TY - JOUR
AU - Liang,, En-Wei
AB - ABSTRACT The tentative 1.4 TeV e+e− excess observed by DAMPE, if not a statistical fluctuation, may be explained by dark matter (DM) annihilation within a nearby subhalo with a distance of <0.3 kpc. The process of DM annihilating to e+e− is accompanied by the production of gamma-ray photons, which could lead to detectable signals of Fermi-LAT. In this work, we focus on the model that the tentative 1.4 TeV signal is from a nearby ultracompact mini halo (UCMH). Due to the small angular extension, the counterpart gamma-ray signal would be hidden among Fermi-LAT unassociated point sources. We examine the point sources in 4FGL systematically by analyzing the Fermi-LAT data, aiming to investigate whether there exist sources with gamma-ray properties consistent with the UCMH model of the 1.4 TeV excess. We find more than 10 sources could be the candidates. Furthermore, we test the possibility that the excess signal is from a DM mini-spike around the nearest BH, but our result does not favour such a scenario. dark matter, gamma rays: general 1 INTRODUCTION DArk Matter Particle Explorer (DAMPE) is a satellite-based telescope, which aims to observe high-energy cosmic rays and gamma rays in the GeV to TeV energy range with an unprecedentedly high energy resolution. It has an energy resolution of |$\sim 1.0{{\ \rm per\ cent}}$| at 100 GeV (Chang et al. 2017). The DAMPE was launched on 2015 December 17 and results of its measurements of the cosmic-ray electron and proton spectra were released (DAMPE Collaboration et al. 2017; An et al. 2019). The e+e− spectrum observed with DAMPE covers an energy range from 25 GeV to 4.6 TeV. It has the highest precision among other similar projects at these energies. It is characterized by two features: a spectral break around 900 GeV, which has also been detected by CALET (Adriani et al. 2018), HESS (Aharonian et al. 2008, 2009), etc., and a peak-like excess at |$\sim 1.4\, {\rm TeV}$|⁠. Both features have been widely discussed in the literature (Yuan et al. 2017; Athron et al. 2018; Cao et al. 2018; Fan et al. 2018; Fang, Bi & Yin 2018; Ghosh et al. 2018; Huang et al. 2018; Niu et al. 2018; Pan, Zhang & Feng 2018; Yuan & Feng 2018; Belotsky et al. 2019; Chan & Lee 2019; Zhao et al. 2019). In this paper, we focus on the intriguing 1.4 TeV peak. The DAMPE 1.4 TeV excess appears in a very narrow energy range and seems to be a line-like structure. The narrowness of the peak indicates that it may originate from a nearby source because the cooling effect of electron cosmic rays would broaden the spectral feature effectively. It is reported that the local (global) significance of the 1.4 TeV excess is 3.7σ (2.5σ) (Huang et al. 2018). Though the global significance is still lower than 3σ, such a feature has attracted many concerns (Yuan et al. 2017; Ghosh et al. 2018; Huang et al. 2018; Pan et al. 2018; Belotsky et al. 2019; Chan & Lee 2019; Zhao et al. 2019) due to that it may relate to intriguing novel physics. If the signal is not a statistical fluctuation, it could originate from astrophysical sources, e.g. phase-space shrinking of burst-like electron injection from nearby sources (such as PWNe/SNRs) (Huang et al. 2018) or cold, ultrarelativistic e+e− plasma winds from a pulsar (Yuan et al. 2017). A more intriguing interpretation for this narrow peak is related to the dark matter (DM), which could annihilate directly to e+e− within a nearby subhalo/local overdensity region (Yuan et al. 2017) and generate a monochromatic injection of e+e−. Some previous results suggested that the DM origin of the 1.4 TeV excess seems to be in tension with gamma-ray observations (Ghosh et al. 2018; Belotsky et al. 2019). The low probability of appearing a subhalo/local enhancement in the nearby region also challenges the model (this constraint could be relaxed by introducing an enhancement mechanism of the standard cross-section, such as the Sommerfeld enhancement or non-thermal production mechanism) (Yuan et al. 2017). Nevertheless, these problems suffered mainly by nearby ‘standard’ substructures [such as those with a Navarro–Frenk–White (NFW; Navarro, Frenk & White 1997) density profile]. An alternative possibility is that the 1.4 TeV signal is generated from very compact substructures of DM, known as ‘ultracompact mini halo’ (UCMH). The UCMHs can be formed in the early epochs of the Universe (Ricotti & Gould 2009; Yang et al. 2011). Due to their very small spatial extension, they should appear in the gamma-ray sky as point-like sources. Even if the expected gamma-ray flux exceeds the detection threshold, the non-detection of UCMHs can be interpreted as that it hides behind the unassociated point sources of Fermi-LAT source catalogue (i.e. 3FGL, 4FGL). Such a possibility has been briefly discussed in Huang et al. (2018) and Zhao et al. (2019), here we present a more detailed analysis by analyzing the Fermi-LAT data. Our analysis is based on the UCMH, however, it is also applicable for the case of a mini-spike around a black hole (BH), since the latter share similar density profile with UCMH and is also point-like in the gamma-ray sky. In Section 3, we discuss the mini-spike of a specific BH, A0620-00. It has been shown that the annihilation channel of χχ → e+e− can better fit the observed electron spectrum, while ττ, μμ, and quarks channels cannot generate prominent peak feature (Yuan et al. 2017). Therefore, we only consider the e+e− channel in this work. Note some other annihilation channel with large enough annihilation branching ratio directly to e+e− (for example annihilation to eμτ) may fit the spectrum as well. 2 DM GAMMA-RAY SIGNALS FROM UCMH Both the fluxes of gamma rays and cosmic rays from DM annihilation rely on the annihilation rate of the DM particles within UCMH, $$\begin{eqnarray*} R=\frac{\left\langle \sigma v\right\rangle }{2m_\chi ^2}\int \rho ^2{\rm d}V, \end{eqnarray*}$$ where 〈σv〉 is the velocity-averaged annihilation cross-section for χχ → e+e−, mχ is the mass of DM particle, and ρ represents the DM density distribution in UCMH. For monochromatic DM injection, the annihilation rate is related to the energy injection density through |$\dot{Q}=R\cdot 2m_\chi$|⁠. For the cosmic rays of local origin, assuming the CRs have a spherical symmetric distribution around the source, their propagation are described by (Ginzburg & Syrovatskii 1964; Huang et al. 2018) $$\begin{eqnarray*} \frac{\partial f}{\partial t}=\frac{D(E)}{r^2}\frac{\partial }{\partial r}r^2\frac{\partial }{\partial r}f+ \frac{\partial }{\partial E}(b(E)f)+q, \end{eqnarray*}$$(1) where f(r, t, E) is the number density of the cosmic rays with r the distance to the CR source, and E the energy of CR particle. Effect of convection and re-acceleration have been neglected as they are only prominent at low energies. The energy loss rate is parametrized by b(E). At the energies around 1.4 TeV, the electrons mainly loss energy by the synchrotron and inverse Compton scattering. However, the narrow feature of the peak requires that the electrons must be produced from nearby source, i.e. r ≪ λ, where λ is the cooling length for 1.4 TeV electron. In such a case, the cooling effect b(E) can be neglected and the equation (1) can be solved analytically. By solving the equation (1), the energy density reads (Atoyan, Aharonian & Völk 1995; HESS Collaboration et al. 2016) $$\begin{eqnarray*} w_{\rm e}(r)=\frac{\dot{Q}}{4\pi D(E)r}. \end{eqnarray*}$$ F or a DM source of distance d, the above equation gives an injection power of $$\begin{eqnarray*} \dot{Q} &\approx & 5\times 10^{32}\, {\rm erg\,\,s^{-1}}\, \left({d\over 0.1\, {\rm kpc}}\right)\left({D(E)\over 10^{29}\, {\rm cm^{2}\,{s}^{-1}}}\right) \nonumber \\ &\times &\left({w_{\rm e}\over 1.2\times 10^{-18}\, {\rm erg\,cm^{-3}}}\right), \end{eqnarray*}$$(2) where D(E) = D0(E/GeV)−δ with |$D_0=5.3\times 10^{28}\, {\rm cm^2s^{-1}}$| and δ = 1/3 is the energy-dependent spatial diffusion coefficient (Ackermann et al. 2012; Yuan et al. 2017). The energy density of the 1.4 TeV peak is estimated to be about we ∼ 1.2 × 10−18 erg cm–3 (Yuan et al. 2017). For gamma rays generated from DM annihilation, the expected flux is $$\begin{eqnarray*} \phi =\frac{1}{4\pi }\frac{\left\langle \sigma v\right\rangle }{2m_\chi ^2}\frac{{\rm d}N}{{\rm d}E}\times J, \end{eqnarray*}$$(3) where dN/dE is the differential photon production per annihilation which can be obtained using PPP4DMID (Cirelli et al. 2011). The term J is the so-called J-factor that is related to the DM spatial distribution. If the distance d of the source is far greater than its virial radius, the J-factor can be expressed as $$\begin{eqnarray*} J=\frac{\int \rho ^2{\rm d}V}{{\rm d}^2}=\frac{\dot{Q}m_\chi }{\left\langle \sigma v\right\rangle {\rm d}^2}, \end{eqnarray*}$$(4) so that (Belotsky et al. 2019) $$\begin{eqnarray*} \phi =\frac{1}{4\pi }\frac{1}{2m_\chi }\frac{{\rm d}N}{{\rm d}E}\times \frac{\dot{Q}}{d^2}. \end{eqnarray*}$$(5) The spectrum of monochromatic electrons will be broadened after propagation. To interpret the narrow width of the peak, the distance of the source is constrained to d < 0.3 kpc (Huang et al. 2018) so that the cooling effect is not significant within such distance. On the other hand, if the source is too close to us, its angular extension may be greater than the point spread function of Fermi-LAT. Thus, it will be identified as spatially extended sources. The only two tentative extended subhalos reported in literature do not have spectra consistent with χχ → e+e− (Bertoni, Hooper & Linden 2016; Wang et al. 2016; Xia et al. 2017; Ackermann et al. 2018). We therefore consider the UCMHs in the range of d = 0.05 − 0.3 kpc. Through out the paper, we assume a canonical thermal relic cross-section of |$\left\langle \sigma v\right\rangle =3\times 10^{-26}\, {\rm cm^3\, {s}^{-1}}$| (Steigman, Dasgupta & Beacom 2012). Note that the expected e+e− flux relies not only on the cross-section, but also the mass/density profile of the subhalo. So other values of 〈σv〉 are permissible for the 1.4 TeV excess as well, as long as adopting appropriate subhalo mass. From equation (4) and (5), we obtain |$J=(0.51{-}3.06)\times 10^{23}\, {\rm GeV^2\,cm^{-5}}$| for d = 0.05 − 0.3 kpc, which corresponds to a photon flux in 1–100 GeV energy range |$\Phi _{\rm ucmh}=(3.06-18.35)\times 10^{-11}\, {\rm ph\,cm^{-2}\,{s}^{-1}}$|⁠. In the next section, we select the Fermi-LAT unassociated sources consistent with these fluxes to identify possible UCMH candidates. 3 IDENTIFYING UCMH CANDIDATES OF 1.4 TEV DM IN THE FERMI-LAT DATA UCMHs candidates, if detected, should be characterized by some features. Before performing likelihood analysis of Fermi-LAT data to identify UCMH candidates, we carry on preliminary selections applying the following criteria. (1) A DM source normally cannot be detected in other wavelength, thus they should be members of Fermi-LAT unassociated point sources. (2) The gamma-ray signal emitted through DM annihilation should be steady in flux, those sources with high variability can therefore be excluded. (3) The detected flux of the sources should match the prediction of DM subhalo (⁠|$\Phi _{\rm ucmh}=(3.06-18.35)\times 10^{-11}\, {\rm ph\,cm^{-2}\,{s}^{-1}}$|⁠). The detailed selection methods are described below. Our selection started with the fourth Fermi-LAT source catalogue (4FGL) (The Fermi-LAT collaboration 2020), which is compiled based on 8 yr of LAT observation. The Fermi-LAT is mainly operated in a survey mode and cover the full sky every 3 h (Atwood et al. 2009). In total, 5065 sources above 4σ significance level are recorded in the 4FGL, in which 1337 sources do not have a plausible electromagnetic counterpart in other wavelength. We first filter out sources with possible associations by parameters ASSOC1 and ASSOC2 (1337/5065), which flag sources (point or extended sources) that possibly associated with AGN, pulsar, SNR, etc. To filter sources whose light curves have high variability, we use the parameter Variability_Index. Sources having |${\tt Variability\_Index}\gt 18.48$| are excluded from our sample as they are not steady at |$\gt 99{{\ \rm per\ cent}}$| confidence level (The Fermi-LAT collaboration 2020), and 1105 sources remain after this selection (1105/1337). We also ignored the sources with galactic latitude |b| < 20° (820/1105) because these regions occupy only a small fraction of the sky, yet the background is complicated and the Fermi-LAT sensitivity is much lower. Corresponding to criterion (3), we compared the expected UCMH flux, Φucmh, with the observations and filtered out sources whose fluxes don’t consistent with model prediction. In this comparison, we use parameters Flux1000 and Unc_Flux1000 in 4FGL (The Fermi-LAT collaboration 2020), and 70 sources pass our initial selection (70/820). For these 70 unassociated sources, Fermi-LAT data analyses are conducted by using Fermitools1 to find out which sources may come from 1.4 TeV DM annihilation. In order to keep consistent with the results of 4FGL, we analyse 8 yr of Pass 8 data, which range from 2008 August 4 to 2016 August 2 (239557417–491809444 in MET). Considering the hard spectrum of the ∼1.4 TeV DM signal, the gamma rays should mainly appear in high energy range. Thus, the data are extracted in the energy range of 1–500 GeV with SOURCE event class (evclass = 128, evtype = 3). Benefited from the good angular resolution of Fermi-LAT at energies above 1 GeV, we adopt an small region of interest (ROI) of 5° centred on each target source to improve the efficiency of analysis process. And events with zenith angles larger than 90° have been ignored in the analysis to eliminate the contamination from the Earth Limb. We also apply a data quality cut (DATA_QUAL>0)&&(LAT_CONFIG= = 1) to guarantee that data are suitable for science use. Corresponding to the adopted data, the P8R3_SOURCE_V2 instrument response function (IRFS) is used. During the analysis, the script make4FGLxml.py2 is employed to generate xml model file, which contains the model information of sources 10° around the target based on 4FGL catalogue. The Galactic diffuse emission and extragalactic isotropic diffusion are described by gll_iem_v07.fits and iso_P8R3_SOURCE_V2_v1.txt, respectively. The likelihood analysis of the 70 sources are implemented by command gtlike, and the spectral parameters are fixed during fitting to speed up the computations. Each source is modelled by an 4FGL model (e.g. Power-law, Log-parabola) and a built-in DM model DMfitFunction. For the DM model, the following parameters are fixed: |$\left\langle \sigma v\right\rangle =3\times 10^{-26}\, {\rm cm^{-3}\,{s}^{-1}}$|⁠, |$m_{\chi }=1.4\, {\rm TeV}$|⁠, and the annihilation channel is limited only to e+e−. We compare the likelihood values of the two models and pick out sources which favour DM interpretation with ΔlnL < 4.5 and TSDM > 16. 4 RESULTS Applying the procedures described in Section 3, we find that there are totally 14 point sources in our sample whose spectra are compatible with the model of 1.4 TeV DM annihilating to e+e− and TSDM > 16. They are listed in Table 1. As shown in the table, both a 4FGL model and a DM model give similar TS values for these sources. The 4FGL model always provides better fit to the data, which, however, is reasonable as it has more free parameters than the DM model. The ΔlnL < 4.53 listed in the last column of Table 1 indicates that the two models match the data comparably. The possibility that these sources are from DM UCMHs thus should not be ignored. We also note that all these sources are just marginally detected by the Fermi-LAT. The maximal TS value is only ∼40 from 4FGL J2030.3-5038. Such a result implies that it is still possible the DM UCMH generating the 1.4 TeV peak has not been detected by the Fermi-LAT yet, though it is shown that the expected gamma-ray flux exceeds the sensitivity of the instrument. One of the reasons is that the reported nominal sensitivity curve is usually a median one, meaning that only half of the sources at this flux will be detected. Table 1. 4FGL sources with spectra compatible with DM signal from a nearby UCMH. 4FGL Name . RA . Dec. . |$\rm TS_{4FGL}$| . |$\rm TS_{DM}$| . ΔlnL . σHAWC . |$\Phi _{\rm HAWC}\,^{a}$| . . (°) . (°) . . . . . (⁠|$\rm ph\, cm^{-2}s^{-1}$|⁠) . 4FGL J0308.9 − 4702 47.24 −47.04 31.18 28.00 1.59 − − 4FGL J0633.9 + 5840 98.48 58.68 21.60 18.01 1.78 −0.82 3.72 × 10−12 4FGL J0741.0 − 5226 115.27 −52.44 32.56 31.31 0.16 − − 4FGL J1018.4 + 2210 154.62 22.17 30.10 30.05 0.02 1.61 1.41 × 10−12 4FGL J1021.8 − 6308 155.47 −63.15 25.03 23.31 0.85 − − 4FGL J1641.5 + 2017 250.38 20.29 28.74 26.86 0.93 −0.81 4.99 × 10−13 4FGL J2021.9 + 3609 305.49 36.16 33.84 32.50 0.67 3.05 |$1.77^{+2.93}_{-0.60}\times 10^{-12}$| 4FGL J2030.3 − 5038 307.59 −50.63 45.50 40.30 2.60 − − 4FGL J0055.7 + 4507 13.94 45.12 27.52 18.53 4.48 −1.51 7.28 × 10−13 4FGL J0058.3 − 4603 14.59 −46.06 23.03 16.81 3.11 − − 4FGL J0327.6 + 2620 51.92 26.33 26.96 22.74 2.10 0.22 9.73 × 10−13 4FGL J1528.4 + 2004 232.12 20.08 24.83 20.05 2.39 0.42 9.58 × 10−13 4FGL J2207.1 + 2222 331.79 22.37 23.92 20.66 1.62 −0.18 8.31 × 10−13 4FGL J2331.6 + 4430 352.90 44.51 26.15 18.57 3.80 0.26 1.81 × 10−12 4FGL Name . RA . Dec. . |$\rm TS_{4FGL}$| . |$\rm TS_{DM}$| . ΔlnL . σHAWC . |$\Phi _{\rm HAWC}\,^{a}$| . . (°) . (°) . . . . . (⁠|$\rm ph\, cm^{-2}s^{-1}$|⁠) . 4FGL J0308.9 − 4702 47.24 −47.04 31.18 28.00 1.59 − − 4FGL J0633.9 + 5840 98.48 58.68 21.60 18.01 1.78 −0.82 3.72 × 10−12 4FGL J0741.0 − 5226 115.27 −52.44 32.56 31.31 0.16 − − 4FGL J1018.4 + 2210 154.62 22.17 30.10 30.05 0.02 1.61 1.41 × 10−12 4FGL J1021.8 − 6308 155.47 −63.15 25.03 23.31 0.85 − − 4FGL J1641.5 + 2017 250.38 20.29 28.74 26.86 0.93 −0.81 4.99 × 10−13 4FGL J2021.9 + 3609 305.49 36.16 33.84 32.50 0.67 3.05 |$1.77^{+2.93}_{-0.60}\times 10^{-12}$| 4FGL J2030.3 − 5038 307.59 −50.63 45.50 40.30 2.60 − − 4FGL J0055.7 + 4507 13.94 45.12 27.52 18.53 4.48 −1.51 7.28 × 10−13 4FGL J0058.3 − 4603 14.59 −46.06 23.03 16.81 3.11 − − 4FGL J0327.6 + 2620 51.92 26.33 26.96 22.74 2.10 0.22 9.73 × 10−13 4FGL J1528.4 + 2004 232.12 20.08 24.83 20.05 2.39 0.42 9.58 × 10−13 4FGL J2207.1 + 2222 331.79 22.37 23.92 20.66 1.62 −0.18 8.31 × 10−13 4FGL J2331.6 + 4430 352.90 44.51 26.15 18.57 3.80 0.26 1.81 × 10−12 aThe photon fluxes in the 500 GeV to 1.4 TeV energy range estimated by adopting power-law spectra with the index of –2.7 and the differential fluxes at 7 TeV. Except the 4FGL J2021.9 + 3609, 2σ confidence level upper limit is reported. Open in new tab Table 1. 4FGL sources with spectra compatible with DM signal from a nearby UCMH. 4FGL Name . RA . Dec. . |$\rm TS_{4FGL}$| . |$\rm TS_{DM}$| . ΔlnL . σHAWC . |$\Phi _{\rm HAWC}\,^{a}$| . . (°) . (°) . . . . . (⁠|$\rm ph\, cm^{-2}s^{-1}$|⁠) . 4FGL J0308.9 − 4702 47.24 −47.04 31.18 28.00 1.59 − − 4FGL J0633.9 + 5840 98.48 58.68 21.60 18.01 1.78 −0.82 3.72 × 10−12 4FGL J0741.0 − 5226 115.27 −52.44 32.56 31.31 0.16 − − 4FGL J1018.4 + 2210 154.62 22.17 30.10 30.05 0.02 1.61 1.41 × 10−12 4FGL J1021.8 − 6308 155.47 −63.15 25.03 23.31 0.85 − − 4FGL J1641.5 + 2017 250.38 20.29 28.74 26.86 0.93 −0.81 4.99 × 10−13 4FGL J2021.9 + 3609 305.49 36.16 33.84 32.50 0.67 3.05 |$1.77^{+2.93}_{-0.60}\times 10^{-12}$| 4FGL J2030.3 − 5038 307.59 −50.63 45.50 40.30 2.60 − − 4FGL J0055.7 + 4507 13.94 45.12 27.52 18.53 4.48 −1.51 7.28 × 10−13 4FGL J0058.3 − 4603 14.59 −46.06 23.03 16.81 3.11 − − 4FGL J0327.6 + 2620 51.92 26.33 26.96 22.74 2.10 0.22 9.73 × 10−13 4FGL J1528.4 + 2004 232.12 20.08 24.83 20.05 2.39 0.42 9.58 × 10−13 4FGL J2207.1 + 2222 331.79 22.37 23.92 20.66 1.62 −0.18 8.31 × 10−13 4FGL J2331.6 + 4430 352.90 44.51 26.15 18.57 3.80 0.26 1.81 × 10−12 4FGL Name . RA . Dec. . |$\rm TS_{4FGL}$| . |$\rm TS_{DM}$| . ΔlnL . σHAWC . |$\Phi _{\rm HAWC}\,^{a}$| . . (°) . (°) . . . . . (⁠|$\rm ph\, cm^{-2}s^{-1}$|⁠) . 4FGL J0308.9 − 4702 47.24 −47.04 31.18 28.00 1.59 − − 4FGL J0633.9 + 5840 98.48 58.68 21.60 18.01 1.78 −0.82 3.72 × 10−12 4FGL J0741.0 − 5226 115.27 −52.44 32.56 31.31 0.16 − − 4FGL J1018.4 + 2210 154.62 22.17 30.10 30.05 0.02 1.61 1.41 × 10−12 4FGL J1021.8 − 6308 155.47 −63.15 25.03 23.31 0.85 − − 4FGL J1641.5 + 2017 250.38 20.29 28.74 26.86 0.93 −0.81 4.99 × 10−13 4FGL J2021.9 + 3609 305.49 36.16 33.84 32.50 0.67 3.05 |$1.77^{+2.93}_{-0.60}\times 10^{-12}$| 4FGL J2030.3 − 5038 307.59 −50.63 45.50 40.30 2.60 − − 4FGL J0055.7 + 4507 13.94 45.12 27.52 18.53 4.48 −1.51 7.28 × 10−13 4FGL J0058.3 − 4603 14.59 −46.06 23.03 16.81 3.11 − − 4FGL J0327.6 + 2620 51.92 26.33 26.96 22.74 2.10 0.22 9.73 × 10−13 4FGL J1528.4 + 2004 232.12 20.08 24.83 20.05 2.39 0.42 9.58 × 10−13 4FGL J2207.1 + 2222 331.79 22.37 23.92 20.66 1.62 −0.18 8.31 × 10−13 4FGL J2331.6 + 4430 352.90 44.51 26.15 18.57 3.80 0.26 1.81 × 10−12 aThe photon fluxes in the 500 GeV to 1.4 TeV energy range estimated by adopting power-law spectra with the index of –2.7 and the differential fluxes at 7 TeV. Except the 4FGL J2021.9 + 3609, 2σ confidence level upper limit is reported. Open in new tab We further derive the spectral energy distributions (SEDs) of these sources, they are demonstrated in Fig. 1. The SEDs are generated by repeating the likelihood analysis for different energy bins to derive the fluxes and corresponding error bars. In each energy bin, the parameter values of the background sources are fixed to those obtained in the above global fits (except the normalization of the Galactic and isotropic diffuse sources) and the target sources are modelled with the 4FGL model, in which only normalization is allowed to vary. Considering the relatively small number of the photon counts for these sources, the SED are produced in eight energy bins. The SEDs are generated down to |$100\, {\rm MeV}$|⁠. Although the gamma rays from massive DM annihilation are expected to appear at energies |$\gt 1\, {\rm GeV}$|⁠, the analysis at lower energies is also crucial for differentiating models. The SEDs show that except for the sources of 4FGL J0055.7 + 4507 and 4FGL J0058.3 − 4603, which have gamma-ray emission at lower energies thus do not favour the DM model, the DM model indeed match the observation well. However, due to the limited statistics, no more conclusive results can be obtained from the SEDs. Figure 1. Open in new tabDownload slide The Fermi-LAT SEDs of the 14 unassociated 4FGL sources selected in this work with spectra compatible with the UCMH DM model. The red lines are for the model of 1.4 TeV χχ → e+e− and the blue lines are corresponding 1σ uncertainties. The shaded bars show the TS value in each energy bin. Upper limits are plotted if the TS value are <4. Figure 1. Open in new tabDownload slide The Fermi-LAT SEDs of the 14 unassociated 4FGL sources selected in this work with spectra compatible with the UCMH DM model. The red lines are for the model of 1.4 TeV χχ → e+e− and the blue lines are corresponding 1σ uncertainties. The shaded bars show the TS value in each energy bin. Upper limits are plotted if the TS value are <4. We want to emphasize that the sources listed in Table 1 do not consist of a full sample of the candidates. First, we have ignored the data of the Galactic plane region of |b| < 20°. In addition, if the DM annihilate through other channel, e.g. eμτ, the counterpart signal will have different gamma-ray spectrum, thus misses the selection in this work. Furthermore, in calculating the expected gamma-ray fluxes, we have chosen a specific diffusion coefficient (see Section 3) and do not consider its uncertainty. With the uncertainty taken into account, the allowed values of the model expected flux will have a broader range 4 and more unassociated sources may be included into the candidate list. Also, as already been discussed above, the source may have not been detected by Fermi-LAT yet. Nevertheless, through our analysis, we find that >10 sources have passed our selection and one of them could be the source of the 1.4 TeV excess. We thus suggest that a model of DM annihilation in nearby UCMHs can interpret the 1.4 TeV peak in the DAMPE electron–positron spectrum and do not conflict with the Fermi-LAT gamma-ray observation. 5 DISCUSSION 5.1 Search for the candidates in the HAWC data As demonstrated in the fig. 3 of Belotsky et al. (2019), the expected gamma-ray flux of the DM model also exceeds the detection sensitivity of HAWC instrument. Thus, the UCMH, if exists, may be detectable by the HAWC. We perform searches to examine whether there are counterpart signals in the HAWC observations for the candidates listed above. The data of HAWC is not fully publicly available, we use the 2HWC Survey Interactive Tool 5 (Abeysekara et al. 2017) to conduct the search. This tool allows us to derive TS value of a putative point source and its corresponding flux upper limit for a given direction in the sky. A limitation of this tool is that we could not change the spectral index of the putative point source, which is fixed to –2.7, while below 1.4 TeV the expected spectral index for DM signal is ∼−1.0. For all UCMH candidates within HAWC’s field of view, their detection significance and flux upper limits of HAWC are listed in Table 1. The significance corresponds to |$\sqrt{\rm TS}$|⁠, a minus value means that it is the result of an under fluctuation (please see the website for details). We find that for all the Fermi-LAT candidates, no significant emission is detected by HAWC. It seems existing weak signals in the direction of one source, 4FGL J2021.9 + 3609. However, by examining the significance map around this source, we find the faint excess beyond the HAWC background is due to contamination of a nearby source, 2HWC J2019 + 367. The non-detection of a subhalo has also been pointed out by the HAWC Collaboration in Abeysekara et al. (2019), consistent with the results presented here. Though the HAWC observations do not support the hypothesis that they are from UCMH, the non-detection may also be interpreted as a statistical fluctuation. As discussed in Section 4, a signal with its expected flux marginally beyond detection sensitivity could have not been detected by the instrument yet. Furthermore, the brief analysis here cannot achieve the full performance of HAWC. Future gamma-ray telescopes at these energies, such as LHAASO, may provide some more hints for this question. 5.2 The spatial extension of the UCMH gamma-ray signal A question one would concern is that whether the UCMH can be robustly treated as point-like sources in our analysis. As presented in literature Scott & Sivertsson (2009) and Bringmann, Scott & Akrami (2012), a UCMH would consist of two parts separated by a cut-off radius rcut. The DM density of the inner region, dominated by DM annihilation, could be set as a constant ρχ, max. Meanwhile, the outer region has a density profile described by a power law with very steep index ρχ ∝ r−9/4: $$\begin{eqnarray*} \rho _{\chi }=\left\lbrace \begin{array}{lcl}\rho _{\chi , {\rm max}}, & 0\lt r\le r_{\rm cut} \\ \rho _{\chi , {\rm max}}\left(\frac{r}{r_{\rm cut}}\right)^{-\frac{9}{4}}, & r_{\rm cut}\lt r\le R_{\rm UCMH}. \\ 0, & r\gt R_{\rm UCMH} \end{array} \right. \end{eqnarray*}$$(6) With this density profile, together with the annihilation rate presented in Section 2, one can determine the parameters of the above density profile and calculate the effective radius RUCMH of the UCMH (Scott & Sivertsson 2009; Bringmann et al. 2012; Yang, Su & Zhao 2017). The RUCMH is in the order of 1 pc, corresponding to an angular extension of ∼1°. However, in the case of DM annihilation, most of the gamma-ray photons are emitted within a small core region with high DM density. In fact, by integrating the density profile, we find that |$99{{\ \rm per\ cent}}$| of the total gamma-ray flux is from the region within |$r_{99}\sim 10^{-4}\, R_{\rm UCMH}$|⁠. For a UCMH located 0.3 (0.05) kpc away from the Earth, its r99 is ∼3.6 × 10−4 (∼2.0 × 10−4) pc, corresponding to a spatial extension ∼2.9 × 10−5 (∼9.6 × 10−5) degrees. Such a small extension is much lower than the angular resolution of Fermi-LAT, which is at best ∼|$0{_{.}^{\circ}}1$| for all the sensitive energy range.6 It is reported the slope of −4/9 of the UCMH profile is not supported by the N-body simulation results, which prefer an inner slope of ∼−1.5 (Delos et al. 2018). We thus also use this shallower density profile to calculate the expected angular extension of UCMH signal. We adopt the benchmark parameters reported in Delos et al. (2018) (⁠|$r_{\rm s}=1.05\times 10^{-4}\, {\rm kpc}$|⁠, |$\rho _{\rm s}=1.29\times 10^{12}\, {\rm M}_\odot \, {\rm kpc^3}$|⁠). We find the |$\dot{Q}$| derived from such a set of parameters can just give the right energy density ωe of the 1.4 TeV excess if the UCMH is within 0.05–0.3 kpc. Our calculation shows that a UCMH at 0.3 (0.05) kpc with this profile will have an angular extension of ∼|$0{_{.}^{\circ}}03$| (⁠|$0{_{.}^{\circ}}2$|⁠). Therefore, the UCMHs which can account for the 1.4 TeV excess could act as point sources in the Fermi-LAT gamma-ray sky. 5.3 The constraint from the Fermi-LAT IGRB observation The relatively short distance (<0.3 kpc) of the nearest UCMH implies that the Milky-Way halo may host many UCMHs, like the one causes the 1.4 TeV excess. All these UCMHs will emit gamma rays due to DM annihilation, and they should contribute to the diffuse gamma-ray background. Here, we use the Fermi-LAT measurements of the isotropic gamma-ray background (IGRB) (Ackermann et al. 2015) to set constraints on the UCMH model. We assume the UCMHs distribute in the Milky Way following an Einasto function (Springel et al. 2008), $$\begin{eqnarray*} \frac{{\rm d}N}{{\rm d}V}=N_0\, {\rm exp}\left[-\left(\frac{2}{\alpha }\right)\left[\left(\frac{R}{R_0}\right)^{\alpha }-1\right]\right], \end{eqnarray*}$$(7) where R represents the distance to the halo centre. We use the α, R0 parameters in Liang et al. (2017), which are determined by fitting the N-body simulation data of subhalos. To account for the 1.4 TeV excess, at least one UCMH should locate within the 0.3 kpc region, this corresponds to a UCMH number density of |$N_{\rm local}=1/({4}/{3}\pi d^3)$| (d = 0.3 or 0.05 kpc). The N0 in equation (7) thus can be determined by requiring the number density at R = 8.5 kpc equals Nlocal. For simplicity, all UCMHs are assumed to have the same annihilation rate |$\dot{Q}$| (thus the same UCMH mass) in our calculation. The contribution of the galactic UCMHs (from 0 to ∼300 kpc) are presented in Fig. 2 (dashed lines). The blue and red lines are for that the 1.4 TeV UCMH is at 0.05 kpc and 0.3 kpc respectively. As shown in the figure, the total flux of UCMHs is prominent in the energies around 1.4 TeV and is constrained by the IGRB observation. However, it is possible the real density is not as high as Nlocal and we are lucky that one UCMH is just located within 0.3 kpc distance. To not conflict with the IGRB observation, the number density must be reduced by >1 order of magnitude. According to Poisson statistics, to have a |$\gt 5{{\ \rm per\ cent}}$| chance observing the UCMH within 0.3 (0.05) kpc, the lower limits of the number density is ∼0.4 (95) kpc−3. In Fig. 1, we also show the expected gamma-ray flux for this number density. It is demonstrated that only the 0.3 kpc case can marginally survive from the IGRB constraints. Figure 2. Open in new tabDownload slide The Fermi-LAT measurements of IGRB (black points) and the expected gamma-ray spectrum of the 1.4 TeV UCMH model. The blue and red lines are for the 1.4 TeV UCMH being at 0.05 kpc and 0.3 kpc, respectively. The dashed lines are derived using a UCMH number density of Nlocal. The solid lines corresponds to the lower limits of the number density of having |$\gt 5{{\ \rm per\ cent}}$| chance to observe one UCMH within 0.3 kpc distance. Figure 2. Open in new tabDownload slide The Fermi-LAT measurements of IGRB (black points) and the expected gamma-ray spectrum of the 1.4 TeV UCMH model. The blue and red lines are for the 1.4 TeV UCMH being at 0.05 kpc and 0.3 kpc, respectively. The dashed lines are derived using a UCMH number density of Nlocal. The solid lines corresponds to the lower limits of the number density of having |$\gt 5{{\ \rm per\ cent}}$| chance to observe one UCMH within 0.3 kpc distance. 5.4 DM mini-spike around a nearby black hole The adiabatic growth of a BH may enhance the DM density around the region close to the BH and form a mini-spike. The electrons and positrons emitted from a nearby DM mini-spike may also account for the sharp 1.4 TeV peak (Huang et al. 2018; Chan & Lee 2019). The DM profile in the mini-spike is (Lacroix & Silk 2018) $$\begin{eqnarray*} \rho (r) = \left\lbrace \begin{array}{@{}l@{\quad }l@{}}0 & r \leqslant 2 R_{\mathrm{S}}, \\ \rho _{\mathrm{sat}} & 2 R_{\mathrm{S}} \lt r \leqslant R_{\mathrm{sat}} \\ \rho _{0} \left(\dfrac{r}{R_{\mathrm{sp}}} \right)^{-\gamma _{\mathrm{sp}}} & R_{\mathrm{sat}} \lt r \leqslant R_{\mathrm{sp}}, \end{array}\right., \end{eqnarray*}$$(8) with γsp = 9/4. The profile is similar to that of a UCMH and is point-like in the gamma-ray sky. Moreover, as we demonstrated in Section 3, once the annihilation rate is known by fitting to the electron spectrum, the expected gamma-ray flux is determined, no matter what density profile is. Thus, the discussion above applies for the case of a mini-spike around the nearby BH as well. Here, we discuss a specific source, A0620-00. It is the nearest black hole from the Earth and has previously been reported as a promising source for the 1.4 TeV peak (Chan & Lee 2019). The mass and distance of this BH are |$M_{\rm BH}=6.61\pm 0.25\, {\rm M}_\odot$| and |$d=1.06\pm 0.12\, {\rm kpc}$| (Cantrell et al. 2010). For a source of 1.06 kpc away, from equation (5), the expected gamma-ray flux would be only 10 per cent of that of a 0.1 kpc source. However, the cooling effect for the source at this distance cannot be fully ignored any more. To account for the e+e− excess, much higher annihilation rate is need. From Yuan et al. (2017), we see that the expected J-factor is rather larger than those of 100 pc sources, thus would also generate detectable gamma-ray signals. Here, we search the Fermi-LAT and HAWC observations on the direction of BH A0620-00. Fig. 3 is a Fermi-LAT TS map around A0620-00, which demonstrates the significance of existing a putative gamma-ray emission in each corresponding direction. No point sources are found with TS>9 (i.e. local significance of >3σ) within the |$0{_{.}^{\circ}}4$| region around the target. The HAWC gives only ∼−0.6σ in this direction. Our results thus do not favour A0620-00 as a source that generates the 1.4 TeV peak. In fact, Yuan et al. (2017) and Huang et al. (2018) have shown that a continuous injection source with |$d\approx 1.0\, {\rm kpc}$| cannot well fit the e+e− spectrum, since the cooling effect will make the width of the single injection peak wider than the observation. Figure 3. Open in new tabDownload slide 0.8 × 0.8 deg2 residual TS map in the direction of black hole A0620-00 (green point). No gamma-ray point source with TS>25 can be found in this region. Figure 3. Open in new tabDownload slide 0.8 × 0.8 deg2 residual TS map in the direction of black hole A0620-00 (green point). No gamma-ray point source with TS>25 can be found in this region. 6 SUMMARY While the existence of a DM subhalo that can account for the 1.4 TeV e+e− excess seems to be challenged by the gamma-ray observations, the UCMH provides an alternative solution. For such type of sources, even the expected gamma-ray flux exceeds the detection sensitivity of Fermi-LAT, it may hide among Fermi-LAT unassociated point sources and thus escape the constraints. In this work, we focus on discussing the accompanying gamma-ray signal in UCMH. By examining the Fermi-LAT and HAWC data, we find that at least a dozen sources have spectra consistent with the 1.4 TeV DM model and have not been detected in other wavelengths. Since the spectra of these sources are compatible with the DM signal, one of them may come from UCMH. It is supposed the Milky Way halo hosts many UCMHs. If all of them emit gamma rays from DM annihilation, they will contribute to the IGRB. By calculating the expected contribution to the IGRB, we find that to not conflict with the observation, a UCMH that can account for the 1.4 TeV excess has only |$\lesssim 5{{\ \rm per\ cent}}$| probability to be located within 0.3 kpc distance. Nevertheless, the DM annihilation within UCMH could still be an interpretation of the DAMPE 1.4 TeV peak, since it is possible one UCMH is just located nearby. We have also searched for gamma-ray emission in the direction of the nearest BH, A0620-00, which has previously been suggested as a promising source of 1.4 TeV excess. However, we do not find any significant signal from this source. Considering the significance of the tentative 1.4 TeV peak is still low, it may also be a statistical fluctuation. The most important thing at present is to verify the reality of the excess. Future telescope like LHAASO and CTA may help to confirm the true origin of the signal. If the significance of the 1.4 TeV peak keep increasing in the next release of DAMPE data, or it is confirmed by other instruments, we think at that time the sources listed in this works worth further notice. ACKNOWLEDGEMENTS This work has made use of data and software provided by the Fermi Science Support Center. This work is supported by the National Natural Science Foundation of China (Nos. 11851304, U1738136, 11533003, U1938106) and the Guangxi Science Foundation (2017AD22006, 2018GXNSFDA281033) and special funding for Guangxi distinguished professors. DATA AVAILABILITY The Fermi-LAT data underlying this paper are publicly available in the Fermi Science Support Center, at https://fermi.gsfc.nasa.gov/ssc/data/access/. 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TI - On the gamma-ray signals from UCMH/mini-spike accompanying the DAMPE 1.4 TeV e+e− excess
JO - Monthly Notices of the Royal Astronomical Society
DO - 10.1093/mnras/staa2092
DA - 2020-09-11
UR - https://www.deepdyve.com/lp/oxford-university-press/on-the-gamma-ray-signals-from-ucmh-mini-spike-accompanying-the-dampe-1-JRaFchtGpr
SP - 2486
EP - 2492
VL - 497
IS - 2
DP - DeepDyve
ER -