In-Class Assignment 9

In-Class Assignment 9#

Exploring Brown Dwarfs & Planets with MESA#

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

Download the following model files locally.

Brown Dwarf#

Using the 0.03\(M_\odot\) model MESA profile:

a.#

Compare the opacity profile with the approximate opacity due to \(\rm{H}^{-}\) from HKT 4.65.

## a results here

b.#

Using the dominant nuclear energy generation rate (\(\epsilon\)), luminosity and other necessary variables, compute the estimate lifetime from HKT eq. 1.89. Consider plotting \(^{2}\)H as a function of time, how far through the stars lifetime is this model?

## b results here

Planet#

Using the \(0.97 M_\rm{Jup}/ 2 R_{\rm{Jup}}\) model MESA history data:

Each of these models uses a set value of irradiation flux of 0, \(1\times10^{6}\), or \(1\times10^{8}\) (\(\rm{erg \ cm^{2} \ s^{-1}}\)) at a fixed column density of 300 (\(\rm{cm^{2} \ g^{-1}}\))

c.#

Plot the pressure vs radius for all 3 models. Which model has the largest radius? Why?

## c results here

d.#

Shallower atmospheric \(T\)-gradient leads to slower interior cooling, and larger radius at a given age.

Plot the pressure vs temperature (x-axis) profiles for all 3 models. Which model has the flattest \(T-\)gradient?

## d results here
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