HYPERNOVA AND GAMMA-RAY BURST REMNANTS AS TeV UNIDENTIFIED SOURCES

The simplest and most plausible process for TeV gamma-ray emission associated with CRs is the π⁰ decay from pp interactions between the interstellar medium (ISM) and CRs accelerated by the SN/hypernova shocks. Although the π⁰ decay for SNRs (Naito & Takahara 1994; Drury et al. 1994) and GRB remnants (Atoyan et al. 2006) has been discussed in detail, there are few works dealing with π⁰ decay in hypernova remnants, except for the specific source HESS J1303-631 (Atoyan et al. 2006). Since hypernovae are more energetic than SNe and GRBs and more frequent than GRBs, it is worth considering their implications for TeV unIDs.

By scaling the SNR calculation (Naito & Takahara 1994; Drury et al. 1994), we obtain a TeV gamma-ray flux

$$\begin{eqnarray} &&\varepsilon _\gamma F_{\varepsilon _\gamma } \sim 10^{-12} \zeta _{-1} E_{51} n d_{10\,{\rm kpc}}^{-2}\,{\rm erg\ s}^{-1}\, {\rm cm}^{-2}, \end{eqnarray} \tag{ 3 }$$

comparable to the observed values. Here, n is the ISM density in cm⁻³, d_10 kpc = d/10 kpc, and ζ is the fraction of the total CR energy E per logarithmic energy interval. Since the kinetic energy of hypernovae is huge, E_k ∼ 10⁵² erg, a CR energy of E ∼ 10⁵¹ erg is reasonable, for a conventional CR acceleration efficiency of ∼10%.

Since the flux in Equation (3) is independent of time, most sources are likely old, e.g., t_age ∼ 10⁵ yr old. Such old SNRs are possible TeV unIDs because the maximum energy of primary electrons is so small that the leptonic emission is suppressed. As shown in Figure 1, the synchrotron emission from secondary electrons can also be below upper limits for TeV unIDs in the radio to X-ray bands (Yamazaki et al. 2006; Atoyan et al. 2006).

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Remarkably, the observed number of old hypernova remnants may be comparable to that of the more numerous old SNRs, if the observations are flux-limited. For old remnants, which are larger than the angular resolution (see Equation (8)), the source size should be taken into account. As the search region is expanded, more background is included. The sensitivity is proportional to the inverse square of the background, for background-dominated counting statistics. Therefore, the flux sensitivity to an extended source with a physical radius r is given by $F_{\varepsilon _\gamma }^{\rm extend} =F_{\varepsilon _\gamma }^{\rm point}(r/d \theta _{\rm cut})$, where $F_{\varepsilon _\gamma }^{\rm point}$ is the sensitivity to a point source and θ_cut is the angular cut in the analysis (Konopelko et al. 2002; Lessard et al. 2001). With Equation (3), and

$$\begin{eqnarray} &&F_{\varepsilon _\gamma }^{\rm point}\left(\frac{r}{d \theta _{\rm cut}}\right) <F_{\varepsilon _\gamma } \propto E n d^{-2}, \end{eqnarray} \tag{ 4 }$$

we have the maximum distance to a source as

$$\begin{eqnarray} &&d_{\max } \propto E n r^{-1}, \end{eqnarray} \tag{ 5 }$$

and hence the observable volume in the Galactic disk is

$$\begin{eqnarray} &&V \propto d_{\max }^2 \propto E^2 n^2 r^{-2} \propto E^{8/5} n^{12/5}, \end{eqnarray} \tag{ 6 }$$

where we use r ∝ E^1/5n^−1/5t^2/5_age, which is approximately correct even for the radiative phase of the remnants. Since the hypernova energy is ∼10 times larger, the observable number of hypernova remnants is larger than that of SNRs by

$$\begin{eqnarray} &&\frac{N_{\rm HNR}^{\rm obs}}{N_{\rm SNR}^{\rm obs}} \sim \frac{R_{\rm HNR} V_{\rm HNR}}{R_{\rm SNR} V_{\rm SNR}} \sim \frac{10^{-4}\,{\rm yr}^{-1} \cdot 10^{8/5}}{10^{-2}\,{\rm yr}^{-1} \cdot 1^{8/5}} \sim 0.4, \end{eqnarray} \tag{ 7 }$$

where R_SNR ∼ 10⁻² yr⁻¹ and R_HNR ∼ 10⁻⁴ yr⁻¹ (∼7% of the SNe Ibc rate) are the event rates of SNe and hypernovae, respectively (Guetta & Della Valle 2007), and we assume a similar age t_age and ISM density n for both remnants. The actual numbers in our Galaxy would be R_SNRt_age ∼ 10³ (SNRs) and R_HNRt_age ∼ 10 (hypernova remnants) for t_age ∼ 10⁵ yr. Since the observed number of TeV unIDs is also ∼10, we may be reaching the farthest hypernova remnants in our Galaxy.

The angular size of the t_age ∼ 10⁵ yr old remnants,

$$\begin{eqnarray} &&\frac{r}{d} \sim \frac{30\,{\rm pc}}{d} \sim 0\mbox{$.\!\!^\circ $}2 \left(\frac{d}{10\,{\rm kpc}}\right)^{-1}, \end{eqnarray} \tag{ 8 }$$

is consistent with TeV unIDs for hypernovae,³ but the same may not be true for SNe since the observable distance d_max is smaller and hence the angular size is more extended (r/d ∼ 2°(1 kpc/d)). Such an extended object can be found only if the search region is expanded to the degree scale in the analyses. Therefore, if TeV unIDs are hypernova remnants, we can predict more extended (and more numerous) TeV SNRs than observed, which may be discovered by expanding the search region even with the current instruments.

The flux of hypernova remnants could be further enhanced if the density n is higher around hypernovae than around usual SNe. The GRBs and SNe Ic, which are the only type of core collapse SNe associated with GRBs and hypernovae, are far more concentrated in the very brightest regions of their host galaxies than are the other SNe (Kelly et al. 2008; Fruchter et al. 2006), suggesting that GRBs and hypernovae are associated with star-forming regions with high density. Conversely, hypernovae could be runaway massive stars ejected several hundreds of parsec away from high density stellar clusters (Hammer et al. 2006). In this case, no flux enhancement is expected.

It is necessary to check any possible side effects of this mechanism at other wavelengths which might violate the hypothesis that they remain unidentified. In particular, we need to check what is the possible X-ray emission from electrons in these sources. We may constrain the electron acceleration in the old hypernova remnants. In Figure 1, we have plotted the bremsstrahlung, synchrotron, and IC emission from primary electrons with the same spectral index p = 2.2, for an electron-to-proton ratio of (e/p)_10GeV ∼ m_e/m_p ∼ 10⁻³ at 10 GeV. The radio observations limit the (e/p)_10GeV ratio to ≲10⁻³, which is somewhat smaller than the observations ∼0.02. Note however that the injection of thermal electrons into the acceleration process is poorly understood, and the observed electron CRs might be produced by other sources such as usual SNRs or pulsars. In any case, the leptonic model for TeV unIDs seems unlikely. Note that we take the Coulomb losses for low energy electrons into account according to Uchiyama et al. (2002) (see also Baring et al. 1999) and this makes the bremsstrahlung spectrum hard in the X-ray band. On the other hand, the thermal bremsstrahlung emission is not bright in the X-ray band, in contrast with the usual young SNRs (Katz & Waxman 2008), because the temperature of old SNRs is much below the X-ray energy, T ∼ 0.04 keV E^2/5_k,52n^−2/5(t/10⁵ yr)^−6/5 (Reynolds 2008).

A fraction of SNe/hypernovae is associated with long GRB and their jets. Another process for generating TeV gamma-rays is the (time-delayed) β decay of the neutron component of the CR outflow accelerated by the jets followed by IC scattering (Ioka et al. 2004). We have applied this process to the SNR W49B (G43.3-0.2), which is a possible GRB remnant (Keohane et al. 2006; Miceli et al. 2006, 2008). Since the β decay can occur outside the remnant, the jet-like emission would appear outside of the SNR. Note that the GRB-associated SNe are not necessarily energetic hypernovae since the luminosity distribution of GRB-associated SNe is statistically consistent with that of local SNe Ibc (Soderberg et al. 2006b).

As shown in Figure 2, old jet remnants with t_age ∼ 10⁵ yr are potentially TeV unIDs since the usual SNR emission goes down at this age, while electrons that emit ∼TeV gamma rays (i.e., γ_e ∼ 10⁷ electrons) need t_cool ∼ 10⁵ yr to cool (see Equations (3) and (4) in Ioka et al. 2004). (However a spectral cutoff at ∼10 TeV may be seen at this age.) Then the expected total number is 0.1–1 for a Galactic GRB rate of ∼10⁻⁵–10⁻⁶ yr⁻¹ (Guetta & Della Valle 2007). The actual number would be larger because a larger fraction of SNe may have lower-luminosity jets that were not identified (e.g., Toma et al. 2007), and LL jets can also accelerate CRs to energy ∼10^16-17 eV (e.g., Murase et al. 2006, 2008), which is necessary for the TeV gamma-ray emission. The most optimistic rate consistent with the late-time radio observations is ∼10⁻⁴ yr⁻¹ (∼10% of the SN Ibc rate) (Soderberg et al. 2006a), yielding a total number of ∼10, comparable to that of TeV unIDs. All of these remnants could be detected, i.e., d_max ∼ 10 kpc, if the total energy in accelerated CRs is comparable to the typical GRB energy.

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The chemical composition of jets which may be associated with SNe/hypernovae is currently unknown. One interesting possibility is that they entrain radioactive isotopes, in particular ⁵⁶Ni and ⁵⁶Co. The SN/hypernova shock leads to explosive nucleosynthesis, predominantly forming ⁵⁶Ni via complete silicon burning (Maeda & Nomoto 2003). The inner ⁵⁶Ni would fall back onto the central engine (in those objects where there is one), and a fraction of accreted ⁵⁶Ni could be ejected with the ensuing jet. The photodisintegration of heavy nuclei would be suppressed in the LL jets whose temperature is less than ∼MeV. Even if heavy nuclei may disintegrate in the innermost accretion disk, ⁵⁶Ni could be produced again in a cooling wind (MacFadyen 2003). ⁵⁶Ni could be also entrained into the jet from the surroundings. The subsequent photodisintegration can be avoided in large fraction of parameter space (Wang et al. 2008; Murase et al. 2008). The spectrum and light curve modeling of GRB-associated hypernovae suggests that the total amount of ⁵⁶Ni is larger than that in ordinary SNe and heavy elements are aspherically ejected along the jet direction (Maeda & Nomoto 2002).

⁵⁶Ni decays into ⁵⁶Co in t_Niln 2 = 6.1 days essentially by electron capture (McLaughlin & Wijers 2003). The decay proceeds primarily through the excited states of ⁵⁶Co, emitting ∼2 MeV gamma rays. ⁵⁶Co also decays primarily by electron capture into excited ⁵⁶Fe with a half-life of t_Coln 2 = 77.2 days,

$$\begin{eqnarray} &&{}^{56}{\rm Co} + e^{-} \rightarrow {}^{56}{\rm Fe}^{*} + \nu _e, \end{eqnarray} \tag{ 9 }$$

followed by ε_RI ∼ 2 MeV gamma-ray emission

$$\begin{eqnarray} &&{}^{56}{\rm Fe}^{*} \rightarrow {}^{56}{\rm Fe} + \gamma. \end{eqnarray} \tag{ 10 }$$

If the nuclei are fully ionized, they decay by emission of a positron (β⁺ decay), e.g.,

$$\begin{eqnarray} &&{}^{56}{\rm Co} \rightarrow {}^{56}{\rm Fe}^{*} + e^{+} + \nu _e, \end{eqnarray} \tag{ 11 }$$

followed by gamma-ray emission, since free electron capture is negligible in our case. The half-life for ionized ⁵⁶Co is a factor of ∼5 higher than for ⁵⁶Co with electrons, while that of ionized ⁵⁶Ni is longer than 3 × 10⁴ yr. Since nuclei can recombine in an expanding jet (McLaughlin & Wijers 2003), the decay chain ⁵⁶Ni → ⁵⁶Co → ⁵⁶Fe can start from the ⁵⁶Ni electron capture.

The outflowing jet is shocked as it interacts with the ISM, leading to particle acceleration. Unlike in the ordinary SNe, the RI acceleration can occur before the RI decay in the objects considered here, involving jets reaching relativistic speeds. Our interest is in the ⁵⁶Co acceleration, since the accelerated nuclei are completely ionized and the ionized ⁵⁶Ni is essentially stable (the half-life is longer than 3 × 10⁴ yr). For the ⁵⁶Co acceleration, the shock radius should be smaller than the ⁵⁶Co decay length, r < ct_Co(ln 2)βΓ and larger than the ⁵⁶Ni one, r > ct_Ni(ln 2)βΓ, where Γ is the Lorentz factor of the jet. Since the shock radius may be estimated by E_j ∼ (4π/3)r³nm_pc²β²Γ², we have

$$\begin{eqnarray} &&2 E_{j,51}^{1/5} n^{-1/5} < \beta \Gamma < 8 E_{j,51}^{1/5} n^{-1/5}, \end{eqnarray} \tag{ 12 }$$

where E_j is the total energy of the jet. The Lorentz factor ranges between that of GRBs and hypernovae. Note that the shock radius is relatively large ≳10¹⁶ cm that no heavy nuclei may disintegrate (Murase et al. 2008; Wang et al. 2008).

Once ⁵⁶Co is accelerated, the observed mean lifetime is extended by the Lorentz factor,

$$\begin{eqnarray} &&t_{\gamma }=\gamma t_{\rm iCo} \sim 10^5 \,{\rm yr}\, \gamma _{5} \end{eqnarray} \tag{ 13 }$$

enabling long-lasting emission, where t_iCo = 5t_Co is the half-life of ionized ⁵⁶Co. The observed energy of the decay gamma rays is also Lorentz-boosted to

$$\begin{eqnarray} &&\varepsilon _{\gamma }=\gamma \varepsilon _{\rm RI} \sim 0.2\, {\rm TeV} \gamma _{5}, \end{eqnarray} \tag{ 14 }$$

potentially applicable to TeV unIDs. The ratio of gamma-ray energy to the ⁵⁶Co CR energy is about f = ε_RI/56m_pc² ∼ 4 × 10⁻⁵. The gamma-ray flux is then estimated as

$$\begin{eqnarray} &&\varepsilon _\gamma F_{\varepsilon _\gamma } =\frac{f \zeta E}{4\pi d^2 t_\gamma } \sim 10^{-12}\,{\rm erg}\ {\rm s}^{-1}\ {\rm cm}^{-2} \frac{\zeta _{-1} E_{51}}{\gamma _{5} d_{3\,{\rm kpc}}^{2}}, \end{eqnarray} \tag{ 15 }$$

interestingly comparable to that of TeV unIDs, where d_3 kpc = d/3 kpc and E is the total energy of ⁵⁶Co CRs. In a sense, this is a relativistic version of the SN emission since the energy source is the RI decay.

In the RI model, a similar way to the β-decay model, the total source number is 0.1–1 for a Galactic GRB rate of ∼10⁻⁵–10⁻⁶ yr⁻¹ (Guetta & Della Valle 2007), while the most optimistic number is ∼10 for a rate consistent with the late-time radio observations ∼10⁻⁴ yr⁻¹ (∼10% of the SN Ibc rate) (Soderberg et al. 2006a). We can detect a fraction ∼(3 kpc/10 kpc)² ∼ 0.1 of these sources, if CRs comprise an energy comparable to the typical GRB energy. For a rare event with high energy and/or with reacceleration by the hypernova shock, the observable distance may be farther.

We note that other RI species may also contribute. In particular, the ⁵⁷Ni emission via β⁺ decay dominates in the young (∼10³ yr) remnants because its half-life 35.6 hr is ∼10² times shorter than ⁵⁶Ni though its yield is less by 0.1–0.01 (Maeda & Nomoto 2002, 2003).

The shocked ⁵⁶Co is accelerated to a power-law spectrum dN_Co ∝ ε^−p_Codε_Co for ε_Co < ε_Co,max. The maximum energy can be ε_Co,max ∼ 3 × 10¹⁷ eV (e.g., Murase et al. 2008), which provides ε_γ,max ∼ f × (3 × 10¹⁷eV) ∼ 10 TeV decay gamma ray. Hereafter, we adopt this maximum energy. The Larmor radius of ⁵⁶Co CRs is ∼4(ε_Co/10¹⁷eV)B⁻¹₋₆ pc, leading to the isotropic emission of decay gamma rays.

As shown in Figure 3, the decay gamma rays have a unique spectrum,

$$\begin{eqnarray} &&\varepsilon _\gamma F_{\varepsilon _\gamma } \propto \varepsilon _\gamma ^{-p+1} \exp \left(-\frac{{\varepsilon _{p}}}{{\varepsilon _\gamma }}\right) \end{eqnarray} \tag{ 16 }$$

with an exponential cutoff⁴ below

$$\begin{eqnarray} &&\varepsilon _p=\varepsilon _{\rm IR} \left(\frac{t}{t_{\rm iCo}}\right) \sim 0.2\, {\rm TeV} \left(\frac{t}{10^5\,{\rm yr}}\right) \end{eqnarray} \tag{ 17 }$$

and a power law above it, where the power-law index is softer than that of parent CRs by 1. This is because the low energy CRs have already decayed while the high energy CRs are decaying with a rate (d/dt)exp(−t/γt_iCo) ∝ ε⁻¹_γexp(−ε_p/ε_γ). The spectrum of TeV unIDs is characterized as a power law with index 2.1–2.5 (Aharonian et al. 2008), which corresponds to p = 1.1–1.5 in Equation (16). This is slightly harder than the p = 2 expected in the test particle acceleration case. The harder spectrum could suggest nonlinear shock effects in jets where the CR pressure is nonnegligible (Ellison 2001). This is consistent with the fact that the necessary CR energy is comparable to the total energy of jets, E ∼ E_j.

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In Figure 3, we also show the synchrotron and IC emission from decay positrons in Equation (11), which have an energy comparable to that of decay gamma rays. The positron spectrum is dN_e ∝ ε^−p_edε_e for Γm_ec² < ε_e < ε_p and dN_e ∝ ε^{−p − 1}_edε_e for ε_p < ε_e < ε_max. The synchrotron frequency is ν^syn = qBε²_e/2πm³_ec⁵ ∼ 10⁻⁴B₋₆(ε_e/0.1TeV)² eV while the IC frequency is ν^IC ∼ 9_CMB(ε_e/m_ec²)² ∼ 10⁸(ε_e/0.1TeV)² eV, where we consider cosmic microwave background (CMB) as main target photons (Ioka et al. 2004).

However, the cooling time t_c = 3m²_ec³/4σ_Tε_eU ∼ 10⁷(ε_e/0.1TeV)⁻¹U⁻¹₋₁₂ yr is usually longer than the decay time t_γ in Equation (13) for ε_e < ε_max ∼ 10 TeV, where U is the total energy density of magnetic fields and CMB. Then the luminosity is suppressed by t_γ/t_c ∼ 10⁻²(t_γ/10⁵ yr)(ε_e/0.1TeV)U₋₁₂ compared with decay gamma rays in Equation (15). This is favorable for the interpretation of such sources as TeV unIDs. Note that the ∼eV photons by decay positrons come from an extended region in which the optical background dominates the remnant flux.

The accelerated RI CRs may suffer the adiabatic energy losses during the expansion of the remnant (Rachen & Mészáros 1998), which will greatly suppress the RI emission. This is a potential problem for the RI decay model. However, the CR escape from a remnant is not fully understood yet. For instance, it is common to assume the free escape of CRs in models where the GRB reverse shocks are the sites for the ultra high energy CR production (e.g., Waxman 2006; Murase et al. 2008). In the same sense, the RI decay model is a viable possibility for TeV unIDs.