# Traveling the Heart of a Supernova Explosion via a Dynamic Stream of Neutrinos

## What is a Supernova?

__ Type II Supernova__e (

__), triggered by the__

**SN**__of__

**Gravitational Collapse**__s, emit a__

**Massive Star****substantial portion**of their

**energy**in the form of

__s (__

**Neutrino**__Figure 1__). These

**elusive particle**s, constituting what is known as the

**Supernova Relic Neutrino**(

**SRN**)

**background**[

__1__], could potentially be detected by large

**underground neutrino detectors**, such as the

__and__

**Super - Kamiokande**__(__

**Sudbury Neutrino Observatory**__)__

**SNO****detectors**.

The **primary objective** of these detectors is to capture **traces** of this **elusive SRN background**. The **SN II Rate Evolution** [__2__], coupled with the **Metal Enrichment History** [__3__], forms the **basis** of predicting the **SRN Flux**. By relating observations of __ Star Formation__ and metallicity enrichment, one establishes a

**robust framework**for estimating the supernova rate and, consequently, the SRN flux.

**Figure 1**. Representation of an Exploiting Supernova

## The Photophysical Fingerprint of Neutrinos

The **composition** of **neutrino**s reaching **Earth**, originating from **past supernovae**, relies on **several factors**. **First**, it hinges on the **differential flux** of neutrinos **per unit energy interval emitted** by each supernova. **Secondly**, it is influenced by the **distribution** of **supernova rate**s with respect to __ Redshift__. Additionally, it's contingent upon a

__, typically characterized by__

**Friedmann-Robertson-Walker Cosmology****parameters**such as the

__,__

**Hubble Parameter**__and the__

*H*_{0}**Matter Density Parameter**, [math]\small{\Omega_{0}}[/math] (further information in

**, Section 4).**

__here__The __ Spectrum__ (

__Figure 2__) of

**neutrinos emitted**from a supernova is characterized by a

__with__

**Fermi-Dirac Distribution****zero**

__, normalized to the__

**Chemical Potential****total energy emitted**by the supernova. For each

**Neutrino Specie**s, [math]\small{\nu}[/math], the

**Neutrino Luminosity**,

**L**[math]\small{{_{\nu}}^{S}}[/math]([math]\small{\epsilon}[/math]) can be defined as:

**Equation 1**. Neutrinos Luminosity Equation

where the apex [math]\small{S}[/math] stands for "**Spectrum**"; [math]\small{\epsilon}[/math] is the **Neutrino Species Energy ** for a singluar neutrino; [math]\small{E_{\nu}}[/math] and [math]\small{T_{\nu}}[/math] are, in the order, the **Neutrino Species Total Energy** and the **Temperature Parameter ** derived by the neutrinosphere during the collapse, and both dependent on the __ Progenitor Mass__ of the supernova. However, obtaining the

__(__

**Initial Mass Function**__)-averaged neutrino flux is simplified because [math]\small{T_{\nu}}[/math] doesn't vary significantly with the progenitor mass.__

**IMF**Assuming that the **Supernova Rate**, [math]\small{N_{SN}}[/math]([math]\small{z}[/math]) follows the **Metal Enrichment Rate**, it can be expressed like below.

**Equation 2**. The form of Supernova Rate

[math]\Large{z}[/math] is the **Redshift** value; [math]\large{Z}[/math] is __ Atomic Number__ of a chemical element; [math]\large{\dot{\rho}_{Z} (z)}[/math] represents the

**Metal Enrichment Rate**per unit comoving volume and [math]\large{\langle M_{Z} \rangle}[/math] denotes the

**Average Yield**of

__s per supernova.__

**Heavy Element**To track the metal enrichment rate, one can assume a **constant supernova rate** at **higher redshifts** ([math]\small{z > 1} [/math]) due to the **limited knowledge** of high-redshift evolution. This **assumption** is supported by various independent studies showing **consistent evolutionary patterns**.

## Looking for Elusive Particles!

Detecting relic neutrinos from supernovae poses **significant challenges**, particularly across various energy ranges. **SuperKamiokande**, for instance, has an **observable energy window** estimated to span from 19 to 35 MeV. However, below 10 MeV, the contribution from neutrinos generated by reactors and those from Earth is expected to **overshadow** any relic neutrino signal. Beyond 10 MeV but still below the observable window, background sources include **solar neutrinos**, **external radiation**, and events induced by **Cosmic** - **Ray** __ Muon__s [

__4__] within the detector.

**Atmospheric neutrinos **become the **primary background** above 19 MeV. As energy surpasses approximately 35 MeV, the **rapidly diminishing flux** of relic neutrinos becomes **less significant** compared to atmospheric neutrinos. The **Efficiency** [__5__] of this detector within the observable energy window is assumed to be **100%**.

Given the **detector's specifications**, the **predicted event rate** at SuperKamiokande for SN relic neutrinos can be calculated, and it is suggested being a peaked distribution. The flux at the detector is assessed across **various energy ranges**, with considerations for **background sources** and **detector capabilities**.

**Figure 2**. The Rainbow is an example of Electromagnetic Spectrum including Radiation in the Visible Energy Window

## A Troublesome Research

One can present **conservative upper bounds** on the expected SRN event rates, indicating challenges in detecting these elusive particles. Despite **advancements** in detector technology, the __ Signal - to - Background Ratio__ remains a

**significant obstacle**. Future research directions, including refining metal enrichment history models and exploring alternative detection strategies will be discussed.

- ScienceDirect. "Discovery potential for supernova relic neutrinos with slow liquid scintillator detectors
"
__https://www.sciencedirect.com/science/article/pii/S0370269317302629__ - STScl. "The Evolution of the Cosmic Supernova Rates"
__https://www.stsci.edu/files/live/sites/www/files/home/jwst/about/history/design-reference-mission-drm/_documents/drm11.pdf__ - Springer. "Metal enrichment history of the proto-galactic interstellar medium"
__https://link.springer.com/article/10.1023/A:1019527307631__ - PhysicsOpenLab.org. "Cosmic Ray Muons & Muon Lifetime
"
__https://physicsopenlab.org/2016/01/10/cosmic-muons-decay/__ - KNS.org. "Detection Efficiency Calculation and Evaluation for Condenser Off-gas
Radiation Monitoring System
"
__https://www.kns.org/files/pre_paper/45/21S-123-%EA%B9%80%EC%9B%90%EA%B5%AC.pdf__