Diffuse emission of TeV Neutrinos and Gamma-rays from young pulsars by Photo-meson interaction in the galaxy
aa r X i v : . [ a s t r o - ph . H E ] A p r Research in Astronomy and Astrophysics manuscript no.(L A TEX: pulsars2.tex; printed on March 23, 2018; 14:25)
Diffuse emission of TeV Neutrinos and Gamma-rays from youngpulsars by Photo-meson interaction in the galaxy
Zhi-Xiong Li , Gui-Fang Lin , ,Wei-Wei Na Department of Physics, Yunnan University, Kunming 650091, China; [email protected] Yunnan Astronomical Observatory, National Astronomical Observatories, Chinese Academy ofSciences, Kunming 650011, China Laboratory for the Structure and Evolution of Celestial Objects,Chinese Academy of Sciences,Kunming650011,China Department of Physics, Yuxi Normal University, Yuxi 653100, China; [email protected]
Received 2013 ; accepted 2013
Abstract
It’s generally believed that young and rapidly rotating pulsars are important sitesof particle’s acceleration, in which protons can be accelerated to relativistic energy above thepolar cap region if the magnetic moment is antiparallel to the spin axis( µ · Ω < ). To obtainthe galactic diffusive neutrinos and gamma-rays for TeV, firstly,we use Monte Carlo(MC)method to generate a sample of young pulsars with ages less than yrs in our galaxy ;secondly, the neutrinos and high-energy gamma-rays can be produced through photomesonprocess with the interaction of energetic protons and soft X-ray photons ( p + γ → ∆ + → n + π + /p + π ) for single pulsar, and these X-ray photons come from the neutron star surface.The results suggest that the diffusive TeV flux of neutrinos are lower than background flux,which indicated it is difficult to be detected by the current neutrino telescopes. Key words: pulsars: general — stars: neutron — neutrinos and gamma-rays: stars — ele-mentary: neutrinos
Very high-energy[VHE,
E >
GeV ] neutrinos and gamma-rays from astrophysical objects can providea clear indication of the origins of galactic and extragalactic cosmic rays. The radiations probably comefrom gamma-ray bursts,active galactic nuclei,pulsars etc. In our Galaxy most high-energy gamma-rays andneutrinos are associated with pulsars, supernova remnant and pulsar nebula(Bednarek et al. 2005;Kistler& Beacom 2006). Young pulsars are persistent and periodic sources; they also have shorter distances toEarth than extragalactic sources. If they emit high-energy neutrinos/gamma-rays, we can spend longer time
Z.-X. Li et al. searching for the signals.If the TeV neutrinos and gamma-rays can be detected from pulsars, it will helpimprove our knowledge about the hadronic process taking place in the magnetosphere.Recently, some studies (Link & Burgio 2005, 2006;Bhadra & Dey 2009;Jiang et al. 2007) have shownthat if pulsar(age less than yr ) magnetic moment is antiparallel to the spin axis ( µ · Ω < ), ∆ -resonancewill be produced when pulsars-accelerated ions interact with these thermal radiation field. Then high-energyneutrinos and gamma-rays decay by ∆ -resonance. Link&Burgio(hereafter LB) considered that near thesurface of the neutron stars, the protons or heavier ions can be accelerated by polar caps to PeV energy.Whenthe thermal radiation flied of pulsar interact with accelerated ions with PeV energy, ∆ -resonance statemay occur. This process is effective,and pions subsequently decay to muon neutrinos or gamma-rays . LBcalculated energy spectrum of muon neutrinos from some pulsars and estimated the event rates at Earth. Thespectrum sharp rise at ∼
50 TeV, corresponding to the onset of the resonance. The flux drops with neutrinoenergy as ǫ − ν up to an upper energy cut-off that is determined by either kinematics or the maximum energyto which protons are accelerated. Bhadra & Dey(2009)estimated TeV gamma-ray flux at the Earth from afew nearby young pulsars and compared with the observation, they found that proper consideration of theeffect of the polar cap geometry in flux calculation is important,then they revised the event rates.In this paper we find the η (ratio of polar cap area to neutron star surface area)is double the Bhadra & Deygive.We use revised polar cap geometry to calculate TeV neutrinos and gamma-rays spectrum from someyoung pulsars,and estimate the event rates at Earth. In order to estimate diffuse TeV neutrinos and gamma-rays radiation from Galactic Plane, a galaxy pulsar sample is required. It is the better way to simulatea pulsar sample with MC method (Cheng & Zhang 1998;Zhang & Harding 2000;Jiang et al. 2007). Atlast,we obtain the TeV diffuse Neutrinos and Gamma-rays flux from young pulsars in our galaxy.In section 2,we reviewed the model of LB. In section 3,we calculate neutrino and gamma-ray spectrumfrom single pulsar by revised polar cap geometry.In section 4 and 5,we obtain a sample of young pulsars inour galaxy with Monte Carlos method, then estimate the diffuse neutrinos and gamma-rays emission fromGalactic young pulsars.At last the discussion and conclusion are presented. Neutron stars have enormous magnetic fields( B ≥ G ) and high rotation rates(tens of Hertz)which act asa very powerful generator. Charges will be stripped off the highly conductive surface and accelerated some-where above the stellar surface. The acceleration of particles mechanisms from pulsars generally has beendivided into the polar gap model (Ruderman & Sutherland 1975;Arons & Scharlemann 1979;Daugherty& Harding 1996;Gonthier et al. 2002) and outer-gap model(Zhang & cheng 2004;Cheng et al. 1986). Inthe former, particles are accelerated in charge-depleted zone region near the magnetic pole of the neutronstar. In the outer-gap, it will take place in the vacuum gaps between the neutral line and the last open linein the magnetosphere. Therefore, acceleration region in the polar-gap model is close to the neutron starsurface,whereas in the outer-gap model it is near to the light cylinder.In polar gap model, because of existing large rotation-induced electric fields, particles can be ex-tracted from the polar cap surface, and then be accelerated, finally form the primary beam. The po-tential drop cross the field of a pulsar from the magnetic pole to the last field line open to infinity is iffuse emission of Neutrinos and TeV Gamma-rays from young pulsars 3 ∆ φ = B s R Ω / c (Goldreich & Julian 1969),where B s is the strength of the dipole component of thefield at the magnetic poles ( B s ∼ G ) and R = 10 R is the radius of the neutron star and p m is thespin period in milliseconds , Ω = 2 π/p is the angular velocity(where p is the period ) and c is the speed of thelight. The magnitude of the potential drop ∆ φ could be × B P − ms volts ( B s ≡ B × )(Goldreich& Julian 1969).L B consider that If electric filed is no or little screening and µ · Ω < ( expected to holdfor half of total pulsars), ions and protons will be accelerated to PeV energy near the surface of pulsars. µ ismagnetic moment, Ω is angular velocity. Protons or ions accelerated by pulsars will interact with the ther-mal radiation of pulsars. If they have sufficient energy and exceed the threshold energy for the ∆ -resonancestate( ∆ + is an excited state of proton,with a mass of 1232MeV).The ∆ -resonance state may occurr. Thethreshold condition for the production of ∆ -resonance state in p − γ interaction is given by ǫ p ǫ γ (1 − cosθ pγ ) ≥ . GeV , (1)where ǫ p and ǫ γ are the proton and photon energy, and θ pγ is the incidence angle between the protonand the photon in the lab frame.Young pulsars have typically temperatures of T ∞ ≃ . keV , and photoenergy ǫ γ = 2 . kT ∞ (1 + Z g ) ∼ . keV , where Z g ≈ . is the gravitational red shift and T ∞ is thesurface temperature measured at infinity. In a young pulsar’s atmosphere, the condition of production ∆ -resonance is B P − ms T . keV ≥ × − (Link & Burgio 2005;Link & Burgio 2006), where T . keV ≡ ( kT ∞ / . keV ) , T ∞ ∼ . keV is typical surface temperature of young pulsars. This condition holds formany young pulsars,so ∆ -resonance could existed in many pulsar’s atmosphere. Gamma-rays and neutrinossubsequently decayed through following channels p + γ → ∆ + → p + π o → p + 2 γnπ + → n + e + + ν e + ν µ + ¯ ν µ . In this part, based on the L B model;we estimated emitting neutrinos and gamma-rays from pulsars. Theflux of protons accelerated by polar gap can be estimated I pc = cf d (1 − f d ) n o A pc , (2)where n o ( r ) ≡ B s R Ω / (4 πZecr ) is the Goldreich-Julian density of ions in distance r , f d < is thefraction depletion in the space charge in the acceleration region. It’s a model dependent quantity ( f d = 0 correspond to no depletion and f d = 1 is full depletion), so the density in the depleted gap can be written as f d (1 − f d ) n o ,where A pc = η πR is the polar cap area, η is the ratio of polar cap area to the half of neutronstar surface area, when η = 1 is the half of neutron star surface area. In LB(2006)and Jiang(2007)they usehemisphere surface area to calculate.The typical radius r pc = R (Ω R/c ) / (beskin et al. 1993),the polargap surface is A pc = πr pc = π Ω R /c ,so η = Ω R/ (2 c ) . So the maybe η = Ω R/ (2 c ) is more appropriate.For young pulsars with surface temperature T ∞ , the photon density close to the neutron star surface is n γ ( R ) = ( a/ . k )[(1+ z g ) T ∞ ] , a is the Stefan-Boltzman constant. Numerically n γ ( R ) ≃ × T . kev .At radial distance r , photon density will be n γ ( r ) = n γ ( R )( R/r ) . The probability that a PeV energyproton staring from the pulsar surface will produce ∆ particle by interacting thermal filed which is givenby(link&Burgio 2005) p c = 1 − R rR p ( r ) . Where dP/P = − n γ ( r ) σ pγ dr . Thus the total flux of gammaray/neutri generated in pulsars from the ∆ + resonance is I = 2 cξA pc f d (1 − f d ) n o P c , (3) Z.-X. Li et al. -19 -18 -17 -16 -15 Vela(T =0.6)(GeV) dd ( G e V - m - s - ) -18 -17 -16 -15 -14 Crab(T =1.7) (GeV) dd ( G e V - m - s - ) Fig. 1
The neutrino flux displayed for crab,vela, the case of linear(solid line ) and quadraticproton acceleration (doted line).where ξ is / and / for gamma rays and muon neutrinos,respectively. At the distance of d , the phaseaveraged gamma ray/neutrino flux at Earth from a pulsar is φ ≃ cξζηf b f d (1 − f d ) n o (cid:18) Rd (cid:19) P c , (4)where f b is duty cycle of neutrino or gamma-ray beam, ζ is the effect due to neutrino oscillation (the decaysof pions and their muon daughters result in initial flavor ratios φ ν e : φ ν µ : φ ν τ of nearly but atlarge distance from the source the flavor ratios is expected to become due to maximal mixing of ν µ and ν τ ). ζ = 1 and 1/2 is gamma rays and muon neutrinos respectively. We want to obtain the spectrum ofneutrinos and gamma-rays, using the following differential from dφ ν dǫ ν = 2 cξζηf b f d (1 − f d ) n o (cid:18) Rd (cid:19) dP c dǫ ν , (5)Taking f d = 1 / and Z = A = 1 for estimating upper limits on the flux. The neutrino and Gamma-raysenergy flux are estimated as dφ ν dǫ ν = 3 × − ξζηf b B p − ms d − kpc T . kev dP c dx . (6)Where d kpc is the distance of pulsar to earth, and dP c /dx is the probability of proton converting to ∆ + perunit energy interval; the details have been shown in equation(26) at Link & Burgio(2006). We use the equation (6) to estimate flux of neutrinos and gamma-rays and take Z=1 and f d = 1 / throughout this work. Taking linear ( γ = 1) and quadratic ( γ = 2) proton acceleration laws. Linearacceleration is corresponding to an accelerating filed which is constant space and quadratic acceleratingfield grows linearly with height above the star. We calculate the neutrinos and gamma-rays energy flux ofcrab,vela,PSR B1509-58 and PSR B1706-44,when η = Ω R/ c showed in the fig.1 and fig.2. The parameterof source presents in Table.1.For either acceleration law, the spectrum turns sharply at ε ν ≃ − . keV T eV corresponding to theonset of ∆ -resonance. At the top of energy it drops approximately as ǫ − ν ,as the phase space because the iffuse emission of Neutrinos and TeV Gamma-rays from young pulsars 5 -18 -17 -16 -15 (GeV) dd ( G e V - m - s - ) Vela(T =0.6) -18 -17 -16 -15 -14 Crab(T =1.7) (GeV) dd ( G e V - m - s - ) Fig. 2
The gamma-ray flux displayed for crab,vela,the case of linear(solid line) and quadraticproton acceleration (doted line).
Table 1
The parameter of some pulsars
Source d p B T . keV f b dNdAdt (LB06) dNdAdt kpc ms G km − yr − km − yr − Crab 2 33 3.8 ∼ . B − B − Table 2
The integral Tev gamma-ray fluxes comparison betweenthe predicated and the observed.The observed upper limits forCrab, Vela,PSR B1509-58 and PSR B 1706-44 (Aharonian et al.2006) source η = 1 η = Ω R/ (2 c ) observed upper limit of integral flux − cm − s − − cm − s − − cm − s − Crab 1038 3.297 8(56)Vela 204.98 0.242 10(20) B − B − conversion becomes restricted. The flux is lower about 3 magnitude when we use pulsar surface to calculate.But it is more consistent with the observed upper limits of gamma-ray fluxes.numerical values of theintegral TeV gamma-ray fluxes are obtained for pulsars listed in Table 2.In table 2, The gamma-rays flux estimated with η = 1 is obviously higher than the observed upper limits.But with η = Ω R/ c it is a little lower and more consistent with the observed upper limits; Thus taking η = Ω R/ (2 c ) is more reasonable.Large-area neutrino detectors use the Earth or ice as a medium for conversion of muon neutrino tomuon, detecting the Cerenkov light through the high energy upward-moving muons produced by neutrino Z.-X. Li et al. interactions below a detector on the surface of earth. We can use the flux of neutrino estimate the count ratein the detector. The conversion probability in the Earth is(Gaisser et al. 1995). P ν µ → µ = 1 . × − ( ǫ ν / T eV ) , (7)The muon event rate is dNdAdt = Z dǫ ν dφ ν dǫ ν P ν µ → µ . (8)In Table 1,expected count rates what we estimated present in the last column of for the crab,vela,PSRB1509-58 and PSR B1706-44,use L = 0 . and linear acceleration. Expected count rates (LB06)are shownin the penultimate column.Compared with the expected count rates shown in the last column, expectedcount rates(LB06)are higher. It means that the detectable by IceCube will not look bright.(Abbasi et al.2012) It shows that IceCube data severely constrain these optimistic predictions of LB, and (Bhadra & Dey2009) pulsars are unlikely to be strong source of TeV neutrino. So proper consideration of the effect of polarcap geometry in flux calculation is important. Over 1800 radio pulsars are known (Manchester et al 2005), more than 400 pulsars ages are less than yr ,most of which are candidates. If the magnetic moment is antiparallel to the rotating axis( µ · Ω < ),ions canbe accelerated in the charge-depleted gap near the star surface.So young pulsars are also potential neutrinosources, although some of them are likely weak source, the total contributions maybe significant. Thereforewe use MC method simulate pulsars sample with ages less than yr ,then determine which is neutrinopulsars in sample. We also estimate the diffuse neutrino flux and gamma-ray flux. In other words,we willcumulate all potential neutrino pulsars in the sample. We produce the Galactic young pulsar population by following assumptions.(e.g.Sturner & Dermer1996;Cheng & Zhang 1998;Zhang & Harding 2000;Zhang & cheng 2004; Jiang & Zhang 2006). Pulsarsample is simulated by MC method which is described by following steps in this paper.(see Jiang et al.2007 for detail).Following the steps, we use the conventional assumption for Galactic pulsars birth rate ( ∼ / yr )and enlarge 10 times, generate about 160000 pulsars in Galactic plane during past millions years. In thissample about 3890 pulsar could be detected radio.A lot of pulsars are not be observed because of selectioneffect. Compared with the ATNF catalogue pulsars, our simulated sample is consistent with the distributionof the observation. The normalized histogram distribution of pulsar period, pulsar surface magnetic fieldand distance are shown in fig.3. The shadow histogram represents the ANTF sample,the solid histogramrepresents simulated sample. We also compare the distribution Galactic Longitude and Galactic Latitudewith the observed sample which is shown in fig.4. The shadow histogram represents the ANTF sample,solidhistogram represents the simulated sample. Obviously,most pulsars distribute in Galactic Latitude | b | < ◦ region. So our simulated is succeed. iffuse emission of Neutrinos and TeV Gamma-rays from young pulsars 7 N o r m a li z ed D i s t r i bu t i on Log (Pdot)(10 -15 ss -1 ) N o r m a li z ed D i s t r bu t i on Log B(G) N o r m a li z ed D i s t r i bu t i on Period(s) N o r m a li z ed D i s t r i bu t i on Distancs(kpc)
Fig. 3
Normalized histogram distribution of pulsar period, distance,surface magnetic field andperiod derivation. Shadow histogram represent observations sample sample. Solid histogram rep-resent simulated sample.
The diffuse neutrinos and gamma-rays emission, both in Galactic and extragalactic are very interest forastrophysics, particle physics, and cosmology. The diffuse Galactic emission is produced by interac-tions of cosmic rays, mainly protons or electrons interact with the interstellar gas (via π -production andbremsstrahlung) and radiation field (via inverse compton scattering). We estimate the gamma-rays and neu-trinos flux ( dφ v,i ) /dǫ ν by using equation(6). Then we can obtain the flux of neutrinos and gamma-rays fromall pulsars φ ( ǫ ν ) = N X i =1 dφ v,i dǫ ν d Ω i , (9)where N is the number of gamma-ray or neutrinos pulsars, and d Ω i is the solid angle for the i pulsar, d Ω i = 4 πf b,i ∼ . The results of neutrino energy flux are shown in fig.5. The energy flux sharply increaseat about T eV ,corresponding to the onset of the resonance. Most energy is emitted between 50TeV and0.8TeV. After the onset of the resonance,the spectrum drops approximately as ǫ − ν , because the phase spacefor conversion becomes restricted. Just like the spectrum for a single pulsar,it is a typical of first-order Fermiacceleration(Abbasi et al. 2012). The linear proton acceleration is about 5 times than quadratic acceleration,so the linear proton acceleration is the main acceleration. From the figure 5,it will be not easier to searchfor neutrino signals, because it only exceeds the lower limit atmospheric neutrino flux’s background a Z.-X. Li et al. -10 -5 0 5 100.000.050.100.150.200.250.300.350.40 N o r m a li z ed D i s t r i bu t i on Galactic Latitude(Deg.) -200 -150 -100 -50 0 50 100 150 2000.000.050.100.150.200.25 N o r m a li z ed D i s t r i bu t i on Galactic Longitude(Deg.)
Fig. 4
Normalized histogram distribution of pulsars in Galactic Longitude and Galactic Latitude.Shadow histogram represents observations sample. Solid histogram represents simulated sample.little. For comparison, we also give the predicted fluxes with sensitivities of AMANDA-II, ANTARES, andIceCube detectors. AMANDA detector reached a sensitivity of . × − GeV cm − s − sr − after the first4 years of operation in 2000-2003 (Hill 2006). The ANTARES detector sensitivity reached . ± . × − GeV cm − s − sr − after 1 year of data on diffuse flux, and . ± . × − GeV cm − s − sr − after 3 years of data on diffuse flux (Montaruli 2005).The IceCube detectors have reached a sensitivity of (2 − × − GeV cm − s − sr − after 3 years of operation (Ribordy 2006). It sees clearly that it noteasier to detect the signals of neutrino flux from young pulsars, because the neutrino flux energy is lowerthan the background atmospheric neutrino flux. From Figure 5, we also compare the predicted diffuseneutrino fluxes from Active Galactic Nuclei (AGNs)(Stecker 2005)and Gamma Ray Bursts (GRBs)(Liu &Wang 2013). Whereas we can find the diffuse neutrino fluxes from AGNs are larger than young pulsars andGRBs at the energy from 60TeV to 3PeV. The diffuse neutrino fluxes from GRBs and young pulsars at theranges from 100TeV to 1PeV almost the same and lower than ATM. The distribution of estimated diffuseneutrino flux from these young pulsars is narrower than AGNs and GRBs; the flux from AGNs and GRBspeaks at about 20PeV and 1PeV respectively(He et al. 2012). The neutrino production in young pulsars isconstrained by the accelerating efficiency of the protons, while the AGNs are more powerful acceleratorsthan pulsars. Maybe the most violent processes in the universe such as AGNs or GRBs can contribute in iffuse emission of Neutrinos and TeV Gamma-rays from young pulsars 9 this energy range. The predicted diffuse neutrino from pulsars in Galaxy(Jiang et al. 2007) is easier to bedetected, because the flux is above the sensitivity threshold of IceCube. Why they obtained higher flux thanus,because the polar cap area we calculated is different. (5)(4) Log ( (GeV)) (3)(2)(1)neutrino Log ( d / d ( G e v c m - s - s r - )) Fig. 5
The estimated diffuse neutrinos flux from young pulsars in ourGalaxy. Solid and Dot line correspond to the fluxes computed for thecases of linear and quadratic proton acceleration. The solid lines labeled(1),(2),and(3)represent the sensitivities of AMANDA-II,ANTARES, andIceCube, respectively.The lines labeled (4),(5)represent the predicted fluxesfrom AGNs(Stecker 2005)and GRBs(Liu & Wang 2013) The region labeled”ATM” is the background atmospheric neutrino flux(Ribordy 2006).The results of diffuse gamma-rays flux are shown in fig.6,Solid and Dashed line correspond to the fluxescomputed for the cases of linear and quadratic proton acceleration.
To summarize, based on the LB model and Bhadra(2009), we calculated the neutrinos and gamma-rayspectrum of some pulsars with appropriate polar cap area. we use MC method simulate pulsar sample withages less than yr and µ · Ω < in our galaxy. Compared with the ATNF catalogue pulsars, our simulationis succeed. According to the sample, we also estimated the diffuse neutrinos and gamma-rays in our galaxy.Our results show that the diffuse flux distributing in the energy range from ∼ T eV to ∼ P eV is lowerabout 3 magnitude than Jiang(2007)only due to different methods on dealing polar cap area.These results show that the signals of neutrino flux from young pulsars are not easier to be detected,because the energy range about ∼ T eV to ∼ P eV is lower than the sensitivity threshold of IceCubeand the atmospheric background neutrino flux. Presently, any significant statistically signals excess have
Log ( (GeV)) Log ( d / d ( G e v c m - s - s r - )) gamma-ray Fig. 6
The estimated diffuse gamma ray flux from young pulsars in ourGalaxy. Solid and Dashed line correspond to the fluxes computed for the casesof linear and quadratic proton acceleration.not been detected from the direction of any pulsar by the AMANDA-II telescope(Ackermann et al. 2005;Ackermann et al. 2008; Ahrens et al. 2004). So proper consideration of the effect of polar cap geometry influx calculation is important and pulsars are unlikely to be strong source of TeV neutrinos. Compared withthe TeV diffuse neutrinos flux emitted from AGNs(Stecker 2005) and GRBs(Liu & Wang 2013), AGNsmaybe be the primary TeV neutrinos source.The energy data on the diffuse gamma-rays fluxes from Galactic plane around ∼ T eV to ∼ P eV have not been found now. So we cannot give the percentage of gamma-rays produced through ∆ -resonanceamong the whole diffuse gamma-rays in our galaxy. We expect experiments like the proposed High AltitudeWater Cherenkov (HAWC) detector will be constantly used to survey large regions of the sky, in particularthe Galactic plane, at gamma-ray energies up to 100TeV with 10 to 15 times the sensitivity of Milagro. Ifwe have the energy data on the diffuse gamma-rays fluxes from the Galactic plane around ∼ T eV to ∼ P eV . We can estimate the percentage of pulsar’s contribution on this energy range.This work have some uncertainties, such as pulsar’s birth rate and how many pulsars satisfy µ · Ω < .Estimating thermal photons from the neutron star surface is not well determined and the physical processesin the magnetosphere are still not clear, resulting in some uncertainties in the LB model as mentioned by(Link & Burgio 2005, 2006). Therefore, in order to improve the prediction of the diffuse muon neutrinoand gamma-ray flux from young pulsars, it is crucial to understand more about the neutrino flux and spectraemitted by a Single pulsar. Acknowledgements
The authors are indebted to Professor Ze-Jun Jiang for his constructive ideas andhelpful suggestions on the manuscript. We thank the referee for helpful comments and suggestions. iffuse emission of Neutrinos and TeV Gamma-rays from young pulsars 11
This work is partially supported by Science Research Foundation of Yunnan Education Department ofChina(2012Y316)and Yunnan Province Grant No. 2010CD112.