CoCalc Public FilesHUBBLE / step1.ipynbOpen with one click!
Author: Hal Snyder
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Description: Simplified Hubble Diagram
Compute Environment: Ubuntu 18.04 (Deprecated)

Simplified Hubble Diagram

This is a tutorial exercise from the Sloan Digital Sky Survey (SDSS) website:

In [1]:
# astropy imports - we can ignore the warning :-) # astroquery is one of 42 affiliated packages from astropy import coordinates as coords from astroquery.sdss import SDSS
/usr/lib/python3/dist-packages/astroquery/sdss/__init__.py:29: UserWarning: Experimental: SDSS has not yet been refactored to have its API match the rest of astroquery (but it's nearly there). warnings.warn("Experimental: SDSS has not yet been refactored to have its API "
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# general-purpose imports import numpy as np import pandas as pd import sys
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# this spreadsheet was uploaded from the SDSS tutorial site # it has RA & Dec for 6 sample galaxies fname = "exercise1.xls" df = pd.read_excel(fname, encoding=sys.getfilesystemencoding())
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df
Object ID RA Dec Magnitude Redshift
0 1237666408439939277 354.35000 0.39167 NaN NaN
1 1237663784195195105 354.98998 0.13519 NaN NaN
2 1237648704592806164 219.31858 0.17731 NaN NaN
3 1237659895636296017 260.80622 58.58956 NaN NaN
4 1237656529458233684 263.94885 54.36385 NaN NaN
5 1237651800697274648 150.09651 -0.27059 NaN NaN
6 NaN NaN NaN NaN NaN
7 NaN NaN NaN NaN NaN
8 What magnitude did you use? NaN NaN NaN NaN
In [5]:
# ignore rows without data df.drop([6,7,8], axis=0, inplace=True) df
Object ID RA Dec Magnitude Redshift
0 1237666408439939277 354.35000 0.39167 NaN NaN
1 1237663784195195105 354.98998 0.13519 NaN NaN
2 1237648704592806164 219.31858 0.17731 NaN NaN
3 1237659895636296017 260.80622 58.58956 NaN NaN
4 1237656529458233684 263.94885 54.36385 NaN NaN
5 1237651800697274648 150.09651 -0.27059 NaN NaN
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# Fill in the 'Magnitude' column: # look up observed magnitude in one of the 5 wavelengths available with SDSS # Green (g) - 4770 Å for index, row in df.iterrows(): ra, dec = (row['RA'], row['Dec']) co = coords.SkyCoord(ra, dec, unit="deg") result = SDSS.query_crossid(co, photoobj_fields=['modelMag_g']) x = (result['modelMag_g']) print(index, x[0]) df.loc[index,'Magnitude'] = x[0]
0 15.75727 1 16.25334 2 17.0536 3 17.8716 4 18.94336 5 20.13298
/usr/lib/python3/dist-packages/astroquery/sdss/core.py:856: VisibleDeprecationWarning: Reading unicode strings without specifying the encoding argument is deprecated. Set the encoding, use None for the system default. comments='#'))
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# Fill in the 'Redshift' column # to save time, look up redshifts with the SDSS GUI and fill in here df['Redshift']=[0.009, 0.060, 0.105, 0.152, 0.238, 0.314]
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# using Magnitude as a proxy for distance, here's our first look at a Hubble-like plot df.plot(x='Magnitude', y='Redshift', style='x-');

Flux is proportional to 2.51(Magnitude)2.51^{(-Magnitude)}

In [9]:
# Add a column for Flux df['Flux'] = df['Magnitude'].map(lambda x: 2.51**(-x)) df
Object ID RA Dec Magnitude Redshift Flux
0 1237666408439939277 354.35000 0.39167 15.75727 0.009 5.037711e-07
1 1237663784195195105 354.98998 0.13519 16.25334 0.060 3.191296e-07
2 1237648704592806164 219.31858 0.17731 17.05360 0.105 1.528003e-07
3 1237659895636296017 260.80622 58.58956 17.87160 0.152 7.197657e-08
4 1237656529458233684 263.94885 54.36385 18.94336 0.238 2.684336e-08
5 1237651800697274648 150.09651 -0.27059 20.13298 0.314 8.982081e-09

Distance is proportional to 1(Flux)\frac{1}{\sqrt(Flux)}

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# Add a column for Relative Distance import math df['Relative Distance'] = df['Flux'].map(lambda x: 1/math.sqrt(x)) df
Object ID RA Dec Magnitude Redshift Flux Relative Distance
0 1237666408439939277 354.35000 0.39167 15.75727 0.009 5.037711e-07 1408.910386
1 1237663784195195105 354.98998 0.13519 16.25334 0.060 3.191296e-07 1770.175975
2 1237648704592806164 219.31858 0.17731 17.05360 0.105 1.528003e-07 2558.219991
3 1237659895636296017 260.80622 58.58956 17.87160 0.152 7.197657e-08 3727.386607
4 1237656529458233684 263.94885 54.36385 18.94336 0.238 2.684336e-08 6103.537178
5 1237651800697274648 150.09651 -0.27059 20.13298 0.314 8.982081e-09 10551.434821
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# Make all distances relative to distance to first galaxy in the list d0 = df['Relative Distance'][0] df['Relative Distance'] /= d0 df
Object ID RA Dec Magnitude Redshift Flux Relative Distance
0 1237666408439939277 354.35000 0.39167 15.75727 0.009 5.037711e-07 1.000000
1 1237663784195195105 354.98998 0.13519 16.25334 0.060 3.191296e-07 1.256415
2 1237648704592806164 219.31858 0.17731 17.05360 0.105 1.528003e-07 1.815744
3 1237659895636296017 260.80622 58.58956 17.87160 0.152 7.197657e-08 2.645581
4 1237656529458233684 263.94885 54.36385 18.94336 0.238 2.684336e-08 4.332098
5 1237651800697274648 150.09651 -0.27059 20.13298 0.314 8.982081e-09 7.489074
In [12]:
# Revised approximation of Hubble plot df.plot(x='Relative Distance', y='Redshift', style='x-');
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