User:Astroriya/Supernova Neutrinos

Supernova neutrinos are astronomical neutrinos produced during core-collapse supernova explosion.

Production Mechanisms
Supernova neutrinos are produced when a massive star collapses at the end of its life to produce a neutron star. The dying star radiates about 99% of its gravitational binding energy through neutrino-burst within 10 seconds.

The reaction is powered by weak nuclear forces, where electrons interacts with protons, producing neutrinos and neutrons.

The produced neutrinos are affected by flavor conversions after they thermally decouple from the proto-neutron star. In the neutrino-bulb model, it is assumed that all the neutrinos thermally decouple at a single sharp surface close to the surface of the proto-neutron star. . 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.

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

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

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.

Neutrino luminosity is found by following relation :

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

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

The evolution of density operator is given as :

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

The Hamiltonian $$\hat{H}_t(E,r) $$ covers vacuum oscillations, charged-current interaction of neutrinos from electrons and protons as well as neutrino-neutrino interactions.

Characteristics
Neutrinos are small charge-less particles with low interaction probability. During a supernova, neutrinos and antineutrinos of all flavors are emitted. The average energy of supernova neutrinos is of the order 10 MeV. The low interaction probability combined with low energy, makes their observation difficult. On the Earth, they have been detected as ~ 10 second long burst.

Neutrino luminosity during a supernova is approximately $$10^{52} ergs $$ $$s^{-1}$$ which is about 100 times its optical luminosity.

Effects
During a supernova, neutrinos are produced in enormous numbers inside the core. Therefore, they have fundamental influence on the collapse and supernova explosions.

During the collapse of a massive star (masses greater than 6-8 solar mass), a shock wave is generated due to bouncing out of the materials falling onto the highly compressed inner core. This shock wave may lead to an explosion, but the supernova simulations implies that it is not always energetic enough. Neutrino heating is predicted to be responsible for energization of the supernova shock wave, driving it outward which ultimately cause the supernova explosion. Phenomenon like neutrino oscillations in dense matter is being researched upon to understand the flux and flavor content of the neutrinos behind the shock wave, whose knowledge is important to implement the neutrino-driven mechanism in computer simulations of supernovae.

Further, neutrinos might be responsible for the nucleosynthesis of heavier elements, and may have their own gravitational waves.

Detection Mechanism
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 charged current weak interaction, where an electron antineutrino interaction on a proton produces a positron and a neutron:

$$\bar\nu_e + p \rightarrow  e^+ + n $$

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

Experiments
Detectors capable of detecting neutrinos from supernovae has been shown in following table. With current sensitivities, we expect to witness thousands of neutrino-events for a galactic core-collapse supernova. Large-scale detectors such as Hyper-Kamiokande or IceCube themselves can detect up to $$10^{5}$$ events. Sadly, there have not been any galactic supernova in the Milky Way in last 120 years, despite the expected rate of 0.8-3 per century. 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.

SN1987A
Supernova neutrinos have been observed only once yet. They arrived from the collapse of a blue supergiant star known as Sanduleak -69° 202, located in the Large Magellanic Cloud outside our Galaxy, 51 kpc away. The event called SN1987A, happened in 1987. About $$10^{58}$$ lightweight weakly-interacting neutrinos were produced, carrying away almost all of the energy of the supernova. Two kiloton-scale water Cerenkov detectors, Kamiokande II and IMB, detected 20 neutrino-events between them over a period of about 13 seconds. In addition the Baksan scintillator detector 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. The SN1987A neutrino data, although sparse, confirmed the salient features of basic supernova model of gravitational collapse and associated neutrino emission. It put strong constraints on neutrino properties such as charge and decay rate. 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.

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. Their existence was predicted even before the observation of supernova neutrinos. DSNB can be used to study physics on cosmological scale, such as the cosmic star formation rate. 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. The theoretically estimated flux is only half this value. 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. Due to their weakly interacting nature, the neutrino signals from a galactic supernova can give information about the physical conditions at a very early stages of core collapse, which is inaccessible to other kinds of astronomy. In fact, an optical supernova display may never be seen at all for a given core collapse as some collapsing stars may never blow up into supernovae, or the star may live in an obscured region of the galaxy.

Due to their weakly interacting nature, neutrinos emerge out promptly after collapse, whereas the photon-signal may take hours or days to emerge from the stellar envelope. Therefore, a supernova will be observed foremost in neutrino observatories. For example, neutrino signals were received about 20 hours before the first visual observation of SN1987A. 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.

Supernova neutrinos propagate through the dense turbulent interior of supernova where the flavor evolution is dominated by collective behavior associated with neutrino-neutrino interactions. Therefore, they offer a unique opportunity to examine neutrino flavor mixing under high-density conditions.