dark stars, or how dark matter can make a star shinegcosmo.bao.ac.cn/sites/default/files/ppt_naoc...

Dark Stars are made of ordinary matter and shine thanks to the annihilation of dark matter.

Paolo GondoloUniversity of Utah (Salt Lake City)Oskar Klein Centre (Stockholm)

Dark Stars, or How Dark Matter Can Make a Star Shine

Friday, October 21, 11

Dark StarsThe first stars to form in the universe may have been powered by dark matter annihilation instead of nuclear fusion.

They were dark-matter powered stars or for short Dark Stars

• Explain chemical elements in old halo stars

• Explain origin of supermassive black holes in early quasars

Artist’s impression

Spolyar, Freese, Gondolo 2008Freese, Gondolo, Sellwood, Spolyar 2008Freese, Spolyar, Aguirre 2008Freese, Bodenheimer, Spolyar, Gondolo 2008Natarajan, Tan, O’Shea 2009Spolyar, Bodenheimer, Freese, Gondolo 2009


PreliminariesResults

BackgroundTheorySimulations

The idea in a nutshell (cartoon version)

Pat Scott IDM 2008 Main sequence dark stars at the Galactic Centre

Salati, Silk 1989Moskalenko, Wai 2006Fairbairn, Scott, Edsjö 2007Spolyar, Freese, Aguirre 2008Iocco 2008Bertone, Fairbairn 2008Yoon, Iocco, Akiyama 2008Taoso et al 2008Iocco et al 2008Casanellas, Lopes 2009

Galactic center example courtesy of Scott

Dark Matter BurnersStars living in a dense dark matter environment may gather enough dark matter and become Dark Matter Burners

Dark Matter Burners Dark Stars

• Explain young stars at galactic center?

• Prolong the life of Pop III Dark Stars?

Text

Renamed in Fairbairn, Scott, Edsjö


• A WIMP in chemical equilibrium in the early universe naturally has the right density to be Cold Dark Matter

Weakly Interacting Massive Particles (WIMPs)

• One can experimentally test the WIMP hypothesisThe same physical processes that produce the right amount of WIMPs make their detection possible

Dark matter particles

Cold DarkMatter

Dark Energy

Photon

sBar

yons

Neutr

inos

DirectAccelerator Indirect

LHC DAMA, XENON, etc Fermi IceCube PAMELA


Dark matter creation with particle accelerators

Børge Kile Gjelsten, University of Oslo 44 IDM, Aug 2008

The ATLAS detector Particle production at the Large Hadron Collider

Searching for the conversionprotons → energy → dark matter E=mc 2 in action


Direct detection of particle dark matter

Darkmatterparticle

crystal (or gas or liquid)

Low-background underground detector

CRESST

The principleDark matter particles “kick” nuclei in a detector

CDMSEDELWEISSDAMACRESSTKIMSDRIFTXENONCOUPPCoGeNTTARPDMTPCTEXONOPANDA-X.....


The DAMA modulation

8.2σ detection

Drukier et al 1986Bernabei et al 2003-10 2-6 keV

Time (day)

Res

idua

ls (c

pd/k

g/ke

V) DAMA/LIBRA 5 250 kg (0.87 ton×yr)

DAMA finds a yearly modulation as expected for dark matter particles


Interpretation of DAMA modulation

Light WIMPs are compatible with other experimentsGondolo, Gelmini 2005; Petriello, Zurek 2008Fairbairn, Schwetz 2008; Savage, Gelmini, Gondolo, Freese 2008

25

100 101 102 10310!8

10!7

10!6

10!5

10!4

10!3

10!2

10!1

100

MWIMP !GeV"

!"p!pb"

spin#independent CDMS I Si

CDMS II Ge

XENON 10

Super#K

CoGeNT

TEXONO

CRESST I

DAMA !3!#90$"

with channeling

DAMA !7!#5!"

with channeling

DAMA !3!#90$"

DAMA !7!#5!"

FIG. 5: Experimental constraints and DAMA preferred parameters for SI only scattering. TheDAMA preferred regions are determined using the likelihood ratio method with (green) and without(orange) the channeling e!ect.

100 101 102 10310!4

10!3

10!2

10!1

100

101

102

103

104

MWIMP !GeV"

!"p!pb"

spin#dependent

!an % 0, proton only"CDMS I Si

CDMS II Ge

XENON 10

Super#K

CoGeNT

TEXONO

CRESST I

DAMA !3!#90$"

with channeling

DAMA !7!#5!"

with channeling

DAMA !3!#90$"

DAMA !7!#5!"

FIG. 6: Experimental constraints and DAMA preferred parameters for SD proton-only scattering.The DAMA preferred regions are determined using the likelihood ratio method with (green) andwithout (orange) the channeling e!ect. The CoGeNT and TEXONO constraints are too weak tofall within the shown region.

Savage, Gelmini, Gondolo, Freese 2008

with channeling

w/o channeling


CoGeNT “irreducible excess”CoGeNT observes an annually-modulated “irreducible excess of events” compatible with ~7 GeV WIMPs

Aalseth et al 2010

Noise or WIMPs?

Aalseth et al 2011


Indirect detection of particle dark matterThe principleDark matter particles transform into ordinary particles, which are then detected or inferred


Indirect detection of particle dark matter

Neutrinos from the Sun

Dark matter particles sink into the Sun where they transform into neutrinos

The principleDark matter particles transform into ordinary particles, which are then detected or inferred

ANTARES

DM spike at galactic center

Gondolo, Silk 1999Gondolo 2000

VisibleGalaxy

Black Hole

DarkMatterSpike

Neutrinos, Photons, ...

If cuspy halo

• neutrino source

• !-ray source

• radio source(too strong)

Black Hole at Galactic Center

Gondolo, Silk 1999

Neutrinos from theGalactic Center

Krauss et al 1985


Indirect detection of particle dark matter

FERMI

PAMELA

VERITAS

AMS

The principleDark matter particles transform into ordinary particles, which are then detected or inferred

Dark matter particles wander through the galaxy

Gamma-rays, positrons, antiprotons from our galaxy and beyond

HEATBESSPAMELAAMSGAPSEGRETHESSMAGICVERITASGLASTSTACEECACTUS…


Energy (GeV)

0.1 1 10 100

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-(e!

)+

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Muller & Tang 1987

MASS 1989

TS93

HEAT94+95

CAPRICE94

AMS98

HEAT00

Clem & Evenson 2007

PAMELA

secondaries from cosmic ray collisions in interstellar medium

Adriani et al. [PAMELA], arXiv: 0810.4995

Cosmic ray positrons

Excess

Abdo et al [Fermi-LAT], arXiv: 0905.0025

Excess

High energy cosmic ray positrons are more than expected


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ON POSSIBLE INTERPRETATIONS OF FERMI ELECTRON SPECTRUM 15

Figure 6. In this figure we compare the electron plus positron spectrum from multiplepulsars plus the Galactic (GCRE) component with experimental data (dotted line). Weconsider the contribution of all nearby pulsars in the ATNF catalogue with d < 3 kpcwith age 5 ! 104 < T < 107 yr by randomly varying Ecut, !e± !t and " in the rangeof parameters given in the text. Each gray line represents the sum of all pulsars for aparticular combination of those parameters. The blue dot-dashed (pulsars only) and bluesolid lines (pulsars + GCRE component) correspond to a representative choice amongthat set of possible realizations. The purple dot-dashed line represents the contribution ofMonogem pulsar in that particular case. Note that for graphical reasons here Fermi-LATstatistical and systematic errors are added in quadrature. Solar modulation is accountedas done in previous figures.

(1) The rationale to postulate a particle dark matter mass in the 0.5 to 1 TeV range,previously motivated by the ATIC data and the detected “bump”, is now muchweaker, if at all existent, with the high statistics Fermi-LAT data;

(2) CRE data can be used, in the context of particle dark matter model building, toset constraints on the pair annihilation rate or on the decay rate, for a given darkmatter mass, di!usion setup and Galactic halo model;

(3) as discussed in Sec.2, unlike the Fermi-LAT CRE result, the PAMELA positronfraction measurement requires one or more additional primary sources in additionto the standard GCRE component, as discussed in Sec. 2; if the PAMELA dataare interpreted in the context of a dark-matter related scenario, Fermi-LAT dataprovide a correlated constraint to the resulting total CRE flux.

We emphasize here that, although not per se needed from data, a dark matter interpre-tation of the Fermi-LAT and of the PAMELA data is an open possibility. Neverthelesswe note that a dark matter interpretation of the Fermi-LAT data is disfavored for at leastthe three following reasons:

16 D. GRASSO, S. PROFUMO, A.W. STRONG, ET AL.

Figure 7. The positron fraction corresponding to the same models used to draw Fig.6 is compared with several experimental data sets. The line styles are coherent with thosein that figure. Solar modulation is are accounted as done in

• Astrophysical sources (including pulsars and supernova remnants) can accountfor the observed spectral features, as well as for the positron ratio measurements(sec. 3.1): no additional exotic source is thus required to fit the data, althoughthe normalization of the fluxes from such astrophysical objects remains a matterof discussion, as emphasized above.

• Generically, dark matter annihilation produces antiprotons and protons in additionto e±. If the bulk of the observed excess high-energy e± originates from dark matterannihilation, the antiproton-to-proton ratio measured by PAMELA (Adriani et al.2009 [53]) sets very stringent constraints on the dominant dark matter annihilationmodes (Cirelli et al. 2009 [17]). In particular, for ordinary particle dark mattermodels, such as neutralino dark matter (Jungman 1996 [49] or the lightest Kaluza-Klein particle of Universal Extra-Dimensions (Hooper & Profumo 2007 [50]), theantiproton bound rules out most of the parameter space where one could explainthe anomalous high-energy CRE data.

• Assuming particle dark matter is weakly interacting, and that it was producedin the early Universe via an ordinary freeze-out process involving the same anni-hilation processes that dark matter would undergo in today’s cold universe, theannihilation rate in the Galaxy would be roughly two orders of magnitude too smallto explain the anomalous e± with dark matter annihilation; while this mismatchmakes the dark matter origin somewhat less appealing, relaxing one or more of theassumptions on dark matter production and/or on the pair annihilation processesin the early Universe versus today can explain the larger needed annihilation rate;

Grasso et al [Fermi-LAT], arXiv: 0905.0636 Bergstrom, Edsjo, Zaharijas 2009

Are the extra positrons emitted by pulsars or dark matter or ... ?

Dark matter mass ~1 TeV


Indirect detection of particle dark matterThe principleDark matter particles transform into ordinary particles, which are then detected or inferred

The first stars to form in the universe may have been powered by dark matter instead of nuclear fusion.

Dark StarsThey were dark-matter powered stars or for short



Artist’s impression Spolyar, Freese, Gondolo 2007


Dark Stars


How do WIMPs get into stars?

Some stars capture them later

Some stars are born with WIMPs

First stars (Pop III)Sun

Stars living in dense dark matter clouds(main sequence stars, white dwarfs,neutron stars, Pop III stars)


• when object forms, dark matter is dragged in into deeper and deeper potential

- adiabatic contraction of galactic halos due to baryons(Zeldovich et al 1980, Blumenthal et al 1986)

- dark matter concentrations around black holes(Gondolo & Silk 1999)

- dark matter contraction during formation of first stars(Spolyar, Freese, Gondolo 2007)

• dark matter scatters elastically off baryons and is eventually trapped- Sun and Earth, leading to indirect detection via neutrinos

(Press & Spergel 1985, Freese 1986)

- stars embedded in dense dark matter regions (“DM burners” of Moskalenko & Wai 2006, Fairbairn, Scott, Edsjo 2007-09)

- dark matter in late stages of first stars(Freese, Spolyar, Aguirre; Iocco; Taoso et al 2008; Iocco et al 2009)

• By gravitational contraction:

• By capture through collisions:

How do WIMPs get into stars?


What do WIMPs do to stars?Provide an extra energy source

Gravitational systems like stars have negative heat capacity.Adding energy makes them bigger and cooler.

May provide a new way to transport energy

Ordinary stars transport energy outward by radiation and/or convection. WIMPs with long mean free paths provides additional heat transport.

May produce a convective core (or become fully convective)

Very compact WIMP distributions generate steep temperature gradients that cannot be maintained by radiative transport.


1989ApJ...338...24S

The main sequenceshifts to lower temperatures and higher luminosities

Salati, Silk 1989

Am

bien

t D

M d

ensi

ty

(M⦿

/pc

3 )

1 M⦿/pc3 = 38 GeV/cm3

σ=4×10-36 cm2

v=300 km/sρ≤4×107 GeV/cm3

What do WIMPs do to stars?

Semi-Dark Stars


Taoso, Bertone, Meynet, Ekstrom 2008

tracks of a star without WIMPs. An important differencefrom standard evolution is that in the first phase, thenuclear reactions are slowed down and therefore the coreH-burning lifetime is prolonged. For dark matter densities!" ! 1:6 1010 GeV cm"3, the picture is qualitatively the

same, and for these models we only show in Fig. 1 the firstphases of the evolution. In Fig. 2, we show the coretemperature as a function of the DM density, at differentstages of the core H-burning phase. At high DM densitieshydrogen burns at much lower core temperatures than inthe usual scenario, until a certain mass fraction is reached,e.g. Xc # 0:3 for !" # 1010 GeV cm"3 and the standard

evolutionary track is joined. For increasing DM densitiesthe nuclear reaction rate is more and more delayed until thecontraction of the star is inhibited, due to the high DMenergy accumulated, and the evolution is frozen. In Fig. 1for !"#2$1010 GeV cm"3 and !"#3$1010 GeV cm"3

the stars seems to remain indefinitely at the ZAMS posi-tion. In Fig. 3 we show the core H-burning lifetime as afunction of the DM density. In the case of a 20M% model,for ! ! 109 GeV cm"3 the core H-burning phase is pro-longed by less then 10% but the delay increases rapidly forhigher DM densities. Extrapolating the curve we determinea critical density, !c # 2:5$ 1010 GeV cm"3, beyondwhich the core H-burning lifetime is longer than the ageof the Universe. All the calculations have been repeated forthe 200M% model and we find that both the 20M% and200M% stars evolutions are stopped for DM densities

higher than 5:3$ 1010!

#SDp

10"38 cm2

""1GeV cm"3: We have

also verified that the results weakly depend on the WIMPmass, e.g. the core H-lifetime is modified by a factor 0.2%and 5%, respectively, for m" # 10 GeV and m" #100 GeV, if !" # 1010 GeV cm"3.

FIG. 2. Temperature of the core as a function of the DMdensity for the 20M% model, at different stages of the core H-burning phase. Xc denotes the mass fraction of hydrogen at thecenter (Xc # 0:76 at the beginning of the core H-burning phase).WIMP parameters as in Fig. 1.

FIG. 3. Variation of the core H-burning lifetime as a functionof the WIMP densities for the Pop III 20 and 200M% models.WIMP parameters as in Fig. 1.

FIG. 1 (color online). Evolutionary tracks of a Pop III 20M%star for different WIMP densities (labels in units of GeV cm"3).We have adopted a WIMP model with m" # 100 GeV and

#SDp # 10"38 cm2.

DARK MATTER ANNIHILATIONS IN POPULATION . . . PHYSICAL REVIEW D 78, 123510 (2008)

123510-3

Main sequence star inside a WIMP cloud

Geneva evolution code

Lifetime longer than age of Universe for ρ≳5x1010 GeV/cm3

σSD=10-38 cm2

v=10 km/s108 GeV/cm3 <ρ<1011 GeV/cm3

Dark Stars by capture


Iocco, Bressan, Ripamonti, Ferrara, Marigo 2008

Zero metallicity star at redshift z≈20 Modified Padova stellar code

σSD=10-38 cm2

v=10 km/s108 GeV/cm3 <ρ<1012 GeV/cm3

1662 F. Iocco et al.

! = 1011 GeV cm!3. The dotted lines mark the position of the starwhen LDM/L" = 1 (i.e. at the beginning of the stalling phase), 0.5and 0.1. As already discussed, for all the considered stellar modelsthe stalling phase takes place along the Hayashi track, and the timingof the other benchmarked points can be inferred by comparison withFig. 3.

Following the stalling phase, these dark matter supported starscontinue their contraction. The SC mechanism becomes more rele-vant as the density increases, and the SC rate grows. For our fiducialset of DM parameters, stars with M" ! 30 M# develop a SC lumi-nosity greater than the gravitational one before reaching the ZAMS,and therefore do not evolve further on the HR diagram. This isclearly shown in the upper panel of Fig. 5, where the dashed tracks,which indicate the pre-MS phase, do not join the main sequence(MS; solid lines) for all stellar models with M" $ 20 M#. Thelower panel of the figure shows the HR diagram of the same set ofstellar models but assuming different DM parameters, namely " 0 =10!39 cm2 and ! = 1011 GeV cm!3. As expected, the evolution isalmost unaffected by the variation of DM parameters during the ACphase whereas the SC effects are significantly reduced: all the starswith M" > 5 M#, reach the MS and even the evolution of the 5 M#model is halted at a later time with respect to the previous case.

In Table 2, we summarize the characteristic time-scales whichcharacterize the evolution of our stellar models under the effect ofSC assuming different DM cross-sections, as compared with thestandard case where DM effects are neglected: once again it isevident the bigger impact of the SC mechanism on smaller massesand the life-prolonging effect of DM on all the masses.

6 ST E L L A R M A S S C O N S T R A I N T S

From the above picture, it is clear that in DM-rich environments,such as the haloes where the first episodes of star formation areexpected to take place, SC luminosity may play a dramatic roleduring the early evolution of a protostar. On the basis of purelyquantitative arguments, this has been suggested by Iocco (2008), andFreese et al. (2008a) derived a constraint on the mass of stars that canform under these conditions. Our analysis reaches conclusions thatare different from those of the latter study as we will comment laterin this section. Now we want to answer the question of which starswill be most affected by this mechanism, and in which environment.Armed with the formalism developed in Section 4, one may simplyimpose the condition LZAMS

DM $ LZAMSnucl , namely that the luminosity

due to DM annihilations inside the star be less than the nuclearluminosity predicted at ZAMS for Pop III stars in the absence ofDM. Fig. 6 summarizes the results of this inequality, obtained byapplying equation (14) to a grid of stellar models at the ZAMS.

In the region above the curve, DM luminosity exceeds the nuclearone and protostellar evolution is inhibited before the objects reachthe ZAMS, as we have discussed in the previous section. Stars in thisregime will ‘freeze’ on the HR diagram for as long as the propertiesof the DM distribution around them remain the same. Below thecurve (shaded area) stars are instead able to reach the ZAMS andthereafter evolve along the MS.

Note, however, that the distinction between ‘frozen’ and ‘evolv-ing’ stars has to be taken with care. In fact, as we have shown inFig. 4 for our reference 100 M# stellar model, the ignition of nu-clear reactions can occur at very low rates, producing a very lownuclear luminosity, but still allowing the star to evolve, eventuallyexhausting its nuclear fuel, although on much longer time-scales(#H = 4.9 Myr against the # 0

H = 2.6 Myr time-scale predicted for a100 M# Pop III star in the absence of DM effects, see Table 2).

Figure 6. DM constraints on stellar mass. The shaded area represents theregion of the parameter space where stars can reach the ZAMS and evolve.The vertical axis on the left represents the quantity " 0 ! and on the right thecorresponding values of ! if " 0 = 10!38 cm2. In the region above the curve,stars are prevented from reaching ZAMS and freeze on the HR diagram, asit is shown in Fig. 5.

Fig. 6 has to be considered as a quantitative indication: it showsthat both low- and high-mass stars are affected by DM capture. Therange of stellar masses that can reach the ZAMS, for the fiducialDM parameter combination (" 0 ! = 10!27 GeV cm!1), is 40 ! M"! 1000 M#.

This is due to a change in the index k of the relation L" %Mk

", following the transition of the star to a completely adiabaticsystem when M" " 200 M#. In their analysis, Freese et al. (2008a)derive only an upper limit to the stellar mass in the presence ofDM SC because they impose the above condition making use of theEddington luminosity, which has a linear dependence on the stellarmass, instead of the actual nuclear luminosity at ZAMS. Therefore,their analysis somehow underpredicts the effects of DM on low-and intermediate-mass stars. In fact, our numerical results showthat most significant effects are obtained for objects with massesM" ! 200 M#, as shown in Fig. 6. This happens because the SCmechanism becomes efficient only when the stars are in a relativelyadvanced phase of their pre-MS evolution.

It is also extremely interesting to notice that the mass–luminosityrelation in low-mass stars is not particularly sensitive to metallicity.This implies that the results we have presented can be also applied tometal-enriched stellar populations, as long as they continue to formin environments with characteristics similar to those we have con-sidered (see Section 2). Our results are in agreement with those ofSalati & Silk (1989), Scott, Edsjo & Fairbairn (2007) and Fairbairnet al. (2008), who studied WIMP-burning objects and observed thatZAMS stars if ‘fed’ with captured DM annihilation energy movetowards the red region of the HR diagram, at increasing DM den-sities. In particular, the latter analysis focused on low-mass stars(M" $ 4 M#) and found they eventually reach the Hayashi line fordifferent DM density values at different masses (! = 1010 GeV cm!3

for 1 M#), using the same current upper limit on " 0 we adopt, anda different value for v, of the order of the relative velocity betweenWIMPs and the Sun, v & O (102 km s!1).

7 C O N C L U S I O N S

We have studied the effects of WIMP DM annihilation on the firststars in the Universe. As initial condition of our model, we consider aDM halo with mass 106 M# at z = 20, i.e. a typical minihalo where

C' 2008 The Authors. Journal compilation C' 2008 RAS, MNRAS 390, 1655–1669

Lifetime longer than age of Universe

Dark Stars by capture


90 P. Scott, M. Fairbairn and J. Edsjo

Figure 4. Evolutionary tracks followed in the HR diagram by stars of various masses, when WIMPs provide different fractions of their total energy budgets.Filled, unlabelled circles indicate the starting points of tracks, whilst labelled ones give indicative ages during the evolution of 1.4 M! stars. Tracks have beenhalted when the star exhausts the supply of hydrogen in its core or reaches the current age of the Universe. Stars with a greater luminosity contribution fromWIMPs push further up the Hayashi track and spend longer there before returning to the main sequence. Stars which come to be entirely dominated by WIMPannihilation (bottom right-hand panel) evolve quickly back up the Hayashi track and halt, holding their position in the HR diagram well beyond the age of theUniverse.

and 2.19), so we see that "! av#0 makes no difference to the amountof energy generated. When equilibrium has not been achieved, thiswill not be the case. Such an effect can be seen in the slight upturnof the WIMP luminosity in the uppermost curve of the upper panelin Fig. 3. In this case the very high "# and very low "! av#0 sig-nificantly change the stellar structure before equilibrium has beenreached, causing LW to peak prior to equilibrium. The dependenceof LW on m# in Fig. 3 shows roughly an inverse square relationship,which is a result of using the full capture expressions in the RSC.As can be seen from careful inspection of equation (2.19) for ex-ample, for small v and v$ such as those used in the context of theearly Universe by e.g. Iocco (2008) and Freese et al. (2008a), thedependence disappears.

In Figs 4 and 5 we show evolutionary tracks in the HR andcentral equation-of-state diagrams of stars with different massesand WIMP luminosities. At low WIMP luminosities, the evolution isessentially normal. As WIMPs are allowed to provide more energy,the negative heat capacity of a star causes it to expand and cool.The central temperature and density drop, nuclear burning reducesand the star moves some distance back up the Hayashi track. Thereduction in central temperatures and overall luminosities providedby pp-chain and CNO-process hydrogen burning are illustrated inFig. 6. These values are taken at the time tadjust when a star hascompleted its initial reaction to the presence of WIMPs, which

corresponds to the central temperature and density reaching theirminima and the star arriving at the bottom leftmost point of its travelsin Fig. 5. At very high WIMP luminosities, the stellar core expandsand cools drastically, moving stars a long way back along the pre-main sequence and effectively shutting down nuclear burning alltogether. Such an object becomes a fully fledged dark star, poweredentirely and perpetually by WIMP annihilation.

At intermediate WIMP luminosities, nuclear burning is sup-pressed rather than completely extinguished. Its continued contri-bution to nuclear processing slowly raises the core temperature anddensity once more, in turn increasing the rate of nuclear reactionsand accelerating the process. The star burns hydrogen alongsideWIMPs, and goes on to evolve through a hybrid WIMP-hydrogenmain sequence. Such evolution can be best seen in the bottom left-hand panel of Fig. 4. Thanks to the energy input from WIMP anni-hilation, the time it takes such a star to consume its core hydrogenis lengthened, so its effective main-sequence lifetime is extended(Fig. 7). The increase in main-sequence lifetime is notable at allmetallicities, but most prominent at low Z, essentially because nor-mal main-sequence lifetimes are shorter at lower metallicity. Wedid not see changes with metallicity in the central temperatures,pp-chain or CNO luminosities of the stars in our grid.

We should point out here that in the extreme case of a verylarge WIMP luminosity, it is highly questionable whether a star

C$ 2009 The Authors. Journal compilation C$ 2009 RAS, MNRAS 394, 82–104

Scott, Fairbairn, Edsjo 2009

Main sequence star entering a WIMPcloud

low density

high density

DarkStarsevolution code(based on EZ)

What do WIMPs do to stars? Semi-Dark Stars


Dark Stars

Population III stars


• Formation Basics

- first luminous objects ever

- made only of H/He

- form inside DM halos of 105-106 M⊙◉☉⨀

- at redshift z=10-50

- baryons initially only 15%

- formation is a gentle process

• Dominant cooling mechanism to allow collapse into star is H2 cooling (Peebles & Dicke 1968)

First stars: standard picture


102

103

104

gas number density [cm-3]

gas

tem

pera

ture

[K

]

adiabaticcontraction

H2 formationline cooling(NLTE)

loitering(~LTE)

3-bodyreaction

heatrelease

opaque tomolecular line

collisioninducedemission

opaque tocontinuum

adiabaticphaseMust be cool to contract

First stars: standard picture

Thermal evolution of Pop III protostar

Courtesy of N. Yoshida


First stars: three conditions for a dark star

(1) Sufficiently high dark matter density to get large annihilation rate

(2) Annihilation products get stuck in star

(3) Dark matter heating beats H2 cooling

Leads to new stellar phase

Spolyar, Freese, Gondolo, arxiv:0705.0521, Phys. Rev. Lett. 100, 051101 (2008)


(1) Adiabatic contraction of dark matter

(a) using cosmo-hydrodynamical simulationsAbel, Bryan, Norman 2002

(b)using prescription from Blumenthal, Faber, Flores & Primack 1986 (circular orbits only)Spolyar, Freese, Gondolo 2008

(c) using full phase-space a la Young 1991Freese, Gondolo, Sellwood, Spolyar 2009

(d)using cosmo-hydrodynamical simulationsNatarajan, Tan, O’Shea 2009

r M(r) = constant

From cosmology. No extra free parameter.


(1) Adiabatic contraction of dark matter

No. 1, 2009 DARK MATTER ANNIHILATION AND PRIMORDIAL STAR FORMATION 577

Figure 2. Dark matter density profiles (spherical averages) for simulations A (top), B (middle), and C (bottom) are shown with the open squares. Power law fits to theouter, well-resolved regions (fit #1) are shown with the dashed lines, while fits to the inner (but not innermost—see text), less well-resolved, regions (fit #2) are shownwith the dotted lines.

significant steepening compared to the outer regions. This islikely to be the result of adiabatic contraction, since it occurs ata scale ! 1 pc where the density of baryons begins to dominate.We emphasize again that the simulation points on which DMfits #2 are based correspond to bins with only a small (<100)number of particles and must be treated with caution. We donote, however, that on the very innermost scales (! 0.01 pc)the dark matter density profiles in the numerical simulations areeven steeper than the analytic DM fits #2.

If adiabatic contraction of dark matter in the baryon-dominated potential is responsible for sculpting these profiles,one expects that the maximum steepness of the dark matterdensity profile will be equal to that of the baryons, which hasbeen shown in simulations to have an approximate power lawprofile of !gas " r#2.2 (see Section 3.2). The baryonic den-sity profile inevitably flattens in its center, so that the powerlaw profile is only valid inwards to some core radius rc. Thiscore radius shrinks as collapse proceeds. In situations wherewe are interested in the global luminosity provided by WIMPannihilation in the halo (Section 3.3), we will assume that thedark matter density profile also exhibits this core radius, insideof which its density is also constant. For the fiducial case, weassume a dark matter particle mass of m" = 100 GeV, which istypical for a weakly interacting particle. We then consider factorof 10 variations in this mass.

The photon multiplicity function dN# /dE# for mixedgaugino-higgsino dark matter is given by the form (Bergstromet al. 1998; Feng et al. 2001) dN# /dx = ae#bx/x1.5 wherex = E# /m" and (a, b) are constants for the particular anni-hilation channel. We average over the important annihilationchannels, namely WW,ZZ, t t , bb, and uu, considered by theauthors (given in Feng et al. (2001), and average over the dif-ferent channels to obtain (a = 0.9, b = 9.56). We assume that

$$av% & a + bv2 + · · · is largely constant, that is, the constantterm a is non-zero. We may then estimate $$av% using the sim-ple freeze-out condition n" (TF) $$av% = H (TF) at the freeze-outtemperature TF. n" is the particle number density, and H is theHubble parameter. Since the entropy per comoving volume re-mains constant as the universe expands, we may equate n"/sat freeze-out with the value today, to solve for $$av%. Deter-mined in this way, $$av% depends on the particle mass m" onlythrough the quantity x/

'g. x = m"/TF while g is the num-

ber of relativistic degrees of freedom at freeze-out. FollowingGreen et al. (2005), we find that for the range of m" we consider(10 GeV to 1 TeV), x varies from &25 to 27. Assuming x & 25,we find that g varies from 65 to 100 in the relevant mass range(see, i.e., Jungman et al. 1996; Kolb & Turner 1990). In ourfollowing analysis, we neglect the mass dependence of x/

'g

(i.e., a factor of 1.15 as m" varies from 10 GeV to 1000 GeV),and we assume $$av% & 3 ( 10#26 cm3 s#1 (see, e.g., Jungmanet al. 1996). We shall see that much larger uncertainties resultfrom the shape of the dark matter density distribution.

The variation of H (r) on the WIMP mass, m" , is also shownin Figure 3. We consider cases with m" = 10 GeV and 1 TeV,that is, factors of 10 below and above our fiducial value. Once thesimple m#1

" dependence of H (r) (Equation (10)) is accountedfor, we see that remaining variations in H (r) are within about afactor of 2. These are due to the m" dependencies of the photonmultiplicity function, the energy integral, and the

!S(r, r ), E)

"

function.It is also informative to compare H (r) to the energy generated

by WIMP annihilation per unit volume, per unit time

G(r) =!2

" (r) $$av%2m"

# 1

0dx x

dN#

dx. (12)

Original NFW profile

Using Blumenthal et al

Using Young

Figure 2: Adiabatically contracted DM profiles in the first protostars for an initial NFWprofile (dashed line) using (a) the Blumenthal method (dotted lines) and (b) Young’smethod (solid lines), for Mvir = 5 ! 107M!, c = 2, and z = 19. The upper panel showsthe resultant DM density profiles, and the lower panel shows the enclosed DM mass asa function of radius. The four sets of curves in each panel correspond to a baryonic coredensity of 104, 108, 1013, and 1016cm"3. Our main result is that the two di!erent approachesto obtaining the DM densities find values that di!er by less than a factor of two.13

Natarajan et al

Abel et al

Spolyar, Freese, Gondolo 2008; Freese, Gondolo, Sellwood, Spolyar 2008

From cosmology. No extra free parameter.


Qann: Rate of energy production from annihilation (per unit volume)

Qann = n2�h�vim�c2 = c2⇢2

�h�vim�

(2) Dark matter heatingHeating rate = Qann fQ

fQ: Fraction of annihilation energy deposited inside star

• 1/3 neutrinos, 1/3 photons, 1/3 electrons/positrons

• Neutrinos escape

• Electrons ≳ Ec ≈ 280 MeV → electromagnetic cascades

• Photons ≳ 100 MeV → electromagnetic cascades≲ 100 MeV → Compton/Thomson scattering

≲ Ec ≈ 280 MeV → ionization

Particle physics factor


(3) Birth of a dark star

m = 100 GeV〈σv〉 = 3×10-26 cm3/s

102

103

104

gas number density [cm-3]

gas

tem

pera

ture

[K

]

HEATING DOMINATES

COOLING DOMINATES

m = 100 GeV〈σv〉 = 3×10-26 cm3/s

Thermal evolution of Pop III protostarMust be cool to contract


(3) Birth of a dark star

Spolyar, Freese, Gondolo 2008


Dark matter that can form dark stars

0 10 20 30 40 50 60 700

0.5¥10-5

1.0¥10-5

1.5¥10-5

2.0¥10-5

2.5¥10-50 10 20 30 40 50 60 70

0

0.5¥10-5

1.0¥10-5

1.5¥10-5

2.0¥10-5

2.5¥10-5

m HGeVLf Q

Almost all thermal dark matter particlesExceptions: resonant annihilation, co-annihilation, neutrinophilic dark matter below ~50 GeV

Neutralino Neutrinophilic

Coannihilations

Resonances

p-waves

Thresholds

NO DARK STAR

NO DARK STAR

Gondolo, Huh, Kim, Scopel 2010

��! ⌫⌫,⌫ ⌫W,⌫ ⌫Z


Structure of a dark star

• Polytropes (p=Kρ1+1/n) supported by dark matter annihilation rather than fusion

• Dark matter is less than 2% of the mass of the star but provides the heat source (The Power of Darkness)

Freese, Bodenheimer, Spolyar, Gondolo 2008Spolyar, Bodenheimer, Freese, Gondolo 2009


Life of a dark star

Spolyar, Bodenheimer, Freese, Gondolo 2009

Young Dark Star(first ~104 yr)

Mature Dark Star(stalls for ~5x105 yr)

Kelvin-Helmholtz Contraction

Main Sequence Star

Sequence of polytropes with gas and dark matter accretion


Life of a dark star


Young Dark Star(first ~104 yr)

Mature Dark Star(stalls for ~5x105 yr)

Main Sequence Star

Kelvin-Helmholtz Contraction



Life of a dark star



Sun

normal stars

darkstars


Life of a dark starSpolyar, Bodenheimer, Freese, Gondolo 2009

The dark star phase ends onto Zero Age Main Sequence stars that are massive (500-1000 M⊙), bright (106-107 L⊙), and hot (Teff~105K).

For 0.2-1 Myr, dark stars are massive (200-1000 M⊙), bright (106-107 L⊙), and cold (Teff~104K).

Mass accretion is not stopped by feedback because ionizing UV radiation is negligible.

These very massive stars undergo core-collapse into intermediate mass-black holes and may produce the chemical composition of extremely metal poor halo stars Ohkubo et al 2006, 2009

Pair-instability region is avoided because core density is small (10-7-10 g/cm3).


Quasars from dark stars?

Quasars have been observed at redshift 6 and beyond.

There is not enough time to form high-redshift quasars from standard Population III remnants of ~100M⨀

An old problem: quasars form too early

A suggested solution: direct collapse to seed black holes

But how does one get seed black holes that are massive enough?

e+e- pair instability prevents the formation of massive stars.

Bromm & Loeb (2003) suggest superfast gas accretion rates devoid of molecular hydrogen.

Dark stars provide another way.


Quasars from dark stars?Extended capture and appropriate gas accretion rate give dark stars that can solve the high-redshift quasar formation problem.

Umeda, Yoshida, Nomoto, Tsuruta, Sasaki, Ohkubo 2009

JHEP00(2009)000

3. Dependence on the gas mass accretion rates

The stellar evolution for models with constant gas mass accretion already shows several

interesting features. Fig. 1 shows the evolution of mass and radius for the accreting stars

without (upper panel) and with (lower panel) DM annihilation heating.

Figure 1: Stellar mass - radius evolution for each model. The upper and lower panels showthe models without and with the DM annihilation energy, respectively. The model names forM = 10!2, 10!3, 10!4M"yr!1 cases are A, B, C, and Ad, Bd, Cd, for the cases without and withthe DM heating, respectively.

The adopted constant gas mass accretion rates are, M = 10!2 (Model A, Ad), 10!3 (B,

Bd), and 10!4 (C, Cd) M" yr!1, for without and with DM (for the letters without and with

– 4 –

JHEP00(2009)000

Figure 4: The evolution of Model Bd after the DM density is reduced by a factor of 0.3 when thestellar mass is M = 12, 000M!. The upper panel shows the central He mass fraction as a function ofcentral density. Vertical lines with numbers indicate the time to collapse. At first, hydrogen burningtakes place and helium mass fraction increases from 0.5 to 1.0 in 17Myr. After the beginning ofHe-burning the star collapses only in 3 days. The middle panel shows the energy generation rate atthe center by DM annihilation and nuclear burning. The nuclear energy generation rate becomesnegative (as shown by the dashed line) after entering the (He) photo-dissociation region. In thebottom panel the dashed line shows the central density - temperature trajectory. The thick solidline indicates that the star is unstable above this line.

the photosphere, that may locate far above the star for an accreting star [29]. The geometry

of the photosphere may not even be spherical if the accretion is aspherical. In that case,

only the reliable observational data will be the total luminosity of the star, which correlates

– 10 –

JHEP00(2009)000

nuclear energy generation rate is not negligible; CNO-cycle hydrogen burning is indeed

taking place in the central part. The stars evolve on the main-sequence track over a few

million years, with their luminosity increasing with mass. Fig.2 also shows the central

temperature and density as a function of stellar mass, for B and Bd models.

We find that the fate of the stars depends importantly on the accretion rate. The DM

annihilation supplies an extra energy to support a star against gravitational contraction,

and thus the star consumes less hydrogen per unit time, with its lifetime prolonged. The

luminosity vs. “final” mass relation for various models are shown in Fig. 3. Besides

the steady accretion models A(d), B(d), and C(d), various models with time-dependent

accretion are also shown. In many cases, the final stellar mass is larger than 1000M!.

Figure 3: Final mass and luminosity for various models. Models A(d), B(d), C(d) are the sameas in Fig.1. Models D, Y, F, and G are the cases with the accretion rate M = 10!5M"yr!1, ratesin [33], [31], and [34], respectively. Lower case letters ‘d’ in the model names, such as Dd, indicatethat the fiducial dark matter annihilation energy is included. Models M and Md use the ratesin [31] with a cut o! at M = 300M". In the models Cd!3 and Fd!3, the dark matter capturerate is enhanced by a factor of 3 than the models Cd and Fd, respectively. The solid straight linerepresents the Eddington Luminosity. The mass range bounded by the dotted lines, labeled PISN,shows the mass range in which the stars explode as pair-instability supernovae and do not formmassive BHs. The models with arrows are “stalling”, or, their central temperatures are decreasing.Therefore, their mass may increase further.

The most interesting is Model Bd, the case with M = 10"3M!yr"1 (see Figs. 1,

– 6 –


No extended capture

Sivertsson, Gondolo 20108

0

2⋅106

4⋅106

6⋅106

8⋅106

107

1.2⋅107

1.4⋅107

1.6⋅107

1.8⋅107

0 0.1 0.2 0.3 0.4 0.5 0.6

Lum

inos

ity [

L !]

Time [Myr]

Sivertsson & Gondolo, 2010

with scatteringwithout scattering

FIG. 3: The time evolution of the dark star luminosity fromWIMP-WIMP annihilations. The top solid (red) line includesWIMP-nucleon scattering in addition to annihilation; the bot-tom dashed (blue) line does not include scattering.

0.0001

0.001

0.01

0.1

1

0 0.1 0.2 0.3 0.4 0.5 0.6

Tota

l mas

s of

WIM

Ps c

ross

ing

the

star

[M

!]

Time [Myr]


no annihilationannihilation only

+ scattering

FIG. 4: The dark matter mass accessible to the star as afunction of time. In other words, the total mass of the WIMPson orbits intersecting the star at the di!erent stellar evolutionstages. The dotted (blue) line includes both WIMP scatteringand annihilation. The dashed (green) line includes WIMPannihilation but no scattering. The solid (red) line includesneither scattering nor annihilation.

but at a much smaller rate; in the case we study, the anni-hilation after contraction is suppressed by (very roughly)about 15 orders of magnitude (five orders of magnitudecoming from the change in stellar volume and two timesfive orders of magnitude coming from the decrease in den-sity due to annihilation and scattering, extracted fromFig. 5 below).

When WIMPs scatter, they lose energy, go on smallerorbits, and spend more time near the center of the starwhere the density is higher and the annihilation faster.Both annihilation and scattering remove WIMPs fromorbits that cross the star. This is illustrated in Fig. 4,where the mass of dark matter accessible to the star (i.e.

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

1.2⋅101310138⋅10126⋅10124⋅10122⋅10120

Den

sity

[g/

cm3 ]

Radius [cm]


t = 0.40 Myrt = 0.28 Myr

FIG. 5: The density profile of dark matter around the starjust before (dotted blue line) and just after (solid red line)the Kelvin-Helmholtz contraction at the end of the dark starphase (scattering is included when generating this graph).The vertical straight line marks the radius of the star af-ter contraction; before contraction, the radius of the star is4.2!1013 cm, about four times the length of the horizontalaxis.

the total mass of WIMPs on orbits crossing the star) isplotted as a function of time. The three lines illustratethe e!ect of the stellar evolution as well as that of scat-tering and annihilation. The top (solid red) line is similarto the curve in Fig. 2, and includes just the gravitationalresponse of the WIMPs to the star and neither scatter-ing nor annihilation. It shows that the mere contrac-tion of the star already makes it a much smaller targetfor WIMP capture, by about one order of magnitude inthe accessible mass. Annihilation reduces the number ofWIMPs that cross the star (green dotted line), as anni-hilation removes WIMPs from the system. The inclusionof scattering reduces this number further, which mightat first not seem obvious. The reason is that WIMPs onorbits not crossing the star cannot scatter in the star.Hence the total mass of WIMPs on orbits crossing thestar can never increase due to scattering. Furthermore,scattering puts WIMPs onto lower energy orbits, makingthem more vulnerable to annihilation. Thus the num-ber of WIMPs in stellar contact is further reduced (seeFig. 4). As discussed in Section IV, our Monte-Carlo onlyincludes WIMPs from the inner 1 percent of the NFWhalo scale radius rs, but WIMPs from regions further outdo not contribute significantly to the annihilation rate in-side the dark star.

From the Monte-Carlo one can also extract the darkmatter density profile around the formed star. This isshown in Fig. 5 for two di!erent times, just before andjust after the KH contraction (blue dotted line and redsolid line, respectively). The solid red line is for the time0.4 Myr, which is just after nuclear burning has started.The blue dotted line shows the time 0.28 Myr, which isjust before the star contracts enough for scattering to

On the throat of death , the dark star burns all of the dark matter it can get.

The rest of the dark matter stays in orbit out of reach of the dead dark star.

Once the dark star contracts to the Zero Age Main Sequence, the supply of dark matter ends.

Radius of the dark star after Kelvin-Helmholtz contraction

Original dark matter density

Dark matter density after Kelvin-Helmholtz contraction


Supermassive dark stars?

Perhaps some dark stars become much more massive (107 vs 102 M⨀) and much brighter (1011 vs 107 L⨀)

Freese, Ilie, Spolyar, Valluri, Bodenheimer 2010

Figure 1: Hertzsprung-Russell diagram for dark stars for accretion rate M =10!3M"/yr. and a variety of WIMP masses as labeled for the two cases:(i) “without capture” but with extended adiabatic contraction (dotted lines)and (ii) “with capture” (solid lines). The case with capture is for productof scattering cross section times ambient WIMP density !c"! = 10!39cm2 !1013GeV/cm3. Also labeled are stellar masses reached by the DS on its wayto becoming supermassive. The final DS mass was taken to be 1.5! 105M"

(the baryonic mass inside the initial halo), but could vary from halo to halo,depending on the specifics of the halo mergers.

29

In triaxial dark matter halos, centrophillic orbits (box and chaotic) may extend the supply of dark matter to the dark star.

However, orbits in the dark star potential are not expected to be centrophillic (exception Valluri et al 2010).


Dark stars and reionizationA dark star phase can delay reionization

Scott, Venkatesan, Roebber, Gondolo, Pierpaoli, Holder 2011

8 Scott et al.

Redshift z

Hyd

rogenIonizationFraction[H

ii]

MC

(Meager Capture)

tDSNMS = 3Myr

11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4

0.2

0.4

0.6

0.8

1.0

fDS = 1

fDS = 0.6

fDS = 0.1

fDS = 0

Redshift z

Hyd


ii]

MC

(Meager Capture)

tDSNMS = 6Myr

11.0 11.2 11.4 11.6 11.8 12.0 12.2 12.4

0.2

0.4

0.6

0.8

1.0

fDS = 1

fDS = 0.8

fDS = 0.6

fDS = 0.3

fDS = 0.1

fDS = 0

FIG. 2.— Ionization histories of a Universe containing dark stars, in the meager capture (MC) scenario, where dark stars effectively receive a small extensionto their main-sequence lifetimes. The two panels compare histories for different dark star fractions fDS, where dark stars live in the DSNMS phase for close tothe maximum time allowed by core hydrogen depletion (tDSNMS = 3 and 6 Myr). Longer DSNMS lifetimes and larger dark star fractions lead to small increasesin the speed of reionization (note the zoomed axes relative to Fig. 1). Non-dark aspects of the calculations are as described for Fig. 1.

Redshift z

Hyd


ii] PopII+III only

(fDS = 0)

6 8 10 12 14 16 18 200.0

0.2

0.4

0.6

0.8

1.0

f?fesc = 1⇥ 10�4

f?fesc = 5⇥ 10�3

f?fesc = 2⇥ 10�2

Redshift z

Hyd


ii] EC

(Extreme Capture)

tDSP = 150Myr

fDS = 1

6 8 10 12 14 16 18 200.0

0.2

0.4

0.6

0.8

1.0

f?fesc = 1⇥ 10�4

f?fesc = 5⇥ 10�3

f?fesc = 2⇥ 10�2

FIG. 3.— Impacts of varying astrophysical parameters upon the reionization history of a Universe containing no dark stars (left), and one containing EC darkstars with tDSP = 150 Myr, fDS = 1 (right). Here we show the effects of varying the product of the star-forming baryon fraction f? and the ionizing photon escapefraction fesc. The variation of astrophysical parameters induces a similar change in the reionization history of the Universe to dark stars (left), but has a slightlyreduced impact when applied to reionization scenarios that include dark stars (right). Variations in f? fesc can not only delay reionization as EC dark stars do, butalso speed it up, to a much greater extent than MC dark stars are able to do.

and for an EC example with fDS = 1, tDSP = 150 Myr. Here,we see that within this range of astrophysical uncertainties, alarge range of reionization histories is possible. Indeed, in themost extreme cases, dark stars have a similar magnitude effectas the variation of astrophysical parameters. This degeneracyis unfortunate, but not unexpected; substantial uncertainty ex-ists in reionization models at present, even before introduc-ing the possibility of stellar populations including dark stars.Hearteningly however, the impact of the astrophysical uncer-tainties is reduced in situations where dark stars play a sig-nificant role, as can be seen by comparing the two panels ofFig. 3.

The results we present here agree broadly with those ofSchleicher et al. (2009), but the correspondence is not imme-diately obvious. Schleicher et al. considered reionization from‘MS-dominated’ (main sequence), and ‘CD’ (capture domi-nated) dark stars, roughly corresponding to our own MC andEC scenarios, respectively. They investigated the case wherefDS = 1, showing that the higher ionizing photon fluxes of theDSNMS phase hasten reionization, whereas the lower fluxesof the DSP phase delay it. This is in good agreement withwhat we show here, and earlier predictions by Yoon et al.(2008). Where we differ from Schleicher et al.’s analysis is inour atmospheric modeling (we use actual model atmospheres

Dark stars, reionization and the CMB 7

Redshift z

Hyd


ii] EC

(Extreme Capture)

tDSP = 150Myr

6 8 10 12 14 16 18 200.0

0.2

0.4

0.6

0.8

1.0

fDS = 1

fDS = 0.9

fDS = 0.8

fDS = 0.6

fDS = 0.3

fDS = 0.1

fDS = 0

Redshift z

Hyd


ii] EC

(Extreme Capture)

tDSP = 500Myr

6 8 10 12 14 16 18 200.0

0.2

0.4

0.6

0.8

1.0

fDS = 1

fDS = 0.9

fDS = 0.8

fDS = 0.6

fDS = 0.3

fDS = 0.1

fDS = 0

Redshift z

Hyd


ii] EC

(Extreme Capture)

fDS = 0.6

6 8 10 12 14 16 18 200.0

0.2

0.4

0.6

0.8

1.0

tDSP = 500Myr

tDSP = 150Myr

tDSP = 50Myr

tDSP = 15Myr

tDSP = 5Myr

PopII+III only

Redshift z

Hyd


ii] EC

(Extreme Capture)

fDS = 1

6 8 10 12 14 16 18 200.0

0.2

0.4

0.6

0.8

1.0

tDSP = 500Myr

tDSP = 150Myr

tDSP = 50Myr

tDSP = 15Myr

tDSP = 5Myr

PopII+III only

FIG. 1.— Ionization histories of a Universe containing dark or semi-dark stellar populations, in the extreme capture (EC) scenario, where dark stars liveextended lives as cool, diffuse objects. Here we plot the fraction of hydrogen in H II as a function of redshift. Top panels compare histories for different dark starfractions fDS, in situations where dark stars live a long time in the DSP phase (tDSP = 150 Myr and 500 Myr). Bottom panels compare histories for different DSPlifetimes, in situations where dark stars make up a substantial fraction of the mass budget of the first population of stars ( fDS = 0.6 and 1). Longer-lived and morenumerous EC dark stars delay reionization. Here we have assumed that the fraction of the initial star-forming baryonic mass budget of the Universe that does notform dark stars instead forms normal Pop III stars, which die after 10 Myr and are replaced by newly-born Pop II stars. Following the death of the population ofdark stars, and depending upon their time of death, they are replaced either directly with newborn Pop II stars, or with newborn Pop III stars, which themselveslater die and get replaced by newborn Pop II stars.

and fDS = 0.9 - 1, or tDSP = 500 Myr and fDS & 0.75, wouldbe ruled out at face value if we were to compare directly withthe WMAP7 limit that zreion = 9.4-11.8. Similarly, one mightalso conclude that many models with low tDSP and fDS areruled out for producing zreion and ⌧e exceeding the upper limitof the WMAP7 error band. Whilst this is indeed true whenf? fesc = 0.005 as we assume here, such limits are not really ro-bust to variations in astrophysical parameters. We discuss in-tegrated optical depths and corresponding constraints in moredetail in the following section.

For the meager capture (MC) scenario, the effects are lessdramatic; in Fig. 2 we show a zoomed-in section of the fullhistory of reionization, for a few combinations of fDS and theDSNMS lifetime tDSNMS. Here, increasing fDS and tDSNMSresults in progressively earlier reionization, the exact oppo-

site trend relative to the EC cases. This is because QDSNMS >QPop III, so extending the DSNMS phase and increasing thefraction of baryons contained in it causes reionization to hap-pen more quickly than with only a normal Pop III IMF.Again, as expected the effects increase with increasing fDSand tDSNMS. The reason the MC scenario has a much smallereffect on reionization than the EC scenario is that its dura-tion is already much more strongly constrained, in this caseby the fusion-burning timescale of core hydrogen during theDSNMS phase.

In Fig. 3 we show the impact of varying the product of theastrophysical parameters f? and fesc from our canonical valueof f? fesc = 0.005 to the extreme values of 0.02 ( f? = 0.1, fesc =0.2) or 10-4 ( f? = fesc = 0.01). We give the resulting reioniza-tion histories both for a standard Pop III without dark stars,

With capture With extended capture

Without capture, no effect on reionization.


Dark stars and the CMBA dark star phase can affect the cosmic microwave background


With capture With extended capture

Without capture, no effect on the CMB.

10 Scott et al.

Redshift z

Thom

son-ScatteringOpticalDepth

⌧ e(z)

EC

(Extreme Capture)

tDSP = 150Myr

0 5 10 15 20

0.02

0.04

0.06

0.08

0.10

0.12 WMAP 1�, 7 years

Planck 1�, 14 months

fDS = 0

fDS = 0.1

fDS = 0.3

fDS = 0.6

fDS = 0.8

fDS = 0.9

fDS = 1

Redshift z

Thom


⌧ e(z)

EC

(Extreme Capture)

tDSP = 500Myr

0 5 10 15 20

0.02

0.04

0.06

0.08

0.10



fDS = 0

fDS = 0.1

fDS = 0.3

fDS = 0.6

fDS = 0.8

fDS = 0.9

fDS = 1

Redshift z

Thom


⌧ e(z)

EC

(Extreme Capture)

fDS = 0.6

0 5 10 15 20

0.02

0.04

0.06

0.08

0.10



PopII+III only

tDSP = 5Myr

tDSP = 15Myr

tDSP = 50Myr

tDSP = 150Myr

tDSP = 500Myr

Redshift z

Thom


⌧ e(z)

EC

(Extreme Capture)

fDS = 1

0 5 10 15 20

0.02

0.04

0.06

0.08

0.10



PopII+III only

tDSP = 5Myr

tDSP = 15Myr

tDSP = 50Myr

tDSP = 150Myr

tDSP = 500Myr

FIG. 4.— Evolution of the lookback optical depth from the present day to redshift z according to Eq. 6, for EC dark stars of varying lifetimes and abundances.These curves, and the corresponding dark stellar populations, correspond to the reionization histories presented in Fig. 1. Larger dark star fractions and moreextended lifetimes reionize later, producing smaller optical depths. For comparison, we show the WMAP7 measured 1� band (Komatsu et al. 2011) for theoptical depth to the surface of last scattering, and the corresponding error band expected from Planck (Colombo et al. 2009), assuming it measures the samecentral value. Whilst these strictly correspond to a redshift z ⇠ 1090, the optical depth curves have largely begun to plateau by z ⇠ 20 anyway.

stead of the simple hydrogen reionization model included inCAMB, our modified version uses the H ionization fractionspresented in Sec. 5 as the basis for its reionization calcula-tions. We include contributions to the total electron fractionfrom H II, He II and He III with the assumptions stated ear-lier, as well as a residual electron fraction. As in the stan-dard CAMB reionization calculation, we assume that elec-trons from He II track those from H II, and model contribu-tions from He III with a smoothed step function centered atz ⇠ 3.5. We take the residual electron fraction after recom-bination to be xe = 2.1⇥ 10-4, based on the output of REC-FAST within CAMB. Using CAMB’s highest accuracy set-ting, we calculated the temperature (TT), polarization (EE)and cross (TE) power spectra, as well as integrated opticaldepths. We checked that the optical depths computed withCAMB agree to within their stated numerical accuracy withthose from Eq. 6 (as presented in Table 1), and verified that the

slight difference in the treatment of He III here and in Sec. 6.1has a negligible impact upon integrated optical depths.

In Fig. 8 we plot EE polarization spectra for the same ECcases as illustrated in Figs. 1 and 4. The spectra are normal-ized to the corresponding EE spectrum obtained in the stan-dard fDS = 0, Pop III+II scenario, in order to investigate theability of CMB experiments to distinguish dark stars fromstandard reionization. To this end, we also plot the uncer-tainty on the normalization due to cosmic variance, and thecombination of cosmic variance and total readout noise ex-pected across the 70, 100 and 143 GHz channels in the first14 months of Planck operation (Colombo et al. 2009). Largeparts of the parameter space are distinguishable from fDS = 0in a cosmic-variance-limited experiment, and a number of themore extreme scenarios are even detectable by Planck at bet-ter than 1�. Although essentially all such models may be dis-favored anyway by Planck’s measurement of the integrated


⌧e =

0.10

⌧e =

0.09

⌧e = 0.08

⌧e = 0.07

0.2

0.4

0.6

0.8

1.0

Darkstar

fraction

f DS

0 100 200 300 400 500

DSP lifetime tDSP (Myr)

Integrated

opticaldepth

⌧ e

0.06

0.08

0.10

FIG. 5.— Contours of equal integrated CMB optical depth to z = 1090 in theEC scenario, as a function of fDS and tDSP. Here we performed the interpola-tion on the optical depths in Table 1 using two-dimensional exponential ten-sion splines (Renka 1996b), based on a Delauney triangulation (Renka 1996a)and an iterative determination of the appropriate tension factors. Longer life-times and larger dark star fractions generically lead to smaller integrated op-tical depths; the slight upturn at large tDSP in the ⌧e = 0.08 and 0.09 contoursis an artifact of the interpolation.

Redshift z

Thom

son-ScatteringOpticalDep

th⌧ e(z)

MC

(Meager Capture)

tDSNMS = 6Myr

10 12 14 16 18 20

0.095

0.100

0.105

0.110

WMAP 1�, 7 years


fDS = 1

fDS = 0.8

fDS = 0.6

fDS = 0.3

fDS = 0.1

fDS = 0

FIG. 6.— Evolution of the lookback optical depth from the present day toredshift z according to Eq. 6, for MC dark stars with the maximum allowedDSNMS lifetime (tDSNMS = 6 Myr). These curves, and the correspondingdark stellar populations, correspond to the reionization histories presented inthe right panel of Fig. 2. In the MC scenario, earlier reionization caused byincreasing values of fDS results in a slight increase in optical depth. We alsoshow WMAP7 and Planck 1� detection/prediction bands, as per Fig. 4. Notethe zoomed-in axes relative to Fig. 4.

optical depth, the EE spectrum would nonetheless provide acomplementary (albeit weak) statistical handle via which toincrease the power of full parameter scans to exclude suchdark star models.

We do not show TT or TE spectra for the EC scenario, asthey exhibit less striking deviations from the correspondingspectra of the standard Pop III+II scenario at low multipoles l(large angular scales) than the EE curves do. We do point outhowever that the TT and TE spectra exhibit damping at largel due to the changing optical depth, which is more clearly


WMAP 1�, 7 years

0.2

0.4

0.6

0.8

1.0

Darkstar

fraction

f DS

0 100 200 300 400 500


FIG. 7.— Implied 1� detection/exclusion regions in the fDS–tDSP planefor EC dark stars, based on the integrated optical depth to last scattering ob-served by WMAP7 (Komatsu et al. 2011). We also show projected Planckconstraints (Colombo et al. 2009), assuming that the same central value(⌧e = 0.088) is measured by Planck as by WMAP7. To guide the eye, thedepth of shading is proportional to the likelihood of each parameter com-bination. For a product f? fesc = 0.005 of the star-formation efficiency andUV photon escape fraction, parameter combinations outside the red WMAPshaded region are excluded at greater than 1� by existing data. Combinationsoutside the shaded blue region will be excludable at better than 1� by Planck.Note however that variations in f? fesc will shift these regions substantially;refer to discussions in the final paragraph of Sec. 6.1 and in Sec. 6.3. Thesame interpolation methods were employed in this figure as in Fig. 5; theslight upturn of the boundaries of the Planck region at large tDSP is again anartifact of the interpolation.

visible than in the EE spectra. We also do not show powerspectra for the MC or NC cases, as they show little deviationin general from the standard Pop III+II case.

6.3. Astrophysical uncertainties and implications forparameters of reionization models

In Fig. 9 we show the impacts of varying astrophysical pa-rameters upon CMB observables. Here we give the variationsin optical depth and EE polarization resulting from the samevariations of f? fesc as in Fig. 3. For EE spectra, we nor-malize to the corresponding curve with default astrophysicalparameters in each case; i.e. to the standard f? fesc = 0.005Pop III+II spectrum for the fDS = 0 curves, and to the fDS = 1,tDSP = 150 Myr, f? fesc = 0.005 spectrum for the curves wherefDS = 1, tDSP = 150 Myr. Comparing with Figs. 4 and 8, we seeagain that variations in the astrophysical parameters withinreasonable ranges can have similar effects (both in strengthand character) to variations in the dark star parameters. Al-though this means that the impact of dark stars on the CMB isvery difficult to unambiguously disentangle from existing the-oretical uncertainties in reionization modeling, it also servesas a clear indication that the potential effect of dark stars uponCMB observables affected by reionization could be quite sig-nificant.

In some cases, it is possible that specific regions of thereionization parameter space that are ruled out in standardPop III+II-only scenarios by the current WMAP7 (or pro-jected Planck) data, are reopened by the possibility of havingdark stars. For example, Fig. 9 reveals that the extreme casesof varying astrophysical parameters ( f? fesc = 0.02 or 10-4) are


Dark stars and the CMBA dark star phase can affect the cosmic microwave background



⌧e =

0.10

⌧e =

0.09

⌧e = 0.08

⌧e = 0.07

0.2

0.4

0.6

0.8

1.0

Darkstar

fraction

f DS

0 100 200 300 400 500


Integrated

opticaldep

th⌧ e

0.06

0.08

0.10

FIG. 5.— Contours of equal integrated CMB optical depth to z = 1090 in theEC scenario, as a function of fDS and tDSP. Here we performed the interpola-tion on the optical depths in Table 1 using two-dimensional exponential ten-sion splines (Renka 1996b), based on a Delauney triangulation (Renka 1996a)and an iterative determination of the appropriate tension factors. Longer life-times and larger dark star fractions generically lead to smaller integrated op-tical depths; the slight upturn at large tDSP in the ⌧e = 0.08 and 0.09 contoursis an artifact of the interpolation.

Redshift z

Thom

son-ScatteringOpticalDep

th⌧ e(z)

MC

(Meager Capture)

tDSNMS = 6Myr

10 12 14 16 18 20

0.095

0.100

0.105

0.110

WMAP 1�, 7 years


fDS = 1

fDS = 0.8

fDS = 0.6

fDS = 0.3

fDS = 0.1

fDS = 0

FIG. 6.— Evolution of the lookback optical depth from the present day toredshift z according to Eq. 6, for MC dark stars with the maximum allowedDSNMS lifetime (tDSNMS = 6 Myr). These curves, and the correspondingdark stellar populations, correspond to the reionization histories presented inthe right panel of Fig. 2. In the MC scenario, earlier reionization caused byincreasing values of fDS results in a slight increase in optical depth. We alsoshow WMAP7 and Planck 1� detection/prediction bands, as per Fig. 4. Notethe zoomed-in axes relative to Fig. 4.

optical depth, the EE spectrum would nonetheless provide acomplementary (albeit weak) statistical handle via which toincrease the power of full parameter scans to exclude suchdark star models.

We do not show TT or TE spectra for the EC scenario, asthey exhibit less striking deviations from the correspondingspectra of the standard Pop III+II scenario at low multipoles l(large angular scales) than the EE curves do. We do point outhowever that the TT and TE spectra exhibit damping at largel due to the changing optical depth, which is more clearly


WMAP 1�, 7 years

0.2

0.4

0.6

0.8

1.0

Darkstar

fraction

f DS

0 100 200 300 400 500


FIG. 7.— Implied 1� detection/exclusion regions in the fDS–tDSP planefor EC dark stars, based on the integrated optical depth to last scattering ob-served by WMAP7 (Komatsu et al. 2011). We also show projected Planckconstraints (Colombo et al. 2009), assuming that the same central value(⌧e = 0.088) is measured by Planck as by WMAP7. To guide the eye, thedepth of shading is proportional to the likelihood of each parameter com-bination. For a product f? fesc = 0.005 of the star-formation efficiency andUV photon escape fraction, parameter combinations outside the red WMAPshaded region are excluded at greater than 1� by existing data. Combinationsoutside the shaded blue region will be excludable at better than 1� by Planck.Note however that variations in f? fesc will shift these regions substantially;refer to discussions in the final paragraph of Sec. 6.1 and in Sec. 6.3. Thesame interpolation methods were employed in this figure as in Fig. 5; theslight upturn of the boundaries of the Planck region at large tDSP is again anartifact of the interpolation.

visible than in the EE spectra. We also do not show powerspectra for the MC or NC cases, as they show little deviationin general from the standard Pop III+II case.

6.3. Astrophysical uncertainties and implications forparameters of reionization models

In Fig. 9 we show the impacts of varying astrophysical pa-rameters upon CMB observables. Here we give the variationsin optical depth and EE polarization resulting from the samevariations of f? fesc as in Fig. 3. For EE spectra, we nor-malize to the corresponding curve with default astrophysicalparameters in each case; i.e. to the standard f? fesc = 0.005Pop III+II spectrum for the fDS = 0 curves, and to the fDS = 1,tDSP = 150 Myr, f? fesc = 0.005 spectrum for the curves wherefDS = 1, tDSP = 150 Myr. Comparing with Figs. 4 and 8, we seeagain that variations in the astrophysical parameters withinreasonable ranges can have similar effects (both in strengthand character) to variations in the dark star parameters. Al-though this means that the impact of dark stars on the CMB isvery difficult to unambiguously disentangle from existing the-oretical uncertainties in reionization modeling, it also servesas a clear indication that the potential effect of dark stars uponCMB observables affected by reionization could be quite sig-nificant.

In some cases, it is possible that specific regions of thereionization parameter space that are ruled out in standardPop III+II-only scenarios by the current WMAP7 (or pro-jected Planck) data, are reopened by the possibility of havingdark stars. For example, Fig. 9 reveals that the extreme casesof varying astrophysical parameters ( f? fesc = 0.02 or 10-4) are

With extended capture

WMAP7 excludes the region outside the red band

Star formation efficiency and UV photon escape rate shift these regions substantially.

Planck will probe the blue band


Finding dark stars with JWSTDark stars at redshift z~6-15 are too dim to be detected, but....

Figure 3: Black body spectra of two dark stars formed via extended adiabaticcontraction (“without capture”) for m!=100 GeV. Left panel: 1.7! 105 M!

SMDS in a 106 M! halo. Right panel: 1.5! 107 M! SMDS in 108 M! halo.The black body flux is shown at z = 15 (formation redshift) and at z = 10and 5 (see line legends) assuming that the dark star survives till the lowerredshifts. Blue dashes show sensitivity limit and bandwidth of NIRCam 2µ(R=4) while the green dashes show the sensitivity limit and band width of theNIRCam 3.5µ (R=4) band. The upper and lower dashes show the sensitivitylimits after exposure times of 104s, 106s respectively. The sensitivity of MIRI(10µ, R=5) is shown for exposure time of 106s (orange dash). All sensitivitiesare computed assuming a S/N=10. The red vertical lines show the locationof the 1216A line redshifted from the rest-frame wavelength of the star ateach of the three redshifts. The observed flux to the left of the vertical lineswill decrease relative to the black curves depending on the model assumedfor IGM absorption up to the redshift of reionization.

31

Idea: Dark stars may become supermassive

Figure 4: Similar to Fig. 3 for dark stars formed “with capture”. Left panel:1.7 ! 105 M! SMDS formed in 106M! halo (m! = 50Gev). Right panel:1.7! 107 M! SMDS formed in 108M! halo (m! = 100Gev).

32

Freese et al 2010


Finding dark stars with JWST

Idea: Use a magnifying lens Zackrisson et al 2010

Dark stars at redshift z~6-15 are too dim to be detected, but....


Finding dark stars with JWST

Finding dark stars with the JWST 9

(purple lines). The three rows of panels in Fig. 4 corre-spond to the cosmic population III star formation histo-ries with standard LW (top row), reduced LW (middlerow) and no LW feedback (bottom row). The di!erentmarkers within each panel indicate the AB-magnitudesand numbers of dark stars at redshifts z = 10 (triangle),z = 15 (star) and z = 20 (square).

In general, long dark star lifetimes ! imply larger num-bers of dark stars at detectable brightnesses. In thecase of the 690 M!, Te! = 7500 K dark star (right col-umn), considerable numbers (! 10) of dark stars are ex-pected to be su"ciently bright for detection (at 5" after3.6 " 105 s) in the high-magnification regions of MACSJ0717.5+3745 at z # 10–11, provided that their lifetimesare # 5 " 108 yrs. This holds regardless of which of thethree feedback scenarios is adopted. For the reduced LWand no LW feedback models, significant dark stars areexpected even if the lifetime is closer to ! = 107 yrs.In the no LW scenario, even ! = 106 yrs dark stars canbe detected behind MACS J0717.5+3745, but only inmodest numbers (< 10). The situation for the 716 M!,Te! = 23000 K dark star (right column) is similar, ex-cept that this model remains detectable up to a redshiftof z # 15.

Dark stars with ! = 5"108 yr do not show the same de-cline in their expected numbers when going from z = 15to z = 10 as dark stars with shorter lifespan do. Thishappens because ! = 5"108 yr dark stars have lifetimesthat exceed the cosmic age intervals between adjacentredshift bins, allowing their signatures to accumulate atlower redshifts, even though the cosmic star formationrate of population III stars is declining at these epochsfor all three feedback scenarios. The Trenti & Stiavelli(2009) models do not allow us to trace the star forma-tion history to epochs at z < 10, even though the starformation rate clearly remains non-zero at z = 10 in boththe reduced LW and no LW feedback scenarios. In fact,! = 5 " 108 yrs dark stars forming at z ! 10 in thesefeedback scenarios will survive in detectable numbers toeven lower redshifts (z # 6), even if one artificially setstheir formation rates to zero at z < 10.

In summary, cool (Te! $ 30000 K) and long-lived(! ! 107 yr) dark stars may well be detected at z # 10in sizeable numbers within a single, ultra deep JWSTfield if one takes advantage of the magnifying power of aforeground galaxy cluster. In the case of high ! (! 108

yr) and cosmic star formation scenarios which imply sig-nificant dark star formation at z < 15, several darkstars may be even seen even if only a minor fraction(fDS % 0.01–0.1) of all population III stars forming inminihalos become dark stars with temperatures in thedetectable range.

4. DISCUSSION

4.1. How to distinguish isolated dark stars from otherobjects

As demonstrated in Fig. 3.2, certain varieties of z #

10 dark stars may be su"ciently bright and numerousto be detected by JWST/NIRCam survey of the high-magnification regions of a foreground galaxy cluster. Buthow does one identify such objects among the overwhelm-ing number of mundane interlopers located in front of,inside or beyond the lensing cluster?

−2 −1 0 1 2 3 4−6

−4

−2

0

2

4

6

m356−m444

m200−m277

Fig. 5.— The JWST/NIRCam m356 ! m444 vs. m200 ! m277

colours of Te! < 10000 K dark stars at z = 10 (red star sym-bols) compared to a number of potential interlopers in multibandsurveys: star clusters or galaxies at z = 0–15 (black dots), AGNtemplate spectra at z = 0–20 (yellow dots), Milky Way stars withTe! = 2000-50000 K and Z = 0.001 ! 0.020 (blue dots) and MilkyWay brown dwarfs with Te! = 130–2200 K. Since the dark starsreside a region of this colour-colour diagram that is disconnectedfrom those occupied by these other objects, it should be possi-ble to identify possible dark star candidates in deep multibandJWST/NIRCam surveys of the high-magnification regions of lens-ing clusters.

Given the many degeneracies involved in the interpre-tation of broadband photometry, there may well be un-resolvable ambiguities in some cases. However, many ofthe cooler high-redshift dark stars should stand out inmultiband survey data because of their unusual colours.This is demonstrated in Fig. 5, where we plot the colourindices m356 & m444 vs. m200 & m277 (based on AB-magnitudes in the JWST/NIRCam F200W, F277W,F356W and F444W filters) at z = 10 for all dark starsfrom Table 1 with Te! < 10000 K. The colours of thesemodels (red star symbols) are compared to the coloursprediced for a wide range of galaxies, star clusters, activegalactic nuclei (AGN) and Milky Way stars. The cloudof black dots in Fig. 5 indicate the colours of integratedstellar populations (star clusters and galaxies) gener-ated with the Zackrisson et al. (2001) spectral synthesismodel. These predictions are based on instantaneous-burst13, Salpeter-IMF stellar populations at redshiftsz = 0–15 with metallicities in the range Z = 0.001-0.020,ages ranging from 106 yr up to the age of the Universeat each redshift and a rest-frame stellar dust reddeningof E(B & V ) = 0–0.5 mag assuming the Calzetti et al.(2000) extinction law. Also included in Fig. 5 are theexpected colours of foreground stars with Te! = 2000-50000 K and Z = 0.001 & 0.020 in the Milky Way (i.e.at z = 0), based on the Lejeune et al. (1998) compila-tion of synthetic stellar atmosphere spectra (blue dots),and the colours of Milky Way brown dwarfs in the 130–2200 K range based on the Burrows et al. (2003, 2006)models (green dots). The yellow dots represent the tem-plate AGN spectra of Hopkins et al. (2007) for bolomet-ric luminositites log10 Lbol/L! = 8.5–14.0, at redshiftsz = 0–20. Since none of these potential interlopers have

13 This is a conservative choice, since allowing for more extendedstar formation histories would only result in a more restrictedcolour coverage for these synthetic galaxies

6 Zackrisson et al.

0 0.5 1 1.5

20

25

30

35

40

45

50log10 ! (micron)

mAB

z = 6

a)

JWST detection limits

0 0.5 1 1.5

20

25

30

35

40

45

50log10 ! (micron)

mAB

z = 10

b)

JWST detection limits

Fig. 2.— The predicted apparent AB magnitudes of dark stars at z = 6 (a) and z = 10 (b), as a function of central wavelength of theJWST broadband filters. Each solid line corresponds to a separate dark star model from Table 1. These lines have been colour-codedaccording to the e!ective temperatures of the dark stars: Te! ! 8000 K (red), 8000 K < Te! ! 30000 K (green) and Te! > 30000 K(blue). The dashed horizontal lines correspond to the JWST detection limits for a 10! detection of a point source after 104 s of exposure(thick dashed) and for a 5! detection of a point source after 3.6 " 105 s (100 h) of exposure (thin dashed). The progressively brighterdetection thresholds at central wavelengths higher than 4.4µ (log10 " > 0.65) reflect the lower sensitivity of the MIRI instrument (centralfilter wavelengths log10 " > 0.65) compared to NIRCam (central filter wavelengths log10 " ! 0.65). In both panels, all dark star modelslie significantly faintward of the detection thresholds in all filters, implying that their intrinsic brightnesses are too low to be detected byJWST. However, a magnification of µ = 160 due to gravitational lensing by a foreground galaxy cluster (see Sect. 3.2) would shift allmodels downward by 5.5 magnitudes (as indicated by the vertical arrow) and allow certain varieties of dark stars into brightness regimedetectable by the NIRCam instrument. This is the case for some of the Te! ! 30000 K dark stars (green and red lines) at both z = 6 andz = 10. The reason why the red lines end abruptly at 1.15 µm (log10 " = 0.06) for z = 6 and at 2.0 µm (log10 " = 0.3) for z = 10 is thatthe short-wavelength limit (0.13 µm) of the MARCS model spectra have entered the bluer filters at these redshifts. Since this happens atmAB > 38, which is a brightness regime inaccessible to the JWST, this has no impact on the present study.

body and the synthetic stellar atmosphere spectra in theNIRCam F444W filter. The di!erent lines represent thesix dark star models from Table 1 for a WIMP mass of1 GeV. The solid lines correspond to the MARCS (thickline) and TLUSTY (thin lines) dark star SEDs plottedin Fig. 3a. As seen, there are substantial di!erences forthe cooler (! 10000 K) dark stars, whereas the di!er-ences for hotter dark stars are below 0.5 mag. This isprimarily because the hotter stars become progressivelymore black body-like at the relevant wavelengths. For in-stance, the 0.36µm break (which makes the black bodyspectra overpredict the F444W fluxes at z " 9) is farless prominent in the hotter dark stars. We conclude,that while black body spectra may be useful for deriv-ing order-of-magntiude estimates of JWST fluxes for thehotter dark stars, detailed stellar atmosphere models arerequired to accurately predict the fluxes for cool darkstars at high redshifts.

3.2. Dark stars magnified by gravitational lensing

Fig. 1 and 2 demonstrate that all dark stars in Ta-ble 1 are intrinsically too faint at z ! 6 to be de-tected by JWST, even if extremely long exposure times(texp = 3.6times105 s, i.e. 100 h) are considered. Theonly hope of detecting isolated dark stars with JWST atthese redshifts would then be to exploit the gravitationallensing provided by a foreground galaxy cluster. Galaxyclusters at z " 0.1–0.6 can in principle boost the fluxes ofhigh-redshift objects by up to factors # 100 (e.g. Bradacet al. 2009; Maizy et al. 2009). As shown in Fig. 2, thiswould be su"cient to lift some of the cooler (Te! < 30000K) dark star models above the JWST detection thresh-old. For each separate dark star model, the entries inthe max(zobs) column in Table 1 indicate the maximum

redshifts at which 5! detections are possible in at leastone JWST filter after 3.6 $ 105 s (100 h) exposures, as-suming a magnification of µ = 160 (see below). No darkstars are detectable at z > 15, even when this boost dueto lensing is taken into account.

How many dark stars at z " 10 would one then expectto detect in a survey of a single lensing cluster? Thisdepends on the magnification properties of the cluster,on the cosmic star formation history of dark stars andon their typical lifetimes " . While gravitational lens-ing boosts the fluxes of background objects, their surfacenumber densities are at the same time diluted by a factorequal to the magnification µ. In a region with angulararea #2 and magnification µ, one can show that the ex-pected number of dark stars NDS in the redshift interval[zmin, zmax] is given by:

NDS = c#2

! zmax

zmin

! t(z)!!

t(z)

SFR(t)dos(z)2(1 + z)3

µ(z)MDS

dt

dzdt dz

(3)where SFR(t) is the star formation rate (in units ofM" Mpc!3yr!1) of dark stars at cosmic epoch t(z), MDSis the dark star mass (assumed to be the same for all suchobjects) and dos(z) is the angular size distance betweenthe observer and source at redshift z. In the case of flat#CDM cosmologies, the derivative dt

dz in eq.(3) is givenby:

dt

dz=

1

H0(1 + z) [$M (1 + z)3 + $"]1/2(4)

When exploring the prospects of detecting isolateddark stars in the high-magnification regions of aforeground galaxy cluster, we have adopted MACS

Detectable with JWST via gravitational lens magnification ~100

Star clustersGalaxies

Brown dwarfs

AGNs

MW stars

Dark stars

Dark star spectra

x100

Dark stars at redshift z~6-15 are too dim to be detected, but....

Idea: Use a magnifying lens Zackrisson et al 2010


Conclusions

The first stars to form in the universe may have been powered by dark matter annihilation instead of nuclear fusion.



Artist’s impression

Dark Stars are stars made of ordinary matter that shine thanks to the annihilation of dark matter.


dark stars, or how dark matter can make a star shinegcosmo.bao.ac.cn/sites/default/files/ppt_naoc...

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