Constraining decaying dark matter with neutron stars

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Constraining decaying dark matter with neutron stars

M. Angeles Perez-Garcia, Joseph Silk

To cite this version:

M. Angeles Perez-Garcia, Joseph Silk. Constraining decaying dark matter with neutron stars. Physics

Letters B, Elsevier, 2015, 744, pp.13-17. �10.1016/j.physletb.2015.03.026�. �hal-01274104�

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Constraining

decaying

dark

matter

with

neutron

stars

M.

Ángeles Pérez-García

a

,

∗

,

Joseph Silk

b

,

c

,

d

a_{DepartmentofFundamentalPhysicsandIUFFyM,UniversityofSalamanca,PlazadelaMerceds/n, 37008, Spain} b_{Institutd’Astrophysique,UMR7095CNRS,UniversitéPierreetMarieCurie,98bisBlvdArago,75014Paris,France} c_{DepartmentofPhysicsandAstronomy,TheJohnsHopkinsUniversity,HomewoodCampus,Baltimore, MD21218,USA} d_{BeecroftInstituteofParticleAstrophysicsandCosmology,DepartmentofPhysics,UniversityofOxford,OxfordOX13RH,UK}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory: Received18July2014

Receivedinrevisedform12January2015 Accepted13March2015

Availableonline16March2015 Editor:S.Dodelson

The amount of decaying dark matter, accumulated in the central regions in neutron stars together withtheenergydepositionrate fromdecays,mayset alimitontheneutronstarsurvivalrateagainst transitionstomorecompactobjectsprovidednuclearmatterisnottheultimatestablestateofmatter and thatdarkmatterindeedisunstable.Moregenerally,thislimitsetsconstraintsonthedarkmatter particledecaytime,

τ

χ.Wefindthatintherangeofuncertainties intrinsictosuchascenario,masses (mχ/TeV)9×10−4or(mχ/TeV)5×10−2andlifetimes

τ

χ1055s and

τ

χ1053s canbeexcluded

inthebosonicorfermionicdecaycases,respectively,inanoptimisticestimate,whilemoreconservatively, itdecreases

τ

χ byafactor1020.Wediscussthevalidityunderwhichtheseresultsmayimprovewith

othercurrentconstraints.

©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

Disentangling the nature of dark matter (DM) is one of the greatest current challenges in physics. Whether this is realized through a stable or a decaying particle remains unknown to date. There is a vast literature with many well-motivated par-ticle physics models containing unstable, long-lived DM particle candidates, see e.g. [1] for a review. Possible DM decay time-scales,

τ

χ ,areconstrainedbycosmicmicrowavebackground(CMB)

anisotropies,FermiLATlimitsongalaxyclustersandgalactic

γ

-ray diffuseemission, antiprotonsandtheobservedexcess inthe cos-mic electron/positron flux [2,3]. It is usually assumed that the decay daughter particles are (nearly) massless although a more genericsituationwitharbitrarynon-zeromasses,mD,mayalso

oc-cur[4–6].ThespreadofthecurrentboundsontheDMlifetime

τ

χ

or,equivalently,ontheDMdecayrate



χ

=

1

/τ

χ islarge.For

ex-ample,PAMELA[7]andFermiLAT[8]datacanbeinterpretedina scenariowhereadecaying

χ

-particlehasalifetime

τ

e+e−

∼

1026s

forDMmassesmχ



300GeV andwellintotheTeVrange[9](we usec

=

1).Suchlifetimesmayappearinthecontextof supersym-metric grand unification theories through dimension 6 operators

[10]with

τ

GUT

∼

1027 s



TeV mχ



5



_M GUT 2×1016 _GeV



4

.Onthe other hand, CMBdataprovideaconstraint



_χ−1



30 Gyr formasslessdaughter

*

Correspondingauthor.

E-mailaddresses:mperezga@usal.es(M.Á. Pérez-García),silk@iap.fr(J. Silk).

particles whileforsufficiently heavyones, mD



mχ ,decaytimes

remainunrestricted[5].

Here we consider a scenario where weakly interacting scalar bosonic or fermionic metastable DM is gravitationally accreted onto neutron stars (NSs), and possibly first onto the progenitor stars.Inbrief,NSsareastrophysicalobjectsbelievedtohavea cen-tral core, whichconstitutesthe bulk ofthe starandwhere mass densitiesaresupranuclear,i.e.inexcessof

ρ

0



2

.

4

×

1014g

/

cm3.

Although thereis arich phenomenology onthe possibleinternal corecomposition,forthesakeofsimplicity,weconservatively con-sideritheretobecomposedofnucleon(n)fluid,withmass densi-ties

ρ

n

∼ (

1

−

10

)ρ

0.Undertheseconditions,NSsareefficientDM

accretors.They caneffectively capturean incomingweakly inter-acting

χ

-particlepassingthroughthestarsinceitsmeanfreepath ismuch smallerthanthetypical NSradius.Explicitly,

λ

χ



_σχ1_nnn

where

σ

χn is the

χ

-nucleon elastic scattering cross-section that

we will usein the S-waveapproximation andnn

=

ρ

n

/

mn is the

nucleonparticledensity,withmn thenucleonmass.

Compilation of the latest results in direct detection searches

[11] allows analysis to set limits at a level of

σ

χn



10−44 cm2

inthemχ

∼ (

10–104

₎

_{GeV range.Forthesakeofdiscussioninthis}

work,we willconsiderthis

σ

χn value asrepresentative fora DM

particlecandidatehavinginmindthatcurrentexperimentalefforts can potentially providemore stringentlower values. Inthe same fashion, assuming an average NS with typical radius R



12 km

http://dx.doi.org/10.1016/j.physletb.2015.03.026

0370-2693/©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

14 M.Á. Pérez-García, J. Silk / Physics Letters B 744 (2015) 13–17

andmassM



1

.

5M_ eachDMparticlewillscatterinsidea num-beroftimesgivenby

R

/λ

χ



6

.

1



R 12 km

 

_σ

_χn 10−44_cm2

 

_ρ

_n 3

ρ

0



.

(1)

However,accretionofDMwillproceednotonlyduringtheNS lifetime,butalsointhepreviouslatestagesoftheprogenitorstar wherethedensenuclearashcentralcoreallowsthebuild-upofa

χ

-distribution,nχ

(

r

)

,over time.In previous workswehave con-sideredtheeffectofaself-annihilatingDMparticleontheinternal NSdynamics[12–15]butherewewillfocusonthepossibilitythat theonlyprocessdepletingDMisdecay.

The picture is thus similar to proton decay searches such as thoseperformedbySuperKamiokande[16]consistingofa50kton waterdetectorlookingforprotondecaychannelsp

→

e+

π

0

,

ν

¯

K+.

This volume involves

∼

1033 _{protons and is thus sensitive to}

τ

p

∼

1033-34yr asshowedbyanalysisofdata[17].Byanalogy,we

considertheNScoreasatankofDMthatbuildsupintime start-ingasearlyastheprogenitorstarphase.Thenumbersofcaptured particles will depend on the size, mass and composition of the progenitorstar(aswellasontheNSphase)oncetheDM-ordinary matterscatteringcross-sectionisfixed.

The DM accretionprocess onto NSs has beenpreviously esti-mated,seeforexample[18,19],bymeansofthecapturerate,Cχ ,

given an equation of state for regular standard-model matter in theinterioroftheNSatagivengalacticlocationandwitha cor-respondingambientDMdensity.Taking asreferencealocalvalue forDMdensity

ρ

ambient

χ,0



0

.

3 GeVcm3,itisapproximatedby Cχ



3

×

1022 f



M_R





M 1

.

5M_

 

R 10 km

 

1 TeV mχ

 

_ρ

ambient χ 0

.

3_cmGeV3

s−1

,

(2) with f



M_R



=

1

−

0

.

4



_1.5MM 

 

10 km R



a redshift correction fac-tor. Following [20] we do not consider a reduction ofthe DM-n cross-sectionsincewe usecurrentexperimental sensitivity

σ

χn



10−44_cm2_{, wellabove the geometricalcross-section. Itis}

impor-tant to note that this dependence sets a limit on the intrinsic capabilityofNSs toaccumulatea criticalamountofDMand pos-siblyserveasatest-benchforDMproperties.

IntheNS,theDMparticlenumber,Nχ ,canbeobtainedsolving thedifferentialequation dNχ

dt

=

Cχ

− 

Nχ , consideringcompeting

processes,captureanddecay,thelattertreatedviaagenericdecay rate



.TheDMpopulationattimet isthus

Nχ

(

t

)

=

Cχ



+



Nχ

(

tcol

)

−

Cχ





e−(t−tcol)

_,

_t

_>

_t col

.

(3)

Thissolutiontakesintoaccount thepossibilityofan existing DM distributionintheprogenitor starbeforethetimeofthecollapse,

tcol, that produced the supernova explosion. Depending on the

χ

-mass and thermodynamical conditions inside the star, it may be possible to thermallystabilize a DM internal distribution. For the

σ

χn

,

mχ rangevaluesdiscussedsofarthisisindeedthecase.

The DM particle density takes the form nχ

(

r

,

T

)

=

_mρχ

χ

=

n0,χ e− mχ

kB T(r), withn0,χ the central value.

(

r

)

=

r 0

G M(r)dr r2 is

the gravitationalpotential. Assuming a constant baryonic density inthecoreM

(

r

)

=

₀r

ρ

n4

π

r2dr,wefinallyobtain

nχ

(

r

,

T

)

=

n0,χe−(r/rth)

2

,

(4)

withathermalradiusrth

=



3kBT 2πGρnmχ.

In order to asses the importance of the progenitor DM cap-ture efficiency and thus the Nχ

(

tcol

)

value, let us consider a

15M_ progenitor star and its composition through the burning ages [21]. After the He-burning stage for tHe→CO



2

×

106 yr,

a CO mass

∼

2

.

4M_ sits in the corewith a radius R

∼

108 cm. The gravitationally-captured DM population is CHe→CO

χ tHe→CO



3

.

35

×

1039



1 TeV mχ

 

_ρambient χ 0.3 GeV/cm3



. Coherence effects may play a roleforslowlymoving,lowmχ incomingDMparticleswhentheir associated de Broglie wavelength is comparable to the nuclear size, and in this case one should include a multiplicative fac-tor to account fornucleus (N)instead ofnucleon scatterings,i.e.

σ

χN



A2



μ mn



2

σ

χn where A is thebaryonicnumberand

μ

the

reducedmassforthe

χ

−

N system.Sincethelaterburningstages proceedrapidly,theHe

→

CO stagegivesthemaincontributionto theDMcaptureintheprogenitor.

As the fusion reactions happen at higher densities and tem-peratures, the DM thermal radius contracts. In this way, for ex-ample, for mχ

=

1 TeV in the He

→

CO, rth



470 km, while

for Si

→

FeNi, rth



70 km. The thermalization time t−th1

=



3kBT mχ



1/2

σ

χN₍n_mNmχmN χ+mN)2, where nN

=

ρN

mN,for both cases is small

comparedtothedynamicalburningtimescalestth

/

tHe→CO



10−5, tth

/

tSi→FeNi



10−7.Howeverduringthecorecollapse,the

dynam-ical timescale involved is



tdyn col





3

8πρ¯G



10−

3 _{s where}

_ρ

_¯

is an average matter density. Assuming a proto-NS (PNS) forms with T



10 MeV, central density nn

=

5n0 and a

neutron-rich fraction Yneut

∼

0

.

9, nneut

=

Yneut5n0



p3_F,neut

3π2 ,

thermaliza-tion time in this phase takes longer to be achieved [22] tth

=



2m2 χ 9mnkBT pF,neut mn 1 nnσχn





10−2 _s.

ThecorecollapsemaythusaffecttheDMpopulationinsidethe star sincethose DMparticles remaining outsidethePNSmay ef-fectively not be considered to play a role in the NS phase. The number ofDMparticles inthestar interior,r

<

R_∗,is writtenas

Nχ

=

0R∗n0,χ e−(

r/rth)2_{dV anditisa dynamicalquantitysincerth}

is temperature(time)-dependent. As long as R_∗



rth, we obtain Nχ

=

n0,χ

(π

rth

)

3.Theretainedfractionis

fχ

=

N−χ1 RPNS



0 n0,χe−(r/rth) 2 dV

,

(5)

so that for RPNS



10 km, fχ



2

×

10−3.The retained DM

pop-ulation in the PNSafter the collapseis thus Nχ

=

Nχ

(

tcol

)

fχ



6

.

7

×

1036



fχ 2×10−3

 

1 TeV mχ



.LetusnotethatthecentralDM den-sity in the newly formed PNS n0,χ



3

×

1023 cm−3 is much

smallerthanthatinthebaryonicmedium

∼

1038_cm−3_.

At this point one should check that the DM content does not exceed the fundamental Chandrasekar limiting mass for the star to survive. If this was the case, it may lead to gravita-tional collapse of the star (see [23,24]). Therefore, for fermionic DM, we expect Nχ

(

t

)

<

NCh, where NCh

∼ (

MPl

/

mχ

)

3

∼

1

.

8

×

1054

(

1 TeV

/

mχ

)

3 with MPl thePlanck mass,andforthe bosonic

case NCh

∼ (

MPl

/

mχ

)

2

∼

1

.

5

×

1032

(

1 TeV

/

mχ

)

2.In caseaBose–

Einsteincondensateisconsidered[25] NBEC



1036

(

T

/

105 K

)

5and

theconditionisNχ

(

t

)

<

NCh

+

NBEC.Asdescribed,inthefermionic

case, DMremains at all times belowthe limiting mass, butthis may not be the case in the cooling path of the PNS if a Bose– EinsteincondensateisformedforaDMparticleinthe

∼

TeV mass range.Thescenariodescribedheremaybeindeedattheborderof the collapse case, howeverwe will restrict our discussion to the

precollapsedstate,leavingthepossibilityofadditionalcomplexity forfurtherinvestigation.

We can estimate the number of DM decays in the NS phase withina timeinterval



t

=

t

−

tcol



−1 usinga linear

approx-imation inthe exponential expansion in Eq.(3) and withaid of Eq.(5), ND,χ

=

Nχ

(

tcol

)

fχ



t. Fora timeintervalcomparableto

knownagesofancientpulsars(likethatestimatedfortheisolated pulsar PSR J0108-1431



t



τ

old NS

=

1

.

7

×

108 yr [26]), decays

mayhaveprofoundimplications.

Neglecting any phase space blocking effects, the number of decays assuming decay times similar to those in the cosmic positron/electron anomaly

τ

e+e−, is given in the present

sce-nariobyND,χ

=

4

.

2

×

1026



_f χ 2×10−3

 

1 TeV mχ

 

1026s τe+e−

 

t τold NS



.This numberofdecaysovertheNSlifetimemayposeaproblemifthere issufficientenergydepositedinthenuclearmediumtotrigger fur-thermicroscopiceffectsthatmayaffectthestellarstability,aswe willargue.Thus,thepossibleimplicationsoftheabsenceofthese observationsmayindeedservetoconstrainthenatureofsuch de-cays.

Ifwenowfocusonthetypicaldecayfinalstatesofinterestfor fermionicorbosonic(neutral)DM,wecanestimatetheenergy de-positioninthemedium.Strictlyspeaking,injectionanddeposition arerelatedbyaninjectionfractionthatremainsunknownsincewe donotknowthepreferreddecaychannels.Inthisworkandin or-dertocomputethesizeoftheeffect,wewillconsiderthephoton contribution to decays by two-body channels with intermediate (massive) state daughter particles, quarks, leptons, weak bosons



w or, more generic



bosons and photons. Reactions include

χ

→ 

w



w

,

l+l−

,

q+q−

,

2

,

γ

,

χ

→ 

wl, keepinginmindthat

moregeneric decay final states[27] maywell happen.Using the photonspectrum dNγ

dE from[28,29],weestimatetheinjectionrate

per unit volume and unit energy from the contribution of each channelwithcorrespondingdecayrate



i atstellarradiallocation r asQ

(

E

,

r

)

=

nχ

(

r

)

_i



i

dNi

γ

dE .Thentheenergyrateinjectedinthe

promptdecaychannelsiswrittenas

dE dt

=

 

E Q

(

E

,

r

)

dEdV

.

(6)

Energy release fromDM decay is injected locally as microscopic sparks [12] in the inner NS core over a central volume Vth

=

4

3

π

r3th,whereheating andcooling processescompete.Asa result,

inthethermalvolumetheaverageenergydensityinatime inter-val



t is

udecay

  

t



E Q

(

E

,

r

)

dE

.

(7)

However, for single events the energy deposit in a tiny local volume

δ

V canbe muchlarger udecay



Ei_spark

/δ

V foreach

chan-nelandEi_spark



EdN i

γ

dEdE.IndeedDMdecaymaybe regardedas

aspark-seedingmechanisminsimilarfashion tomodernversions ofdirectdetectionnucleationexperiments (PICO,MOSCAB)based onSeitz’stheory on heatspike triggering[30].Thermally induced quarkbubblenucleationinthecontextoftheappearanceofquark starshasbeenalreadysuggested[31] andsome studies[32] con-cludethatquark matter bubblesmaynucleateifthetemperature locallyexceeds

δ

T



few MeV, providedthe MITmodelbag con-stantisB1/4

₌

₁₅₀

_±

_{5 MeV.}

Inthe scenariodepicted here, decaysmayprovide theenergy injection to create a bubble. In order to see this, we estimate theminimumcriticalwork[32] neededtonucleatea neutral sta-blesphericalquark bubble inthecoreof thecold NS.It isgiven by Wc

=

163π



2γ3

P where



P

=

Pq

−

Pn and Pq ( Pn) is the

quark(nucleon)pressure.Foratwo-flavourud-quarksystemPq

=

i=u,d μ4

i

4π2

−

B andassuminganeutron-richsystemPn



(μ

2

n−m2n)5/2 15π2_m

n

asmost ofthe pressure will effectively be provided by neutrons inthefluid.

γ

=

i=u,d μ2

i

8π2,isthecurvaturecoefficientand

μ

i (

μ

n)

isthequark(nucleon)chemicalpotentialrelatedtotheFermi mo-mentum of the degenerate system

μ

i

=

pF i (

μ

n

=



mn2

+

p2F n).

Electrical charge neutrality requires for the ud matter nd

=

2nu

and nn

= (

nu

+

nd

)/

3 with ni

=

μ3

i

π2 in the light quark massless

limit. Note that we do not include further refinements due to non-zeroquark masses,in-medium orCoulombeffects ordroplet surfacetensionsincethey donot changetheglobalpictureaswe wanttokeep acompactmeaningfuldescriptionofthenucleation process. Bubbles haveat least a radius Rc

=



2

γ

/

P and their stability is granted asthey reachthe minimumbaryonic number

Amin

∼

10[33]when A

∼

4₃

π

R3cnn

>

Amin.Althoughtheremaybe

additionalefficiencyquenchingfactorsweexpectthattheydonot significantly alter the picture presented herebut we discussthis possibilitybelowasapossiblesourceofuncertainty.

Inprevious work by Harkoetal.[34],it was assumedthatto convertthefullNS,atleastonestablecapable-to-growquark bub-ble should be formed. However, in order to be conservative we willrequirea numberN0 ofbubblesthatcouldleadtoasizeable

amountofnucleatedmatter,thenonecanwritethiscondition us-ingthesparkseedingrateas

Nbub





dNbub dE dE dtdt

≥

N0

.

(8)

Ifthiswasindeedthescenario,apossiblycatastrophicNStoquark star transitioncould occur when the macroscopicdeconfinement proceedsvia detonation modesto rapidlyconsumethe star[36]. TheGRBsignalemittedhasbeenestimatedin[14]andsubsequent emissionincosmicraychannelsisalsoexpected[15].

In our galaxy, the supernova rateis about R

=

10−2 _yr−1 _so

that an average rate of NS formation over the age of the uni-verse

τ

U

∼

4

.

34

×

1017 s yields NN S

∼

R

τ

U

∼

108–9. Assuming

this population is formed by regular nucleonic NSs, and under the conditions discussed so far regarding DMproperties a lower limit optimistic value (provided one bubble is formed, N0

=

1)

for

τ

χ can be accordingly set from the age of the old NSs as

τ

χ



Nχ

(

tcol

)

fχ



told NS.

The energy density necessary to create such a quark bub-ble withvolume Vd



4₃

π

R3c is therefore ubub



Wc

/

Vd



5

.

4

×

1035_erg

_/

_cm3_{.Thisestimateisinagreementwithsimilarandmore}

detailed calculations [34]. To allow the quark bubbles to nucle-ate,thelocalenergydensitiesmustthenfulfilludecay



ubub.Some

attemps to computationally model progression of seeds of quark matterinsideNSshavebeenrecentlyperformedin[37].

In Fig. 1 we plot the logarithm of

τ

χ versus mχ for bosonic

(upper panel)andfermionic(lower panel)DMparticlecases.We considertheoptimisticvalue N0

=

1 whereonesinglestable

bub-blecanproceedtoconvertthefullstar[34].Thedifferentpartially overlapping rectangular-shapedcoloredregions (solidorhatched) represent exclusion regions for each of the decay channels con-sidered in this work. Particle decays in this region would pro-duce NS transitions over ages below those assumed for regular old NSs. We assume aDM density

ρ

ambient

χ,0



0

.

3cmGeV3 and,in line

withour previous discussion,we set nn

=

5n0. Wecan see there

is a threshold mass belowwhich energy injectionis not ableto growstablebubbles.Wefindthatformasses

(

mχ

/

TeV

)



9

×

10−4 or

(

mχ

/

TeV

)



5

×

10−2 _{in the bosonic or fermionic cases}

16 M.Á. Pérez-García, J. Silk / Physics Letters B 744 (2015) 13–17

Fig. 1. LogarithmofDMdecaytimeasafunctionofmass.Upper(lower)panel de-pictsbosonic(fermonic)channels.Coloredregionsshowourexcludedvalues assum-ingN0=1.Weshowcurrentconstraintsfromupperlimitscomingfromgamma

raysintheGalacticCenterandingalaxyclusters,positronandantiprotonfluxes, andIceCubeandSuperKamiokande.Dashedlinesonbothpanelsdenoteourmost pessimisticgloballowerboundondecaytimearisingfromtheuncertaintiesinthe percolationscenario(seedetailsinthetext).

excluded.Asalreadymentioned,thereisanaturallimitforNSsto effectivelytestdecaying DM,fromtheirability toaccrete and re-tain DM during its lifetime

τ

old NS. We can use thisresult to set

exclusionregions for

τ

χ complementary tothose showninother

worksundertheconditionsofvalidityofourscenario.Weplot up-perlimitconstraintscomingfrome+e−,gammas,antiprotonfluxes andIceCube andSuperKamiokande[2,3].Notethatbosonic decay channelsare ableto probea widerrangeof DMmassesas com-paredto fermionic decays.Our optimistic limitsare considerably strongerthanearlierresults,includingtheCMBconstraints[35].

Atthispointweshouldcriticallyassestheseveraluncertainties thatmayaffectourestimate.Asaresultwedepictagloballower bound on decay time in dashed lines in Fig. 1. In the following we explain the differentoriginof theproposed reduction factors intheDMlifetimes.

Inthemechanismofbubble nucleationinside thecoreofNSs presented in this work, a major uncertainty concerns quenching efficiencies,whichmayrequiremorethanasinglebubbleto trig-gertheNScollapse.Inamoreconservativescenario,theminimum number of bubbles to effectively distort the internal NS struc-ture may be linked to the mechanical instability one can create bynucleation.Theassociatedvariationinpressureisproportional to the volume affected or number of bubbles, this is estimated asgiven by

δ

P





∂P

∂Nbub



0

δ

Nbub where the coefficient is related

to regular nuclearmatter compressibility(in theabsence of bub-bles). In order to quantify the effect,let usconsider an old and cold NS with T

∼

105 K and

ρ

n

=

5

ρ

0 for a DM particle with mχ

∼

1 TeV. TheDMparticle numberinsidethe NSthermal vol-ume is Ath



Vthnn



1042. If each possibly formed bubble has

a baryonic number Amin



10 thena macroscopic N0 numberof

bubbles account for Abub

∼

10N0. In principle, a standard

varia-tioninthenumberofnucleonsdepletedfromthethermalvolume nucleonsea,

√

Ath



1021,could providealargeenough variation

in pressure to trigger transitioning. Then the number of bubbles to create this perturbation is N0



√

Ath

/

Amin



1020.In such a

pessimistic scenario, the limits on DM decay lifetimes wouldbe reducedbyasimilarproportion.

In addition, heavy-ioncollision simulations usingperturbative QCD[38]giveestimatesofthetypicalquenchingfactororratioof energyspreadinthiscontextasQ



O(

0

.

1

)

.Onemustnote how-ever that the jet-sized regions in heavy-ion collisions are about three orders of magnitudeor more smaller in local energy den-sity i.e.

∼

GeV

/

fm3 than the ranges presentedin thiswork with

∼

a few fm spatial spread on a time-scale of several fm/c. This size is comparable to typical bubble sizes. We expect that this correction doesnot significantlyaffecttheresultspresentedhere. In addition oneshould consider that Pauliblocking effectsof or-dinary matter may reduce the kinematicalphase spaceavailable for the DM-n interaction effects atthe few percent for low mχ

whilebeingnegligibleintheTeVrangeandabove.Alsothe uncer-tainty onthe quotedminimumbubble sizeandbaryonicnumber can somewhat further constrain the lower mχ range,and so we should be safe for somewhat larger masses. Note however that some works havesuggesteda decaying PeVmassDM particleas an explanation to IceCube PeV cascadedata [40,41]. Such a PeV mass DM particle would be however at the limit of thermaliza-tionfor

σ

χn

∼

10−44 cm2,a smallercross-section invalidatingthe

thermalization procedure quoted in our NS scenario and cannot be ruled out in light of our current findings. However, existing data,asdepictedinFig. 1allowsfora

∼

104–105factorinlifetime to vary proportionally the cross-section and DMmass parameter space, andself-consistentlyother parametersinthemodel.Aswe do not intend to perform a detailed analysis in this work, we leave thistask forfuture contributions. Linked to thisargument, we haveconsideredan average-sized massiveNS,however, varia-tionsinmassandradiusincurrentsurveysareoftheorderof30%

[39] and thecapturerate wouldbe affected ina similar fashion, resultinginamoderatelyreducedcaptureefficiency.

In summary, we have shown that the current population of galactic NS may constrain the nature of a decaying bosonic or fermionic DM particle with mass in the GeV–TeV range. Since there are a number of uncertainties intrinsic to the model, we discussinparticulartwo cases,namelythe optimisticcasewhere we find that DM particles with lifetimes

τ

χ



1055 s exclude

masses

(

mχ

/

TeV

)



9

×

10−4 or

τ

χ



1053s excludes

(

mχ

/

TeV

)



5

×

10−2_{inthebosonicorfermioniccases,respectively.}

Uncertain-ties associatedmay substantially reduce theselimits. Inthe pes-simisticcase, aglobalboundisset withlifetimes afactor



1020 smallerthat stillimproveonrivalboundsfrome+e−,

γ

, p fluxes

¯

and IceCube andSuperKamiokande, leavinga combinedfactor of

∼

104_–105 _{in lifetime if different cross-sections or masses are}

considered. Theseresults areobtainedfromthe prior ofavoiding nucleation of quark bubbles ina NS coredue toefficient energy injectionbysparkseeding.Ifthiswas thecase, aconversionfrom NSintoquarkstarwouldbetriggered,therebyreducingthe popu-lationofregularNSinthegalaxy.

Acknowledgements

M.A.P.G.wouldliketothankusefuldiscussionswithR.Lineros, C.Muñoz andP. Panci. She acknowledges thekind hospitalityof IAPwherepartofthisworkwasdeveloped.Thisresearchhasbeen supported at University of Salamanca by the Consolider MULTI-DARKandFIS2012-30926MINECOprojectsandatIAP bytheERC project267117 (DARK)hostedbyUniversité PierreetMarieCurie –Paris6andatJHUbyNSFgrantOIA-1124403.

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