Search for gamma-ray emission from the 12 nearby dwarf spheroidal galaxies with 12 years of Fermi-LAT data

Many astrophysical observations suggest that there is a large amount of dark matter (DM) in the universe. According to the latest observation results, non-baryonic cold dark matter (DM) constitutes $\sim$ 84% of the matter density of the Universe Ade et al. (2016). The nature of DM particles is still unknown and the most promising DM candidates are weakly interacting massive particles (WIMPs). WIMPs can annihilate or decay into Standard Model (SM) particles and finally produce GeV-TeV $\gamma$-rays or cosmic rays Jungman et al. (1996); Bertone et al. (2005); Hooper and Profumo (2007); Feng (2010); Evans et al. (2004). The primary aim of the dark matter indirect detection is to identify these products from a dark matter origin through astronomical experiments such as the Fermi Large Area Telescope (Fermi-LAT Atwood et al. (2009)) and the Dark Matter Particle Explorer (DAMPE Chang et al. (2017); Ambrosi et al. (2017)).

The Milky Way dwarf spheroidal (dSph) galaxy is considered to be one of the most promising targets for indirect detection of DM. The reasons include that they are close to us ($<100\,{\rm kpc}$ for many of them) and the kinematic observations show that they are DM-dominated systems. In addition, benefit from the lack of astrophysical $\gamma$-ray production mechanisms Lake (1990); Baltz and Wai (2004); Strigari (2013), the diffuse $\gamma$-ray background for searching for DM signal with dSphs is very low. For a long time, no potential evidence of DM signal was found in the direction of dSphs and based on the non-detection people have set very strong constraints on the mass $m_{\chi}$ and the annihilation cross section $\left<\sigma v\right>$ of the particle DM Ackermann et al. (2011); Geringer-Sameth and Koushiappas (2011); Cholis and Salucci (2012); Tsai et al. (2013); Ackermann et al. (2014); Zhao et al. (2016); Geringer-Sameth et al. (2015); Ackermann et al. (2015). Especially, the stacked analysis of 15 dSphs with Fermi-LAT Pass 8 data excludes the thermal DM particle of the mass $<$ 100 GeV Ackermann et al. (2015).

N-body cosmological simulations suggested that there are many dSphs in the Milky Way halo. In the past few years, more than 20 new dSphs and candidates were found by several newly launched optical imaging surveys Bechtol et al. (2015); Drlica-Wagner et al. (2015b); Laevens et al. (2015a, b); Kim et al. (2015); Homma et al. (2016, 2017); Drlica-Wagner et al. (2016); Torrealba et al. (2016), making the total number of discovered dSphs/candidates is over 50. Many groups have searched for the $\gamma$-ray emission from these newly discovered dSphs¹¹1Hereafter we use the term dSph to express both identified dSphs and candidates for brevity. with Fermi-LAT data Geringer-Sameth et al. (2015b); Hooper and Linden (2015); Drlica-Wagner et al. (2015a); Li et al. (2016); Albert et al. (2017); Liang et al. (2016). Although no significant signals were robustly found, very weak $\gamma$-ray signals were reported in the directions of Reticulum II Geringer-Sameth et al. (2015b); Hooper and Linden (2015); Drlica-Wagner et al. (2015a); Albert et al. (2017); Li et al. (2018), Tucana III Li et al. (2016); Albert et al. (2017) and Tucana II Bhattacharjee et al. (2019). More intriguingly, these tentative emission spectra resemble the Galactic GeV excess reported in Hooper and Goodenough (2011); Gordon and Macias (2013); Hooper and Slatyer (2013); Daylan et al. (2016); Zhou et al. (2015); Calore et al. (2015); Huang et al. (2016); Ackermann et al. (2017); Abdughani et al. (2021).

In a previous work (Li et al. (2018), hereafter L18), we have studied the $\gamma$-ray emission of the 12 nearest dSphs at distances $\leq$ 50 kpc and found out that there are weak $\gamma$-ray excesses in several sources. In particular, the local significance of the $\gamma$-ray signal in Reticulum II is $>$ 3$\sigma$ and the significance is increasing with time (i.e., having a temporal behavior like a true steady source). Moreover, the combination analysis of the 12 sources yields a local test statistic (TS, see Eq. (2) for its definition) value of $\sim 18.4$ of the tentative $\gamma$-ray emission. From then on, more data have been accumulated and the new analysis software and background templates of Fermi-LAT are released. If the weak excess reported in L18 is a real signal (no matter astrophysical or DM origin), the local significance for the combined analysis is expected to increasing to the value of TS $\sim 25$ with the observation of 3 more years. Therefore, in this work we use the latest Fermi-LAT software as well as background models to search for $\gamma$-ray emission from the 12 nearby dSphs with 12 years of Fermi-LAT Pass 8 data. We aims to examine the existing tentative signals and search for new possible signals. The sample is listed in Table 1.

We use twelve years (i.e. from 2008 October 27 to 2020 October 27) of Fermi-LAT Pass 8 data in 500 MeV to 500 GeV. In order to remove the effect of the Earth’s limb, we reject the $\gamma$ events with zenith angle greater than $100^{\circ}$. Meanwhile, the quality-filter cuts (DATA_QUAL==1 && LAT_CONFIG==1) are applied to ensure the data can be used for scientific analysis. We take a $5^{\circ}$ region of interest (ROI) for each target. The latest version of Fermitools is employed to analyze the Fermi-LAT data. The script make4FGLxml.py²²2https://fermi.gsfc.nasa.gov/ssc/data/analysis/user/python3/make4FGLxml.py is used to generate the background models, with all 4FGL-DR2³³3https://fermi.gsfc.nasa.gov/ssc/data/access/lat/10yr_catalog/ sources within 10^∘ of the center of each target and the latest diffuse models (i.e gll_iem_v07.fits and iso_P8R3_SOURCE_V3_v1.txt) included. Due to the lack of information about the spatial expansion of the dark matter halos in the twelve dSphs, we model them as point-like sources.

Firstly, a standard unbinned likelihood analysis⁴⁴4https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/likelihood_tutorial.html is applied to get the best-fit parameters for the background sources. During the likelihood analysis, the parameters of all the 4FGL-DR2 sources within ROI, as well as the normalizations of the two diffuse backgrounds are set free. Secondly, we apply a likelihood profile method to derive the TS value and flux upper limit of the potential $\gamma$-ray emission for each target. We divided the whole data set in the energy range of 500 MeV - 500 GeV into 24 logarithmically-spaced energy bins. For each energy bin $k$, we derive the relation $L_{k}(f_{k})$ between the likelihood $L_{k}$ and the target’s flux $f_{k}$. A power-law spectral model ($dN/dE\propto E^{-\Gamma}$) with $\Gamma$=2 Ackermann et al. (2015) is used to model the putative dSph source. In order to get better sensitivity, we also apply an unbinned likelihood analysis to generate the likelihood profile. The likelihood profile can then be used to scan a series of DM masses and different annihilation channels in later analysis.

A broadband likelihood function for DM models with parameter $\bm{\alpha}$ can be obtained by multiplying the bin-by-bin likelihoods together,

The analysis method here is similar to that developed in Ackermann et al. (2011); Tsai et al. (2013); Ackermann et al. (2014) and more details can be found in these articles. The test statistic (TS) is used to quantify the significance of the target sources, which is defined as Mattox et al. (1996)

where the $L_{\rm bkg}$ and $L_{\rm dsph}$ are the best-fit likelihood values for the background-only model and the model containing a putative dsph, respectively.

The dSphs are good targets for DM search because the kinematic observations show that they are DM-dominated objects. The expected $\gamma$-ray flux from DM annihilation is expressed as Jungman et al. (1996); Bertone et al. (2005); Hooper and Profumo (2007); Feng (2010)

where ${m_{\chi}}$, ${\left<{\sigma}v\right>}$, $dN_{\gamma}/dE_{\gamma}$ are the DM particle mass, the velocity-averaged DM annihilation cross section and the differential $\gamma$-ray spectrum per annihilation. In this paper, the DM spectra are obtained from PPP4DMID Cirelli et al. (2011). The term

is the line-of-sight integral of the square of the DM density (i.e., the so-called J-factor).

In this section, we search for the $\gamma$-ray emission from each of the 12 dSphs. We use the likelihood profile method to scan a range of DM masses from 6 GeV to 10 TeV for two typical DM annihilation channels (i.e., ${b\bar{b}}$ and ${\tau^{+}\tau^{-}}$). The TS values as a function of DM mass are presented in Fig. 1. Even though much more data and the latest background models are considered in our work, no significant (i.e., $\rm TS>25$) signals are found in our analyses and most of the sources result in ${\rm TS}\sim 0$ (see Table 1). However, the local significances of the $\gamma$-ray emissions in the directions of three dSphs (i.e., Reticulum II, Bootes II, Willman 1) are $>$ 2$\sigma$. The most significant excess appears in the direction of Reticulum II (${\rm TS}\sim 11$, i.e. the local significance is $>$ 3.0$\sigma$), coinciding with previous results Geringer-Sameth et al. (2015b); Hooper and Linden (2015); Drlica-Wagner et al. (2015a); Albert et al. (2017); Li et al. (2018). The modeling of a power-law spectrum (i.e., $dN/dE\propto E^{-2}$) to the tentative $\gamma$-ray signals yields similar results. The maximal TS values for both PL and DM models are summarized in Table 1. In the following, we will investigate the three sources, Reticulum II, Bootes II and Willman 1, more detailedly in Section IV.

We also perform a combined analysis of these 12 objects. For the analysis method, we refer readers to the Sec. III B of L18 and the references therein for more details. The combined analysis can improve the sensitivity of the analysis by stacking multiple sources, and can take into account whether the signal strength in individual dSph matching the J-factor of the source. In L18, we find that the combination of the 12 nearest ($<50$ kpc) dwarf galaxies shows a possible signal of TS$\sim$18.4. We examine this tentative signal here. More specifically, if the signal is physically real (no matter astrophysical or DM origin), then adding 3 more years of data the TS value is expected to reach $\sim$25. However, in our analysis of the 12-year data, the TS value drops to $\sim$9.3 ($\sim$10.0) for $b\bar{b}$ ($\tau^{+}\tau^{-}$). The above results are based on J-factors from Simon et al. (2015) and Geringer-Sameth et al. (2015a). As mentioned above, for the combined analysis, we obtain a high significance only when the tentative gamma-ray excess from every source is consistent with its expected J-factor. It is very important to accurately determine the J-factors of dSphs for the combined analysis. Therefore, we also investigate how the results will change by using the J-factor values in Evans et al. (2016) or Sanders et al. (2016). These works include effects like flattening, and for some sources they give J-factor values different from Simon et al. (2015) and Geringer-Sameth et al. (2015a). With the Evans et al. (2016) and Sanders et al. (2016) J-factors, we obtain TS values of 7.4 (8.0) and 9.0 (9.7) for the $b\bar{b}$ ($\tau^{+}\tau^{-}$) channel, which are similar to the above results. Such a result is likely not supportive of the DM origin. The excess, if not due to the statistical fluctuations, should be contributed by variable astrophysical sources.

The Milky Way dwarf spheroidal galaxies are dominated by DM and are ideal objects for indirect detection of DM signals. Currently, no significant $\gamma$-ray signals have been found in dSphs and people only reported weak possible ’excesses’ from some dSphs Geringer-Sameth et al. (2015b); Hooper and Linden (2015); Drlica-Wagner et al. (2015a); Albert et al. (2017); Li et al. (2018, 2016); Bhattacharjee et al. (2019). No matter due to DM annihilation or astrophysical process, the discovery of $\gamma$-ray signals in dSphs is an important progress in our understanding of this type of objects, which motivates ongoing efforts to search for such emission. In this paper, we performed a comprehensive $\gamma$-ray analysis on the Fermi-LAT observation to the 12 nearest dSphs (including candidates), which is an update of our previous work Li et al. (2018). We use longer dataset and the latest Fermi-LAT software and the latest background models to carry out the analysis aiming to examine the tentative $\gamma$-ray excesses reported previously.

We find no significant ($>5\sigma$) $\gamma$-ray signals but just very weak $\gamma$-ray excesses in the direction of Reticulum II, Bootes II and Willman 1, for which the largest TS values are $\sim$10.9, $\sim$ 6.4 and $\sim$7.6 in the scenario of DM annihilation, respectively. In the past, Reticulum II had attracted wide attention since it displays the most significant, though still weak, $\gamma$-ray signal among all dSphs/candidates. However, with the 12-year Fermi-LAT data we find that the position of the weak excess is significantly away from the center of Reticulum II any more, which strongly suggests that the excess is irrelevant to the dark matter annihilation. Other clues disfavoring a DM origin of the excess include: the decline of the TS value in the new analysis (compared to previous works), a sudden increase of the photons above 10 GeV in recent years. Reticulum II has a half-light radius of $r_{\rm h}\approx 55$ pc. The offset by an angular of $0.15^{\circ}$ corresponds to a radius of $\sim 83$ pc, which is comparable with $r_{\rm h}$. We suggest that the GeV emission with a TS value of $\sim 22.0$ has the regular astrophysical origin. It is however unclear whether this “new” source is within Reticulum II or not.

For Bootes II and Willman 1, they are the first time being reported to have mild $\gamma$-ray excesses. Due to the faintness of the excesses, we can not determine their origin at this time. They may be from astrophysical processes, DM annihilations or, most probably, background fluctuations. Even so, considering the dark matter origin of the GeV excess from Reticulum II is not supported by observation, at present these two targets are the most promising ones. It is therefore worth to pay more attention to them. The Fermi-LAT and other operating/future $\gamma$-ray telescopes Galper et al. (2013); Zhang et al. (2014)⁵⁵5http://www2.yukawa.kyoto-u.ac.jp/~mmgw2019/slide/5th/Fan.pdf may reveal the nature of these tentative signals in the future.