A&A 484, 267-273 (2008)
J. Fang1 - L. Zhang1 - C. Y. Yang1 - G. F. Lin1 - A. M. Zheng2
1 - Department of Physics, Yunnan University, Kunming, PR China
2 - Department of Physics, Zhaotong College, Zhaotong, PR China
Received 2 January 2008 / Accepted 26 March 2008
Based on a time-dependent model of particle production and non-thermal photon emission, we study high-energy neutrino emission from shell-type supernova remnants (SNRs). In such a model, particles are accelerated to relativistic energies through the shock acceleration mechanism and evolve with time in an SNR. For a given SNR, therefore, the temporal evolution of the particle energy distribution, the non-thermal spectrum of photons, and the spectrum of neutrinos can be calculated numerically. We apply the model to two young SNRs, G347.3-0.5 and G266.2-1.2, and two old ones, G8.7-0.1 and G23.3-0.3. For each SNR, we determine the parameters involved in the model by comparing the predicted non-thermal spectrum with the observed radio, X-ray and -ray data. We study the properties of the corresponding neutrino emission, including the neutrino spectrum and the event rates expected in the next-generation km3-scale neutrino telescope, KM3NeT. Our results indicate that the high-energy TeV -rays from the four SNRs are produced predominately via hadronic interaction and that young SNRs such as G266.2-1.2 and G347.3-0.5 are the potential neutrino sources whose neutrinos are most likely to be identified by next-generation km3 neutrino telescopes.
Key words: gamma rays: theory - neutrinos - radiation mechanisms: non-thermal - supernova remnants
Hadronic interpretations of TeV -rays from SNRs have been widely proposed. The young SNR G347.3-0.5 has been detected twice by HESS and is the most intense shell-type SNR in the TeV -ray sky (Vissani 2006). The CANGAROO collaboration has indicated that the spectrum of the VHE -rays from the SNR matches that expected if the -rays are produced via decay from proton-proton collisions (Enomoto et al. 2002). Therefore, the SNR G347.3-0.5 is an important potential neutrino source which can be identified as a discrete neutrino source by neutrino telescopes. More recently, a survey of the inner part of the Galactic Plane in VHE -rays has been performed with the HESS Cherenkov telescope system. Aharonian et al. (2006b) presented detailed spectral and morphological information of some new sources along with discussion of possible counterparts in other wavelength bands. Some TeV sources discovered in the survey, such as HESS J1804-216 and HESS J1834-087, can be associated with old SNRs (Aharonian et al. 2006b; Fang & Zhang 2008; Tian et al. 2007), and the TeV photons from the old SNRs are probably of hadronic origin because high-energy protons can exist for a long time due to the long energy loss time for p-p interactions (Fang & Zhang 2008). Thus, old TeV SNRs are also important possible neutrino sources in the Galaxy.
The neutrino spectrum for a given SNR with observed TeV photons can be estimated by assuming that the TeV -rays are produced predominately via hadronic processes (Carr et al. 2007; Kappes et al. 2007; Kistler& Beacom 2006). In this paper, we use the time-dependent model in Fang & Zhang (2008) with which the evolved non-thermal spectra of both the primary particles accelerated directly by the shock wave and the secondaries produced via p-p interaction can be calculated numerically. We investigate the high-energy neutrino emission from shell-type SNRs and estimate the detected neutrino signals that may be measured by the next-generation telescope, KM3NeT, using the newest simulation results in Carr et al. (2007). The parameters involved in the model for a given source can be limited by comparison of the calculation results with the multi-wavelength observations, and then the corresponding neutrino spectra can be calculated. This paper is organized as follows. The calculation model are briefly illustrated in Sect. 2. The results from the applications of the model to two young SNRs, G347.3-0.5 and G266.2-1.2, and two old ones, G8.7-0.1 and G23.3-0.3, are shown in Sect. 3. The main conclusions and some discussion are given in Sect. 4.
Originally, Sturner et al. (1997) presented a temporal-evolving model for non-thermal particle and photon spectra at different stages in the lifetime of a shell-type SNR. Zhang & Fang (2007) modified the model to explain the multi-waveband observations of young SNRs and shown that the TeV -rays from the two young shell-type SNRs, G347.3-0.5 and G266.2-1.2, are primarily of hadronic origin. Moreover, Fang & Zhang (2008) studied the non-thermal emission from old SNRs by including the evolution of secondary electrons and positrons produced in p-p interactions in the model, and applied the model to two old SNRs, G8.7-0.1 and G23.3-0.3. Their results indicated that the VHE -rays with energies above 1 TeV from the two SNRs mainly had hadronic origin. In this section, we first review the model for non-thermal particle and photon spectra, and then give the detailed formula that we use to tackle the p-p interactions in which high-energy photons and neutrinos are produced.
The analytical model of shock dynamics of SNRs expanding into the
uniform ambient medium with a constant density
magnetic field strength
is used to describe the SNR
evolution (see details in Sturner et al. 1997). The density and the
magnetic field strength of the upstream and downstream regions of
the shock satisfy the following relations:
where the shock compression
for a strong shock, neglecting nonlinear effects
(Sturner et al. 1997). In the analytical model, assuming the initial
explosion energy of an SNR is
E = 1051E51 ergs, and the
initial velocity of the shock is v0, the SNR evolves through
three stages : the free expansion stage (shock velocity
yr), the Sedov stage (
yr), and the radiative stage
is the mean atomic weight of the
interstellar medium assuming 1 helium atom for every 10 hydrogen
is the mass of hydrogen; for simplicity, the
hydrogen inside the SNR is assumed to be fully ionized and the SNR
interior is thought to be homogenous. This does not affect the final
result because the resulting non-thermal spectrum only relates to
the initial spectrum and the total number of the instantaneously
accelerated particles, and the subsequent evolution, with a constant
and a magnetic field strength
The non-thermal charged particles
inside the SNR are produced through diffusive shock acceleration,
after taking the particle's energy-loss processes and the effect of
the free escape from the shock region into account. The
of the shock
accelerating electrons and protons are approximated as
Once the volume-averaged emissivities of the shock accelerated
particles are given for a certain SNR, the temporal evolution of the
particle energy distribution can be obtained by solving the
Fokker-Planck equations for both electrons and protons in energy
space, which are given by
For a given SNR, the time-dependent electron and proton intensities can be obtained by solving Eqs. (5) and (6), so the multi-wavelength non-thermal photon spectrum can be calculated. These photons can be produced by electron synchrotron radiation, bremsstrahlung, inverse Compton scattering of the CMB, Galactic IR and optical background, and neutral pion decay gamma-rays from the proton-proton interaction. The details of the photon emission can be seen in Fang & Zhang (2008). Here, we introduce the high-energy neutrino production processes briefly.
The corresponding volume-averaged emissivities for secondary
produced in the p-p interactions
can be given by
Three flavor oscillations of neutrinos should be considered
to obtain the observed neutrino flux on the Earth for an SNR. After
propagation, the neutrino flux can be expressed as
Many astrophysical TeV -ray sources have been detected in
recent years, and km3 scale detectors are needed to investigate
the corresponding neutrinos (Carr et al. 2007). The event rate in a
neutrino telescope can be calculated by (Kappes et al. 2007)
Table 1: The parameters used and the expected neutrino event rates in KM3NeT after five years of observation for each SNR. The visibility indicates the fraction of time when the source is below the horizon to KM3NeT, and we take the visibility and the expected atmospheric neutrino event rates for each source from Kappes et al. (2007).
We now apply the time-dependent model of non-thermal particle, photon and neutrino spectra to SNRs. The unknown parameters involved in the model are usually limited by comparison of the model result with the multi-band observations for a given SNR (Zhang & Fang 2007; Fang & Zhang 2008). We fit the parameters empirically due to the many uncertainties in the model such as the age, the distance, the initial ejected mass, the initial velocity of the shock, the conversion efficiency, and in the observations, especially in the X-ray band for an SNR. Firstly, a set of appropriate parameters are chosen to describe the multi-wavelength non-thermal emission for each SNR, and then the corresponding neutrinos from the SNR can be investigated. In this section, the model is applied to two young SNRs, G347.3-0.5 and G266.2-1.2, and two old ones, G8.7-0.1 and G23.3-0.3.
|Figure 1: a) Comparison of the model results with the multi-wavelength observations for the SNR G347.3-0.5. The emission from primary particles (electrons and protons), and secondary pairs are indicated by solid line and dashed line, respectively. b) The photon (solid line) and (dotted line) spectra of the SNR produced from p-p interactions. The radio data (Lazendic et al. 2004), X-ray data (Slane et al. 1999), EGRET upper limit and VHE -ray data (Aharonian et al. 2006a) for the whole SNR are indicated. The parameters used are shown in Table 1.|
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The shell-type SNR G347.3-0.5 (RX J1713.7-3946), which is compatible with a core collapse supernova that exploded in A.D. 393 at a distance of about 1 kpc (Wang et al. 1997), is a prominent potential neutrino source that probably would be detected by KM3NeT. VHE -rays from the SNR have been detected with HESS, and the hard differential -ray spectrum, measured over two orders of magnitude from 190 GeV to 40 TeV, deviates from a power law distribution above 10 TeV (Aharonian et al. 2006a). X-ray observations indicate that the non-thermal X-ray spectrum for the whole SNR has a power-law with index of 2.4 although the spectra in different regions have slightly different photon indexes (Slane et al. 1999), so we adopt that the non-thermal X-ray spectrum of the whole SNR is a power law with photon index 2.4 and the flux from 0.5-10 keV is - erg cm-2 s-1. The high-resolution radio observations were performed with the Australia Telescope Compact Array (ATCA) (Lazendic et al. 2004). Note that the radio flux given in their paper is just for the northwest part of the shell so we multiply by a factor of two to account for the whole SNR, as treated in Aharonian et al. (2006a).
The probable neutrino signals in KM3NeT for the SNR G347.3-0.5 have been investigated by assuming that the TeV -ray photons are predominately of hadronic origin (Kistler & Beacon 2006; Kappes et al. 2007; Carr et al. 2007), and that the expected event rates ( ) is about 10 in 5 yrs of observations. It had been shown that, for a given SNR with specific age and distance, the parameters involved in the model can be limited by comparison of the model results with multi-band observations (Zhang & Fang 2007; Fang & Zhang 2008). For the SNR G347.3-0.5, we use an age of 1600 yr and a distance of 1 kpc, and choose other appropriate parameters to model the multi-band emission. The details of the parameters used are shown in Table 1, and the resulting photon and neutrino spectra are illustrated in Fig. 1. Obviously, the non-thermal emission from radio to hard X-ray bands is predominately from the synchrotron radiation of the primary electrons, whereas the observed TeV -rays are mainly from the p-p interactions between the accelerated protons and the ambient matter (see panel (a) in Fig. 1). Moreover, the -ray and spectra resulting from the p-p interactions as high-energy protons collide with the ambient matter are shown in panel (b) in the figure. The number of reaching the Earth is just about half of the original number at the source due to flavor oscillations of neutrinos. Finally, the calculated neutrino event number for 5 yrs of observations with the 1 km3 KM3NeT detector for energies above 1 TeV is about 8 (see Table 1), which is consistent with the result in Carr et al. (2007) because the resulting TeV -rays from the hadronic processes in our model dominate those from leptonic processes which is in agreement with the assumption in Carr et al. (2007).
The HESS group reported its detection of TeV -rays from the shell-type SNR G266.2-1.2 (RX J0852.0-4622) on observations in February 2004 and the differential spectrum in the energy range from 500 GeV to 15 TeV is well described by a power law with a photon index of about 2.1 (Aharonian et al. 2005). Enomoto et al. (2006) reported the CANGAROO observations of the SNR, and the results are consistent with those detected with HESS. Furthermore, HESS re-observed the SNR between December 2004 and May 2005 for a total observation time of 33 h, above an average gamma-ray energy threshold of 250 GeV (Aharonian et al. 2007). The newest HESS observation results include more statistics especially at high energies and the spectrum extends from 300 GeV to 20 TeV with a spectral index of .
|Figure 2: a) Comparison of the model results with the multi-wavelength observations for the SNR G266.2-1.2. b) The photon (solid line) and (dotted line) spectra of the SNR produced from p-p interactions. The radio data (Duncan and Green 2000), X-ray data (Lemoine-Goumard et al. 2007), and VHE -ray data (Aharonian et al. 2007), for the whole SNR are indicated. Others are the same as Fig. 1.|
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The SNR G266.2-1.2 was discovered by Aschenbach (1998) based on the X-ray data from the ROSAT All-sky survey. The SNR was observed with ASCA for 120ks and the X-ray spectra were featureless and well described by a power law (Slane et al. 2001). The X-ray spectral analysis of the whole remnant in the 2-10 keV energy band was also presented in Aharonian et al. (2007), and the non-thermal spectrum is well described by a power-law with a spectral index of and a flux of erg cm-2 s-1 (Lemoine-Goumard et al. 2007). There are uncertainties in the distance and the age of the SNR. Bamba et al. (2005) derived an age of 425-1400 yr and a distance of 0.25-0.5 kpc based on observation of very thin hard X-ray filaments in the north-western edge with the high angular resolution of the Chandra satellite. In this paper, we use an age of 1000 yr and a distance of 0.3 kpc to model the non-thermal emission from the SNR. Details of the other parameters are shown in Table 1 and the resulting photon and neutrino spectra are illustrated in Fig. 2. The model results are consistent with the radio (Duncan and Green 2000), ASCA (Lemoine-Goumard et al. 2007) and HESS (Aharonian et al. 2007) observations; moreover, the VHE -rays from the SNR are produced mainly via p-p interactions. The expected event rates ( ) with KM3NeT after 5 yrs of observations is about 11, which makes it the source most likely be identified as a discrete neutrino source in the Galaxy by the next-generation km3-scale neutrino telescopes.
Aharonian et al. (2006b) reported a survey of the inner part of the Galactic Plane in VHE -rays detected with the HESS Cherekov telescope system. Fourteen previously unknown sources were detected. HESS J1804-216 is the brightest of the new sources, with a steep photon index of and a flux of nearly of the flux from the Crab Nebula above 200 GeV. The source can be associated with the south-western part of the shell of the SNR G8.7-0.1 of radius 26 arc minutes with 80 Jy flux at 1 GHz (Aharonian et al. 2006b). Cui & Konopelko (2006) reported high-resolution X-ray observations taken with the Chandra X-Ray Observatory of the field that contains the TeV -ray source HESS J1804-216; a total of 11 discrete sources were detected. Among those sources, only one, CXOU J180351.4-213707, which is the most probable X-ray counterpart of HESS J1804-216, is significantly extended, with a photon index 1.2+0.5-0.4.
|Figure 3: a) Comparison of the model results with the multi-wavelength observations for the SNR G8.7-0.1. b) The photon (solid line) and (dotted line) spectra of the SNR produced from p-p interactions. The radio data (Odegard et al. 1986; Kassim & Weiler 1990; Green 2006), X-ray data (Cui & Konopelko 2006), and VHE -ray data (Aharonian et al. 2006b; Enomoto et al. 2006) for the whole SNR are indicated. Others are the same as Fig. 1.|
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In this paper, we assume that the sources CXOU J180351.4-213707 and HESS J1804-216 are associated with the SNR G8.7-0.1 at a distance of 6 kpc, and apply our model to it. To make the resulting spectrum consistent with the observations by Chandra with a low energy flux and a photon index of about 1.2, the SNR must be in the radiative phase when the roll-off energy of synchrotron radiation of the primary electrons decreases quickly and the X-rays detected by Chandra X-Ray Observatory are most probably from bremsstrahlung radiation or inverse Compton scattering of leptons (Fang & Zhang 2008). Thus, the highest-energy TeV photons are mainly from the p-p interactions as high-energy protons collide with the ambient matter in the SNR, and the proton hydrogen density around the SNR must be about 6 cm-3 to make the calculation results consistent with the HESS observations. The details of the other parameters are given in Table 1. From Fig. 3, we have following results for the SNR: (i) the emission from the primary electrons dominates that from the secondary pairs in the entire energy band besides the narrow soft X-ray band around 0.5 keV; (ii) the detected radio emission is mainly from the synchrotron radiation of the primary electrons whereas the X-rays observed with Chandra are primarily produced via bremsstrahlung of these electrons; and (iii) the TeV photons with energies <1 TeV are primarily from both bremsstrahlung of the primary electrons and the p-p interaction of the primary protons. However, those with higher energies are mainly from the p-p interactions as the high-energy protons collide with the ambient matter.
In our model, for an SNR in the radiative stage, the sources of the primary particles are cut off and the primary electrons experience strong energy loss, whereas the secondary pairs can be produced continuously for a long time due to the large energy loss time for the p-p interaction. Therefore, the emission from the primary electrons diminishes quickly and that from the secondary pairs becomes more and more prominent as the SNR ages. Moreover, the high-energy protons also experience energy loss due to the p-p interactions and escape from the SNR. The secondary products from the p-p interactions are also deceasing as the age of the SNR increases. As a result, the expected event rates of the SNR G8.7-0.1 with KM3NeT in 5 yrs of observations is only about 0.9, which is about an order of magnitude smaller than that for the young SNRs G347.3-0.5 and G266.2-1.2.
|Figure 4: a) Comparison of the model results with the multi-wavelength observations for the SNR G23.3-0.3. b) The photon (solid line) and (dotted line) spectra of the SNR produced from p-p interactions. The radio data (Tian et al. 2007) and VHE -ray data (Aharonian et al. 2006b; Albert et al. 2006) for the whole SNR are indicated. Others are the same as Fig. 1.|
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G23.3-0.3 is an asymmetric shell-type SNR, and has a spectral index of 0.5 and a flux of 70 Jy at 1 GHz (Green 2006). Tian et al. (2007) reported new HI observations from the VLA Galactic Plane System and a new XMM-Newton observation for HESS J1834-087. They estimated that G23.3-0.3 is an old SNR with a distance of kpc and an age of 105 yr. The new XMM-Newton observation reveals diffuse X-ray emission within the HESS source and suggests an association between the X-ray and the VHE -ray emission. More recently, Leahy & Tian (2008) measured a distance of 3.9-4.5 kpc with high precision for the SNR with HI and CO line observations, which is direct evidence supporting that W41 is physically associated with the giant molecular cloud at a radial velocity of 78 km s-1 in the direction of the center of W41. Furthermore, the matter density around the SNR will be 2 to 3 times larger than previously estimated ( ), but uncertainties also exist because there are a few adjustable parameter assumptions in estimating the density (Tian, W. W. private communication).
Finally, we use a distance of 4.2 kpc and an age of 80 000 yr to model the non-thermal spectrum for the SNR. The other parameters are shown in Table 1 and the resulting photon and neutrino spectra are illustrated in Fig. 4. The observed radio and VHE -ray emissions can be reproduced well by a synchrotron mechanism for the primary electrons and the p-p interactions of the high-energy protons; the emission from secondary pairs dominates that from the primary electrons in the energy band from about 0.1 eV to 0.5 keV. For the old SNR G23.3-0.3, the expected event rates at KM3NeT after 5 yrs of observations is about 0.5. Therefore, the SNR is more difficult to identify as a discrete neutrino source with neutrino telescopes than the other three sources, G347.3-0.5, G266.2-1.2, and G8.7-0.1.
VHE -rays from a few shell-type SNRs have been reported. The resulting TeV -rays can be produced either via inverse Compton scattering and/or via the p-p interaction. In the latter case, the TeV -rays are of hadronic origin, and then the number of neutrinos from SNRs should be significant, making SNRs are important possible neutrino sources in the Galaxy as a target for the next-generation km3-scale neutrino telescope, KM3NeT. In this paper, based on a time-dependent model of non-thermal particle and photon spectra for both young and old SNRs, we investigate the possible neutrino emission from two young and two old SNRs and estimate the event rates expected for the four sources to be observed with KM3NeT using the newest simulation results given by Carr et al. (2007). Firstly, the unknown parameters can be limited by comparison of the model result with the multi-band photon observations for a given SNR; then the neutrinos from the SNR can be investigated. The calculation results show that the TeV -rays with energies above 1 TeV from the four sources primarily have a hadronic origin. The predicted neutrino spectra are shown in Figs. 1-4. The number of signals reaching the Earth from an SNR is about half of the original number at the source due to flavor oscillations of neutrinos. The expected event rates at next-generation neutrino telescope KM3NeT after 5 yrs of observations of the four sources are shown in Table 1. Our results indicate that young SNRs such as G266.2-1.2 and G347.3-0.5 are the potential neutrino sources whose neutrinos are the most likely to be identified by the next-generation km3neutrino telescope. Our results justify the assumption proposed by many other authors that the high-energy TeV -rays from SNRs are produced mainly through hadronic interactions. However, due to the many uncertainties for a given SNR involved in the model such as the initial ejecta mass, the initial shock velocity, age, distance, and uncertainties in the multi-band observations, especially in the X-ray band, the results in Table 1 are rough approximations of the event rates potentially detected by KM3NeT.
We estimate the possible neutrinos observed from SNRs with KM3NeT using a time-dependent model by limiting the unknown parameters to improve consistency of the model result with the multi-band observations for each SNR. Of course, GLAST will provide a much more significant limitation on the parameters and check the correctness of our calculation more effectively due to its high sensitivity in the energy range from 30 MeV to 300 GeV. SNRs with detected VHE -rays are good candidates for high-energy neutrino observations with next-generation km3-scale neutrino telescopes. It is widely accepted that SNRs are the prime sites accelerating cosmic rays in the Galaxy, and the observations of neutrinos from SNRs will substantially improve our understanding of the acceleration mechanism and the hadronic processes involved in SNRs.
This work is partially supported by a Distinguished Young Scientists grant from the National Natural Science Foundation of China (NSFC 10425314), NSFC grant 10778702, and a grant from the Department of Education of Yunnan Province (07J51074). We appreciate the use of the high performance computer facilities at Yunnan University, Kunming, PRC.