A statistical classification of the unassociated gamma-ray sources in the second Fermi Large Area Telescope Catalog

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Research in Astron.Astrophys. 2013 Vo1.13 No.8，952-960 htp：# http.'///journals/raa ResearchinAstronomyandAstrophysicsA statistical classification of the unassociated gamma·ray sourcesin the second Fermi LargeZhu M ao and Yun-W ei YluArea Telescope CatalogInstitute of Astrophysics，Central China Normal University，Wuhan 430079，China；yuyw###phy.ccng.edu.cnReceived 2013 January 24；accepted 2013 April 13Abstract Witl1 the assistance of the identified/associated sources in the second FermiLarge Area Telescope(LAT)catalog，we analyze an d resolve the spatial distributionand the distributions of the gamma.ray spectral and variability indices of the remaining575 unassociated Fermi LAT sources.Consequently.it is suggested that the unasso-ciated sources could statistically consist of Galactic supernova remnants/r)ulsar windnebulae，BL L，acertae objects，flat spectrum radio quasars and other types of activegalaxies with fractions of 25%，29%，41% and 5%，respectively。

Key words：gamma rays：generM·---catalogs·---methods：statistical1 INTRODUCTIoNA routine whole.sky survey in the 100MeV to 100 GeV band with the Large Area Telescope(LAT：Atwood et a1.2009)onboard the f Gamma-Ray 口ace Telescope has been carried out sincethe science phase of the mission began in August 2008.By analyzing the observational results ofthe first 24 months，the Fermi LAT Colaboration published the second Fermi LAT Source Catalogcontaining l873 gamma.ray sources fNolan et a1.2012).Great efforts have been made to identifythe LAT sources by periodic emission or variability correlation with other wavelengths，and also toprovide associations for many more LAT sources with previous gamma-ray catalogs and with likelycountemart sources from known or suspected source classes(based on Bayesian probabilities in aL error box).As a result 1298 L sources have been identified as or associated with pulsarssupemova remnants(SNRs)，pulsar wind nebulae(PWNe)，blazars，active galaxies(AGs)，etc(seeT：lb1e 11.However，nearly one third of the LAT sources are still unclassified(i.e.575 out of 1873)。

Such a situation is similar to that of the third Energetic Gamma Ray Experiment Telescope(EGRET)catalog(Hartman et a1.1999)。

The dimculty in the identifcation/association of these unclassified sources arises because ofthe 1ocation accuracy of the LAT sources.which is typicaly insuficiently precise.In other words，in a typical LAT eror box，there are too many stars，galaxies，X-ray sources，infrared sources andradio sources.Therefore，besides the source positions，more information is required to determinethe nature of the unassociated LAT sources，including the spectral information，time variability，andavailabilicV of a plausible physical process at the source to produce gamma-rays with suficiently-high energy.Stephen et a1.(2010)made such an attempt with the R0SAT catalog，which is usefu1SuppoRed by the National Natural Science Foundation of China。

A Statistical Classification of the Unassociated Fermi L SourcesTable 1 The Numbers of Identified/Associated Sourcesin the Second Fermi L r CatalogType NOPulsarPulsar wind nebulaSupernova remnantSupernova remnant/Pulsar wind nebulaGlobular clusterHigh-mass binaryNova10831O581141BL Lacerate obiectFlat spectrum radio quasarActive galaxy with all uncertain typeNon-blazar active galaxyRadio galaxySeyfertgalaxyNOrlTlal galaxyStarburst galaxy4363702571112664953in finding a positionaly corected，highly unusual object that might be expected to produce gamma-rays.As a result.30 unassociated LAT sources are tentatively suggested to be associated with a尺D跗 T counterpart.More directly.Ferrara et a1.(20 1 21 proposed that a comparison of the spectra1and variability indices between the associated and unassociated L sources can provide insightinto the likelv classes of the unassociated sources.Following such a consideration.in this papeL weprovide statistics on the gamma-ray spectral and variability indices of the unassociated Fermi LATsources.Based on these statistics，we try to discover how many components the unassociated sourcesconsist of and what these components could be。

2 SKY DlSTRIBUTION oF THE UNASSOCIATED FERMI LAT SOURCESThe spatia1 distribution of the 575 unassociated Fermi LAT sources is presented in the lefl panel ofFigure 1，which exhibits an obvious concentration of the sources in the galactic plane(GP).In moredetail.we show the latitude distribution of these sources in the right pane1 of Figure 1.where a spikein the source number appears in the central 10。of the Galaxy.Such a spike naturaly indicatesa Galactic origin for a significant fraction of the unassociated sources.However，it should be notedthat the spike could also be partly contributed by some active galactic nuclei(AGNs)because of theanisotropic distribution of the identifed/associated AGNs。

As shown in Figure 2，a big dip appears in the AGN number distribution，which is caused by thelimited/no coverage of the AGN catalogs in the GP fAckerm ann et a1.2012).Therefore，by consid-ering the actual isotropic distribution of AGNs.an extra component consisting of potential AGNs isexpected to exist in the unassociated sources.According to the fitting to the latitude distribution of aI1identified/associated AGNs in Figure 2.the number density of the potential AGNs per square degreeas a function of galactic latitude can be empirically described by the folowing Gaussian functionnpAGN(6)npAGN，maxe-(b-Ib)。/with npAGN，m ax 0.02 deg- ， b -1.6。and o-b 6.5。.Besides these potential AGNs，theunassociated sources could still contain an isotropically-distributed(ISO)component and a GP com-ponent.For a simple empirical description，we express the number densities of the ISO and GP corn-ponents by a constant and a Gaussian function，respectively.Then，as shown in the right panel ofA Statistical Classification of the Unassociated Ferrni LAT SourcesTable 2 Fitting Parameters for Distributions of F and Vr logV。 oISO-I 2.075 0.204 1.345 0.187ISO-Ⅱ 2.451 0.174 1.380 0.073GP 2.440 0.207 1.364 0.132955sources have Galactic origins，while the other three quarters are possible extragalactic sources.Ofcourse，such a conclusion can be somewhat modified by some pulsars and some possible exoticsources fe.g.due to dark matter annihilation(Zechlin&Homs 2012))，which could be located in theGalactic halo and contribute to the ISO component。

3 POSSIBLE NATURES oF THE UNASSoCIATED FERMI LAT SOURCESAs provided by the Fermi LAT collaboration(Abdo et a1.2010；Nolan et a1.2012)，the gamma-rayproperties of the unassociated sources can be characterized by four basic parameters of flux S，timevariability index V，spectral index r an d curvature index C，which quantifies the departure of thespectrum from a single power-law shape.In this PapeL we make a basic assumption that a quantitywhich reflects al intrinsic physical property of a source type should exhibit a norma1 or lognormaldistribution.However，due to the distance-dependence of S and the possible flux-dependence of CfAckermann et a1.2012)，these two parameters are not considered to be good statistical quantities。

Therefore.we will only include the spectral and variability indices，F and V，in our work。

3.1 The ISO ComponentIn order to reveal the possible nature of the ISO component，we select the unassociated sources atlatitudes higher than l 18。，the number of which is ⅣHL 205.According to the fiting givenin the right pane1 of Figure 1，it is certain that al1 of these 205 high-latitude(HL)sources are part oftheIS0 component。

In Figure 3，we display the number distributions of the spectral and variability indices of the205 HM SO unassociated sources by histograms.What do these distributions tel usFolowing ourbasic assumption.the distributions of r and V are fited simultaneously and tentatively by one，twoor three Gaussians.By comparison，the best fit is obtained with two Gaussians，as shown in Figure 3。

The fitting function readsⅣhi 7己 I/2丌 e-(b- I)。/2 O'ii 27r e-(6- ii)。/2 2I (3)and the fitIing parameters are listed in 11ab1e 2 for 7-Z 1.5.Here we would like to emphasize thatthe ratio佗 between the numbers of the two Gaussian components should be the same in bOm ther and V fittings.According to the above fittings.we can further separate the ISO component intotwo subcomponents.denoted bv IS0.I an d ISO-II.Relative to the total unassociated sources，thepercentages of the ISO-I and ISO-I components can be estimated as so-I，Iso 33%and t广Iso-ii l广Iso 22u/0，respectively。

In the left pan e1 of Figure 4.we draw a scatter plot for the 205 HL/ISO unassociated sourcesin the r- V plane an d show the 2 regions of the ISO.I an d ISO-II components by the rectanglesdefined by Equation f3).As can be seen.most of the data are covered by the two rectangles，exceptfor the data at the far left and the top right comer.In the right pan e1 of Figure 4。nearly all of theA Statistical Classification of the Unassociated Fermi L Sources 957in pulsars，could indicate a low probability of pulsars for the unassociated sources.By ignoring thepossibility of being a pulsar，the numbers of unassociated sources which are candidates of BLOs andFSRQs can be estimated to beNBLO ca dNu o (fIso-ifpAGN/BLO)235NFSRQ cand：Nunas。c(kso-ifpAGNfFSRQ)165，(4)(5)where Nunas8。c575，and the fractions fBLO39%and fFSRQ34%are obtained by countingthe numbers of identified/associated AGNs.Additionaly，the remaining sources in the potentialAGNs could be AG candidates，the number of which is aboutNAG。 dNu 。 fpAGN(1-/BLO-fFSRQ)313.2 The GP ComponentAs a similar treatment，we select the unassociated sources at latitudes lower than lb1： 8。，thenumber of which isⅣI L288.According to the fiting in the right pane1 of Figure 1，we know thatthe low-latitude fLL1 sources could be dominated by the sources that have a Galactic origin。

In Figure 5，we firstly display the distributions of P and V for the 288 LL unassociated sourcesby the grey histograms.However，these distilbutions cannot directly reflect the intrinsic properties0f the GP component.because a significant fraction of the LL sources are actually extragalacticsources.According to Equation(2)，we can derive the percentages of the diferent components inthe latitude range of Ibl 8。as fLL，GP52%，，LL，ISO16%and fLL pAGN32%.Therefore，the intrinsic distributions of F and V for the GP sources can be obtained by the following methodNGp，bin：ⅣlLL1bin-ksoNiso，bin-fpaGNNpAGN.bin (7)whereⅣIso，bin andⅣDAGN，bin are the numbers ofthe ISO unsociated sources and potential AGNsin each F or log V bin.As a result，the corrected distributions of.P and V with only the GP componentare presented by the dark yellow histograms in Figure 5，wfiere two single-Gaussian fittings areprovided.The fitting parameters are also listed in 11ab1e 2. 。

In the left panel of Figure 6，we draw a scatter plot for the 288 LL unassociated sources in ther - V plane.where the 2a region of the GP component is presented by the rectangle.As can beseen，a remarkable number of data points are located beyond the rectangle.in particular，in the low-F range，which is classified as the ISO sources and potential AGNs.In me right panel of Figure 6。

we compare the 2a region of the GP component wim the identifed/assocated GP sources includingpulsars.SNRs and PWNe，The comparison suggests that most of the unassociated GP sources areprobablycandidatesofSNRs/PWNe，ratherthan thegenerally expectedpulsars.ThenumberoftheseGP sources isNSN/PWN candⅣunas8。cfop144 (8)Additionaly，the GP component may also contain some globular clusters，because most identi-fled/associated globular clusters are located in the bottom-left comer of the 2a region，althoughtheir number is not very large。

3.3 Identifcation EficiencyIn Figure 7 we present the identification efficiencies of BLOs， FSRQs，AGs，SNRs/PWNe and pul-sars by comparing the numbers of identified/associated sources with unassociated ones，where thepotential AGNs are not considered in order to avoid the complication in the GEA Statistical Classification of the Unassociated Fermi LAT Sources 959Firstly.the identification e珩ciencies of BLOs and FSRQs are comparable to each other，whereasthe efhciency of SNRs/PWNs is much lower than the forrner two types.Such a situation could beunderstood as folows.On one hand，most BLOs and FSRQs can easily be distinguished from othertypes of sources by their characteristic rapid variability(1arge ).Moreover，the spectral energydistributions of BLO and FSRQ emission usualy peak at two energy bands，i.e.the IR to X-rayband and the MeV to TeV band.The 1ow-energy Deak thus makes it relatively easy to find an IR(e.g.DAbmsco et a1.2013；Massaro et a1.2013)or X-ray(e.g.R0MA.BZCAT sources；Massaroet a1.2009)counterpart.On the other hand。for SNRs.two types of gamma.ray emission scenar-ios have been widely investigated in 1iterature.i.e.hadronic and leptonic scenarios(Blandford&Ostriker 1978：Becker et a1.20l1：Schuppan et a1.2012).In the former case，gamma-ray emissionis produced by neutral pion decay.whereas in the latter case it is by inverse.Compton scattering ofrelativistic electrons on some seed photons.It could be expected that，in the hadronic scenario，the1ow-energy emission is probably negligible unless there are some other emission regions.This makesit dificult to find low-energy counterparts for the gam ma-ray SNRs.In other words.the low identifi-cation efficiency of SNRs may indicate that their gam ma.ray emission is produced by hadrons.Vervrecently，Mandelartz&Becker Tius(20 1 31 indeed claimed that hadronic emission can be found inmost Galactic SNRs.Future searches of TeV photons fe.g.by H.E.S.S.1 could be helpfu1 f0r dis。

tinguishing these two scenarios.because in the 1eptonic scenario the GeV and TeV photons havedifferent origins。

Secondly，our statistical classification indicates that candidates of pulsars and AGs in unassoci。

ated sources must be very limited.In other words，the identification efficiencies of pulsars and AGsin the Fermi LAT catalog are close to unity.except for the GP region for AGs.Such high efficien-cies could be due to fi)the plentifu1 multi-wavelength observations of AGs。which provide SUficientlow-energy counterparts and(ii)the apparent gamma-ray pulsations of pulsars which signifcantlyweakens the requirement of counterparts in other bands necessary for their identification。

4 CONCLUSIoNSAccording to their spatia1 distribution.575 unassociated Fermi LAT sources can be separated em-pirically into G ISO and potential AGN components.the fractions of which are 25%.55% and20%.respectively.By comparing the specgal and variability properties of the different classes ofunassociated sources with identified/associated sources，we conclude that the nature of the GP com-ponent is probab1v SNRs，PWNe.while the ISO component can further be separated into ISO-I andIS0-II subcomponents which are likely to be associated with BLOs and FSROs，respectively.Tb bespecifc，the 575 unassociated sources could statisticaly consist of 144 SNRs/PWNe.-235 BLOs，- 1 65 FSRQs and-3 1 AGs.where the constituents of the potentia1 AGNs in the GP are consideredto be the same as the identifed/associated AGNs.The identification efficiencies of BLOs.FSRQsand SNRs/PWNe can further be estimated as 61%。65% an d 33%.respectively.except for the GPregion where the e ciencies of BLOs and FSRQs become very low.BY conast.our result indicatesthat the identification e珩ciencies of pulsars and AGs could be very high.Anyway.the above conclu。

sions are only viable statistically.The existence of some exotic sources cannot be ruled out，becausewe cannot individually determine the nature of the unassociated sources.Nevertheless.statisticalclassification may still be helpfu1 for future identification or association of the sources。

Acknowledgements We than k Prof.K.S.Cheng for a useful discussion which motivated this workand Prof.S.N.Zhang for his instructive comments.This work is supported by the National NaturalScience Foundation of China(Grant No.1 1 103004)and the Foundation for the Authors of NationalExcellent Doctoral Dissertations of China(Grant No.201225)。

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