Effects of electromagnetic fluctuations in plasmas on solar neutrino fluxes

2025-08-18 0 0 209.36KB 13 页 10玖币

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arXiv:2211.00907v1 [astro-ph.SR] 2 Nov 2022

Eﬀects of electromagnetic ﬂuctuations in plasmas on solar neutrino ﬂuxes

Eunseok Hwanga, Dukjae Jangb,∗, Kiwan Parka, Motohiko Kusakabec,d, Toshitaka Kajinoc,d,e, A. Baha Balantekinf,d,

Tomoyuki Maruyamag,d, Youngshin Kwona, Kyujin Kwakh, Myung-Ki Cheouna,c,d

aDepartment of Physics and OMEG Institute, Soongsil University, Seoul 156-743, Republic of Korea

bCenter for Relativistic Laser Science, Institute for Basic Science (IBS), Gwangju 61005, Republic of Korea

cSchool of Physics and International Research Center for Big-Bang Cosmology and Element Genesis, Beihang University, Beijing 100083, China

dNational Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

eThe University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan

fPhysics Department, University of Wisconsin-Madison,1150 University Avenue, Madison, Wisconsin 53706, USA

gCollege of Bioresource Sciences, Nihon University, Fujisawa 252-0880, Kanagawa-ken, Japan

hDepartment of Physics, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea

Abstract

We explore the eﬀects of electromagnetic (EM) ﬂuctuations in plasmas on solar neutrino ﬂuxes exploiting the ﬂuctuation-

dissipation theorem. We ﬁnd that the EM spectrum in the solar core is enhanced by the EM ﬂuctuations due to the

high density of the Sun, which increases the radiation energy density and pressure. By the EM ﬂuctuations involving

the modiﬁed radiation formula, the central temperature decreases when the central pressure of the Sun is ﬁxed. With a

help of the empirical relation between central temperature and neutrino ﬂuxes deduced from the numerical solar mod-

els, we present the change in each of the solar neutrino ﬂuxes by the EM ﬂuctuations. We also discuss the enhanced

radiation pressure and energy density by the EM ﬂuctuations for other astronomical objects.

Keywords: Electromagnetic ﬂuctuation, solar neutrino ﬂuxes, stellar evolution

1. Introduction

Astrophysical plasmas in nucleosynthesis sites have been generally presumed to be ideal, implying that the ther-

monuclear reaction rate is determined by equilibrium velocity distribution and nuclear reaction cross sections for bare

nuclei. However, the collective motions and collisions of constituent particles in astrophysical plasmas could aﬀect

the electromagnetic interactions in the nucleosynthesis, which motivated studies of impact of astrophysical plasmas

on nucleosynthesis yields. A typical example is electrons near an ion screen the nuclear charge enhancing the nuclear

reaction rates [1]. Such screening eﬀects on thermonuclear reaction rates in plasmas have been widely discussed for

the solar interior [2, 3, 4] and the early universe [5, 6, 7, 8, 9, 10]. Also, studies on big bang nucleosynthesis (BBN)

with Tsallis distribution function involving soft energy spectra [11] have suggested a partial solution to the primordial

lithium problem [12, 13, 14]. A solution has been proposed by a transient model of the photon distribution function

during BBN, which has speculated that the transition is related to the plasma properties [15].

∗Corresponding author

Email address: djjang2@ibs.re.kr (Dukjae Jang)

Preprint submitted to November 3, 2022

In this paper, we mainly discuss another notable phenomenon in a plasma: the electromagnetic (EM) ﬂuctuations.

Thermal ﬂuctuations exist even in a homogeneous plasma maintaining the thermal (or nearly thermal) equilibrium.

In other words, the root mean square of EM ﬁelds may manifest themselves even without external ﬁelds. The level

of EM ﬂuctuations can be evaluated by the ﬂuctuation-dissipation theorem [16]. Pioneering works have studied the

EM ﬂuctuations near the zero-frequency in cold and warm plasmas [17, 18, 19], and subsequently one has discussed

the implication of EM ﬂuctuations on the origin of cosmological magnetic ﬁelds [20], radiation spectrum in the BBN

epoch [21], and nuclear reaction rates by highly damped modes in the stellar interior [22].

Since the eﬀect of EM ﬂuctuations is more dominant under the high density and low temperature conditions, we

expect that the modiﬁcation of the radiation spectrum by EM ﬂuctuations becomes signiﬁcant in the core of the Sun

rather than in the early universe studied previously in the literature [17, 18, 19]. Exploiting the ﬂuctuation-dissipation

theorem, we ﬁnd that the radiation spectrum is signiﬁcantly enhanced in the solar core which has higher density.

This implies that the energy of photons in the solar core could be larger at a given temperature than the blackbody

spectrum, which aﬀects the pressure and energy density of the radiation in the solar core where Planck distribution

is adopted in the standard treatment. In the core, if the pressure is kept as a constraint, the enhanced EM spectrum

causes a decrease in the temperature. On the other hand, when the temperature is retained, the total pressure including

the EM ﬂuctuations is higher than the pressure in the standard solar model (SSM).

If the plasma temperature changes due to the EM ﬂuctuations, it aﬀects the nuclear reaction rates in the Sun,

and also the production of the solar neutrinos. Then, the solar neutrino ﬂuxes, especially for the uncertain CNO

neutrino ﬂuxes, would diﬀer from the prediction in the SSM. In this paper, adopting the empirical relation between

the solar neutrino ﬂuxes and the central temperature of the SSM [23], we estimate the feasible change in the solar

neutrino ﬂuxes resulting from the changed central temperature aﬀected by the EM ﬂuctuations. The result based on the

empirical relation would provide a guidance to study the EM ﬂuctuation eﬀects on the Sun, although a rigorous study

requires solving the stellar structure equations. We also discuss the eﬀects of EM ﬂuctuations on other astronomical

objects and provide the modiﬁed radiation pressure in a wide parameter space of density and temperature.

The rest of this paper is organized as follows. In section 2, we introduce the formalism of the ﬂuctuation-

dissipation theorem for EM ﬁelds and show the distorted EM spectrum in the solar core. In section 3, using the

EM spectrum, we derive a formula for the modiﬁed radiation pressure in the Sun. Then, we present the changes

in central temperature and solar neutrino ﬂuxes. Finally, in section 4, we discuss the eﬀects of the EM ﬂuctuations

on stellar evolution and summarize our conclusion. We adopt the natural units for all equations in this paper, i.e.,

~=c≡1.

2. Electromagnetic spectrum by ﬂuctuations

From the ﬂuctuation-dissipation theorem, the ﬂuctuations of magnetic (B) and transverse electric (ET) ﬁelds are

derived as [16],

DB2Ek,ω

8π=2

exp[ω/T]−1 k

ω!2Im ǫT(ω, k)

ǫT(ω, k)−k

ω2

2,(1)

DE2

TEk,ω

8π=2

exp[ω/T]−1

Im ǫT(ω, k)

ǫT(ω, k)−k

ω2

2,(2)

where ω,k, and Tdenote the angular frequency, wavevector, and temperature, respectively. The transverse dielectric

permittivity ǫT(ω, k) is obtained from the ﬁrst order Vlasov equation with Bhatnagar-Gross-Krook (BGK) collision

term, which is given as [19]

ǫT(ω, k)=1+X

ω2

pα

ω2 ω

√2kvα!Z ω+iηα

√2kvα!,(3)

where ωpα,ηα, and vαare the plasma frequency, collision rate, and thermal velocity of species α, respectively. We

adopt the typical collision frequency for an electron given as ηe=4√2πnee4ln Λ/(3m1/2

eT3/2), where ne,me, and ln Λ

are the number density and mass of electron, and the Coulomb logarithm taken as ln Λ = 17, respectively. We do not

consider the collision frequency for the ion as it is inversely proportional to the mass of the ion. The plasma dispersion

function also known as Fried-Conte function Z(z) is deﬁned as1[24]

Z(z)=1

√πZ∞

−∞

e−t2

t−zdt.(4)

In fact, a more precise approach requires the Boltzmann collision term involving the integration of all relevant colli-

sions over the momentum space. However, for simplicity, we adopt the BGK collision term as used in Refs. [17, 19,

20, 21].

Integrating Eqs. (1) and (2) over k, the EM spectrum is obtained as follows:

S(ω)=Z



DB2Ekω

8π+DE2

TEkω

8π





dk.(5)

As shown in Eq. (3), for ω≫ωpα, the real and imaginary parts of ǫT(k, ω) goes to unity and zero, respectively. For

this condition, the terms of the dielectric permittivity in Eqs. (1) and (2) give a Dirac-delta function of the argument

ω2−k2c2for high frequency. Therefore, the EM spectrum at the high frequency region sustains the blackbody shape

satisfying the dispersion relation in free space. In contrast, at the low frequency region of ω.ωpα, a change in

the transverse dielectric permittivity causes a distortion of EM spectrum depending on the plasma temperature and

density. In other words, the collective eﬀects of plasma are signiﬁcant for a low frequency mode with long wavelength.

1We note that references [19, 21] wrote the et2instead of e−t2, which is a typo.

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摘要：

arXiv:2211.00907v1[astro-ph.SR]2Nov2022EﬀectsofelectromagneticﬂuctuationsinplasmasonsolarneutrinoﬂuxesEunseokHwanga,DukjaeJangb,∗,KiwanParka,MotohikoKusakabec,d,ToshitakaKajinoc,d,e,A.BahaBalantekinf,d,TomoyukiMaruyamag,d,YoungshinKwona,KyujinKwakh,Myung-KiCheouna,c,daDepartmentofPhysicsandOMEGInsti...

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Effects of electromagnetic fluctuations in plasmas on solar neutrino fluxes

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