JHEP07(2020)081 b Springer June 9, 2020 July 13, 2020 May 28, 2020 : : : February 10, 2020 : Revised Accepted , Published Received and Matthew Talia b,a Published for SISSA by https://doi.org/10.1007/JHEP07(2020)081 [email protected] , Leszek Roszkowski b [email protected] , . 3 Ekaterina Karukes, a 2001.09156 The Authors. c Cosmology of Theories beyond the SM, Beyond Standard Model

We use the state-of-the-art high-resolution cosmological simulations by Illus- , [email protected] National Centre for NuclearPasteura Research, 7, Warsaw 02-093, Poland AstroCeNT, Nicolaus Copernicus Astronomical Centerul. Polish Rektorska Academy 4, of Warsaw Sciences, 00-614,E-mail: Poland [email protected] b a Open Access Article funded by SCOAP dependence on the astrophysical uncertainties will become significantly reduced. Keywords: ArXiv ePrint: using electron scattering inmatter germanium search is and strongly silicon affectedheavier targets. by dark these matter, We uncertainties, especially find unliketo in nuclear that the recoil multiple sub-GeV scattering searches electron-hole dark for cross-section modes,lower is for ionization also which thresholds weaker. the not sensitivity Therefore, only by projected improving sensitivities the will sensitivity to be boosted but also the Abstract: trisTNG to derive thelike our velocity Milky distribution Way and andings find local a to density substantial examine spread the of in sensitivity dark both to quantities. matter the dark Next in matter we galaxies velocity use profile our of find- underground searches Andrzej Hryczuk, Impact of uncertainties indirect the detection halo of velocity sub-GeV profile dark on matter JHEP07(2020)081 2 ] to infer lo- 6 – 4 6 ] for earlier work). As we shall see, in 8 ], where the latter is based on the recent 3 – 1 4 – 1 – 2 8 ]). Even though our results can be applied to this case as well, 7 1 The search program for dark matter detection has widened up considerably in recent In this paper we use the cosmological simulations of IllustrisTNG [ 2.1 Selection of2.2 MW-like galaxies Dark matter velocity distributions years. This is especiallybeen true on on WIMPs the (weaklyweak direct interacting scale. detection massive front, particles) More where withtion recently the techniques mass a applicable primary around to lot focus and sub-GeV of had above DM. effort the These include, has but been are dedicated not to limited to developing electron novel detec- searches of heavy —detailed of discussion a in few [ GeV,in or this more work — wesub-GeV DM focus dark based on matter on a via nuclear previouslythis electron recoils basically scattering detection (see, unexplored (see technique e.g., [ impact DMplay a on halo a direct properties, significant detection role. especially of its velocity distribution, start to cal properties of thefindings DM to halo examine structure the of impactsearches. of MW-like Until recently the galaxies significant estimated and effortent astrophysical was subsequently assumptions devoted uncertainties apply about to on studying the our direct the local DM implications DM of density and differ- the velocity profile for the direct detection often been based on numericalrecently suffered simulations of from lacking large to scaleimplementation account structures. of for These, the its however, baryonic until role.with component, or state-of-the-art an Only baryonic oversimplified very physicsaccurately recently simulate effects Milky progress included Way (MW)-like in allowed galaxies. hydrodynamical for simulations sufficient precision to Our limited understanding of the darkconstitutes matter (DM) one halo of structure, the both largest localastrophysical sources and observations of Galactic, present uncertainty many in challenges direct inand and determining velocity the indirect mass, DM profile density, searches. of shape dark As results matter from (see, the e.g., Gaia [ satellite), the method of choice for studying DM halo properties has 1 Introduction 3 Uncertainties in sub-GeV DM4 electron recoil Discussion and conclusions Contents 1 Introduction 2 Dark matter velocity distributions from IllustrisTNG simulation JHEP07(2020)081 ]. 52 – (2.1) ] and ]. The 48 36 55 , – 35 53 ], topological in- 20 – ], either for simplicity we apply our findings 18 43 3 ] excitations in crystals, 32 , , = 544 km/s. esc esc esc v v ≥ we construct and discuss several v < v v 2 (taken to be the local circular speed,
2 0 0 v /v 2 ] and magnon [ ], superconductors [ v 17 − 31 – ]. Sub-GeV DM can be searched for also via , 9 – 2 – 25 30 – exp 23 N 0 ], an extension to the Illustris simulations [ ( ) in the Galactic rest frame and truncated at the escape ] proposed recently. 6 – 42 4 ) = – v ( 37 ], through dissociation or excitation in molecules [ gal f peak speed 34 ], single phonon [ , 29 33 – 26 provides discussion of the results and conclusions. 4 ] and Dirac materials [ ]. Nevertheless, in recent years by using more realistic high resolution cos- 22 , 47 is a normalization factor. The local circular speed is usually assumed to be – 21 44 N A departure from this commonly assumed model changes the predicted event rate in This paper consists of two main parts: in section = 220 km/s and the commonly adopted escape speed is 0 distribution functions for some selected halos. 2.1 Selection ofThe MW-like IllustrisTNG galaxies project is anamic publicly cosmological available simulations suite [ of state-of-the-art magneto-hydrody- mological simulations, which includematter baryonic velocity physics distributions actually effects, agree it rather wellspeed was with of shown the the SHM. that Yet, Maxwellian the the distribution localIn dark and circular this the escape section, velocity we mayproject. focus well be We on first different investigation [ introduce ofselection the criteria the general used to MW-like properties identify galaxies of the MW the from analogues. used the We simulation IllustrisTNG then and present the describe resulting the velocity from what isof normally the assumed. DM halo Onecosmological is way simulations. to to examine For accesshave the example, shown the dark the that information matter DM-only the on distribution velocity simulationsshape distributions of the of [ have the properties structure substantial MW formation deviations analogues from in a Maxwellian the where v direct detection experiments. In fact, the true dark matter distribution could be different velocity distribution with thehereinafter dispersion referred velocity to as speed from the Galaxy, As outlined in the introduction,estimating dark matter direct velocity dark distribution matter isdark a detection matter crucial in halo ingredient the for model Milky followsor Way. the to Most Standard Halo studies provide Model assume aisothermal, (SHM) that platform [ spherical the dark for halo comparison with among an different isotropic experiments. Maxwell-Boltzmann (MB) The dark SHM matter is an DM profiles inferred from theto Illustris study their simulation, effect while on in electrontargets. section recoil Section searches of DM with sub-GeV mass in semiconductor 2 Dark matter velocity distributions from IllustrisTNG simulation sulators [ the Migdal effect [ in superfluid helium [ also through other methods [ transitions: in atoms and semiconductors [ JHEP07(2020)081 ]; 64 8159 . . The ]. This , where 10 65 12 = 0 10 1, as not to 10 8 × 5 × 6 , σ ∗ 2 6 M 677 ]) with respect to ]. We then select 6 .

/ 57 66

M gas / = 0. For more details, = 0 ∗ M /M z M 6 200 , h 6 M 03 . 10 0486 6 . 10 11 × , respectively. = 0 5 10 .

], the MW-mass galaxies of the Illus- b × M 60 Ω 5 6 , 1 10 × 3089 . 5 – 3 – . ]. We also look at the gaseous mass to stellar mass = 0 = 7 63 box. The baryonic and dark matter mass resolutions m 3 DM m and 7 Mpc) .

], namely Ω 110 M 56 6 ≈ 10 /h × 4 . 9667. IllustrisTNG is evolved using the moving mesh hydrodynamics code . ]. Furthermore, as it was shown in [ = 1 68 and we end up with 164 galaxies. 7, i.e., those stars that have significant (positive) rotational support. Here we is defined as the mass enclosed within the sphere that contains a mean density . ] and it contains a number of improvements of sub-grid physics models (e.g. . 62 6 0 – = 0 200 = 0 58 S baryon among those 340 galaxiescomponent. we In identify order galaxiesonly to that galaxies do have that so a contain we substantial > more follow stellar than the disc approach 50%also of of require ref. that stars [ selected withz galaxies the do circularity not parameter have any significant merger after redshift is related to the factsimulation, that see the for effects more of details blackfraction [ hole that feedback we are choose too to dominanthave in very be TNG poor/reach in gas the galaxies. following range: At this 0 step we end up with 340 galaxies; 200 times the criticalassumed density. mass The range, MW for mass the compilation is of usuallywithin recent estimated MW 2456 to mass galaxies be estimates identified within seestellar in the e.g. mass the [ within previous the stepmass following we mass range select range: is the slightly ones 2 lower that than have that the usually inferred from MW, see e.g. [ we identify all galaxiesM in the mass range , ]. n 5 For each galaxy in the sample, we align the coordinate system with the principal axes. In order to identify simulated galaxies which satisfy MW observational constraints we In this paper we make use of the highest (to date) resolution version of the IllustrisTNG m These halo mass cuts were selected to better match MW-like galaxies in TNG100 simulations, as stressed • • • 63 1 We then select DM particles in torus, along the planein [ in the stellar disc, around the solar adopt the following criteria: study. project, which is TNG100. Fromanalogues the in suite of a TNG100 (75 simulationsare we select candidate MW in the observed galaxies, suchand as high the redshift, stellar the masssee fraction function [ of and dark the matter sizetrisTNG within distribution reproduce at galaxies low at adequately thematter distribution observed in MW the simulated rotationin MW-mass the galaxies curve, dark is this matter realistic are and suggests properly the that modelled. baryonic effects the That makes them of particular relevance for our laboration 2015, XIII [ and AREPO [ models for stellar andthe AGN original feedback, Illustris as project. well These as simulations black are hole able growth to [ reproduce many key relations cosmological parameters were chosen to be those derived from the analysis of the Planck col- JHEP07(2020)081 (2.2) 1, and in our ≤ = [181–238] km/s 2 χ 0 v ), is normalised to unity v ), by ( v f ( 2 kpc. This region contains a ˜ f  ) to perform a fit to the resultant , ) v 2.1 ( ˜ f 20% of galaxies in our sample can be v Ω ∼ d = [435–558] km/s. The peak speeds of the Z 2 – 4 – esc v v ) while the escape speed is taken to be the highest is an infinitesimal solid angle around the direction ) = 2.1 v v ( Ω f d ]) or used zoom-in simulations where a few halos are preselected and 70 ) = 1. Here v ( ˜ f ]. The relatively large spread in the speed distributions owes to the fact we present the local dark matter speed distributions in the Galactic rest v 3 52 ]), we believe that our choice is still sufficient to examine our main task which 1 d = 8 kpc, with both radial and vertical extents 69 700–900 dark matter “particles”. ) = 1, and is related to the velocity distribution, R – v

( ∼ R 67 , 3 dvf The derived ranges are consistent with, though somewhat larger than, those found, for In figure R . We then use MB distribution introduced in eq. ( IllustrisTNG100 simulations employ a simulationPrevious box studies size of of the dark roughlyused matter 100 simulations Mpc velocity with distribution side higher in length. resolution cosmological (e.g.length simulations EAGLE in either simulations reference with [ a boxthen of re-simulated 25 Mpc with side a higher resolution. Therefore, statistically the larger cosmological the potential welldefinition of does all not of alter the the main particles results of in theexample, the paper. in halo. [ that We in have this verified work that welower resolution find using simulation many within this more a halos larger that cosmological volume. fulfill the The point selection here criteria is due that to the using a in the speed distribution.and The the SHM escape peak speedsdistribution speeds are are are found in in by the fitting thespeed range eq. range ( of of anydefinition particle of observed the in latter would the be torus to choose around the the speed Sun’s of the location. particle needed to An escape alternative from fuller sample would likelyrelevance produce to a this analysis. broadened range of the astrophysicalframe parameters for of the 36velocity distribution. MW-like halos As can selected be from seen in the the figure, TNG100 there simulations is quite that large exhibit halo-to-halo variation MB e.g. [ is to examine the effectsub-GeV of astrophysical dark uncertainties matter on via projectedeffect electron sensitivities of recoil. of detecting the While it fullercurrent would paper sample be but of interesting in DM to any velocity investigate case the distributions, it is this likely is to beyond only further the strengthen scope our of findings the since the v DM velocity distribution.well described We by find the thatfurther MB only analysis velocity distribution, we i.e. restrictactual have ourselves DM the to resulting velocity this distribution choice. function While of there the are MW arguments has that a the more complicated form (see, as such that total of 2.2 Dark matter velocityTo distributions derive the dark matterparticles distribution in we the compute torus the defined average above. speed distribution The of speed DM distribution, radius, JHEP07(2020)081 1 700 of the peak 2 600 500 SHM v0=181 km/s vesc=435 km/s SHM v0=238 km/s vesc=558 km/s SHM v0=202 km/s vesc=502 km/s SHM v0=220 km/s vesc=544 km/s . The resulting local velocity profiles 400 1 [km/s] v – 5 – 300 ]. 71 200 . Additionally, for each case we calculate the local dark matter 1 100 0 in green and red, respectively. We also define the median values 002 001 000 003 005 004 . The histograms of the local dark matter speed distribution in the galactic rest frame

......

1

0 0 0 0 0 0 − [(km ) v ( f ] s) / 1 Nevertheless, it would be interesting to cross-check our results within the sameIn suite order to study the impact of inferred ranges of the speed distributions on the direct The median values are not specific to a particular galaxy since we define them as medians among the 2 density in the torus region,are that first we of also our list in main table results of this work. velocities/densities of the selected 36 galaxies. in figure speed and the escapein velocity, the blue. corresponding We refer velocity to distributionmedian them is and as shown MIN, maximal in MED expected and figure present strength MAX the profiles, of results as the in they table signal correspond in to minimal, direct detection experiments. We of simulations but using aof higher resolution TNG50 box. become This publicly can available become [ possible once theDM results searches we choose the halos with the minimum and the maximum peak speeds, shown and green solid lines represent(MED) the best-fit and Maxwellian maximum distribution for (MAX)the the peak MIN minimum (MIN), speed and median MAX values, distributions respectively. are The highlighted. histograms corresponding to volume is assumed the moreidentified. galaxies it will contain and the more MW-like galaxies can be Figure 1 for the 36 hydrodynamical TNG100 Milky-Way-like halos selected by our analysis. The red, blue JHEP07(2020)081 e 3 m , ] the (3.1) 2 | 10 ) e q, E ( crystal f | 2 ) which corresponds to ] q ) contains information 1 eV, and so allows for ( 3 e 2 ∼ F /q cm  1 / q, E )) ( e ∝ 0.31 0.33 0.23 ) [GeV q, E q ( ( crystal χ f ρ F min is given in events/kg/day by [ v ( is the number of unit cells in the crystal 4 η e q E cell ], could affect the projected sensitivities in a non- [km/s]  N parameterizes the strength of the interaction, 558 502 435 79 q e esc – 6 – σ ln v d e E ln d Z 238 202 181 [km/s] 2 ) 0 χ v 2 χ m + m e ) = 1 is equal to the cross-section for an elastic scattering of DM m q ( ( MIN MED MAX Name α F e ¯ ]. These studies accommodated a wide range of circular and escape σ are the local density and mass of the DM particle, respectively, and 78 cell χ – N m 72 χ χ ρ m ) follows a symmetric MB distribution, and v is the fine structure constant and ¯ = ( χ . The best-fit values of the Maxwellian distribution of the local DM speed distribution and f α ρ The scattering DM-electron rate in a semiconductor, assuming that DM speed distri- This is of course an idealized model of the properties of the DM halo. More detailed modelling including Note, however, that the escape velocity from our IllustrisTNG-inferred MIN profile is substantially crystal 4 3 R lower which can haveexperiments some as well. non-negligible impact on limits onlocal low-mass effects, WIMPs e.g., in gravitationaltrivial nuclear focusing way. recoil of However, based this theastrophysical is Sun uncertainties, not which [ expected come to fromthis change a effect significantly wide is our range beyond of the conclusions considered scope about MB of the profile this magnitude parameters. work. of Studying target, which in the case of on a free electron.electron-DM scattering We through also a light consider mediator. the case where where is the mass ofabout the the electronic electron. structure of the The material, crystal form factor, bution following: However, nuclear recoil experiments areFor insensitive such to light dark DM matterrecoils, one in which of the can sub-GeV the provide range. semiconductors. most a For promising strong silicon detection signal anddetection techniques through germanium of is this electron dark gap based ionization matter is on even in typically as electron small light band-gap as hundreds of keV. in the previous sectionof to astrophysical direct uncertainties detection on searchesarea, the of with sub-GeV sub-GeV most studies dark dark so matter. matterexperiments far focusing range The [ on is impact WIMP a detectionvelocities through largely compatible standard unexplored nuclear with recoil the calculations given in the Illustris simulation in this work. the corresponding escape velocityTNG100 as MW-like well halos. as average dark matter density in the torus3 region of the Uncertainties in sub-GeVAs DM an electron illustrative recoil and timely example we apply the DM speed distribution profiles found Table 1 JHEP07(2020)081 ] ex- (3.4) (3.2) (3.3) 80 and mo- e E as a function of . Hence, energy , and the number 0 Q ε v since it represents the Q = 240 km/s such that we E , v ) min . v , χ will be approximately given by the q  − m q 2 v ionization threshold gap + E is the electron velocity which is typically ε e )Θ ( q − v e E ( e v ) such that g E v – 7 – 3 ) = v min  is a function of the electron energy e d v . The stark contrast between electron excitation ( e η E Z min q, E v , where ( for silicon and germanium are 1.11 eV and 0.67 eV, e ]. Among other considerations, improvements in leak- = 1 + ], we define the v ) = e 81 ) takes only integer values for Q 10 min gap m v min E 3.4 v ≈ ( η q ). With this consideration, the astrophysical properties of the halo , E e v E , + , is also determined to be 3.6 eV and 2.9 eV for silicon and germanium, q to the electron, additional secondary scatterings redistribute this energy ε v e ( momentum and energy f E q ≡ ) v ( g For example, the DAMIC experiment that is currently running at SNOLAB [ The interaction between an incoming DM particle and an electron in the crystal is in To calculate the rate for the detector we must first boost the DM velocity with the level of leakage currentbe (produced very by low thermal in the excitationage prototype in current run the reduction [ crystal) throughin demonstrated operation reaching to low temperature thresholds. and Hence,properties material in on quality this multiple is study thresholds. we imperative examine the consequences of halo DM gap, denoted by respectively. The expressiontotal ( number of electron-holeparameter pairs in produced calculating experimental for sensitivity a curves single for direct DM detection. interaction.pects to reach This a threshold is as low a as 2–3 key electrons in a total of 1 kg of detector with its current where the energyrespectively. band The energy gaps needed to produce an additional electron-hole pair above the band initial energy between lower-lying electron orfall hole below energy a states. certain energyof Eventually threshold total the for pairs secondary electron-hole generated scatterings pairand is following production, what the conventions is in measured.the [ electron Assuming energy pair creation is linear in energy, an order of magnitudetransitions to larger states than above the thethe band DM circular gap velocity are velocity profile. sensitive of to the the distribution halo, around thefact tail a of rather complicated process. It is understood that after the DM particle deposits the This determines the minimum speed DMtransferring particles required to excite electrons inand the nuclear crystal, recoil based experimentsthan is the a fact nucleon. that the Therefore,momentum electron the of is momentum much the lighter transfer electron and faster where, through energy conservation, mentum transfer average Earth velocity relativedefine to the DM halo,are taken then to encapsulated be by the function JHEP07(2020)081 4 (b) and right e σ corresponding plots that is achievable (for 6 we compare normalized Q for silicon and in figure 2 and 3 ). For light DM masses near 5 3.3 24 eV. Despite interacting with a & , translates to more extended tails e 0 v ]). E 10 ] for the electron wave-functions and energy 82 – 8 – [ . This leads to higher expected rates, with the the impact of the velocity profile is quite significant, ] in accordance with the plane wave self-consistent e E 10 [ (a) ) = 1 form factor and in figures q ( QEdark the uncertainty reaches a constant, since the minimal velocity F χ m Quantum ESPRESSO . Left panels show the projected limits on the cross-section ¯ is utilized to numerically compute the crystal form factors for both cases, 2 /q ) code in 1 ∝ ) QEdark q PWscf ( What is worth stressing is that: The final results for projected 95% C.L. sensitivities for a 1 kg-year exposure with the To illustrate the impact of different velocity profiles in figure To calculate the direct detection limits for silicon and germanium targets, we employ F well as — from the point— of extreme view of MIN predicted and sensitivity of MAXof DM profiles. this direct work detection These experiments and profiles can amountto be quantify, to for adopted first the in of first updated the time,DM direct the two searches. astrophysical detection main uncertainties analyses. results of Next the sub-GeV we electron used recoil them 4 Discussion and conclusions In this paper we analyzed theand results obtained of the the recent local IllustrisTNG DM hydrodynamical halo simulation properties. We identified the resulting best fit (MED) as more detailed discussion of the backgrounds see [ and is comparable to thethe change between lower consecutive the electron-hole pair electron-hole thresholds,only pair and the threshold overall sensitivity is but experimentally also achievable, the the robustness better of the is detection not method. the detection thresholds thethe uncertainty circular in and the sensitivity escapethe grows velocity precise significantly of position where the of both projected DM the sensitivities profile minimum reachable are contribute mass sizableunderstanding calculated for that effects. under it a the is particular This effectively pair assumption shifts parameterized threshold. of by the no The value background, of with the for germanium targets for for show the relative sizethe of limit the of uncertainty very dueessentially large becomes to independent the of DM the density DM and mass, see velocity eq. profile. ( In moving 3d-shell electrons that dominatelarger at momentum around transfer with thethe DM smaller particle, thresholds. their contributions are not significant for astrophysical uncertainties taken into account are given in figure event rates for the MINand (green), two MED (blue) different andprofiles, DM MAX parametrized mass (red) cases, mostly values. forin by Ge the the The and Si value electron large targets difference of energy difference being the distribution in more the pronouncedshape in velocity of the tails the higher of rate ionization histogram these thresholds. for The germanium characteristic (bottom right panel) is a result of the fast- the publicly available code field ( levels. and then subsequently the total scattering rate and sensitivity curves. JHEP07(2020)081 , 1 �� �� �� �� �� � �� = � ��� �� �� = � ��� χ � χ �� � � �� �� � � �� �� � [��] [��] � � � ���)=��� �(� ��� �(�)=��� � � � �� �� � � � ; only electron energies to the � ���������� ���������(�) ���������� ���������(�) �� �� 4 � � � � � and � 3 � � � =1 GeV. The color coding is as in figure � � . In many electron recoil based detec- -� -� -� -� -� -� -� -� χ e �� ��

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m m ���� �� ������ ���� ���� �� ������ ���� ] / / [ ] / / [ ∼ χ m – 9 – , the velocity profile of DM can play a significant �� e �� �� �� m �� �  �� �� �� = �� ��� = �� ��� χ � χ χ �� m � � �� �� � � �� �� � [��] [��] � � � ���)=��� �(� � � ��� �(�)=��� � =10 MeV and the right ones for χ �� �� � � m � � ���������� ���������(�) ���������� ���������(�) �� �� � � � � � the impact of the velocity profile is to shift the DM minimal mass threshold, and . Normalized event rate vs. electron energy and ionization threshold (number of electron- � � (a) � � � � Qualitatively, based on experience with nuclear recoil based searches, one would expect -� -� -� -� -� -� -� -� that the effect is most pronounced for

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���� �� ������ ���� ���� �� ������ ���� ] / / [ ] / / [ the measurable signal even for that: (b) tion techniques, however, because of their sensitivity to the energy deposition in generating the left ones are for corresponding to the central MEDare (blue), normalized MAX to (red) the and firstpair bin MIN of (green) ionization the velocity thresholds MED profiles. as distribution.right All will The of events be vertical a lines shown given indicate below line the electron-hole are in sufficient figures to produce a given number of pairs. Figure 2 hole pairs). The top panels show germanium target, while the bottom ones silicon target, whereas JHEP07(2020)081 -47% -56% +397% +174% +108% +62% -9% -29% -48% -69% +249% +183% +99% +63% -10% -26% 4 4 10 10 1 pair 1 pair 5 pairs 3 pairs 5 pairs 3 pairs 10 pairs 10 pairs 3 : 1 (gray), 3 3 � ��-���� � ��-���� Si,F(q)=1 ����(�)=� Q 10 10 2 2 10 10 [MeV] [MeV] χ χ m m 1 1 10 10 0 0 10 10 8 4 2 1 8 4 2 1

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but for germanium target. MED MIN MAX MED MIN MAX σ / } σ σ { σ / } σ σ { , , 3 4 4 – 10 – 10 10 3 3 � ��-���� � ��-���� Si,F(q)=1 Ge,F(q)=1 10 10 . The same as figure 2 2 10 10 [MeV] [MeV] 10 pairs χ χ 10 pairs m m 5 pairs 5 pairs 1 1 Figure 4 3 pairs 3 pairs 10 10 1 pair 1 pair 0 0 . The projected 95% C.L. sensitivities (left panel) and the size of the astrophysical 10 10 -40 -41 -38 -39 -37 -40 -41 -42 -37 -38 -39 -36 Quantitatively, our results show that the uncertainty reaches more than an order of ) = 1. The results are given for four different values of ionization threshold

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cm ( 2 2 measuring only the directexact effect value of of single themore recoil energy closely or resembling transfer, absorption, the suffer known without from case sensitivity much of to nuclear smaller the recoils. astrophysicalmagnitude uncertainties, for two most studied semiconductor targets, silicon and germanium. More role. We expect thistentially also to detectors be using Dirac the materials case or for superconductors. not In only contrast, experiments semiconductor-based detectors, but po- central MED profile. InIn all the the right cases panel theto the difference the size MED in of profile, the the andthe local uncertainty on best-fit DM is the case. density right shown is hand as taken side the into of ratio account. the of frame the also MIN as and the percentage MAX difference profiles from Figure 3 uncertainty (right panel) forF a silicon(blue), target with 5 DM (orange)correspond interaction and to described 10 the by (light MIN the green) (green) form electron-hole and factor MAX pairs. (red) velocity In profiles, all while cases the the dotted lines limiting show solid the lines JHEP07(2020)081 -58% -65% +557% +291% +148% +69% -13% -41% -64% -77% +333% +262% +125% +79% -20% -35% 4 4 2 2 10 10 1 pair 1 pair 5 pairs 3 pairs 5 pairs 3 pairs 10 pairs 10 pairs � ��-���� � ��-���� Si,F(q)~1q Ge,F(q)~1q 1000 the sensitivity 1000 2 /q 1 100 100 ∝ [MeV] [MeV] χ χ ) m m q form factor. form factor. ( 2 2 F 10 /q /q 10 1 1 (8–16) depending on the target ∝ ∝ O ) ) q q 100 MeV), the sensitivity difference ( ( 1 1 F F & χ 8 4 2 1 8 4 2 1

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MED MIN MAX MED MIN MAX σ / } σ σ { σ / } σ σ { , , but for but for 4 3 4 4 – 11 – 2 2 10 10 � ��-���� � ��-���� Si,F(q)~1q Ge,F(q)~1q 1000 1000 ) = 1, while other form factors favoring interactions with q ( F 100 100 . The same as figure . The same as figure [MeV] [MeV] pairs χ χ m m 5 pairs 5 pairs 10 3 pairs 10 3 pairs 1 pair Figure 6 Figure 5 1 pair (12–30). Moreover, for lower DM masses the effect is much larger, due to O 1 1 -41 -37 -38 -39 -40 -40 -41 -42 -37 -38 -39 -36 Therefore, to summarize, the second main result of this work underlines how crucial it

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2 2 of the not yetsensitive well to known the dark lowest matter possible halo ionization profile thresholds. is much less severe if one is able to be difference is higher sensitivity of the tail of the velocity distribution. is to develop background reduction techniquesnot for only experiments the based sensitivity on grows electron and recoils, as theoretical uncertainty diminishes, but also the impact precisely, even in thebetween limit MIN of and large MAX DMmaterial velocity mass profiles and ( reaches more factor like importantly interaction the form ionization factor smaller threshold. momentum transfer, This lead is to even larger for effect. the contact- E.g. for JHEP07(2020)081 ] ]. ]. SPIRE SPIRE IN Mon. Not. IN , ][ ][ ] appeared which ]. 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