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# Contents

## Abstract

This paper uses baryonic matter which is composed of baryons. Baryons include subatomic particles such as protons, neutrons, and all objects composed of them (atomic nuclei), however it excludes leptons and electrons. This paper uses baryonic matter and a mathematical relation known as the Tully-Fisher relation (bTFR) to better calculate the H0, which is the hubble constant. The hubble constant is a number that can change with time, but is the ratio of the velocity to the distance of the expansion of the universe. This paper utilizes the baryonic Tully-Fisher relation as a better indicator of distance to better calibrate the Hubble constant H0. The researchers accomplish this by applying it to a variety of databases such as SPARC, and the CosmicFlows-3, which contain thousands of galaxies that they test their procedure on. They find this constant to be roughly 75.1.

## Introduction

The Tully Fisher relation links the rotational velocity of a galaxy to its stellar mass and/or luminosity. It has played a huge role as a key tool to calculate distance. However, this relation does not work for galaxies with a high gas content because this relation does not account for gas. Therefore, the galaxies appear to be a lower mass, and the relation does not work anymore. To combat this, the bTFR will account for the baryonic gas increasing the accuracy by decreasing the scatter. Scatter is essentially portions of the light rays that we measure that are lost to various optical issues. However, the identity of the gas can be deduced using information from the rotational velocity. This combined will help to produce an accurate estimation of the galaxy.

An accurate hubble constant is vital to the calculation of various other values. Therefore, an accurate way to measure it is important. There exist a variety of methods that attempt to measure it such as the Cepheid © calibration, using the tip of the red giant branch (TRGB), cosmic microwave background (CMB) with Planck data and the CDM models, or various other methods. This paper presents the use of a redshift-independent calibration of the bTFR using galaxies from various databases to measure the hubble constant.

## Data

After combing through the data from SPARC, the researchers found a set of 125 galaxies that met their specific parameters. However, the bTFR is dependent upon the luminosity of the galaxy as that measurement is used to calculate the baryonic mass of the galaxy. This luminosity to baryonic mass relation utilizes a mass-to-light ratio established by stellar population models.

Due to the variety of uncertainty that exists in the various relationships used to estimate the mass and from observational uncertainty, the researchers used six different scenarios to account for the uncertainty. The researchers used 30 galaxies and their associated data from the SPARC and 20 galaxies and their associated data from the Ponomaerva CosmicFLows-3 model to establish a baseline comparison by using a maximum likelihood fit model. This method will find a line of best fit through the data and calculate pertinent information for researchers. This helped to establish where the uncertainty in the results can be decreased. This helped with acquiring more accurate values.

This data was then used to find an estimated value of the hubble constant which was then tested using three techniques to validate its credibility. All three techniques showed that the slopes acquired in the data graphing are consistent and valid.

## Results

This study shows that regardless of using the redshift independent C/TRGB distances or the Cosmic Flows-3 velocities when placed through a bTFR, the uncertainty in each sample was identical. The CosmicFlows-3 model and using a maximum likelihood fit model provide the best representation to calculate the hubble constant.

## Conclusions

The bTFR is the best method for empirical correlations of extragalactic astronomy. Other methods involve too many correlations or correlations with too much uncertainty in the measurements. The bTFR uses two variables. The first variable is the rotation velocity, which is measured and calculated with minimal uncertainty and error. The second variable required for the bTFR is the baryonic mass, which when using the near-IR luminosities to determine the stellar mass component of baryonic mass has greatly minimized a large portion of uncertainty. This study presents the use of bTFR to calculate distances required for the calculator of the hubble constant. Models like the CMB model do not measure the hubble constant directly, but merely predict the constant given certain parameters established by the CDM. This explains why measured values of the hubble constant do not align with those predicted by models like CMB. More data will help to improve the slope and zero point on a graph, which essentially boils down to a more precise measurement of distance and thus a more precise hubble constant.