Contribution of dark matter annihilation to gamma-ray burst afterglows near massive galaxy centers

The existence of dark matter (DM) is strongly supported by convincing evidence in cosmology and astrophysics (e.g., Bertone et al., 2005). Numerous astronomical processes and evolutions are partly or predominantly affected by DM. However, the nature of DM remains a mystery, and its direct detection has yet to be achieved. The mainstream DM model invokes DM particles, the most promising candidate being the weakly interacting massive particles (WIMP, see e.g., Jungman et al., 1996; Bertone et al., 2005; Bergström, 2012). The WIMP model can be tested by detecting potential signals from WIMP annihilations, which can ultimately produce Standard Model particles, such as neutrinos, photons, electrons, and positrons. Searching for gamma-ray emissions produced by DM annihilation is one method to indirectly detect DM; for this task, nearby galaxy centers and dwarf spheroidal galaxies are appealing targets (e.g., Ackermann et al., 2015; Abdallah et al., 2018; Johnson et al., 2019). Moreover, the radio detection of synchrotron radiation induced by electrons and positrons produced by DM annihilation in galaxies is considered a promising method to constrain the particle nature of DM (e.g., Storm et al., 2013; Egorov & Pierpaoli, 2013). However, such emissions are generally weak, and possible detections are limited to galaxies in the local universe.

If significant signals can be powered by electrons produced by DM annihilation, an accelerator should be established in a high-density DM halo. In addition, the number density of system-provided electrons should be comparable to that of DM electrons (DMEs). The jets generated from gamma-ray bursts (GRBs) near galaxy centers are ideal accelerators.

GRBs are the most luminous explosions in the universe. The ultrarelativistic jets in the line of sight launched by newly born magnetars or hyperaccreting black holes can trigger observable GRBs (see the reviews by Mészáros, 2006; Zhang, 2007, 2018; Liu et al., 2017). The prompt gamma-ray emissions and multiband afterglows of GRBs generally originate from the internal and external shock phases, respectively (e.g., Mészáros & Rees, 1993; Rees & Mészáros, 1994; Mészáros & Rees, 1997; Sari et al., 1998; Piran, 2004). Most GRB afterglows can be explained by synchrotron and synchrotron self-Compton (SSC) processes under the conditions of external shocks sweeping the interstellar medium (ISM, or interstellar wind) and accelerating electrons. This explanation has been thoroughly verified by multi-wavelength observations of GRB 190114C (MAGIC Collaboration et al., 2019; Wang et al., 2019; Fraija et al., 2019). In the prompt emission phase, the number of DMEs is much less than that of electrons emitted from the central engine, so the electromagnetic radiation of DMEs might be observable only in the afterglow phase.

In this paper, the lightest supersymmetric particle in the WIMP model, namely, the neutralino, is chosen; this particle has four different annihilation channels, i.e., $w^{+}w^{-}$, $b\bar{b}$, $\mu^{+}\mu^{-}$, and $\tau^{+}\tau^{-}$. We then study the acceleration and radiation mechanisms of DMEs in external shocks and subsequently predict and analyze the DM contributions to the light curves and spectra of GRB afterglows. In Section 2, we provide a detailed description of the method employed to calculate the light curves and spectra of GRB afterglows, including the effects of DM. In Section 3, the results using different DM parameters are shown. In Section 4, we analyze the locations of GRBs in massive galaxies associated with the effects of DM. The conclusions and discussion are presented in Section 5.

Following the above method, we can calculate the light curves and spectra of GRB afterglows, including the effects of DM. The universal parameters of the external shock model are set as the isotropic kinetic energy $E_{\rm k,iso}=10^{53}\,{\rm ergs}$, $\epsilon_{\rm e}=10^{-1}$, $\epsilon_{B}=10^{-3}$, $\Gamma=200$, $p=2.3$, $\theta_{\rm j}=0.1$, and $z=1$.

Figure 1(a) shows the light curves of GRB afterglows including and excluding the effects of DM with $n=0.1\,{\rm cm^{-3}}$. DM annihilation occurs in the $b\bar{b}$ channel, and the DM particle mass is $M_{\rm\chi}=10\,{\rm GeV}$. The solid and dashed lines represent the light curves and spectra with $\rho_{\chi}=5.0\times 10^{4}\,{\rm GeV~{}cm^{-3}}$ and 0, respectively. The magenta and blue lines correspond to the synchrotron emission in the optical $R$ band and $0.3-10\,{\rm KeV}$, respectively. The red lines correspond to the synchrotron + SSC emissions in the range of $0.1-1\,{\rm GeV}$, and the green lines correspond to the SSC emissions in the range of $0.3-1\,{\rm TeV}$. The fluxes in the ranges of $0.3-10\,{\rm KeV}$ and $0.3-1\,{\rm TeV}$ are multiplied by $10$ and $100$, respectively. In this case, the annihilation DM effects are adequately displayed in the multiband light curves of GRB afterglows. Figure 1(b) shows the synchrotron $+$ SSC spectra in the same situation as Figure 1(a). The green, red, and blue lines represent the spectra at $10^{3}\,{\rm s}$, $10^{4}\,{\rm s}$ and $10^{5}\,{\rm s}$, respectively. Once the effects of DM are considered, in addition to fluence increasing, the shapes of the spectra also change.

Figure 2 shows the synchrotron $+$ SSC spectra of GRB afterglows with different parameters, i.e., DM density, particle DM mass, annihilation channel, and CME density. Figure 2(a) displays the synchrotron $+$ SSC spectra of GRB afterglows with different $n$ at $t=10^{4}~{}{\rm s}$ after the GRB is triggered. The DM density is set to $5\times 10^{4}\,{\rm GeV~{}cm^{-3}}$ or $0\,{\rm GeV~{}cm^{-3}}$, and the DM particle mass is taken as 10 GeV. The red, blue, green, and magenta lines represent $n=1.0\,{\rm cm^{-3}}$, $10^{-1}\,{\rm cm^{-3}}$, $10^{-2}\,{\rm cm^{-3}}$, and $10^{-3}\,{\rm cm^{-3}}$, respectively. The solid and dashed lines represent the cases including and excluding the contribution of the DMEs, respectively. Different CME densities result in different spectral shapes, and the inclusion of DMEs further makes the variety of the spectra. For a lower CME density, the DME effect is more significant.

The spectra in four different annihilation channels are presented in Figure 2(b). It is obvious that the fluxes in the $w^{+}w^{-}$ and $b\bar{b}$ annihilation channels are higher than those in the $\tau^{+}\tau^{-}$ and $\mu^{+}\mu^{-}$ annihilation channels.

Figure 2(c) shows the synchrotron $+$ SSC spectra of GRB afterglows for different DM densities and DM masses at $t=10^{4}~{}{\rm s}$. The values of the DM density is set to $5\times 10^{4}\,{\rm GeV~{}cm^{-3}}$ and $5\times 10^{5}\,{\rm GeV~{}cm^{-3}}$, and the values of DM particle mass are taken as 10 GeV and 100 GeV. The DM annihilation channel is assumed to be the $b\bar{b}$ channel, and the CME number density is $n=1\,{\rm cm^{-3}}$. Figure 2(d) presents the afterglow spectra for the same parameters of Figure 2(c), except the parameters $n=10^{-3}\,{\rm cm^{-3}}$, and $\rho_{\chi}$ = $5\times 10^{3}\,{\rm GeV~{}cm^{-3}}$ and $5\times 10^{4}\,{\rm GeV~{}cm^{-3}}$. The black solid lines in Figures 2(c) and 2(d) denote the spectra excluding the contributions of the DMEs. The flux values of the black lines are slightly higher than those of the red solid lines (corresponding to lower DM densities and high DM particle masses) because $\gamma_{\rm e,min}$ decreases slightly when the effects of DM are considered. According to all the lines, a higher DM density and lower DM particle mass can dramatically increase the fluxes. As shown by the blue dashed line in Figure 2(d), the flux exhibits prominent improvements in the low- and high-energy parts due to the contributions of inefficiently accelerated DMEs and the increased number of seed photons, respectively.

Since many parameters related to jets are uncertain and the ISM and DM can prominently influence the light curves and spectra of GRB afterglows, it is difficult to distinguish the distributions of DM unless the properties of the circumburst medium can be constrained by observations. For a full description of the medium properties of GRB afterglows, the location of GRBs in the galaxy should be considered, as discussed below.

To simplify, we assume a DM halo with the virial mass $M_{\rm vir}$ in the virial radius $R_{\rm vir}$. The mean density is equal to the virial overdensity $\Delta_{\rm vir}$ times the mean background density $\rho_{\rm u}$, given by (e.g., Bullock et al., 2001)

$\Delta_{\rm vir}=200$ is generally preferred, which is independent of cosmology. Thus, the corresponding virial radius and virial mass are $R_{\rm 200}$ and $M_{\rm 200}$, respectively. Furthermore, the concentration parameter (e.g., Bullock et al., 2001) can be defined as

which is also related to the virial mass (e.g., Buote et al., 2007), i.e.,

Moreover, the virial mass can be derived by integrating different DM density profiles in the viral radius $R_{200}$,

The DM density of the galaxies is a function of radius. The general Navarro-Frenk-White (NFW) density profile reads (Navarro et al., 1997)

where $\rho_{\rm c}$ and $r_{\rm c}$ are the characteristic density and radius, respectively. Here, we consider four values of the slope: $\gamma_{\rm c}=1.0$, $1.1$, $1.2$, and $1.3$, respectively. The profile proposed by Moore et al. (1999) corresponding to the slope $\gamma_{\rm c}=1.5$ is derived according to N-body simulations, which suggests a steeply rising DM density towards the galaxy center. In addition, the Einasto law is written as (Merritt et al., 2006)

where $d_{N}\approx 3N-1/3+0.0079/N$ for $N\gtrsim 0.5$.

Combining the above equations, one can obtain the characteristic radius and density of the DM density profiles with the virial mass $M_{\rm 200}=10^{12}\,{M}_{\odot}$. The results are shown in Figure 3. The blue and green solid lines represent the Einasto law and Moore law, respectively. The red lines represent the NFW formula, where the solid, dashed, dotted, and dashed-dotted lines denote the NFW profile with the following four values of the inner slope: $1.0$, $1.1$, $1.2$, and $1.3$, respectively. The gray shaded region indicates the DM density range of $\sim 10^{3}\,-\,10^{5}\,{\rm GeV~{}cm^{-3}}$. The vertical black dashed line denotes the location 1 pc from the center of the galaxy. According to the magnetic field model used in the galaxy center (Aloisio et al., 2004), $B_{\rm ISM}$ increases rapidly with decreasing radius within $1\,{\rm pc}$, so the value of $B_{\rm ISM}$ assumed above would be inappropriate within $1\,{\rm pc}$. Finally, the brown shaded region represents the possible locations of GRBs with significant contributions from DM, i.e., several to tens of parsecs from the center of a galaxy with virial mass $\sim 10^{12}\,{M}_{\odot}$.

Moreover, the effects of DM spatial diffusion (e.g., Colafrancesco et al., 2006), re-acceleration, and advection (e.g., Strong et al., 2007) might be important at the galaxy scale or beyond, which would decrease the DME densities around GRBs. These effects are neglected for our calculations.

In this paper, we study the contributions of DM annihilation to GRB afterglows. If GRBs occur at distances of several to tens of parsecs from the centers of massive galaxies, the effects of DMEs should be significant. Moreover, the influences of different DM particle masses and annihilation channels on GRB afterglows are adequately reflected in the flux changes.

To date, no GRB has been discovered at a distance of tens of parsecs from a galaxy center, but one may expect that these events could be detected in the future because the density of stars near the galaxy center is generally higher than that in other regions within the host galaxy. Observations show that the majority of stars formed at distances of a few parsecs from the center of the Milky Way are older than $5$ Gyr (e.g., Blum et al., 2003), and one pulsar, PSR J$1745-2900$, was detected $\sim$ 0.12 pc from Sagittarius $\rm A^{\star}$ (Eatough et al., 2013). Of course, the dense gas and bright galaxy center will trouble the observations of those distant GRBs.

In addition to DMEs, gamma-ray emission is another final product of DM annihilation due to $\pi^{0}$ decay. The gamma-ray flux produced by $\pi^{0}$ decay from a galaxy with $M_{\rm vir}=10^{12}\,M_{\odot}$ at $z=1$ is far below the observational threshold and hence can be neglected. However, if this galaxy is located near the Milky Way, the gamma-ray flux can be detected. Therefore, we use observations of a neighboring galaxy, M31, which has a virial mass of $\sim 10^{12}\,M_{\odot}$, to test our model under the assumption that the gamma-ray emission near the center of M31 originated from DM annihilation. In the observation, a gamma-ray excess with a flux of $(5.6\pm 0.6)\times 10^{-12}\,{\rm erg\,cm^{-2}\,s^{-1}}$ was detected in the energy range from $0.1\,{\rm GeV}$ to $100\,{\rm GeV}$ within the central M31 region of $\sim 5\,{\rm kpc}$ (Ackermann et al., 2017). We can calculate the gamma-ray flux by the formula

where ${dN_{\gamma}(E_{\gamma})}/{dE_{\gamma}}$ is the gamma-ray spectrum corresponding to $M_{\chi}=100\,{\rm GeV}$ and the $b\bar{b}$ annihilation channel and $r_{\rm max}=5\,{\rm kpc}$, and $D_{A}$ is the distance of M31. The NFW profile with $\gamma_{\rm c}=1.3$ is adopted. By integrating the energy range from $0.1\,{\rm GeV}$ to $100\,{\rm GeV}$, the gamma-ray flux is $5.7\times 10^{-13}\,{\rm erg\,cm^{-2}\,s^{-1}}$. This flux is less than that observed in M31, indicating that our model is self-consistent.