Neutrino magnetohydrodynamic instabilities in presence of two-avor oscillations Debjani Chatterjee1Amar P. Misra2yand Samiran Ghosh1z 1Department of Applied Mathematics University of Calcutta Kolkata 700 009 India

2025-05-02 0 0 420.27KB 9 页 10玖币

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Neutrino magnetohydrodynamic instabilities in presence of two-ﬂavor oscillations

Debjani Chatterjee,1, ∗Amar P. Misra,2, †and Samiran Ghosh1, ‡

1Department of Applied Mathematics, University of Calcutta, Kolkata 700 009, India

2Department of Mathematics, Siksha Bhavana, Visva-Bharati University, Santiniketan-731 235, India

The inﬂuence of neutrino ﬂavor oscillations on the propagation of magnetohydrodynamic (MHD)

waves and instabilities is studied in neutrino-beam driven magnetoplasmas. Using the neutrino

MHD model, a general dispersion relation is derived which manifests the resonant interactions of

MHD waves, not only with the neutrino beam, but also with the neutrino ﬂavor oscillations. It is

found that the latter contribute to the wave dispersion and enhance the magnitude of the instability

of oblique magnetosonic waves. However, the shear-Alfv´en wave remains unaﬀected by the neutrino

beam and neutrino ﬂavor oscillations. Such an enhancement of the magnitude of the instability of

magnetosonic waves can be signiﬁcant for relatively long-wavelength perturbations in the regimes

of high neutrino number density and/or strong magnetic ﬁeld, giving a convincing mechanism for

type-II core-collapse supernova explosion.

I. INTRODUCTION

Neutrinos are generally produced due to very high ex-

plosions in the core of massive stars and can have signif-

icant impact on the cooling of white dwarfs and neutron

stars [1, 2]. The most apparent source of neutrinos is the

Sun, where they are produced due to the simplest nuclear

fusion reaction in which two protons combine to form a

deuterium nucleus with the emission of a positron and a

neutrino. All other complex reaction processes that lead

to heavier elements can also produce neutrinos which get

away from the Sun at the speed of light in vacuum. Neu-

trinos are also produced by cosmic rays hitting up nu-

clei in the Earth’s atmosphere, similar to the reactions

of terrestrial high-energy particle accelerators. Such nu-

clear reactions result not only in electron neutrinos as

in the Sun, but also in two other ﬂavors, namely, muon

neutrinos and tau neutrinos–all of which were detected

by super-Kamiokande detector [3]. On the other hand,

the neutrino-producing fusion reactions in stars do not

release energy in the form of light or heat that could pro-

vide pressure to stop gravitational collapse of the stellar

core. So, the collapse occurs and it continues until the

density in a nucleus is close to that in the core and sud-

denly a massive explosion occurs in producing all ﬂavors

of neutrinos. Such a sudden and higher optical gleam is

known as a core-collapse supernova, e.g., SN1987A [4].

Although the interaction between neutrinos and matter

is weak, in the gamma-ray bursts of a supernova explo-

sion, the energy emitted from neutrinos can be very high

(almost 99% of the gravitational binding energy of col-

lapsing stars) and the intensity can be more than 1028

W cm−2. Furthermore, in the ﬁrst few seconds of explo-

sion, the neutrino burst that originates from the core of

supernova is a source of free energy to drive collective os-

cillations and instabilities which may lead to the revival

∗chatterjee.debjani10@gmail.com

†apmisra@visva-bharati.ac.in; apmisra@gmail.com

‡sran g@yahoo.com

of a stalled supernova shock [5, 6]. Typically, neutrinos

produced in the solar atmosphere or in the core-collapse

of stars have energies ranging from 1 to 30 MeV. How-

ever, recent observations with IceCube data have indi-

cated that neutrinos can have energies more or less 1015

eV [3, 7]. Such high-energy neutrinos are expected to be

produced in astrophysical objects via the interactions of

highly relativistic charged particles (Cosmic rays) with

either target particles or photons [3].

Neutrinos produced from diﬀerent sources can play sig-

niﬁcant roles in the formation of galaxies, galaxy clusters,

and various coherent structures at large scales. Apart

from their possible gravitational interactions, neutrinos

interact weakly with matter and thus are very impor-

tant in astrophysics. In regions where other particles get

trapped or move through slow diﬀusion processes, neutri-

nos can still escape from them and thus connect those of

matter without being detached from each other. In very

hot or dense astrophysical objects, the emission of neu-

trinos can be an important energy-loss mechanism. The

energy transfer rate can be faster and very eﬃcient since

neutrinos have almost zero mass and can travel at rel-

ativistic speeds. Furthermore, since neutrinos produced

in the Sun can be detected at the Earth, they are use-

ful to study nuclear reactions that can occur in the core

of massive stars. Also, because neutrinos are electrically

neutral like photons and hence uninﬂuenced by the strong

magnetic ﬁelds, they tend to move back to the creation

regions, and thus can provide useful information about

the regions where particle creation and acceleration take

place in the Universe. For more information about roles

of neutrinos, see, e.g., [8].

In stellar environments, the collective plasma eﬀects

can remarkably modify the production rate of neutrinos,

e.g., the decay of photons and plasmons into neutrino

pairs, which is the dominant neutrino emission mech-

anism at high-density plasmas. The neutrino emission

can also be possible in dense hot matter due to electron-

positron annihilation [9], in ultra-relativistic plasmas due

to positron and plasmino annihilation [10]. The neutrinos

interacting with plasmas play key roles in many astro-

physical situations including supernova explosions. Such

arXiv:2210.09590v2 [physics.plasm-ph] 4 Mar 2023

interactions not only reform the neutrino ﬂavor oscilla-

tions (in which neutrinos oscillate from one ﬂavor state

to another) and initiate resonant interactions of diﬀer-

ent ﬂavors [11–13], but also produce an induced eﬀective

neutrino charge as well as induced electric and magnetic

ﬁelds that can lead to collective plasma oscillations and

an enhancement of collision cross sections. In this con-

text, several authors have studied the neutrino-plasma

interactions considering neutrino ﬂavor oscillations, See,

e.g., [14–17]. To discuss a few, in Ref. [16], it has

been shown that the two-ﬂavor neutrino-plasma oscilla-

tion equations admit an exact analytic solution for arbi-

trarily chosen electron neutrino populations. A hydrody-

namic model has been introduced by Mendon¸ca and Haas

[17] to study the plasma and neutrino ﬂavor oscillations

in turbulent plasmas.

In other contexts, the neutrino-plasma coupling in

magnetized plasmas can lead to diﬀerent types of hy-

drodynamic instabilities which may inﬂuence the neu-

trino beam transport by improving the properties of the

background medium. Several studies have focused on

the physics of collective neutrino-plasma interactions in

diﬀerent astrophysical situations [6, 18, 19]. Also, the

parametric instabilities in intense neutrino ﬂux and col-

lective plasma oscillations have been studied by Bingham

et al. [5]. Furthermore, the generation of neutrino-beam

driven wakeﬁelds [20], neutrino streaming instability [21–

23], and neutrino Landau damping [22] have been stud-

ied in diﬀerent contexts. The latter eﬀect can be imple-

mented to the cooling process of strongly turbulent plas-

mas. Furthermore, it has been shown that neutrinos can

contribute to the generation of both the inhomogeneities

and magnetic ﬁelds in the early universe [24, 25].

Recently, Haas et al. [26] proposed a neutrino MHD

(NMHD) model in magnetoplasmas by considering the

neutrino-plasma interactions as well as the coupling be-

tween MHD waves and neutrino ﬂuids. This model was

studied for the propagation of magnetosonic waves in a

speciﬁc geometry, i.e., when the propagation direction

is perpendicular to the external magnetic ﬁeld. How-

ever, the theory was later advanced with an arbitrary

direction of propagation [27]. Motivated by these works,

the inﬂuence of intense neutrino beams on the hydrody-

namic Jeans instability has been studied by Prajapati in

a magnetized quantum plasma [28]. It turns out that the

NMHD model has become very useful to establish con-

nections between various astrophysical phenomena and

neutrino-plasma coupling processes in magnetized media.

In this work, we aim to advance the previous theory

of NMHD waves [27] by considering (in addition to the

neutrino beam eﬀects) the inﬂuence of two neutrino fa-

vor (electron- and muon-neutrinos) oscillations on the

neutrino-beam driven MHD waves and instabilities. We

show that the two-ﬂavor oscillations, not only resonantly

interact with the oblique magnetosonic wave, but can

have a signiﬁcant contribution to the growth rate of in-

stability.

The paper is organized as follows: In Sec. II, we de-

scribe the NMHD model, which is coupled to the dynam-

ics of two neutrino ﬂavors, namely, the electron-neutrino

and muon-neutrino. Using the perturbation analysis, a

general linear dispersion relation is derived in Sec. III

to show the coupling of MHD waves with the resonant

neutrino beam and the resonant neutrino ﬂavor oscilla-

tions. The instability growth rates for both the fast and

slow magnetosonic waves are obtained in Sec. IV, and

analyzed numerically in Sec. V. Finally, Sec. VI is left

for concluding remarks.

II. PHYSICAL MODEL

We consider a homogeneous magnetized system com-

posed of electrons and ions, as well as the neutrino beams

of electron neutrinos and muon neutrinos. We also as-

sume that the ﬂuid descriptions for both the plasma elec-

trons and ions, and the neutrino beams are valid for the

length scale of the order of electron skin depth and the

time scale of the order of ion gyroperiod. In the NMHD

description, the continuity and momentum equations for

the MHD ﬂuids read [27]

∂ρm

∂t +∇ · (ρmU)=0,(1)

∂U

∂t +U· ∇U=−V2

s∇ρm

ρm

+(∇ × B)×B

µ0ρm

+Fν

,(2)

where ρm=mene+mini≈nmi(with ne=ni=n)

is the mass density, U= (meneue+miniui)/(mene+

mini)≈(meue+miui)/miis the plasma velocity, µ0

is the permeability of free space, Vs=pkBTe/miis

the ion-acoustic velocity, and Fνis the neutrino-plasma

(electroweak) interaction force. Here, me(i)denotes the

electron (ion) mass, ne(i)the electron (ion) number den-

sity, ue(i)the electron (ion) ﬂuid velocity, Bis the mag-

netic ﬁeld, Teis the electron temperature, and kBthe

Boltzmann constant. In addition, the equation for the

magnetic ﬂux modiﬁed by the electroweak force is given

∂B

∂t =∇ × U×B−Fν

e,(3)

where eis the elementary charge, Fν=√2GF(Eν+U×

Bν) with GFdenoting the Fermi coupling constant and

Eν(Bν) the eﬀective electric (magnetic) ﬁeld induced by

the weak interactions of neutrinos with plasmas, given

by,

Eν=−∇Ne−1

∂

∂t (Neve),(4)

Bν=1

c2∇ × (Neve).(5)

Here, Ne(ve) denotes the number density (velocity) of

electron neutrinos. For a coherent neutrino beam with

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Neutrinomagnetohydrodynamicinstabilitiesinpresenceoftwo-avoroscillationsDebjaniChatterjee,1,AmarP.Misra,2,yandSamiranGhosh1,z1DepartmentofAppliedMathematics,UniversityofCalcutta,Kolkata700009,India2DepartmentofMathematics,SikshaBhavana,Visva-BharatiUniversity,Santiniketan-731235,IndiaTheinuenceofne...

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Neutrino magnetohydrodynamic instabilities in presence of two-avor oscillations Debjani Chatterjee1Amar P. Misra2yand Samiran Ghosh1z 1Department of Applied Mathematics University of Calcutta Kolkata 700 009 India.pdf

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Neutrino magnetohydrodynamic instabilities in presence of two-avor oscillations Debjani Chatterjee1Amar P. Misra2yand Samiran Ghosh1z 1Department of Applied Mathematics University of Calcutta Kolkata 700 009 India

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