In-Class Assignment 12

In-Class Assignment 12#

Star Formation and the Pre-Main Sequence#

Learning Objectives#

  • explore conditions for star formation

  • compute estimated star formation rates

  • qualitatively describe the hayashi track, henyey track and pre main-sequence phases

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

a. Jeans ’ mass for an average molecular cloud.#

Individually/with the person next to you:#

  1. Calculate the density for an average molecular cloud:

    • Assume \(T=10\) K, \(M_{\rm{cloud}}=1000M_{\odot}\) and a number density \(n\) of \({\rm{H}_{2}}\) molecules of \(n= 1000 (\rm{cm}^{-3})\).

Hint: Recall the mean molecular weight \(\mu=\rho/n m_{\rm{H}}\).

Hint: What is the mean molecular weight assuming the entire cloud is \({\rm{H}_{2}}\).

  1. Using the density from part 1. Compute the Jeans’ mass for this cloud in terms of \(M_\odot\).

msun_cgs = 2e33# grams
n = 1000       # cm^-3
m_H = 1.67e-24 # grams
k_B = 1.38e-16 # erg / K
G_cgs = 6.67e-8

#compute rho

# compute M_J here

With your larger group, try to answer the following:#

  1. Is this cloud stable or unstable according to Jeans’ Criterion? That is can it collapse, why or why not?

Your group’s thoughtful response.

  1. Based on your response to part 3. What is the next step in the star formation process for this particular cloud?

Your group’s thoughtful response.

b. Star Formation Timescale#

Individually/with the person next to you:#

  1. Calculate the free-fall timescale for the molecular cloud from a. in (Myr)

\[ \tau_{\rm{ff,cloud}} \approx \left ( \frac{3\pi}{32 G \rho_{\rm{cloud}}} \right )^{1/2} \]
## compute tau here
sec_in_a_year = 3.154e+7

With your larger group, try to answer the following:#

  1. Compare the free-fall timescale and compare it to the typical lifetime of a solar-like star. Is it longer, shorter, or about the same?

Your group’s thoughtful response.

c. The Pre Main-Sequence#

Individually/ with the person next to you:#

Download, or reuse from a previous class:

Using the all three MESA history data:

  1. Plot the an HR diagram (\(\textrm{log}T_{\rm{eff.}}-\textrm{log}L\)) and label each model by their initial mass.

  2. Label the approximate location of the “Hayashi track”, the “Henyey Track”, and the “Zero-Age Main Sequence”.

Hint: Compare with Pols Figure 9.3 and Example Henyey Tracks

# load data with pandas
#one_m_ms_history = pd.read_csv('###',sep=r'\s+',header=4)
#three_m_ms_history = pd.read_csv('###',sep=r'\s+',header=4)
#five_m_ms_history = pd.read_csv('###',sep=r'\s+',header=4)
#list(one_m_ms_history)

# load variables here

# trim the noisy data for this 1m model only via indexing
#one_m_ms_history_logTeff = one_m_ms_history['##'][100:300] # log_Teff
#one_m_ms_history_logL = one_m_ms_history['##'][100:300] # log_L

#three_m_ms_history_logTeff = # log Teff
#three_m_ms_history_logL = # log L

#five_m_ms_history_logTeff =# log Teff
#five_m_ms_history_logL =# log L

## 1-2 result here
#plt.title('MESA Models HR Diagram')

#plt.plot(#,label=r'$1M_{\odot}$')

#plt.plot(#,label=r'$3M_{\odot}$')

#plt.plot(#,label=r'$5M_{\odot}$')



#plt.annotate('Hayashi \n Track', xy=(xloc, yloc),xycoords='data')
#plt.annotate('Henyey \n Track', xy=(xloc, yloc),xycoords='data')
#plt.annotate('ZAMS', xy=(xloc, yloc),xycoords='data')


#plt.gca().invert_xaxis()

#plt.legend()
#plt.xlabel(r'$\rm{log}_{10}~T_{\rm{eff}}~(\rm{K})$')
#plt.ylabel(r'$\rm{log}~L \ (L_{\odot})$')

With your larger group, try to answer the following:#

  1. Based on the plots, which stars spend more time on the Hayashi track, low mass, or high mass? What about the Henyey track? Why might this be?

Your group’s thoughtful response.

  1. Why does the location of the ZAMS move as a function of initial mass?

Your group’s thoughtful response.

  1. What might an stellar object that never reaches the main-sequence look like? Is that a star?

Your group’s thoughtful response.

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