evolution of magnetic fields in supernova remnants
TRANSCRIPT
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RevMexAA (Serie de Conferencias), 36, CD350–CD354 (2009)
EVOLUTION OF MAGNETIC FIELDS IN SUPERNOVA REMNANTS
K. M. Schure,1 J. Vink,1 A. Achterberg,1 and R. Keppens1,2,3
RESUMEN
Actualmente se acepta generalmente que los remanentes de supernova (SNR) son la fuente de los rayos cosmicos(CRs) hasta una energıa de 1015eV. Los campos magneticos requeridos para acelerar los CRs a energıas suficien-temente altas necesitan ser mucho mayores de los que pueden resultar de la compresion del medio circunestelar(CSM) por un factor 4, como ocurre choques fuertes. Mapas de emision sincrotron de estas regiones indican quede hecho el campo magnetico es mucho mayor, y que tiene una configuracion radial para remanentes jovenes ytoroidal para remanentes viejos. Tanto el mecanismo de fortalecimiento del campo como la razon de su config-uracion radial (para remanentes jovenes) no son entendidos en forma satisfactoria. Usamos el codigo MHD demalla adaptativa AMRVAC para simular la evolucion de remanentes de supernova, y ver si podemos reproducirla configuracion de campo magnetico radial en los estados evolucionarios tempranos. Seguimos la evoluciondel SNR con tres configuraciones iniciales del campo magnetico en el CSM: un campo inicialmente toroidal,un campo turbulento, y un campo paralelo al eje de simetrıa. A pesar de que en los ultimos dos casos unacomponente radial apreciable se genera en la discontinuidad de contacto como resultado de la inestabilidad deRayleigh-Taylor, no se genera una componente de campo radial en la zona inmediatamente interior al choqueexterno. Aparentemente, la MHD ideal no parece producir el efecto observado. Posiblemente, una mayorcompresion y turbulencia adicional debida a la presencia dominante de CRs nos podrıan ayudar a reproducirmejor las observaciones.
ABSTRACT
Supernova remnants (SNR) are now widely believed to be a source of cosmic rays (CRs) up to an energy of1015 eV. The magnetic fields required to accelerate CRs to sufficiently high energies need to be much higher thancan result from compression of the circumstellar medium (CSM) by a factor 4, as is the case in strong shocks.Non-thermal synchrotron maps of these regions indicate that indeed the magnetic field is much stronger, andfor young SNRs has a dominant radial component while for old SNRs it is mainly toroidal. How these magneticfields get enhanced, or why the field orientation is mainly radial for young remnants, is not yet fully understood.We use an adaptive mesh refinement MHD code, AMRVAC, to simulate the evolution of supernova remnants andto see if we can reproduce a mainly radial magnetic field in early stages of evolution. We follow the evolutionof the SNR with three different configurations of the initial magnetic field in the CSM: an initially mainlytoroidal field, a turbulent magnetic field, and a field parallel to the symmetry axis. Although for the latter twotopologies a significant radial field component arises at the contact discontinuity due to the Rayleigh-Taylorinstability, no radial component can be seen out to the forward shock. Ideal MHD appears not sufficient toexplain observations. Possibly a higher compression ratio and additional turbulence due to dominant presenceof CRs can help us to better reproduce the observations in future studies.
Key Words: MHD — supernova remnants
1. INTRODUCTION
Supernova remnants (SNRs) are interesting ob-jects in which particles are accelerated and vari-ous magnetic-field morphologies have been detected.
1Astronomical Institute, University ofUtrecht, Postbus 80000, NL-3508 TA Utrecht,The Netherlands ([email protected];J.Vink, [email protected]).
2Centre for Plasma Astrophysics, K.U. Leuven, Belgium([email protected]).
3FOM-Institute for Plasma Physics “Rijnhuizen”,Nieuwegein, The Netherlands.
The widths of the observed X-ray synchrotron fil-aments indicate that the magnetic field is muchstronger than can be expected from compression ofthe interstellar field by the supernova blast wavealone (e.g. Volk et al. 2005; Vink 2005), and thespectral properties indicate that the magnetic fieldturbulence is high enough that cosmic ray diffusionmust be near optimal for cosmic ray acceleration (theso-called Bohm-diffusion; e.g. Vink 2005; Stage et al.2006). Polarization measurements in radio show thatyoung supernova remnants have a predominantly ra-
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MAGNETIC FIELDS IN SUPERNOVA REMNANTS CD351
dial magnetic field, whereas the dominant orienta-tion of the field in older remnants is parallel to theshock front (Gull 1973).
The radial field in young SNRs is thought to arisebecause of the Rayleigh-Taylor (R-T) instability thatoccurs at the contact discontinuity, which separatesthe shocked ejecta from the shocked, more tenuouscircumstellar medium (CSM). The R-T instabilitycreates fingers into the more tenuous medium, whichstretch the magnetic field radially (Gull 1973). Mag-netohydrodynamic (MHD) simulations by e.g. Junet al. (1995) have indeed shown that the R-T fin-gers cause a preferred polarization of the field alongthe fingers. While this causes the dominance of theradial field signature in part of the remnant, for atypical shock compression ratio of 4, it does not ex-plain the radial field polarization observed near theforward shock. As shown in hydrodynamic simula-tions by Blondin & Ellison (2001), when the com-pression ratio is higher, the R-T fingers can almostreach, and perturb the forward shock. The presenceof cosmic rays could justify an adiabatic index lowerthan that for a monatomic gas, where γ = 5/3, andthus a higher compression ratio (s = (γ+1)/(γ−1)).For a gas that is dominated by relativistic particles,such as cosmic rays, γ = 4/3. Additionally, the es-cape of high energy cosmic rays (CRs) drains energyfrom the shock region, thus further lowering the adi-abatic index. The signature toroidal magnetic fieldof older SNRs is thought to arise by compression ofthe circumstellar magnetic field.
We explore the development of Rayleigh-Taylorfingers and magnetic field variations of a SNR insidea stellar wind medium (ρ ∝ r−2) for different initialmagnetic topologies, and compare our results withthose from various studies that have been performedon this subject in a homogeneous and/or unmag-netized medium. One of the magnetic field topolo-gies we will consider is that of a magnetized stellarwind. Even for a slowly rotating star, the field willbe mainly toroidal at a distance much larger than thestellar radius. Another topology we consider is oneof magnetic turbulence. The interstellar magneticfield has a large turbulent component, so this is avery relevant scenario for a SNR in a homogeneousmedium. In a CSM created by a stellar wind how-ever, a large turbulent component could be driven bycosmic rays streaming ahead of the shock front andsmall perturbations of the blast wave. Alternatively,an ordered magnetic field, as observed on galacticscales, can be used to initialize the magnetic topol-ogy. This will be the third case we consider. Fornow, we focus on the early stages of evolution and
try to see whether or not a radial field component isdominant in regions of a young SNR.
2. METHODS
We model the evolution of a SNR in a CSM thatis shaped by a pre-supernova wind, in this case aslow, cool wind, such as that originating from a RedSupergiant (RSG), before explosion. The adoptedmass loss rate is M = 1.54 × 10−5 M� yr−1, thewind velocity is v = 4.7 km s−1 and the temper-ature is T = 1000 K. We use the Adaptive MeshRefinement version of the Versatile Advection Code:AMRVAC (van der Holst & Keppens 2007) to solvethe MHD equations in the r − θ plane of a spheri-cal grid, with symmetry around the polar axis. Thegrid spans 1.8 × 1019 cm radially, and the full πrad angle. Since the supernova remnant does notreach beyond the radius where the red supergiant(RSG) wind meets the main sequence bubble in thetimescales we consider, the initial grid is filled with aRSG wind. This is done by inducing the stellar windat the inner radial boundary, and let this evolve untilit fills the grid and a stationary situation has beenestablished. We then artificially introduce the mag-netic field in the entire grid, and supernova ejectainto the inner 0.3 pc.
The initial ejecta density profile consists of aconstant-density core, with an envelope for whichthe density decreases as ρ ∝ r−9, which is thetypical density profile of the ejecta after propaga-tion through the star in explosion models (c.f. Tru-elove & McKee 1999). In order to match the ob-servationally determined ejecta mass and energy, inthis case chosen to be Mej = 2.5 M� and Eej =2 × 1051 erg, we iteratively determine the value forthe density in the ejecta core and the velocity atwhich the core ends and the power law envelopebegins. For the parameters adopted in our simu-lations, this happens for a central density of theejecta core of 5.1 × 10−20 g cm−3, and the powerlaw envelope begins where the velocity of the ejectais 8.7 × 108 cm s−1. The velocity linearly increasesfrom zero at the core, to 15,000 km s−1 at the outerpart of the envelope.
The number of grid zones in the simulations is300 × 90 on the first level, with 3 refinement lev-els (with ratio 2) for the wind-stage, and 5 refine-ment levels (refinement ratio 2) for the SNR stage.The refinement is based on the density and velocityof the fluid. We thus reach an effective resolutionof 4800 × 1440, corresponding to 2.75 × 1015 cm by0.125◦, in the regions where strong density and ve-locity gradients are present. We implement three
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CD352 SCHURE ET AL.
toy models with different magnetic field topologiesin the wind and track what happens when the SNRevolves. In all cases the ratio of magnetic energydensity to kinetic energy density is about 0.01. Thisis low enough that the equilibrium wind solution isnot significantly perturbed on time-scales relevantfor our supernova remnant evolution.
In Model A, we set up the field as if the RSGwind were magnetized and the star slowly rotating.The field at r � Rstar is predominantly toroidal,but has a very small radial component (Chevalier &Luo 1994; Garcıa-Segura et al. 1999), i.e. Bφ ∝ r−1,Br ∝ r−2. Far from the star, the toroidal field dom-inates. Since the toroidal field has to vanish at thepoles, we induce a sin θ dependence, similar to thatused by Garcıa-Segura et al. (1999). It was sug-gested by Biermann & Cassinelli (1993) that such aprogenitor magnetic field may be responsible for highmagnetic fields in SNRs, leading to efficient cosmicray acceleration.
In Model B, we set up a random 2D magneticfield in the r and θ directions at the time when weintroduce the ejecta. The Bφ component is keptzero. At all times, we implement an initial analyt-ically divergence-free magnetic field. The randomfield is calculated on a 2D cartesian grid, follow-ing Giacalone & Jokipii (1999), and transcribed tospherical coordinates in the r, θ plane. In a centereddifference evaluation, we find that the initial condi-tion of the magnetic field is close to divergence-free(|(∇·B)|/|B| � 1/|v∆t|). The field is set up accord-ing to:
δB(x, y) = ΣNnk
n=1A0k−0.5αn i(cos φny − sinφnx) (1)
× eikn(x cos φn+y sin φn)+iβn ,
with 256 different wavenumbers k, and the phaseβ and polarization φ are randomly chosen between0 and 2π for each wavenumber. The smallestwavenumber spans the entire grid. The wavenum-bers are logarithmically spaced, and the largestwavenumber represents a wavelength that covers twogrid cells at the lowest resolution. For an approxi-mation of a Kolmogorov spectrum, we set α = 5/3.The above equation gives us a complex value for themagnetic field. To get a real magnetic field, we takethe real part of the above equation, by tacitly assum-ing that the complex part of A0 has been combinedwith the phase in β. A turbulent magnetic field maybe a natural outcome of cosmic ray induced mag-netic field amplification. Since the amplification isstronger around the fast shocks of young SNRs, thismay help explaining why only young SNRs have ra-dial magnetic fields, if turbulent magnetic fields in
Fig. 1. Simulation of SNR into CSM with a mostlytoroidal initial field (Model A). The upper left quadrantshows the logarithm of the density, which clearly showsthe occurence of the Rayleigh-Taylor instability at thecontact discontinuity. The lower left panel shows thelogarithm of the absolute value of the radial magneticfield. The lower right part shows the logarithm of |Bφ|,and the upper right quadrant shows the logarithm of theratio of the radial field component relative to the totalfield (|Br|/|B|).
front of the shock lead to radial magnetic fields in-side the SNR.
In Model C, the magnetic field is set up paral-lel to the rotation axis, representing a situation likethe dominant ordered magnetic field observed, e. g.,in spiral galaxies. In spherical coordinates, this isrepresented by Br = B cos θ, Bθ = −B sin θ.
In all simulations, the divergence of the magneticfield is controlled by adding a source term propor-tional to ∇·B in the induction equation, while main-taining conservation of momentum and energy (Kep-pens et al. 2003; Janhunen 2000).
3. RESULTS
The results from Models A, B and C, are plottedin Figures 1 to 3. The density, radial and toroidalmagnetic field, and additionally the ratio of the ra-dial to the total field are plotted for the three mag-netic field topologies. The results shown here are forremnants that have evolved for a period of 634 yr.The radial scale is 1018 cm.
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Fig. 2. Simulation of the SNR into CSM with a turbulentinitial field (Model B). Similar to Figure 1, the densityand magnetic field are plotted. Note that in this casethe lower right part shows the logarithm of |Bθ|, and theupper right quadrant shows the ratio of the radial fieldcomponent relative to the total field (|Br|/|B|).
The supernova ejecta sweeps up the circumstellarmatter into a dense shell. Four distinct regions canbe identified: the unshocked circumstellar medium(CSM) ahead of the blast wave, the shocked CSM,the shocked ejecta, and the freely expanding ejecta.The shocked CSM is separated from the unshockedCSM by a strong shock (in Figures 1–3 at a ra-dius Rf ≈ 1.3 × 1019 cm), characterized by a pres-sure jump, which increases the density by a factor(γ+1)/(γ−1) and decreases the velocity in the shockframe by the same amount. The shocked CSM is sep-arated from the third region, the shocked ejecta, bythe contact discontinuity, characterized by a jump inthe density but constant pressure. This is the loca-tion where the R-T instability develops. The reverseshock, at a radius Rr ≈ 6.5 × 1018 cm, marks theboundary with the unshocked ejecta. The decelera-tion of the shocked ejecta by the less dense shockedCSM is Rayleigh-Taylor unstable. Since the mag-netic field is very weak, it does not influence thedynamics of the blast wave, and we do not see a dif-ference in the development of the R-T instabilitiesand the propagation of the blast wave between thethree models.
Fig. 3. Simulation of SNR into CSM with an initial mag-netic field parallel to the symmetry axis, i.e. verticallyaligned (Model C). The upper quadrants show again thelogarithm of the density and the ratio of radial field overthe total field. The lower quadrants show the absolutevalues of Br and Bθ.
The magnetic field is carried along by the plasma.Since the velocity field initially only has a radialcomponent, the induction equation gives us that thetoroidal field is swept up, while the radial field re-mains: ∂tB = ∇× (v × B). Not surprisingly there-fore, in the ejecta, the radial field component is thedominant one. Starting at the R-T region at thecontact discontinuity, the toroidal field starts to bepresent again. The R-T instability induces a vθ com-ponent, which subsequently causes changes also inthe radial component of the magnetic field. Alongthe R-T fingers, for Models B and C, the field ismostly radial with toroidal components at the tipsand bases of the fingers, in agreement with resultsfrom e.g. Jun et al. (1995). In Model A however, wedo not see a significant radial component in the R-Tunstable region, which may have to do with the smallscale of the initial radial field, something requiringfurther investigation.
The radial field along the R-T fingers in Models Band C is not sufficient to explain the observations ofa dominant radial polarization of the field in youngSNRs up to the shock front. In Model B, a few fea-tures in which the field is predominantly radial can
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be seen out to the forward shock, but not enough toexplain observations. As the R-T is not yet fully sat-urated at this time in the evolution, the radial fieldmay stretch out closer to the forward shock. How-ever, since in very young remnants the field is al-ready predominantly radial, this alone is insufficientto explain observations.
4. CONCLUSIONS AND DISCUSSION
Unlike what is observed, the radial field does notdominate in the outer region of the remnant in ourmodels. Although in model B the field fluctuatesmore due to the random initial condition, there isno distinct radial field in the remnant. Specificallywith an initial toroidal field, it is difficult to createa field that is mainly radial. Turbulence could be anessential component in creating a radial field, but asshown in the result of model B, this is by itself notsufficient to reproduce the observed geometry of themagnetic field of young remnants.
It appears that additional physics is needed to ex-plain the observations of a high radial field in youngSNRs, such as a softened equation of state as sug-gested by Blondin & Ellison (2001): a situation thatmay occur when cosmic rays become dynamically im-portant at the shock. A turbulent magnetic fieldmay arise and be amplified by CR streaming (Bell &Lucek 2001). The turbulence in turn, can increasethe maximum energy that CRs can attain. In futurestudies we plan to explore the interaction betweencosmic rays and magnetic fields in supernova rem-nants.
This study has been financially supported byJ.V.’s Vidi grant from the Netherlands Organisa-tion for Scientific Research (NWO). This work wassponsored by the Stichting Nationale Computerfa-ciliteiten (National Computing Facilities Founda-tion, NCF) for the use of supercomputer facilities,with financial support from the Nederlandse Or-ganisatie voor Wetenschappelijk Onderzoek (Nether-lands Organization for Scientific Research, NWO).
REFERENCES
Bell, A. R., & Lucek, S. G. 2001, MNRAS, 321, 433Biermann, P. L., & Cassinelli, J. P. 1993, A&A, 277, 691Blondin, J. M., & Ellison, D. C. 2001, ApJ, 560, 244Chevalier, R. A., & Luo, D. 1994, ApJ, 421, 225Garcıa-Segura, G., Langer, N., Rozyczka, M., & Franco,
J. 1999, ApJ, 517, 767Giacalone, J. & Jokipii, J. R. 1999, ApJ, 520, 204Gull, S. F. 1973, MNRAS, 161, 47Janhunen, P. 2000, J. Comput. Phys., 160, 649Jun, B.-I., Norman, M. L., & Stone, J. M. 1995, ApJ,
453, 332Keppens, R., Nool, M., Toth, G., & Goedbloed, J. P.
2003, Comp. Phys. Comm., 153, 317Stage, M. D., Allen, G. E., Houck, J. C., & Davis, J. E.
2006, Nature Physics, 2, 614Truelove, J. K., & McKee, C. F. 1999, ApJS, 120, 299van der Holst, B., & Keppens, R. 2007, J. Comp. Phys.,
226, 925Vink, J. 2005, AIP Conf. Proc. 745, High Energy
Gamma-Ray Astronomy, ed. F. A. Aharonian, H. J.Volk, & D. Horns (Melville: AIP), 160
Volk, H. J., Berezhko, E. G., & Ksenofontov, L. T. 2005,A&A, 433, 229