Evidence for Cosmic Ray Acceleration in Cassiopeia A
aa r X i v : . [ a s t r o - ph . H E ] A ug Submitted to ApJ on 5/10/2010
Evidence for Cosmic Ray Acceleration in Cassiopeia A
Miguel Araya and Wei Cui Department of Physics, Purdue University, West Lafayette, IN 47906, USA
ABSTRACT
Combining archival data taken at radio and infrared wavelengths with state-of-the-art measurements at X-ray and gamma-ray energies, we assembled a broad-band spectral energy distribution (SED) of Cas A, a young supernova remnant.Except for strong thermal emission at infrared and X-ray wavelengths, the SEDis dominated by non-thermal radiation. We attempted to model the non-thermalSED with a two-zone leptonic model which assumes that the radio emission isproduced by electrons that are uniformly distributed throughout the remnantwhile the non-thermal X-ray emission is produced by electrons that are local-ized in regions near the forward shock. Synchrotron emission from the electronscan account for data from radio to X-ray wavelengths. Much of the GeV–TeVemission can also be explained by a combination of bremsstrahlung emission andinverse Compton scattering of infrared photons. However, the model cannot fita distinct feature at GeV energies. This feature can be well accounted for byadding a π emission component to the model, providing evidence for cosmic rayproduction in Cas A. We discuss the implications of these results. Subject headings:
ISM: individual objects (Cassiopeia A), - ISM: supernova rem-nants, - radiation mechanisms: non-thermal
1. Introduction
Ever since their discovery, cosmic rays have been studied extensively. They consist ofmostly protons and helium ions (but also heavy nuclei) and reach energies up to 10 eV. Atenergies below ∼ eV, cosmic rays are thought to be of Galactic origin. [email protected] [email protected] Chandra X-Ray Obser-vatory opened a new era of high-resolution X-ray imaging of SNRs. There is clear evidencefor the existence of higher-energy electrons within these objects, which usually producethin X-ray “filaments” associated with shocks (e.g., Gotthelf et al. 2001; Hwang et al. 2002;Long et al. 2003; Rho et al. 2002). The X-ray spectra of the filaments are consistent withsynchrotron emission from particles as they move in an amplified magnetic field (e.g.,Berezhko et al. 2002; Vink & Laming 2003; Berezhko & V¨olk 2004; Araya et al. 2010).Despite all the findings that link SNRs with high-energy electrons, direct evidence forthe acceleration of ions by these objects is still lacking. In order to find a signature forhadronic acceleration, studying the photon spectrum of the sources at gamma-ray energiesbecomes fundamental. It is expected that at least a fraction of the emission at high en-ergies would be caused by the decay of neutral pions, which should be produced throughcollisions of accelerated hadrons with cold ambient protons and ions. Other mechanisms canalso contribute to the gamma-ray spectrum besides hadronic interactions. The high-energyelectrons that are responsible for the synchrotron emission at radio and X-ray wavelengthscan upscatter ambient photons to TeV energies; and interactions between these electronsand other charged particles result in bremsstrahlung emission, which can also contributeto the emission in the GeV – TeV range. It then becomes important not only to obtainobservations in the gamma-ray regime but also to model the broadband leptonic emission indetail, in order to separate and quantify the hadronic contribution.An example of a young SNR where high-quality broadband data are available is Cas A.The data should allow detailed studies of the properties of high-energy electrons in this rem-nant. For instance, radio images of Cas A indicate that the synchrotron emission is spreadout within its shell, implying that the electrons responsible for it are likewise more or less uni-formly distributed. The X-ray emitting electrons are mainly confined near the forward shock,with their displacement being strongly limited by synchrotron loss (Gotthelf et al. 2001).In this work, we present evidence for cosmic ray acceleration in Cas A from modelingits SED over a broad spectral range (from radio to gamma ray). 3 –
2. Data2.1. Archival data
In order to construct a broadband SED, we used results from the literature, except forthe GeV band where we analyzed public data from the LAT instrument on the
Fermi satel-lite. The radio fluxes were measured at the DKR-1000 radio telescope of the Pushchino Ra-dio Astronomy Observatory (Vitkevich & Kalachev 1965; Artyukh et al. 1967) and at theStaraya Pustyn’ Radio Astronomy Observatory and taken from Vinyaikin (2006; 2007),at the frequencies 38, 151.5, 290, and 927 MHz for the epoch 2005.5. An additionalVery Large Array (VLA) flux at 74 MHz corresponding to the epoch 2005.2 was included(Helmboldt & Kassim 2009). The VLA images of the remnant show that the radio emissionis more diffuse, compared to the X-ray emission.The infrared fluxes were taken from the Infrared Astronomical Satellite ( IRAS ) surveyfrom 12 µ m to 100 µ m (Dwek et al. 1987). They are likely dominated by thermal emissionfrom dust. Although we are only interested in non-thermal emission from Cas A, the infraredemission may be an important source of seed photons for leptonic gamma ray production.The X-ray fluxes were obtained from deep exposures of Cas A with the Chandra X-rayObservatory (Hwang et al. 2004). Data reduction was carried out as described in Arayaet al. (2010). We excluded events from the central compact object in deriving the X-ray spectrum of the remnant. The X-ray spectrum of the remnant is dominated by thermalemission from highly ionized ejecta (Borkowski et al. 1996; Favata et al. 1997), as evidencedby the presence of numerous lines. Non-thermal X-ray emission manifests itself in thinfilaments associated with the forward shock, as well as in the hard tail of the X-ray spectrum.The TeV gamma-ray measurements were taken from Acciari et al. (2010). They arebased on observations of Cas A with VERITAS.
Fermi
LAT data
We analyzed the
Fermi
LAT data that were obtained between 2008 August 4 and 2010March 10. For details of the instrument, see Atwood et al. (2009). The VLA array is an instrument of the National Radio Astronomy Observatory, a facility of the NationalScience Foundation operated under cooperative agreement by Associated Universities, Inc. See the National Radio Astronomy Observatory image archive, http://images.nrao.edu/395 . The cutsand selection criteria applied to the data were those recommended by the Fermi ScienceSupport Center. We selected diffuse events by excluding events with the lowest probabilityof being gamma rays with the gtselect tool and used the current version of the instrumentresponse functions given by P V DIF F U SE (Rando et al. 2009). The energy of theselected events ranges from 200 MeV to 300 GeV. We made appropriate time selectionswith the gtmktime tool. Specifically, we used a value of 105 ◦ for the zenith-angle cut toexclude times of high background that is associated with gamma rays produced in the Earthatmosphere.Due to the large LAT point-spread function at low energies, it becomes necessary toinclude events within a region around the source. This region of interest is taken here asa 10 ◦ radius circle around the cataloged position of Cas A. The accuracy of the analysis isimproved when the contributions from other sources within a larger region (“source region”)are also included. We used a 20 ◦ radius source region, which is recommended for sourcesnear the Galactic plane such as Cas A. The background included point sources at fixedpositions located in the source region, based on the recently released 11 month Fermi LATSource Catalog(Abdo et al. 2010a) , as well as the galactic diffuse component (as specified in gll iem v02.fit ) and the isotropic extragalactic emission (as specified in isotropic iem v02.txt ).Figure 1 shows a LAT image of the region near Cas A. A maximum likelihood method (asimplemented in the gtlike tool) is usually used to determine spectral parameters describingLAT sources of interest and their statistical significances (Mattox et al. 1996). We foundthat Cas A was detected only at energies above 500 MeV. Between 500 MeV and 60 GeV,it was detected at a significance of 20 . σ . The best-fit position of the source, calculatedwith the gtfindsrc tool, was R.A. (J2000)= 23h23m21.9s, decl. (J2000)= 58 ◦ ′ ′′ .4, with astatistical uncertainty circle of radius 0 ◦ .
033 at the 90% confidence level. This position is inagreement with that derived by Abdo et al. (2010b). It also lies inside the VERITAS errorbox (Acciari et al. 2010).The
Fermi
LAT spectrum of the source can be fitted with a power-law, dN/dE ∝ E − p ,with a photon index of p = 2 . ± .
07. The measured 0.5–60 GeV flux is (1 . ± . × − photons cm − s − . Note that only statistical errors are shown here. The systematic errorson flux measurements have been estimated to be 5% at 500 MeV and 20% at 10 GeV(Rando et al. 2009). Our results are in overall agreement with those reported by the Fermi
LAT team based on a smaller data set (Abdo et al. 2010b). See http://fermi.gsfc.nasa.gov/ssc See also http://fermi.gsfc.nasa.gov/ssc/data/access/lat/1yr catalog/
3. Theoretical Modeling
Figure 2 shows the broadband SED of Cas A. At infrared wavelengths, the SED isdominated by thermal emission from dust (which lies much above the extrapolated radiospectrum). Similarly, at X-ray wavelengths, the thermal emission from hot plasma standsout as the main component, as evidenced by the presence of numerous lines. In this work,we do not attempt to model the thermal emission, but instead focus on the radiation ofnon-thermal origin.At radio frequencies the spectrum of the source is of power-law shape, characteris-tic of optically thin synchrotron emission by high-energy electrons whose spectral energydistribution is also a power law. The existence of non-thermal electrons at even higher en-ergies has been most clearly reaffirmed by observations obtained with the
Chandra X-rayObservatory , which reveal the presence of thin compact regions of non-thermal X-ray emis-sion (Gotthelf et al. 2001). To provide a measure of the contribution of non-thermal emissionto the overall X-ray spectrum, we also show, in Figure 2, the scaled-up X-ray spectrum of arepresentative non-thermal filament. Note that the X-ray spectrum is quite similar amongnon-thermal filaments near the forward shock (Araya et al. 2010).To account for the observed radio and X-ray emission, we constructed a model thatinvolves two populations of electrons: diffuse electrons that are assumed to be uniformly dis-tributed over the entire SNR and localized electrons that are spatially concentrated near theforward shock. The synchrotron radiation from the former is expected to contribute mainlyto radio and IR fluxes (but could also reach X-ray wavelengths if there are enough particlesof sufficient energy) while that from the latter mainly to X-ray fluxes. Both populationsmay contribute to the observed gamma-ray fluxes via inverse Compton (IC) scattering andbremsstrahlung processes.
The two populations of electrons are modeled as zone 1 consisting of spherical “blobs”that approximate the non-thermal filaments seen, and zone 2 consisting of electrons uniformlydistributed over a sphere of radius R SNR = 2 . d SNR = 3 . ν ∼
30 GHz have been explained byAtoyan et al. (2000), who developed a two-zone model for the radio emission consistingof a diffuse component as well as localized “radio structures”, such as an internal ring and 6 –very compact knots. For simplicity, here we assumed that the synchrotron photons at radiofrequencies are all associated with the diffuse electrons in zone 2.The description of zone 1 is based on our previous results from a detailed study ofnon-thermal X-ray filaments near the forward shock of Cas A (Araya et al. 2010). In thatwork we used a synchrotron model that also takes into account the effects of diffusion andadvection to explain the spectral evolution across the filaments. The analysis allowed us todetermine the SED of the X-ray emitting electrons in the filaments as well as other propertiessuch as magnetic field and level of turbulence. We found that the electron distributions aresimilar among the filaments examined. Here, we assumed that the electron populations inthe blobs follow a power-law distribution of index 2 .
6, in a local magnetic field of 50 µ G.Note that the adopted value of the magnetic field is significantly lower than those estimatedby associating the width of filaments only with synchrotron cooling of radiating electrons(e.g., Vink & Laming 2003).For zone 2, we modeled the electron distribution as a power law with a spectral indexof 2.54, which reproduces the observed radio spectrum J ν ∝ ν − . (Baars et al. 1977).The maximum energy of the electrons is poorly constrained by the data. To assess themaximum contribution from zone 2 to gamma-ray production in Cas A, we pushed themaximum electron energy to as high as possible without causing inconsistency with the X-ray measurement (see Figure 2). A mean magnetic field of ∼ µ G was used to fit thedata. This value is consistent with previous estimates derived from fits to the radio fluxesfrom the remnant (Atoyan et al. 2000). The overall normalization chosen gives an energycontent in the particles that is also consistent with previous results (see Section 4). The highmagnetic field could be caused by reverse shock (or secondary shocks) in the interior of theremnant (e.g., Laming 2001; Uchiyama & Aharonian 2008).Figure 2 also shows the results from leptonic modeling of the SED. The synchrotronemission from zones 1 and 2 is able to account for the non-thermal radio and X-ray fluxes.From the particle distributions, we calculated the number of gamma-ray photons emitted atthe source per unit volume per second in the energy range ǫ γ to ǫ γ + dǫ γ as dn γ ( ǫ γ ) dt = Z ∞ dn γ ( T e , ǫ γ ) dt (cid:18) πv e (cid:19) (cid:18) dJdT (cid:19) e dT e , (1)where (4 π/v e )( dJ/dT ) e is the number density per unit kinetic energy of electrons ( T e ) and dn γ ( T e , ǫ γ ) /dt is the emissivity of one electron. The expected photon flux can then bedetermined for zones 1 and 2 (with volumes V and V , respectively) as V , πd SNR dn , γ ( ǫ γ ) dt . (2) 7 –For the two zones, we included bremsstrahlung emission from electron–electron andelectron–ion interactions, as well as IC scattering. The production rate of bremsstrahlungphotons by an electron interacting with ambient protons, electrons, and helium ions withdensities n p , n e , and n He , respectively, is given by dn γ ( T e , ǫ γ ) dt = v e [( n p + 4 n He ) σ e,p ( T e , ǫ γ ) + n e σ e,e ( T e , ǫ γ )] , (3)where σ e,e and σ e,p are the electron–electron and electron–ion cross sections, differential inphoton energy and v e is the relative speed in bremsstrahlung collisions. The electron–ioncross section depends on the charge as σ e,p ∝ Z , which explains the factor n p + 4 n He inEquation 2. We considered only interactions of electrons with other electrons, protons, andfully ionized helium. This implies that n e = 1 . n p . We also assumed an abundance forhelium of n He = 0 . n p .The values of n p used in the calculations of expected bremsstrahlung fluxes can bedifferent for the two zones. For diffuse electrons in zone 2, the density n (2) p is determined bythe average density of protons in the remnant. If we consider uniform distribution of massin a sphere of radius R SNR, then we get a mass for Cas A of M Cas A ∼ (2 . M ⊙ ) n p − . Therefore, for an estimated remnant mass of ∼ M ⊙ (Willingale et al. 2003), we get n (2) p ∼ . − . We fixed this value in the calculations. On the other hand, for the bremsstrahlungflux from electrons in zone 1 the density of ambient protons, n (1) p , cannot exceed 0 . − ,in order for the model to be compatible with the Fermi
LAT measurements (see Figure 2).The fit shown in Figure 2 was based on n (1) p = 0 . − .As for IC scattering, we considered various sources of seed photons. The most importantone turns out to be infrared photons from the dust in the SNR. The IC scattering of thesephotons by electrons in zone 2 is calculated under the assumption that the infrared radiationis distributed uniformly across the SNR (which is another gross simplification, as the IRintensity is seen to decrease going outward (Dwek et al. 1987)). On the other hand, in orderto fit the TeV fluxes, we found that about 15% of the total infrared photons reported bythe IRAS observation should interact with the X-ray-emitting electrons located in zone 1near the boundary of Cas A. The IC scattering of other seed photons such as the cosmicmicrowave background (CMB) by electrons in zones 1 and 2, as well as the scattering ofradio synchrotron photons from zone 2 by electrons in zone 1, were also included in thecalculation. Figure 2 shows that these IC processes are only a minor contributor to theoverall gamma-ray production in Cas A. 8 –As also shown in Figure 2, even with the choice of extreme electron energies for zone2, the gamma-ray emission from this zone is still less than that from zone 1. It appears,therefore, that leptonic gamma-ray production in Cas A originates mainly near the forwardshock.
It is clear from Figure 2 that our leptonic modeling fails to explain the observed gamma-ray emission at GeV energies. An additional component is needed to account for a distinctGeV feature of the SED. The presence of high-energy protons would naturally provide sucha spectral component. Collisions between these protons and ambient (cold) protons lead tothe production of pions. The decay of neutral pions produces gamma rays.Figure 3 shows the SED of Cas A with an additional component produced by π decay.The gamma-ray spectrum from hadronic interactions was calculated as in Kamae et al.(2006), with a nuclear enhancement factor of 1.9 (Mori 2009). The data seem to requirethat the spectral distribution of relativistic protons be a broken power law. In terms of thekinetic energy of the protons ( T p ), the required distribution has the form dN/dT p ∝ T − . p for T p <
11 GeV and dN/dT p ∝ T − . p for T p >
11 GeV.The model shown in Figure 3 was obtained with the parameters in Table 1. For con-sistency with the upper limit obtained by the
Fermi
LAT in the 200–500 MeV band, alocal density of n (1) p = 0 . − was required for the bremsstrahlung emission from zone 1,which is lower than the value used for the model shown in Figure 2 (which has no hadroniccontribution).
4. Discussion
The
Fermi satellite, launched on 2008 June 11, has opened a new window of excitingobservations in the GeV regime. Hints of hadronic processes in SNRs have been seen. Forinstance, the
Fermi
LAT spectrum of the middle-aged SNR W51C seems to indicate adominant π -decay contribution (Abdo et al. 2009). With respect to Cas A, the Fermi
LATteam discarded the possibility that the GeV emission comes from the compact object near thecenter of the remnant on the basis of spectral and timing analysis (Abdo et al. 2010b). Theycarried out modeling of only the GeV–TeV gamma-ray spectrum in leptonic and hadronicscenarios separately.In this work, we modeled the radio and X-ray emission from Cas A as synchrotron radi- 9 –ation from two populations of electrons. The radio emission is attributed to diffuse electronsdistributed over the whole remnant, while the X-ray emission to electrons localized in about430 “blobs”, each with a fixed diameter of 0 .
32 pc, which is a typical scale for the width ofX-ray filaments near the forward shock. The combined volume of the “blobs” is about 1 / W e ∼ . × erg or about3% −
6% of the estimated kinetic energy in the explosion of Cas A (Laming & Hwang 2003).Bremsstrahlung radiation from the electrons can account for bulk of gamma-ray emissionbelow about 1 GeV, while IC scattering of infrared photons by the electrons seems to bemainly responsible for gamma rays at TeV energies. Although there is considerable degen-eracy in modeling the radio to X-ray SED of the source, we found it difficult to account forthe GeV spectrum of Cas A with leptons alone.Adding a π component to the model can explain the distinct feature of the SED betweenabout 1 and 40 GeV. The best match to the data is obtained for protons whose kineticenergies follow a broken power law with indices of ∼ . T p <
11 GeV and 2 . T p > π components are comparable between 40 and 500 GeV, where the SED is relativelyflat. The total energy in the protons is about W p ∼ . × erg. However, this value couldget higher if a lower percentage of infrared emission is assumed to be interacting with theX-ray filaments (which would make IC contribution less important).Our model contains several simplifications. For instance, we neglected the spatial inho-mogeneities in the radio brightness distribution, which point at the existence of additionalelectron populations (Atoyan et al. 2000). However, as calculated by Atoyan et al. (2000),the expected bremsstrahlung flux from these electrons is considerably less than that of thediffuse component at GeV energies due to their steeper distributions. It can be argued sim-ilarly that the expected emission from IC scattering of ambient photons off these electronsis low, which justifies neglecting their contribution to the SED. We also assumed a uniformproton density inside Cas A, which is not realistic. We will investigate the effects of a morerealistic density profile for young SNRs in a future work.Vink and Laming (2003) also modeled the emission from Cas A with two populationsof electrons. They adopted a higher magnetic field (80-160 µ G) near the shock, which isobtained when comparing a typical width of an X-ray filament with the synchrotron coolinglength of a typical high-energy electron (see also Parizot et al. 2006). In our model wedecided to use a lower value (50 µ G) derived by Araya et al. (2010) who took into accountthe effects of diffusion, in addition to those of synchrotron loss and advection. With theirmodel, Vink and Laming (2003) predicted a gamma-ray flux from IC scattering of ambient 10 –photons that lies below the HEGRA observation at TeV energies which, they argued, mightbe a hint to a pion decay origin of the radiation. In our model, most of the emission atTeV energies is attributed to IC scattering of infrared photons, which is a consequence ofadopting a lower magnetic field at the shock front. It should be stressed that the data pointsat GeV energies, which were not available to previous studies, hold the key to revealing thepresence of hadronic processes in Cas A.Although we believe that the lower value of the magnetic field that we adopted is morereliable, the measurement of the field is still quite uncertain. We also ran models with highermagnetic field. As an example, Figure 4 shows a reasonable fit to the data with B = 90 µ Gin zone 1. The higher field causes a reduction in the IC contribution, which is compensatedby a harder proton distribution (with a spectral index of 2 . T p > n (1) p = 1 . − ) and a lowervolume for zone 1 ( ∼ V SNR / B > µ G in zone 1, we found it difficult to explainthe observed high-energy SED with our model.In summary, we were unable to account for the observed gamma-ray fluxes of Cas Aat GeV energies with leptons alone in our model. The GeV “excess” can be well explainedby additional gamma rays from the decay of neutral pions, which may be produced in theinteractions between relativistic hadrons and dense matter in the remnant. This constitutesevidence for cosmic ray acceleration in Cas A.We thank T. Kamae for kindly providing us with his code for calculating the crosssections and gamma-ray fluxes in pp interactions, and S. Funk for providing his Fermi LATfluxes of Cas A in electronic format for comparison. We also thank M. Lyutikov and D.Lomiashvili for useful discussions. This research has made use of data obtained from the Chandra
Data Archive and the
Chandra
Source Catalog, and software provided by the
Chandra
X-ray Center (CXC) in the application package CIAO. This work has also madeuse of NASA’s Astrophysical Data System. We gratefully acknowledge the financial supportfrom NASA and Purdue University. 11 –
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This preprint was prepared with the AAS L A TEX macros v5.2.
13 –Table 1: Model Parameters Leptonic Component Hadronic ComponentParameter Zone 1 Zone 2Magnetic field ( µ G) 50 300 -Ambient proton density (cm − ) 0.5 4.4 4.4Minimum Lorentz factor 1 1 1 . × × . × Volume ∼ V SNR V SNR V SNRSpectral index ∗ T p <
11 GeV2.7, T p >
11 GeVTotal energy (erg) 1 . × . ×
14 –
Galactic longitude G a l ac t i c l a t i t ud e J2347.1+5142 +5949 J2214.5 J2250.8+6336 J0003.1+6227 J0000.8+6600c
110 104108 106112116 114118-8-6-4-2024
PSR J2229+6114PSR J2238+59
Cas A
Fig. 1.— Smoothed
Fermi
LAT count map (0.5-60 GeV) of a 16 ◦ × ◦ region around CasA. A binning of square pixels 0 ◦ .
08 in size was used and smoothing was done (in ds9) witha Gaussian kernel of 2 pixel width. Contours are shown at the levels of 14, 28, 43, and 57counts. The positions of additional sources found in the
Fermi
Catalogue and included inthe LAT data analysis are also indicated. 15 –Fig. 2.— SED of Cas A and leptonic components. The dashed lines correspond to contribu-tions from zone 2 and the dash-dotted lines to those from zone 1. Shown in the GeV–TeVbands are bremsstrahlung fluxes (using a proton density for zone 1 of 0 . − ), synchrotronself-Compton and IC scattering of CMB (IC/CMB), infrared (IC/IR), and radio (IC/radio)photons. For comparison with the model, we show, separately, the scaled-up X-ray spectrumof a non-thermal filament (in green). Note that the spectrum is “contaminated” by thermalemission at low energies (see Araya et al. 2010). 16 –Fig. 3.— Modeling of the SED of Cas A with an additional hadronic component. The SEDof protons is described by a broken power law in kinetic energy (see the text). For calculatingthe bremsstrahlung flux from zone 1, we adopted the value 0 . − for the ambient protondensity, as opposed to 0 . − used in Figure 2. 17 –Fig. 4.— Same as Figure 3, but with a magnetic field of 90 µ G and an ambient protondensity of 1 . −3