---
title: ASTR 511 W23 HW 3
author: Andy Tzanidakis and friends
tags: Galaxies Class
---

[TOC]

# Homework 7 - ASTR 511 W23
- Author: Anastasios (Andy) Tzanidakis
- Course ID: ASTR 511 W23

# Problem 1
## Part 1.1 - Data Basics
>Get your data. Download the (large) .fits file from the SDSS website. Note: this server is a bit slow, it may be faster to use a thumb drive from one of your colleagues. Read the file into your notebook (I like Astropy Tables for this). How many rows are there (each row is 1 star)? How many columns?

This sample contains roughly 733901 stars and 191 columns! :star-struck:

## Part 1.2 - Wallerstein–Tinsley Diagram
>You'll need to select only stars with finite $\lfloor\alpha / M\rfloor$ and $\lfloor\mathrm{Fe} / \mathrm{H}\rfloor$ measurements (i.e. no NaN's). Probably best to create a 2-D histogram plot. Play with color scales or log-scaling the color map to make the best-looking figure. What features or stellar populations can you identify here? (i.e. Thick/Thin disks) It can be helpful to define a polygon or region to separate the high- vs low- $\alpha$ populations.

Below, we can see our GALAH Wallerstein–Tinsley Diagram for 733901 stars. Right away, we see that there ate two distinc poppulations in this phase space - one is the low alpha and high alpha population - which I'm assuming is the thick and think disk. We can also see for the lower alpha abundances that there's several substructures. One of the most prominent among these is the Gaia-Enceladus substructure that appears most obvious in this phase space. In the above plot, I have made a simple line with some slope to separate the alpha abundance populations which we will use later!

## Part 1.3 - Dwarf vs Giants
> Select based on something like: $\log g \geq 3.5$ for dwarfs, $<3.5$ for giants. N.B. this is a VERY rough evolution cut... The APOGEE sample is dominated by giants because they probe much further reaches of the Galaxy. Which galactic disk(s) can you see for each of these two stellar populations?

In the above plot we display the log density Wallerstein–Tinsley Diagram for the dwarfs vs. giants given a log(g) cut. It is evident that the giant sample contains both high-$\alpha$ and low-$\alpha$ populations. I suspect this is due to the simple fact that the giant population is probing a much larger volume thus both the thin and thick disk populations will appear. On the other hand, the the dwarfs are probing a smaller volume but overall abundances closer to the sun.

# Problem 2

## Problem 2.1 - XYZ Plane
> Probably best to use Astropy for this. For distance, I would suggest using the column: GAIAEDR3_R_MED_GEO. Plot the vertical (Z) distribution of stars chemically identified in Q1.2 as Thick vs Thin. Do Dwarfs or Giants trace each disk better? Helpful to normalize your histograms here. Can you estimate the scale-height for these populations? You could fit a Gaussian to the log number of stars as a function of height. N.B. this will be a bad estimate, since there are many sample biases we are not accounting for!

Yes from the diagram below, we plot the Z scale height for the $\alpha$-heavy and $\alpha$-low populations (i.e thin vs. thick disk). We can see from a Gaussian fit that the median values of each distribution are close - roughly at 750 pc. However, the more interestng part is the secondary bump for the low-$\alpha$ cut that is likely caused by the substructures present (i.e Gaia Encaladus... and possibly other substructure). Our results seem consistent with values reported in the lieterature of ~1kpc ([Lee et al. 2011](https://iopscience.iop.org/article/10.1088/0004-637X/738/2/187/pdf))

## Problem 2.2 - Mean Metallicity in (R,Z) Projection
> Plot the mean metallicity $[\mathrm{Fe} / \mathrm{H}]$ of stars in the $(\mathbf{R}, \mathbf{Z})$ plane What trend(s) do you notice? What does the same plot colored by mean $[\alpha / M]$ look like?

In the above diagram, as we expect we see the higher metallicity stars within the plane of the disk between z$\pm$ 5 kpc. As we go further out into higher scale heights we quickly see how the metallicity drops and we find more metal poor stars. Interestingly, something at >20 kpc and below the Galactic plane there's a feature that is generally more metal rich than the surrounding stars that is likely the substructure that is present in this data... On the other hand we can also plot the $\alpha$ abundance and generally see somewhat of a similar pattern. Here we see that above the Galactic plane the $\alpha$ abundances are generally higher versus below the plane. Again, we can see that large substructure that appears in this geometric projection.



# Problem 3
## Problem 3.1 - Looking for the Gaia-Enceladus Structure
> Can you find the Gaia-Enceladus/Sausage stars? You can either try recreating [Mg/Mn] versus [Al/Fe] plot or look in the action space.

In the above diagram we plot the abundances of [Mg/Mn] and [Al/Fe] where the Gaia-Enceladus appears most obvious from the foreground and background stars. We draw a manual box arround this feature to roughly trace it - now we can find these stars and trace them in other phase spaces and abundances.


## Problem 3.2 - Where is it?
> Where do these accreted stars land on the Wallerstein-Tinsley diagram? Where do they land on the $(\mathrm{R}, \mathrm{Z})$ plane?

Here I plot the Wallerstein-Tinsley diagram for the Gaia-Enceladus diagram and we can see how it appears generally with more metal rich stars and lower alpha elements... We can also see that this selection contains possibly a few other substructures that might be due to the impefect cut that we mad in the initial cut. Below we plot the scale height versus radius of the identified Gaia-Enceladus substructure, and we see that this feature is generally above the Galactic plane according to our plots. Again, we see that our approach here is not ideal because we're also getting a scatter above and below the disk - this is due to our simple selection polygon where we are most likely selecting also field stars that are not associated with this substructure.



## Problem 3.3 - Other Substructures?
> Any clusters? Halo stars? The “Jurassic” structure? The “Sequoia”?

It is evident that looking at the [Mg/Mn] and [Al/Fe] abundance space that there's likely way more substructure here. We can see that there are other smaller clusters present in the data that are likely some other well known disk substructures that may appear in this abundance space. Using the GALAH datya we can also explore if any other new features appear in other abundance ratios. One can imagine if we ran a Gaussian Mixture Model and did more robust searching for unique clusters in these abudance ratios spaces - it is likely we would find unique substructure present in the disk.