ЖЭТФ, 2022, том 161, вып. 4, стр. 583-589

DETECTABILITY OF LARGE CORRELATION

LENGTH INFLATIONARY MAGNETIC FIELD

WITH CHERENKOV TELESCOPES

A. Korochkin^a,b,c, A. Neronov^a,d, G. Lavaux^e, M. Ramsøy^a,e, D. Semikoza,b,f*

^a Université de Paris, CNRS, Astroparticule et Cosmologie

F-75006, Paris, France

^b Institute for Nuclear Research of the Russian Academy of Sciences

117312, Moscow, Russia

^c Novosibirsk State University

630090, Novosibirsk, Russia

^d Laboratory of Astrophysics, Ecole Polytechnique Federale de Lausanne

1015, Lausanne, Switzerland

^e Institut d’Astrophysique de Paris (IAP), CNRS & Sorbonne Université

F-75014, Paris, France

^f National Research Nuclear University MEPHI (Moscow Engineering Physics Institute)

115409, Moscow, Russia

Received November 9, 2021,

revised version November 19, 2021

Accepted for publication November 19, 2021

Contribution for the JETP special issue in honor of A. E. Chudakov’s 100th anniversary

DOI: 10.31857/S0044451022040125

ble for the generation of a relic magnetic field. First

EDN: DQQDYL

order phase transitions that might have happened at

quark confinement or during the Electroweak epoch can

Observations of extended and delayed gamma-ray

produce short correlation length magnetic field that

emission around extragalactic sources of TeV γ-rays

evolves through turbulent decay toward a magnetic

provides a possibility of measurement of magnetic field

field configuration with correlation length and strength

in the voids of the Large Scale Structure (LSS) [1-3].

satisfying a relation λ_B ∼ 0.1[B/10-12 G] kpc today

This emission is generated by electron-positron pairs

[9, 10]. Alternatively, a field generated at the epoch of

deposited by the pair production by γ-rays on the Ext-

inflation can have a very large correlation length, up to

ragalactic Background Light. The combination of data

the present day Hubble scale [11-19].

from current generation Cherenkov telescopes, HESS,

MAGIC, and VERITAS with data from the Fermi-LAT

Magnetic fields from galactic outflows, if they effi-

telescope currently constrains the void field strength to

ciently pollute the voids (as suggested e. g. by Bertone

be stronger than ∼ 10-17 G [4-6]. The next-generation

et al. [20]), would be distinguishable from both in-

Cherenkov Telescope Array (CTA) will provide a pos-

flationary and phase transition field based on their

sibility to explore the magnetic field over a wide range

galaxy scale correlation length (10-100 kpc). This

of possible strength and correlation lengths, up to the

is much larger than that of the phase transition in-

field strength of the order of B ∼ 10-11 G [7, 8].

duced field, but not reaching the Hubble scale of the

Several physical phenomena that took place a frac-

correlation length of the inflationary field. However

tion of a second after the Big Bang can be responsi-

even though magnetised outflows from galaxies can

spread non-cosmological magnetic fields in the inter-

^* E-mail: semikoz@gmail.com

galactic medium, these outflows are most likely not

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A. Korochkin, A. Neronov, G. Lavaux et al.

ЖЭТФ, том 161, вып. 4, 2022

strong enough to fill the voids [21, 22]. This suggests

gical voids where the impact of processes are likely to be

that the volume-filling magnetic field in the voids is a

small [22,31]. As a result of this the magnetic field is a

relic from the Early Universe [19].

smoothed tracer of the dark matter density field. Only

In what follows we explore the possibility of dis-

sufficiently massive objects are capable of producing

tinguishing between these two possibilities observation-

large enhancements of the gas density field. Regions

ally. Large correlation length fields break isotropy by

with overdensities greater than approximately 3 were

selecting a unique direction in a cosmologically large

thought to be close enough to structures that generate

volume. This selected direction imposes a correlated

magnetized outflows that they are at risk of being “pol-

asymmetry on magnetic field dependent extended emis-

luted” by magnetic fields of non-cosmological origin, as

sion patterns around γ-ray sources across the sky. We

indicated in [21]. The magnetic field strength in such

explore if it is possible to detect this asymmetry and

regions may deviate from simple scaling imposed by the

measure the inflationary magnetic field direction. We

amplification due to pure adiabatic contraction. As a

use a magnetic field generated from a realistic model of

result we therefore mark as high magnetic field region

the LSS derived from Borg constrained cosmological

any area with an overdensity greater than 3 averaged

simulations [23] that reproduces the location of known

over a thin cylinder with radius 2.7 Mpc (3 cells in the

LSS elements (galaxies, clusters) in the local Universe.

zoom region) along the line of sight during the course

Our analysis relies on magneto-hydrodynamic (MHD)

of our analysis.

simulations using the Ramses code [24] to estimate

Ramses-MHD was used due to its implementation

the effect of the structure formation on the initial mag-

of a constrained transport scheme [32]. Potentially spu-

netic field configuration. Modelling the properties of

rious amplification of the magnetic field seen in codes

secondary γ-ray signal is performed with the CRbeam

that use divergence cleaning schemes (e. g. [33,34]) are

code [25]. We use calculations of electromagnetic cas-

suppressed by this scheme. In any case, this effect is

cades along lines of sight to known nearby blazars to

most important in high density regions such as the cen-

estimate the influence of large correlation length mag-

tres of clusters and should have a minimal effect in this

netic field on the properties of secondary γ-ray signal

work.

from the cascade.

There are several known TeV blazars whose posi-

We calculate intergalactic magnetic field (IGMF)

tion falls within the high resolution simulation volume,

out to a distance of 200 Mpc from the Milky Way

Mkn 421, Mkn 501, QSO B2344+514, Mkn 180, 1ES

by running MHD simulations using the Ramses-MHD

1959+650, AP Librae and TXS 0210+515. All the

code [26] on the initial conditions (ICs) from Borg

sources are well-established TeV emitters. The prox-

[27]. Using a Markov Chain Monte Carlo approach,

imity of the sources enables measurements of their in-

the Borg methodology generates ICs that are con-

trinsic spectra attenuated by the pair production effect

strained to reproduce the structure of positions of real

up to 10 TeV. This is important because the extended

galaxies and galaxy clusters of the 2M++ survey [28]

emission in the energy range above 100 GeV is produced

within 200 Mpc cube around Milky Way. A cosmologi-

by electrons and positrons injected in interactions of

cal zoom of one variant of the Borg ICs was produced

γ-rays with energies above 10 TeV. Measurement of

using Music algorithm [29] to generate a high resolu-

the flux above 10 TeV allows us to obtain reliable es-

tion region 200 Mpc around the Milky Way with spatial

timates of the expected power of the secondary flux in

resolution at z = 0 of 0.7 h-1 · Mpc and mass resolu-

the E > 100 GeV range.

tion 2.1 · 10¹⁰ h-1 · M_⊙. This is a factor 4 increase over

The lines of sight toward 7 sources are oriented at

the original Borg ICs spatial resolution. Note however

different angles with respect to the direction of initial

that the density fluctuations on this scale are uncon-

homogeneous field chosen in simulation. This provides

strained. The initial configuration of the magnetic field

a possibility to study how variations of the misalign-

is uniform across the simulation volume with strength

ment of the cosmological field direction affects the ob-

up to 10-12 G. Its direction is chosen to be in the di-

servational appearance of the extended emission. Lines

rection of north (Dec = 90^◦) of the ICRS coordinate

of sight toward two sources, 1ES 1959+650 and Mkn

system. The hydrodynamical variables and magnetic

180 are more strongly aligned to the direction of the

field were evolved on the AMR grid using the HLLD

magnetic field than, say, the lines of sight to Mkn 421

solver [30] with the MinMod slope limiter being used

and Mkn 501. The line of sight toward AP Librae has

to reconstruct variables at cell interfaces.

the largest misalignment angle in our sample.

The simulation was run without cooling, star forma-

Figure 1 show the line-of-sight profiles of magnetic

tion or feedback as the focus of this study are cosmolo-

field toward Mkn 501. The top panel of the figure

584

ЖЭТФ, том 161, вып. 4, 2022

Detectability of large correlation length inflationary...

We model the secondary cascade γ-ray signal with

the CRbeam Monte Carlo code [25] which propagates

high energy γ-rays through the cosmic medium taking

into account most important physical interactions: pair

production by γ-ray absorption and inverse Compton

scattering of secondary electrons and positrons on the

EBL [35] and CMB. Electrons and positrons are also

deflected in magnetic field whose strength is obtained

from IGMF model described above.

For intrinsic point source spectrum we assume bro-

ken power law spectrum with break position around

100 GeV and maximum energy 100 TeV. All primary

γ-rays have the same direction of initial momenta which

coincides with the direction from the source to the ob-

server. The γ-rays are propagated until they reach the

sphere whose center coincides with the position of the

source and radius is equal to the distance to the ob-

server. To model primary γ-ray emission into a jet with

an opening angle α_jet we select γ-rays whose positions

on the sphere lie inside the cone with the opening an-

gle α_jet = 5^◦ and direction of the axis coincides with

the direction of jet. We do not take into account sec-

ondary photons that were created in the regions with

an overdensity above 3, see Fig. 1. To explore different

strengths of seed magnetic field we rescale the magnetic

field profile by a constant factor keeping the shape of

the profile unchanged.

Jet-like, rather than halo-like extended emission is

Fig. 1. (Color online) Density profile (a), magnetic field (b)

generically expected even for short correlation length

for a line of sight in the direction of Mkn 501. The magnetic

field is split into total (blue), along the line of sight (orange)

IGMF (originating from a cosmological phase transi-

and perpendicular to line of sight (green). The location of the

tion) [36]. Thus, the azimuthal asymmetry of the ex-

source with uncertainty is shown with a grey band. Regions

tended signal is not an indication of the presence of

where the overdensity is greater than 3 are indicated by red

large correlation length IGMF. However, there are two

bands

important differences in the properties of the jet-like

extended emission in the two alternative cases of phase

show the line-of-sight profile of the density field. Re-

transition and inflationary magnetic field. The jet-like

gions with overdensities above 3 that are excluded from

extensions are one-sided in the case of a short corre-

our further analysis because of possible “contamina-

lation length field [36], whereas the jet-like extensions

tion” of the magnetic field by baryonic feedback [22]

are two sided for inflationary field. In addition, in the

are indicated with vertical red bands. In those regions

case of the phase transition IGMF, the position angle of

secondary electrons are randomized by high magnetic

the one-sided jet-like extended emission is determined

fields and their signal in direction to observer can be

by the orientation of the jet of the blazar rather than

safely neglected. Grey bands indicate the distance to

by the direction of the field. It is expected to be ran-

the blazars. The γ-ray source is situated in moder-

dom for different sources, whereas in the case of the

ately overdense regions that are unlikely to be affected

inflationary large correlation length field the extended

by strong magnetised outflows from galaxies. None of

sources associated to different blazars have the same

the three sources have a line-of-sight aligned with a fil-

position angle.

ament of the LSS. This makes Mkn 501 suitable for

If the blazar jet is closely aligned with the line of

the IGMF measurement. Same is true for other two

sight, the two sides of the extended emission are sym-

sources, Mkn 421 and 1ES 1959+650. The bottom

metric, they have comparable surface brightness. This

panel of the figure show the strength of the IGMF along

symmetry can be broken by the misalignment of the

the lines of sight.

jet with the line of sight. The orientation of the two-si-

585

ЖЭТФ, вып. 4

A. Korochkin, A. Neronov, G. Lavaux et al.

ЖЭТФ, том 161, вып. 4, 2022

Fig. 2. (Color online) Images of the extended emission signal in the energy range 200 GeV-2 TeV for the three brightest sources

in our sample. The assumed initial cosmological magnetic field strength is B = 10-13 G. The direction of the jet axis coincides

with the direction from the source to the observer and the jet opening angle is 5^◦

ded extension that is due to the presence of the large

We extracted the extended source fluxes from

correlation length field is, always perpendicular to the

wedges of the angular width 0.3^◦ that contain the sig-

direction of magnetic field projected on the sky. If the

nal. From the wedges, we excluded the regions in which

cosmological IGMF is correlated on the distance scales

the primary source emission dominates, namely, we did

larger than hundreds of Megaparsecs, orientations of

not take into account those regions of the wedges that

the two-sided extensions around different sources all

are located at a distance from the centers less than the

over the sky are all expected to be aligned. Measure-

angular resolution of the CTA. From Fig. 2 one can

ment of aligned extended emission features around mul-

judge that the extended emission is dominated by the

tiple sources can provide an unambiguous evidence for

flux in a much narrower wedge, with opening angle of

the presence of magnetic field of inflationary origin. In

just a few degrees.

this case position angles of the two-sided extensions

This gives a conservative estimate of the detectable

provide the measurement of the direction of the pri-

extended source flux. In principle, stronger signal can

mordial field.

be extracted using the azimuthal asymmetry of the ex-

tended emission. If the shape of the point spread func-

Figure 3 shows spectra of the point and extended

tion is known, the extended emission can be detected

source emission for different assumptions about the

also from within the extent of the point spread function.

magnetic field strength. For each source we choose

Systematic uncertainty of the knowledge of the point

the model of the intrinsic spectrum in such a way that

spread function limits the sensitivity of Cherenkov tele-

it fits the spectral measurements of the “low state” of

scopes for detection of extended emission [43,44]. This

the source and/or the time-averaged spectral measure-

uncertainty can be mitigated by the direct measure-

ments on multi-year time scales. For all sources we

ment of the point spread function in the direction per-

consider two alternative Fermi spectral data: the spec-

pendicular to the direction of extended emission. This

tral measurements reported in the Fermi source cata-

is possible even if the source line of sight is nearly

log [37] and the spectra extracted using the aperture

aligned with the field direction, as illustrated by the

photometry approach for the full 13-year exposure of

example of 1ES 1959+650, shown in the right panel of

Fermi/LAT up to July 2021. This allows us to extend

Fig. 2.

the Fermi catalog measurements up to the 3 TeV ener-

The linear, one-dimensional shape of the extended

gy.

source also provides an improvement of sensitivity for

For Mkn 501 we used MAGIC and VERITAS ana-

another reason. The sensitivity for extended sources

lyses from 2009 [38], and long term observations from

typically worsens with the increase of the solid angle

ARGO [39] and HAWC [40]. For Mkn 421 we used long

spanned by the extended source on the sky, because of

term observations from ARGO [41] and HAWC [40] and

the increase of the background on top of which the sig-

very low state from VERITAS measurement [42].

nal is detected. Concentration of the extended signal

586

ЖЭТФ, том 161, вып. 4, 2022

Detectability of large correlation length inflationary...

Fig. 3. (Color online) Spectra of intrinsic point source and extended emission for different assumed magnetic field strengths upper

panels: 0, 10-14, and 3 · 10-14 G, lower panels: 10-13, 3 · 10-13, and 10-12 G, for the three brightest sources in the sample.

Point source spectra from Fermi LAT, MAGIC [38], VERITAS [38], ARGO [39], and HAWC [40]. Total flux from the cascade

in case B = 0 is shown with dotted line. Extended emission outside of the PSF of point source is shown with colored lines for

magnetic fields between 10-14 G and 10-12 G. Dashed green line show sensitivity of CTA to point sources

in a narrow wedge reduces the solid angle and hence

scopes for detection of extended sources. This compar-

increases the signal-to-noise ratio.

ison shows how challenging the search for the two-sided

jet-like extensions might be. The model predictions for

All the sources in our sample have steep spectra in

the extended signal are at the limit of sensitivity for the

the 10 TeV range. This diminishes the power of the

50 hr exposure of each of the three brightest sources in

secondary emission observable in the 0.1-1 TeV range.

our source sample. However, use of possible improve-

The total flux that would be available for detection (as

ments of the method with “in situ” measurement of the

a contribution to the point source flux) in the absence of

telescope point spread function and careful choice of the

an IGMF is shown by the brown dotted lines in Fig. 3.

wedge for the extended signal measurements may im-

The IGMF deflects electrons and positrons away from

prove the sensitivity. Otherwise, much longer exposure

the line of sight, so that the secondary γ-rays produced

of several hundred hours (instead of 50 hr considered

by the inverse Compton scattering of the Cosmic Mi-

here) can also boost signal-to-noise ratio and make the

crowave Background becomes unobservable. This effect

correlated extended emission signal measureable in all

is stronger at lower energies. This explains the sup-

the three brightest nearby blazars considered above.

pression of the extended flux (that we collect from the

wedge-shaped regions containing the secondary flux)

In this paper we studied a possibility of detec-

at the energies below 100 GeV. If the magnetic field

tion of primordial magnetic field from inflation [12, 19]

is too weak to deflect electrons and positrons, the sec-

with gamma-ray telescopes. Such field can be coher-

ondary flux just contributes to the point source flux

ent on cosmological scales and induce wedge-like ex-

and is also undetectable. This explains the suppression

tended emission around nearby blazars, with aligned

of the secondary signal at higher energies. Both low-

wedge orientations in multiple sources across the sky.

and high-energy suppression depends on the strength

This alignment can be used to distinguish the es-

of magnetic field.

tablish the inflationary origin of IGMF, because it is

Figure 3 shows a comparison of the expected sec-

not expected if the IGMF originates from cosmological

ondary flux levels with the sensitivity of the CTA tele-

phase transitions. For small coherence scale IGMF, the

587

A. Korochkin, A. Neronov, G. Lavaux et al.

ЖЭТФ, том 161, вып. 4, 2022

wedge like appearance of the extended emission is also

R. Banerjee and K. Jedamzik, Phys. Rev. D 70,

generically expected, but the position angles of wedged

123003 (2004), arXiv:astro-ph/0410032.

extended emission around different sources would not

10.

T. Kahniashvili, A. G. Tevzadze, A. Brandenburg,

be correlated, because it is determined by the orienta-

and A. Neronov, Phys. Rev. D 87, 083007 (2013),

tion of the jets in the primary blazar source.

arXiv:1212.0596 [astro-ph.CO].

The morphology of the secondary emission depends

on the jet orientation also for the inflationary magnetic

11.

M. S. Turner and L. M. Widrow, Phys. Rev. D 37,

field. However, the jet orientation does not affect the

2743 (1988).

position angle of the extended source.

12.

B. Ratra, Astrophys. J. Lett. 391, L1 (1992).

Acknowledgements. This work has made use of

13.

W. D. Garretson, G. B. Field, and S. M. Car-

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this cluster smoothly for us. This work has been done

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within the Aquila Consortium (https://www.aquila-

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M. Gasperini, M. Giovannini, and G. Veneziano,

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V. Demozzi, V. Mukhanov, and H. Rubinstein, JCAP

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