Compact Stars & Dark Matter

Chris Kouvaris

MIAPP Munich, 4 February, 2015 Astrophysical Observations

WIMP annihilation and Cooling of Stars WIMP annihilation as a heating mechanism for •neutron stars (CK ’07, CK Tinyakov ’10, Lavallaz Fairbairn ’10) •white dwarfs (Bertone Fairbairn ’07, McCullough ’10)

WIMP collapse to a WIMPs can be trapped inside stars and later collapse forming a black hole that destroys the star (Goldman Nussinov ’89, CK Tinyakov ’10, ‘11,’13 McDermott Yu Zurek ’11, CK’11,’12 Guver Erkoca Reno Sarcevic ’12, Fan Yang Chang ’12, Bell Melatos Petraki ’13, Bramante Fukushima Kumar Stopnitzky ’13, Bramante Linden ’14, Autzen CK ‘14)

New effects WIMPs can slow down the rotation of a (Perez-Garcia,CK ’14) WIMP capture in Stars

Condition: The energy loss in the collision should be larger than the asymptotic kinetic energy of the WIMP far out of the star.

Even if current limit of CDMS Only one out of a million WIMPs scatters!

! CK’07 ! For cross section larger than the critical one, every WIMP passing through the will be on average interact inside the star.

heat WIMP capture in Stars

Press Spergel ’85, Gould ’86, Nussinov Goldman ’89, CK’07, CK Tinyakov ’10

higher local DM density f=1 if σ>σcrit gives higher accretion smaller velocities enhance capture f=0.45σ/σcrit if σ<σcrit

For typical NS Thermalization

Goldman Nussinov’89, CK Tinyakov ’10 Bertoni Nelson Reddy ’13

Evaporation

Krauss Srednicki Wilczek ’86

for WIMPs with mass larger than ~2 keV evaporation can be ignored WIMP Annihilation in Neutron Stars

Energy Release we have to compare with other heating/cooling mechanisms Basics of Neutron Star Cooling

Direct Urca

However for nuclear matter triangle For quark matter it inequalities are not satisfied holds!

! Emissivity: ! Modified Urca presence of Emissivity: bystander

Photon Emission Emissivity: ... more cooling mechanisms

! ! Cooling of Neutron Stars

neutrino emission

photon emission CK’07

dark matter heating Cooling of Neutron Stars

Galactic Center Globular Cluster

CK, Tinyakov ’10 Nearby old neutron stars Fairbairn Lavallaz’10 J0437-4715 temperature ~10^5 K J2124-3358 temperature ~10^5 K 130-140 pc away Cooling of Neutron Stars

log( σ /cm 2 )

−38

−39

−40 direct −41 searches

−42 3 6 m, GeV −43 10 10

−44 observation of NS in M4 with T=7x10 4 K −45

Old neutron stars in Globular Clusters ! X7 in 47 Tuc! 1620-26 in M4 ! ! both have temperatures roughly 10^6 K! Another scenario for asymmetric DM

Excluding Light Asymmetric Bosonic Dark Matter

Chris Kouvaris∗ CP3-Origins, University of Southern Denmark, Campusvej 55, Odense 5230, Denmark

Peter Tinyakov† Service de Physique Th´eorique, Universit´eLibre de Bruxelles, 1050 Brussels, Belgium

We argue that current neutron star observations exclude asymmetric bosonic non-interacting dark matter in the range from 2 keV to 16 GeV, including the 5-15GeVrangefavoredbyDAMA and CoGeNT. If bosonic WIMPs are composite of fermions, the same limits apply provided the Excludingcompositeness Light Asymmetric scale is higher Bosonic than ∼ 10 Dark12 GeV Matter (for WIMP mass ∼ 1GeV).Incaseofrepulsive self-interactions, we exclude large range of WIMP masses andinteractioncrosssectionswhichcom- Chris Kouvaris∗ 3 plements the constraints imposed by observations of the Bullet Cluster. CP -Origins, University of Southern Denmark, Campusvej 55, Odense 5230, Denmark PACS numbers: 04.50.+h 04.30-w 95.35+d 98.80.Cq Peter Tinyakov† Service de Physique Th´eorique, Universit´eLibre de Bruxelles, 1050 Brussels, Belgium

We argue1. that Introduction. current neutronAn star appealing observations solution exclude to asymmetric the dark bosonicasymmetric non-interacting WIMPs with a spin-dependent cross section, dark mattermatter in problemthe range from is off 2ered keV to by 16 Weakly GeV, including Interacting the 5-15GeVrangefavoredbyDAMA Massive these constraints are competitive to direct dark matter and CoGeNT.Particles If (WIMPs)bosonic WIMPs emerging are composite in many of fermions, theories the beyond same limits the applysearch provided experiments the [11]. compositeness scale is higher than ∼ 1012 GeV (for WIMP mass ∼ 1GeV).Incaseofrepulsive self-interactions,Standard we Model exclude (SM). large range However, of WIMP WIMPs masses an aredinteractioncrosssectionswhichcom- very diffi- In this letter we focus on asymmetric bosonic dark plementscult the to constraints detect, imposed and therefore by observations little ofis the known Bullet about Cluster. their matter and derive constraints on the dark matter param- properties. Experimentally, the situation is rather un- eters from the formation of black holes inside neutron PACS numbers:clear (see 04.50.+h e.g. limits 04.30-w from 95.35+d CDMS 98.80.Cq [1]), with DAMA [2] and stars. We show that for fundamental asymmetric non- CoGeNT [3] suggesting the existence of a light WIMP interacting bosonic WIMPs, current observational data 1. Introduction.withAn a appealing mass around solution to10 the GeV. dark asymmetric WIMPs with a spin-dependentexclude all the cross masses section, from 2 keV to 16 GeV (includ- ∼ matter problem is offeredApart by from Weakly direct Interacting searches, Massive constraintsthese constraints on WIMPs are can competitiveing the to direct range dark of masses matter 2 5 15 GeV favored by DAMA − Particles (WIMPs)be emerging set by in observations many theories of beyond compact the objectssearch experiments such as white [11]. and CoGeNT). If WIMPs are composite particles made Standard Model (SM). However, WIMPs are very diffi- In this letter we focus on asymmetric bosonic dark It is easy to see from eq. (1) that for cross sections where Tc is the temperatureof fundamental of the star core. fermions, When their the above constraint does not dwarfsσ andM 4 neutron/m2 10−104 starscm2(m/ [4–12].GeV)−2,thesecondterm These constraintstotal mass canM increases beyond the mass of the ordinary cult to detect, and therefore≫ littlePl is∼ known about their matter and derive constraints on the dark matter param- properties. Experimentally,be groupeddominates, the in situation and two the types. minimum is rather The required un- first mass typeeters scales targets from (at thematter WIMPs formation within the of sameapply. black radius, holes However, inside neutron if the compositeness scale is above constant λ) in the same way as for the fermionic parti- 12 −3/2 that can annihilate inside the star producing heat that 4 3 10 GeV46 (likem in Grand Unified Theories (GUT)), clear (see e.g. limits from CDMScles with [1]), a diff witherent DAMA (and potentially [2] and muchstars. smaller) We co- showM>M thatsg for= fundamentalπρ r =2.2 10 asymmetricGeV non-, 3 c∼candidatesth × like thatGeV are again excluded in the same mass CoGeNT [3] suggestingcan change theefficient. existence the The thermal best of experimental a light evolution WIMP constraints ofinteracting the on the star self- [5]. bosonic WIMPs WIMPs, current observational# $ data(7) interaction cross section come from the Bullet Cluster, with a mass aroundof this10 GeV. type can− arise24 2 in supersymmetricexclude extensions all thetheir masses of own the gravitational fromrange. 2 keVfield starts toIn 16 addition, to dominate GeV (includ- over we that constrain the case of fundamental ∼ σ/m < 2 10 cm /GeV [32]. ing the rangeof of the masses star and 5 the self-gravitation15 GeV favored regime by sets DAMA in, leading Apart from directSM searches, (seeSeveral [13] constraints× conditions and references on have WIMPs to be satisfied therein), can for a or gravita- in Technicolor self-interacting bosonic WIMPs. We show that if the in- and CoGeNT).to the If WIMPsgravitational− are collapse composite provided particles the condition made (3) is be set by observationsmodels oftional compact [14, collapse 15]. objects of Constraints WIMPs such inside as white a neutron of the star second to occur. typesatisfied. target It can beteraction seen from eq. (2)is repulsive, that (7) is satisified a vast area of self-interaction cross dwarfs and neutron starsFirstly, [4–12]. a su Thesefficient number constraints of dark can matter particlesof fundamental must if the fermions, WIMP mass the is above larger than constraint1GeV( does143 not GeV) asymmetricbe accumulated dark matter during the models. lifetime of the In neutron these star. models the an- 3 sections3 complementary∼ ∼3 to the one excluded by observa- be grouped in two types. The first type targets WIMPs apply. However,for ρdm if=10 theGeV compositeness/cm (ρdm =0.3GeV scale/cm is), above but not The accretion of WIMPs onto a typical 1.4M⊙ neutron12 tions of the Bullet Cluster [32] is excluded. that can annihilatenihilation inside the of star dark producing matter heat in thethat present-day10 GeV Universefor (like lighter in WIMPs. is Grand Unified Theories (GUT)), star in a globular cluster, taking into account∼ relativis- However, if WIMPs2. are bosonsBosonic as we Dark assume Matter. in this of a can change the thermalimpossible evolutiontic effects, because of has the been star only calculated [5]. particles, WIMPs in [9]. The and totalcandidates mass no anti-particlesof like that are again excluded in the same mass letter, they can form a Bose-Einstein condensate (BEC). 2 of this type can arise(hence in supersymmetricaccreted the term WIMPs “asymmetric”) is extensions of the remainrange. [16–31]. In addition,Since An this we ad- state constrain is moreself-gravitating thecompact, case the of self-gravitationfundamental lump of in particles happens differently in this case starts for a smaller number of particles before SM (see [13] andditional references bonus therein), in46 or these in Technicolorρdm models ist thatself-interacting the asymmetry bosonic WIMPs.case We of show bosons that and if the fermions. in- In the case of fermions of Macc =4.3 10 f GeV, the condition (7) is satisfied. The particle density re- 3 models [14, 15]. Constraints of the× second103GeV type/cm target3 109yearsteraction is repulsive, a vast area of self-interaction cross It is easy to seeof WIMPs from eq. might (1) that be! linked for cross through"! sections sphalerons" wherequired withTc is to the the form temperature BECmass is m, a of large the star number core. of When particles theirN (MPl/m) is re- asymmetric4 dark2 matter−104 models.2 In these− models2 the an- sections(2) complementary to the one excluded by observa- ≃ σ M /marXiv:1104.0382v1 [astro-ph.CO] 3 Apr 2011 10baryoncm asymmetry(m/GeV) [24],,thesecondterm which can explain thetotal today’s mass M ra-increasesquired beyond to overcome the mass3/ the2 of Fermi the ordinary pressure, where MPl is the Pl where the “efficiency” factor f = 1 if the WIMP- m 3/2 T nihilation≫ of dark∼ matter in the present-day Universe is −45 tions2 of the Bulletn Cluster4.7 10 [32]28cm is−3 excluded. c . dominates, andtio theΩ minimumDMnucleon/ΩB cross required section5 provided satisfies mass theσn scales> WIMP10 cm (at,and hasf amatter= mass around within the samePlanck radius, mass. In5 the bosonic case this number is para- −45 2 −45 2 2. Bosonic Dark≃ Matter.× GravitationalGeV collapse10 K of a impossible because only particles,σn/(10 cm∼ and) if σ non < anti-particles10 cm . The condition # $ ! " 2 constant λ) in the5 GeV. same Note way as that for this the value fermionic is not parti- very far from the one metrically smaller, N (2/π)(3M2Pl/m) , because in the self-gravitatingAssuming lump an of4 old particles neutron starhappens with a di temperaturefferentlyT inc2 =m − / (hence the term “asymmetric”) remain [16–31]. An ad- 5 3 46 ≃ cles with a differentsuggested (and potentially by the DAMA muchMacc >M and smaller)crit CoGeNT co- experiments.(3)M>M10 K,sg the= In numberπρcabsence ofrth WIMPs=2. needed2 of self-interactions,10 in orderGeV for BEC only the, uncertainty princi- I.ditional INTRODUCTION bonus in these models is that the asymmetry case of bosons and fermions. In the36 case of fermions of It is easy to see from eq. (1) that for cross sections whereto formT isisN theBEC3 temperature2 10 of. All the the star× WIMPs core. When accreted theirGeV in efficient. The best experimental constraints on the self- c ≃ ple× opposes the collapse.3 If the bosons have a repulsive 2 of WIMPs might beview linked ofguaranteesσ this throughM coincidence,4 /m that sphalerons2 the10−104 accumulatedcm2 the with(m/GeV) models the dark−2,thesecondterm mattermass with massm WIMP, isa largetotalexcess masses number mass of thisM increases valueof particles will beyond go intoN the the mass( condensedMPl of/m the) ordinary state.is re-# For $ (7) ≫ Pl ∼ ≃ arXiv:1104.0382v1 [astro-ph.CO] 3 Apr 2011 interactionbaryon asymmetry crossin [24], section the whichabove GeVdominates, come can the range critical explain from and have value the the the minimum (1). becometoday’s Bullet required ra- Cluster, quite massquired popular. scales to (at overcomemattermost of within the cases Fermi the ofsameinteraction our pressure, radius, interest, wherethe it number providesMPl ofis accreted the an extra pressure, so the required −24 2 Secondly, the newly-formed black hole must accretetheir own gravitational field starts to dominate over that σ/m < 2 10 cm /GeVconstant [32].λ) in the same way asIt for is the easy fermionicPlanck to see parti- mass. fromWIMPs eq. In (1) the will that bosonic be4 for larger cross case than sections thisNBEC number,soeq.(7)hastobewherem is− para-T3/c2 is the temperature of the star core. When their tio ΩDM /ΩB 5 providedSincematter the in WIMP the faster asymmetric than has it a evaporates mass around dark due to matter Hawking radia- modelsof the star WIMPs and thenumber self-gravitation3 of46 particles regime is sets larger in, leading in this case (obviously, an × ∼ cles with a different (and potentiallyσ M much4 /m smaller)2 10− co-104 cmreconsidered.2M>M(m/GeV)sg =−2πρ,thesecondtermcrth =2.2 10 2 GeV total mass, M increases beyond the mass of the ordinary 5 GeV.Several Note conditions that this value havetion. is In to not the be very Bondi satisfied far regime from of for accretion, the a one gravita- thePl changemetrically of the smaller, N 3(2/π)(MPl/m× ) , becauseGeV in the cannot annihilate,efficient. The bestn ifTB experimental a= largenB number≫ constraints ofon∼ the them self-to the is accreted gravitationalThe size≃ of the condensedattractive(1) collapse state provided interaction is determined# the$ by condition(7) leads the to the (3) opposite is effect). Tak- black hole mass M with time isdominates, given by theabsence and equation the of minimum self-interactions, required mass only scales the uncertainty (at matter princi- within the same radius, tionalsuggested collapse by the of DAMA WIMPs andinteraction inside CoGeNTa cross neutron experiments. section come star from to In the occur. Bullet Cluster, theirradius own of gravitational the waveing function field a λφ starts of4 the tomodel dominate ground as state over a generic thatin the example, the minimum mass during theσ/m < lifetime2 10−24cm of2/ aGeV neutron [32].constant star,λ) in they thesatisfied. same may waygravitational collapse as It for can the potential be fermionic seen of the from parti- star, eq. (2) that (7) is satisified −3/2 view of this coincidence, the models× with WIMP2 2 masses ple opposes theof the collapse. star and the If self-gravitation the bosons regime have sets a repulsive in, leading 4 3 46 m Firstly, a sufficient numberSeveral of darkdM conditionsM matter4TBπρc=5GeVG haveM particles tocles be satisfied with1 must a for di afferent gravita- (and potentially muchof (2) smaller) a self-gravitating co- M>M lumpsg = whichπρcr can=2.2 form10 aGeV black hole is , forming a small= black hole inside theinteraction, starif(4) that the itto provides WIMP eventu-the gravitational an mass extra collapse− is1/4 pressure, larger provided than so the the condition required1GeV(1/2 (3) is 143 GeV)th in the GeV range have becometional quite collapsedt popular. of WIMPsc3 inside− 15360 a neutronπG2M star2 to occur. 8π GeV 3 × GeV be accumulated during the lifetime of thes neutroneBosonicfficient. star. The best experimental Asymmetricsatisfied.r = constraints ItG can3ρ m be2 seen on from3 the1. eq.6 self-10 (2) −Dark that4 (7)∼ is satisifiedcm .Matter(8)∼3 c c [33] # $ (7) Since in the asymmetrically destroyFirstly, dark matter a the sufficient latter. models number Therefore of WIMPs dark matter particles thenumber existence mustfor of particlesρdm of=10 old3 is largerGeV/ incm this≃ (ρ× casedm =0 (obviously,m.3GeV/ ancm ), but not interaction cross sectionif come the WIMP! from massthe" Bullet is larger Cluster, than 1GeV(! "143 GeV) The accretion of WIMPswherebe onto accumulatedcs and a typicalρc 1are during the5=5 the1.4 speed lifetimeM of⊙ soundneutron of the and neutron the24 mass star.2 3 (3)3 ∼ their∼3 own gravitational field starts to dominate over that cannot annihilate,neutron if a large stars number can of them impose is accreted constraintsattractive− on thefor interaction lighter propertiesfor ρdm WIMPs.=10 leadsGeV/ tocm the(ρdm opposite=0.3GeV e/ffcmect).), but Tak- not density of the neutron star core,σ/m respectively. < 2 10 Thecm first4 /GeVSubstituting [32]. this size in place of rth in eq.of (7) the we star get and2 the self-gravitation regime sets in, leading star in a globular cluster,The taking accretion into of WIMPs account onto a typical relativis-× 1.4ingM⊙ aneutronλφ modelfor lighter as a generic WIMPs. example, the minimum mass2M M 2 during the lifetimeof of asymmetric a neutrontermstar corresponds in star, a globular WIMPs. they to cluster, the may Bondi In taking collapse fact, accretionSeveral into in account while conditionsthe relativis- the case sec- haveofHowever, fermionic to be satisfied if WIMPs for a are gravita- bosons−3/ as2 we assumePl in thisPl 1/2 4 3 No Fermi pressure but HeisenbergHowever, if WIMPs uncertainty are27 bosons asm keeps weM assumeto thebosons= in gravitational this from1+ collapsecollapse providedσ the condition(1) (3) is ticforming effects, a small has been black calculated holeond inside represents the ine the [9]. star10 energy The that18 loss total eventu- duetional5(4) to mass Hawking collapseof of radiation. a of self-gravitating WIMPs inside a lump neutronM> which8 star10 can toGeV occur. form a blackcrit. hole is(9) tic effects, has been calculated⇤ ⇥ in [9]. The total massletter, of letter, they they can can form form× a Bose-Einstein a Bose-EinsteinGeV condensatesatisfied. condensate (BEC).π Itm can! be (BEC). seen4 from√πm eq. (2) that (7) is satisified accreted WIMPs is Sinceaccreted the accretion WIMPs isincreases while the Hawking[33] radiation ally destroy the latter. Therefore the existenceFirstly, of old a sufficientSince numberSinceIn this of view dark this stateof eq.state matter (2), is the more more particles amount compact, compact, of must# dark the matter self-gravitation$ if the the suffi self-gravitation WIMPcient in for mass is larger in than 1GeV( 143 GeV) decreases as a function of M, itbe is theaccumulated initial mass during of the thethis lifetime case starts of for the a neutronsmaller number star. of particles before 3 3 ∼ ∼3 neutron stars can impose constraints on46 the propertiesρdm t WIMP self-gravitation in the condensed statefor ρ candm always=10GeV/cm (ρdm =0.3GeV/cm ), but not blackM hole=4 that.3 10 determines2 its fate. Requiring thatf GeVthis the, case starts2 forwhere a smaller we2 have number expressed of particles the result before in terms of the self- 46 ρaccdm GNm 3 t The3 accretion9 of WIMPsthebe onto accumulated condition a typical2M (7) provided is 1.4 satisfied.M⊙ thatMneutron the The WIMP particle is density heavier re-than 2 2 Mof asymmetric=4.3 WIMPs.10 ∗ Infirst fact, term in dominates the× case when10 ofGeV thefermionic/~cm blackf hole10GeV isyears formed, gives Pl Pl 1/2 for lighter WIMPs. acc Electronic3 address:3 [email protected]! 9 star"! in a globular" cluster,the(2) conditionMquiredcrit taking0.1 eV,= to form whichinto (7) BEC account covers isinteraction1+(5) is satisfied. all relativis- cases ofσ interest. cross The Thus, section particle due(1) toσ density= λ /(64 re-πm ). Here and be- × † 10theGeV condition/cm 10 years ∼ πm 4√πm However, if WIMPs are bosons as we assume in this r ⇤ r the formation of! BEC the requirement3/2 of self-gravitation3/2 ! Electronic! where address: the “e"!ffi [email protected]” factorticf" eff=ects, 1 if has the been WIMP-quired calculated to form in [9]. BEC Thelow total is we massm use of theTc natural units = c = kB =1. 36 −45(2)2 n 4.7 1028cm−3 letter,. they can form a Bose-Einstein condensate (BEC). nucleon cross sectionM>5 satisfies.7 10accretedσnGeV> 10. WIMPscm ,and isf(5)= does not provide an extra condition. 5 The accretion of WIMPs onto a−45 typical2 1.4M×−45 102 km neutronwhere star we have in a expressed globular≃ × cluster the resultGeV in terms10 ofSinceK the this self- state3/ is2 more compact, the self-gravitation in where the “efficiency”σ factorn/(10 cmf )= if σn 1< 10 if thecm . The WIMP- condition Finally, the accumulation# of$ WIMPs! may3/"2 become in- ∗ 38 3 Assuming an old neutron28 2 star−3 with2m a temperature TTc= Electronic address: [email protected] we have used ρc =5−4510 2GeV/cm andinteractioncs =0.17. crossρefficient section if theyσ may=t λ escape/(64 fromπm the). Here neutronthis and case star be-c oncestarts for a smaller number of particles before nucleon cross section satisfies σ > 10 ×cmJ ,andf = 46 ndm5 4.7 10 cm . taking† into account relativisticAny black eects holen has with thebeenM initialacc calculated>M massMcritacc satisfying=4. in...3 eq.10 The (5) will(3) total10captured, massK, the of which number WIMPs is of a! danger WIMPsf atGeV needed small, in WIMP orderthe conditionmasses. for BEC5 It (7) is satisfied. The particle density re- Electronic−45 address:2 [email protected]−45 2 low× we use103 theGeV natural/≃cm3 × units109years=36c = kGeVB =1. 10 K σn/(10 cm ) if σn Mcrit the newly-formed black hole(3) must accrete10 K,WIMPs the will number be− larger45 of than2 WIMPsNBEC,soeq.(7)hastobe neededn in order4.7 10 forcm BEC . Macc =4.3lapse10 into a black3 hole is3 thenucleon onset9 cross of the section WIMPf GeV satisfies, tail ofσ then > Maxwell-Boltzmann10 cm(6) ,andf distribution= of velocities 5 matter faster10 thanGeV it evaporates/cm due10 toyears45 Hawking2 radia- reconsidered.45 2 36 ≃ × GeV 10 K self-gravitation. WIMPs capturedσ /(10 by− thecm neutron) if σ starto< form10may− iscm escape.N.BEC The The condition rate2 F 10of WIMP. All evaporation the WIMPs can be accreted in ! " tion. In the Bondi regime of accretion,⇥n the change⇥ ofn the The size of the≃ condensed× state is determined by the # $ guarantees that the accumulatedquicklyblack hole thermalize mass darkM [9]with and matter time concentrate is given mass by thein is the equation centerexcessestimated of this as value follows will [34], go into theAssuming condensed an old state. neutron For star with a temperature Tc = We are interested in constraintswithin the coming radius from possible formation of a blackradius hole of the that wave will function of the ground state5 in the Maccgravitational>Mcrit potential1/2 of the star,(3) 10 K, the number of WIMPs needed in order for BEC above the critical value (1). 2 2 most of the casesT of our interest, the number of accreted36 dM 4πρcG M 1/2 1 F = n (1 + GMm/RT )exp( GMm/RT ), destroy the neutron star within its lifetime.= Therefore− one1/2 , necessary(4) conditions for− the1/4 to1 form/2 is NBEC 2 10 . All the WIMPs accreted in Secondly, the newly-formed black holeT3c mustm accrete2 2 2πm − rthdt 2m cs −guarantees15360πG M that, theWIMPs(6) accumulated will8!π bedark" larger2 matter than mass−N is4 BECGeV,soeq.(7)hastobe≃ × ≃ 105K GeV rc = Gρcm 1.6 10 excesscm of. (8) this(10) value will go into the condensed state. For matter faster than it evaporates due! to Hawking" above the radia- critical value (1). 3 ≃ × m formation of the black hole is Mwhereacc >Mcs andcritρc .are However, the speed# thisof sound$ constraint and the massreconsidered. by itself is! not su⇥"cient ! most" of the cases of our interest, the number of accreted Secondly, the newly-formed black hole must accrete tion. In the Bondi regimedensity of accretion, of the neutron the star change core, respectively. of the The firstTheSubstituting size of this the size condensed in place of rth statein eq.WIMPs (7) is we determined get will be larger by than the NBEC,soeq.(7)hastobe to guarantee the destruction ofterm the corresponds star. Even to the if Bondi amatter black accretion hole faster while is than formed, the sec- it evaporates ti might due evaporate to Hawking radia- −3/2 black hole mass M with time is given by the equation 27 m reconsidered. ond represents the energy loss due to Hawking radiation.radius of theM> wave8 10 functionGeV of the. ground(9) state in the Evolutiontion. In the Bondi of regime the of accretion, Black the ×Hole change ofGeV the The size of the condensed state is determined by the very fast due to Hawking radiationSince the before accretion it increases manages while to the destroy Hawking radiation thegravitational star. A black hole potential loses of the star, 2 2 black hole mass M with timeIn view is of given eq. (2), by the the amount equation of# dark matter$ radius sufficient of for the wave function of the ground state in the dM 4πρcG decreasesM as a function1 of M, it is the initial mass of the WIMP self-gravitation− in1 the4 condensed stategravitational can always potential1 2 of the star, energy due to Hawking= radiation3 black as hole that determines2 its2 , fate. Requiring(4) that the 2 2 / / dt c − 15360πG M dM 4πρcG Mbe accumulated8π 1 provided that the WIMP is heavierGeV than s first term dominates when the black hole is formed= gives 2 , (4) −4 −1/4 1/2 rc 3= 0.1 eV,G whichρcm covers2 2 all cases1 of.6 interest.10 Thus, due to cm. (8) the condition 6 dt cs − 15360πG M 8π 2 −4 GeV dM c the∼ formation3 of BEC the requirement≃ × of self-gravitationrc = m Gρcm 1.6 10 cm. (8) ~ ! " ! 3 " ≃ × m where cs and ρc are the speed of= sound and36 the. mass does not provide an extra(7) condition. dt M>153605.7G10where2MGeV2 c. s and ρc are(5) the speed of sound and the mass ! " ! " density of the neutron star core, respectively.× The first SubstitutingFinally, the this accumulation size in place of WIMPs of mayrSubstitutingth becomein eq. in- (7) this we size get in place of r in eq. (7) we get Bondi accretion38density of3 the neutron star core, respectively. The first Hawking Radiation th Here we have used ρc =5 10 GeV/cm and cs =0.17. efficient if they may escape from the neutron star once term corresponds to the Bondi accretion× whileterm the corresponds sec- to the Bondi accretion while the sec- −3/2 −3/2 On the other hand a black holeAny blackaccretes hole with simultaneously the initial mass satisfying mass eq. from (5) will the star.captured, If whichrotation is a danger is 27 at small WIMPm masses. It 27 m ond represents the energyeventually loss due destroy to theHawking whole star,ond radiation. while represents the smaller the black energy loss dueM> to Hawking8 10 radiation.GeV M>. 8 10(9)GeV . (9) can be seen from eq.× (6) that for WIMPGeV masses in the × GeV insignificantSince the (as accretion we are going increases toholes argue whilewill evaporate later the on), Hawking with nomatter detectableSince radiation is the accreted eff accretionect. via increases BondikeV while range accretion the the radius Hawking with of the radiation WIMP lump# becomes$ com- # $ The third condition necessarydecreases for the as WIMP a functionIn col- view ofparableM of, it eq. is to the the (2), initialsize the of the massamount star, of so the of that dark WIMPsIn view matter in of the eq. su (2),fficient the amount for of dark matter sufficient for decreases as a function oflapseM, into it is a theblack initial hole is themass onset of of the the WIMP tail of the Maxwell-Boltzmann distributionWIMP of velocities self-gravitation in the condensed state can always arate black hole that determinesWIMP itsself-gravitation fate. Requiring in that the the condensed state can always black hole that determinesself-gravitation. its fate. WIMPs Requiring captured2 2 that by the the neutron star may escape. The rate F of WIMP evaporationbe accumulated can be provided that the WIMP is heavier than quickly thermalizedM 4 [9]⇥ andG M concentratefirst term dominates in the center whenestimated the black as follows hole is [34], formed gives first term dominates when the black= hole is formedthe, condition gives be accumulated provided(8) that the WIMP0.1 eV, is which heavier covers than all cases of interest. Thus, due to within the radius 3 1/2 ∼ dt cs 0.1 eV, whichT covers all cases ofthe interest. formation Thus, of BEC due the to requirement of self-gravitation the condition 1/2 −1/2 F = n36s (1 + GMm/RT )exp( GMm/RT ), Tc m ∼ 2πm −does not provide an extra condition. r 2m , M>the(6) 5 formation.7 10 GeV of. BEC the requirement(5) of self-gravitation where cs and ⇥ are the speed of soundth and the5 mass density of the star at× the! core." Since 36 ≃ 10 K GeV Finally,(10) the accumulation of WIMPs may become in- M>5.7 10 GeV.! " # $ (5) does not38 provide an3 extra condition. Bondi accretion scales proportional× to the squareHere of the we have black used holeρc =5 mass10 whileGeV Hawking/cm and cs =0.17. efficient if they may escape from the neutron star once Any black hole with theFinally, initial× mass the satisfying accumulation eq. (5) will of WIMPscaptured, may which become is a danger in- at small WIMP masses. It 38 3 radiationHere we scales have inversely used ρc proportional,=5 10 GeV it/ iscm evidentandeventually thatcs =0 the.17. destroy initial thee massffi wholecient of star, ifthe they while black may the hole smaller escape black fromcan the be neutron seen from star eq. once (6) that for WIMP masses in the Any black hole with the initial× mass satisfyingholes eq. (5) will will evaporatecaptured, with no detectable which iseffect. a danger at smallkeV range WIMP the masses. radius of the It WIMP lump becomes com- determines also its fate. If accretion wins at the formation of the black hole, more mass eventually destroy the whole star, while the smallerThe blackthird conditioncan be necessary seen from for the eq. WIMP (6) that col- forparable WIMP to masses the size in of the star, so that WIMPs in the lapse into a black hole is the onset of the WIMP tail of the Maxwell-Boltzmann distribution of velocities is accretedholes will and evaporate Hawking with radiation no detectable gets smaller effect. andself-gravitation. smaller. Demanding WIMPskeV range captured this the to by radius be the the neutron of the star WIMPmay lump escape. becomes The rate com-F of WIMP evaporation can be The third condition necessary for the WIMPquickly thermalize col- parable [9] and toconcentrate the size in of the the center star, soestimated that WIMPs as follows in [34], the lapse into a black hole is the onset2 of thewithin WIMP the radius tail of the Maxwell-Boltzmann distribution of velocities T 1/2 self-gravitation. WIMPs captured by the neutron star may escape.1/2 The− rate1/2 F of WIMPF = evaporationns can(1 + beGMm/RT )exp( GMm/RT ), Tc m 2πm − quickly thermalize [9] and concentrate in the centerrth 2m , (6) ! " ≃ estimated105K asGeV follows [34], (10) within the radius ! " # $ T 1/2 1/2 −1/2 F = ns (1 + GMm/RT )exp( GMm/RT ), Tc m 2πm − rth 2m , (6) ! " ≃ 105K GeV (10) ! " # $ 3

mDM 2 log( σ /cm ) Hawking evaporation excluded by Bullet Cluster 16 GeV −20

1 GeV −30 4 ρ = 10 GeV/cm 3 3 3 excluded range −40 ρ = 10 GeV/cm 1 MeV −50 1 10 3 106 m, GeV

−60 1 keV thermal evaporation excluded by neutron stars −70 Hawking radiation prevents 0123 3 10 10 10 10 ρ (GeV/cm ) −80 BH growth

FIG. 1: The range of excluded masses as a function of the FIG. 2: Constraints on weakly interacting bosonic dark mat- dark matter density at the location of the neutron star. ter from observations of neutron stars in globular clusters. Excluded region (pink) is shown for two background dark Bosonicmatter densities Asymmetric as indicated on the plot. The Dark cyan region Matter where T , M and R are respectively the temperature, shows constraints from the observation of the Bullet Cluster. mass and radius of the star, and ns is the WIMP density at the surface. Calculating ns from the Boltzmann distri- 3 bution and plugging the parameters for a typical neutron 2 m log( σ /cm ) DM log( σ /cm 2 ) star, we found that the evaporation can be safely ignored that there are enoughHawking particlesevaporation to collapse gravitation- excluded by Bullet Cluster −40 for masses larger than 2keV. ally16 according GeV to Eq. (1). As WIMPs start occupying−20 ∼ excluded by BH formation inside neutron starssmaller and smaller volume towards the Schwarzschild In summary, accumulation and subsequent gravita- 1 GeV −30 4 radius, they might reach the density at which the mean ρ = 10 GeV/cm 3 tional collapse of WIMPs captured inside a neutron star 3 excluded range 10 GeV/cm 3 occurs for WIMPs heavier than 2 keV and satisfying distance between WIMPs is comparable to the− scale40 of ρ = −45 1 MeV CK, Tinyakov PRL ’11 ∼ −6 −5 −4 −3 −2 −1 conditions (3) and (5). In the case of10 no10 self-interaction10 10 10 10 1compositeness. 10 m, GeV At this point the Fermi pressure−50 comes 1 10 3 106 m, GeV ρ = 0.3 GeV/cm 3 the collapse to a black hole inside the neutron star hap- into play and might stop further collapse. If on the−60 other pens for WIMP masses 2 keV ! m ! 16 GeV. hand,1 keV the lump ofthermal WIMPs evaporation reaches its Schwarzschild ra- excluded by neutron stars −70 Hawking −50 radiation 3 dius3 before the distance between particles becomes com- Several old neutron stars in globular clusters have beenρ = 10 GeV/cm 0123 prevents

Hawking radiation prevents BH growth 10 10 10 10 3 BH growth observed. A characteristic example is the pulsar B1620- parable to the scale of compositeness,ρ (GeV/cm the ) black−80 hole is formed and compositeness plays no further role. 26 found in the outskirts of the core of M4. Another ex- FIG. 1: The range of excluded masses as a function of the FIG. 2: Constraints on weakly interacting bosonic dark mat- Todark estimate matter density the at theminimum location of the compositeness neutron star. scaleter fromΛ observations, of neutron stars in globular clusters. ample is X7 from 47 Tuc [35]. Both−55 globular clusters are critSelf-Interacting DM Excluded region (pink) is shown for two background dark older than several billion years. This excludes the non- we express the mean distance d between WIMPsmatter densities in as indicated on the plot. The cyan region interacting bosonic dark matter candidates with masses the nearly-collapsingwhere T , M and R are (i.e. respectively having the size temperature, comparableshows constraints to its from the observation of the Bullet Cluster. from 2keVto16GeV. Schwarzschildmass and radius radius) of the star, lump and ns ofis the dark WIMP matter density in terms of ∼ If WIMPat the is surface. a Calculatingcompositens from the Boltzmann of distri- fermions Almost the same range of WIMP masses is excluded its massbutionM and. plugging Ignoring the parameters the numerical for a typical coe neutronfficients, we have d = star,GM we2/ found3m1 that/3. the Taking evaporation the can mass be safely to ignored be equalthatto there the are enough particles to collapse gravitation- by the observations of neutron stars close to the Earth for masses larger than 2 keV. ally according to Eq. (1). As WIMPs start occupying ⇥ where the age has been established (much more accu- criticalIn one, summary, eq. (1),accumulation we get and subsequent gravita- smaller and smaller volume towards the Schwarzschild rately) to be again several billion years. Typical exam- tional collapse of WIMPs captured inside a neutron star radius, they might reach the density at which the mean occurs for WIMPs heavier than 2 keV and satisfying2 −1/3 distance between WIMPs is comparable to the scale of ples are the J0437-4715 [36], and J0108-1431 [37]. They ⇥ λm compositeness. At this point the Fermi pressure comes conditionsΛ (3)= andm (5).1/3 InM the2/3 case1+ of no self-interactionpl , (11) are at distances of 140 and 130 pc with an expected local the collapsecrit to a black holePl inside the neutron32πm star2 hap- into play and might stop further collapse. If on the other pens for WIMP masses 2 keV . m!. 16 GeV. " hand, the lump of WIMPs reaches its Schwarzschild ra- dark matter density similar to the one around the Earth. Several old neutron stars in globular clusters have been dius before the distance between particles becomes com- The dependence of the excluded mass range on the dark observed. A characteristic example is the pulsar B1620- parable to the scale of compositeness, the black hole is In the non-interacting case this gives Λcritformed=2 and compositeness plays no further role. If WIMP is a composite of12 fermions26 found in the above outskirts1/3 of that the core scale, of M4. Another the ex-bosonic constraints× still hold matter density at the star location is shown in Fig.1. 10 ampleGeV( ism/ X7 fromGeV) 47 Tuc, [35]. which Both is globular well belowclusters are the GUTTo estimate mass the minimum compositeness scale crit, In the case of a repulsive interaction, the exclusion scaleolder of order than several10 billion16 GeV years. forThis all excludes masses the non- of interestwe express (cf. the mean distance d between WIMPs in interacting bosonic∼ dark matter candidates with masses the nearly-collapsing (i.e. having size comparable to its region that follows from eqs. (3) and (5) is shown in Fig.from 1). Thus,2 keV ourto 16 constraints GeV. are also valid for compositeSchwarzschild radius) lump of dark matter in terms of ⇥ Fig. 2. Depending on the interaction cross section, the WIMPsAlmost provided the same the range compositeness of WIMP masses is scale excluded is higherits mass thanM. Ignoring the numerical coe⇤cients, we have d = GM 2/3m1/3. Taking the mass to be equal to the constraints extend to much higher masses and are com- 10by12 theGeV. observations of neutron stars close to the Earth ∼ where the age has been established (much more accu- critical one, eq. (1), we get plementary to those derived from the observation of the 4.rately) Discussion to be again and several conclusions. billion years. TypicalTwo exam- remarks are in 1/3 ples are the J0437-4715 [36], and J0108-1431 [37]. They m2 Bullet Cluster. order. In the above analysis we have assumed that the = m1/3M 2/3 1+ pl , (11) are at distances of 140 and 130 pc with an expected local crit Pl 2 32⇥m ⇥ 3. Composite Dark Matter. The discussion above blackdark hole matter that density is similar formed to the inside one around a neutron the Earth. star and is The dependence of the excluded mass range on the dark refers specifically to fundamental bosonic dark matter. If not destroyed by the Hawking radiation eventuallyIn the con- non-interacting case this gives crit =2 matter density at the star location is shown in Fig.1. 1012 GeV(m/GeV)1/3, which is well below the GUT mass instead the latter is composite of fermions, the situation sumesIn the the whole case of a star. repulsive However interaction, plausible, the exclusion thisscale assump- of order 1016 GeV for all masses of interest (cf. might change. There are two possibilities. Let’s assume tionregion requires that somefollows fromjustification. eqs. (3) and In (5) eq. is shown (4) wein haveFig. 1). taken Thus, our⇥ constraints are also valid for composite Fig. 2. Depending on the interaction cross section, the WIMPs provided the compositeness scale is higher than constraints extend to much higher masses and are com- 1012 GeV. plementary to those derived from the observation of the ⇥ 4. Discussion and conclusions. Two remarks are in Bullet Cluster. order. In the above analysis we have assumed that the 3. Composite Dark Matter. The discussion above black hole that is formed inside a neutron star and is refers specifically to fundamental bosonic dark matter. If not destroyed by the Hawking radiation eventually con- instead the latter is composite of fermions, the situation sumes the whole star. However plausible, this assump- might change. There are two possibilities. Let’s assume tion requires some justification. In eq. (4) we have taken 2

pothetical possibility of black hole formation in particle where M is the black hole mass and cs =0.17 is the collisions at the LHC. sound speed of matter in the core of a neutron star far There is a common element in all the constraints that away from the black hole. At r

It subtracts angular momentum at the initial stage where the black hole is still small in the final stages Bondi accretion is not valid but the star is seconds away from destruction! 2

pothetical possibility of black hole formation in particle where M is the black hole mass and cs =0.17 is the collisions at the LHC. sound speed of matter in the core of a neutron star far There is a common element in all the constraints that away from the black hole. At rMcrit for the After formationstantially thethe estimates black for the accretionhole rate. spins First, one down,mass M of then the black hole.it Inspins other words, up once and the black at the last stages it spins down again has to check whether the Bondi accretion regime is valid hole mass grows beyond the critical value through the entire star consumption process. Second, it 2 3 has to be checked that the black hole itself does not be- 1 3 ω0 1 crit come maximally rotating and the Schwarzschild solution M = 3/2 3 , (3) 12 4πρc G ψ remains a good approximation. ! " # $ the angular momentum of the accreting matter cannot stall the accretion and can be safely ignored. Using a A. Validity of the Bondi regime typical value ρ =5 1038 GeV/cm3,wefind c × 46 −3 Mcrit =2.2 10 P1 GeV, (4) In the Bondi regime, the accreted matter is charac- × terized by an r-dependent energyTemperature density, pressure and Considerations where P1 is the star rotation period P measured in sec- velocity [30]. This description holds down to the Bondi onds. In practice, we are interested in constraints from radius rs, nearby old neutron stars (e.g. J0437-4715 and J2124- Radiation from in fallingGM matter can in3358) principle that have periods impede of P 5 ms. For further such a period accretion in two ways: rs = 2 , (1) 53 ∼ −4 4c one finds Mcrit =1.7 10 GeV 10 M⊙. s Reduce viscosity× ∼ Increase radiation pressure e-e Bremsstrahlung close to the horizon is the dominant radiation mechanism Self-Interacting Dark Matter

The self-gravitating“Chandrashekhar WIMP sphere may collapse into a black holeLimit if the Fermi for pressure WIMPs” of the WIMPs cannot counterbalance the gravitational attraction. The onset of the gravita- tional collapse occurs when the potential energy of a WIMP exceeds the Fermi momentum, and therefore Pauli blocking cannot prevent the collapse anymore. This happens when

!GNm2 32N 9 1/3 N 1/3 >k = = . N=10^57/m^3!!!(11) r F V 4 r ⇤ ⌅ ⇤ ⌅ In the derivation of the above limit, we have considered that WIMPs are (semi)-relativistic, which is justified since once WIMPs self-gravitate themselves, they get closer and closer, Yukawa-typebuilding up a Fermi WIMP momentum self-interactions that eventually corresponds to relativistic velocities. From can explainthe the above flatness equation we of can dwarf deduce thegalaxies number of Spergel- WIMPs needed for the collapse to take Steinhardtplace, ’99, Loeb-Weiner ’11 9 1/2 m 3 m 3 N = Pl 5 1048 , (12) 4 m ⇥ TeV ⇤ ⌅ ⇥ ⇥ where m is the WIMP mass and mPl is the Planck mass.

YukawaIV. CONSTRAINTSself-interactions ON DARK MATTER can alleviate the effect of the Fermi

pressure,Having leading derived the accretion to rate a formula gravitational for a generic star and the collapse amount of dark matter with dramatically needed in order to form a mini-black hole, we can proceed to the constraints that arise from lowerthe amount requirement that suchof mini-black captured holes are not WIMPs created inside newly-formed white dwarfs and neutron stars. We consider two dierent cases, i.e. constraints on spin-dependent cross sections from white dwarfs, and from neutron stars.

A. Constraints on Spin-Dependent cross section from White Dwarfs

Dark Matter WIMPs can have purely spin-independent, or spin-dependent interactions with nuclei, or even both types at the same time. Due to the coherence eect, the spin- independent interactions are usually stronger than the spin-dependent ones. However, there are cases where the spin-independent cross section is either suppressed or absent. Such cases arise naturally in models where dark matter candidates have an axial coupling to gauge bosons. One characteristic example is Majorana particles. Majorana fermions scatter o nuclei without the N 2 enhancement mentioned earlier because the amplitudes of scat- tering on dierent nucleons add up incoherently. Since most of the nucleons within the

9 Self-Interacting Dark Matter

Exclusion regions

CK PRL’12

Loeb-Weiner Pulsar Spindown spin down according to 2 basic mechanisms

๏ Magnetic Dipole Radiation

๏ Aligned Rotator

Contopoulos, Spitkovsky ‘06

Julian Goldreich ‘69 Pulsar Spindown

Can accretion of millicharged particles affect the spinning? At steady state a NS should expel as much charge as it accumulates

Observable independent of the magnetic field braking index

If the DM current is similar to the GJ current, the braking index can significantly different than 3 Pulsar Spindown

Dark Matter accretion

Condition Electromagnetic

Gravitational Pulsar Spindown

CK, Perez- Electromagnetic Garcia ‘14

Gravitational

Dolgov,Dubovsky,Rubtsov,Tkatchev ‘13

Can be satisfied for example for MeV, ε~10^-6 and either higher DM density or lower magnetic field

Davidson,Hannestad, Raffelt ‘00 Stopping WIMPs

Different mechanisms of slowing down WIMPs: • Nuclear Stopping • Conductor Stopping • Insulator Stopping

WIMPs don’t have enough energy to ionise atoms, Bohr-Bethe formula is not applicable

Conductor Stopping Free Fermi gas approximation

Insulator Stopping Stopping WIMPs

Different mechanisms of slowing down WIMPs: • Nuclear Stopping • Conductor Stopping • Insulator Stopping

Nuclear Stopping

Millicharged & Light mediators

Contact Interactions Diurnal Modulations & Light DM

There is phase space that will not be covered by underground experiments even if they lower their energy threshold due to effective stopping by the rock.

Need for detectors in shallow sites or on surface However this would increase the background!

Diurnal Modulation

DM particles can reach from top but not from the bottom

This gives a signal that modulates on a daily basis Ideal for portable experiments like DAMIC

CK, Shoemaker ‘14 Dark Matter wind

Detector Dark Matter wind

rotation Dark Matter wind

rotation Dark Matter wind

rotation Dark Matter wind

rotation Dark Matter wind

rotation Estimating the Asymmetry

length traveled underground How the Asymmetry can be detected?

• Portable detectors like DAMIC can be placed either on the surface or in shallow sites • The best latitude for most candidates is where α is the angle between the earth’s rotation axis and earth’s velocity ~ 43 degrees • Best locations at the south hemisphere e.g. Chile, Argentina, New Zealand • The signal varies during the year due to the change in the velocity of the earth with respect to the rest frame of the dark matter halo. The Dark Side of the Stars

Compact stars can reveal a lot of information about the nature of DM putting constraints on its properties complementary to direct searches. ! ๏ Observation of cold neutron stars can exclude thermally produced dark matter. ๏ Asymmetric dark matter: 1.keV to few GeV non-interacting bosonic dark matter is excluded. 2.Part of fermionic WIMP self-interactions excluded. 3.Constraints on WIMP-nucleon spin-dependent interactions. ๏ Millicharged dark matter could slow down pulsars faster than other mechanisms predict.

Diurnal Modulated Signal from WIMP-nucleus stopping as DM travels underground