Understand stars in Gaia data#

Prerequisites

  • \(\texttt{numpy}\), \(\texttt{matplotlib}\), and stats 101.

New \(\texttt{python}\) skills

  • \(\texttt{pandas}\): a package for loading and manipulating tables of data (you can think of this as \(\texttt{python}\)’s version of Excel or google sheets).

Astro concepts

  • The Gaia mission

  • Magnitude and absolute magnitude scales

  • Basic properties of stars: radius, temperature, color, etc.

# Let's start with importing our packages
import numpy as np
import pandas as pd
import matplotlib
import matplotlib.pyplot as plt

# We can beautify our plots by changing the matplotlib settings a little
plt.rcParams['font.size'] = 18
matplotlib.rcParams['axes.linewidth'] = 2
matplotlib.rcParams['font.family'] = "serif"

1. Reading a table with \(\texttt{pandas}\)#

# Let's load in the data
import os
from google.colab import drive
from astropy.table import Table

drive.mount('/content/drive/')
os.chdir('/content/drive/Shareddrives/AST207/data')

gaia = pd.read_csv('./gaia_15pc.csv',index_col=[0])

Mounted at /content/drive/

What’s in the table and how can we access it?#

# Let's print the first couple rows of data
gaia.head()
radius teff distance gmag rmag bmag ecl_lon ecl_lat
0 0.5023 3224.9536 13.3978 10.241307 9.135763 11.498909 279.484182 8.627836
1 0.4488 3508.4785 13.5867 10.019066 8.943984 11.186045 63.836273 38.387682
2 0.4814 3310.7295 13.5787 10.193903 9.102655 11.395733 63.836924 38.388986
3 0.6412 3473.9587 7.0383 7.756715 6.747296 8.790974 7.104283 71.152618
4 0.4892 3155.9285 8.5053 9.495382 8.347611 10.836117 249.618870 -15.836896 
# We can also print the last couple rows of data
gaia.tail()
radius teff distance gmag rmag bmag ecl_lon ecl_lat
501 0.1677 2878.0027 12.7056 13.652472 12.276646 15.956352 212.820918 21.919965
502 0.1887 2959.8933 12.2233 13.079426 11.746457 15.165963 271.133288 60.948970
503 0.8268 4914.2610 11.0935 6.129808 5.502101 6.585531 273.994073 61.861649
504 0.6636 3889.6328 3.4947 5.450645 4.556912 6.272253 336.994179 51.894370
505 0.6760 4353.7437 3.4904 4.766713 3.977203 5.439793 336.994324 51.903146 
# What columns are in the table?
gaia.columns

Index(['radius', 'teff', 'distance', 'gmag', 'rmag', 'bmag', 'ecl_lon',
       'ecl_lat'],
      dtype='object')

# Let's access a single column
gaia['teff']
teff
0 3224.9536
1 3508.4785
2 3310.7295
3 3473.9587
4 3155.9285
... ...
501 2878.0027
502 2959.8933
503 4914.2610
504 3889.6328
505 4353.7437

506 rows × 1 columns


2. Getting started with data#

Exercise 1

  1. Using \(\texttt{numpy}\) calculate the mean, median, and standard deviation of the distance column.

  2. It’s hard to how what these numbers mean without visualizing the data. Let’s make a histogram of the distances. Be sure to include labels on the x and y axis. Include the mean and median as vertical lines.

  3. What can we learn about the distances of near by stars based on the histogram? For instance, is the histogram skewed towards very high or very low values? or is the histogram symmetric? What does this tell us about stars near the Sun?

  4. In astronomy, we often ask how different properties of stars depend on each other. For example, does the size of a star depend on it’s temperature? First let’s make scatter plots of temperature vs. radius, distance vs. radius, and distance vs. temperature. Bonus: try using for loops to reduce duplicated code

  5. Write a single sentence summary of each plot. Based on your scatter plots, which properties are most strongly correlated?

3. Practicing with magnitudes#

As we discussed in lecture, magnitudes appear everywhere in astronomy. Let’s practice using magnitudes with our Gaia stars. Remember, the definition of magnitude is:

\[ m_1 - m_2 = - 2.5 \log_{10} (F_1 / F_2), \]

where \(m_1, m_2\) are the magnitudes of two stars (creatively named 1 and 2) and \(F_1, F_2\) are the fluxes of those two stars.

Exercise 2

To get some practice, let’s convert the magnitudes listed in the table to fluxes. Let’s calculate our fluxes relative to the Sun: \(m_1 + 26.83 = - 2.5 \log_{10} (F_1 / F_\mathrm{Sun})\), we’ve set \(m_2 = −26.83\) and \(F_2 = F_\mathrm{Sun}\), where \(F_\mathrm{Sun}\) is the flux (aka. brightness) of the Sun as measured from Earth.

  1. Make a histogram of \(\log_{10}(F_1 / F_\mathrm{Sun})\) for the \(g\), \(r\), and \(b\) Gaia filters (the Gaia magnitudes are stored under the \(\texttt{gmag, rmag, bmag}\) columns). Bonus: write a function for the flux to magnitude conversion

  2. Based on your histograms how much brighter does the Sun appear to us than the brightest nearby star (in gaia g-band)?

So far, we have considered how bright stars appear in the sky. However, we know this depends on the stars’ distances from the Earth. Remember the apparent brightness of a star (aka flux \(F\)) is related to its luminosity \(L\) (the amount of energy output by the star each second) and distance \(d\) by:

\[ F = \frac{L}{4 \pi d^2} \]

Exercise 3

  1. Use the above equation to write an equation for \(L\). Then write an equation for \(L / L_\mathrm{sun}\). Using your equation, make a histogram of \(\log_{10} (L / L_\mathrm{Sun})\) (based on the \(g\)-band magnitude).

  2. What can we learn from this histogram? Is the Sun typical compared to nearby stars?