- freely available
Galaxies 2020, 8(1), 5; https://doi.org/10.3390/galaxies8010005
2. HAWC Unidentified Sources
2.1. HAWC and the TeV Sky
2.2. Target Selection
- Why HAWC?—HAWC is currently the only VHE observatory able to survey a significant fraction of the whole sky. Indeed, the combination of its 1.5 sr FoV, Earth rotation and location in Mexican soil, above the Equator, makes it possible to observe 2/3 of the sky every day.2 In contrast, IACTs are pointing telescopes, i.e., they need to know the location of the sources in advance and, thus, just point towards specific targets. For the purposes of this work, it becomes critical to have observations of a large fraction of the sky. This is so because we adopt the methodology introduced in  to set constraints on the DM annihilation parameter space using unIDs. The method is based on a comparison between the number of catalogued unID sources and subhalo predictions derived from N-body cosmological simulations. Large fractions of the sky, observed with a nearly uniform exposure, will allow for a more accurate comparison to N-body simulations, as we can derive a more robust statistical determination of the subhalo annihilation fluxes for significantly large sky areas. We remind that these fluxes are proportional to the so-called J-factor:
- Why high latitude?CDM predicts the existence of DM subhalos at all Galactic latitudes distributed nearly isotropically from the Sun’s position in the Galaxy. On the other hand, the majority of Galactic VHE astrophysical sources, such as pulsars, binaries, supernova remnants and pulsar wind nebulae, are expected to cluster heavily along the Galactic plane, where most of the stars and gas reside. Since many of these objects are expected to also be hidden among the pool of unIDs awaiting for a proper classification, we expect the distribution of unIDs to peak around zero Galactic latitude as well (as already discussed in Figure 1). For our purposes, these low-latitude sources only add contamination to our sample of potential DM subhalo candidates. Therefore, we apply a cut in our analysis at Galactic latitudes . For consistency, this cut will also need to be done on our predicted subhalo distribution. On average, our Galactic cut removes only ∼11% of the simulated subhalos, while 87% of 2HWC unIDs are left out. Actually, in practice we cut a larger region in the N-body simulation in order to match the 2/3 sky coverage of HAWC, and in this way we have a totally fair one-to-one comparison among observed and simulated sky.
2.3. 2HWC J1040+308 as a DM Subhalo Candidate
- Spatial extension—Spatial extension has been hailed as a “smoking gun” for DM annihilation [24,25,26,47]. Indeed, low-mass yet sufficiently close DM subhalos may be expected to appear as extended unID sources. 2HWC J1040+308 is found to be spatially extended in HAWC data with a radius of . This fact is even more notable for the case of very high latitude sources like this one (), as sources at high latitudes are typically extragalactic and thus the majority of them are expected to be point-like. Indeed, it would be hard to explain all these features with a single astrophysical source – AGNs would appear as point-like sources, while Galactic sources could appear as extended, yet this source’s high latitude would imply a small distance and thus it would be surprising not to have a detection in any other wavelengths. On the other hand, as these unIDs correspond to very faint sources near the detection threshold, it is currently unclear whether they would appear as extended, even if being actual DM subhalos, as the DM annihilation flux profile decreases very rapidly with distance to the subhalo center.
- Multi-wavelength search—As already mentioned, dark satellites are not massive enough to retain baryons and, as a result, they are not expected to shine at any wavelengths due to astrophysical processes. However, gamma-ray emission is expected to happen should these objects be composed of WIMP DM.3 A dedicated search at different wavelengths was performed for 2HWC J1040+308, with null results. In particular, a combined search in less energetic gamma rays with Fermi-LAT and VERITAS was performed in , with no detection. An additional search can be performed with the SSDC online tool,4 where no significant emission at lower energies is found.
- Heavy WIMP mass—It is interesting to note that a joint analysis of Fermi LAT , VERITAS  and HAWC data was recently done in  and no gamma-ray emission was reported for 2HWC J1040+308 in the comparatively lower energy range covered by the LAT and VERITAS. This is so despite the fact that 2HWC J1040+308 exhibits a hard spectrum with a photon spectral index of in the HAWC energy range , which would in principle make a detection at low energies easier to realize. If interpreted in a DM scenario, these results suggest heavy, TeV WIMP masses as we would not expect a detection by Fermi LAT or VERITAS only in case of significantly high values of the WIMP mass, for which a DM spectrum beyond the range of sensitivity of these two instruments would be generated. Also, interestingly, this unID slightly prefers a fit to a “Cutoff Power Law” instead of a “Simple Power Law” , which is a parametric form that better reproduces a typical DM annihilation spectrum [22,23]. Heavy WIMPs are well motivated [55,56,57] and, probably, favoured in the light of current DM constraints in the usual (velocity-averaged annihilation cross section) vs. (WIMP mass) parameter space: IACTs are still far from being able to probe the thermal relic cross section values  for large, TeV WIMP masses, while for much lighter, (GeV) masses there are already robust and strong constraints, e.g., [23,59].
3. DM Constraints
3.1. Minimum Detection Flux
4. Summary and Conclusions
Conflicts of Interest
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In fact, HAWC applies a zenith cut of , which for a daily exposure translates in 8.4sr, corresponding exactly to 66.85% of the sky.
This is so because, by default, this quantity is computed for a source spectrum with a power law index , while the DM is better parametrized by a “Power Law with SuperExponential Cutoff” , where the index and cutoff energy vary over the annihilation channel and WIMP mass.
This sensitivity is computed for the Crab, which is located at DEC, while our source is at instead. Fortunately, the HAWC sensitivity for both locations is expected to be very similar .
We note that, should we have had more than one unID, we would have computed a mean value after averaging the corresponding differential sensitivities for each source’s declination.
The spectral index is reported to have an uncertainty . We checked that this uncertainty translates into a factor ∼4 uncertainty in at most (factor 2 when compared to the benchmark ).
The J-factor of our brightest subhalo is comparable to the one typically quoted for dwarf spheroidal satellite galaxies (see e.g., ), which are expected to be well above the extragalactic isotropic DM-induced gamma ray background. On the other hand, the value of the DM-induced Galactic diffuse emission is comparable to the isotropic contribution at high latitudes , and therefore also negligible compared to the brightest subhalo J-factor. Finally, the boost due to Galactic unresolved substructure contributing to the diffuse emission in the line of sight of this unID is expected to be at the level of a few percent and, thus, not relevant here. The boost due to substructures is only particularly important when integrating the subhalo signal for the whole host halo; see e.g., the discussions and results in .
Namely the lack of both the HAWC IRFs and a Galactic diffuse TeV emission model.
We note that tidal stripping is implicitly included in our simulations. Yet, we note that the mentioned works claim that the disruption of a large fraction of low-mass subhalos in simulations may be artificial and numerical in origin—if this was indeed the case, the distribution of J-factors of the entire subhalo population would surely reach larger values, as we would expect more and closer-to-Earth subhalos. Therefore, our results are conservative, as the DM limits would become even more stringent for resilient subhalos.
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