we divided with the Sun's values:
from the above relations we have that:
for main sequence:
here i used the effective temperature of sun equal to
- Draw a dashed line in constants stelar radius equal to
.
- Betelgeuse star has
and
. Show the position of this star on your HRD.
At the moment the resulting HRD is:
Where the line represent the mathematical aproximation for stars on main sequence, the blue points are stars on main sequence from the G-appendix in An Introduction to Modern Astrophysics (2nd Edition) - Bradley W. Carroll & Dale A. Ostile and the dashed lines will be regions where stars will have these star's radius.