# γ-ray and ν Searches for Dark-Matter Subhalos in the Milky Way with a Baryonic Potential

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## Abstract

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`CLUMPY`code. The latter is used to produce a thousand realizations of the $\gamma $-ray and $\nu $ sky. Compared to predictions based on DM only, we conclude a decrease of the flux of the brightest subhalo by a factor of 2 to 7 for annihilating DM and no impact on decaying DM: the discovery prospects or limits subhalos can set on DM candidates are affected by the same factor. This study also provides probability density functions for the distance, mass, and angular distribution of the brightest subhalo, among which the mass may hint at its nature: it is most likely a dwarf spheroidal galaxy in the case of strong tidal effects from the baryonic potential, whereas it is lighter and possibly a dark halo for DM only or less pronounced tidal effects.

## 1. Introduction

`CLUMPY`code [4,5,6] to generate $\gamma $-ray skymaps, accounting for the whole population of subhalos. For each combination of subhalo properties we explored, hundreds of skymap realizations were drawn, allowing us to calculate the average properties of the brightest clump. In the context of the future CTA $\gamma $-ray observatory [7] and its foreseen extragalactic survey, we concluded that the limits on DM set from this brightest clump should be “competitive and complementary to those based on long observation of a single bright dwarf spheroidal galaxy”.

`CLUMPY`. Section 3 lists the subhalo critical parameters, highlighting the very different spatial distributions considered in this analysis. Section 4 presents updated statistics of the subhalo population and provides probability density functions (PDFs) of the brightest subhalo’s properties (distance to the observer, mass, brightness, etc.). The analysis is performed for both annihilating DM [30,31,32] via the so-called J-factors, or decaying DM [33,34] (D-factors). We also show one realization of a subhalo skymap for all configurations considered. We conclude and briefly comment on the consequences for DM indirect detection limits in Section 5.

## 2. Important Quantities and Methodology

#### 2.1. $\gamma $-ray and $\nu $ Fluxes from Dark Matter

#### 2.2. Generating Skymaps with `CLUMPY` v3.0

`CLUMPY`code described in [4,5,6]. It is a flexible code that efficiently emulates the end-product of numerical simulations in terms of $\gamma $-ray and neutrino signals for DM annihilation or decay. It allows easy exploration of how results are affected when changing the properties of the DM halos.

`CLUMPY`v2.0 [5] was used for this purpose, to estimate the sensitivity of the CTA [1] and HAWC [27]$\gamma $-ray telescopes to galactic DM subhalos. Aside from galactic subhalo studies,

`CLUMPY`has also been used by several teams to model DM annihilation or decay in $\gamma $-rays or $\nu $ in many targets: dwarf spheroidal galaxies [37,38,39,40,41,42,43,44,45,46], the galactic halo [47,48,49], the Smith HI cloud [50], nearby galaxies [51], galaxy clusters [52,53,54], and also for the extragalactic diffuse emission [55].

`CLUMPY`v3.0 [6].3 For completeness, we recap below the main steps of the

`CLUMPY`calculation used for this work:

`CLUMPY`and the particle physics term: Equation (1) shows that the particle physics term and the astrophysical terms are decoupled.4 As the flux depends on the specific DM candidate chosen, we provide results in terms of J- and D-factors only;`CLUMPY`can easily be used to transform those into $\gamma $-ray or $\nu $ fluxes for any user-defined DM candidate (see`CLUMPY`’s online documentation5).`CLUMPY`and the astrophysics term: to calculate skymaps of $\mathrm{d}J/\mathrm{d}\mathsf{\Omega}$, one should rely in principle on Equation (2). However, this is impractical in terms of computing time, as ∼${10}^{14}$ subhalos are expected in a Milky Way-sized DM halo. This problem can be overcome by formally separating Equation (2) in an average and “resolved” component,$$\frac{\mathrm{d}{J}_{\mathrm{tot}}}{\mathrm{d}\mathsf{\Omega}}=\frac{\mathrm{d}{J}_{\mathrm{sm}}}{\mathrm{d}\mathsf{\Omega}}+\u2329\frac{\mathrm{d}{J}_{\mathrm{subs}}}{\mathrm{d}\mathsf{\Omega}}\u232a+\u2329\frac{\mathrm{d}{J}_{\mathrm{cross}-\mathrm{prod}}}{\mathrm{d}\mathsf{\Omega}}\u232a+\sum _{k=1}^{{N}_{\mathrm{subs}}^{\mathrm{drawn}}}\frac{\mathrm{d}{J}_{\mathrm{drawn}}^{k}}{\mathrm{d}\mathsf{\Omega}}.$$With this ansatz, only a limited number ${N}_{\mathrm{subs}}^{\mathrm{drawn}}$ of subhalos need to have their J-factor profiles calculated individually, while an average description is sought for the remaining “unresolved” DM. The criterion to discriminate between resolved and unresolved components often relies on a simple subhalo mass threshold, e.g., as done in works directly relying on numerical simulations [57] or their subhalo catalogs [58].`CLUMPY`has been developed to treat this problem in a more efficient way, acknowledging the fact that rather light, but close-by subhalos may show J-factors comparable to heavier, more distant objects. The`CLUMPY`approach relies on the notion that the overall DM signal fluctuates around an average description, $\langle {J}_{\mathrm{tot}}\rangle \pm {\sigma}_{{J}_{\mathrm{subs}}}$, and we refer to [4] for a detailed description of our criterion to accordingly discriminate between unresolved and resolved halos. For the purpose of this work (and also the previous [1]), this approach allows us to preselect halos likely to shine bright at Earth and to consider all decades down to the smallest subhalo masses in the calculation.

## 3. Modeling the Galactic Subhalo Distribution

#### 3.1. Fixed Subhalo-Related Quantities

- Index ${\alpha}_{m}$ of the power-law subhalo mass PDF $\mathrm{d}\mathcal{P}/\mathrm{d}m\propto {m}^{-{\alpha}_{m}}$ and subhalo mass range: We choose ${\alpha}_{m}=1.9$, ${m}_{\mathrm{min}}={10}^{-6}\phantom{\rule{0.166667em}{0ex}}{\mathrm{M}}_{\odot}$, and ${m}_{\mathrm{max}}=1.3\times {10}^{10}\phantom{\rule{0.166667em}{0ex}}{\mathrm{M}}_{\odot}$. The maximum clump mass for all models is set to ${10}^{-2}\times {M}_{200}$ of the NFW halo from Section 3.2.3. This is motivated by the fact that we do not consider the possibility of any subhalos heavier than the Magellanic clouds, the heaviest satellites of our galaxy. The minimal clump mass and ${\alpha}_{m}$ mostly affect the diffuse emission boost from unresolved halos. For a fixed normalization ${N}_{\mathrm{calib}}$, a steeper mass function (${\alpha}_{m}=2.0$) decreases the number of bright halos ($J\gtrsim {10}^{20}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{GeV}}^{2}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{-3}$) by not more than ∼30%.
- Subhalo density profile: We model all subhalos with a spherically symmetric NFW profile [65]. Using an Einasto profile [65,66] instead amounts to a global increase ∼2 of the number of subhalos per flux decade within the considered integration regions $\Delta \mathsf{\Omega}$. Please note that micro-halos with $m\ll {\mathrm{M}}_{\odot}$ may show steeper inner slopes [67,68,69]; however, we have found that these micro-halos do not provide new bright, resolved subhalo candidates [1].
- Level of sub-substructures: We do not consider an emission boost from substructure within subhalos. Such a boost from additional levels of substructure8 increases the number of subhalos per flux decade, with the largest increase of almost a factor 2 for the largest luminosities. Sub-substructures actually increase the signal in the outskirts of halos (see Figure 4 of [1]), the impact of which depends on the instrument angular resolution or containment angle used in the analysis. For instance, in [1], no impact was found for dark clumps within the angular resolution of CTA.

#### 3.2. The Spatial Distribution $\mathrm{d}\mathcal{P}/\mathrm{d}V$ of Subhalos

#### 3.2.1. Model #1: DM only (as Implemented in Hütten et al., 2016)

#### 3.2.2. Model #2: DM + Galactic Disk Potential (Numerical, Phat-ELVIS)

`CLUMPY`the normalization of the number of subhalos to ${N}_{\mathrm{calib}}={N}_{\mathrm{surviving}}=90$. In the same way as in the DM-only model # 1, we define and calculate subhalo masses based on their cosmological radii.

#### 3.2.3. Models #3 and #4: DM + Disk Potential (Semi-Analytical, SL17)

#### 3.2.4. $\mathrm{d}\mathcal{P}/\mathrm{d}V$ Model Comparison

## 4. Results

`CLUMPY`, we generate fullsky subhalo populations and corresponding J- and D-factors according to the models from Table 1. For all configurations, the distance between the Sun and the Galactic center is set to ${R}_{\odot}=8.21$ kpc [71]. We consider two estimations of the J-/D-factors, integrating either over the full angular extent of a subhalo or up to a radius of ${\alpha}_{\mathrm{int}}={0.5}^{\circ}$. Averages and PDFs are then obtained from a statistical sample of 1000 realizations of the subhalo population for each model.

#### 4.1. Subhalo Source Count Distributions

- Model #2 (Phat-ELVIS, red lines) predicts about a factor 5 less halos per flux decade than the Aquarius-like DM-only reference model #1. The average brightest halo (within ${0.5}^{\circ}$) is about a factor 4 fainter than expected for the DM-only case. This drastic decrease of bright objects is both attributed to the fact that the Phat-ELVIS simulations [10] find (i) overall less subhalos in Milky Way-like galactic halos (${N}_{\mathrm{calib}}=90$ vs. ${N}_{\mathrm{calib}}=300$) and (ii), no subhalos are found close to Earth in the innermost 30 kpc of the galactic halo.
- Model #3 (SL17, yellow lines) predicts almost the same abundance of bright halos as the DM-only model #1. Model #3 starts from an initial subhalo distribution biased towards the Galactic center following the overall DM distribution, and accounts for tidal subhalo disruption and stripping afterwards according to the semi-analytical model of [15]. With ${\u03f5}_{\mathrm{t}}=0.01$ few subhalos are affected. In turn, the DM-only model #1 already includes a subhalo distribution anti-biased towards the Galactic center in an evolved galactic halo according to the Aquarius simulations (although the considered fitting to the Aquarius simulations [74] does not account for a mass dependence of the halo depletion).
- Model #4 (SL17, green lines) applies a much stronger condition on tidal stripping and total depletion than the model #3 configuration within the semi-analytical approach of [15]. Illustratively, we calculate a total of $1.41\times {10}^{6}$ initial subhalos (in the full range between ${m}_{\mathrm{min}}={10}^{-6}\phantom{\rule{0.166667em}{0ex}}{\mathrm{M}}_{\odot}$ and ${m}_{\mathrm{max}}=1.3\times {10}^{10}\phantom{\rule{0.166667em}{0ex}}{\mathrm{M}}_{\odot}$) for the subhalo models #3 and #4, out of which 20,000 are completely disrupted for the model #3 (${\u03f5}_{\mathrm{t}}={10}^{-2}$). In contrast, 530,000 halos are disrupted for ${\u03f5}_{\mathrm{t}}=1$ in the model #4.13 In result, a factor 2 less halos are present above the lower end of the displayed brightness distributions, the ratio increasing for the brightest decades. Recall that surviving halos are truncated at the same tidal radius in models #3 and #4.

- Changing the signal integration region $\Delta \mathsf{\Omega}$ drastically impacts the collected signal, as the emission shows a much broader profile than for annihilation. This loss is most drastic for the brightest halos.
- For an integration angle of ${\alpha}_{\mathrm{int}}={0.5}^{\circ}$, all models are in remarkable agreement at the brightest end. For fainter flux decades and considering the signal over the full halos extent, models differ by a factor ∼5 (however, with a rather large spread in the D-factor PDF of the brightest halo in the individual models, see the later Figure 5). This suggests that predictions for the largest subhalo flux from decaying DM should be rather model-independent.

`HEALPix`resolution of ${N}_{\mathrm{side}}=1024$,

`CLUMPY`requires ∼$30\phantom{\rule{0.166667em}{0ex}}\mathrm{CPUh}$ for its computation in case of annihilation (∼$20\phantom{\rule{0.166667em}{0ex}}\mathrm{CPUh}$ in case of decay). Please note that we did not select the shown random sky realizations to reflect some particular average or extreme case. In Appendix A, we list some properties of the brightest objects in these maps, which can be compared to the average properties derived in the remainder of this section.

#### 4.2. Statistical Properties of the Brightest Halo

## 5. Conclusions

`CLUMPY`, and our results illustrate how this code can quickly be used to incorporate and exploit any progress made by numerical simulations and/or semi-analytical calculations. All computations and drawing of random realizations of the discussed models can be repeated at one’s own account. Also, the subhalo skymaps and catalogs shown here as illustration for the various models are available upon request.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Properties of the Brightest Subhalos in the Example Maps

**Table A1.**Properties of the brightest subhalos in the random realizations displayed in Figure 4.

Position in Map $(\mathit{l},\phantom{\rule{0.166667em}{0ex}}\mathit{b})$ | Distance ${\mathit{l}}^{\star}$ $\left[\mathbf{kpc}\right]$ | Mass ${\mathit{m}}^{\star}$ $\left[{\mathbf{M}}_{\odot}\right]$ | ${\mathit{J}}_{0.5{}^{\circ}}$ | ${\mathit{J}}_{\mathbf{tot}}$ | ${\mathit{D}}_{0.5{}^{\circ}}$ | ${\mathit{D}}_{\mathbf{tot}}$ | |
---|---|---|---|---|---|---|---|

$\left[{\mathbf{GeV}}^{2}\phantom{\rule{0.166667em}{0ex}}{\mathbf{cm}}^{-5}\right]$ | $\left[\mathbf{GeV}\phantom{\rule{0.166667em}{0ex}}{\mathbf{cm}}^{-2}\right]$ | ||||||

DM only | $(-54{}^{\circ},-13{}^{\circ})$ | $16.3$ | $4.0\times {10}^{9}$ | $1.8\times {10}^{20}$ | $5.5\times {10}^{20}$ | $1.1\times {10}^{19}$ | $1.8\times {10}^{21}$ |

Phat-ELVIS | $(-141{}^{\circ},+31{}^{\circ})$ | $42.2$ | $2.0\times {10}^{9}$ | $\mathbf{1.4}\times {\mathbf{10}}^{\mathbf{19}}$ | $\mathbf{2.3}\times {\mathbf{10}}^{\mathbf{19}}$ | $3.6\times {10}^{18}$ | $\mathbf{1.3}\times {\mathbf{10}}^{\mathbf{20}}$ |

$(+37{}^{\circ},+8{}^{\circ})$ | $69.5$ | $3.8\times {10}^{9}$ | $1.4\times {10}^{19}$ | $2.0\times {10}^{19}$ | $\mathbf{4.1}\times {\mathbf{10}}^{\mathbf{18}}$ | $9.2\times {10}^{19}$ | |

SL17, ${\u03f5}_{\mathrm{t}}={10}^{-2}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}$ | $(-19{}^{\circ},-73{}^{\circ})$ | $7.8$ | $3.7\times {10}^{6}$ | $\mathbf{3.3}\times {\mathbf{10}}^{\mathbf{19}}$ | $\mathbf{6.1}\times {\mathbf{10}}^{\mathbf{19}}$ | $2.3\times {10}^{18}$ | $7.1\times {10}^{18}$ |

$(-73{}^{\circ},+20{}^{\circ})$ | $54.8$ | $2.3\times {10}^{9}$ | $1.0\times {10}^{19}$ | $2.6\times {10}^{19}$ | $\mathbf{4.1}\times {\mathbf{10}}^{\mathbf{18}}$ | $\mathbf{9.0}\times {\mathbf{10}}^{\mathbf{19}}$ | |

SL17, ${\u03f5}_{\mathrm{t}}=1$ | $(+71{}^{\circ},-25{}^{\circ})$ | $30.1$ | $1.3\times {10}^{8}$ | $\mathbf{9.0}\times {\mathbf{10}}^{\mathbf{18}}$ | $\mathbf{1.5}\times {\mathbf{10}}^{\mathbf{19}}$ | $2.3\times {10}^{18}$ | $1.6\times {10}^{19}$ |

$(+93{}^{\circ},-50{}^{\circ})$ | $68.5$ | $3.4\times {10}^{9}$ | $5.2\times {10}^{18}$ | $1.4\times {10}^{19}$ | $\mathbf{3.4}\times {\mathbf{10}}^{\mathbf{18}}$ | $\mathbf{8.4}\times {\mathbf{10}}^{\mathbf{19}}$ |

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1. | We assume here the DM particle to be a Majorana particle, so that $\delta =2$ (for a Dirac, $\delta =4$). |

2. | |

3. | When releasing CLUMPY v3.0, we corrected a misprint that was present in v2.0, related to our implementation of the virial overdensity from [56]. This issue was responsible for obtaining in [1] about a factor 3 more subhalos than expected per flux decade (see full details in the CLUMPY documentation). We recall that in [1], we found that galactic variance is responsible for a factor $\lesssim 10$ uncertainty on the value of the brightest subhalo, and that other subhalo properties were responsible for another factor ∼6. Given these very large uncertainties, the conclusions on DM limits set from dark clumps with CLUMPY v2.0 are not qualitatively changed, but we urge users to rely on CLUMPY v3.0 for future studies. |

4. | Strictly speaking, this factorization holds true only for DM candidates for which $\langle \sigma v\rangle $ is independent of the velocity and consideration of small redshift cells, $\Delta z/z\ll 1$. |

5. | |

6. | The concentration is defined to be $c={r}_{\Delta}/{r}_{-2}$, with ${r}_{\Delta}$, taken to be the subhalo boundary, is the radius at which the mean subhalo density is $\Delta $ times the critical density (see, e.g., [6]), and ${r}_{-2}$ is the position in the subhalo for which the slope of the density is $-2$. We use $\Delta =200$ in this work. |

7. | This range was recently shown to be in agreement with the observed number of dwarf spheroidal galaxies SDSS corrected by the detection efficiency [59], alleviating the tension caused by the so-called missing satellite problem in CDM scenarios [60,61]. Given the minimal mass of subhalos, ${m}_{\mathrm{min}}$, ${N}_{\mathrm{calib}}$ can be used to calculate the mass fraction, ${f}_{\mathrm{DM}}$, of DM in subhalos. |

8. | As shown in [5] (see their Figure 1), only the first level of substructure significantly boosts the halo luminosity, the next levels bringing a few extra percent at most. |

9. | We still provide later the total DM profile for the semi-analytical configurations (model #3 and model #4) because it is one of the building blocks of the model. |

10. | The difference between using the space-dependent or field halo concentration was found to be a factor ∼2 larger on the brightest subhalo in [1]. |

11. | The Milky-Way-like halos in the Phat-ELVIS simulations have masses ranging from $7\times {10}^{11}\phantom{\rule{0.166667em}{0ex}}{\mathrm{M}}_{\odot}$ to $1.9\times {10}^{12}\phantom{\rule{0.166667em}{0ex}}{\mathrm{M}}_{\odot}$, and virial radii from 235 kpc to 329 kpc respectively. The fit above was performed on the radial range common to all host halos, namely from 0 to 235 kpc. The value of the parameters remain compatible at the one-sigma level when increasing the radial range to 329 kpc, or when cutting on masses above $5\times {10}^{6}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{M}}_{\odot}$. |

12. | We checked for convergence in order to obtain a complete ensemble of objects above these thresholds. |

13. | Please note that most drawn subhalos are disrupted at masses below a tidal mass of ${10}^{4}\phantom{\rule{0.166667em}{0ex}}{\mathrm{M}}_{\odot}$, the scale above which subhalos are shown in the later Figure 4. |

14. | Probability distributions were derived using a kernel density estimation (KDE) with an adaptive Gaussian kernel according to [87] (except $\mathrm{d}\mathcal{P}/\mathrm{d}(cos{\theta}^{\star})$, which was obtained from a histogram). To handle the boundary conditions of $\mathrm{d}\mathcal{P}/\mathrm{d}m(m>{m}_{\mathrm{max}}=1.3\times {10}^{10}\phantom{\rule{0.166667em}{0ex}}{\mathrm{M}}_{\odot})=0$ and $\mathrm{d}\mathcal{P}/\mathrm{d}V(R>{R}_{200}=231.7\phantom{\rule{0.166667em}{0ex}}\mathrm{kpc})=0$, we use the PyQt-Fit KDE implementation by P. Barbier de Reuille, https://pyqt-fit.readthedocs.io (not anymore maintained as of submission of the manuscript), which accounts for a renormalization algorithm at the boundary. Please note that for a precise power-law source count distribution, the PDF of ${J}^{\star}$/${D}^{\star}$ follows a Fréchet distribution, see App. B of [1]. |

**Figure 1.**Spatial PDFs of subhalos surviving interaction with the baryonic disk potential. (

**Left panel**): directly computed from the catalogs of the Phat-ELVIS simulations [10]. Dots correspond to the average over the 12 Milky-Way-like halos in the simulations, with error bars obtained from the dispersion over the 12 halos. The best-fit model (red curve) has been computed using the parametrization given by Equation (5). (

**Right panel**): SL17 model for various mass ranges (line styles) and values of ${\u03f5}_{\mathrm{t}}$ (colors). See Figure 2 for a comparison between all $\mathrm{d}\mathcal{P}/\mathrm{d}V$ models used in the analysis.

**Figure 2.**The four spatial PDFs of subhalos considered in this work: SL17 models for subhalos with $m>{10}^{6}\phantom{\rule{0.166667em}{0ex}}{\mathrm{M}}_{\odot}$ (yellow and green), PDF based on the Phat-ELVIS simulation (red) [10], and on the Aquarius simulation (blue) [74]. To highlight the behavior at low radii where tidal effects are the most relevant, the curves are shifted to match the value of $\mathrm{d}\mathcal{P}/\mathrm{d}V(231.7\phantom{\rule{0.166667em}{0ex}}\mathrm{kpc})$ in the Phat-ELVIS configuration.

**Figure 3.**Cumulative source count distribution of galactic subhalos (full sky, averaged over 1000 simulations) for all configurations gathered in Table 1. (

**Left panel**): annihilating DM. (

**Right panel**): decaying DM. In both panels, the solid lines show the distribution of the J-factors within ${\alpha}_{\mathrm{int}}={0.5}^{\circ}$, whereas the dashed lines for integrating over the full halo extents up to ${r}_{200}$ or ${r}_{\mathrm{t}}$.

**Figure 4.**One random realization of the Galactic DM subhalo sky (all subhalos above ${10}^{4}\phantom{\rule{0.277778em}{0ex}}{\mathrm{M}}_{\odot}$, ignoring the smooth contribution) in case of annihilation (

**left**) or decay (

**right**), derived from the models gathered in Table 1. Maps are drawn in galactic coordinates (Mollweide projection) with $(l,b)=(0,0)$ at their centers. (

**From top to bottom**): Model #1 emulating numerical DM-only simulations (1,214,313 drawn halos); model #2 emulating the Phat-ELVIS simulations [10] (364,064 drawn halos); and the semi-analytical models #3 (subhalos more resilient against tidal disruption, 549,572 surviving halos) and #4 (less subhalos surviving tidal destruction, 546,096 surviving halos) according to SL17 [15]. The displayed maps (

`fits`format, 50 MB in file size) can, along with their subhalo catalogs, be provided upon request. In Appendix A, we list some properties of the brightest objects in these maps.

**Figure 5.**PDFs of the $\gamma $-ray (or $\nu $) brightest galactic subhalo properties for the four investigated models. (

**Left panel**): annihilating DM. (

**Right panel**): decaying DM. Solid lines show the statistics for only the emission from the innermost ${\alpha}_{\mathrm{int}}={0.5}^{\circ}$ of a subhalo, dashed lines the emission over the full extent.

**Table 1.**Subhalo parameters for the models investigated in this study, with model #1 based on results of DM-only numerical simulations, while models #2 to #4 are different implementations of DM subhalos post-processed in the Milky Way halo and baryonic disk potential. For models #2, #3, and #4, we also show the number of surviving subhalos with tidal masses between ${10}^{8}\phantom{\rule{0.166667em}{0ex}}{\mathrm{M}}_{\odot}$ and ${10}^{10}\phantom{\rule{0.166667em}{0ex}}{\mathrm{M}}_{\odot}$. See Section 3 for details and parameters common to all subhalo configurations.

Model #1 | Model #2 | Model #3 | Model #4 | |
---|---|---|---|---|

$\frac{\mathrm{d}\mathcal{P}}{\mathrm{d}V}$ | Aquarius [74] | Phat-ELVIS [10] | SL17 [15] with ${\u03f5}_{\mathrm{t}}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}{10}^{-2}$ | SL 17 [15] with ${\u03f5}_{\mathrm{t}}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}1$ |

Einasto | Sigmoid-Einasto Equation (5) | $\propto {\rho}_{\mathrm{sm}}$ | $\propto {\rho}_{\mathrm{sm}}$ | |

${\alpha}_{E}=0.68$ | ${\alpha}_{E}=0.68$ | NFW ${}^{\star}$ | NFW ${}^{\star}$ | |

${r}_{-2}=199$ kpc | ${r}_{-2}=128$ kpc | ${r}_{-2}={r}_{\mathrm{s}}=19.6$ kpc ${}^{\star}$ | ${r}_{-2}={r}_{\mathrm{s}}=19.6$ kpc ${}^{\star}$ | |

- | ${r}_{0}=29.2$ kpc | - | - | |

- | ${r}_{c}=4.24$ kpc | - | - | |

${N}_{\mathrm{calib}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}$ | 300 | - | 276 ${}^{\star}$ | 276 ${}^{\star}$ |

${N}_{\mathrm{surviving}}$ | - | 90 | $114\pm 11$ | $112\pm 10$ |

$c(m)$ | Moliné et al. [75] | Moliné et al. [75] | Sánchez-Conde & Prada [63] | Sánchez-Conde & Prada [63] |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Hütten, M.; Stref, M.; Combet, C.; Lavalle, J.; Maurin, D.
*γ*-ray and *ν* Searches for Dark-Matter Subhalos in the Milky Way with a Baryonic Potential. *Galaxies* **2019**, *7*, 60.
https://doi.org/10.3390/galaxies7020060

**AMA Style**

Hütten M, Stref M, Combet C, Lavalle J, Maurin D.
*γ*-ray and *ν* Searches for Dark-Matter Subhalos in the Milky Way with a Baryonic Potential. *Galaxies*. 2019; 7(2):60.
https://doi.org/10.3390/galaxies7020060

**Chicago/Turabian Style**

Hütten, Moritz, Martin Stref, Céline Combet, Julien Lavalle, and David Maurin.
2019. "*γ*-ray and *ν* Searches for Dark-Matter Subhalos in the Milky Way with a Baryonic Potential" *Galaxies* 7, no. 2: 60.
https://doi.org/10.3390/galaxies7020060