Implications of photon-ALP oscillations in the extragalactic neutrino source TXS 0506056 at sub-PeV energies Bhanu Prakash PantSunanda Reetanjali Moharanaand Sarathykannan S.

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Implications of photon-ALP oscillations in the extragalactic neutrino source TXS

0506+056 at sub-PeV energies

Bhanu Prakash Pant,∗Sunanda, Reetanjali Moharana,†and Sarathykannan S.

Department of Physics, Indian Institute of Technology Jodhpur, Karwar 342037, India.

(Dated: November 28, 2023)

Photon-axion-like particle (ALP) oscillations result in the survival of gamma rays from distant

sources above TeV energies. Studies of events observed by CAST, Fermi-LAT, and IACT have con-

strained the ALP parameters. We investigate the eﬀect of photon-ALP oscillations on the gamma-

ray spectra of the ﬁrst extragalactic neutrino source, TXS 0506+056, for observations by Fermi-LAT

and MAGIC around the IC170922-A alert. We obtain a constraint on the ALP coupling param-

eter gaγ <5×10−11 GeV−1with 95% C.L. when focusing on the ALP mass range 0.1 neV ≤

ma≤1000 neV. Importantly, we study the implications of ALP-γoscillations on the counterpart

γrays of the sub-PeV neutrinos observed from TXS 0506+056. We also show the diﬀuse γ-ray

ﬂuxes and observabilities from ﬂat-spectrum radio quasars, high-synchrotron peaked sources, and

low-intermediate-synchrotron peaked sources, assuming similar gamma-ray emissions as that from

TXS 0506+056.

I. INTRODUCTION

Axion-like particles (ALPs) are pseudoscalar (spin-0)

bosons with very light mass and are potential candi-

dates for dark matter [1, 2]. The axions are also pro-

posed to solve the CP problem in QCD [3, 4]. In the

presence of an external magnetic ﬁeld, ALPs can couple

to photons via two coupling vertices which leads to the

photon-ALP oscillation. In astrophysical environments,

photon-ALP conversion drastically reduces the absorp-

tion of very-high-energy (VHE) photons by extragalactic

background light (EBL) and the cosmic microwave back-

ground (CMB) through pair production above 100 GeV

[5–10].

This increased transparency can modulate and en-

hance the observed γ-ray spectra of the TeV photons

originating from higher-redshift sources using observa-

tions of γ-ray spectra from VHE sources [11–28] to set

stringent constraints on the ALP mass, ma, and cou-

pling constant gaγ . Interestingly, the recent observations

of nearly 18-TeV photons by the Large High Altitude

Air Shower Observatory (LHAASO) with the kilometer-

square area (KM2A) [29] and an astonishing 251-TeV

photon by Carpet-2 [30] from the long gamma-ray burst

GRB 221009A at redshift 0.1505 has motivated the com-

munity to understand the survival of photons at this

energy through ALP-photon oscillation [31, 32]. We

note that the above-mentioned 251-TeV photon observed

by Carpet-2 also has the candidate sources LHAASO

J1929+1745 and 3HWC J1928+178, as reported in Ref.

[33]. Most of these studies focused on photons at energies

observed by the Imaging Atmospheric (or Air) Cherenkov

Telescope (IACT). Observations from the axion ﬂux of

the Sun have also been studied by the CERN Axion Solar

Telescope (CAST), giving the most stringent constraint

∗pant.3@iitj.ac.in

†reetanjali@iitj.ac.in

on the ALP parameters, ma<0.01 eV, gaγ <6.6×10−11

GeV−1[34, 35].

The eﬀect of ALP-photon oscillation at sub-PeV ener-

gies and higher has recently been explored with Galac-

tic diﬀuse gamma rays using High Altitude Water

Cherenkov (HAWC), Tibet AS-γ, and LHAASO events,

resulting in a limit of ma<2×10−7eV, gaγ <2.1×10−11

GeV−1with 95% conﬁdence limit (C.L.) [36], and exclud-

ing gaγ >3.9−7.8×10−11 GeV−1for ma<4×10−7eV

[37] at 95% C.L., respectively. The intrinsic photon ﬂux

would be diﬀerent at these energies than at lower ener-

gies due to the addition of hadronic channels. With the

observations of sub-PeV neutrinos, we may understand

the energetics of the source.

In this work, we investigate the implications of photon-

ALP oscillation for the ﬁrst ever non-Galactic sub-PeV

neutrino source [38] TXS 0506+056 situated at a red-

shift z0= 0.3365 [39]. It was ﬁrst discovered as a ra-

dio source [40] and later as high-energy gamma radia-

tion with space missions, like the Energetic Gamma Ray

Experiment Telescope and Fermi-Large Area Telescope

(Fermi -LAT)[41–43]. On September 22, 2017 (IC170922-

A), the IceCube Neutrino Observatory detected a very-

high-energy ∼290-TeV muon neutrino coinciding with

the direction of a ﬂaring state of TXS 0506+056 [44].

Soon, follow-up observations were performed in various

energy bands by Fermi -LAT (γrays) [45], the Nuclear

Spectroscopic Telescope Array (X rays) [46], and Swift

(X rays, UV, optical) [47], and VHE γ-ray observations

were made by the Major Atmospheric Gamma Imag-

ing Cherenkov Telescopes (MAGIC) [48], High Energy

Stereoscopic System [49], HAWC [50] and Very Ener-

getic Radiation Imaging Telescope Array System [51].

Notably, prior to the IC170922-A alert, this source was

also observed with a neutrino ﬂare, making it a sub-PeV

neutrino source with a signiﬁcance of 3.5σ[52]. However,

there was no signiﬁcant ﬂaring in MeV-GeV gamma rays

during this epoch. A hadronic-originated photon coun-

terpart will contribute to the intrinsic ﬂux at sub-PeV

for such neutrino sources. Hence, TXS 0506+056 is the

arXiv:2210.12652v2 [astro-ph.HE] 27 Nov 2023

candidate source to study the ALP-photon oscillation at

several-TeV to sub-PeV energies.

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

scribe the propagation of photon-ALP beam in an exter-

nal magnetic ﬁeld. In Sec. III we describe the various

magnetic ﬁeld models used for the analysis. In Sec. IV

we discuss the methodology used for data ﬁtting and pre-

dicting the expected γ-ray ﬂux. In Sec. V we describe

the signiﬁcance of the ALP eﬀect in TXS 0506+056 and

its Fermi -LAT analysis. In Sec. VI we discuss the re-

sults for the ALP-γoscillations. This section also in-

cludes the implication of this oscillation for the diﬀuse

gamma-ray ﬂux from TXS 0506+056-like sources. Here

we calculate the diﬀuse gamma-ray ﬂux from sources,

ﬂat-spectrum radio quasars(FSRQs), high-synchrotron

peaked (HSP) sources, and low-intermediate-synchrotron

peaked (LISP) sources, and their future observability.

II. PHOTON-ALP OSCILLATION AND

PROPAGATION IN MAGNETIC FIELDS

The minimal interaction coupling gaγ between photons

of energy E′

γand ALPs in the presence of an external

magnetic ﬁeld Band electric ﬁeld Ehas been proposed

in the literature [5, 53].

A polarized, monoenergetic photon beam propagating

along the ˆ

zdirection in a cold plasma medium with a

homogeneous Bﬁeld along the ˆ

yaxis, has the equation

of motion,

id

dz +E′

γ+M0ψ(z)=0E′

γ≫ma

,(1)

where M0represents the photon-ALP mixing matrix and

ψ(z) = A1(z)A2(z)a(z)Tdenotes the state function.

Here, A1(z) and A2(z) are the photon amplitudes with

linear polarizations along the x and y axis, respectively,

whereas a(z) is the amplitude associated with the ALP

state.

Assuming weak magnetic ﬁelds and E′

γat VHE, the

QED vacuum polarization and Faraday rotation can be

neglected, and the mixing matrix becomes

M0=



∆xx 0 0

0 ∆yy ∆y

aγ

0 ∆y

aγ ∆zz

a

,(2)

where ∆xx = ∆yy =−ω2

pl/2E, ∆zz

a=−m2

a/2E, and

∆y

aγ =gaγγ By/2. Here, ω2

pl is the plasma frequency re-

sulting from the charge-screening eﬀect. The propagation

region of the photon-ALP beam is divided into N subre-

gions. In each region, the probability for photon survival

is calculated. The initial beam state is

ρ(0) = 1

2diag.(1,1,0).(3)

The ﬁnal photon survival probability can be written

as:

Pγγ =T r (ρ11 +ρ22)T(s)ρ(0)T†(s)),(4)

where ρ11 = diag(1, 0, 0) and ρ22 = diag(0, 1, 0) denote

the polarization along the x and y axis, respectively, and

T(s) = T(s3)Gal ×T(s2)Ext ×T(s1)Source is the whole

propagation transfer matrix. Here, the subregions are

the source, the extragalactic medium, and the Milky Way

region.

III. MAGNETIC FIELD MODELS

In this section, we give a brief overview of the magnetic

ﬁeld models used in our calculation.

A. Blazar jet region

We consider the photon-ALP oscillation at the source

in the presence of blazar jet magnetic ﬁeld (BJMF). The

magnetic ﬁeld in the jet region can be modeled with

poloidal (along the jet axis, B∝r−2) and toroidal (trans-

verse to the jet axis, B∝r−1) components. At distances

large enough from the central black hole, the toroidal

component dominates over the poloidal component and

thus the latter can be neglected. We adopt the toroidal

magnetic ﬁeld strength Bjet(r) given by [54, 55]:

Bjet(r) = Bjet

0r

rV HE η

,(5)

where Bjet

0is the magnetic ﬁeld strength at the core and

rV HE is the distance between the VHE γ-ray-emitting

region and the central black hole. We assume rV HE ∼

RV HE /θj, where RV HE is the blob radius of the VHE

emitting region and θjis the angle between the jet axis

and the line of sight.

Assuming equipartition between the magnetic ﬁeld and

particle energies, the electron density proﬁle nel(r) can

be modeled as a power law given by [56]:

nel(r) = n0r

rV HE ξ

,(6)

where n0is the electron density at rV H E . In Ref. [57], a

more realistic model was provided that takes into account

the fact that the electron distribution is nonthermal in a

relativistic active galactic nuclei Jet.

The photon energy E′

γin the jet frame is related to

the lab-frame energy Eγby E′

γ=Eγ/δD, where δD=

ΓL(1 −β2

jcosθj)−1is the Doppler factor with ΓLand

βjbeing the bulk Lorentz and beta factor, respectively.

We assume that at r > 1 kpc the BJMF strength is

negligible. Further details of the BJMF model can be

found in Refs. [7, 8].

B. Intercluster magnetic ﬁelds

The intercluster medium magnetic ﬁeld (ICMF),

BICM F can be modeled as,

BICM F (r) = BICMF

0nel(r)

nel(r0)η

,(7)

with 0.5≤η≤1.0, where BICM F

0and nel(r0) are the

magnetic ﬁeld strength and electron density at the cluster

center, respectively. The electron density distribution

nel(r) at a distance rfrom the cluster center is

nel(r) = nICM F

01 + r

rcore ζ

,(8)

with rcore is the core radius and ζ=−1. The typical

order of the electron density and the core radius is ∼

O(10−3) cm−3and ∼ O(100) kpc, respectively.

In a cluster-rich environment, the turbulent magnetic

ﬁeld is of order ∼ O(1)µG [58–60]. Such a cluster can

have a signiﬁcant eﬀect on the conversion between pho-

tons and ALPs [61, 62]. Since there is no evidence that

TXS 0506+056 is located in a cluster-rich environment,

we do not consider the photon-ALP oscillations in the

ICMF model.

C. Extragalactic magnetic ﬁelds

The actual strength of the extragalactic magnetic ﬁeld

on the cosmological scale ∼ O(1) Mpc, is still unknown,

but the currently accepted limit is ∼ O(1) nG [63, 64]. In

this work, we neglect the eﬀect due to the magnetic ﬁeld

(See Ref. [65] for possible eﬀects of the magnetic ﬁeld)

and consider only the absorption eﬀect due to EBL.

The optical depth of EBL attenuation can be written

as [66]

τ(Eγ, z0) = cZz0

(1 + z)H(z)Z∞

Eth

dEBG

dn(z)

dEBG

×˜σ(Eγ, EBG

γ),(9)

with

˜σ(Eγ, EBG

γ) = Z1−2(mec2)2

EBG

γEγ

−1

dcosθ (1 −cosθ)

×σγγ (Eγ, EBG

γ, θ),(10)

and Eth = 2 ·(mec2)2/(Eγ(1 −cosθ)),where z0is the

redshift of the source, H(z) is the rate of Hubble ex-

pansion, Eth is the threshold energy for pair production,

dn(z)/dEBG

γis the proper number density of the EBL,

σγγ (Eγ, z, EBG

γ) is the pair-production cross section, θ

is the angle between the projectile and target photons,

Eγis the projectile photon energy, and EBG

γis the tar-

get background photon energy. Several EBL models have

been proposed in the literature [67–73], and we consider

the model from Ref. [74] in this work.

TABLE I. Summary of the best-ﬁt spectral parameters for all

phases.

Phase N0(x10−11)α β Ecutoff

[MeV−1cm−2s−1] [GeV]

Neutrino Flare 2014 0.65 1.79 0.1 71.01

VHE Flare 1 4.04 1.99 0.54 66.27

VHE Quiescent 1.59 1.94 0.63 58.37

D. Milky Way region

Finally, we consider the eﬀect of photon-ALP oscilla-

tion in the presence of a Galactic magnetic ﬁeld (GMF).

This eﬀect can have both a large-scale regular compo-

nent and a small-scale random component. Due to the

fact that the coherence length is smaller than the oscil-

lation length, we neglect the random component [61] in

our analysis and consider only the regular GMF compo-

nent model given in [75]; the latest model can be found

in Refs. [76, 77].

IV. METHODOLOGY

The photon beam of the blazar can be considered as

the intrinsic photons generated by the accelerated leptons

or hadrons. In general, one can consider the intrinsic

spectrum to follow the superexponential cutoﬀ power law

(SEPWL) to ﬁt the observed data points under the null

hypothesis,

Φint(E) = N0E

E0−α

exp "−E

Ecutoff β#,(11)

where E0is taken to be 1 GeV, and N0,α,Ecutof f , and

βare treated as free parameters. The best-ﬁt parameters

are given in Table I. It is to be noted that we also tested

other forms of the intrinsic spectrum and found that the

SEPWL gives the smallest value of the best-ﬁt χ2under

the null hypothesis.

We use the open-source PYTHON-based package

gammaALPs1[78] to compute the photon-ALP oscillation

probability PALP

γγ .

The modulated γ-ray spectrum obtained after the

photon-ALP oscillation is given by ΦwALP (E) =

PALP

γγ Φint(E). In order to get the expected γ-ray spec-

trum observed in the detector, we must consider the en-

ergy resolution of the detector. One can assume the en-

ergy dispersion function D(Et, Ei

γ, Ej

γ) to be a Gaussian

with the variance being the energy resolution. Then the

expected ﬂux between energy bins Ei

γand Ej

γis given by

1https://gammaalps.readthedocs.io/en/latest/index.html

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Implicationsofphoton-ALPoscillationsintheextragalacticneutrinosourceTXS0506+056atsub-PeVenergiesBhanuPrakashPant,∗Sunanda,ReetanjaliMoharana,†andSarathykannanS.DepartmentofPhysics,IndianInstituteofTechnologyJodhpur,Karwar342037,India.(Dated:November28,2023)Photon-axion-likeparticle(ALP)oscillationsr...

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Implications of photon-ALP oscillations in the extragalactic neutrino source TXS 0506056 at sub-PeV energies Bhanu Prakash PantSunanda Reetanjali Moharanaand Sarathykannan S.

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