arXiv subjects

A. M. Bykov

Publications and source records attributed to A. M. Bykov.

At least 19 recordsLinked to original sources

arXiv2026

Dark and Luminous Matter in the Coma Cluster: Probing Galaxy Cluster Assembly Through Filaments with Weak Lensing and Multiwavelength Observations

The Coma cluster (Abell 1656; $z=0.023$) is a nearby rich galaxy cluster and a key laboratory for studying cluster assembly in the Cosmic Web. We characterize its projected dark matter distribution and connection to galaxies, the intracluster medium, and reported intracluster filaments (ICFs) with wide-field ($\sim$12-deg$^2$) Subaru/Hyper Suprime-Cam weak-lensing (WL) analysis. We reconstruct the two-dimensional mass distribution, fit Navarro-Frenk-White (NFW) models, derive an aperture mass densitometry profile, and compare the WL signal with optical spectroscopy, eROSITA X-ray observations, radio data, and gas fraction diagnostics. A single-halo NFW fit yields $M_{200\mathrm{c}}=8.2\pm0.7\times10^{14}~M_{\odot}$. The aperture mass profile agrees with the best-fit NFW model and the X-ray hydrostatic mass at $R\gtrsim20'$ ($\sim$560 kpc), suggesting little merger-induced bias in the global WL mass, while the inner region shows substantial hydrostatic bias. A two-halo NFW fit centered on NGC 4874 and NGC 4839 gives masses of $7.8\pm0.6$ and $0.9\pm0.2\times10^{14}~M_{\odot}$, implying a $\sim$1:8 minor merger. The gas mass fraction suggests that the system is returning from first apocenter. We find a positive spatial correlation between the WL signal and X-ray surface brightness, strongest along the ICF directions ($110^{\circ}$ and $340^{\circ}$), where shear-selected subhalos are predominantly detected. The Coma $r$-band mass-to-light ratio is radially constant with $\langle M/L_r\rangle\simeq250\pm66~M_{\odot}/L_{\odot}$ within $R_{200\mathrm{c}}$, whereas the northern and western ICFs show higher values of $\sim1000~M_{\odot}/L_{\odot}$, suggesting stronger dark matter dominance. These results show that joint WL and multiwavelength analyses can effectively probe cluster assembly and the dark matter content of ICFs.

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arXiv2026

Direct simulations of very high energy cosmic ray acceleration in 3D MHD model of a compact star cluster

Young compact clusters of massive stars contain dozens of O-, B- and WR-type stars with fast powerful winds in a small $\sim$ pc radius core. The particle acceleration by ensembles of shocks accompanied with long-wavelength compressions and rarefactions in the turbulent environment of young massive star clusters (YMSCs) is an alternative to the standard paradigm of Galactic cosmic ray acceleration on supernova shocks. In recent years, the topic has been of great interest due to the fact that modern gamma- and X-ray observatories have detected the radiation from YMSCs, which indicates particle acceleration processes in these objects. We study particle propagation and acceleration in a YMSC with the help of 3D magnetohydrodynamic (MHD) modeling using an open source PLUTO code. The code allows modeling of the turbulent environment of YMSCs and obtaining crucial for particle acceleration values of velocity, density, and magnetic field inside the cluster core. The Particle module implemented in PLUTO allows solving the equations of motion for test charged particles together with MHD equations for the medium. We obtained that protons acceleration up to hundreds of TeV takes place in the cluster core near the termination shocks of O-stars, which are surrounded by shocks of their neighbour stars. We also modeled an interesting case of a young supernova remnant expanding inside the cluster core. In this case a very fast acceleration takes place: particle energies $\gtrsim$ 100 TeV can be obtained in $\lesssim$ 100 years. The particle spectra and spatial distribution are discussed.

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arXiv2026

On the contribution of the bow shock pulsar wind nebula PSR J0437-4715 to the observed fluxes of GeV-TeV positrons and antiprotons

The orbital observatories PAMELA and AMS-02 have detected a significant excess in the cosmic ray (CR) positron flux at energies above several tens of GeV. The measured values exceed those expected in models of secondary origin of positrons due to inelastic collisions of CR nuclei with the interstellar matter. This excess may be due to the annihilation or decay of hypothetical dark matter particles or, alternatively, to the contribution of the nearest pulsars. The measured positron-to-antiproton flux ratio is virtually independent of energy from 60 to 400 GeV. This can be understood if the observed local spectra of positrons and antiprotons in the range of tens to hundreds of GeV are formed by the same source. Fast-moving pulsars form pulsar wind nebulae with bow shocks (BSPWNe), which accelerate both the positrons and electrons of the pulsar wind and the hadrons and leptons of galactic CRs from the interstellar medium via the Fermi acceleration mechanism in colliding flows. Such a system can produce identical particle spectra regardless of the site of particle injection. The nearest to the Earth millisecond pulsar PSR J0437-4715 forms a pulsar wind nebula (PWN) with a bow shock observable in optical and ultraviolet wavelengths. This BSPWN is a possible candidate for the main near-Earth ``factory'' of antiparticles along with the Geminga PWN. Considering PSR J0437-4715, we provide the Monte Carlo simulations of particle acceleration in its BSPWN and the analytical model of anisotropic diffusion in the local interstellar medium. We show that this pulsar's contribution can explain the observed positron flux from 30 GeV to 1 TeV, and simultaneously the antiproton flux at hundreds of GeV with an almost energy-independent positron-to-antiproton flux ratio using $\sim 25\%$ of the PSR J0437-4715 pulsar wind power to accelerate positrons and electrons and re-accelerate antiprotons.

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arXiv2026

How many VHE gamma-ray binaries with young pulsars can be observed?

A population of Galactic gamma-ray binaries is currently emerging due to ever increasing sensitivity of gamma-ray observatories. The detection of very high energy (VHE) photons with energies well above 10 TeV from a dozen of sources and the estimated power of those sources make them potentially interesting cosmic ray accelerators. Multi-wavelength observations of gamma-ray binaries revealed that most of them include a young massive star in pair with a relativistic companion, either a black hole or energetic pulsar. Fast stellar winds interacting with powerful relativistic outflows from pulsars or the black hole jets in microquasars are favorable sites for VHE particle acceleration. To estimate the expected number of gamma-ray binaries, we present results of population synthesis calculations of Galactic binaries in which a young massive OB- or Be-star is accompanied by a pulsar capable of producing a powerful relativistic outflow. The distributions over the binary eccentricities, orbital periods, Be-disk inclinations, and the pulsar braking energy losses are taken into account. Conditions for a binary to accelerate VHE particles, radiate and absorb the non-thermal photons that may reach the observer are discussed. We model the anisotropic structure of the zone of interaction of the relativistic pulsar wind with the strongly magnetized massive star's wind. The stellar winds with strong ($\sim$ Gauss) magnetic fields at $\sim$ AU distances colliding with powerful pulsar outflows are capable of accelerating particles up to PeV energies at some orbital configurations and phases. The strong magnetic field in the interaction region produces a highly anisotropic structure of the particle accelerator and emitter in the pulsar outflow. The anisotropic radiation pattern may affect the gamma-ray photon absorption and the number of the observed gamma-ray loud systems.

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arXiv2026

Southern eROSITA bubble as a forward shock and the low-metallicity CGM. South-east side story

Unlike the complicated X-ray and radio structure observed in the North Polar Spur area, the South-Eastern part of the eROSITA bubbles can be reasonably well described as a propagating forward shock, plausibly created by the transient energy release at the Galactic Center. In this model, the physical radius of the bubble is $R_{\rm b}\sim 7-8\,{\rm kpc}$ and the age of the outburst is $t_{\rm age}\sim 5-8\,{\rm Myr}$. The latter quantity is plausibly a lower limit on the true age. The visible segment of the shock front (located at a distance of $\sim 10-12\,{\rm kpc}$ above the Galactic Disk and at a similar distance from the Sun) is currently expanding with the velocity $\sim 700\,{\rm km\,s^{-1}}$ through the gas with density $n_e\sim 3\times 10^{-4}\,{\rm cm^{-3}}$, and the abundance of heavy elements in this gas is low $Z\sim 0.1-0.2 \times Z_\odot$ (depending on the adopted reference Solar abundances). Unlike constraints derived from the line-of-sight-integrated quantities, these are effectively in situ measurements of the circumgalactic medium (CGM) properties. Given the simplifying assumptions used in deriving the density and abundance, we assign a factor of 2 systematic uncertainty to the final estimates. An eventual decisive test for the shock properties can be provided by the velocity measurements of the X-ray-emitting gas with soft X-ray bolometers. The extended forward shock propagating through low-metallicity gas is a favorable site to accelerate very high-energy cosmic rays, which might contribute to the recently discovered proton-rich Galactic cosmic ray component at PeV energies impinging on the Earth's atmosphere.

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arXiv2026

Relativistic astrospheres of gamma-ray binaries: modeling of non-thermal processes

A long standing problem in high energy astrophysics is the nature of galactic accelerators of particles with energies above PeV. Such objects are sources of galactic cosmic rays and can produce PeV-regime photons observed by ground-based observatories. Among very likely accelerators are astrospheres of pulsars in gamma-ray binaries. These binaries have long been observed as bright sources of TeV gamma-rays. Recently, 2D relativistic magnetohydrodynamic (rMHD) simulations have shown that the astrospheres can accelerate particles to energies well above PeV, provided that they harbor a Gauss-range magnetic field. Such a strong field is necessary in the region of two colliding winds: the relativistic outflow of the pulsar or accreting black hole and the wind of its stellar companion, a massive early-type star. Here, the wind collision region is explored as the site of PeV protons acceleration. The local structure of colliding flows is illustrated using rMHD simulations of a powerful pulsar wind in 2D and 3D models. The relativistic outflow of a pulsar or black hole, evolving inside the strongly magnetized stellar wind, have an elongated shape and surrounded by a kind of magnetic cocoon providing favorable conditions for acceleration of ultra high energy ions. The simulated spectra of particles, accelerated by intermittent relativistic turbulence in these systems, have piece-wise power-law shape and extend well above PeV energies for powerful outflows. The model indicated that gamma-ray binaries harboring a powerful relativistic outflow, produced either by a pulsar or accreting black hole, can be bright sources of synchrotron MeV-regime photons and multi-PeV regime gamma-rays, as recently detected from galactic microquasars like Cyg X-3. The Gauss-range magnetic field of a massive star wind strongly influences the non-thermal emission of gamma-ray binaries with relativistic companions.

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arXiv2026

Shells and bubbles around compact clusters of massive stars: 3D MHD simulations

We present the results of three-dimensional magnetohydrodynamic (3D MHD) simulations of the plasma flow structure in the vicinity of a compact cluster of young massive stars. The cluster is considered at the evolutionary stage dominated by Wolf-Rayet stars. This stage occurs in clusters with ages of several million years, close to the onset of supernova explosions; the well-known objects Westerlund 1 and 2 are the prototypes. The collisions of powerful winds from massive stars in the cluster core, calculated as interactions of individual outflows, are accompanied by their partial thermalization and produce a collective cluster wind. The MHD dynamics of the cluster wind bubble expansion into the interstellar medium is considered, depending on the density of the surrounding medium with a uniform magnetic field. We show that when expanding into a cold neutral medium, the cluster wind is able to reshape its surrounding environment over the Wolf-Rayet star lifetime, sweeping up more than $10^4$ $M_{\odot}$ of gas in $\sim 2 \times 10^5$ yr and producing extended, thin and dense shells with an amplified magnetic field. In a cold neutral medium with a density of $\sim 20$ cm$^{-3}$ and a magnetic field of $\sim 3.5$ $μ$G, a thin shell forms around the cluster wind bubble, characterized by a cellular structure in its density and magnetic field distributions. The cellular magnetic field structure appears in parts of the shell expanding transversely to the orientation of the external magnetic field. Magnetic fields in the shell are amplified to strengths $\gtrsim 50$ $μ$G. The formation of the cellular structure is associated with the development of instabilities. The expansion of the bubble into a warm neutral interstellar medium also leads to the formation of a shell with an amplified magnetic field.

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arXiv2025

PeV particle acceleration and non-thermal emission in the `minimalist' model of the extended jets in W50/SS433

The W50 nebula around microquasar SS~433, powered by supercritical accretion, features two `extended jets' (tens of pc long and a few pc wide) from which polarized X-ray and very high energy radiation above 100 TeV is detected. Here we present a model of very high energy particle acceleration in these extended jets. In the `minimalist' model (discussed in Churazov, Khabibullin, and Bykov, 2024), a collimated outflow aligned with the rotation axis is propagating through a more isotropic wind produced by the accretion disk. The observed extended X-ray jets with bright knots in this model are associated with the formation of strong recollimation MHD shocks after the collision of the collimated outflow with the isotropic wind termination surface. The spectra of electrons and protons up to PeV energies are simulated with a nonlinear Monte Carlo model of diffusive shock acceleration with turbulent magnetic field amplification. The overall efficiency of the jets power transfer to accelerated protons in this model is above 10\% and about 0.5\% for electrons above 50 TeV. The magnetic field amplification by Bell's instability due to the electric current of cosmic rays escaping the accelerator produces highly anisotropic magnetic turbulence in the shock downstream. This results in the polarized synchrotron X-ray emission with the photon electric vector predominantly transverse to the jet direction and the degree of polarization above 20\%. The model is able to reproduce the observed spectra and intensity profiles of non-thermal X-ray and gamma-ray emission, which are both dominated by the leptonic radiation.

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arXiv2024

North Polar Spur: gaseous plume(s) from star-forming regions at $\sim$3-5 kpc from Galactic Center?

We argue that the North Polar Spur (NPS) and many less prominent structures are formed by gaseous metal-rich plumes associated with star-forming regions (SFRs). The SFRs located at the tangent to the 3-5~kpc rings might be particularly relevant to NPS. A multi-temperature mixture of gaseous components and cosmic rays rises above the Galactic disk under the action of their initial momentum and buoyancy. Eventually, the plume velocity becomes equal to that of the ambient gas, which rotates with different angular speed than the stars in the disk. As a result, the plumes acquire characteristic bent shapes. An ad hoc model of plumes' trajectories shows an interesting resemblance to the morphology of structures seen in the radio continuum and X-rays.

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arXiv2024

An Approach to Gamma-Hadron Separation via Measurements of the Middle-UV Fraction of EAS emission by an Imaging Atmospheric Cherenkov Telescope with UV-Sensitive SiPM detectors

The operation of a small-size Cherenkov gamma-ray telescope TAIGA-IACT with camera on SiPMs OnSemi MicroFJ-60035 has been modelled by multiparticle Monte Carlo (MC) methods. The model implies that telescope camera is equipped with two specific types of filters of 290-590 nm (visible+NUV) and 220-320 nm (MUV+UVB)-bands, each covering half of the camera pixels in some uniform order. This allows one to measure the fraction of UV-radiation in total amount of Cherenkov radiation of an extensive air shower (EAS), that can be used for efficient gamma-hadron separation. The corresponding quality factor takes values up to 5.07 in the 10-100 TeV range depending on the distance to EAS axis and camera orientation.

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arXiv2024

Minimalist model of the W50/SS433 "Extended X-ray Jet": anisotropic wind with recollimation shocks

W50 is a radio nebula around hyper-accreting Galactic microquasar SS~433. Here we focus on one peculiar feature of W50 - a pair of so-called "extended X-ray jets" (EXJs). These "jets" have a size of $\sim20\, {\rm pc}$, a sharp inner boundary, and their spectra are well represented by a featureless X-ray continuum. We argue that EXJ could be an outcome of a powerful {\it anisotropic} wind produced by a super-critical accretion disk. In the simplest version of this model, the wind itself consists of two components. The first component is a nearly isotropic outflow that subtends most of the solid angle as seen from the compact source and creates the quasi-spherical part of the W50 nebula. The second component is a more collimated wind aligned with the binary system rotation axis (polar wind). The isotropic outflow passes through the termination shock and its increased thermal pressure creates a sequence of recollimation shocks in the polar wind, giving it the appearance of an extended X-ray structure. In this model, the EXJ continuum spectrum is due to synchrotron emission of electrons accelerated at the shocks arising in the polar wind. At variance with many other studies, in this model, the EXJ structures are not directly related to the highly collimated and precessing $0.26\;\!c$ baryonic jets. Instead, the EXJ and the W50's ears are produced by the part of the wind with an Eddington-level kinetic luminosity confined to a half-opening angle of 5-10 degrees, which is not necessarily a recollimated version of the $0.26\;\!c$ jets.

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arXiv2024

Cosmic ray acceleration and non-thermal emission from fast luminous optical transient sources

Fast blue optical transients (FBOTs) represent a new class of highly energetic sources observed from radio to X-rays. High luminosity, light curves and spectra of the sources can be understood if they are associated with supernova-like or tidal disruption events. Radio observations of the transient sources revealed a mildly relativistic expansion of some of the remnants. The high power and mildly relativistic shock velocities are providing favorable conditions for very high energy particle acceleration. In this paper we present a model of particle acceleration in mildly relativistic magnetohydrodynamic (MHD) outflow of the transient source. To construct the non-thermal radiation and cosmic ray spectra in a broad range of energies we combined the microscopic particle-in-cell (PIC) simulations of electron and proton injection at mildly relativistic shock with Monte Carlo technique for high energy particle transport and acceleration. The kinetic PIC simulations provided the energy partition parameter $ε_{e}$ used to fit the observed non-thermal radio emission using the magnetic field amplification mechanisms modelled with Monte Carlo simulations. The model allowed to describe the radio-spectrum of CSS161010 and it's X-ray luminosity. The high X-ray luminosity of AT2018 and AT2020mrf detected during the first weeks can be connected to the jet interaction with the stellar companion in a binary system. The model predicts that FBOTs can accelerate cosmic rays to energies above 10 PeV with a possible upper limit of maximum energy of 100 PeV. With the expected event rate of FBOTs they can contribute to the very high energy cosmic rays population in galaxies.

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arXiv2024

PeV proton acceleration in Gamma-ray Binaries

Current generation of ground based gamma-ray telescopes observed dozens of sources of photons above 100 TeV. Supernova remnants, pulsar wind nebulae, young stellar clusters and superbubbles are considered as possible sites of PeV-regime particles producing the radiation. Another possible source of PeV particles could be gamma-ray binary systems. In these systems, a strong relativistic outflow from a compact object (neutron star or black hole) collides with the dense wind from a massive companion early-type star. Gamma-ray binaries are observed from radio to high energy gamma-rays as luminous non-thermal sources. Apart from acceleration of very high energy leptons producing most of the non-thermal radiation, these systems may also efficiently accelerate protons. We present here the results of numerical simulation of the PeV-regime proton acceleration in gamma-ray binaries. The simulation is based on relativistic MHD modeling of local flows of magnetized plasma in the region of interaction of two colliding winds. We then inject 0.1 PeV protons into the system and directly follow their trajectories to demonstrate that they are accelerated to energies above PeV. High magnetization of the wind of the young massive star providing a Gauss range field in the winds interaction region is of paramount importance for the acceleration of protons above PeV. The maximum energies of protons accelerated by colliding winds in gamma ray binaries can significantly exceed the energy of the pulsar potential's drop, which limits from above the energy of particles accelerated by an isolated pulsar.

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arXiv2023

Core-collapse supernova inside the core of a young massive star cluster: 3D MHD simulations

Young massive stars in compact stellar clusters could end their evolution as core-collapse supernovae a few million years after the cluster was built. The blast wave of a supernova propagates through the inner cluster region with multiple stellar winds of young luminous stars. We present the results of 3D magnetohydrodynamic simulations of the plasma flows produced by a supernova event inside a cluster with a population of massive stars similar to that in Westerlund 1. We followed its evolution over a few thousand years (i.e. a few shock crossing times). The plasma temperature, density and magnetic field, which are highly disturbed by supernova event, relax to values close to the initial over the studied period. The relaxation time of a cluster is a few thousand years, which is a sizeable fraction of the period between the successive supernova events for a massive cluster of a few million years age. The spectra of the cluster diffuse X-ray emission simulated here should be representative for the galactic and extragalactic young massive clusters. The resultant magnetic fields are highly intermittent, so we derived the volume filling factors for a set of magnetic field ranges. Highly amplified magnetic fields of magnitude well above 100 $μ$G fill in a few per cent of the cluster volume, but still dominate the magnetic energy. The structure of the magnetic fields and high velocity plasma flows with shocks in the system are favorable for both proton and electron acceleration to energies well above TeV.

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arXiv2023

Weibel-dominated quasi-perpendicular shock: hybrid simulations and in situ observations

We directly compare hybrid kinetic simulations and in situ observations of a high Mach number high-$β$ shock in the Solar wind. We launch virtual probes to demonstrate that the model quantitatively reproduces the observations. The observed wave properties are caused by the ion Weibel instability in the shock foot. Parameters of reflected ions in the shock foot are extracted from simulations, and their coordinate dependencies are linearly approximated. These approximations could be used in analytical models. Due to strong magnetic variations at ramp the reflected ions density can be locally very high (nearly that of the incoming flow), which makes favourable conditions for the instability.

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arXiv2023

X-ray emission from Westerlund 2 detected by SRG/ART-XC and Chandra: search for radiation of TeV leptons

We present the results of current observations of the young compact cluster of massive stars Westerlund 2 with the Mikhail Pavlinsky ART-XC telescope aboard the Spectrum-Roentgen-Gamma (SRG) observatory which we analysed together with the archival Chandra data. In general, Westerlund 2 was detected over the whole electromagnetic spectrum including high-energy gamma rays, which revealed a cosmic ray acceleration in this object to the energies up to tens of TeV. The detection of Westerlund 2 with ART-XC allowed us to perform a joint spectral analysis together with the high resolution Chandra observations of the diffuse emission from a few selected regions in the vicinity of the Westerlund 2 core in the 0.4 - 20 keV range. To fit the Westerlund 2 X-ray spectrum above a few keV one needs either a non-thermal power-law emission component, or a hot plasma with temperatures $\sim$ 5 keV. Our magnetohydrodynamic modeling of the plasma flows in Westerlund 2 shows substantially lower electron temperatures in the system and thus the presence of the non-thermal component is certainly preferable. A kinetic model of the particle acceleration demonstrated that the non-thermal component may originate from the synchrotron radiation of multi-TeV electrons and positrons produced in Westerlund 2 in accordance with the TeV photons detection from the source.

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arXiv2023

SRG/eROSITA discovery of a radio faint X-ray candidate supernova remnant SRGe J003602.3+605421=G121.1-1.9

We report the discovery of a candidate X-ray supernova remnant SRGe J003602.3+605421=G121.1-1.9 in the course of \textit{SRG}/eROSITA all-sky survey. The object is located at (l,b)=(121.1$^\circ$,-1.9$^\circ$), is $\approx36$ arcmin in angular size and has a nearly circular shape. Clear variations in spectral shape of the X-ray emission across the object are detected, with the emission from the inner (within 9') and outer (9'-18') parts dominated by iron and oxygen/neon lines, respectively. The non-equilibrium plasma emission model is capable of describing the spectrum of the outer part with the initial gas temperature 0.1 keV, final temperature 0.5 keV and the ionization age $\sim 2\times10^{10}$ cm$^{-3}$ s. The observed spectrum of the inner region is more complicated (plausibly due to the contribution of the outer shell) and requires substantial overabundance of iron for all models we have tried. The derived X-ray absorption equals to $(4-6)\times10^{21}$ cm$^{-2}$, locating the object at the distance beyond 1.5 kpc, and implying its age $\sim(5-30)\times1000$ yrs. No bright radio, infrared, H$_α$ or gamma-ray counterpart of this object have been found in the publicly-available archival data. A model invoking a canonical $10^{51}$ erg explosion (either SN Ia or core collapse) in the hot and tenuous medium in the outer region of the Galaxy $\sim$9 kpc away might explain the bulk of the observed features. This scenario can be tested with future deep X-ray and radio observations.

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arXiv2022

Tempestuous life beyond R500: X-ray view on the Coma cluster with SRG/eROSITA. II. Shock & Relic

This is the second paper in a series of studies of the Coma cluster using the SRG/eROSITA X-ray data obtained during the calibration and performance verification phase of the mission. Here, we focus on the region adjacent to the radio source 1253+275 (radio relic, RR, hereafter). We show that the X-ray surface brightness exhibits its steepest gradient at $\sim 79'$ ($\sim 2.2\,{\rm Mpc}\approx R_{200c}$), which is almost co-spatial to the outer edge of the RR. As in the case of several other relics, the Mach number of the shock derived from the X-ray surface brightness profile ($M_X\approx 1.9$) appears to be lower than needed to explain the slope of the integrated radio spectrum in the diffusive shock acceleration (DSA) model ($M_R\approx 3.5$) if the magnetic field is uniform and the radiative losses are fast. However, the shock geometry is plausibly much more complicated than a spherical wedge centered on the cluster, given the non-trivial correlation between radio, X-ray, and SZ images. While the complicated shock geometry alone might cause a negative bias in $M_X$, we speculate on a few other possibilities that may affect the $M_X$-$M_R$ relation, including the shock substructure that might be modified by the presence of non-thermal filaments stretching across the shock and the propagation of relativistic electrons along the non-thermal filaments with a strong magnetic field. We also discuss the "history" of the radio galaxy NGC4789, which is located ahead of the relic in the context of the Coma-NGC4839 merger scenario.

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