Estimating Hubble's constant from Redshifts and Distances of Type Ia SNae

What is the value of Hubble's constant as found from a linear regression of the redshifts and distances of Type Ia supernovae within a redshift of 0.1?

Background

Hubble's law is a relationship that describes the expansion of the universe by connecting the speed at which galaxies move away from each other with the distance between the two objects. For small distances, Hubble's law is a linear relationship between the velocity of the object and the distance:

$v=H_0 d$ or $z=\frac{H_0}{c}d$

where $z$ is the redshift, $v=cz$ is the velocity of the object, $H_0$ is Hubble's constant. The faster a body moves away from the observer, the more redshifted the light emitted from that body is. Thus, further bodies will move away faster and have a higher redshift. The linear scaling of this redshift increase is determined by Hubble's constant.

Type Ia supernovae provide one possible route for investigating Hubble's law. These objects are standardizable candles, meaning that their distance to the observer can be determined with few parameters.

Literature Reference: Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples

Data

Source: VizieR
GoogleDrive

Column Description:.

Column	Description
zcmb	CMB Frame Redshift
zhel	Heliocentric Redshift
mb	B band peak magnitude (in mB)
e_mb	Error in mb
x1	SALT2 shape (stretch) parameter
e_x1	Error in x1
c	SALT2 color parameter
e_c	Error in c
logMst	$Log_{10}$ Host Stellar Mass

Software setup to run the notebook

Python version used: 3.10.12

We recommend using a conda environment to install the requirements and run the notebook.

Install Conda Conda can be installed from this page: https://conda.io/projects/conda/en/latest/user-guide/install/index.html.
Create a conda environment

conda create --name ast5731_group3_project2 --file requirements.txt

You can change the name of the environment from ast5731_group3_project2 to the one you want.

Install Jupyter notebook from this page: https://jupyter.org/install
The notebook can be run using by starting the jupyter notebook server

# to start the server
jupyter notebook

Navigate to the file and run the Group3_Project2.ipynb

Team

_{Hari Veeramallu}

_{Jacynda Alatoma}

_{Nicholas Kruegler}

_{Daniel Warshofsky}