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PoS(ICRC2021)571 International th 12–23 July 2021 July 12–23 37 SICS CONFERENCE SICS CONFERENCE Berlin | Germany Berlin Berlin | Germany Cosmic Ray Conference Ray Cosmic Julien ∗ , c ICRC 2021 THE ASTROPARTICLE PHY ICRC 2021 THEASTROPARTICLE PHY https://pos.sissa.it/ Martin Stref, b ONLINE -wave) and the boost factor p b -wave and s Judit Pérez-Romero, a and Miguel A. Sánchez-Conde d Gaétan Facchinetti, a David Maurin [email protected] a International Cosmic Ray Conference (ICRC 2021) Presenter ∗ th Laboratoire Univers et Particules de Montpellier (LUPM),Eugène Bataillon, Université de 34095 Montpellier Montpellier & Cedex CNRS, 05, Place France Instituto de Física Teórica (IFT) UAM/CSIC, Universidad13-15, Autónoma 28049 de Madrid, Madrid, Spain Calle Nicolás Cabrera, Laboratoire d’Annecy-le-Vieux de Physique Théorique (LAPTh), UniversitéSavoie Grenoble Mont Alpes, Blanc, Université CNRS, F-74000 Annecy, France Laboratoire de Physique Subatomique & Cosmologie53 (LPSC), avenue Université des Grenoble Alpes, Martyrs, CNRS/IN2P3, 38026 Grenoble, France E-mail: Indirect searches with gamma raysdark matter set particle strong candidates. constraints Observations of oninteresting. dwarf the and properties Here clusters of we are self-annihilating especially revisitdependent cross-section the (Sommerfeld calculation enhanced, for of both the annihilation flux by considering a velocity- due to dark matter substructure.dramatic We enhancements show of that the the gamma-ray combinationbrightest flux, of targets in these and the two possibly sky. effects modify can the lead hierarchy to between the Copyright owned by the author(s) under the terms of the Creative Commons c a b d © Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). Lavalle, Thomas Lacroix, 37 July 12th – 23rd, 2021 Online – Berlin, Germany Classification of targets for gamma-ray darksearches matter with speed-dependent annihilation and substructure boost PoS(ICRC2021)571 (1) Martin Stref plays the role X , and the masses α ) X α c /( , where v -wave process which leads X p = v π α  4 √ = X g , S . Its shape depends on the partial wave i.e. ) × χ in the following). This long-range interaction 0 ) m 2 − 2 rel X v α 10 σ with coupling ( /( = φ φ (see e.g. [2]). Another interesting configuration arises if = m m X 2 rel rel α v = v ∝ σ φ  rel v of mass σ φ -wave) annihilation cross-section set by the relic abundance. However the s depends on the velocity through a parameter S -wave annihilation cross-section in the following way s can be evaluated by solving Schrödinger’s equation for an attractive Yukawa potential. The S This study is dedicated to the prediction of the astrophysical factor governing the DM-induced We consider the phenomenological scenario in which DM particles self-interact through the Astrophysical observations are a prime avenue to shed light on the nature of dark matter (DM), In the context of gamma-ray searches, most of the effort has been dedicated to the study of gamma-ray flux, including velocity dependence and subhalos.needed The for different the theoretical calculation ingredients mass are range presented (dwarf spheroidal in galaxies Sec.2. andWe galaxy investigate clusters) Several how are the targets considered particle of and models presented interesttargets and in in covering Sec.3. the Sec.4. different modeling This of proceedings subhalos is based impact on the Lacroix ranking et of al. these 20212. (to be published). Theoretical ingredients 2.1 Velocity-dependent annihilation exchange of a (light) mediator annihilation is mediated by a particle lighterthis than leads the to the DM. Sommerfeld In effect the which presencevelocity can of greatly dependence. an enhance attractive the potential, cross The section andside. phenomenology create a of Cold specific particle DM candidates canpopulation are also expected of be to substructures collapse complicated within on on galacticknown very to the DM small impact halos astrophysics scales predictions for which [3]. velocity-independent leads annihilation,given to however These to less a their attention small vast interplay has subhalos been with have velocity-dependent annihilation. long been modifies the where Sommerfeld factor and coupling through a parameter whether it is madegravity. of particles, In macroscopic the case objectto of or complementary particle it constraints DM is on candidates, the duesearches underlying indirect to in properties searches particular our of using have lack the proven multiple of particle toself-annihilate probes be [1]. candidate. understanding have a of led Gamma-ray powerful tool to constrain scenarios where thethe DM can simplest weakly interacting massivevelocity-independent ( particle (WIMP) scenario where the DM particle has a Classification of targets for speed-dependent annihilation 1. Introduction absence of any confirmedyears. detection has In lead particular, tosection which many a leads to broadening theoretical a of models richerannihilates phenomenology search predict through which a strategies we a scalar investigate in here. mediator, velocity-dependent annihilation the Forto annihilation proceeds a instance, recent through strong if cross- velocity a dependence the DM of dark fine structure constant (we fix PoS(ICRC2021)571 (3) (2) , and there 3 , Martin Stref v / rel 1 ì v are proportional 3 ∝ p d -wave annihilation 2 S p p − rel S v ) and rel s and ì v S v , ì / r . ( 1 f ì r 3 ∝ d over the subhalo parameter-space s ¹ s S  L = rel

ì v -wave. Although these factors have a 2 3 p − rel d v )

for an integer where rel v p n ( S 1 s S with ' ) with i 3 p rel 2 ) S / ì v 2 1 , n ' − ì r ( 2

s f 2 π S − rel /( -wave cross-section leads to a luminosity v s

6 ¹  h = ) s ì r S φ (  2 ' ρ rel ì ¹ v 3 φ  ∝ d ) s -wave and a different factor L rel s v , the Sommerfeld factor becomes almost independent of the velocity, except , this corresponds to the Coulomb regime, . ( 1 1 s

for S be the relative phase-space distribution function (pdf) of DM particles inside a M ) s   S ) 6 , there is again no enhancement rel , there is no enhancement φ v − ì v  1  rel 1 , ì v ì r 10 2 , (    ì  v r f ( / v v φ φ f 1     ¹ on a series of resonances at if is no dependence in if if if to Due to their close proximity (a few tens of kpc), their high DM density and low astrophysical To compute the enhancement of the annihilation rate induced by substructures, we use the Let • • • • background, dwarf spheroidal galaxies (dSphs) in the are among the most interesting density function and adding the contribution of the smooth DM component. 3. Targets 3.1 Dwarf spheroidal galaxies where the relative velocity moment isexpressions and computed approximations using are Eddington’s established inversion for methodcase. the [7]. Sommerfeld-enhanced The luminosity Similar of the full object is obtained by integrating complicated expression, different asymptotic regimes can be identified In practice, rather than computingapproximations the phase-space pdf for each subhalo, we make the following In practice, instead of numericallythe solving analytic Schrödinger’s solution equation available for for a a Yukawa Hulthén potential, potential we which use is very2.2 similar [4]. Dark matter subhalos and phase-space modeling analytical model of ref [5].of subhalos This (which model depends allows onIt to the relies compute concentration, the on mass parameter-space and theoreticaldistribution) density position) inputs function and inside from gravitational any cosmology given dynamics DM (Seth-Tormenprinciple (tidal halo halo. related effects). to mass the function, The kinetic decouplingand concentration minimal of is subhalo set the to mass, DM particle which6], [ is is in a free parameter ofsubhalo, the then model a Sommerfeld-enhanced Classification of targets for speed-dependent annihilation there is a factor PoS(ICRC2021)571 is so (4) 2 eff − ρ , which 10 1 '  v Martin Stref [9, 10]. The  φ 1  in the Coulomb regime. -factor can reached much φ J  we are in the Coulomb regime. 2 − 10 , , hence the -wave and subhalos are ignored, < ) s φ s φ  (  eff 2 ρ in1. Fig. We recall that when s -wave case, although the amplitude is strongly d φ does not depend on p  . s S . 4 o . l ¹ Ω d ∆Ω of this mass is DM. The rest is baryonic matter in the form of ¹ % = J -factor along a given line of sight (l.o.s) J in this case while φ  / -wave and the shape is slightly different. 1 s and up to 80 ∝

S M we are in the resonant regime and when 15 2 − -10 can be reached because the velocity dispersion is very low in these objects. This means 10 14 is an effective DM density. If the annihilation is v  > eff φ ρ  Galaxy clusters are the largest gravitationally-bound objects in the . Their masses are Elements related to astrophysics in the expression of the DM-induced gamma-ray flux are https://clumpy.gitlab.io/CLUMPY/ 1 -factor for the Sommerfeld case as a function of J when higher values compared to theresonances smooth because case. The enhancement can be very large even in-between that the resonant regime extends to much lower values of corresponds to rightmost part of eachdSphs panel, first there which is are shown no in Sommerfeld the enhancement.while upper the panel. Let dashed us curves The focus show solid the on curves result show assumingturned the all result off, the including subhalos DM subhalos is only smooth. provide a Whenand very Sommerfeld solid effect small is boost, curve of are order very a close. few tens In of a percent, dwarf and galaxy theThis without dashed can clumps, be we typically seen have onvalues of the dashed curves. However, the presence of subhalos implies much lower The phenomenology is essentially the same in the suppressed compared to equal to the true DM density, otherwise it has to be modified as discussed in Sec.2. We show the between 10 contained within the so-called Classification of targets for speed-dependent annihilation targets for DM indirectultra-faints. searches. In DSphs this aretwo study, separated ultra-faint we dSphs in pick ( two three II categories, classicaltargets and for Coma dSphs the DM Berenices) (, annihilation classical which [8]. Ursa were and foundfrom Minor In to the a and be the Markov among latter ) Chain the study, Monte and best the CarloDM DM (MCMC) density profile engine profile parameters in coupled were the to reconstructed dSphs the is CLUMPY modeled code using the3.2 Einasto profile. Galaxy clusters galaxies, gas and dust. Although someclusters gamma-ray emission still is constitute expected excellent due targets tothese cosmic-ray for objects activity, indirect since searches. the boost to DMWe the rely subhalos on annihilation ref play signal [11] is an and expected important pick toThe three in be galaxy DM much clusters profile (Coma, larger of than the and in clusters ) dSphs. are is for the subject modeled present by to study. the large NFW uncertainties, profile.analysis. hence Galaxy One we cluster estimate rely mass stems measurements from on X-ray twoSunyaev-Zeldovich measurements [12]. different ("hydro" mass) estimates while for the each other cluster is in based on our 4. Results where PoS(ICRC2021)571 1 2 2 10 10  no sub no sub , no sub φ , , no sub ,  no sub 1 , 1 no sub no sub , 10 , 10 no sub , Martin Stref Coma hydro Coma hydro Fornax hydro Fornax hydro Perseus hydro Perseus hydro Draco Draco Ursa Minor Sculptor Sculptor UMa II UMa II Coma Berenices 0 is significantly 0 10 10 1 dSphs 1 Fornax − φ , clusters -wave case and the right − J φ  -factors of the different  , s 10 10 J wave , reaching several orders of 2 2 - wave − φ - − p , the  p 10 φ 10  -wave with a different hierarchy p 3 3 − − = 0 = 0 10 10 β β gets lower, the annihilation in the most 4 4 − − φ  10 20 19 18 17 16 15 14 13 12 11 10 10 -wave case, with the amplitude being again 19 18 17 16 15 14 13 12 11

p

10 10 10 10 10 10 10 10 10 10 10

10 10 10 10 10 10 10 10 10 S

−

sr] cm [GeV J S −

sr] cm [GeV J

5 2 5 2 . As 5 2 2 10 10 UMaII -wave first, without subhalos, we see that for J s . If substructures are included, no sub no sub , no sub , , no sub , no sub < , 1 1 no sub no sub , , no sub Draco 10 10 , J Draco Draco Ursa Minor Ursa Minor Sculptor Sculptor UMa II UMa II Coma Berenices Coma Berenices Coma hydro Coma hydro Fornax hydro Fornax hydro Perseus hydro Perseus hydro Draco < . Going down to lower values of J , with and without subhalos. The top panels show the results for dSphs 0 0 φ 10 10  < IC10 J UMaII 1 1 dSphs J clusters − − φ φ ,   , -wave. Fornax < 10 10 s J wave < 2 2 wave - -factor of an object is shown for each of the source category we consider : − − - IC10 s J s J 10 10 IC10 < -wave. J p 3 3 − − = 0 = 0 10 10 β β -factor as a function of Fornax J J 4 4 − − 10 10 16 25 22 19 16 31 28 25 22 19 31 28 For galaxy clusters, which are shown in the bottom panel of1, Fig. the trend is the same but In2, Fig. the The interplay between the Sommerfeld effect and subhalos not only impacts the hierarchy

10 10 10 10 10 10 10 10 10 10 10 10

S S − −

cm [GeV J sr] cm [GeV J sr]

5 2 5 2 -wave annihilation. Even without Sommerfeld enhancement, the boost can be as high as 30 in the s case of the . The boost takes much larger values at low Figure 1: the effect is even more dramatic because the subhalo boost factor is much larger than in dSphs for Classification of targets for speed-dependent annihilation magnitude. Similar observations can be made in the and the bottom panels show thepanels results show for the . The left panels show the Fornax for the galaxydSphs, clusters, and Draco IC10 for for the the dIrrs. classical dSphs, Looking Ursa at Major II for the ultra-faints suppressed compared to we have targets get closer and closer.: The same here behavior we is have observed for massive objects (Fornax and IC10) get significantlythe boosted lightest and ones. catches up with the annihilation in boosted and gets very close to PoS(ICRC2021)571 2 10 ◦ 5 . no sub , Perseus = 0 1 factor of no sub 150 , no sub , no sub J 10 , fov UMa II Martin Stref , θ Fornax hydro Fornax hydro Draco Draco UMa II UMa II IC10 IC10 IC10 0 Fornax 10 (off-resonances). UMi 4 subhalos − Coma Berenices , 100 1 Coma 4 Sculptor Draco WLM [deg] − − φ 10  0 comparison 10 10 between the line of sight ψ , ' 0 ≈ (i.e. without Sommerfeld) ψ ) φ 2 . 1  − -wave case and the right panel s wave - 10 50  p (off res φ φ ,  NGC6822 3  − = 0 MW Classical dwarfs Ultrafaint dwarfs dIrrs Galaxy clusters 10 wave β - s 4 − 0 24 23 22 10 19 18 17 16 15 14 13 12 11

. The case

10 10 10

10 10 10 10 10 10 10 10 10

fov S 0 ,θ S ◦ −

−

[GeV ) ψ ( J sr] cm sr] cm [GeV J

5 2 5 5 2 . 0 6 2 10 ◦ 5 . no sub , Perseus 1 = 0 no sub 150 , no sub , no sub 10 , UMa II fov Fornax hydro Fornax hydro Draco Draco UMa II UMa II IC10 IC10 , θ IC10 0 Fornax 10 -factors of the various targets in this work and the expected foreground UMi J subhalos Coma Berenices 100 , 1 Coma Sculptor Draco WLM [deg] − φ  0 comparison 10 ψ , 2 − wave 10 - 50 s no Sommerfeld , NGC6822 3 − = 0 MW Classical dwarfs Ultrafaint dwarfs dIrrs Galaxy clusters 10 wave -factors comparison for all targets. The left panel shows the β - -wave case. J s Comparison between p 4 − 0 18 17 21 20 19 10 16 25 22 19 31 28

10 10 10 10 10

10 10 10 10 10 10

fov 0 S ,θ S −

−

J sr] cm [GeV ) ψ ( cm [GeV J sr]

5 2 2 5 We see that some targetsSommerfeld effect can in be plugged-in or above not. orleft For below panel, instance, the but Fornax is slightly MW slightly above the foreground below the right depending blue panel. on curve in whether the the is shown in the left panel while the right panel shows the results for from DM annihilation in the Milky Way halo. and the . The resulteach is object shown in as the the study. blue solid The line integration in angle3 Fig. is along with the Figure 3: shows the between targets of interesthalo but foreground annihilation. can This also annihilation impactsubhalos. is also We their have impacted computed detectability this by contribution Sommerfeld above as enhancement a the and function of Milky the angle Way (MW) Figure 2: Classification of targets for speed-dependent annihilation PoS(ICRC2021)571 ]. (2020) -wave p 02 (2005) 003, (2010) Martin Stref The 37 ]. 0508 JCAP , 1610.02233 (2008) 1685–1711, JCAP 391 , J. Phys. G , 1810.01680 (2017) 063003,[ 95 Robust cosmic-ray constraints on (2019) 061302,[ The First wimpy halos 99 A Global Analysis of Dark Matter Signals from 7 Mon. Not. Roy. Astron. Soc. Phys. Rev. D , , Phys. Rev. D , -factors for some of these objects and shown that the hierarchy in J Modeling dark matter subhalos in a constrained galaxy: Global ]. ]. ]. ]. Sommerfeld factor for arbitrary partial wave processes 0903.5307 1812.06986 0809.0898 astro-ph/0503387 012,[ 27 Dwarf Spheroidal Galaxies using 11 Years of Fermi-LAT Observations annihilating MeV dark matter Project: the subhalos of galactic halos [ 105009,[ mass and boosted annihilation profiles [ In this study, we have achieved a consistent calculation of the astrophysical factor for gamma- TL has received funding from the European Union’s Horizon 2020 research and innovation [1] S. Hoof, A. Geringer-Sameth and R. Trotta, [2] M. Boudaud, T. Lacroix, M. Stref and J. Lavalle, [3] V. Springel, J. Wang, M. Vogelsberger, A. Ludlow, A. Jenkins, A. Helmi et al., [6] A. M. Green, S. Hofmann and D. J. Schwarz, [5] M. Stref and J. Lavalle, [4] S. Cassel, ray searches including asubhalos. Sommerfeld-enhanced annihilation We cross-section have shown andexpected that the gamma-ray these flux effect two from of effects targets DM have of combine explicitly interest can computed such lead the as to dwarf a galaxies dramatic and increase galaxy clusters. of the We program under the Marie Skłodowska-Curie grant agreementand No. JPR 713366. is supported The by work the of Spanish TL,095161-B-I00, Agencia MASC Estatal de IFT Investigación through Centro the grants deMultiDark PGC2018- FPA2017-90566-REDC. Excelencia GF and Severo JL Ochoa areCE31-0006, the SEV-2016-0597, partly OCEVU Labex supported and (ANR-11-LABX-0060), the by national Red CNRS-INSU the programsand PNHE ANR Consolider PNCG, projectANR-18- and European Union’s Horizon 2020Sklodowska-Curie research grant and agreements innovation program No under 690575 the andby Marie CNRS-IN2P3 No and 674896 the – University inaddition of toAlpes. Montpellier. recurrent DM MS funding is is supported supported by by the the CNRS. University Grenobles References Classification of targets for speed-dependent annihilation 5. Conclusion terms of luminosity canforeground also annihilation be from the impacted. MW DMabove Finally, halo that we and foreground found have depending that compared on some the targets thesewe can value will luminosities be of discuss either to the how below these the particle or results physics impact parameters. the In constraints on future the works, DMAcknowledgments microscopic properties. PoS(ICRC2021)571 , (Sep, , 2018 Martin Stref CLUMPY : Dark matter ]. Comput. Phys. , signals from dark matter at ν (2015) 849–867, 453 1806.08639 (Apr, 2017) 3738–3761. (Dec, 2011) 011–011. -ray and γ 469 2011 ]. 8 (2019) 336–345,[ CLUMPY v3: Hicosmo – cosmology with a complete sample of 235 Anatomy of eddington-like inversion methods in the 1506.07628 Journal of Cosmology and Astroparticle Physics , Mon. Not. Roy. Astron. Soc. , fluxes from dark matter (sub-)structures ν Dark matter annihilation and decay in dwarf spheroidal galaxies: The -ray and γ (2016) 336–349,[ ]. Comput. Phys. Commun. 200 , 1504.02048 Monthly Notices of the Royal Astronomical Society galaxy clusters – i. data analysis, sample selection and luminosity–mass scaling relation all scales searches with cherenkov telescopes: nearby dwarfJournal galaxies of or Cosmology local and galaxy clusters? Astroparticle Physics Commun. classical and ultrafaint dSphs context of dark matter searches 2018) 040–040. [ Jeans analysis, [7] T. Lacroix, M. Stref and J. Lavalle, [8] V. Bonnivard et al., [9] V. Bonnivard, M. Hütten, E. Nezri, A. Charbonnier, C. Combet and D. Maurin, [12] G. Schellenberger and T. H. Reiprich, [10] M. Hütten, C. Combet and D. Maurin, [11] M. A. Sánchez-Conde, M. Cannoni, F. Zandanel, M. E. Gómez and F. Prada, Classification of targets for speed-dependent annihilation