Non-thermal radio supernova remnants of exiled Wolf-Rayet stars
MMon. Not. R. Astron. Soc. , 000–000 (0000) Printed 12 February 2021 (MN L A TEX style file v2.2)
Non-thermal radio supernova remnants of exiled Wolf-Rayet stars
D. M.-A. Meyer (cid:63) , M. Pohl , , M. Petrov and L. Oskinova , Universit¨at Potsdam, Institut f¨ur Physik und Astronomie, Karl-Liebknecht-Strasse 24/25, 14476 Potsdam, Germany DESY Platanenallee 6, 15738 Zeuthen, Germany Max Planck Computing and Data Facility (MPCDF), Gießenbachstrasse 2, D-85748 Garching, Germany Department of Astronomy, Kazan Federal University, Kremlevskaya Str 18, Kazan, Russia
Received; accepted
ABSTRACT
A signification fraction of Galactic massive stars ( (cid:62) (cid:12) ) are ejected from their parentcluster and supersonically sail away through the interstellar medium (ISM). The winds ofthese fast-moving stars blow asymmetric bubbles thus creating a circumstellar environmentin which stars eventually die with a supernova explosion. The morphology of the resultingremnant is largely governed by the circumstellar medium of the defunct progenitor star. Inthis paper, we present 2D magneto-hydrodynamical simulations investigating the effect of theISM magnetic field on the shape of the supernova remnants of a
35 M (cid:12) star evolving through aWolf-Rayet phase and running with velocity and
40 km s − , respectively. A µ G ambientmagnetic field is sufficient to modify the properties of the expanding supernova shock frontand in particular to prevent the formation of filamentary structures. Prior to the supernova ex-plosion, the compressed magnetic field in the circumstellar medium stabilises the wind/ISMcontact discontinuity in the tail of the wind bubble. A consequence is a reduced mixing effi-ciency of ejecta and wind materials in the inner region of the remnant, where the supernovashock wave propagates. Radiative transfer calculations for synchrotron emission reveal thatthe non-thermal radio emission has characteristic features reflecting the asymmetry of exiledcore-collapse supernova remnants from Wolf-Rayet progenitors. Our models are qualitativelyconsistent with the radio appearance of several remnants of high-mass progenitors, namelythe bilateral G296.5+10.0 and the shell-type remnants CTB109 and Kes 17, respectively. Key words: methods: MHD – radiation mechanisms: non-thermal – stars: massive – ISM:supernova remnants.
Massive stars are born with masses M (cid:63) (cid:62) (cid:12) . Despite theirrareness, they are of prime importance in the cycle of matter inthe interstellar medium (ISM) of our Galaxy (Langer 2012). Af-ter a relatively long hydrogen-burning main-sequence phase, theyexperience a series of evolutionary phases characterised by abruptchanges in their surface properties (radius, effective temperature,mass-loss rate and wind velocity). Those evolutionary phases al-ternate between hot, possibly eruptive phases of dilute supersonicwinds (Brott et al. 2011) and colder periods of inflated radiuswith a dense, slow stellar wind (Ekstr¨om et al. 2012). The numberand characteristics of the post-main-sequence phases are, amongstother, a function of the initial mass, the intrinsic rotation (Yoon &Langer 2005), and the chemical composition of the star (Sanyalet al. 2017). These various winds produce shells in the circum-stellar medium that develop instabilities and eventually collide to-gether (Garcia-Segura et al. 1996; Freyer et al. 2003, 2006). They (cid:63) E-mail: [email protected] chemically enrich the ISM and drive turbulence in it, on accountof the large amount of momentum and energy the winds deposit inthe stellar surroundings. Finally, the majority of massive stars endtheir life as core-collapse supernova, whose shock wave expandsinto their circumstellar medium (Woosley et al. 2002), shaped bystellar winds and radiation.Wolf-Rayet stars are an advance evolutionary stage of starswith initial mass (cid:62)
20 M (cid:12) , generally following a supergiant phase.Their stellar winds are fast, dense, and chemically enriched in C,N and O elements (Hamann et al. 2006; Bestenlehner et al. 2014;Sander et al. 2012). The interaction of fast Wolf-Rayet wind withslower wind material expelled at previous evolutionary stage resultsin complex stellar surroundings such as ring nebulae (Gvaramadzeet al. 2010a; Stock & Barlow 2010; Meyer et al. 2020) or bipolarbubbles (Gvaramadze et al. 2010b). A fraction of Wolf-Rayet starsare located at high Galactic latitude (Munoz et al. 2017; Toal´a et al.2018; Moffat et al. 1998). These fast-moving Wolf-Rayet stars thatleft their parent stellar clusters and reached low-density regions ofthe ISM. There, they eventually explode as a core-collapse super-nova inside the cavity carved by the stellar wind (Franco et al. 1991; © 0000 RAS a r X i v : . [ a s t r o - ph . H E ] F e b D. M.-A. Meyer et al.
Rozyczka et al. 1993; Dwarkadas 2007). Wolf-Rayet-evolving starsare therefore ideal progenitor candidates for core-collapse super-nova remnants (Katsuda et al. 2018).Several mechanisms determine the morphology of the super-nova remnants of massive progenitors. Clumpiness affecting theshock-wave propagation can arise from wind-wind interaction asobserved in the supernova remnant Cas A (van Veelen et al. 2009).In addition to instabilities directly developing in the supernova ex-plosion itself (Janka et al. 2016), asymmetries in supernova rem-nants may be a direct consequence of interactions between the ex-panding shock wave and an anisotropic circumstellar medium. Ofprime importance for the shaping of supernova remnants is the pe-culiar motion of very high-mass progenitors moving through theISM (Meyer et al. 2020). As an example, RWC 86 (Broersen et al.2014; Gvaramadze et al. 2017) or the Cygnus Loop (Aschenbach& Leahy 1999; Fang et al. 2017) reveal features consistent withthe typical characteristics of off-center explosions in massive stel-lar wind bubbles, suggesting that they might have been producedby a fast-moving progenitor, see also Toledo-Roy et al. (2014). Allthe numerous mechanisms, that induce deviations from spheric-ity in supernova shock waves, can operate in parallel, providinga huge parameter space governing the evolution of core-collapsesupernova remnants. Explanations of their observed morphologiesare subject to degeneracies and alternative scenarios. RunawayWolf-Rayet stars constitute therefore the ideal candidates for theproduction of isolated, asymmetric core-collapse supernova rem-nants (Meyer et al. 2015).The structure and properties of the ISM are also involved inthe shaping of supernova remnants (Ferreira & de Jager 2008). TheISM has an intrinsic filamentary, turbulent, and magnetised nature.Its gravito-turbulent evolution, powered by the formation of mas-sive pre-stellar cores, stellar wind outflows, and supernova feed-back enriching the ISM, drives turbulence in it and participates inthe formation of the next generation of stars. Native ISM magneticfield is an important player in the evolution of the circumstellarmedium around massive stars. As an example, the internal physicsof bow shock nebulae around runaway stars (Gvaramadze et al.2014; Meyer et al. 2014; van Marle et al. 2014; Meyer et al. 2017),as well as the organisation of supernova remnants (Orlando et al.2007; Ferreira & de Jager 2008; Orlando et al. 2008; Schneiter et al.2010; Orlando et al. 2012) are partially determined by the local am-bient magnetic field. Furthermore, the local direction of magneticfield makes thermal conduction anisotropic (Balsara et al. 2008;Meyer et al. 2017) and can suppress (magneto-)hydrodynamicalinstabilities (Viallet & Baty 2007; van Marle et al. 2014). Impor-tantly, it has been shown that the magnetisation of the ISM stronglyelongates stellar wind bubbles around static massive stars along thedirection of the local field lines (van Marle et al. 2015). The ques-tion is therefore, how important for the shaping of the supernovaremnants are the effects of the ISM magnetisation as compared tothose of the motion of runaway Wolf-Rayet progenitors?In this work, we investigate, by means of numerical magneto-hydrodynamical (MHD) simulations, the effects of a backgroundISM magnetic field on the morphological evolution of supernovaremnants generated by runaway massive progenitors. We adoptthe standard two-dimensional axisymmetric approach developed bymany authors (Comer´on & Kaper 1998; Mackey et al. 2012; Meyeret al. 2016). It consists in first modeling the pre-supernova circum-stellar medium of massive progenitors before launching a super-nova blastwave in it (Vel´azquez et al. 2006; Chiotellis et al. 2012;van Marle et al. 2012; Meyer et al. 2015). We examine the rem-nant morphologies and perform radiative transfer calculations for their non-thermal radio synchrotron emission maps. The mixing ofsupernova ejecta, stellar winds and ISM material is also discussed,comparing models with and without ISM magnetic field. Last, wediscuss these remnants in the context of cosmic-ray acceleration be-fore comparing them to Galactic supernova remnants from massiveprogenitors.Our study is organised as follows. First, we present the numer-ical methods used for the MHD simulations of supernova remnantsof
35 M (cid:12) runaway massive stars in Section 2. We describe our re-sults for the dynamical evolution of both the stellar surroundingsand the supernova remnant, together with predictive non-thermalradio synchrotron emission maps of these objects in Section 3. Weanalyse therein the effects of the presence of the ISM magneticfield onto the remnants evolution. Our results are further discussedin Section 4, and finally, we present our conclusions in Section 5.
This section describes the methods used to perform simulations ofthe circumstellar medium of a
35 M (cid:12) massive star evolving up tothe Wolf-Rayet phase and ending its life in a supernova explosion.We simulate the stellar surroundings from the zero-age phase ofthe progenitor to the late phase of supernova remnant evolution,varying the velocity of the star relative to the ISM and investigat-ing the role of the ISM magnetic field. The simulations are usedfor further radiative-transfer calculations of non-thermal radio syn-chrotron emission.
The pre-supernova circumstellar medium around the progenitorstar is the wind-blown bubble generated by interaction betweenthe stellar wind and the local ISM. We simulate it as describedin Meyer et al. (2020). We first perform 2D cylindrical, axisymmet-ric, magneto-hydrodynamics numerical models with a coordinatesystem [ z min ; z max ] × [ O ; R max ] which is mapped with a uniformgrid of spatial resolution R max /N R . The stellar wind of the
35 M (cid:12) star is released at the center of the domain into a uniformly dis-tributed ISM. A circular wind zone of radius cells is filled withthe wind density profiles, ρ w ( r ) = ˙ M πr v w , (1)where ˙ M is the wind mass-loss rate at different evolutionary phasesinterpolated from a stellar evolutionary track, r is the distance tothe origin of the domain, O , and v w is the velocity of the stellarwind (Comer´on & Kaper 1998; van Marle et al. 2011, 2014).In Fig. 1 we show the evolutionary path of the star and itswind, that we use in the simulations. The stellar mass (panel a, in M (cid:12) ), the mass-loss rate (panel b, in M (cid:12) yr − ), and the terminalwind velocity (panel c, in km s − ) are displayed beginning at theage . The wind properties of this zero-age-main-sequence,non-rotating - M (cid:12) star at Galactic metallicity has been interpo-lated from the Geneva library of stellar models calculated with the GENEC code (Ekstr¨om et al. 2012) by means of the online interface
SYCLIST . The terminal speed, v w , is modified for high effective , 000–000 adio supernova remnants of Wolf-Rayet stars M / M (a) l o g M / M y r (b) Stellar age (Myr) v w / k m s (c) Main-sequenceRed supergiant Wolf-Rayet
Figure 1.
Stellar properties at the end of the main-sequence and during thepost-main-sequence evolution of the
35 M (cid:12) star. The panels show the stel-lar mass (top, panel a), mass-loss rate (middle, panel b), and wind velocity(bottom, panel c) as function of time (in
Myr ). temperatures and massive stars using the approximation of Eldridgeet al. (2006), v w = (cid:112) β ( T ) v esc = (cid:114) β ( T ) 2 GM (cid:63) R (cid:63) , (2)where v esc is the escape speed of the star, R (cid:63) the stellar radius, and, β w ( T ) = . if T (cid:54) , . if T (cid:54) , . if T > , (3)a corrective function depending on the temperature T .The star first experiences a rather long main-sequence phaselasting about . , blowing winds with ˙ M ≈ − . M (cid:12) yr − and v w ≈ − . After the long main-sequence phase,the star becomes cooler and inflates to become a red supergiantwith mass-loss rate ˙ M ≈ − M (cid:12) yr − and wind speed v w ≈
50 km s − . It finally evolves to the Wolf-Rayet phase, characterisedby both a high mass-loss rate ( ˙ M ≈ − . M (cid:12) yr − ) and a largewind speed ( v w ≈ − ). To study the circumstellar medium around runaway Wolf-Rayet stars, we conducted a series of simulations with varying stel-lar velocities spanning from v (cid:63) = 10 to v (cid:63) = 40 km s − . Thestar moves in z -direction, and we simulate in the frame of the star,ISM gas of number density n ISM ≈ .
79 cm − and temperature T ISM ≈ as in the H II regions around hot stars. The ISMmaterial flows in with speed v (cid:63) at the boundary z = z max . Outflowboundaries conditions are set at z = z min and R = R max , respec-tively. Each value of v (cid:63) is explored with and without magnetizationof the ISM. The ISM magnetic field direction is parallel to the Oz axis, as a direct consequence of the simulation geometry, and it isset to B ISM = 7 µ G that is typical value for the warm phase of theISM (van Marle et al. 2014, 2015; Meyer et al. 2017). The flow ofmaterial past the stellar wind is characterised by the Alfv´en speed, v A = (cid:114) B ISM · B ISM πnm H , (4)that together with the sound speed (Eq. 18) determines the Alfv´enicand sonic Mach number of the stellar wind bubble in the ISM. Welist both for each model in Table 1.A continuity equation, ∂ ( ρQ ) ∂t + ∇ · ( v ρQ ) = 0 , (5)is used to trace the mixing of stellar wind material into the ISM,with ρ the mass density, respectively. Initially, the tracer Q is setto Q ( r ) = 1 in the wind and to Q ( r ) = 0 in the ISM. After establishing the circumstellar medium around the pre-supernova massive star, we simulate the supernova explosion asa spherically-symmetric shock wave expanding into the freely-expanding stellar wind of the progenitor. The supernova-wind in-teraction then serves as initial condition of a subsequent two-dimensional calculation of the corresponding remnant (Meyer et al.2015, 2020). The properties of the blastwave are parametrised bythe explosion energy, E ej = 10 erg , and the ejecta mass, M ej = M (cid:63) − (cid:90) t SN t ZAMS ˙ M ( t ) dt − M NS = 11 .
64 M (cid:12) , (6)where t ZAMS and t SN denote the times of zero age and supernova,respectively, and M NS = 1 . (cid:12) is the mass of the remnant neu-tron star left behind the supernova explosion. Note that we use thecanonical explosion energy typically taken in hydrodynamical sim-ulations of supernova remnants (van Veelen et al. 2009; van Marleet al. 2010, 2012). However, detailed dedicated studies estimate theenergy released throughout the explosion of a core-collapse pro-genitor to be rather in the range E ej = 1 − × erg (Smartt2009; Janka 2012; Moriya et al. 2018). A passive scalar, Q ( r ) ,obeying the continuity equation, ∂ ( ρQ ) ∂t + ∇ · ( v ρQ ) = 0 , (7)is used to distinguish supernova ejecta from stellar wind or ISMmaterial, by setting Q ( r ) = 1 in the supernova-ejecta region and Q ( r ) = 0 otherwise.The supernova shock wave is released into the progenitor’sstellar wind bubble (Whalen et al. 2008; Zirakashvili & Ptuskin2018) by superposing a 1D blastwave density profile, ρ ( r ) , onto thepre-supernova wind distribution. We used a typical ejecta profilefor the early expansion of a core-collapse supernovae. It involves © 0000 RAS, MNRAS , 000–000 D. M.-A. Meyer et al. a homologuous expansion, v = r/t , the radius of the progenitorstar’s core at the time of the supernova, r core , and the outermostextension r max of the blastwave. We start the calculations at t max = r max v max , (8)where v max = 30000 km s − is the ejecta velocity at r max (vanVeelen et al. 2009). The value of r max is determined by the ex-plosion energy and ejecta mass (Whalen et al. 2008). The densityprofile of the ejecta is set as ρ ( r ) = (cid:40) ρ core ( r ) if r (cid:54) r core ,ρ max ( r ) if r core < r < r max , (9)where ρ core ( r ) = 14 πn (10 E n − ) − / (3 M n − ) − / t , (10)is constant, whereas the ejecta density further out follows a power-law, ρ max ( r ) = 14 πn (10 E n − ) ( n − / (3 M n − ) ( n − / (cid:18) rt max (cid:19) − n , (11)with n = 11 (Chevalier 1982; Truelove & McKee 1999).Beyond r max , the density profile is that of the freely-expanding wind as found in the pre-supernova wind bubble sim-ulations. The ejecta speed at the distance r core from the center ofthe explosion is (Truelove & McKee 1999) v core = (cid:18) n − E ej n − M ej (cid:19) / . (12)This 1D ejecta-wind interaction solution is mapped onto the 2Ddomain of the subsequent simulation. We integrate the equationsup to
150 kyr after the supernova.
The dynamics of a magnetised flow is described by the equations ofideal magneto-hydrodynamics plus losses and heating by optically-thin radiation, ∂ρ∂t + ∇ · (cid:0) ρ v ) = 0 , (13) ∂ m ∂t + ∇ · (cid:16) m ⊗ v + B ⊗ B + ˆI p t (cid:17) = , (14) ∂E∂t + ∇ · (cid:16) ( E + p t ) v − B ( v · B ) (cid:17) = Φ( T, ρ ) , (15)and, ∂ B ∂t + ∇ · (cid:16) v ⊗ B − B ⊗ v (cid:17) = , (16)with the linear momentum vector, m = ρ v , and the magnetic-fieldvector, B . The total energy of the system reads, E = p ( γ −
1) + m · m ρ + B · B , (17)where γ = 5 / is the adiabatic index for ideal gas and p is thethermal pressure. The definition of the adiabatic sound speed, c s = (cid:114) γpρ , (18) closes the system, which we integrate using the so-calledeight-wave algorithm. This second-order unsplit scheme satisfies ∇ · B = . The time-march of the algorithm obeys the standardCourant-Friedrich-Levy condition that is set to C cfl = 0 . at thebeginning of the simulations.The source term, Φ ( T, ρ ) = n H Γ( T ) − n Λ( T ) , (19)accounts for optically-thin radiative cooling, Λ ( T ) , and heating, Γ ( T ) . The gas temperature is T = µ m H k B pρ , (20)where µ = 0 . is the mean molecular weight, k B the Boltzmannconstant, and m H the proton mass. The hydrogen number densityis computed as n H = ρµ (1 + χ He , Z ) m H , (21)with χ He , Z the mass fraction of all coolants heavier than H . Thefunctions Γ( T ) and Λ( T ) are described in details in Meyer et al.(2017). The forward shock of the supernova remnant in particular will ac-celerate charged particles, such as electrons, to high energy. Inthe presence of magnetic field relativistic electrons produce syn-chrotron emission that is an excellent diagnostic (Reynolds 2008).To permit a comparison with the vast observational data of non-thermal radio synchrotron emission from supernova remnants, weproduce synthetic emission maps on the basis of our magneto-hydrodynamical simulations.Energy losses of GeV-scale electrons are likely negligible, andso we assume the electron spectrum, N ( E ) = KE − s , (22)where E denotes the electron energy and the index, s = 2 , is ex-pected for a strong shock. Diffusive transport is typically slowerthan advection in the GeV band, and so the accelerated electrondensity follows the gas density and is in fact proportional to it, ifthe injection efficiency at the forward shock is a constant (Drury1983b,a). Amongst the several prescriptions for the non-thermalsynchrotron emission coefficient of a magnetised gas available inthe literature, we choose to make use of that of Jun & Norman(1996). We refer the reader interested in details regarding to ourchoice of emission coefficient within this core-collapse supernovaremnant problem in our Appendix A. Therefore, at a given fre-quency, ν , the radio synchrotron emission coefficient reads, j sync ( ν ) ∝ K − s p s − B ( s +1) / ⊥ ν − ( s − / , (23)which reduces to j sync ( ν ) ∝ n − s p s − B ( s +1) / ⊥ ν − ( s − / , (24)where p is the gas thermal pressure and B ⊥ is the magnetic-fieldcomponent perpendicular to the line of sight.Let (cid:126)l be the unit vector of the observer’s line of sight. Defin-ing the viewing angle of the observer as θ obs = ∠ ( (cid:126)l, (cid:126)B ) , the totalstrength of the magnetic field and its perpendicular component areobtained as B ⊥ = | (cid:126)B | sin( θ obs ) (25) © 0000 RAS, MNRAS , 000–000 adio supernova remnants of Wolf-Rayet stars Figure 2.
Density rendering of the supernova remnant of a - M (cid:12) progenitor moving with v (cid:63) = 20 km s − through uniform ISM of number density n ISM = 0 .
78 cm − . Before exploding, the remnant passed through main-sequence, red supergiant and Wolf-Rayet phases (Ekstr¨om et al. 2012). The toppanel displays the hydrodynamical model, whereas the bottom one shows the magneto-hydrodynamical picture for a - µG ambient magnetic field orientedparallel to the stellar motion in z-direction. Inset boxes highlight the dynamic filamentary structures developing from ejecta-wind-ISM interactions (left inset)and the structure of the stellar wind cavity produced by the progenitor’s motion and located behind the center of the explosion (right inset). The red lines areiso-temperature contours ( T = 10 and K ), and the blue contours trace the region with a contribution of supernova ejecta in number density.© 0000 RAS, MNRAS , 000–000 D. M.-A. Meyer et al.
Figure 3.
As Fig. 2, but for the supernova remnant of a progenitor moving with
40 km s − .© 0000 RAS, MNRAS000
40 km s − .© 0000 RAS, MNRAS000 , 000–000 adio supernova remnants of Wolf-Rayet stars Table 1.
List of models. The columns indicate the velocity of the star, v (cid:63) , the grid resolution and size in pc, and the sonic and Alf´enic Mach number of themoving star with respect to the ISM. The runs are labelled ”CSM” for the pre-supernova modelling and ”SNR” for the remnant simulations, and likewise”HD” for hydrodynamics and ”MHD” for magneto-hydrodynamics. Model v (cid:63) ( km s − ) Grid size Grid mesh M M A Run-35-MHD-20-CSM
20 [0; 175] × [ − × . . Run-35-HD-20-CSM
20 [0; 175] × [ − × . . Run-35-MHD-40-CSM
40 [0; 150] × [ − × . . Run-35-HD-40-CSM
40 [0; 150] × [ − × . . Run-35-MHD-20-SNR
20 [0; 200] × [ − × . . Run-35-HD-20-SNR
20 [0; 200] × [ − × . . Run-35-MHD-40-SNR
40 [0; 200] × [ − × . . Run-35-HD-40-SNR
40 [0; 200] × [ − × . . and | (cid:126)B | = (cid:113) B + B . (26)Then, at a given frequency the emission coefficient finally reads, j sync ( θ obs ) ∝ n − s p s − (cid:32) | (cid:126)B | (cid:115) − (cid:16) (cid:126)B · (cid:126)l | (cid:126)B | (cid:17) (cid:33) ( s +1) / , (27)which we use in our radiative transfer calculations.For each simulation, we selected snapshots that are represen-tative of the phases of the supernova remnant evolution, namely attimes , and
40 kyr after the explosion, respectively. The cor-responding density, temperature, and magnetic-field distributionsare first translated from the two-dimensional cylindrical coordi-nates system to a three-dimensional spherical coordinate system( r , θ , φ ) with cells and the same origin, for which we rotatethe cylindrical solution around the symmetry axis. On each gridzone we pre-calculate the local component of the magnetic fieldthat is normal to line-of-sight of the observer. Finally, we use amodified version of the radiative transfer code RADMC-3D toperform ray-tracing integration of the radio synchrotron emissioncoefficient along a given line-of-sight with aspect angle θ obs . Thenon-thermal radio intensity, I = (cid:90) SNR j sync ( θ obs ) dl, (28)is then used to synthesize normalised emission maps. We present in this section the results for the pre- and post-supernova circumstellar medium of a runaway Galactic
35 M (cid:12) pro-genitor star, investigate how the stellar motion and the magnetisa-tion of the ISM affect the mixing of materials, and present the evo-lution of their projected radio synchrotron emission.
Fig. 2 presents our results for a star moving with v (cid:63) = 20 km s − ,comparing the hydrodynamical picture (top) with the magneto-hydrodynamical description (bottom). The red isocontours trace Q = 0 . , which marks the places in the remnant with a 50/50proportion of ISM and stellar wind. The wind of the massive star ∼ dullemond/software/radmc-3d/ generated an ovoid bubble of size ∼
100 pc (Fig. 2a) in which thestar is off-centered on account of stellar motion (cf. Weaver et al.1977; Meyer et al. 2020). The large-scale stellar-wind bow shock isorganised according to the classical picture of Weaver et al. (1977),made of an inner termination shock, a contact discontinuity, and anouter forward shock. They distinguish the expanding stellar wind,the hot low-density shocked wind, the cold dense ISM gas, and theambient medium, respectively. The post-main-sequence wind, i.e.the red supergiant and Wolf-Rayet materials, are released inside ex-panding stellar wind and develop instabilities at the interface sepa-rating the cold and hot gas (Fig. 2).For a larger speed of the star, v (cid:63) = 40 km s − , the sphericalsymmetry is broken, and the star reaches the forward shock of itsown wind bubble, itself distorted under the effects of stellar mo-tion (Fig. 3a,b). A chimney of unperturbed stellar wind is carvedinto the layer of shocked ISM, and the post-main-sequence windis blown through the tube (red isocontours). This phenomenon iseven more pronounced in the case of a very fast progenitor starwith v (cid:63) = 70 km s − (Meyer et al. 2015). Interestingly, once thestar has left its wind bubble, direct wind-ISM interaction resumesat the distance, R SO = (cid:115) ˙ Mv w πn ISM v (cid:63) , (29)and a new bow shock forms (Baranov et al. 1971). An analyticestimate for the location of the contact discontinuity of bow shocksreads R ( θ ) R SO = (cid:112) − θ )cotan( θ )sin( θ ) , (30)where θ is the angle to the direction of stellar motion (Wilkin 1996).This bow shock is in its turn subject to instabilities (Brighenti &D’Ercole 1995b,a) and constitutes the location in which the super-nova explosion takes place (Brighenti & D’Ercole 1994; Chiotelliset al. 2012; Meyer et al. 2015).The interstellar magnetic field has strong impact on the distri-bution of shocked ISM, as demonstrated in van Marle et al. (2015).As an example, in Figs. 2b and 3b one clearly sees that the layerof shocked ISM is puffed up along the local magnetic field as aresult of the damping of Alfv´en waves (van Marle et al. 2015).The effect is weaker for a fast-moving progenitor on account of thelower ratio of magnetic and ram pressure (Fig. 3b). The entire inte-rior structure of the wind bubble is elongated when the star movesquickly. The magnetic-field lines are aligned with the terminationshock and discontinuities, providing additional pressure that mod-ifies the circumstellar gas dynamics (Figs. 2b). It can also damp © 0000 RAS, MNRAS , 000–000 D. M.-A. Meyer et al.
Figure 4.
Mixing of material in supernova remnants from massive runaway progenitors. The top row displays results for v (cid:63) = 20 km s − and the bottompanels are for v (cid:63) = 40 km s − . The left column shows purely hydrodynamical models while the right column is for MHD runs. Each remnant is shown attime
40 kyr after the supernova explosion. Each image gives the ISM fraction ( − Q ) and the fraction of stellar-wind material ( Q ) in the left and rightpart, respectively. The black temperature contours have the levels T = 10 , , K and the white number density contours stand for n = 1 . , , , cm − . The blue contours make the locations with
10 % ejecta fraction by number. instabilities at the contact discontinuity between hot shocked windand cold shocked ISM gas, primarily in the tail of the wind bubble.Our models combine the asymmetry in the stellar wind bubbles ofmoving stars (Meyer et al. 2015) with the magnetic-pressure ef-fect that were previously explored for static stars (van Marle et al.2015).
Fig. 4 displays the structure of the supernova remnant at time
40 kyr after the explosion. Each panel corresponds to a differentsimulation, with density plotted on the left-hand part of the paneland the temperature on the right-hand part of the panel, respec-tively. The blue isocontour marks the regions with 10% abundanceof ejecta in number density. The left panels are derived from hy- © 0000 RAS, MNRAS , 000–000 adio supernova remnants of Wolf-Rayet stars Figure 5.
Comparison between the diffusion timescale, ∆ diff , and the ad-vection timescale, ∆ adv , of a particle accelerated at the forward shock ofthe supernova remnant in our simulation Run-35-MHD-40-SNR of a - M (cid:12) progenitor moving with v (cid:63) = 40 km s − . The quantity ∆ diff / ∆ adv is plotted as a function of remnant age for several values of η and syn-chrotron frequency ν sync , respectively. Values well below unity imply thatdiffusion can be neglected in the estimate of radio emission maps. drodynamical simulations, to be compared with MHD results onthe right. The stellar velocities are v (cid:63) = 20 km s − (top) and v (cid:63) = 40 km s − (bottom), respectively.The shape of the supernova remnants are governed by the dis-tribution of the pre-supernova circumstellar medium (Meyer et al.2015, 2020). Figs. 4b,d show that the faster the progenitor movesthrough the ISM, the sooner the supernova shock wave interactswith the termination shock of the progenitor’s wind bubble. Forsmaller v (cid:63) , the elongated shape of the MHD wind bubble permitsthe Wolf-Rayet wind to expands freely into the unperturbed red su-pergiant stellar wind and to generate by wind-wind collision a ringof dense swept-up material (Meyer et al. 2020), inside of which theblastwave is subsequently released and expands spherically. A sim-ilar situation has been explored for static progenitor in the contextof Cas A (van Veelen et al. 2009). This phenomenon is particularlyprominent for small ISM density, n ISM (cid:28) , since the radius of themain-sequence wind termination shock is much larger (van Marleet al. 2015), and so is the region filled by the last free-streamingwind.The effects of the ISM magnetic field are also more pro-nounced for low progenitor speed, v (cid:63) = 20 km s − . The super-nova remnant shock wave rapidly interacts with the wind bubble inthe progenitor’s direction of motion, and it is first reverberated to-wards the center of the explosion and subsequently channelled intothe wind cavity carved during the main-sequence phase, inducing ahot region hosting a lot of mixing of wind, ejecta and shocked ISMgas (Fig. 4a). The reflections are different in the MHD case, wherethey occur both parallel and normal to the progenitor’s motion, onaccount of the tubular shape of the shocked-wind region (Fig. 4b,d).A different morphology arises for fast-moving progenitors, with arather unmixed lobe of shocked ISM ahead of the stellar motion,and a channelled region of mixed ejecta and wind material in thetail (Figs. 4c,d). Magnetic field changes the morphology of the pre-supernova stel-lar wind bubble, which will eventually influence the structure of the
Figure 6.
Normalised projection of the magnetic field perpendicular to theline of sight, B ⊥ /B , for model Run-35-MHD-40 model with progenitorspeed v (cid:63) = 40 km s − at time
80 kyr after the supernova explosion. Theblack arrow marks the direction of the observer’s line-of-sight, making anangle θ obs = 45 ◦ with the z -axis. remnant and the mixing of material in it. At a magnetized shock,the component of the magnetic field along the shock normal re-mains unchanged, and that in the shock plane is compressed (Shu1992). This results in an increased magnetic pressure in the shockedISM and, consequently, in an enlargement of the bubble perpendic-ular to the direction of motion, which for static wind bubbles hasbeen demonstrated by van Marle et al. (2015). Further effects area reduced compression ratio of the forward shock and a puffing-upof the shocked ISM gas layer. Although the MHD jump conditionsimply that the ISM field is not compressed ahead of the star, sincethe cylindrical coordinate system imposes a parallel field, we cannot exclude that this is an artefact. We refer the reader to the thor-ough discussion in Meyer et al. (2017). Fully three-dimensionalsimulations of both the pre-supernova and remnant phase of mov-ing massive progenitor star are necessary to address this questionin appropriate detail. We perform a back-of-the-envelope estimate of the validity of ourassumptions regarding the radio synchrotron emission. We selectone-dimensional cross-section of the flow variables ρ , p and T orig-inating from the center of the explosion and following the directionof stellar motion, along the axis of symmetry, Oz , in the models, re-spectively. We then measure the time-dependent position, R FS ( t ) ,and speed, v FS ( t ) , of the forward shock, using the shock-finder al-gorithm of the RATPAC code (Telezhinsky et al. 2012, 2013; Bhattet al. 2020). The radiation synthesis is based on the assumption thatthe forward shock accelerates a certain fraction of particles passingthrough it, and that the subsequent transport of radio-emitting elec-trons in the downstream region is entirely advective.In our radiation transfer model, diffusion is neglected and weshall now verify this assumption. Upstream of the forward shockthe density of electrons re-accelerated as cosmic-rays exponentially © 0000 RAS, MNRAS , 000–000 D. M.-A. Meyer et al.
Figure 7.
Normalised maps of radio synchrotron intensity of supernova remnants with progenitor speed v (cid:63) = 20 km s − at times (top),
40 kyr (middle)and
80 kyr (bottom) after the supernova explosion, respectively. The viewing angle between the equatorial plane and the line of sight is θ obs = 0 ◦ (left), θ obs = 45 ◦ (middle), and θ obs = 90 ◦ (right). decreases, N ( E, x ) ∝ e − x/x c ( t ) with length scale, x c ( t ) = D ( E ) v FS ( t ) , (31)where D ( E ) the diffusion coefficient and E the energy of the elec-trons. For simplicity, we shall assume that the diffusion coeffi-cient is a multiple of the Bohm limit, D ( E ) ≈ ηD Bohm ( E ) = η c/ r L ( E ) , where r L denotes the Larmor radius of the electronsand η is a scalar controlling the . Using the characteristic frequency of synchrotron radiation, Eq. 31 can be rewritten as x c ( t )pc (cid:39) η (cid:114) ν syn
10 GHz (cid:18) v FS ( t )3000 km / s (cid:19) − (cid:18) B ( t )10 µ G (cid:19) − . . (32)It is evident that for reasonably well developed cosmic-ray scat-tering ( η (cid:28) ) the precursor of radio-emitting electrons is tinycompared to the size of the system and produces a negligible contri-bution of synchrotron emission. Note that a significant abundanceof magnetic field perpendicular the shock surface will slow downdiffusive transport away from the shock and hence reduce η .Diffusion in the downstream region may transport electronsbeyond the discontinuity to the ejecta region. Within time t , ad- © 0000 RAS, MNRAS , 000–000 adio supernova remnants of Wolf-Rayet stars vective transport displaces electrons from the shock by the dis-tance ∆ adv (cid:39) t v FS ( t ) / . Diffusive transport displaces by ∆ dif (cid:39) (cid:112) D ( E ) t , and so ignorability of diffusion requires t v FS ( t ) / (cid:29) (cid:112) D ( E ) t ⇒ t v FS ( t ) (cid:29) x c ( t ) . (33)With x c as given in Eq. 32 we find that the condition is likely met.Fig. 5 plots ∆ diff / ∆ adv as a function of time for our simulationmodel Run-35-MHD-40-SNR and several values of η (cid:54) and ν sync (cid:54) . To be noted from the figure is that ∆ diff / ∆ adv (cid:28) for times (cid:54)
200 kyr , and consequently we can ignore cosmic raydiffusion in the production of radio emission maps.
We generate non-thermal radio emission maps from our MHDmodels of supernova remnants at representative points of time inthe evolution of the supernova remnants. Using the procedure de-scribed in section 2.4 we pre-compute for each viewing angle, θ obs , the distribution of magnetic field normal to the line of sight, B ⊥ . An illustrative example based on model Run-35-MHD-40 attime
80 kyr is given in Fig.6. Then we compute the radio inten-sity with our modified version of the
RADMC D code. In Fig. 7we show intensity maps for supernova remnant ages (top),
20 kyr (middle )and
80 kyr (bottom) for a progenitor moving with v (cid:63) = 20 km s − . We selected three viewing angles to the equato-rial plane, θ obs = 0 ◦ (left), θ obs = 45 ◦ (middle) and θ obs = 90 ◦ (right) and normalised the background-substracted maps. Fig. 8displays corresponding radio maps for v (cid:63) = 40 km s − .Model Run-35-MHD-20 with progenitor moving at v (cid:63) =20 km s − traces the expanding supernova blastwave that is dis-torbed by its interaction with the circumstellar medium. Later,
40 kyr after the explosion, the expanding shock wave has reachedthe unperturbed ISM and is fairly bright there. The radio arcs arenow larger than at time
20 kyr and the brightest region on the sideshave a bilateral morphology. Note that the maps are background-subtracted, and the region of shocked stellar wind may be dimmerthan the galactic radio background, leaving only the filamentaryarcs prominently visible. For an inclination angle θ obs = 45 ◦ theremnants look rounder and more bubbly. One and the same remnantcan appear with bilateral or arced structures depending on θ obs . For θ obs = 90 ◦ the observer’s line-of-sight is aligned with the directionof stellar motion, and the projected remnant appears as a ring-likestructure in the sky, on account of the two-dimensional nature ofthe simulations. Since the magnetic field is parallel to the stellarmotion, B ⊥ (cid:39) in the shocked ISM, and the brightest emissionoriginates from the regions of mixing, primarily in the reflectedshock wave.The radio intensity maps of our simulation Run-35-MHD-40with progenitor speed v (cid:63) = 40 km s − are shown in Fig. 8. Theemission are brighther than in model Run-35-MHD-20 as a resultof the faster progenitor star producing stronger shocks in its super-nova remnant. At time after the explosion, the shock wavehas already been greatly distorted by the Wolf-Rayet circumstellarmaterial and has lost sphericity to become as ovoid-like structure.Later in time, the shock wave adopts a hour-glass-like shape thatappears spherical in the radio map for θ obs = 45 ◦ and to a lesserdegree at θ obs = 0 ◦ . After
40 kyr , the remnant has an bulb-likemorphology which arises from both the shock wave expansion intothe ISM and the channeling of the shock wave into the low-densitycavity of unshocked stellar wind in the tail. The radio intensity peakshifts to the location where the shock wave intercepts the trail of stellar wind (Fig. 8d,e). The density in the region of wind-ISM in-teraction is more important than in the case of a progenitor movingwith v (cid:63) = 20 km s − , and so the stabilising effect of the mag-netic field inside of the remnant is reduced. Hence, more ring-likestructures appear in the emission maps, for example in Fig. 8h. Wewould observe a series of concentric rings for θ obs = 90 ◦ , each ofthem corresponding to a ring in the trail of shocked stellar wind in-teracting with the channelled supernova shock wave. There is morevariety and complexity in the radio appearance for faster-movingprogenitors. This section discusses the limitations of our method, compares ourresults to earlier results, and further examines our findings in thecontext of particle acceleration. Finally, we compare our resultswith observational data.
As any numerical study, our method suffers from simplificationsthat limit the realism of our results. The most obvious one is thecylindrical coordinate system with rotational invariance, which in-trinsically imposes a symmetry axis to the models. This approachis convenient in the modelling of the circumstellar medium of mas-sive stars and their subsequent supernova remnants (Franco et al.1991; Rozyczka & Tenorio-Tagle 1995; Comer`on 1997; Comer´on& Kaper 1998; van Marle et al. 2005, 2007; Ferreira & de Jager2008; van Marle et al. 2014; Green et al. 2019), at the expense offorcing an directional alignment of the motion of the progenitor, thelocal ISM magnetic field, and progenitor’s axis of rotation. Onlyfully three-dimensional simulations permit flexibility in the direc-tional arrangement (e.g. Katushkina et al. 2017, 2018), but they arefar too expensive to permit scanning the parameter space of rem-nants from massive progenitors.Supernova remnants from massive progenitors are multi-phase regions composed of a warm, magnetized interstellarmedium through which the progenitor star moves, the evolving stel-lar wind, and a hot component produced by the interaction betweenthe supernova shock wave and the material of the wind bubble andthe shocked ISM gas. Supernova remnants may be located closeto dense, cold molecular clouds that can further affect their evo-lution and modify the gas chemistry. The pressure of the cosmicrays accelerated in the supernova remnant (Ferrand et al. 2014),anisotropic heat transfer (Orlando et al. 2005), photoionizing pro-genitor radiation, or the turbulence in the ISM should also be in-cluded in the models (Moranchel-Basurto et al. 2017; Villagranet al. 2020), but that is far beyond the scope of the current study andmay be considered in future work. Last, note that intrinsic densemolecular (Zhou & Chen 2011; Zhou et al. 2014, 2016) or low-density components (Arias et al. 2019,?) of the ambient mediumare an additional, in some context an even preponderant element totake into account in the shaping of core-collapse supernova rem-nants.
This study extends earlier work beginning with Meyer et al. (2015)on hydrodynamical models of supernova remnants of runaway starswith initial , and
40 M (cid:12) , that end their lives as red supergiantsand generate Cygnus-Loop-like nebulae. The second study of this © 0000 RAS, MNRAS , 000–000 D. M.-A. Meyer et al.
Figure 8.
As Fig. 7 but here for model Run-35-MHD-40-SNR with progenitor moving with
40 km s − . series explored the appearance of wind nebulae and remnants of a
60 M (cid:12) progenitor star going through Luminous-Blue-Variable andWolf-Rayet phases, with emphasis on the mixing of material in-side the remnant Meyer et al. (2020). What is new and different inthe present study is the inclusion of the ISM magnetic field dur-ing both the pre- and the post-supernova phase, together with thepost-processing of radio synchrotron intensity maps. The effect ofISM magnetisation on the environment of massive stars has beeninvestigated by van Marle et al. (2015), albeit without distinguish-ing ejecta from wind and ISM gas as we do by means of passivescalar tracers. Moreover, our models include a state-of-art stellarevolutionary model for the wind history of the
35 M (cid:12) star that weconcentrate on.
Katsuda et al. (2018) determined several properties, such as the dis-tance and the progenitor mass, of core-collapse supernova remnantsin the Milky Way and in low-metallicity dwarf galaxies such asthe Large and Small Magellanic Clouds. They found that most ofthe identified remnants of massive progenitors in the Galaxy havea zero-age main-sequence mass (cid:62) . (cid:12) . There is a generalagreement between predictive stellar evolution models that the pro-genitor exploded with such mass, either as a red supergiant or as aWolf-Rayet star, although more exotic situations such as blue su-pergiant progenitor star exist (Hillebrandt et al. 1987). Note that, inthe context of massive binary systems, the explosion of the compo-nent can kick the companion, producing runaway stars (Lux et al. © 0000 RAS, MNRAS , 000–000 adio supernova remnants of Wolf-Rayet stars
35 M (cid:12) star. As we concentrate on the evolutionof rather older remnants, about −
80 kyr after the explosion, ourpredictions are applicable to the objects listed between Kes 79 andW51C in Table 1 of Katsuda et al. (2018).Our models constitute baseline models to be further tailoredto specific supernova remnants, in particular Kes 79, G350.1-0.3,G292.0+1.8, RX J1713.7-3946, Kes 79, G290.1-0.8, 3C391, W44,G284.3-1.8 or CTB109. Note that C, N and O enriched material,witness of post-main-sequence winds from massive stars, has beendirectly observed in the remnant G296.1-0.5 (Castro et al. 2011),making it an evident candidate of a supernova remnant with Wolf-Rayet progenitor that is worth exploring numerically with sim-ulations like ours. As underlined by Katsuda et al. (2018), thedistribution of core-collapse supernovae in the Galaxy does notfit any initial mass function, which suggest that there should bemany more unidentified remnants our simulations would be ap-plicable to. Note also that models for core-collapse remnants donot generally apply to the so-called historical supernova remnantssince these are mostly of type Ia (Green & Stephenson 2003), ex-cept for Cas A (van Veelen et al. 2009; Zhou et al. 2018) andRWC 86 (Gvaramadze et al. 2017), respectively.The space motion of the progenitor is the other fundamen-tal ingredient of our simulations, together with the zero-age main-sequence mass. If the massive progenitor is at rest, then its circum-stellar wind bubble remains spherical (Weaver et al. 1977). Thestar, and the center of its subsequent explosion are located at itscenter (Freyer et al. 2006; Dwarkadas 2007). A sub-sonic motionof the progenitor will off-center the remnant with respect to thewind bubble without changing its overall appearance (Meyer et al.2020). Hence, remnants from slowly-moving progenitor star shouldreflect the spherical symmetry of their circumstellar medium. How-ever, as in-situ star formation does not seem to be an obviousroute to explain isolated Wolf-Rayet stars (Gvaramadze et al. 2012;Meyer et al. 2020), static massive stars should live and die insideof their parent star-formation region, where they would participatein the regulation of subsequent star formation (Paron et al. 2009).The feedback from stellar winds and/or jets of other (young) stel-lar objects (Bally et al. 2007; Fendt 2009; Fendt & Sheikhnezami2013) will affect the medium in which massive stars form (Murrayet al. 2018), evolve and die. This should result in a very complexmorphology, possibly further complicated by ISM cavities and en-hanced levels of turbulence, in the ambient medium hosting a hugemix of material in a super bubble in which the supernova subse-quently explodes (van Marle et al. 2012).
Most supernova remnants in the Milky Way lie within ◦ ofthe galactic plane. The dilute ISM at high galactic latitudesmakes (circumstellar) shocks weaker, resulting in fainter super-nova remnants such as, for example, the rather evolved radio sourceG181.1+9.5 (Kothes et al. 2017). This latitude-dependence of theradio surface brightness of supernova remnants is known as the Σ -D relation (Caswell & Lerche 1979). The modelled
35 M (cid:12) run-away star moving with v (cid:63) = 40 km s − travels about
220 pc be-fore exploding, about the same as the height of G181.1+9.5 abovethe galactic plane ( ≈
250 pc ). Dedicated simulations would behighly desirable to explore the differences in the radio propertiesbetween supernova remnants of runaway progenitors in the Galac-tic place and those at higher galactic latitudes, as well as the effectsof metallicities. Our non-thermal radio emission maps authorise a couple of further, direct comparisons with supernova remnants ofmassive, evolved progenitors, namely G296.5+10.0, the shell-typeremnants CTB 109, and Kes 17.First, G296.5+10.0 is a supernova remnant of core-collapseorigin, confirmed by the trace of magnetised wind in which the su-pernova shock wave expands, and the presence of a neutron startherein (Harvey-Smith et al. 2010). Radio observations with theAustralia Telescope Compact Arrary at . GHz reveal a bipolarshape, that is qualitatively similar to those in our model with veloc-ity v (cid:63) = 20 km s − , Run-35-MHD-20-SNR, at time , whenthe shock wave interacts with the stellar-wind bow shock and accel-erates electrons (Fig. 7a). Similarly, Fig. 8a also resembles greatlythe old bilateral supernova remnant G296.5+10.0, implyingthat its progenitor might have been a rather fast moving star of mass −
40 M (cid:12) . Secondly, the shell-type remnant CTB 109 is the rem-nant of a core-collapse supernova remnant of a - (cid:12) progeni-tor, which matches the mass range of the - M (cid:12) stellar model usedin this study. Its age is around , see Katsuda et al. (2018).According to our results, CTB 109 should be surrounded by acircumstellar structure, i.e. a red-supergiant wind bubble engulfinga Wolf-Rayet ring, with which the supernova shock wave interacts,although its overall shape has been reproduced in the context of atype Ia explosion, i.e. without the presence of a dense circumstellarwind bubble generated by a massive progenitor (Bolte et al. 2015).Its opened shell appearance, e.g. as seen with the Canadian Galac-tic Plane Survey at (Kothes & Foster 2012), is similar toour model Run-35-MHD-SNR at times -
40 kyr (Fig. 8b,e). Notealso that CTB 109 is a hadronic gamma-ray emitter (Castro et al.2012). The last example is the supernova remnant Kes 17 that is lessthan old and with a progenitor mass - (cid:12) consis-tent with the Wolf-Rayet scenario (Katsuda et al. 2018). Its double-arced morphology observed with the Australian Telescope Array at
20 cm resembles our model Run-35-MHD-40-SNR at times
40 kyr (Fig. 8c).
We explore the formation, structure, and radio signatures of su-pernova remnants of massive, Wolf-Rayet-evolving supernova pro-genitors ejected from their parent cluster and moving through theinterstellar medium (ISM) of the Milky Way. Our study concen-trates on the coupled impact of stellar motion and the magnetisa-tion of the ISM. We perform magneto-hydrodynamical simulationsover the entire stellar lifetime, as they successively evolve througha long main-sequence phase, a red supergiant and a Wolf-Rayetphase, and eventually spawn a core-collapse supernova remnant.Numerical models are performed with the
PLUTO code (Mignoneet al. 2007, 2012) by simulating the circumstellar medium of mas-sive stars, into which we launch a core-collapse supernova shockwave. We follow its interaction with the stellar surroundings andthe local ambient ISM supported by an organised µ G magneticfield. Considering two speeds of the runaway progenitors and run-ning the simulations up to the oldest evolutionary phase of the su-pernova remnants,
150 kyr after the explosion, their morphologies,their structures, the mixing of material happening in them are ex-plored.The presence of an ISM magnetic field profoundly affects thegas properties. Prior to the supernova explosion, the compressedmagnetic field in the circumstellar medium stabilises the wind/ISMcontact discontinuity in the tail of the bubble. Indeed, compressedmagnetic field in the outer remnant stabilises and elongates the © 0000 RAS, MNRAS , 000–000 D. M.-A. Meyer et al. wind/ISM contact discontinuity of the cavity of unshocked stel-lar wind, in which the ejecta is channelled. A consequence is areduced mixing efficiency of ejecta and evolved stellar-wind ma-terial enriched in C, N and O elements in the inner region of theremnant, where the supernova shock wave propagates. Moreover,after the supernova explosion, the density downstream of the super-nova shock front is reduced in our MHD simulations when it prop-agates into the pristine ambient medium, on account of the damp-ing of turbulence. This must influence the acceleration processesof cosmic-ray electrons and protons in supernova remnants frommassive progenitors and will be investigated in future works (Bhattet al. 2020). We emphasize the need for a careful treatment of thegas microphysics to properly simulate young supernova remnantsinteracting with circumstellar structures. This particularly appliesto runaway massive progenitors whose supernova shock front isreverberated towards the center of the explosion, generating a com-plex region made of shocks, discontinuities, and filamentary struc-tures, in which non-thermal particles can be accelerated.Last, using our modified version of the radiative transfercode
RADMC /3 D (Dullemond 2012) we produced synthetic radio-intensity maps showing projected arcs and filaments that we in-terpret as a morphological characteristic of supernova remnants offast-moving Wolf-Rayet stars. Our radio predictions are qualita-tively in accordance with the morphology of several core-collapseremnants, such as the bilateral G296.5+10.0, as well as the shell-type supernova remnants CTB 109 and Kes 17, identified as orig-inating from - M (cid:12) progenitors (Katsuda et al. 2018) whichmight have undergone a Wolf-Rayet phase. Our simulations andpredictions regarding the non-thermal emission of supernova rem-nants from massive progenitors are relevant for and may be ap-plied to the various galactic and extragalactic core-collapse rem-nants (Katsuda et al. 2018). ACKNOWLEDGEMENTS
Authors are grateful to the referee, P. Velazquez, for comments onsynchrotron emission which greatly improved the quality of themanuscript. The authors thank Allard Jan van Marle from UlsanNational Institute of Science and Technology for his kind adviceson MHD simulations of the surroundings of massive stars. Theauthors acknowledge the North-German Supercomputing Alliance(HLRN) for providing HPC resources that have contributed to theresearch results reported in this paper. M. Petrov acknowledges theMax Planck Computing and Data Facility (MPCDF) for providingdata storage resources and HPC resources which contributed to testand optimise the
PLUTO code. L.M.O. acknowledges partial sup-port by the Russian Government Program of Competitive Growthof Kazan Federal University.
DATA AVAILABILITY
This research made use of the
PLUTO code developed at theUniversity of Torino by A. Mignone (http://plutocode.ph.unito.it/)and of the
RADMC -3 D ∼ dullemond/software/radmc-3d/). The figureshave been produced using the Matplotlib plotting library for thePython programming language (https://matplotlib.org/). The dataunderlying this article will be shared on reasonable request to thecorresponding author. REFERENCES
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APPENDIX A: EMISSION COEFFICIENTS FORNON-THERMAL SYNCHROTRON EMISSION
To the best of our knowledge, three main recipes are available for the emis-sion coefficient of non-thermal radio synchrotron emission in the contextof supernova remnants (Jun & Norman 1996; Orlando et al. 2007; ´Avila-Aroche et al. 2020). Considering the electron spectrum in the vicinity of theshocks, N ( E ) = KE − s , (A1)where E is the electron energy and s = 2 the index and K ∝ n . They readas, j Orlandosync ( ν ) ∝ KB ( s +1) / ⊥ ν − ( s − / , (A2)with θ obs the viewing angle of the observer, B ⊥ the magnetic field compo-nent perpendicular to the line of sight and ν the emission frequency, j Junsync ( ν ) ∝ K − s p s − B ( s +1) / ⊥ ν − ( s − / , (A3)where p is the gas thermal pressure, and j Avilasync ( ν ) ∝ Kv (cid:48) s − B ( s +1) / ⊥ ν − ( s − / , (A4)© 0000 RAS, MNRAS , 000–000 D. M.-A. Meyer et al.
Figure 1.
Normalised maps of radio synchrotron intensity of supernova remnants with progenitor speed v (cid:63) = 20 km s − at time , and calculated usingseveral prescriptions for the non-thermal emission coefficient. The viewing angle between the equatorial plane and the line of sight is θ obs = 45 ◦ (middle). Figure 2.
Same as Fig. 1 with progenitor speed v (cid:63) = 40 km s − at time
80 kyr .where v (cid:48) is the gas velocity in the rest frame of the explosion, respec-tively. This diagnostics has been widely used in, e.g. the context of thecore-collapse but also type Ia progenitors such as the historical supernovaremnants Tycho (Moranchel-Basurto et al. 2020) and SN 1006 (Schneiteret al. 2015; Vel´azquez et al. 2017).We generate comparative normalised non-thermal radio emissionmaps from two selected models of supernova remnants. First, one witha progenitor star moving rather slowly with velocity
20 km s − , and inwhich the thermal pressure compares with the ram and magnetic pressures(Fig. 1). Secondly, a model with a fast-moving progenitor is moving withvelocity
40 km s − and in which the ISM magnetic pressure is dynamicallyunimportant (Fig. 2). Fig. 1a reveals the bright radio synchrotron circum-stellar medium of the progenitor, produced by wind-ISM interaction beforethe explosion of the massive star, while Fig. 1b,c do not. The recipe used inFig. 1a clearly overestimates particle acceleration from the forward shockof the stellar wind bubble, that is much weaker than the forward shock of theexpanding supernova blastwave. Hence, the emission coefficient in Orlandoet al. (2007) is not the most suitable to our core-collapse remnant problem. The models calculated with the other emission coefficients do not permit toselect an optimal one for our study (Fig. 1b,c). The emission coefficient inEq. A3 of Jun & Norman (1996) has a dependence on the thermal pressure p , implying that it is sensitive to cooling and heating by optically-thin radia-tive cooling processes and therefore traces the fast shocks well. Similarly,the recipe of emission coefficient in Eq. A4 of ´Avila-Aroche et al. (2020)goes as j Avilasync ( ν ) ∝ v , that imposes a strong dependence of the chosenframe in which we simulate the stellar wind bubble and the supernova ex-plosion. Consequently, we decide in our study to use the recipe of Jun &Norman (1996). © 0000 RAS, MNRAS000