# Supernova Neutrinos

Supernova neutrinos are neutrinos produced during core-collapse supernova explosion[1]. They carry away almost all of the energy of the dying star as a burst in tens of seconds[2]. They have fundamental influence of supernova. In fact, the neutrino heating is believed to be a critical factor in the supernova explosion.

Neutrinos are generated within the core of the supernova in all the flavors. Therefore, they offer a good natural-laboratory to study neutrino-oscillation in dense matter. However, despite the presence of numerous kiloton-scale detectors, is the only detected event of supernova neutrinos till date[3]. This is because of low cross-sectional area of interaction of neutrinos. Nevertheless, physicists are optimistic that their future observation would be helpful in shedding the lights on various astrophysical and particle physics phenomenon.

## Properties

Supernova neutrinos are produced when a massive star collapses at the end of its life to produce a neutron star.[4] Electrons interacts with protons through weak nuclear forces, producing neutrinos and neutrons.[5] During a supernova, neutrinos and antineutrinos of all flavors are emitted[6]. About 99% of gravitational binding energy of the dying star is emitted as neutrinos[2]. Therefore, neutrino luminosity is about 100 times the optical luminosity of a supernovae.[4] Typically, the neutrino luminosity is of order of $10^{52} ergs$ $s^{-1}$[7].

The average energy of supernova neutrinos is of the order 10 eV[8]. The low interaction probability combined with low energy, makes their observation difficult. On the Earth, they have been detected as ~ 10 second long bursts.[9]

During a supernova, neutrinos are produced in enormous numbers inside the core[10]. Therefore, they have fundamental influence on the collapse and supernova explosions.[11] Neutrino heating is predicted to be responsible for energization of the supernova shock wave, which is otherwise found from simulations, to not be energetic enough for an explosion. Thus, neutrinos are the ultimate cause of a supernovae explosion.[10] Furthermore, neutrinos might be responsible for the nucleosynthesis of heavier elements, and may have their own gravitational waves.[10]

## Neutrino Oscillation

The knowledge of flux and flavor content of the neutrinos behind the shock wave is important to implement the neutrino-driven heating mechanism in computer simulations of supernova explosions.[1] Therefore, neutrino oscillations in dense matter is an active field of research[12].

Neutrinos undergo flavor conversions after they thermally decouple from the wiktionary:proto-neutron_star#:~:text=proto-neutron_star_(plural_proto-neutron_stars)_(stars)_the_degenerate,emergence_after_a_supernova_as_a_neutron_star.|proto-neutron star. In the neutrino-bulb model, it is assumed that the decoupling happens at a single sharp surface near the surface of the star.[13]. Also, the neutrinos travelling in different directions are assumed to travel same path-length in reaching a certain distance R from center. This is known as single angle approximation, which along with spherical symmetricity of supernova, allows us to treat neutrinos emitted in same flavor as an ensemble and describe their evolution only as a function of distance[14].

Density operator for neutrinos on the surface of proto-neutron star is given as[14]:

$\hat{\rho}_t(E,R) = \sum_{\alpha=e, \mu, \tau} \frac{L_{\nu_\alpha}e^{\frac{-t}{\tau}}}{\langle E_{\nu_\alpha}\rangle}f_{\nu_\alpha}(E) |\nu_\alpha \rangle \langle \nu_\alpha|$

Here, $L_{\nu_\alpha}$is initial neutrino luminosity which drop exponentially. Assuming decay time by $\tau$, total energy emitted per unit time for a particular flavor can be given by $L_{\nu_\alpha}e^{\frac{-t}{\tau}}$. $\langle E_{\nu_\alpha}\rangle$ represents average energy. Therefore, the fraction gives the number of neutrinos emitted per unit time in that flavor. $f_{\nu_\alpha}(E)$ is normalized energy distribution for corresponding flavor.

The same formula holds for antineutrinos too[14].

Neutrino luminosity is found by following relation[14]:

$E_B = 6 \times \int_0^\infin L_{\nu_\alpha} e^{-t/\tau}dt$

The integral is multiplied by 6 because the released binding energy is divided equally between the 3 flavors of neutrinos and 3 of antineutrinos[14].

The evolution of density operator is given as[14]:

$\frac{d}{dr}\hat{\rho}_t(E,r) = -i[\hat{H}_t(E,r),\hat{\rho}_t(E,r)]$

The Hamiltonian $\hat{H}_t(E,r)$ covers vacuum oscillations, charged-current interaction of neutrinos from electrons and protons[15] as well as neutrino-neutrino interactions[16]. Neutrino-neutrino interactions result in collective flavor conversions, which are important only when interaction frequency exceeds vacuum oscillation frequency. Typically, they become negligible after a few hundred kilometers from the center, after which MSW resonances can describe the neutrino evolution[15].

## Detection

### Detection Mechanism

Neutrino Scintillation detectors with large fiducial volume have been built to detect Supernova neutrinos, which use the inverse beta decay reaction for the detection. The reaction is a Weak interaction#Charged-current interaction|charged current weak interaction, where an electron antineutrino interaction on a proton produces a positron and a neutron:[17]

Neutron goes undetected but the positron from this reaction, which retains most of the energy of the incoming neutrino[4], produces a cone of Cerenkov light in the water which is detected by photomultiplier tubes (PMT's) arrayed on the walls of the detector.[18]

### Experiments

Detectors capable of detecting neutrinos from supernovae has been shown in following table[18]. With current sensitivities, we expect to witness thousands of neutrino-events for a galactic core-collapse supernova[19]. Large-scale detectors such as Hyper-Kamiokande or IceCube themselves can detect up to $10^{5}$ events[20]. Sadly, there have not been any galactic supernova in the Milky Way in last 120 years[21], despite the expected rate of 0.8-3 per century[22]. Nevertheless, a supernova at 10 kPc distance will enable detailed study of the neutrino signal, providing unique physics insights. Additionally, the next generation of underground experiments like Hyper-Kamiokande are designed to be sensitive to neutrinos from supernova explosions as far as Andromeda or beyond.[23]

 Radiochemical Homestake experiment,Homestake, SAGE (Soviet–American Gallium Experiment) Cerenkov Super-Kamiokande, Hyper-Kamiokande, SNO+, IceCube Neutrino Observatory Liquid Scintillator LVD, Monopole, Astrophysics and Cosmic Ray Observatory ICARUS, Baksan, Liquid Scintillator Neutrino Detector

### SN1987A

Supernova neutrinos have been observed only once yet. They arrived from the collapse of a blue supergiant star known as Sanduleak -69 202|Sanduleak -69° 202, located in the Large Magellanic Cloud outside our Galaxy, 51 kpc away. The event called SN1987A, happened in 1987[3]. About $10^{58}$ lightweight weakly-interacting neutrinos were produced, carrying away almost all of the energy of the supernova[5]. Two kiloton-scale water Cherenkov detector|Cerenkov detectors, Kamiokande II and Irvine–Michigan–Brookhaven (detector)|IMB, detected 20 neutrino-events between them over a period of about 13 seconds[18]. A smaller detector, Baksan Neutrino Observatory|Baksan Observatory also saw 5 events. Since the normal rate of such low energy events originating on the interior of the detector was about one every week, the odds against these events being a statistical fluke are truly astronomical.[18] The SN1987A neutrino data, although sparse, confirmed the salient features of basic supernova model of gravitational collapse and associated neutrino emission[24]. It put strong constraints on neutrino properties such as charge and decay rate[25]. Future observations of supernova neutrinos will constrain the different theoretical models of core collapse and explosion mechanism by testing them against the direct empirical information from the supernova core[9].

### Diffused Supernova Neutrino Background

Diffuse Supernova Neutrino Background (DSNB) is a cosmic background of (anti)neutrinos formed by the cumulation of neutrinos emitted from the all the past core-collapse supernovae[26]. Their existence was predicted even before the observation of supernova neutrinos[27]. DSNB can be used to study physics on cosmological scale, such as the cosmic star formation rate[28]. They can also give information about stellar dynamics and neutrino properties. Super-Kamiokande has put the observational upper limit on the DSNB flux as $5.5 cm^{-2} s^{-1}$ above 19.3 MeV of neutrino energy[29]. The theoretically estimated flux is only half this value[30]. Therefore, DSNB signal is expected to be detected in near future.

## Significance in physics

Physics potential of a supernova neutrino detection is enormous. Study of supernova neutrinos broaden our understanding of various astrophysical and particle physics phenomenon.

Since supernova neutrinos originates from deep inside the stellar core, they are excellent messenger of the supernova mechanism.[11] Due to their weakly interacting nature, the neutrino signals from a galactic supernova can give information about the physical conditions at the center of core collapse, which would be otherwise inaccessible. Furthermore, they are the only source of information for core-collapse who don't blow into supernova or the supernova present in the dust-obscured region[4].

Due to their weakly interacting nature, neutrinos emerge out promptly after collapse, whereas there may be delay of hours or days before photon-signal emerges out of the stellar envelope. Therefore, a supernova will be observed foremost in neutrino observatories[2]. For example, neutrino signals were received about 20 hours before the first visual observation of SN1987A[5]. Therefore, the coincident detection of neutrino signals from different experiments would provide an early alarm to astronomers to direct telescopes to the right part of the sky to capture the supernova’s light. The Supernova Early Warning System is a project which aims to connect neutrino detectors around the world, and trigger the electromagnetic counterpart experiments in case of sudden influx of neutrinos in the detectors[2].

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