A CR-hydro-NEI Model of the Structure and Broadband Emission from Tycho's SNR

0.93 MB·

by  P. Slane

Accepted for Publicationin The Astrophysical Journal
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
A CR-HYDRO-NEI MODEL OF THE STRUCTURE AND BROADBAND EMISSION FROM TYCHO’S SNR
P. Slane 1, S.-H. Lee2, D. C. Ellison3, D. J. Patnaude 1, J. P. Hughes,4, K. A. Eriksen4,5, D. Castro6, and
S. Nagataki2
Accepted for Publication inThe Astrophysical Journal
ABSTRACT
Tycho’s supernova remnant (SNR) is well-established as a source of particle acceleration to very
4 high energies. Constraints from numerous studies indicate that the observed γ-ray emission results
1 primarilyfromhadronic processes,providingdirect evidence ofhighly relativisticions that havebeen
0
accelerated by the SNR. Here we present an investigation of the dynamical and spectral evolution of
2
Tycho’sSNR by carryingouthydrodynamicalsimulations that include diffusive shock accelerationof

n particles in the amplified magnetic field at the forward shock of the SNR. Our simulations provide a
a consistentview ofthe shock positions, the nonthermalemission,the thermal X-rayemissionfrom the
J forwardshock,andthebrightnessprofilesoftheradioandX-rayemission. Wecomparethesewiththe

1 observedpropertiesofTychotodeterminethedensityoftheambientmaterial,theparticleacceleration
1 efficiency and maximum energy, the accelerated electron-to-proton ratio, and the properties of the
shocked gas downstream of the expanding SNR shell. We find that evolution of a typical Type Ia

] supernovainalowambientdensity(n ∼0.3 cm−3), withanupstreammagneticfieldof∼5µG,and
E with ∼ 16% of the SNR kinetic energ0y being converted into relativistic electrons and ions through
H diffusive shock acceleration,reproduces the observedproperties of Tycho. Under such a scenario, the
. bulkofobservedγ-rayemissionathighenergiesisproducedbyπ0-decayresultingfromthecollisionsof
h
energetichadrons,whileinverse-Comptonemissionissignificantatlowerenergies,comprisingroughly
p
half of the flux between 1 and 10 GeV.
-
o Subject headings: accelerationof particles, shock waves,ISM: cosmic rays, ISM: supernova remnants,
r ISM: individual objects (Tycho’s SNR)
t
s
a
[ 1. INTRODUCTION bient photons or through nonthermal bremsstrahlung.

Modeling of the broadband spectra from such SNRs,
1 Efficientaccelerationofchargedparticlesintheshocks
in order to ascertain the nature of the γ-ray emission,
v of supernova remnants (SNRs) has long been cited as
is complicated and has led to mixed interpretations,
6 a likely process through which a significant fraction of
making the evidence for ion acceleration controversial
5 Galactic cosmic-rays (CRs) are accelerated. The evi-
5 dence for such energetic particles is compelling. Radio in some cases. Gamma-ray emission from some SNRs
2 emission from SNRs originates from electrons with en- known to be interacting with molecular clouds seems to
1. ergies Ee > 1 GeV, while observations of nonthermal require a significant component from pion decay (e.g.
Abdo et al.2009;Castro & Slane2010;Abdo et al.2010;
0 X-ray emission from SNRs reveal electrons with ener-
Giuliani et al. 2011; Ackermann et al. 2013), with some
4 gies exceeding tens of TeV. Evidence for energetic ions
remnants requiring nearly all of the SNR kinetic energy
1 accelerated in SNRs is more elusive because of the low
to be converted to relativistic electrons for IC emission
: radiationefficiencyforsuchparticles. TheobservedGeV
v to dominate the flux (Castro et al. 2013; Auchettl et al.
and TeV γ-ray emission from many SNRs – particularly
i 2013). For W44 and IC 443, the γ-ray spectra show
X those known to be located in dense environments – is
clearevidenceofakinematic“pionbump,” firmlyestab-
consistent with the presence of energetic protons that
r lishing the presence of energetic ions in these remnants
a produce γ-rays through the decay of neutral pions cre-
(Ackermann et al. 2013).
ated in collisions with ambient nuclei. But γ-rays can
Ionaccelerationcanhaveobservable dynamicaleffects
also be produced from the energetic electron popula-
on SNR evolution, since this process results in less ther-
tion, through inverse-Compton (IC) scattering of am-
mal heating of the swept-up gas and an increased com-
pression ratio in the postshock region. X-ray studies
1Harvard-Smithsonian Center for Astrophysics, 60 Garden of 1E0102 (Hughes et al. 2000) reveal electron temper-
Street, Cambridge, MA 02138, USA; [email protected];
atures that are much lower than expected from the ob-
[email protected]
2RIKEN, Astrophysical Big Bang Laboratory, 2-1 Hirosawa, servedexpansionvelocitiesoftheremnants,forexample,
Wako, Saitama 351-0198, Japan; [email protected]; shige- indicating that a large fraction of the shock energy has
[email protected], North Carolina State University, Box gone into something other than thermal heating of the
gas. In addition, as we discuss in more detail below, X-
8202, Raleigh,NC27695, USA;don [email protected]
4Department of Physics and Astronomy, Rutgers University, raystudies ofTycho’sSNR (Warren et al.2005)demon-
Piscataway, NJ08854-8019, USA;[email protected] strate that the ratio of the forwardshock (FS) radius to
5XTD-IDA,LosAlamosNationalLaboratory,P.O.Box1663,
thatofthe contactdiscontinuity(CD), as wellas thatof
LosAlamos,NM87545,USA;[email protected]
6MIT-Kavli Center for Astrophysics and Space Research, the reverse shock (RS), is smaller than expected, consis-
77 Massachusetts Avenue, Cambridge, MA 02139, USA; cas- tent with results expected from efficient ion acceleration
[email protected]
2 Slane et al.
Fig.1.— ChandraimageofTycho’sSNR.Insetsidentifyregionsusedforspectralextraction,withdashedregionsindicatingbackground.
(Decourchelle et al. 2000; Ellison et al. 2004). Finally, clumped gas(Inoue et al.2012). Conversely,the density
deep Chandra observationsof Tycho reveala complex of requiredtoproducetheobservedthermalX-rayemission
regularly-spacedstripe-like nonthermalstructures in the from H-like ions of Si in CTB 109 is sufficiently high for
projected interior of the remnant (Eriksen et al. 2011). π0-decay to account for roughly half of the observed γ-
The spacing of these stripes may correspond to the gy- rayflux(Castroetal. 2012). Anycompletepictureofthe
roradii of 1014 −1015 eV protons in an amplified mag- cosmic-raymodifiedemissionanddynamicalevolutionof
netic field (Eriksen et al. 2011), although Bykov et al. Tycho’sSNR must include a self-consistenttreatment of
(2011) suggest that the structures may be the result of thermal X-ray emission.
anisotropic magnetic turbulence produced by instabili- Tycho’sSNRis the productofSN1572. Basedonhis-
ties driven by CR protons with energies of ∼ 1015 eV. torical records of its light curve, the remnant has long
The maximum energy to which such ions are acceler- been understood to have resulted from a Type Ia event
ated in a particular SNR is of critical importance to (Ruiz-Lapuente 2004), corresponding to the thermonu-
our understanding of the role SNRs play in producing clear destruction of a C-O white dwarf star. This has
ions with energies approachingthe knee of the CR spec- been confirmed through direct measurements of the su-
trum. Combined with modeling of the broadband emis- pernova spectrum, taken from light echo measurements
sion that appears to imply that pion-decay dominates (Krause et al. 2008) that identify it as belonging to the
the γ-rayflux (Morlino & Caprioli2012;Giordano et al. normal Type Ia class of SNe. As with many Galactic
2012; Berezhko et al. 2013; Zhang et al. 2013), these ob- SNRs, the distance to Tycho’s SNR is rather uncertain.
servations have thus led to the conclusion that Tycho’s Most estimates fall in the 2−5 kpc range with recent
SNR is a particularly important testbed for models of estimatesof4±1kpcbasedonobservedejectavelocities
particle acceleration in SNRs. and proper motion measurements (Hayato et al. 2010),
The thermal emission from material compressed by 3.8+1.5 kpcbasedonlightechomeasurements(Krauseet
−0.9
the FS provides particularly important information on al. 2008), and 2.5−3 kpc based on kinematic methods
particle acceleration in SNRs. Because the postshock
(Tian & Leahy 2011). Morlino & Caprioli (2012) esti-
temperature is reduced in the case of efficient accelera-
mate d = 3.3 kpc based on broadband modeling of the
tion,the emissioncharacteristicsofthe plasmaaremod-
spectrum(seeSection4below),althoughtheiranalysisis
ified. Moreover, the ionization state of the gas is mod-
basedontheTruelove & McKee(1999)parameterization
ified by both the reduced temperature and the higher
oftheSNRevolutionratherthanaself-consistenthydro-
density associated with the increased compression ra-
dynamical treatment that includes the effects of the CR
tio (Patnaude et al. 2009). As a result, self-consistent
acceleration, such as that used here.
treatment of the thermal emission is crucial in any ef-
The X-ray emission from Tycho’s SNR (Figure
fort to model the effects of cosmic ray acceleration in
1) is dominated by ejecta (Hwang & Gotthelf 1997;
SNRs. This is of particular importance in assessing
Decourchelle et al. 2001; Hwang et al. 2002), accompa-
the nature of any observed γ-ray emission because of
nied by thin filaments of synchrotron emission from ex-
the critical dependence on density shared by both π0-
tremely energetic electrons accelerated at the forward
decay emission and thermal X-ray emission. For exam-
shock (Cassam-Chena¨ıet al. 2004; Eriksen et al. 2011;
ple, the lack of observed thermal X-ray emission from
Bykov et al. 2011). The mean angular radius of the
RX J1713.7−3946 eliminates π0-decay as a significant remnant is 251′′, with an azimuthal variation of about
contributor to the γ-ray emission (Ellison et al. 2010, ±16′′ (Warren et al. 2005). Comparison of the ejecta
2012) unless the postshock medium is filled with cold,
density and composition structure with hydrodynami-
CR-hydro-NEI Model of Tycho 3
cal models for the evolution and nucleosynthesis models NEI code can be found in Lee et al. (2012). The ap-
for the ejecta produced in different classes of Type Ia proach here is similar to that used for investigations of
explosions indicate that the remnant is the result of a RXJ1713.7−3946(Ellisonetal. 2012),CTB109(Castro
delayed-detonation explosion (Badenes et al. 2006) with et al. 2012), and Vela Jr (Lee et al. 2013).
a ∼ 1051 erg explosion expanding into an ambient den- We note that while our model is spherically symmet-
sity n = 0.85−2.1 cm−3, although most other studies ric,itisinhomogeneousinradius. Webeginwitharadial
0
indicatelowerdensities: n0<∼0.3 cm−3basedonlimitsto ejectadensitydistribution(assumedheretobeexponen-
thethermalX-rayemission(Cassam-Chena¨ıetal. 2007); tial, with a total mass of 1.4M⊙), and all parameters
n0<∼0.4 cm−3 basedontheγ-rayflux(V¨olketal. 2008); including the density, temperature, magnetic field, and
ionizationstate,evolveasthe remnantagesandshocked
n0<∼0.2 cm−3 based on measurements of the SNR ex- material advects downstream from the forward shock.
pansion index m, where R ∝ tm (Katsuda et al. 2010);
At the current age, the relativistic electrons and ions,
and n0 ∼ 0.1−0.2 cm−3 (except in distinct regions of as well as the thermal plasma, emit from a “continuous
known dense clump interactions) based on the ratio of zone”environmentbetweentheCDandFS.Ratherthen
70 to 24 µm flux ratios from postshock dust in Tycho assuming a single power law with an exponential cutoff
(Williams et al. 2013). for the acceleration CRs, as in some models (e.g. Zhang
Gamma-ray emission from Tycho has been identified etal. 2013),withthepowerlawindexandcutoffparam-
byobservationswithVERITAS(Acciarietal. 2011)and eter fixed to match the data, we determine the evolving
theFermiLAT(Giordanoetal. 2012),andmodelsofthe full particle spectrum, spatially-resolved and integrated
broadbandspectrumindicatethatthe γ-rayfluxisdom- over time, using a self-consistent model.
inated by emission from π0-decay (Morlino & Caprioli
2012;Berezhkoetal. 2013;Zhangetal. 2013),although
3. MODELING
the details of the models used to reach this conclusion
differ considerably. In addition, arguments have been The primary parameters for driving the simulations
made for models in which the γ-rays may be dominated aretheSNRdistance(d), theupstream(i.e.,unshocked)
by IC emission (Atoyan & Dermer 2012). density (n0) and the upstream magnetic field (B0; both
Here we present a study of the radialstructure, evolu- assumed constant here), the kinetic energy of the explo-
tion, and broadband emission from Tycho’s SNR using sion (E51, in units of 1051 erg), and the DSA injection
hydrodynamical simulations described in Section 2. In efficiency parameter (ξ). We investigateda range of dis-
Section 3 we describe our modeling approach and sum- tances from 2.5 - 5 kpc, and explored a grid of values
marizethe applicationofthese models tothe broadband for the other key parameters for each assumed distance
spectral energy distribution (SED) for Tycho as well as until the observed angular radius was reproduced at the
theX-rayemissionfromthepost-shockregionoftheSNR knownageofTycho. Wecomparedtheangularpositions
blast wave. We discuss the results of our modeling ef- oftheRSandCDforeachmodelwiththe measuredval-
forts in Section 4, in the context of previous studies of uesfromWarrenetal. (2005),andthepredictedangular
Tycho, and our conclusions are presented in Section 5. expansionspeed withmeasurementsfromKatsudaetal.
Weconfirm,inwhatwebelievetobethe mostcomplete, (2010), and rejected models for which the discrepancy
sphericallysymmetric,broadbandmodelofthisSNRyet was larger than ∼ 0.5 arcmin. We initially assumed ex-
performed, that the bulk of the γ-ray emission is from pansionintoaninterstellarmedium(ISM)withconstant
hadronic processes with a significant fraction of γ-ray density n0<∼0.3 cm−3, based onupper limits established
emission contributed by leptonic processes at GeV en- by Katsuda et al. (2010), and adopted E = 1 based
51
ergies. Other important properties of the SNR, such as on the spectral classification of Tycho’s SN as a normal
ambient density, magnetic field strength, the DSA effi- Type Ia event (Krause et al. 2008).
ciency, and the relativistic electron-to-proton ratio, are For models that satisfied the above conditions, we
also constrained. varied additional parameters that primarily impact the
spectrum in subsequent CR-hydro-NEI runs. These in-
2. THECR-hydro-NEIMODEL clude the electron-to-proton number density ratio, K ,
ep
To address the evolution, particle acceleration, and a shape parameter for spectral cutoff around the maxi-
broadband emission for Tycho’s SNR, we have used mum momentum, αcut (see Lee et al. 2012),the ratio of
the CR-hydro-NEI code that models the SNR hydro- the wave damping and growth rates in the acceleration
dynamics with a version of the VH-1 hydro code (e.g., region, and the spatial variation of the Alfv´en speed in
Blondin & Ellison 2001) modified to include the effects the shock precursor, falf.
of non-linear diffusive shock acceleration (DSA) using Usingtheshockeddownstreamandprecursormagnetic
a semi-analytic solution based on the treatments from field and plasma density provided by the hydro calcula-
(Blasi et al. 2005) and (Caprioli et al. 2009). The re- tions,wecalculatedthesynchrotron,IC,andnonthermal
sulting nonthermalprotonand electron spectra,coupled bremsstrahlung emission from the relativistic electrons.
with the calculated (amplified) magnetic field and as- For the IC emission, we used seed photon fields from
sumed ambient photon fields, are used to calculate the the CMB, starlight, and IR emission from local dust,
synchrotron, bremsstrahlung, inverse-Compton, and π0- to which we also addeda localIR field fromTychoitself
decayemission. ThethermalX-rayemissioniscalculated basedonAkariobservations(Ishihara et al.2010). Emis-
byfollowingtheionizationoftheshockedgasthroughthe sion from π0-decay was calculated based on the model
hydro simulation and coupling this to a non-equilibrium fromKamae et al.(2006). Synchrotron,IC,andnonther-
ionization emission code (e.g., Ellison et al. 2007; Pat- mal bremsstrahlung emission from secondary electrons
naude et al. 2009). A full description of the CR-hydro- was calculated as well, though these did not contribute
4 Slane et al.
Fig.2.— Comparisonof model predictions for the angular size, RSNR, the angular expansion rate, dθ/dt, forthe FSand RS, and the
radio, X-ray, and γ-ray fluxes for Tycho’s SNR as a function of ambient density. The left panel shows model results for different DSA
injectionparameters,ξ,forfixedvaluesforthedistanceandupstreammagneticfield. Notethatsmallervaluesofξimplylargeracceleration
efficiencies(seeTable1). Therightpanelshowsresultsfordifferentdistancevalues forfixedefficiencyandmagneticfieldvalues.
significantly to the overallemission. refined these parameters along with Ke−p, and falf un-
Formodelsthatadequatelyreproducedthebroadband til the predicted broadband spectrum provided a good
SED for Tycho, we used the predicted X-ray emission agreement with the observations. The upper panel in
models as templates for fitting Chandra spectra taken Figure 3 shows the results for our best model (Model
from regions along and just behind the forwardshock of A), whose parameters are summarized in Table 1. We
the SNR (see Figure 1). plot the radial variation of the density in order to best
illustrate the model positions for the FS, CD, and RS.
3.1. Parameter Studies The observed average FS radius is indicated in green,
and the uncertainty range for the CD (RS) is indicated
To arrive at a self-consistent model for Tycho’s SNR,
in magenta (red). While there is actually an observed
we first explored the global parameter space by inves-
variation of about 6% in the FS radius for Tycho, all
tigating the effects of varying d, n , B , and ξ. These
0 0 models were constructed to yield the same outer shock
results are summarized in Figure 2 where we plot the
position, to facilitate more direct comparison.
variation with ambient density n of the angular ra-
0 The dashed curve in the upper panel of Figure 3 cor-
dius of Tycho, its angular expansion rate, and the value
responds to the same input parameters as for Model A
of logE2dN/dE at fiducial energy values characterizing
exceptthatefficientparticleaccelerationhasbeenturned
the radio,nonthermalX-ray,high-energyandvery-high-
off. As expected, the FS/RS and FS/CD radius ratios
energy γ-ray bands.7 For each panel, horizontal bands
are smaller for Model A as a result of particle acceler-
indicatetheobserveduncertaintyrangefortheidentified
ation. The RS position for Model A, which we note is
quantity, and the different curves connect model calcu-
sensitive to the assumed density profile of the ejecta, is
lationsfordifferentvaluesofthe efficiency,distance,and
in good agreement with that observed by Warren et al.
unshocked magnetic field, as indicated.
(2005). The radius of the CD falls considerably short
The broad parameter space investigation above pro-
duced reasonable models for input values of d ∼ 3 kpc, of that inferred from the data. This may be the result
n ∼ 0.2 cm−3, B ∼ 5 µG, and ξ ∼ 3.7. We then of Rayleigh-Taylor (R-T) instabilities at the CD result-
0 0 ing in the penetration of ejecta into the shocked ISM.
7WhileFigure2displaysresultsonlyforB=5µG,modelswith Such instabilities in SN Ia remnants were studied by
valuesbetween3−20µGwereinvestigated. Wang & Chevalier (2001), who found that these struc-
CR-hydro-NEI Model of Tycho 5
X-ray spectrum (5 - 10 keV) shown in blue is from
Suzaku observations based on 444 ks of exposure (Ob-
sIds: 500024010, 503085010, and 503085020), including
350ksfromthe Tychokeyproject(PI:Hughes). We use
alocalbackgroundfromthe outskirtsofthefieldofview
andconsiderspectraonlyfromthefront-sideilluminated
chips (XIS0 and XIS3), which we combined into a sin-
gle,mergedspectrumandappropriateresponsefile. The
bestfitoverthe5-10keVband(usingamodelwithasin-
gle power law and 5 Gaussians to describe the thermal
lines)yieldsapower-lawphotonindexof2.83±0.01with
a normalization of 0.116 photons cm−2 s−1 keV−1, val-
uesthatareconsistentwithpreviousmeasurements. For
Figure 3 we plot only the best fit power-law component
with estimated error bars. Black circles represent data
from the Fermi LAT (Giordano et al. 2012) while tri-
angles correspond to data from VERITAS observations
(Acciarietal. 2011). Forthemodels,the magentacurve
represents the synchrotron emission, the blue curve is
from IC emission, the red curve is from π0-decay, and
the green curve is the nonthermal bremsstrahlung emis-
sion. Thedashedredcurverepresentsπ0-decayemission
fromescapingprotons,andthe blackcurveis the sumof
these model components. Weak thermal line features in
the soft X-ray band (∼0.2−2.5 keV), from the shocked
ISMcanbeseeninthemodel. (Wenotethatinterstellar
absorption has not been applied to the SED)
The results ofthis model indicate that the γ-rayemis-
sion from Tycho is dominated by π0-decay at high ener-
gies, although the IC emission at lower energies is very
significant as well, and makes a nearly equal contribu-
tionbetween1and10GeV.Thisconclusionisconsistent
with those presented in several recent studies of Tycho,
althoughour modeling approachcontainsimportant dif-
ferences,aswediscussbelow. Wenotethatthattheradio
spectrumpresentedinFigure3correspondstotheentire
Fig.3.— Top: Radial density profile for Model A. The black SNR while our modeled emission correspondsto the FS.
dashed curve corresponds to the same parameters as Model A,
While significantparticle accelerationis not expected at
butwiththeparticleaccelerationeffectivelyturnedoff. Thegreen
vertical line indicates the position of the FS, while the magenta the RS,anysuchcomponentwouldnotbe accountedfor
andredlinesdelineatetheCDandRSrangesreportedbyWarren in the model.
etal. (2005). ThecyanbandindicatestheextentofexpectedR-T
The results of the evolution for Tycho predicted by
mixing based on the work of Wang & Chevalier 2001). Bottom:
Model A are summarized in Table 1. At its current age,
Broadband SED for Model A, compared with observed emission.
Seetextfordescriptionofdifferentcurves. the remnant has swept up ∼ 2.5M⊙ of ISM material.
tures can extend as much as ∼ 11% beyond the CD
radius at the dynamical age of Tycho’s SNR. This ef- TABLE 1
fective R-T extension region is indicated in cyan in the CR-hydro-NEI ModelParameters
upper panel of Figure 3. Since the CD region identi-
fied by Warren et al. (2005) corresponds to the inter-
Parameter ModelA ModelB ModelC
face between ejecta emission and the shocked ISM, it is
clear that ejecta-filled filaments extending from the CD Input
in Model A can explain the inferred position of this in- d(kpc) 3.18 3.40 2.90
terface. In addition, simulations show that, in the case n0 (cm−3) 0.3 0.2 0.85
ofefficientparticleacceleration,suchR-Tstructurescan falf 0.7 0.5 0.5
extendto evenlargerdistances (Blondin & Ellison2001; ξ 3.6 3.7 3.9
Warren & Blondin2013). Thus,wecontendthatthepo- Kep 0.003 0.008 0.01
sitions of the RS, FS, and CD in Model A are in good Output
agreement with observations. Msw(M⊙) 2.47 2.02 5.33
Rtot 4.64 4.48 4.23
3.2. Broadband SED ECR/ESN 0.16 0.11 0.07
The lower panel in Figure 3 presents the predicted pmaExff/D10S4Ampc 04..236 09..250 05..181
spectrum for Model A, along with the observed spec-
tral measurements for Tycho. Radio points were taken E51=1,B=5µG,andαcut=0.5forallmodels.
from Reynolds & Ellison (1992), and the nonthermal
6 Slane et al.
Fig. 4.— Proton (red) and electron (black) spectra p4f(p) for
ModelA.
Theremnanthasplacedroughly16%ofthe SNRkinetic
energyintorelativisticparticles,witha totalDSA accel-
eration efficiency of ∼26%. The total compressionratio
from the forward shock, R , is about 16% higher than
tot
expected for the case of no particle acceleration. The
electronand protonmomentum spectra for Model A are
showninFigure4;themaximumprotonenergyisnearly
50 TeV.
Figure 5 shows the results from our Model B (see Ta-
ble1),forwhichthedensityisslightlylowerthanthatof
Model A. The dynamical results are in agreement with Fig.5.— SameasFigure5,forModelB.
the measurements of Warren et al. (2005), although the
RS position is just barely consistent with the measured vidual data set, and the resulting images were merged,
value. We note that recent Suzaku measurements sug- resulting in a net exposure of 734.1 ks. Spectra were
gest that the RS radius may be even smaller than pre- extracted from each of the rectangular regions in the
viously recognized (Yamaguchi et al. 2014), potentially northeastern, northwestern, and western portions of the
indicating that the position in this model (and perhaps SNR indicated in Figure 1 (hereafter referred to as NE,
that in Model A) is too large. Model B represents our NW, and W regions). These regions were selected be-
best model in which the γ-ray emission is dominated by causethenonthermalemissioniswellseparatedfromthe
IC emission, althoughthe highestenergies are still dom- brightejecta;theycorrespondcloselywiththoseusedby
inatedbythe π0-decaycomponent. However,the overall Cassam-Chena¨ı et al. (2007). The large outer boxes in
fittoboththe GeVandTeVdataisratherpoorindicat- eachregionwereusedforextractionofbackgroundspec-
ing that a model where leptons dominate the γ-ray flux tra. For each region, spectra from individual ObsIDs
is unlikely for Tycho. werecombinedusingtheciaotaskdmtcalc,andweighted
In Figure 6 we present the time evolution of the FS arf(effective area)and rmf (spectral redistribution) files
(black)andRS(red)angularspeedsforourmodels. Hor- were created using the addresp task.
izontallinesindicatetherangeofmeasuredvaluesforthe TheX-rayspectrafromdirectlyalongtheFSandfrom
angularexpansionrateoftheFSandoftheinneredgeof theregionimmediatelybehindtheshockintheNE,NW,
the shocked ejecta which, particularly for the FS, show and W regions of the SNR are shown in Figures 7-9.
considerableazimuthal variations(Katsuda et al. 2010). Fits were performed with xspec version 12.7.1 using the
BothmodelsAandBadequatelyreproducetheobserved thermal and nonthermal X-ray emission models calcu-
expansion rates. lated in the CR-hydro-NEI runs along with the inter-
stellar absorption model tbabs (Wilms et al. 2000) with
3.3. X-ray Emission
the abundance set from Anders & Grevesse (1989). The
The X-ray image in Figure 1 was created by merging normalizationof the two emission components were tied
observations from a 750 ks Chandra observation carried together, but allowed to vary along with the absorbing
out in 2009 (ObsIDs 10093-10097, 10902-10904, 10906). column density. We obtain goodfits to the spectra from
Standard cleaning procedures were used on each indi- regions 1 and 2 in Figure 1 using results from Model A
CR-hydro-NEI Model of Tycho 7
Fig.6.— Time evolution of the FS and RS angular speeds for Fig.7.— ChandraspectrafromtheNErimofTycho,compared
models described in the text. Horizontal dashed curves outline with the predictions from Model A. The upper (black) spectrum
the measured values for the FS (black) and RS (red). Solid lines correspondstoaregiondirectlyalongtheshock(region1inFigure
correspondtoModelAwhileshort(long)dashedlinescorrespond 1) whilethe lower (red) spectrum is taken from a region immedi-
toModelB(C). atelybehindtheshock(region2).
servationsnear the shock,but declines more slowly than
(shown as a histogram in each Figure), although emis-
the observed brightness at larger distances behind the
sionfromregion3containsadistinctexcessofsoftX-ray
shock,consistentwiththerelativelylowernormalizations
emission,discussedinSection4. Similarfeatureswerere-
obtained in spectral fits from these regions. Meanwhile
ported by Hwang et al. (2002). Given the evidence for
the predicted radio profile, while correctly indicating a
significantdensity variations aroundTycho(Williams et
slow rise to a plateau-like region well behind the shock,
al. 2013), it is not surprising that some regions contain
is less successful at reproducing the exact profile. This
more shocked ISM material than predicted by our 1-D
behaviorissimilartothatfoundbyCassam-Chena¨ıetal.
models which average over the entire SNR. The fit pa-
(2007). Because the radio-emitting electrons do not suf-
rameters for regions 1 and 2 are summarized in Table 2;
fer significant radiative losses, the projected brightness
region 3 was eliminated from these fits because of clear
profileshouldshowacontinuousincreasefromthe FSto
ejecta contamination (see Section 4). The results from
the CD. The observed climb to an early plateau may be
fits to Model B (see Table 2) are similar to that from
an indication that these electrons are confined to a shell
Model A; the goodness-of-fit is actually slightly better
thatis considerablythinner thanthe regionbetween the
thanforModelA,primarilydue toaslightlyflattersyn-
FS and CD in our model. The physical mechanism as-
chrotron component.
sociated with such a picture is not obvious, although a
Because our model is spherically symmetric, the ex-
reduction in the FS/CD separationfrom R-T structures
pected normalizationfrom the spectralfits is simply the
described above could be partially responsible. Alterna-
fraction of the total azimuth of the SNR covered by our
tively,the radialdistributionofthe magneticfieldin the
extraction regions. For region 1, we find that the nor-
postshock region may deviate from that in our model.
malization is in excellent agreement with the expected
Cassam-Chena¨ı et al. (2007) suggest, for example, that
geometric value in the NE region, but is a factor of 2.6
rapid damping of the field at the FS after its rapid ini-
(3.1) higher in the NW (W) region. This is consistent
tial rise (Pohl et al. 2005) could produce both the sharp
with typical variations in the brightness around the rim
riseandthepartialfalloffoftheradioemission,andthat
of Tycho. Moreover,since we have selected brighter fila-
turbulent motions from from the outermost ejecta could
mentsinordertoobtaingoodspectrainsmallregions,it
enhance the downstream field, thus resulting in an in-
isnotsurprisingthattheresultsarebiasedtonormaliza-
creaseinthe radiosynchrotronbrightnessinthis region.
tions somewhat higher than expected. More notable is
ThecorrespondingprofilesfromtheNWregionarecom-
the fact that the normalizations for region 2 falls below
plicatedbyoverlappingshocksthatareevidentinFigure
thatforregion1 inallthreeregionsofthe SNR. We find
1, and are thus not shown in Figure 10.
the same behavior for region 3.
The radial brightness profiles for the NE and W rims
3.4. Additional Models
areshowninFigure10,whereblue/redpointscorrespond
to X-ray data, and green/magenta points represent ra- As noted in Section 1, models of the ejecta emission
dio profiles. The accompanying curves are the predicted from Tycho by Badenes et al. (2006) appear to require
brightness profiles from our Model A. The predicted X- a somewhat higher density than those derived from X-
ray profile is in reasonable good agreement with the ob- ray (Cassam-Chena¨ı et al. 2007, Katsuda et al., 2010)
8 Slane et al.
TABLE 2
X-Ray SpectralFits For Models A,B, andC
NWa NEa Wa
Parameter A B C A B C A B C
Nb 6.3±0.02 5.3±0.02 8.9±0.01 6.6±0.02 5.7±0.02 8.7±0.02 8.0±0.02 6.9±0.02 8.9±0.01
H
K1c 71.8±1.6 35.5±0.8 80.8±1.7 23.3±0.6 11.4±0.4 26.0±0.7 101.0±1.3 49.7±0.9 110.0±1.7
K2c 18.4±0.6 6.5±0.2 13.5±0.4 15.1±0.6 5.1±0.2 9.8±0.3 50.7±1.2 17.0±0.5 33.9±0.8
χ2 1.3 1.2 1.5 1.1 1.0 1.2 1.5 1.3 1.6
r
dof 398 373 533
a)Regionsizesasfractionoftotal azimuthare0.027(NW), 0.023(NE),and0.032(W).
b)Columndensity×1021 cm−2
c)Modelnormalization×10−3
Fig.8.— SameasFigure8,forNWrimofTycho. Fig.9.— SameasFigure8,forWrimofTycho
els that include initial evolution in a small wind cav-
and IR measurements (Williams et al. 2013). Figure 11
ity. They find that the resulting ionization character-
presents our best results for a fixed ambient density of
n =0.85 cm−3(ourModelC),thelowestvaluereported istics provide a somewhat better match than that ob-
0 tained by Badenes et al. (2006) with a modest ambient
byBadenesetal. (2006). TheCDislocatedquitefarbe-
density of ∼0.4 cm−3 and the presence of a wind-blown
hindthepositionestimatedbyWarrenetal. (2005),even
bubble through which the remnant evolves at an early
iftheeffectsofR-Tinstabilitiesareconsidered,although
age. In this model, the ambient density outside the cav-
it is important to note that the exponential density pro-
ity can be somewhat low, as indicated by the X-ray and
fileassumedherediffersfromthatusedbyBadenesetal.
IR measurements, while the effective density associated
(2006),whichwasbasedonactualexplosionmodelswith
with the ionization can be somewhat higher due to the
stratified composition. The radio and γ-ray components
initial expansion through the inner wind region. As this
from the higher-density model also provide poor fits to
model does not consider DSA, it cannot explain the ob-
the data. The integrated X-ray spectrum from Model
served γ-ray emission. Moreover, with DSA included,
C predicts significant line emission, but the overall con-
the proposed density would result in a FS radius that is
tribution of this component to the small regions studied
smallerthanthatobserved,asdiscussedinSection1. We
here is small; the X-ray fits are formally worse than for
havethusinvestigatedasimilarscenario,alsoconsidering
Models A and B, but the differences are not dramatic.
the effects of efficient DSA on the dynamical evolution.
Thus, while we view the high density model case to be
Specifically,weinsertedarelicbubblewithradius0.4pc,
veryunlikelybasedonboththe broadbandemissionand
thedynamicalevolutionoftheshocks,itcannotberuled blownbyastellarwindwithM˙w =3×10−6M⊙ yr−1and
out by the X-ray data alone. The parameters for Model v =10 km s−1,andallowedtheSNRtoevolvethrough
w
C are summarized in Table 1. the bubble and into a uniform ambient medium. We
MostrecentlyChiotellis et al.(2013)haverevisitedthe find that using parameters similar to those from Model
investigation of the RS spectrum for Tycho for mod- A,alongwiththeinclusionofthewindbubble,yieldsvir-
CR-hydro-NEI Model of Tycho 9
Fig. 10.— Observed X-rayand radiobrightness profiles at the
NE/W rims of Tycho, compared with predictions from Model A,
describedinthetext. Blue/red(green/magenta)pointscorrespond
toX-ray(radio)datafromtheNE/W.Distancesaremeasuredfrom
thepositionof theFS. X-rayandradiodatahave been renormal-
izedtoproduceapeakbrightnessvalueof1,andpositionsrelative
totheshockpositionhavebeenshiftedtobestalignwithdatawith
themodelprofiles.
tuallynochangeinourresults;aslightlylowerdensityis
required(n =0.28 cm−3),andthedensityprofileshows
0
structure from reflectedshocks associatedwith the wind
bubble interaction, but the overall dynamics are nearly
identicalandthebroadbandspectrumisindistinguisable
from that of Model A. This is to be expected, because
the total mass contained in the wind component is only Fig.11.— SameasFigure3,butforModelC.
∼ 0.1M⊙, while the total swept-up mass in model A is
∼2.5M⊙(seeTable1). Thus,whileanearlyeffectonthe duce the observedFS radius at the knownage of Tycho,
ionization of the ejecta (which we do not treat here) ap- our Model A reproduces the observed RS radius, but
pears plausible, the impact on the dynamical evolution yieldsaCDpositionthatfallsshortofthatestimatedby
is negligible. Thus, we conclude that the wind bubble Warren et al. (2005). We suggested that R-T filaments
model proposed by Chiotellis et al. (2013) can produce haveresultedinejectamaterialbeingmixedwellbeyond
results consistent with current dynamical and spectral theCD,towardtheFS.InFigure12weshowaspectrum
measurements of Tycho, though when the effects of cos- from region 3 in the NE section of Tycho (see Figure 1)
mic rayaccelerationaretakenintoaccount,the required along with our best-fit CR-hydro-NEI model (black his-
ambient density is <∼0.3 cm−3. togram). Significant residuals can be seen at the posi-
tionsofemissionlinesfromNe(0.92keV),Si(1.85keV),
4. DISCUSSION and S (2.45 keV), which were subsequently fit by Gaus-
Based upon our Model A, we conclude that Tycho’s sians with energies fixed at the line energies for these
SNR has evolved in a medium with an ambient density elements. Similar results were reported by Hwang et al.
n ∼0.3 cm−3 and a magnetic field strength B ∼5 µG. (2002) and Cassam-Chena¨ı et al. (2007), and provide
0
Theremnanthasundergoneefficientaccelerationofelec- strong evidence for the presence of ejecta mixed nearly
trons and ions, with ∼ 16% of the kinetic energy of the allthewaytotheFS,althoughthepresenceofsignificant
supernovaexplosionbeingdepositedintorelativisticpar- amountsofNe is quite unexpected giventhe muchlower
ticles with K ∼ 0.003. The DSA efficiency is ∼ 26% abundance in nucleosynthesis models for SN Ia. It must
ep
at the currentepoch, the amplified magnetic field in the benotedthattherearenumerousFe-Lfeaturesinthere-
immediate postshockregionhasa strengthof∼180µG, gionaround1 keV,whichcomplicates the interpretation
and roughly 11% of the energy that has gone into parti- of this feature.
cle acceleration has been lost to escaping particles. The The broadband emission from Tycho’s SNR has
remnant distance is ∼ 3.2 kpc. This model is consistent been modeled by a number of researchers (e.g.,
withthemeasuredpositionsandexpansionspeedsofthe Morlino & Caprioli 2012; Atoyan & Dermer 2012;
FS and RS in Tycho. Berezhko et al. 2013; Zhang et al. 2013) with most
AsnotedinSection3.1,withourmodelstunedtopro- concluding that the γ-ray emission is dominated by
10 Slane et al.
mulate in a region of lower B-field. The IC emission is
produced from electrons in both zones, while the syn-
chrotron emission arises primarily from the outer zone.
Using several unconstrained parameters to describe the
zones, Atoyan & Dermer (2012) can fit the broadband
continuumwiththe γ-rayemissiondominatedbyICbut
they note that hadronic models are equally viable. As
noted above, our evolving, continuous zone, spherically
symmetric model also has electrons (and ions) radiat-
ing indifferentenvironments,shockedatdifferent times,
where the parameters are determined from the hydro
simulation coupled to the DSA calculation.
ThemostcompletemodelsofTychowerepresentedby
Morlino & Caprioli (2012) and Berezhko et al. (2013).
Berezhko et al. (2013) criticize Morlino & Caprioli
(2012) for their presumably inconsistent treatment
of diffusion. Particle diffusion is indeed critical for
DSA; our treatment is described in detail in Lee et al.
(2012). Briefly, the CR-hydro-NEI simulation includes a
description of magnetic field amplification (MFA) in the
shock precursor, so the B-field turbulence is determined
as a function of position in the precursor. Our diffusion
coefficient is D(x) = (vpc)/[3eδB(x)]. The strength of
the fieldvariationδB fromMFA decreaseswith position
Fig.12.— Spectrum fromNEregion3fromTycho(see Figure in the precursor as the free-escape boundary (FEB) is
1). Theblackhistogramcorrespondstothebest-fitabsorbedCR- approached,resultinginanincreaseinD (i.e.,scattering
hydro-NEImodelforthecorrespondingprojectedregion. Residual
weakens) near the FEB.
emissionfromNe,Si,andSareevident,indicatingthepresenceof
ejecta extended nearly all the way to the FS. The red histogram Our model also includes non-adiabatic heating in the
correspondstoaCR-hydro-NEImodelwithGaussiansaddedatthe shockprecursor. TheMFAproducesturbulence,andthe
energiesexpectedforHe-likeemissionfromNe,Si,andS,although dissipation of turbulent energy and heating of the back-
we note that significant Neemissionis not expected in spectra of
ground flow is parameterized. The Alfv´en wave speed,
TypeIaSNRs.
which impacts the effective compression ratio for DSA,
pion-decay. We reach a similar conclusion, although also varies with position in the precursor. Importantly,
there are significant differences between our model thereisfeedbackbetweentheshapeandnormalizationof
and previous ones. First, unlike all other models, we the accelerated particle spectrum, the MFA and precur-
simultaneously fit the broadband continuum and X-ray sor heating, the speed of the Alfv´en scattering centers,
line emission with a single self-consistent model. As the normalization of D as a function of position in the
has been shown previously (e.g., Ellison et al. 2007; precursor,and p .
max
Patnaude et al. 2009; Ellison et al. 2010; Lee et al. We note that CR-hydro-NEI also addresses the main
2012; Castro et al. 2012; Lee et al. 2013), the X-ray concern Berezhko et al. (2013) have concerning the
observations strongly constrain the ambient density Morlino & Caprioli(2012)model,namelythatthelatter
and can provide a distinction between pion-decay and authors assume a steep spectrum for the CR protons, in
inverse-Comptonemission at γ-ray energies. Second, we order to match the observedspectrum at lower energies,
are able to obtain a satisfactory broadband fit without but then assumed Bohm diffusion for even the highest
invoking an arbitrary multi-component environment energyparticlesinordertoobtainemissionofγ-raysbe-
where some fraction of the swept-up mass is in dense yond400MeV.Thisleadstoamaximumprotonmomen-
clumps as is done in Berezhko et al. (2013). Of course, tum p ∼ 500 TeV. Berezhko et al. (2013) note that
max
we do not argue that dense clumps do not exist; the Bohm diffusion is inconsistent with such a steep spec-
morphology of any SNRs is more complicated than trum, and argue that a two-component spectrum is re-
the spherically symmetric model we use. At present, quired. Here,wedonotmakethesameassumption. The
however, observational evidence of any such clumpy spectrum of the accelerated particles, the normalization
environmentsurroundingTychoisinsufficienttoprovide of the diffusion coefficient, and the resulting maximum
constrained parameters for such modeling. From a momentum are all calculated self-consistently. As noted
modeling perspective, there is thus little motivation above, we obtain p ∼ 50 TeV while still reproducing
max
to add a second component with an additional set of the observed broadband spectrum. In short, we believe
unconstrainedparameterswhen a one-componentmodel the CR-hydro-NEI model addresses all of the criticisms
produces a satisfactory fit. Berezhko et al. (2013) make of the Morlino & Caprioli
It has been argued (Atoyan & Dermer (2012)) that a (2012) model, for which the results of our more detailed
two-zonemodel in which electrons acceleratedat the FS modeling are in good agreement.
shockemitintwodistinctenvironmentsprovidesamore In the results presented here, we do make the Bohm
realistic picture for Tycho’s SNR than the many one- assumption, i.e., that the diffusion coefficient is equal to
zonemodels that havebeenconsidered. Inthis scenario, theparticlegyroradius. However,thegyroradiusisdeter-
a thin outer zone at the FS produces the X-ray syn- mined with the local amplified δB(x) which varies with
chrotron emission while, inside the FS, electrons accu- precursorposition. At this point, we do not believe that