In-Class Assignment 16

In-Class Assignment 16#

In-Class Only, Not Submitted for Credit

Case A Binary Star System#

$M_{1}=10M_{\odot}$

$M_{2}=8.9M_{\odot}$

$P_{i}=2.2$ days

example based on the $MESA_DIR/binary/test_suite/evolve_both_stars example in MESA

Learning Objectives#

identify the various phases of mass transfer in a binary star system
gain a qualitative understanding of Case A evolution in the HR diagram
compare the analytical decay of the orbit to a MESA calculation

Download the following model files locally.

$M_{1}=10M_{\odot}$: m1_history.data;
$M_{2}=8.9M_{\odot}$: m2_history.data;
Binary history data: binary_history.data;

a. - Identifying Various Phases of Mass Transfer#

Using the history data for the primary and secondary,

Plot a mass - radius diagram with both models on the same plot ($M/M_{\odot}$ vs log $(R/R_{\odot})$)
Label - the phase start of ZAMS (A) to the filling of the Roche lobe of the primary (B) using plt.annotate or similar. You can do this via inspection or looking at rl_relative_overflow_1 in the binary data.
Label the beginning of the mass transfer phase with annotation (C) and the end of the phase, (D), using plt.annotate or similar.

B/C will overlap.

What can we infer is the limiting timescale for the mass transfer phase from C to D?

## a results here

a qualitative response here

b. - Case A in the HR#

Using the same data,

Plot an HR diagram for the primary and secondary and label them.
Label the beginning and end of mass transfer phase via first RLOF as in the previous problem.

What is the luminosity response of the primary during the first RLOF? What about the secondary?

## b results here

b qualitative response here

c. - Decay of the Period of the Binary#

Using the binary history data,

Plot the period in days of the system (period_days) as a function of model number or log age.

Using Kepler’s Laws, we can make an estimate for the orbital decay (assuming a conservative system with $\dot{J}$=0) - Eqn. 7.11 in Pols as

\[ \frac{P}{P_{i}} = \left ( \frac{ M_{1,i} }{ M_{1} } \frac{ M_{2,i} }{ M_{2} } \right )^{3}. \]

Using the above equation, plot the decay of the period on the same plot of 1.

Does the computed period decay match the estimate? If not, what does this suggest about $\dot{J}$. Looking briefly at the history data can you identify a dominant source of angular momentum loss?

## c results here

c qualitative response here