Main sequence stars with asymmetric dark matter

0.68 MB·English

by  Fabio Iocco

Main sequence stars with asymmetric dark matter
Fabio Iocco1,2, Marco Taoso34, Florent Leclercq1,5 and Georges Meynet6
1 Institut d’Astrophysique de Paris, UMR 7095, CNRS,
UPMC Univ. Paris 06, 98bis Bd Arago, F-75014 Paris, France
2 The Oskar Klein Center for Cosmoparticle Physics, Department of Physics,
Stockholm University, AlbaNova, SE-106 91 Stockholm, Sweden
3 Multidark fellow at IFIC (CSIC-Universitat de Valencia), Ed.Instituts, Apt.22085, 46071 Valencia, Spain
4 Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
5 E´cole Polytechnique ParisTech, Route de Saclay, F-91128 Palaiseau, France and
6 Geneva Observatory, University of Geneva, Maillettes 51, 1290 Sauverny, Switzerland
(Dated: January 27, 2012)
Westudytheeffectsoffeeblyornon-annihilatingweaklyinteractingDarkMatter(DM)particles
onstarsthatliveinDMenvironmentsdenserthanthatofourSun. Wefindthattheenergytransport
mechanism induced by DM particles can produce unusual conditions in the core of Main Sequence
stars, with effects which can potentially be used to probe DM properties. We find that solar mass
starsplacedinDMdensitiesofρ ≥102GeV/cm3 aresensitivetoSpin-Dependentscatteringcross-
χ
sectionσ ≥10−37cm2 andaDMparticlemassaslowasm =5GeV,accessingaparameterrange
SD χ
2 weakly constrained by current direct detection experiments.
1
0 PACSnumbers: 95.35.+d,97.10.Cv
2

n
Introduction— Identifying the Dark Matter (DM) is stellar structure.
a
one of the most enthralling problems of modern cosmol- WhetherDMparticlesareactuallyintrinsically“asym-
J
ogy and particle physics. Weakly Interacting Massive metric”, or if their self-annihilation rate in stellar envi-
5
Particles (WIMPs) are among the most popular candi- ronment is low enough ((cid:104)σv(cid:105) <10−33cm3/s for the Sun)
2 ∼
datesandarecurrentlysearchedforwithdifferentstrate- is indistinguishable for its effects in stellar evolution, [9];

] gies, see e.g Ref. [1] for reviews. The effects of WIMPs hereafter our definition of “asymmetric” embraces the
R
on stars have been recently investigated as possible ad- previous condition.
S ditional probes for DM searches: in presence of self- ADM in stars— Here we adopt the same formalism as
h. annihilations, WIMPs captured inside a star can pro- in[9],towhichweaddressthereaderfordetails. Athor-
p vide an exotic source of energy. Whereas the effects on ough description of the underlying theory can be found
- the Sun are negligible because of the small DM density also in [2] and references therein. DM particles can be
o
in the solar neighborhood, they may be remarkable on capturedbyastarviascatteringoffnuclei, theevolution
r
t starslivingindenseDMenvironmentssuchastheGalac- of the total number of DM particles N inside the star
s χ
a tic Center, or the first halos to harbor star formation reading:
[ at high redshift [2–5]. In general, indirect searches of
DM would fail for very feebly annihilating DM candi- N˙ =C−2AN2−EN (1)
1 χ χ χ
v dates. Thisisthecase,forinstance,ofmanyasymmetric
7 DM(ADM)models(seee.g.[6]),whereDMannihilations where C is the particle capture rate over the star, A is
8 maynotoccurinpresenceofanasymmetrybetweenDM theannihilationrateandE theevaporationone. Forthe
3 particles and antiparticles. Still, these particles accumu- asymmetricDMcandidatesweareconsidering,theanni-
5 latedinastarcanscatteroffnucleiandtransportenergy hilation rate is null and evaporation is negligible for the
1. within its bosom. This effect results in a modification physical conditions on which we focus, equation 1 there-
0 of the density and temperature profiles which can lead fore becomes trivial for ADM. Here we recall the linear
2 to detectable changes of the solar neutrino fluxes and dependence of the capture rate on the spin-dependent
1 gravity modes [7–10]; more compact objects like neutron scattering cross section σSD and the environmental DM
:
v stars may cumulate enough particles to reach the Chan- density ρχ. Captured particles keep on scattering with
i drasekhar mass and drive the collapse of a central black the stellar gas reaching a thermally relaxed distribution
X
hole, [11,12]. Stellarphysicscanthusprovideastrategy inside the star, nχ(r)=nχ,0e−r2/rχ2. For the DM masses
r
a to indirectly test this class of models. Interestingly, the and cross sections we are going to consider, in a Sun-
evolution of Main Sequence, solar mass stars placed in like star the thermal DM radius r is of the order of
χ
environments with higher ADM densities has not been r <109 cm(∼0.03R ),thusmakingDMparticlescon-
χ ∼ (cid:12)
studied yet (while this paper was being refereed, a re- fined within the nuclear energy generation region. DM
cent study addressing very low-mass stars in ADM has particles weakly interacting with the baryons provide an
been published, [13]). Here we address this topic, show- energy transport mechanism, additional to the standard
ingthattheenergytransportinducedbyADMcumulat- ones. In their orbits, DM particles scatter in the in-
ing inside such stars can provoke dramatic effects on the nermost regions (called the “inversion core” hereafter)
absorbingtheheatandreleasingitintheimmediatesur-
2
3 1.9
ǫnuc (no ADM) T (no ADM)
ǫnuc T (ρχ = 102 GeV/cm3 mχ = 5 GeV)
2 ǫtrans 1.8 T (ρχ = 103 GeV/cm3 mχ = 10 GeVTχ)
T
−1] χ
−1.s K] 1.7
ǫg [erg.g 1 7T [10 1.6
o
l
0
1.5
−1 1.4
0.01 0.02 0.03 ri 0.05 0.06 0.07 0.08 0.09 0.1 0.01 0.1
R/R⊙ R/R⊙
FIG. 1: The structure of (cid:15) and (cid:15) for 1M FIG. 2: Stellar (baryonic) temperature profile for two ADM
trans nuc (cid:12)
star evolved with the ADM parameters ρ =103GeV/cm3, parameterset,asfromtheplot;thesolidblacklineisamodel
χ
σ =10−37cm2, m =10GeV. The profile is taken when the evolved without DM. The profile is taken when the central
SD χ
central hydrogen fraction, X =0.2. Also shown for compari- hydrogen fraction, X =0.2. This corresponds at an age of
c c
son is (cid:15) of a star evolved without ADM, at the same age. approximately5.3,5.4,and5.6GyrforthecasewithnoADM,
nuc
The shaded area -innermost of r - shows where (cid:15) has and increasing ADM density ρ , respectively.
i trans χ
negative sign, thus absorbing energy from the stellar gas.
than the nuclear energy generation term (cid:15) , the global
nuc
roudings, within the nuclear energy production region. properties of the star are not modified. We have verified
Stars in high ADM densities— The effects of the DM that the central temperature and density profile are al-
energytransportisenhancedforincreasingDMdensities teredwithrespecttothesamestarevolvedwithoutDM,
since the number of particles cumulated inside the star accordingtowhatwehaveseenin[9]: neutrinofluxesand
grows linearly with ρ (see the Appendix for a short dis- seismic g-modes of the star get modified with respect to
χ
cussion on this). Hence, we have studied the evolution the standard case and we defer a systematic analysis of
of a solar type star (1M , X=0.72, Y=0.266, Z=0.014) this to later studies.
(cid:12)
for increasing DM densities. In this section we fix the Here we focus on a much more dramatic effect, taking
DM-protonspindependentcrosssectionσSD=10−37cm2 placewhen(cid:15)transbecomescomparablewith(cid:15)nuc. Forour
and DM particle mass mχ=10GeV. We will discuss the choice of DM parameters mχ and σSD this takes place
effect of varying these parameters in the following sec- when the total population of DM particles in the star,
tions, whereas we keep the stellar velocity through the n ∼5×1047# (for this particular choice of parameters
tot
DM halo v¯=220 km/s. andstellarmass,thistakesplaceapproximately5Gyraf-
We have modified the publicly available DarkStars tertheZeroAgeMainSequence). InthisconditionsDM
code [14], in order to use the Spergel & Press formalism is able to transport out of a very central region the en-
(Eq. 4.9 in [15]) rather than the Gould & Raffelt one, tireenergygeneratedbynuclearreactions,thusresulting
[16]. Whereas the latter has been proved to correct the in an efficient sink of energy for the stellar region within
overestimate -of order unity- present in the previous for- theinversionradiusr ∼0.04R ,namelytheregionwhere
i (cid:12)
malism, we have noticed that in critical conditions such theisothermalWIMPtemperatureislowerthanthelocal
as the ones we meet in our study the implementation of baryonictemperature,T <T . Outsideofr ,yetwithin
χ b i
this formalism may easily induce a unphysical behavior the nuclear energy generation region r ∼0.1R , DM
nuc (cid:12)
of the solution obtained by numerical codes. We have particlesdeposittheenergyabsorbedfromtheinnermost,
found this numerical artifact to show up both with the hotter baryons into the local medium, colder than T .
χ
original DarkStars code and the GENEVA stellar evolu- This energy deposit is not crucial: what matters most is
tion code [17], modified for the inclusion of DM effects, the effective diminished efficiency of the nuclear energy
as we have described in [9]. The effects we describe in sourceatthecenter. Thestarisforcedtocompensatefor
thefollowingcouldthereforebeoverestimatedofafactor thisdecreasebyincreasingthenuclearenergyproduction
unity, namely they could show up for DM densities ρ a outsidetheinversioncore. InFigure1weshowtheradial
χ
factor unity bigger than the actually quoted ones. structure of (cid:15) compared to (cid:15) : it is clearly visible
trans nuc
We evolve the star from the Zero Age Main Sequence, howtheDMenergytransportisthemechanismdictating
by adopting an environmental ρ =103GeV/cm3, which theenergeticsoftheregionwithintheinversionradiusr ,
χ i
foraNFWDMdensityprofilecorrespondstoR ∼10pc andtheenergysinkcausedbyDMinthisregioninduces
gal
from the Galactic center. As long as the absolute value atemperaturedrop. Anexampleoftheresultingtemper-
of the DM transport energy term (cid:15) is much smaller atureprofileisshowninFigure2,whereboththecentral
trans
3
drop within r caused by the ADM energy absorption, The modifications of the stellar structure described in
i
and a raise in the shell between r and r are clearly theprevioussection,inducedbyADM,areclearlyvisible
i nuc
visible. Such new temperature profile is the result of in the HR diagram. In our Figure 3 it is possible to see
thenewequilibriumreachedbythestar,whichreadjusts how the model described above detaches from a normal
its structure in order to provide the correct energetics; path in the temperature-luminosity plane once captured
the new nuclear reaction rate (cid:15) is visible in Figure DM particles have achieved the right number n . The
nuc tot
1. These modifications are quite remarkable, modifying new distribution of temperature makes the star more lu-
the chemical evolution of the star as well as its external minous and bigger, thus moving left and upward in the
appearance, see more in the next Section. plane for low ADM densities. The resulting position of
The behavior we have described is reached when DM thestarintheHRdiagramisthereforeunusual,andmore
particles are enough that (cid:15) >(cid:15) in the central re- so as the star ages and gets toward the end of the MS.
trans nuc
gionofthestar,withinri. Forthevalueofenvironmental In Figure 3 it can be appreciated how by increasing ρχ
DM density ρ =103GeV/cm3 and v¯=220 km/s adopted the actual position of the star in the HR changes, finally
χ
in this run, this happens quite early during the evolu- reverting it to lower luminosities as a consequence of the
tion of the star, whereas for DM densities smaller than dramatic drop in temperature, as explained in the pre-
ρ =103GeV/cm3(withm =10GeV),thetimeneededfor vious Section; still, these stars are kept away from the
χ χ
thestartocaptureenoughparticlesislongerthantheMS usual track. This could indeed be used to identify a pe-
itself, so the mechanism we have described can not take culiar generation of stars, and probe ADM parameters
place. Conversely, for increasing DM densities ρ (and or the distribution of ADM in our Galaxy. However, we
χ
thereforethecapturerateC)thisarrivesatshortertimes caution that these observational tests are challenged by
during the Main Sequence. the difficulty of observing stars close to the galactic cen-
ter (or in the very center of Dwarf Galaxies, where DM
Wehaveevolvedseveralstellarmodelsfordifferentval-
environmentalconditionscouldbesimilar), whichmakes
ues of the environmental DM density (keeping constant
currentuncertaintiesonthepositionofthesestarsinthe
σ andm ),findingthatremarkableeffectsonthestel-
SD χ
HR diagram quite large.
larstructurearepresentfordifferentDMdensitiesρ . It
χ
is worthwhile to remark that for increasing ρ , DM par- However, it is worth to remark that, unlike the case of
χ
ticlesstartbeinganeffectivesinkofenergyatdecreasing annihilating DM, the effects of ADM may be “portable”
times. The cumulation of more particles during the MS by the star throughout its journey in space. In the case
boosts the (cid:15) increasingly, with even more remark- of DM annihilating and providing an additional energy
trans
able effects: in Figure 3 we show the impact of increas- sourcetothestar,theeffectsaretightlyrelatedtotheen-
ing ADM densities on the star’s evolution. Whereas for vironmental DM density the star is experiencing within
ρ <104GeV/cm3 |(cid:15) |>(cid:15) forR< r ,itsintegral the short equilibrium time -O(106yr). Self-annihilation
χ ∼ trans nuc ∼ nuc
over the whole star is smaller than the total nuclear lu- depletestheDMcumulatedinsidethestar,andacontin-
minosity of the star, L ≡ (cid:82) |(cid:15) |dV < L : the uous provision is required to keep the effects going, [2].
trans trans nuc
structure reacts to it by finding a new stable configura- ADM does not escape from the star: in principle stars
tionatincreasedluminosities, byreadjustingthenuclear may capture ADM in a dense environment and migrate
reactionratebetweenr andr . Ontheotherhand,at somewhere else in the Galaxy, and the effects would still
i nuc
veryhighADMdensity(ρ >105 GeV/cm3)thetemper- be visible.
χ ∼
atureismitigatedinthewholenuclearenergygeneration The effect of varying DM parameters— For the values
region,ratherthanonlyintheinversioncore. Thisisbe- of σ we are considering, the DM energy transport is
SD
cause the energy reinjected by the WIMPs at R > ri is nonlocal,i.e. theDMfreepathislargerthanrχ andDM
now sufficient to inflate that region, thus cooling it and particlescanefficientlytransportenergybetweendistant
reducing the efficiency of (cid:15)nuc. The envelope then con- regions in the stellar core. In this case, (cid:15)trans is en-
tracts to extract energy from the gravitational potential hanced for larger σ , until the DM energy transport
SD
well . becomes local and so (cid:15) is decreased, this happening
trans
Summarizing, when Ltrans < Lnuc: the star compen- for σSD >∼10−34 cm2. Capture of DM particles is eas-
sate for the deficit of nuclear energy generation in the ier for lighter ones, and heavier DM particles tend to be
center by increasing the nuclear energy generation out- confined in smaller regions inside the core, both effects
side the inversion core. At L > L : the redistri- making the DM transport inside stars more sensitive to
trans nuc
bution of the energy by the WIMPS is such that (cid:15) small values of m .
nuc χ
is reduced in the whole nuclear core and the star must For m =10 GeV and σ =10−38cm2 the dramatic ef-
χ SD
compensatethisdeficitbythecontractionofitsenvelope. fects on the stellar structure which we have previously
Diagnostic power— Is it possible to use such mech- discussed start to appear for ρ ≥105GeV/cm3. This ac-
χ
anism as a possible probe for ADM parameter space, tually demonstrates that smaller SD cross sections can
namely: are stellar observables affected from this mech- be explored, although the price to pay is to shrink the
anism at a testable level? Deviations from the standard regionoftheGalaxypotentiallyprobingthismechanism.
path in the Hertzsprung-Russel (HR) diagram are the On the other hand, for σ =10−36cm2 the same situa-
SD
ideal observable. tion is reached at lower DM densities, ρ =102GeV/cm3.
χ
4
very same environment, low mass stars may be affected
0.4
no ADM bythedramaticADMeffects,whereasmoremassiveones
0.3 ρρχχ = = 1 1030 2G GeVeV//cmcm3 3m mχχ = = 1 50 GGeeVV are insensitive to it.
ρχ = 104 GeV/cm3 mχ = 10 GeV It is also worth discussing the effects produced by this
ρχ = 105 GeV/cm3 mχ = 10 GeV mechanismonthefirststarstoformintheUniverse, the
]! 0.2 ρχ = 106 GeV/cm3 mχ = 10 GeV supposedlymassivePopulationIII.Theseobjectsshould
L
L/ be naturally placed in very high DM density environ-
g [ 0.1 ments, as they are born at the center of a collapsing
o
l
minihalo at high-redhisft, and this is known to enhance
0 DM effects onto such stars, [4, 5].
We have evolved a 100M star with metallicity
(cid:12)
−0.1 Z=10−4, withincreasingADMdensities, findingthatfor
σ =10−37cm2theeffectsillustratedthroughoutthispa-
SD
3.79 3.785 3.78 3.775 3.77 3.765 3.76 3.755 3.75 pershowupatρ ≥5×1010GeV/cm3. Suchdensitiesare
log [Teff/K] likely to be achieχved in the very central regions of a pri-
mordial star forming halo [18]; yet, recent simulations of
FIG. 3: The Hertzsprung-Russel diagram for 1M(cid:12), for first star formation show a fragmentation of the proto-
varying DM parameters as marked in the plot, with stellar core, thus yielding to both smaller stellar masses,
σSD=10−37cm2. The solid black square is the starting point and lower central DM densities [19]. Whereas no conclu-
of our simulation, black solid circles mark an age of 6Gyr,
sions can be drawn at the level of the state of the art, it
not achieved for runs with ρ > 103GeV/cm3. Black solid
χ is worth to remark that the two effects may compensate
triangles mark the fall of central hydrogen fraction X below
c each other, and PopIII may be indeed affected by ADM.
0.1. Thistakesplaceatanageof6.05,6.36,and6.39Gyrfor
the no ADM case, ρ =102,103 GeV/cm3, respectively. No- Conclusions— In this paper we have shown for the
χ
ticethatthefluctuationsmaybenumericalartifacts,seeAp- first time that feebly or non-annihilating DM, carrying
pendix for details. weak interactions with the baryons, can have dramatic
effects on solar mass, Main Sequence stars placed in DM
environments denser than that of our Sun. This is due
For smaller DM masses (but still above the evaporation to the enhancement of DM-driven transport effects, that
mass ∼5 GeV) it is possible to probe smaller σ , for evacuate the nuclear energy produced in center of the
SD
the same value of DM density. core of the star. We have shown that once this happens
Effects on massive stars— In principle, the accumula- this may provoke dramatic changes in the structure and
tion of ADM particles inside massive stars should have external appearance of the star. We have shown that
thesameeffectsasinlow-massones,thetransporteffects such dramatic effects take place in solar mass stars in
of DM not-depending (explicitly) on the burning mech- environments with DM densities ρχ >∼102GeV/cm3, and
anism (hydrogen via p-p or CNO). However, one crucial that they can in principle be used as a probe for DM
fact is to be stressed: transport effects start modifying particle masses as low as m =5GeV and spin-dependent
χ
dramatically the structure of a star when (cid:15)trans is of the cross sections σSD >∼10−37cm2. Such parameter values
same order of (cid:15) within r . Two important things are are quantitavely comparable with those that could be
nuc i
tobenoticed: i)thestellarluminosityscalesnonlinearly placed by the failed observations of neutron stars in re-
withthestellarmass,L ∝M3.5;ii)thelifetimebecomes gions with this very same (fermionic) ADM density, see
∗ ∗
shorter as the stellar mass increases. The latter, com- e.g. Figure 1 of [12], yet for as difficult as the observa-
bined with the fact that the capture rate does not scale tion of MS stars can be at the Galactic Center or ADM
strongly with the stellar mass (roughly C ∝ M ), leads dense environments, they are less challenging than those
∗
totheconclusionthathighermassstarsarelesssensitive of cold neutron stars.
than low-mass ones to the same DM parameters. We Acknowledgements— We thank P. Scott for essential
have evolved models of increasing stellar mass between insights on the structure of the DarkStars code. FI
1 and 10 M for the same ADM parameters, that we has been supported from the European Community re-
(cid:12)
take σ =10−37cm2, ρ =107GeV/cm3, m =5GeV. The search program FP7/2007/2013 within the framework of
SD χ χ
5M model gets out of the typical path on the HR at convention #235878; MT from the Spanish MICINNs
(cid:12)
an age of approximately 90 Myr (X ∼0.2). Stars with ConsoliderIngenio2010ProgrammeundergrantMULTI-
c
masses larger than 6M evolve normally, i.e. the impact DARKCSD2009-00064. Hisworkispartlysupportedby
(cid:12)
of such ADM densities on their evolution is negligible. the Spanish grants FPA2008-00319 (MICINN), PROM-
This shows that stars with masses around the solar ETEO/2009/091 (Generalitat Valenciana) and the Eu-
value-orevensmaller,asin[13]-arebetterADMprobes ropean Council (Contract Number UNILHC PITN-GA-
than bigger ones, and yet this is good news, as approxi- 2009-237920) and by the Institute of Particle Physics
mately60%ofthestellarmassinourGalaxyisexpected (IPP) Theory Fellowship and the Natural Sciences and
to be present in the 0.1M ≤M ≤1M range. In the Engineering Research Council (NSERC) of Canada).
(cid:12) ∗ (cid:12)
5
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