In-Class Assignment 26

In-Class Assignment 26#

Note due for credit, in-class participation only

Low-mass and Intermediate-mass star models in MESA#

Learning Objectives#

  • compare the Schonberg-Chandrasekhar limit to models of low mass and intermediate mass stars

  • compare luminsity relations for low and intermediate mass stars

  • explore the properties of the blue loops between models

  • explore the onset of the first dredge up across models

  • develop a qualitative understanding of a star post main-sequence

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

Download the following model files locally. These data were produced using the 7M_prems_to_AGB test suite.

# load data and see which variables are available
#low_mass_history = pd.read_csv('1m_history.data',sep=r'\s+',header=4)
#low_mass_history.columns

a. - Schonberg-Chandrasekhar limit#

Using the \(1M_{\odot}\) MESA history dataset:

  1. Compute the core mass ratio to the total mass (\(M_{core}/M_{total}\)) for comparison to the Schonberg-Chandrasekhar limit as a function of model number:

\[ \frac{M_{\rm{core}}}{M} \lt q_{\rm{SC}} = 0.37 \left ( \frac{\mu_{\rm{env}}}{\mu_{\rm{core}}} \right )^{2} \approx 0.10~, \]

  1. On the same plot, plot the center he4 mass fraction as a function of model number. Label the lines separately with a legend.

  2. Plot a horizontal line for a value of 0.10, a typical value for a helium core with \(\mu_{\rm{core}}=1.3\) and a H-rich envelope.

  3. Lastly, on the same plot, plot these quantities for the \(5M_{\odot}\) model.

If the two models have different ratios at the point of core He-ignition, explain this difference. Namely, why is one model able to reach a larger ratio?

## a results here

b - Core Mass Luminosity Relation in Low mass Red Giants#

  1. Compute an HR diagram for the \(1M_{\odot}\) model.

  2. Creat a function to estimate the luminosity using the core-mass luminosity for low mass stars:

\[ L \approx 2.3\times 10^{5} L_{\odot} \left ( \frac{M_{\rm{core}}}{M_{\odot}} \right )^{6} \]

  1. Plot the estimated luminosity on the same HR diagram as a vertical line using the core mass at the start of He-ignition.

Hint: You can estimate the helium core mass at He-ignition using the plot from a and the estimated model number.

Does the value match the luminosity in the HR diagram?

## b results here

c. - the blue loop#

  1. Plot an HR diagram for the 5 \(M_{\odot}\) model.

  2. Label the approximate location of the blue loop.

  3. Compute the fraction of time a star spends in the blue loop region of the HRD relative to the main-sequence lifetime. That is, compute roughly \(\tau_{He}/\tau{MS}\) and answer the following:

Given the value found for 3. above, are these stars likely to be observed in the blue loop?

Compare with Figure 1.1 from Pols.

# c result here

d. - the first dredge up#

  1. Plot the surface he4 mass fraction as a function of model number to locate the approximate model number ranges at which the surface is first enriched via the first dredge up for both models.

  2. Use mesaPlot to plot Kippenhahn diagrams for both models. Then, using this information, answer the following:

Say in words where the first dredge up occurs in this models - at what evolutionary epochs?

Reminder: mesaPlot looks into a folder called LOGS for a file named history.data. So, you will need to create this folder then rename the file names making the Kipps one at a time.

# d result here

## first kipp here
#import mesaPlot as mp
#m=mp.MESA()
#p=mp.plot()
#m.loadHistory('LOGS')
#p.plotKip(m)

## second kipp here

Response to c here.

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