Calculating the Hubble Constant with eBOSS

Calculating the Hubble Constant with eBOSS#

Learning Goals#

By the end of this tutorial, you will:

Understand how to use astroquery.mast to download SDSS eBOSS and HST data from the MAST archive.
Plot a sample of galaxies from eBOSS with a line of best fit to determine Hubble’s constant.
Create a color image of Abell 2199 from HST data.

Table of Contents#

Introduction
Imports
Accessing eBOSS Data from MAST
- Querying eBOSS Data
- Sampling eBOSS for Redshifted Galaxies
- Downloading Products from eBOSS
- Making the Hubble-Lemaître Diagram
- Plotting eBOSS Data
  - Importing Abell 2199 Data
- Comparing Calculated H₀ to Other Models
Utilizing HST Data from Mast
- Creating an Image of Abell 2199 Using HST
- Plotting the HST Images
- Colorizing the HST Image
End of Tutorial
Additional Resources
Citations
About this Notebook

Introduction#

The Hubble-Lemaître law is one of the most prominent topics of debate in modern cosmology. In 1927, Georges Lemaître published a paper in a Belgian journal proposing that the Universe was expanding, using data from Vesto Slipher at Lowell Observatory. Around the same time, Edwin Hubble was independently studying the relationship between galaxy distances and their radial velocities at Mount Wilson Observatory. Although Hubble was originally credited with the discovery, in 2018 the International Astronomical Union officially renamed “Hubble’s Law” to the “Hubble–Lemaître Law” to acknowledge Lemaître’s earlier contribution [1].

The Big Bang occurred approximately 14 billion years ago, leading to the expansion of the Universe. We can estimate the speed of this expansion by examining the redshifts of a sample of galaxies. These redshifts can be translated into radial velocities, and then using observed spectral flux, we can the determine the distances to these galaxies. By plotting radial velocities versus distances, we can apply a linear fit model to the data. This allows us to approximate the Hubble constant from the slope as described by Hubble’s Law [2]:

\[ v_{rad} = H_{0}d \]

There are various models used to calculate H₀, some based on observations of the Cosmic Microwave Background (CMB), and others on measurements of galaxies or supernovae. These models typically yield varying values of H₀ ranging from approximately 67 km/s/Mpc to 74 km/s/Mpc. This discrepancy is known as the Hubble Tension [3].

In this notebook, we’ll construct a Hubble-Lemaître Diagram using data from the Sloan Digital Sky Survey’s (SDSS) Extended Baryon Oscillation Spectroscopic Survey (eBOSS). eBOSS gathered over 4 million spectra from stars, quasars, and galaxies. We’ll focus on a subset of galaxies, using their redshifts and spectral data to plot radial velocity against distance. By applying a linear fit to this relationship, we can estimate Hubble’s constant from the slope of the resulting line.

Imports#

The main packages and their use-cases in this tutorial are as follows:

numpy to handle array functions
matplotlib.pyplot for plotting data
astroquery.mast.Observations to access data from MAST
astropy.io.fits for accessing FITS files
astropy.table.vstack for vertically stacking tables
scipy.optimize.curve_fit for creating a linear fit
astropy.visualization.make_luptopn_rgb for creating an RGB image
astropy.wcs.WCS for world coordinate system transformations
reproject for stacking FITS images

%matplotlib inline

import numpy as np
import matplotlib.pyplot as plt

from astroquery.mast import Observations
import astropy.io.fits as fits
from astropy.table import vstack
from scipy.optimize import curve_fit

from astropy.visualization import make_lupton_rgb
from astropy.wcs import WCS
import reproject

If you’re not sure if you have the required versions of packages installed on your device, you can run the following cell:

with open("requirements.txt") as f:
    print(f"Required packages for this notebook:\n{f.read()}")

Required packages for this notebook:
astropy >= 5.3
astroquery >= 0.4.9
matplotlib >= 3.9.1
numpy >= 1.26.4
scipy >= 1.15.3
reproject >= 0.14.0

To ensure these requirements are installed, you can run the following command in the terminal:

pip install -r requirements.txt

Accessing eBOSS Data from MAST#

The Mikulski Archive for Space Telescopes (MAST) hosts a large array of data from several telescope missions. In this tutorial, we will be specifically focusing on data from the Sloan Digital Sky Survey (SDSS) and the Hubble Space Telescope (HST).

The Extended Baryon Oscillation Spectroscopic Survey (eBOSS) was completed using the SDSS-2.5m telescope and BOSS spectrograph at the Apache Point Observatory in New Mexico. Using plug plates and a 1000 fiber-fed spectrograph, eBOSS was able to collect spectra from over 4 million objects including quasars, galaxies, and stars in the northern hemisphere.

Querying eBOSS Data#

You can query data from MAST using the website portal. You can also query MAST data in Python using the package astroquery.mast!

We can query all of the eBOSS data using Observations.query_criteria with provenance_name = 'eBOSS' and obs_collection = 'SDSS'. Since eBOSS has a large amount of data, we can display the first 10 results using the pagesize parameter as well as the page parameter.

We can also limit the number of observations by date. Using the t_min=[58118, 60675] parameter (the modified Julian date of the exposure), we can filter data that has a modified Julian date from 58118 to 60676 (years 2018-2024).

This might take a few minutes depending on your internet connection.

eboss_data = Observations.query_criteria(
    obs_collection="SDSS",
    provenance_name="eBOSS",
    t_min=[58118, 60675],
    pagesize=5,
    page=1,
)

# Show the astropy table
eboss_data

Table masked=True length=5

intentType	obs_collection	provenance_name	instrument_name	project	filters	wavelength_region	target_name	target_classification	obs_id	s_ra	s_dec	dataproduct_type	proposal_pi	calib_level	t_min	t_max	t_exptime	em_min	em_max	obs_title	t_obs_release	proposal_id	proposal_type	sequence_number	s_region	jpegURL	dataURL	dataRights	mtFlag	srcDen	obsid	objID
str7	str4	str5	str4	str4	str4	str7	str21	str6	str27	float64	float64	str8	str18	int64	float64	float64	float64	float64	float64	str56	float64	str3	str1	int64	str56	str64	str64	str6	bool	float64	str9	str9
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 8061-58253-266	QSO	sdss_eboss_8061-58253-0266	247.6561799999999	53.52345	spectrum	SDSS Collaboration	3	58252.42982638889	58253.44824155093	2700.2	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 247.6561799999999 53.52345 0.0002777777777777778	mast:SDSS/eboss/8061/58253/0266/spec-image-8061-58253-0266.png	mast:SDSS/eboss/8061/58253/0266/full/spec-8061-58253-0266.fits	PUBLIC	False	nan	244271644	725056406
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 10938-58514-216	QSO	sdss_eboss_10938-58514-0216	222.12283	32.679912	spectrum	SDSS Collaboration	3	58514.41091435185	58514.45541782407	3600.41	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 222.12283 32.679912 0.0002777777777777778	mast:SDSS/eboss/10938/58514/0216/spec-image-10938-58514-0216.png	mast:SDSS/eboss/10938/58514/0216/full/spec-10938-58514-0216.fits	PUBLIC	False	nan	244271652	725056425
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 8061-58253-504	QSO	sdss_eboss_8061-58253-0504	245.7695699999999	54.336356	spectrum	SDSS Collaboration	3	58252.42982638889	58253.448242592596	2700.2	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 245.7695699999999 54.336356 0.0002777777777777778	mast:SDSS/eboss/8061/58253/0504/spec-image-8061-58253-0504.png	mast:SDSS/eboss/8061/58253/0504/full/spec-8061-58253-0504.fits	PUBLIC	False	nan	244271655	725056433
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 10938-58514-697	GALAXY	sdss_eboss_10938-58514-0697	221.61738	34.345396	spectrum	SDSS Collaboration	3	58514.41091435185	58514.45541851852	3600.41	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 221.61738 34.345396 0.0002777777777777778	mast:SDSS/eboss/10938/58514/0697/spec-image-10938-58514-0697.png	mast:SDSS/eboss/10938/58514/0697/full/spec-10938-58514-0697.fits	PUBLIC	False	nan	244271661	725056449
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 8061-58253-287	QSO	sdss_eboss_8061-58253-0287	247.53341	52.881373	spectrum	SDSS Collaboration	3	58252.42982638889	58253.44824155093	2700.2	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 247.53341 52.881373 0.0002777777777777778	mast:SDSS/eboss/8061/58253/0287/spec-image-8061-58253-0287.png	mast:SDSS/eboss/8061/58253/0287/full/spec-8061-58253-0287.fits	PUBLIC	False	nan	244271671	725056472

The table above provides some basic information for each object:

s_ra and s_dec: Right ascension and declination.
instrument_name: BOSS indicates that the data were collected using the BOSS spectrograph.
obs_id: Observation ID associated with the object. This is based on the plate number, the modified Julian date of observation, and the fiber ID, so the observation ID will look something like sdss_eboss_{PLATE}-{MJD}-{FIBERID}.
target_classification: Indicates the type of object (QSO, STAR, or GALAXY).
t_min and t_max: The modified Julian dates indicating the start and end times of the exposures.
wavelength_region: Indicates the region of the electromagnetic spectrum observed. This should be OPTICAL, since eBOSS observed in the optical wavelength range.
em_min and em_max: The minimum and maximum wavelengths observed by the survey. For eBOSS, this range is 360.0–1040.0 nanometers (optical).
dataproduct_type: Since eBOSS was a spectroscopic survey, this should be spectrum.

Sampling eBOSS for Redshifted Galaxies#

In this tutorial, we will be examining a sample of 311 galaxies, with 32 of those being from the galaxy cluster Abell 2199. This sample was curated for this exercise by randomly selecting 500 galaxies from the LOFAR subprogram of eBOSS across a uniform range of redshifts, and then selecting the most linear portion of the data when plotted on a radial velocity vs. distance plot.

For the purpose of this tutorial, we will only focus on querying by observation ID. The list of observation IDs of the 311 galaxies is located in the .txt file all_galaxies.txt. The galaxies from Abell 2199 are located in abell_2199.txt.

# importing the galaxy IDs
obs_id = np.loadtxt("all_galaxies.txt", dtype=str)

# looping through the .txt file to collect query results
# (this might take a few minutes)
results_tables = []
for i in obs_id:
    query_result = Observations.query_criteria(
        obs_collection="SDSS", provenance_name="eBOSS", obs_id=i
    )
    results_tables.append(query_result)

# combine query results using vstack
combined_results = vstack(results_tables)

# show the first 10 results
combined_results[:10]

Table length=10

intentType	obs_collection	provenance_name	instrument_name	project	filters	wavelength_region	target_name	target_classification	obs_id	s_ra	s_dec	dataproduct_type	proposal_pi	calib_level	t_min	t_max	t_exptime	em_min	em_max	obs_title	t_obs_release	proposal_id	proposal_type	sequence_number	s_region	jpegURL	dataURL	dataRights	mtFlag	srcDen	obsid	objID
str7	str4	str5	str4	str4	str4	str7	str21	str6	str27	float64	float64	str8	str18	int64	float64	float64	float64	float64	float64	str56	float64	str3	str1	int64	str56	str64	str64	str6	bool	float64	str9	str9
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 7563-56810-546	GALAXY	sdss_eboss_7563-56810-0546	242.38543	55.191924	spectrum	SDSS Collaboration	3	56810.23339120371	56810.266540972225	2700.3	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 242.38543 55.191924 0.0002777777777777778	mast:SDSS/eboss/7563/56810/0546/spec-image-7563-56810-0546.png	mast:SDSS/eboss/7563/56810/0546/full/spec-7563-56810-0546.fits	PUBLIC	False	nan	247778078	731713673
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 7562-56799-119	GALAXY	sdss_eboss_7562-56799-0119	242.23545	54.39303	spectrum	SDSS Collaboration	3	56799.26600694445	56799.31052199074	3600.38	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 242.23545 54.39303 0.0002777777777777778	mast:SDSS/eboss/7562/56799/0119/spec-image-7562-56799-0119.png	mast:SDSS/eboss/7562/56799/0119/full/spec-7562-56799-0119.fits	PUBLIC	False	nan	246836643	729532212
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 7563-56810-66	GALAXY	sdss_eboss_7563-56810-0066	246.3541299999999	53.987946	spectrum	SDSS Collaboration	3	56810.23339120371	56810.266540509256	2700.3	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 246.3541299999999 53.987946 0.0002777777777777778	mast:SDSS/eboss/7563/56810/0066/spec-image-7563-56810-0066.png	mast:SDSS/eboss/7563/56810/0066/full/spec-7563-56810-0066.fits	PUBLIC	False	nan	247778139	731713984
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 7564-56804-589	GALAXY	sdss_eboss_7564-56804-0589	241.9422	54.987496	spectrum	SDSS Collaboration	3	56804.29349537037	56804.3494	4500.51	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 241.9422 54.987496 0.0002777777777777778	mast:SDSS/eboss/7564/56804/0589/spec-image-7564-56804-0589.png	mast:SDSS/eboss/7564/56804/0589/full/spec-7564-56804-0589.fits	PUBLIC	False	nan	244576784	725746454
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 7562-56799-322	GALAXY	sdss_eboss_7562-56799-0322	239.64237	53.270835	spectrum	SDSS Collaboration	3	56799.26600694445	56799.31052199074	3600.38	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 239.64237 53.270835 0.0002777777777777778	mast:SDSS/eboss/7562/56799/0322/spec-image-7562-56799-0322.png	mast:SDSS/eboss/7562/56799/0322/full/spec-7562-56799-0322.fits	PUBLIC	False	nan	246835989	729530281
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 7562-56799-946	GALAXY	sdss_eboss_7562-56799-0946	242.29276	55.442419	spectrum	SDSS Collaboration	3	56799.26600694445	56799.31052245371	3600.38	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 242.29276 55.442419 0.0002777777777777778	mast:SDSS/eboss/7562/56799/0946/spec-image-7562-56799-0946.png	mast:SDSS/eboss/7562/56799/0946/full/spec-7562-56799-0946.fits	PUBLIC	False	nan	246835581	729529394
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 7565-56809-575	GALAXY	sdss_eboss_7565-56809-0575	240.7521	55.295251	spectrum	SDSS Collaboration	3	56809.23818287037	56809.27134421296	2700.27	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 240.7521 55.295251 0.0002777777777777778	mast:SDSS/eboss/7565/56809/0575/spec-image-7565-56809-0575.png	mast:SDSS/eboss/7565/56809/0575/full/spec-7565-56809-0575.fits	PUBLIC	False	nan	246919581	729701420
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 7564-56804-655	GALAXY	sdss_eboss_7564-56804-0655	242.15617	54.257776	spectrum	SDSS Collaboration	3	56804.29349537037	56804.3494	4500.51	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 242.15617 54.257776 0.0002777777777777778	mast:SDSS/eboss/7564/56804/0655/spec-image-7564-56804-0655.png	mast:SDSS/eboss/7564/56804/0655/full/spec-7564-56804-0655.fits	PUBLIC	False	nan	244577089	725747202
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 7563-56810-647	GALAXY	sdss_eboss_7563-56810-0647	242.90702	54.704448	spectrum	SDSS Collaboration	3	56810.23339120371	56810.266540972225	2700.3	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 242.90702 54.704448 0.0002777777777777778	mast:SDSS/eboss/7563/56810/0647/spec-image-7563-56810-0647.png	mast:SDSS/eboss/7563/56810/0647/full/spec-7563-56810-0647.fits	PUBLIC	False	nan	247778318	731714416
science	SDSS	eBOSS	BOSS	SDSS	None	OPTICAL	eBOSS 7563-56810-740	GALAXY	sdss_eboss_7563-56810-0740	243.28003	54.632292	spectrum	SDSS Collaboration	3	56810.23339120371	56810.266540972225	2700.3	360.0	1040.0	Extended Baryon Oscillation Spectroscopic Survey (eBOSS)	59554.0	N/A	--	--	CIRCLE 243.28003 54.632292 0.0002777777777777778	mast:SDSS/eboss/7563/56810/0740/spec-image-7563-56810-0740.png	mast:SDSS/eboss/7563/56810/0740/full/spec-7563-56810-0740.fits	PUBLIC	False	nan	247780260	731720216

Downloading Products from eBOSS#

For each object, there are three available files: The preview .png image, the “full spectrum” file, and the “lite spectrum” file. The full spectrum is listed as Minimum Recommended Products for the productGroupDescription parameter.

For more information about eBOSS data products, you can visit the MAST Archive Manual as well as in the search results table.

This will take a few minutes to load.

# Obtaining the product list of all galaxies
products = Observations.get_product_list(combined_results)

# Display the available products
products

Table masked=True length=2170

obsID	obs_collection	dataproduct_type	obs_id	description	type	dataURI	productType	productGroupDescription	productSubGroupDescription	productDocumentationURL	project	prvversion	proposal_id	productFilename	size	parent_obsid	dataRights	calib_level	filters
str9	str4	str12	str30	str235	str1	str69	str7	str28	str14	str61	str5	str7	str3	str31	int64	str9	str6	int64	str4
244093798	SDSS	spectrum	sdss_eboss_10729-58248-0357	Preview-Full	S	mast:SDSS/eboss/10729/58248/0357/spec-image-10729-58248-0357.png	PREVIEW	--	--	--	eBOSS	DR17	N/A	spec-image-10729-58248-0357.png	33843	244093798	PUBLIC	3	None
244093798	SDSS	spectrum	sdss_eboss_10729-58248-0357	SDSS eBOSS lite spectrum file containing the combined spectrum and associated metadata but not the individual exposures.	S	mast:SDSS/eboss/10729/58248/0357/lite/spec-lite-10729-58248-0357.fits	SCIENCE	--	SPECTRA	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	DR17	N/A	spec-lite-10729-58248-0357.fits	216000	244093798	PUBLIC	3	None
244093798	SDSS	spectrum	sdss_eboss_10729-58248-0357	SDSS eBOSS full spectrum file containing the combined spectrum, associated metadata, and the individual exposures.	S	mast:SDSS/eboss/10729/58248/0357/full/spec-10729-58248-0357.fits	SCIENCE	Minimum Recommended Products	SPECTRA	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	DR17	N/A	spec-10729-58248-0357.fits	864000	244093798	PUBLIC	3	None
244093916	SDSS	spectrum	sdss_eboss_10729-58248-0657	Preview-Full	S	mast:SDSS/eboss/10729/58248/0657/spec-image-10729-58248-0657.png	PREVIEW	--	--	--	eBOSS	DR17	N/A	spec-image-10729-58248-0657.png	39087	244093916	PUBLIC	3	None
244093916	SDSS	spectrum	sdss_eboss_10729-58248-0657	SDSS eBOSS lite spectrum file containing the combined spectrum and associated metadata but not the individual exposures.	S	mast:SDSS/eboss/10729/58248/0657/lite/spec-lite-10729-58248-0657.fits	SCIENCE	--	SPECTRA	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	DR17	N/A	spec-lite-10729-58248-0657.fits	216000	244093916	PUBLIC	3	None
244093916	SDSS	spectrum	sdss_eboss_10729-58248-0657	SDSS eBOSS full spectrum file containing the combined spectrum, associated metadata, and the individual exposures.	S	mast:SDSS/eboss/10729/58248/0657/full/spec-10729-58248-0657.fits	SCIENCE	Minimum Recommended Products	SPECTRA	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	DR17	N/A	spec-10729-58248-0657.fits	864000	244093916	PUBLIC	3	None
244094913	SDSS	spectrum	sdss_eboss_10729-58248-0359	Preview-Full	S	mast:SDSS/eboss/10729/58248/0359/spec-image-10729-58248-0359.png	PREVIEW	--	--	--	eBOSS	DR17	N/A	spec-image-10729-58248-0359.png	34149	244094913	PUBLIC	3	None
244094913	SDSS	spectrum	sdss_eboss_10729-58248-0359	SDSS eBOSS lite spectrum file containing the combined spectrum and associated metadata but not the individual exposures.	S	mast:SDSS/eboss/10729/58248/0359/lite/spec-lite-10729-58248-0359.fits	SCIENCE	--	SPECTRA	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	DR17	N/A	spec-lite-10729-58248-0359.fits	216000	244094913	PUBLIC	3	None
244094913	SDSS	spectrum	sdss_eboss_10729-58248-0359	SDSS eBOSS full spectrum file containing the combined spectrum, associated metadata, and the individual exposures.	S	mast:SDSS/eboss/10729/58248/0359/full/spec-10729-58248-0359.fits	SCIENCE	Minimum Recommended Products	SPECTRA	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	DR17	N/A	spec-10729-58248-0359.fits	864000	244094913	PUBLIC	3	None
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
252830431	SDSS	measurements	sdss_eboss_spall	SDSS eBOSS summary catalog. This provides collated summary tables on the observations and data processing from eBOSS, including targeting information, spectroscopic classifications, and redshifts for every observation.	D	mast:SDSS/eboss/spAll-v5_13_2.fits	SCIENCE	--	eBOSS Catalogs	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	v5_13_2	N/A	spAll-v5_13_2.fits	15895373760	248379571	PUBLIC	3	--
252830431	SDSS	measurements	sdss_eboss_spall	SDSS eBOSS summary catalog. This provides collated summary tables on the observations and data processing from eBOSS, including targeting information, spectroscopic classifications, and redshifts for every observation.	D	mast:SDSS/eboss/spAll-v5_13_2.fits	SCIENCE	--	eBOSS Catalogs	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	v5_13_2	N/A	spAll-v5_13_2.fits	15895373760	248380187	PUBLIC	3	--
252830431	SDSS	measurements	sdss_eboss_spall	SDSS eBOSS summary catalog. This provides collated summary tables on the observations and data processing from eBOSS, including targeting information, spectroscopic classifications, and redshifts for every observation.	D	mast:SDSS/eboss/spAll-v5_13_2.fits	SCIENCE	--	eBOSS Catalogs	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	v5_13_2	N/A	spAll-v5_13_2.fits	15895373760	248380410	PUBLIC	3	--
252830431	SDSS	measurements	sdss_eboss_spall	SDSS eBOSS summary catalog. This provides collated summary tables on the observations and data processing from eBOSS, including targeting information, spectroscopic classifications, and redshifts for every observation.	D	mast:SDSS/eboss/spAll-v5_13_2.fits	SCIENCE	--	eBOSS Catalogs	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	v5_13_2	N/A	spAll-v5_13_2.fits	15895373760	248380534	PUBLIC	3	--
252830431	SDSS	measurements	sdss_eboss_spall	SDSS eBOSS summary catalog. This provides collated summary tables on the observations and data processing from eBOSS, including targeting information, spectroscopic classifications, and redshifts for every observation.	D	mast:SDSS/eboss/spAll-v5_13_2.fits	SCIENCE	--	eBOSS Catalogs	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	v5_13_2	N/A	spAll-v5_13_2.fits	15895373760	248380590	PUBLIC	3	--
252830431	SDSS	measurements	sdss_eboss_spall	SDSS eBOSS summary catalog. This provides collated summary tables on the observations and data processing from eBOSS, including targeting information, spectroscopic classifications, and redshifts for every observation.	D	mast:SDSS/eboss/spAll-v5_13_2.fits	SCIENCE	--	eBOSS Catalogs	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	v5_13_2	N/A	spAll-v5_13_2.fits	15895373760	248380647	PUBLIC	3	--
252830431	SDSS	measurements	sdss_eboss_spall	SDSS eBOSS summary catalog. This provides collated summary tables on the observations and data processing from eBOSS, including targeting information, spectroscopic classifications, and redshifts for every observation.	D	mast:SDSS/eboss/spAll-v5_13_2.fits	SCIENCE	--	eBOSS Catalogs	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	v5_13_2	N/A	spAll-v5_13_2.fits	15895373760	248380843	PUBLIC	3	--
252830431	SDSS	measurements	sdss_eboss_spall	SDSS eBOSS summary catalog. This provides collated summary tables on the observations and data processing from eBOSS, including targeting information, spectroscopic classifications, and redshifts for every observation.	D	mast:SDSS/eboss/spAll-v5_13_2.fits	SCIENCE	--	eBOSS Catalogs	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	v5_13_2	N/A	spAll-v5_13_2.fits	15895373760	248381352	PUBLIC	3	--
252830431	SDSS	measurements	sdss_eboss_spall	SDSS eBOSS summary catalog. This provides collated summary tables on the observations and data processing from eBOSS, including targeting information, spectroscopic classifications, and redshifts for every observation.	D	mast:SDSS/eboss/spAll-v5_13_2.fits	SCIENCE	--	eBOSS Catalogs	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	v5_13_2	N/A	spAll-v5_13_2.fits	15895373760	248381483	PUBLIC	3	--
252830431	SDSS	measurements	sdss_eboss_spall	SDSS eBOSS summary catalog. This provides collated summary tables on the observations and data processing from eBOSS, including targeting information, spectroscopic classifications, and redshifts for every observation.	D	mast:SDSS/eboss/spAll-v5_13_2.fits	SCIENCE	--	eBOSS Catalogs	https://outerspace.stsci.edu/display/SDSS/eBOSS+Data+Products	eBOSS	v5_13_2	N/A	spAll-v5_13_2.fits	15895373760	248382373	PUBLIC	3	--

To utilize the data, we must download the FITS files. Any data products dowloaded from MAST will appear in a folder called mastDownload.

We’ll be focusing on using the full spectrum datafile only, which is labeled “Minimum Recommended Products” as the product Group Description. To ensure we’re only downloading this file for each target, we’ll use the parameter mrp_only = True.

This download should take around 45 seconds or so.

# Downloading the full spectra products
manifest = Observations.download_products(
    products, mrp_only=True, verbose=False
)

We’ll send these FITS files to an array so that we can access the redshift and flux values.

# Sending the FITS files to an array
galaxy_array = []

for path in manifest["Local Path"]:
    galaxy_array.append(fits.open(path))

# View available file extensions
galaxy_array[0].info()

Filename: ./mastDownload/SDSS/sdss_eboss_10729-58248-0357/spec-10729-58248-0357.fits
No.    Name      Ver    Type      Cards   Dimensions   Format
PRIMARY       1 PrimaryHDU     134   ()      
COADD         1 BinTableHDU     26   4567R x 8C   [E, E, E, J, J, E, E, E]   
SPALL         1 BinTableHDU    488   1R x 236C   [27A, 14A, 4A, E, E, J, J, E, J, E, E, E, K, K, K, K, K, K, K, K, K, B, B, J, I, 5E, 5E, J, J, J, J, 7A, 7A, 16A, D, D, 6A, 21A, E, E, E, J, E, 24A, 10J, J, 10E, E, E, E, E, E, E, J, E, E, E, J, 5E, E, E, 10E, 10E, 10E, 5E, 5E, 5E, 5E, 5E, J, J, E, E, E, E, E, E, 16A, 9A, 12A, E, E, E, E, E, E, E, E, J, E, E, J, J, 6A, 21A, E, 35E, K, 19A, 19A, 19A, B, B, B, I, 3A, B, I, I, I, I, J, E, J, J, E, E, E, E, E, E, E, E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5J, 5J, 5J, 5E, 5J, 75E, 75E, 5E, 5E, 5E, 5J, 5E, D, D, D, D, D, D, D, D, D, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 5E, 40E, 40E, 5J, 5J, 5E, 5E, 5D, J, J, J, J, J, J, J, E]   
SPZLINE       1 BinTableHDU     48   32R x 19C   [J, J, J, 13A, D, E, E, E, E, E, E, E, E, E, E, J, J, E, E]   
B1-00268372-00268371-00268370    1 BinTableHDU    189   2481R x 8C   [E, E, E, J, E, E, E, E]   
B1-00268373-00268371-00268370    1 BinTableHDU    189   2481R x 8C   [E, E, E, J, E, E, E, E]   
B1-00268374-00268371-00268370    1 BinTableHDU    189   2481R x 8C   [E, E, E, J, E, E, E, E]   
R1-00268372-00268371-00268370    1 BinTableHDU    189   3105R x 8C   [E, E, E, J, E, E, E, E]   
R1-00268373-00268371-00268370    1 BinTableHDU    189   3105R x 8C   [E, E, E, J, E, E, E, E]   
R1-00268374-00268371-00268370    1 BinTableHDU    189   3105R x 8C   [E, E, E, J, E, E, E, E]   

For this tutorial, we will focus on using the spectroscopic flux in the r-band provided by spALL. These are accessed through the second file extension.

The various file extensions are broken down on the SDSS website:

HDU 0: The primary header information.
HDU 1: The coadded observed spectrum.
HDU 2: Metadata from spALL.
HDU 3: Emission line fitting metadata from spZline.
HDU 4+: Individual red and blue spectra that make up the coadded spectrum.

The second file extension is broken down even further, available also on the SDSS website. We’ll be focusing on using SPECTROFLUX. Since this provides us a five-element array for each band (u, g, r, i , z), we’ll use the third element for the r-band flux.

Making the Hubble-Lemaître Diagram#

# Setting up arrays to send all z-values, z-error, and flux to arrays
z_val = []
z_err = []
r_flux = []

# Looping through all the data and adding z-values, z-error, and flux to arrays
for galaxy in galaxy_array:
    galaxy_z = galaxy[2].data["Z"]
    zerr = galaxy[2].data["Z_ERR"]
    spectroflux = galaxy[2].data["SPECTROFLUX"][:, 2]
    z_val.append(galaxy_z)
    z_err.append(zerr)
    r_flux.append(spectroflux)

# Converting lists to arrays
z_val = np.array(z_val)
z_err = np.array(z_err)
r_flux = np.array(r_flux)

In order to determine the relative distance to each galaxy, we can use the inverse square law as we know flux is proportional to \(\frac{1}{d^2}\). Thus, distance is proportional to \(\frac{1}{\sqrt{flux}}\) [4].

# Finding the relative distance by taking 1/sqrt of the radiant flux
relative_distance = 1 / np.sqrt(r_flux)

# Converting the relative distance to kiloparsecs
new_relative_distance = relative_distance / 1e3  # kpc

# Stacking arrays to remove points with nan
plot_array = np.column_stack((z_val, new_relative_distance, z_err))

Due to the behavior of \(\frac{1}{\sqrt{flux}}\), we will create a mask to remove any ‘nan’ values.

# Selecting all distances that are not 'nan'
mask = ~np.isnan(plot_array[:, 1])

# Applying mask
new_plot_array = plot_array[mask]

Since Hubble’s constant is in units km/s/Mpc, we want to convert redshift to velocity. To do this, we can use the relativistic radial velocity equation [5]:

\[ v = c \frac{(1+z)^2-1}{(1+z)^2+1} \]

Using error propagation, the error in redshift becomes:

\[ v_{err} = z_{err}|\frac{4c(1+z)}{((1+z)^2+1)^2}| \]

# Define speed of light constant (c) in km/s
c = 2.998e5  # km/s

# Calculating velocity from redshift
velocity = []
velocity_err = []
for i, j in zip(new_plot_array[:, 0], new_plot_array[:, 2]):
    v = c * (((1 + i) ** 2 - 1) / ((1 + i) ** 2 + 1))
    v_err = np.abs(((4 * c * (1 + i)) / ((1 + i) ** 2 + 1) ** 2)) * j
    velocity.append(v)
    velocity_err.append(v_err)

# Creating new array of distance, velocity, and error in velocity
distance_velocity_array = np.column_stack(
    (new_plot_array[:, 1], velocity, velocity_err)
)

Plotting eBOSS Data#

We can examine the data by creating a scatter plot of the velocity versus the relative distance.

# Plotting eBOSS data
plt.figure(figsize=(8, 5))
plt.scatter(
    distance_velocity_array[:, 0],
    distance_velocity_array[:, 1],
    s=1.5,
    color="blue",
)
plt.title("Velocity vs. Relative Distance of eBOSS Data")
plt.xlabel("Relative Distance")
plt.ylabel("Radial Velocity (km/s)")
plt.grid(True)
plt.show()

../../../_images/45cef68c2268ce7f09c742184624c084e5252c75e04d613908317c968828df03.png

Importing Abell 2199 Data#

In order to obtain the actualized distances for the sample, we can use the relative distance of the first galaxy from Abell 2199 and set it equal to 1. We’ll follow the same procedures as before by importing the abell_2199.txt file and querying eBOSS for those 32 select galaxies.

# Loading the Abell 2199 dataset
obs_id2 = np.loadtxt("abell_2199.txt", dtype=str)

# Querying eBOSS for the 32 Abell 2199 galaxies, sending the data to an array
results_tables2 = []
for i in obs_id2:
    query_result2 = Observations.query_criteria(
        provenance_name="eBOSS", obs_id=i
    )
    results_tables2.append(query_result2)

# Stacking the data into one table
combined_results2 = vstack(results_tables2)

# Ensuring the length of the stacked table is 32
print(f"Length of Abell 2199 dataset = {len(combined_results2)}")

Length of Abell 2199 dataset = 32

We’ll gather and download the products again, and then send the FITS data to an array.

# Gathering and downloading full spectra files
products2 = Observations.get_product_list(combined_results2)
manifest2 = Observations.download_products(
    products2, mrp_only=True, verbose=False
)

# Writing data to an array
abell_array = []
for path in manifest2["Local Path"]:
    abell_array.append(fits.open(path))

# Checking the length of the array matches the dataset
print(f"Length of Abell 2199 array = {len(abell_array)}")

INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_10729-58248-0357/spec-10729-58248-0357.fits with expected size 864000. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_10729-58248-0359/spec-10729-58248-0359.fits with expected size 864000. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_10729-58248-0657/spec-10729-58248-0657.fits with expected size 864000. [astroquery.query]

INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0747/spec-5190-56077-0747.fits with expected size 875520. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0749/spec-5190-56077-0749.fits with expected size 875520. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0753/spec-5190-56077-0753.fits with expected size 875520. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0756/spec-5190-56077-0756.fits with expected size 875520. [astroquery.query]

INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0757/spec-5190-56077-0757.fits with expected size 875520. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0758/spec-5190-56077-0758.fits with expected size 875520. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0759/spec-5190-56077-0759.fits with expected size 875520. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0761/spec-5190-56077-0761.fits with expected size 875520. [astroquery.query]

INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0762/spec-5190-56077-0762.fits with expected size 875520. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0790/spec-5190-56077-0790.fits with expected size 875520. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0793/spec-5190-56077-0793.fits with expected size 875520. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0795/spec-5190-56077-0795.fits with expected size 875520. [astroquery.query]

INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0797/spec-5190-56077-0797.fits with expected size 875520. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0798/spec-5190-56077-0798.fits with expected size 875520. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_5190-56077-0799/spec-5190-56077-0799.fits with expected size 875520. [astroquery.query]

INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0084/spec-6045-56072-0084.fits with expected size 1082880. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0121/spec-6045-56072-0121.fits with expected size 1082880. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0124/spec-6045-56072-0124.fits with expected size 1082880. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0125/spec-6045-56072-0125.fits with expected size 1082880. [astroquery.query]

INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0126/spec-6045-56072-0126.fits with expected size 1082880. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0130/spec-6045-56072-0130.fits with expected size 1082880. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0161/spec-6045-56072-0161.fits with expected size 1082880. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0162/spec-6045-56072-0162.fits with expected size 1082880. [astroquery.query]

INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0163/spec-6045-56072-0163.fits with expected size 1082880. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0164/spec-6045-56072-0164.fits with expected size 1082880. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0165/spec-6045-56072-0165.fits with expected size 1082880. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0167/spec-6045-56072-0167.fits with expected size 1082880. [astroquery.query]

INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0169/spec-6045-56072-0169.fits with expected size 1082880. [astroquery.query]
INFO: Found cached file ./mastDownload/SDSS/sdss_eboss_6045-56072-0206/spec-6045-56072-0206.fits with expected size 1082880. [astroquery.query]
Length of Abell 2199 array = 32

Now we can extract the redshift, error in redshift, and r-band flux values. Following the same processes as before, we can use the flux to find the relative distances.

# Sending redshift, error in redshift, and r-band magnitudes to arrays
z_val_abell = []
z_err_abell = []
r_flux_abell = []

for galaxy in abell_array:
    galaxy_z = galaxy[2].data["Z"]
    zerr = galaxy[2].data["Z_ERR"]
    spectroflux = galaxy[2].data["SPECTROFLUX"][:, 2]
    z_val_abell.append(galaxy_z)
    z_err_abell.append(zerr)
    r_flux_abell.append(spectroflux)

# Converting lists into arrays
z_val_abell = np.array(z_val_abell)
z_err_abell = np.array(z_err_abell)
r_flux_abell = np.array(r_flux_abell)

# Calculate relative distance
relative_distance_abell = 1 / np.sqrt(r_flux_abell)
new_relative_distance_abell = relative_distance_abell / 1e3  # kpc

# Filter out zeros
plot_array_abell = np.column_stack(
    (z_val_abell, new_relative_distance_abell, z_err_abell)
)
mask2 = ~np.isnan(plot_array_abell[:, 1])
new_array_abell = plot_array_abell[mask2]

# Calculate velocity
velocity_abell = []
velocity_err_abell = []
for i, j in zip(new_array_abell[:, 0], new_array_abell[:, 2]):
    v = c * (((1 + i) ** 2 - 1) / ((1 + i) ** 2 + 1))
    v_err = np.abs(((4 * c * (1 + i)) / ((1 + i) ** 2 + 1) ** 2)) * j
    velocity_abell.append(v)
    velocity_err_abell.append(v_err)

# Creating new array of distance, velocity, and error in velocity
distance_velocity_array_abell = np.column_stack(
    (new_array_abell[:, 1], velocity_abell, velocity_err_abell)
)

Now that we have filtered out both datasets, we can normalize the relative distances. To do this, we’ll set up a ratio such that the closest galaxy in the Abell 2199 cluster equals 1:

\[ \frac{d_{1}}{d_{relative}} = \frac{1}{d_{norm}} \]

where \(d_{1}\) is the relative distance of the closest Abell 2199 galaxy, \(d_{relative}\) is the array of relative distances of the eBOSS galaxies, and \(d_{norm}\) is the array of normalized distances. To solve for the array of \(d_{norm}\), we’ll divide the array of relative distances by \(d_{1}\). [4]

Since we know the distance to Abell 2199 is 128 Mpc, we’ll multiply the normalized distances by 128 Mpc to obtain the actualized distances. [6].

# Sorting the Abell 2199 data to find closest galaxy
sorted_abell = np.argsort(distance_velocity_array_abell[:, 0])
sorted_abell_array = distance_velocity_array_abell[sorted_abell]

# Taking the first Abell 2199 galaxy and find the average, setting that to 1
d1_abell = sorted_abell_array[0][0]

# Normalize distances to d1_abell
norm_dist = distance_velocity_array[:, 0] / d1_abell
norm_dist_abell = distance_velocity_array_abell[:, 0] / d1_abell

# Distance to Abell 2199
distance = 128  # Mpc

Now we have normalized distances! We can multiply these by the distance to Abell 2199 and generate a plot with distances and radial velocities. We can use scipy.optimize.curve_fit to perform a linear fit, and in return, we can obtain the value of the slope, i.e., Hubble’s constant!

# Defining linear fit function
def fit_func(x, m, b):
    return m * x + b

# Doing linear fit using scipy.optimize.curve_fit
popt, covariance = curve_fit(
    fit_func,
    norm_dist * distance,
    distance_velocity_array[:, 1],
    sigma=distance_velocity_array[:, 2],
    absolute_sigma=True,
)
m = popt[0]  # slope (Hubble's constant!)
b = popt[1]  # intercept

# Setting up an array of x-values to plot the line of best fit
x_array = np.linspace(0, 2000, 200000)

# Plotting the data as well as the line of best fit
plt.errorbar(
    norm_dist * distance,
    distance_velocity_array[:, 1],
    yerr=distance_velocity_array[:, 2],
    ms=1.5,
    fmt="o",
    label="eBOSS data",
    zorder=1,
)
plt.scatter(
    norm_dist_abell * distance,
    distance_velocity_array_abell[:, 1],
    s=5,
    label="Abell 2199",
    color="purple",
    zorder=2,
)
plt.plot(
    x_array,
    fit_func(x_array, m, b),
    label="linear fit",
    color="orange",
    zorder=3,
)
plt.ylabel("Radial Velocity (km/s)")
plt.xlabel("Actualized Distance (Mpc)")
plt.title(
    f"Radial Velocity vs. Actualized Distance of eBOSS Galaxy Sample \n eBOSS - LOFAR \n $H_{0}$ = {m:.3f} km/s/Mpc \n r - band magnitude"
)
plt.legend(loc="lower right")
plt.grid()
plt.tight_layout()
plt.show()

../../../_images/0a1b6a295c65fa4e45cb1b74d3195054c13893e5a0bde01f2666989aae908691.png

Comparing Calculated H₀ to Other Models#

Using data from eBOSS, we were able to calculate an H₀ value of \(\approx\) 73.66 km/s/Mpc!

The European Space Agency calculated an H₀ value of 67.40 ± 1.40 km/s/Mpc using Planck data. A recent calculation using Cepheid variables and SNe Ia from the SH0ES collaboration provided an H₀ value of 73.04 ± 1.04 km/s/Mpc [3]. Astronomers continue to use both local distance indicators (e.g., Tip of the Red Giant Branch stars) and early-Universe probes like the CMB to constrain H₀, but the Hubble Tension remains unresolved [7].

Due to relativistic effects, H₀ values calculated from CMB observations (which probe the early Universe) tend to be lower than those calculated from nearby objects like Cepheid variables or Type Ia supernovae. Since our H₀ value is based on galaxy observations from eBOSS, it’s reasonable that it falls on the higher end of the range, though this could also be influenced by uncertainties introduced by several assumptions:

We assume galaxies are point sources, using a single static distance for each.
We calculate distances using the inverse square law, but intrinsic galaxy brightness can vary significantly.

Utilizing HST Data from MAST#

The Hubble Space Telescope (HST) is a 2.4 meter serviceable telescope launched in 1990. It’s equipped with three cameras (ACS, WFC3/UVIS, and WFC3/IR). Using observations from HST, we can construct an image of Abell 2199!

While we won’t be covering this in the tutorial, we could use the constructed image from HST to determine the relative distance to Abell 2199 rather than using the one from NED. For example, we could use the apparent brightness of the cluster’s brightest galaxy, or analyze the relative physical sizes of its member galaxies [4].

For more information about HST, check out this overview from MAST!

Creating an Image of Abell 2199 Using HST#

To create an image of Abell 2199 using HST, we’ll query MAST using objectname = 'Abell 2199' and specify HST using obs_collection = 'HST'.

# Query HST using objectname
obs_hst = Observations.query_criteria(
    objectname="Abell 2199",
    # specifying Hubble data
    obs_collection="HST",
    # We want science observations and not calibration files
    intentType="science",
    # Calibrated reduced observations to display final image
    provenance_name="CAL*",
)
# Display results
obs_hst

Table masked=True length=77

intentType	obs_collection	provenance_name	instrument_name	project	filters	wavelength_region	target_name	target_classification	obs_id	s_ra	s_dec	dataproduct_type	proposal_pi	calib_level	t_min	t_max	t_exptime	em_min	em_max	obs_title	t_obs_release	proposal_id	proposal_type	sequence_number	s_region	jpegURL	dataURL	dataRights	mtFlag	srcDen	obsid	objID	objID1	distance
str7	str3	str8	str13	str3	str6	str8	str21	str69	str9	float64	float64	str8	str21	int64	float64	float64	float64	float64	float64	str110	float64	str5	str12	int64	str1098	str34	str35	str6	bool	float64	str9	str9	str9	float64
science	HST	CALNIC	NICMOS/NIC3	HST	F160W	Infrared	NGC6166-WF4	GALAXY;ELLIPTICAL;BCM	n4t204070	247.1793481664	39.55485355641	image	Geisler, Douglas	3	50990.66488426	50990.79190972	3583.872072	1408.3999999999999	1809.4	The Metallicity Distribution of the Globular Cluster Systems of Giant Elliptical Galaxies	51356.53231477	7265	GO	--	POLYGON -112.81429500000002 39.545485 -112.80873299999996 39.559266 -112.80873332280447 39.559266077458844 -112.80851899999999 39.559797 -112.82164528889807 39.56294585492904 -112.82701700000001 39.564234 -112.83257600000002 39.550452 -112.83257587496034 39.550451970020688 -112.83278999999999 39.549921 -112.83210196969837 39.54975607514 -112.83210199999996 39.549756 -112.81429500000002 39.545485 -112.81429500000002 39.545485	mast:HST/product/n4t204070_mos.jpg	mast:HST/product/n4t204070_mos.fits	PUBLIC	False	nan	24861478	109228114	109228114	73.05880201851693
science	HST	CALNIC	NICMOS/NIC2	HST	F160W	Infrared	ABELL2199-SKYS	CALIBRATION;SKY BACKGROUND	n4hd21030	247.160006665	39.47067612935	image	Tonry, John L.	3	50799.99439224537	50800.001336608795	383.990005	1408.3999999999999	1809.4	The SBF Hubble Diagram	51165.55783555	7453	GO	--	POLYGON -112.83682999999996 39.469599 -112.83380699999998 39.47445 -112.840036 39.476763 -112.84305900000004 39.471911 -112.83682999999996 39.469599 -112.83682999999996 39.469599 POLYGON -112.83994899999999 39.464592 -112.836926 39.469444 -112.84315500000002 39.471756 -112.84617700000001 39.466904 -112.83994899999999 39.464592 -112.83994899999999 39.464592	mast:HST/product/n4hd21030_mos.jpg	mast:HST/product/n4hd21030_mos.fits	PUBLIC	False	nan	24854837	109244905	109244905	233.75097836993348
science	HST	CALWFPC	WFPC/PC	HST	F555W	Optical	NGC6166	GALAXY;ELLIPTICAL;RADIO GALAXY;	w10a0k03t	247.1602080555556	39.55083305555556	image	Faber, Sandra M.	2	48912.790486770835	48912.81016269676	1700.0	490.4	605.4	CORES OF EARLY-TYPE GALAXIES	49277.97034713	3912	GO	--	POLYGON 247.16026223 39.55848068 247.16854576 39.55107914 247.158936 39.54468522 247.15065221 39.55208608 247.16026223 39.55848068	mast:HST/product/w10a0k03t_c0f.jpg	mast:HST/product/w10a0k03t_c0f.fits	PUBLIC	False	nan	24734062	121579829	121579829	41.44383128973108
science	HST	CALNIC	NICMOS/NIC3	HST	F160W	Infrared	ABELL2199-SKYS	CALIBRATION;SKY BACKGROUND	n4hd21040	247.1339505311	39.48167425652	image	Tonry, John L.	3	50799.99439305555	50800.02956019	383.990005	1408.3999999999999	1809.4	The SBF Hubble Diagram	51165.55482632	7453	GO	--	POLYGON -112.863315 39.469529 -112.85511399999996 39.482499 -112.85515305545294 39.48251371201912 -112.85199599999999 39.487506 -112.868742 39.493813 -112.87694099999999 39.480841 -112.87690210780677 39.480826359142355 -112.88005699999997 39.475834 -112.863315 39.469529 -112.863315 39.469529	mast:HST/product/n4hd21040_mos.jpg	mast:HST/product/n4hd21040_mos.fits	PUBLIC	False	nan	24854838	125025147	125025147	171.7010033904009
science	HST	CALSTIS	STIS/CCD	HST	MIRVIS	Optical	ANY	UNIDENTIFIED;PARALLEL FIELD	o4k1uq010	247.2330667592	39.4324369098	image	Baum, Stefi A.	3	50990.44631774306	50990.450299421296	300.0	nan	nan	POMS Test Proposal: STIS non-scripted parallel proposal	50990.74260405	7908	GO/PAR	--	POLYGON 247.22159539995113 39.42784078011958 247.22707603758766 39.441280962158395 247.24453811574787 39.437033032856746 247.23905747811133 39.42359285081793 247.22159539995113 39.42784078011958	--	mast:HST/product/o4k1uq010_sx2.fits	PUBLIC	False	nan	24916064	361298289	361298289	425.4196862145258
science	HST	CALSTIS	STIS/CCD	HST	MIRVIS	Optical	ANY	UNIDENTIFIED;PARALLEL FIELD	o4k1w3010	247.2671136734	39.44580006266	image	Baum, Stefi A.	3	50990.66669961806	50990.67190813657	400.0	nan	nan	POMS Test Proposal: STIS non-scripted parallel proposal	50990.74288183	7908	GO/PAR	--	POLYGON 247.25563785375158 39.44120729811321 247.26112615216493 39.45464587159116 247.27858949034362 39.45039282058389 247.27310119193027 39.436954247105945 247.25563785375158 39.44120729811321	--	mast:HST/product/o4k1w3010_sx2.fits	PUBLIC	False	nan	24916087	361298736	361298736	448.96962551989975
science	HST	CALSTIS	STIS/CCD	HST	MIRVIS	Optical	ANY	UNIDENTIFIED;PARALLEL FIELD	o4k1w1010	247.2411980164	39.45178911856	image	Baum, Stefi A.	3	50990.646676655095	50990.65188480324	400.0	nan	nan	POMS Test Proposal: STIS non-scripted parallel proposal	50990.74760404	7908	GO/PAR	--	POLYGON 247.2297229224898 39.44719380296406 247.23520668238115 39.460633596012656 247.25267310760765 39.456384427532456 247.24718934771633 39.44294463448386 247.2297229224898 39.44719380296406	--	mast:HST/product/o4k1w1010_sx2.fits	PUBLIC	False	nan	24916085	361298749	361298749	383.40239361919663
science	HST	CALSTIS	STIS/CCD	HST	MIRVIS	Optical	HI-LATITUDE-FIELD	STAR	o5hjmmvbq	247.1342541244	39.46526553535	image	Baum, Stefi A.	2	51383.33821987268	51383.3399559838	150.0	nan	nan	POMS Test Proposal: STIS non-scripted parallel proposal continuation V	51383.69723367	8406	ENG/STIS/PAR	--	POLYGON 247.1230456105921 39.46029046473415 247.12777066916982 39.473901168582714 247.14546263587928 39.470240599258126 247.14073757730156 39.45662989540956 247.1230456105921 39.46029046473415	--	mast:HST/product/o5hjmmvbq_flt.fits	PUBLIC	False	nan	24458735	361414815	361414815	243.90550319973354
science	HST	CALACS	ACS/WFC	HST	F475W	OPTICAL	NGC-6166	GALAXY;ELLIPTICAL	jbhr01010	247.1599125	39.54200555556	image	Harris, William Edgar	3	55773.28388880787	55773.415844641204	5370.0	390.0	550.0	Supermassive Star Clusters in Supergiant Galaxies: Tracing the Enrichment of the Earliest Stellar Systems	56139.54138886	12238	GO	--	POLYGON -112.86275602999987 39.518147039999995 -112.86271187025956 39.518206797457765 -112.86268716999994 39.518197600000128 -112.82622465999985 39.567498360000144 -112.82627228862017 39.567516100878137 -112.82625031999989 39.567545780000117 -112.85968168000004 39.579991389999996 -112.8597258711428 39.57993164789022 -112.85975055000009 39.579940830000083 -112.89619584000009 39.53062963 -112.89614819747909 39.530611909670405 -112.89617012999996 39.530582209999942 -112.86275602999987 39.518147039999995 -112.86275602999987 39.518147039999995 POLYGON -112.82970656000008 39.506421130000007 -112.82966139750027 39.506480366747262 -112.82963766999983 39.506471690000005 -112.79275050999998 39.554814740000154 -112.7927988487199 39.554832423044175 -112.79277614000011 39.554862160000091 -112.82519745000006 39.566715840000029 -112.82524264329537 39.566656620917342 -112.82526633999981 39.566665279999995 -112.86213722000011 39.51831200000003 -112.86208885359757 39.518294332653461 -112.86211152999992 39.518264570000127 -112.82970656000008 39.506421130000007 -112.82970656000008 39.506421130000007	mast:HST/product/jbhr01010_drz.jpg	mast:HST/product/jbhr01010_drz.fits	PUBLIC	False	nan	24834402	741033393	741033393	0.0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
science	HST	CALWF3	WFC3/UVIS	HST	F336W	OPTICAL	PS15AOT-SN2009EU-HOST	GALAXY;ELLIPTICAL	iey929010	247.1654514304	39.55075434279	image	Kelsey, Lisa	3	59933.10898993056	59933.12674452546	360.0	305.8	367.3	Local Environments of Low-redshift Type Ia Supernova Siblings	59933.48858801	17194	SNAP	--	POLYGON -112.81925200000011 39.522145629999855 -112.80732268999986 39.54258658000002 -112.80737951545382 39.542610020566 -112.80711494851404 39.543063207567947 -112.80689240000011 39.542972830000032 -112.79484269999986 39.563667969999919 -112.7948988548921 39.563690775328347 -112.79454513999994 39.564298070000078 -112.84659405999993 39.58541789 -112.85863210000019 39.564717380000012 -112.85857593339213 39.564694609384638 -112.85892909000003 39.564087120000067 -112.85884136466962 39.564051555105166 -112.87051424999994 39.544025700000113 -112.87045739161762 39.544002285837124 -112.8708110300001 39.543395389999866 -112.81925200000011 39.522145629999855 -112.81925200000011 39.522145629999855	mast:HST/product/iey929010_drz.jpg	mast:HST/product/iey929010_drz.fits	PUBLIC	False	nan	106457966	767238113	767238113	0.0
science	HST	CALACS	ACS/WFC	HST	F814W	OPTICAL	NGC6166	GALAXY;ELLIPTICAL;LINER	j6jt05020	247.1443138604	39.56568924527	image	Ford, Holland	3	52764.767804282405	52764.77748040509	700.0	708.0	959.0	Massive Black Holes in Early Type Galaxies	53131.42950234	9293	GTO/ACS	--	POLYGON -112.81907106000008 39.563255929999912 -112.81404633000007 39.591601029999993 -112.88610806999993 39.603104409999894 -112.89110415000002 39.574756219999934 -112.81907106000008 39.563255929999912 -112.81907106000008 39.563255929999912 POLYGON -112.82436564000002 39.534789040000064 -112.81978306000008 39.562217240000045 -112.8907723199999 39.574315340000112 -112.89532763000001 39.546884369999972 -112.82436564000002 39.534789040000064 -112.82436564000002 39.534789040000064	mast:HST/product/j6jt05021_drz.jpg	mast:HST/product/j6jt05021_drz.fits	PUBLIC	False	nan	26091432	785134894	785134894	0.0
science	HST	CALWFPC2	WFPC2/PC	HST	F673N	OPTICAL	3C338.0	GALAXY;RADIO GALAXY;	u2s07801t	247.1593798559	39.54271951924	image	Sparks, William B.	3	50048.450891898145	50048.45436412037	300.0	670.86	675.58	Snapshots of 3CR Radio Galaxies	50415.09186345	5957	SNAP	--	POLYGON 247.1588745068656 39.54384182979161 247.15046986829364 39.551449716293796 247.16032049263436 39.55793939381302 247.16872670919946 39.5503338532899 247.1588745068656 39.54384182979161	mast:HST/product/u2s07801t_drw.jpg	mast:HST/product/u2s07801t_drw.fits	PUBLIC	False	nan	24561898	788766846	788766846	39.4469579247626
science	HST	CALWFPC2	WFPC2/PC	HST	F673N	OPTICAL	3C338.0	GALAXY;RADIO GALAXY;	u2s07802t	247.1593798559	39.54271951924	image	Sparks, William B.	3	50048.456447453704	50048.45991967592	300.0	670.86	675.58	Snapshots of 3CR Radio Galaxies	50415.09549769	5957	SNAP	--	POLYGON 247.1588745068656 39.54384182979161 247.15046986829364 39.551449716293796 247.16032049263436 39.55793939381302 247.16872670919946 39.5503338532899 247.1588745068656 39.54384182979161	mast:HST/product/u2s07802t_drw.jpg	mast:HST/product/u2s07802t_drw.fits	PUBLIC	False	nan	24561899	788771094	788771094	39.4469579247626
science	HST	CALWFPC2	WFPC2/PC	HST	F606W	OPTICAL	ANY	UNIDENTIFIED;PARALLEL FIELD	u4k2m601r	247.2639535316	39.51530930574	image	Casertano, Stefano	3	50990.44738506944	50990.453172106485	500.0	510.89	661.13	POMS Test Proposal: WFII parallel archive proposal	50990.63297444	7909	GO/PAR	--	POLYGON 247.26529584017683 39.51484093361801 247.27765482259042 39.51184985808498 247.27379760950498 39.502314521624314 247.26144081752278 39.50530203906747 247.26529584017683 39.51484093361801	mast:HST/product/u4k2m601r_drw.jpg	mast:HST/product/u4k2m601r_drw.fits	PUBLIC	False	nan	24602332	789739298	789739298	349.30898244486366
science	HST	CALWFPC2	WFPC2/PC	HST	F606W	OPTICAL	HIGH	EXT-MEDIUM	u4k2lz02r	247.2980470745	39.52866341629	image	Casertano, Stefano	3	50990.67377395833	50990.67956099537	500.0	510.89	661.13	POMS Test Proposal: WFII parallel archive proposal	50990.74797447	7909	GO/PAR	--	POLYGON 247.2993894074153 39.52819464989219 247.31174929014978 39.525199948201404 247.30788663478177 39.51566574427916 247.2955289412657 39.51865688704364 247.2993894074153 39.52819464989219	mast:HST/product/u4k2lz02r_drw.jpg	mast:HST/product/u4k2lz02r_drw.fits	PUBLIC	False	nan	24602316	789745750	789745750	428.30333475443496
science	HST	CALWFPC2	WFPC2/PC	HST	F606W	OPTICAL	ANY	UNIDENTIFIED;PARALLEL FIELD	u4k2m602r	247.2632660938	39.51547482218	image	Casertano, Stefano	3	50990.45849618055	50990.466598032406	700.0	510.89	661.13	POMS Test Proposal: WFII parallel archive proposal	50990.63315963	7909	GO/PAR	--	POLYGON 247.2646084101698 39.51500645775736 247.27696745093658 39.512015453275325 247.27311032077844 39.502480094631046 247.26075347050354 39.505467541033354 247.2646084101698 39.51500645775736	mast:HST/product/u4k2m602r_drw.jpg	mast:HST/product/u4k2m602r_drw.fits	PUBLIC	False	nan	24602333	789745772	789745772	347.3089749576426
science	HST	CALWFPC2	WFPC2/PC	HST	F300W	UV	HIGH	EXT-MEDIUM	u4k2ly04r	247.2714155412	39.53482491055	image	Casertano, Stefano	3	50990.59599618056	50990.61219988426	1400.0	254.97	328.99	POMS Test Proposal: WFII parallel archive proposal	50990.74858789	7909	GO/PAR	--	POLYGON 247.27276176864666 39.53435065873066 247.28511525876343 39.53136396134659 247.28125839985375 39.521834221792595 247.2689065892541 39.52481973537812 247.27276176864666 39.53435065873066	mast:HST/product/u4k2ly04r_drw.jpg	mast:HST/product/u4k2ly04r_drw.fits	PUBLIC	False	nan	24602313	789756114	789756114	351.64648648762767
science	HST	CALWFPC2	WFPC2/PC	HST	F555W	OPTICAL	NGC6166-CENTER	GALAXY;ELLIPTICAL;BCM	u4t20301r	247.1604779253	39.54909217001	image	Geisler, Douglas	3	51383.33765628472	51383.35270258102	1300.0	472.26000000000005	595.1	The Metallicity Distribution of the Globular Cluster Systems of Giant Elliptical Galaxies	51749.69840271	7265	GO	--	POLYGON 247.16184361753605 39.54867518305677 247.17436379619448 39.546100335007374 247.17104405360607 39.53644599006302 247.15852636186068 39.53901759053526 247.16184361753605 39.54867518305677	mast:HST/product/u4t20301r_drw.jpg	mast:HST/product/u4t20301r_drw.fits	PUBLIC	False	nan	24604264	789805403	789805403	40.95574336166708
science	HST	CALSTIS	STIS/CCD	HST	G750L	OPTICAL	ANY	UNIDENTIFIED;PARALLEL FIELD	o4k1v9piq	247.2405111522	39.45195450143	spectrum	Baum, Stefi A.	2	50990.598378125	50990.612544791664	1224.0	524.0	1027.0	POMS Test Proposal: STIS non-scripted parallel proposal	50990.74354161	7908	GO/PAR	--	POLYGON 247.22903608175014 39.447359110323134 247.23451970633545 39.46079893945676 247.2519862199474 39.45654988591336 247.2465025953621 39.44311005677974 247.22903608175014 39.447359110323134	--	mast:HST/product/o4k1v9piq_flt.fits	PUBLIC	False	nan	24442445	794180714	794180714	381.6948436989644

Similar to eBOSS, we’ll retrieve and download the products for Abell 2199, specifically the fully calibrated combined images using productGroupDescription = 'Minimum Recommended Products' and productSubGroupDescription = 'DRZ'.

# Get products from query
products_hst = Observations.get_product_list(obs_hst)

# Select specific products
products_hst = Observations.filter_products(
    products_hst,
    # Specify science files
    productType="SCIENCE",
    # Recommended products,
    productGroupDescription="Minimum Recommended Products",
    # DRZ files -> calibrated combined images
    productSubGroupDescription="DRZ",
)
# Display product list
products_hst

Table masked=True length=11

obsID	obs_collection	dataproduct_type	obs_id	description	type	dataURI	productType	productGroupDescription	productSubGroupDescription	productDocumentationURL	project	prvversion	proposal_id	productFilename	size	parent_obsid	dataRights	calib_level	filters
str9	str3	str8	str37	str67	str1	str97	str9	str28	str11	str1	str8	str20	str5	str52	int64	str9	str6	int64	str9
24801640	HST	image	ibhr01020	DADS DRZ file - Calibrated combined image ACS/WFC3/WFPC2/STIS	D	mast:HST/product/ibhr01020_drz.fits	SCIENCE	Minimum Recommended Products	DRZ	--	CALWF3	3.7.2 (Apr-15-2024)	12238	ibhr01020_drz.fits	217932480	24801640	PUBLIC	3	F475W
24801653	HST	image	ibhr13030	DADS DRZ file - Calibrated combined image ACS/WFC3/WFPC2/STIS	D	mast:HST/product/ibhr13030_drz.fits	SCIENCE	Minimum Recommended Products	DRZ	--	CALWF3	3.7.2 (Apr-15-2024)	12238	ibhr13030_drz.fits	217638720	24801653	PUBLIC	3	F814W
24801654	HST	image	ibhr13040	DADS DRZ file - Calibrated combined image ACS/WFC3/WFPC2/STIS	D	mast:HST/product/ibhr13040_drz.fits	SCIENCE	Minimum Recommended Products	DRZ	--	CALWF3	3.7.2 (Apr-15-2024)	12238	ibhr13040_drz.fits	217638720	24801654	PUBLIC	3	F814W
24834402	HST	image	jbhr01010	DADS DRZ file - Calibrated combined image ACS/WFC3/WFPC2/STIS	D	mast:HST/product/jbhr01010_drz.fits	SCIENCE	Minimum Recommended Products	DRZ	--	CALACS	DrizzlePac 3.9.1	12238	jbhr01010_drz.fits	215023680	24834402	PUBLIC	3	F475W
24834415	HST	image	jbhr13010	DADS DRZ file - Calibrated combined image ACS/WFC3/WFPC2/STIS	D	mast:HST/product/jbhr13010_drz.fits	SCIENCE	Minimum Recommended Products	DRZ	--	CALACS	DrizzlePac 3.9.1	12238	jbhr13010_drz.fits	214859520	24834415	PUBLIC	3	F814W
24834416	HST	image	jbhr13020	DADS DRZ file - Calibrated combined image ACS/WFC3/WFPC2/STIS	D	mast:HST/product/jbhr13020_drz.fits	SCIENCE	Minimum Recommended Products	DRZ	--	CALACS	DrizzlePac 3.9.1	12238	jbhr13020_drz.fits	214859520	24834416	PUBLIC	3	F814W
24834423	HST	image	jbhv02010	DADS DRZ file - Calibrated combined image ACS/WFC3/WFPC2/STIS	D	mast:HST/product/jbhv02010_drz.fits	SCIENCE	Minimum Recommended Products	DRZ	--	CALACS	DrizzlePac 3.9.1	12220	jbhv02010_drz.fits	23569920	24834423	PUBLIC	3	F140LP
26091389	HST	image	j6jt05010	DADS DRZ file - Calibrated combined image ACS/WFC3/WFPC2/STIS	D	mast:HST/product/j6jt05011_drz.fits	SCIENCE	Minimum Recommended Products	DRZ	--	CALACS	DrizzlePac 3.9.1	9293	j6jt05011_drz.fits	214456320	26091389	PUBLIC	3	FR656N
26091432	HST	image	j6jt05020	DADS DRZ file - Calibrated combined image ACS/WFC3/WFPC2/STIS	D	mast:HST/product/j6jt05021_drz.fits	SCIENCE	Minimum Recommended Products	DRZ	--	CALACS	DrizzlePac 3.9.1	9293	j6jt05021_drz.fits	214352640	26091432	PUBLIC	3	F814W
106457965	HST	image	iey929020	DADS DRZ file - Calibrated combined image ACS/WFC3/WFPC2/STIS	D	mast:HST/product/iey929020_drz.fits	SCIENCE	Minimum Recommended Products	DRZ	--	CALWF3	3.7.2 (Apr-15-2024)	17194	iey929020_drz.fits	220492800	106457965	PUBLIC	3	F625W
106457966	HST	image	iey929010	DADS DRZ file - Calibrated combined image ACS/WFC3/WFPC2/STIS	D	mast:HST/product/iey929010_drz.fits	SCIENCE	Minimum Recommended Products	DRZ	--	CALWF3	3.7.2 (Apr-15-2024)	17194	iey929010_drz.fits	220492800	106457966	PUBLIC	3	F336W

# Download products into same directory
Observations.download_products(products_hst, flat=True)

Downloading URL https://mast.stsci.edu/api/v0.1/Download/file?uri=mast:HST/product/ibhr01020_drz.fits to ./ibhr01020_drz.fits ...

 [Done]

Downloading URL https://mast.stsci.edu/api/v0.1/Download/file?uri=mast:HST/product/ibhr13030_drz.fits to ./ibhr13030_drz.fits ...

 [Done]

Downloading URL https://mast.stsci.edu/api/v0.1/Download/file?uri=mast:HST/product/ibhr13040_drz.fits to ./ibhr13040_drz.fits ...

 [Done]

Downloading URL https://mast.stsci.edu/api/v0.1/Download/file?uri=mast:HST/product/iey929010_drz.fits to ./iey929010_drz.fits ...

 [Done]

Downloading URL https://mast.stsci.edu/api/v0.1/Download/file?uri=mast:HST/product/iey929020_drz.fits to ./iey929020_drz.fits ...

 [Done]

Downloading URL https://mast.stsci.edu/api/v0.1/Download/file?uri=mast:HST/product/j6jt05011_drz.fits to ./j6jt05011_drz.fits ...

 [Done]

Downloading URL https://mast.stsci.edu/api/v0.1/Download/file?uri=mast:HST/product/j6jt05021_drz.fits to ./j6jt05021_drz.fits ...

 [Done]

Downloading URL https://mast.stsci.edu/api/v0.1/Download/file?uri=mast:HST/product/jbhr01010_drz.fits to ./jbhr01010_drz.fits ...

 [Done]

Downloading URL https://mast.stsci.edu/api/v0.1/Download/file?uri=mast:HST/product/jbhr13010_drz.fits to ./jbhr13010_drz.fits ...

 [Done]

Downloading URL https://mast.stsci.edu/api/v0.1/Download/file?uri=mast:HST/product/jbhr13020_drz.fits to ./jbhr13020_drz.fits ...

 [Done]

Downloading URL https://mast.stsci.edu/api/v0.1/Download/file?uri=mast:HST/product/jbhv02010_drz.fits to ./jbhv02010_drz.fits ...

 [Done]

Table length=11

Local Path	Status	Message	URL
str20	str8	object	object
./ibhr01020_drz.fits	COMPLETE	None	None
./ibhr13030_drz.fits	COMPLETE	None	None
./ibhr13040_drz.fits	COMPLETE	None	None
./iey929010_drz.fits	COMPLETE	None	None
./iey929020_drz.fits	COMPLETE	None	None
./j6jt05011_drz.fits	COMPLETE	None	None
./j6jt05021_drz.fits	COMPLETE	None	None
./jbhr01010_drz.fits	COMPLETE	None	None
./jbhr13010_drz.fits	COMPLETE	None	None
./jbhr13020_drz.fits	COMPLETE	None	None
./jbhv02010_drz.fits	COMPLETE	None	None

Each FITS file has a corresponding filter in the table above under the filter column. To create a color image, we’ll choose three images that overlap coordinates and have different filters.

The following images were picked based on if they overlapped in the AstroView of the MAST Portal.

# Opening three different filters
img1 = fits.open("j6jt05011_drz.fits")
img1_wcs = WCS(img1[1].header)

img2 = fits.open("j6jt05021_drz.fits")
img2_wcs = WCS(img2[1].header)

img3 = fits.open("iey929020_drz.fits")
img3_wcs = WCS(img3[1].header)

Plotting the HST Images#

We’ll now set up a subplot of the three images we chose. The first two images were taken as a pair of images (hence the small whitespace in the center). You can see the overlap in all three images where there’s a fairly consistent cluster of five galaxy sources. While the shapes of these galaxies aren’t very clear in these images, they’ll become more distinct when we create the color image!

# Set up figure
fig = plt.figure(figsize=(15, 8))

# First image
ax1 = fig.add_subplot(1, 3, 1, projection=img1_wcs)
ax1.imshow(img1[1].data, cmap="Greys_r", vmin=0, vmax=2.5, origin="lower")
ax1.set_title(f"{img1[0].header['INSTRUME']}/{img1[0].header['FILTER1']}")
ax1.set_ylabel("Declination")
ax1.set_xlabel("Right Ascension")

# Second image
ax2 = fig.add_subplot(1, 3, 2, projection=img2_wcs)
ax2.imshow(img2[1].data, cmap="Greys_r", vmin=0, vmax=2.5, origin="lower")
ax2.set_title(f"{img2[0].header['INSTRUME']}/{img2[0].header['FILTER1']}")
ax2.set_ylabel("Declination")
ax2.set_xlabel("Right Ascension")

# Third image
ax3 = fig.add_subplot(1, 3, 3, projection=img3_wcs)
ax3.imshow(img3[1].data, cmap="Greys_r", vmin=0, vmax=2.5, origin="lower")
ax3.set_title(f"{img3[0].header['INSTRUME']}/{img3[0].header['FILTER']}")
ax3.set_ylabel("Declination")
ax3.set_xlabel("Right Ascension")

plt.tight_layout()
plt.show()

../../../_images/2c4b994a251287565ea2a85accc5bac5e3b3ae426f1eace5f68928dbbdbf0bd7.png

Colorizing the HST Image of Abell 2199#

In order to create a color image of Abell 2199, we can assign red, green, and blue to each image, then combine the three images. We must choose the image with the largest pixel dimensions, and then project the other images onto it.

# Checking the shape of each image to determine which ones will be mapped onto the other
print(f"Shape of image 1: {img1[1].data.shape}")
print(f"Shape of image 2: {img2[1].data.shape}")
print(f"Shape of image 3: {img3[1].data.shape}")

Shape of image 1: (4239, 4213)
Shape of image 2: (4238, 4212)
Shape of image 3: (4446, 4130)

The third image appears to have the largest dimensions, so we’ll project the first and second images onto the third using reproject. We’ll assign the first image to red, the second to blue, and the third to green.

# image 1 -> red
r, _ = reproject.reproject_interp(img1[1], img3[1].header)

# image 2 -> green
g, _ = reproject.reproject_interp(img2[1], img3[1].header)

# image 3 -> blue
b, _ = reproject.reproject_interp(img3[1], img3[1].header)

Using a ratio of red, blue, and green, we can now make a colorized image using make_lupton_rgb!

image_hst = make_lupton_rgb(r * 3.8, g * 0.2, b * 0.65, Q=4, stretch=0.75)

/opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/astropy/visualization/basic_rgb.py:153: RuntimeWarning: invalid value encountered in cast
  return image_rgb.astype(output_dtype)

# Plotting the colorized image
plt.figure(figsize=(5, 5))

# Ensuring the coordinates are set to the WCS of the third image
ax = plt.subplot(projection=img3_wcs)
ax.imshow(image_hst)

# Zoom in
ax.set_xlim(1400, 2100)
ax.set_ylim(2200, 2900)

ax.set_xlabel("Right Ascension")
ax.set_ylabel("Declination")
ax.set_title("Colorized Image of Abell 2199")
ax.legend()
plt.tight_layout()
plt.show()

/tmp/ipykernel_2138/2518464466.py:15: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.
  ax.legend()
/tmp/ipykernel_2138/2518464466.py:16: UserWarning: Tight layout not applied. The left and right margins cannot be made large enough to accommodate all Axes decorations.
  plt.tight_layout()

../../../_images/f1925ace2a0e81aacbee0dbc1e89f3265a166ea0feb4c99ddba84709d2ce791c.png

End of Tutorial#

Congratulations, you’ve reached the end of this notebook! You’ve learned how to use astroquery.MAST to calculate Hubble’s constant from eBOSS data and make a colorized image from HST data!

Additional Resources#

Additional resources are linked below:

Citations#

If you use data from MAST for published research, please see the following links for information on which citations to include in your paper:

About this Notebook#

Author(s): Natalie Haugen (nhaugen@terpmail.umd.edu) and Julie Imig (jimig@stsci.edu)
Keyword(s): Tutorial, eBOSS, HST, SDSS, galaxies
First published: July 2025
Last updated: July 2025

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