Dark Stars, or How Dark Matter Can Make a Star Shine
Dark Stars are made of ordinary matter and shine thanks to the annihilation of dark matter.
Paolo Gondolo University of Utah (Salt Lake City) Oskar Klein Centre (Stockholm) Dark Stars The 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
Spolyar, Freese, Gondolo 2008 Freese, Gondolo, Sellwood, Spolyar 2008 Freese, Spolyar, Aguirre 2008 Freese, Bodenheimer, Spolyar, Gondolo 2008 Artist’s impression Natarajan, Tan, O’Shea 2009 Spolyar, Bodenheimer, Freese, Gondolo 2009 Dark Matter Burners Dark Stars Renamed in Fairbairn, Scott, Edsjö Stars living in a dense dark matter environment may gather
Background enough darkPreliminar matteries and become Dark Matter Burners Theory Results Simulations The idea in a nutshell (cartoon version) • Explain young stars at galactic center? • Prolong the life of Pop III Dark Stars? Text Salati, Silk 1989 Moskalenko, Wai 2006 Fairbairn, Scott, Edsjö 2007 Spolyar, Freese, Aguirre 2008 Iocco 2008 Bertone, Fairbairn 2008 Yoon, Iocco, Akiyama 2008 Galactic centerPat Scott exampleIDM 2008 Maincourtesysequence dark starsof atScottthe Galactic Centre Taoso et al 2008 Iocco et al 2008 Casanellas, Lopes 2009 Dark matter particles
Photons Baryons Neutrinos Weakly Interacting Massive Particles (WIMPs) Dark Cold Dark Energy Matter • A WIMP in chemical equilibrium in the early universe naturally has the right density to be Cold Dark Matter • One can experimentally test the WIMP hypothesis The same physical processes that produce the right amount of WIMPs make their detection possible
Accelerator Direct Indirect
LHC DAMA, XENON, etc Fermi IceCube PAMELA How do WIMPs get into stars?
Some stars are born with WIMPs
First stars (Pop III) Sun
Some stars capture them later
Stars living in dense dark matter clouds (main sequence stars, white dwarfs, neutron stars, Pop III stars) How do WIMPs get into stars? • By gravitational contraction : 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) • By capture through collisions : 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) 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 What doWIMPstostars? Semi-Dark Stars
Ambient DM density (M ⦿/pc 3) and higherluminosities shifts tolower temperatures The mainsequence 1 M ⦿ σ=4×10 ρ≤4×10 v=300 km/s /pc 3 = 38GeV/cm Salati, Silk1989 -36 7 GeV/cm cm 2 3 3 What do WIMPs do to stars? Semi-Dark Stars 90 P. Scott, M. Fairbairn and J. Edsjo¨
Main sequence star entering a WIMP low density cloud
DarkStars evolution code (based on EZ) high density
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 indicativeScott, ages during Fairbairn, the evolution of 1.4 Edsjo M stars. 2009 Tracks have been halted when the star exhausts the supply of hydrogen in its core or reaches the current age of the Universe. Stars with a greater luminosity! contributionfrom WIMPs push further up the Hayashi track and spend longer there before returning to the main sequence. Stars which come to be entirely dominated by WIMP annihilation (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 the Universe.
and 2.19), so we see that σ av 0 makes no difference to the amount corresponds to the central temperature and density reaching their of energy generated. When" equilibrium# has not been achieved, this minima and the star arriving at the bottom leftmost point of its travels will not be the case. Such an effect can be seen in the slight upturn in Fig. 5. At very high WIMP luminosities, the stellar core expands of the WIMP luminosity in the uppermost curve of the upper panel and cools drastically, moving stars a long way back along the pre- in Fig. 3. In this case the very high ρχ and very low σ av 0 sig- main sequence and effectively shutting down nuclear burning all nificantly change the stellar structure before equilibrium" has# been together. Such an object becomes a fully fledged dark star, powered reached, causing LW to peak prior to equilibrium. The dependence entirely and perpetually by WIMP annihilation. of LW on mχ in Fig. 3 shows roughly an inverse square relationship, At intermediate WIMP luminosities, nuclear burning is sup- which is a result of using the full capture expressions in the RSC. pressed rather than completely extinguished. Its continued contri- As can be seen from careful inspection of equation (2.19) for ex- bution to nuclear processing slowly raises the core temperature and ample, for smallv ¯ and v$ such as those used in the context of the density once more, in turn increasing the rate of nuclear reactions early Universe by e.g. Iocco (2008) and Freese et al. (2008a), the and accelerating the process. The star burns hydrogen alongside dependence disappears. WIMPs, and goes on to evolve through a hybrid WIMP-hydrogen In Figs 4 and 5 we show evolutionary tracks in the HR and main sequence. Such evolution can be best seen in the bottom left- central equation-of-state diagrams of stars with different masses hand panel of Fig. 4. Thanks to the energy input from WIMP anni- and WIMP luminosities. At low WIMP luminosities, the evolution is hilation, the time it takes such a star to consume its core hydrogen essentially normal. As WIMPs are allowed to provide more energy, is lengthened, so its effective main-sequence lifetime is extended the negative heat capacity of a star causes it to expand and cool. (Fig. 7). The increase in main-sequence lifetime is notable at all The central temperature and density drop, nuclear burning reduces metallicities, but most prominent at low Z,essentiallybecausenor- and the star moves some distance back up the Hayashi track. The mal main-sequence lifetimes are shorter at lower metallicity. We reduction in central temperatures and overall luminosities provided did not see changes with metallicity in the central temperatures, by pp-chain and CNO-process hydrogen burning are illustrated in pp-chain or CNO luminosities of the stars in our grid. Fig. 6. These values are taken at the time tadjust when a star has We should point out here that in the extreme case of a very completed its initial reaction to the presence of WIMPs, which large WIMP luminosity, it is highly questionable whether a star
C C $ 2009 The Authors. Journal compilation $ 2009 RAS, MNRAS 394, 82–104 Dark Stars
Population III stars First stars: standard picture
• Formation Basics - first luminous objects ever - made only of H/He
5 6 - form inside DM halos of 10 -10 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
Thermal evolution of Pop III protostaradiabatic 4 Must be cool to contract phase 10 collision H2 formation induced line cooling emission (NLTE) 3-body reaction 3 opaque to 10 continuum loitering (~LTE) opaque to heat gas temperature [K] gas temperature molecular line adiabatic release contraction Courtesy of N. Yoshida 102 gas number density [cm-3] First stars: three conditions for a dark star
Spolyar, Freese, Gondolo, arxiv:0705.0521, Phys. Rev. Lett. 100, 051101 (2008)
(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 (1) Adiabatic contraction of dark matter From cosmology. No extra free parameter.
(a) using cosmo-hydrodynamical simulations Abel, Bryan, Norman 2002 (b)using prescription from Blumenthal, Faber, Flores & Primack 1986 (circular orbits only) Spolyar, Freese, Gondolo 2008 rM(r) = constant (c) using full phase-space a la Young 1991 Freese, Gondolo, Sellwood, Spolyar 2009 (d)using cosmo-hydrodynamical simulations Natarajan, Tan, O’Shea 2009 No. 1, 2009 DARK MATTER ANNIHILATION AND PRIMORDIAL STAR FORMATION 577
(1) Adiabatic contraction of dark matter From cosmology. No extra free parameter.
Using Blumenthal et al
Natarajan et al
Using Young Abel et al Original NFW profile
Spolyar, Freese, Gondolo 2008; Freese, Gondolo, Sellwood, Spolyar 2008 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 the outer, 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 shown with the dotted lines. 2 significant steepening compared to the outer regions. This is σav a + bv + is largely constant, that is, the constant $ %≈ ··· likely to be the result of adiabatic contraction, since it occurs at term a is non-zero. We may then estimate σav using the sim- $ % ascale 1pcwherethedensityofbaryonsbeginstodominate. ple freeze-out condition nχ (TF) σav H (TF)atthefreeze-out We emphasize∼ again that the simulation points on which DM $ % = Figure 2: Adiabatically contracted DM profiletemperatures in the first protosTtarFs.fonr χan isiniti theal NF particleW number density, and H is the profile (dashed line) using (a) the Blumenthal method (dotted lines) and (b) Young’s 7 fits #2 are based correspond to bins withmeth onlyod (solid alin smalles), for M ( Heating rate = Qann fQ Qann: Rate of energy production from annihilation (per unit volume) v 2 2 2 2 Particle physics factor Qann = n v m c = c ⇢ h i h i m 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 ≲ Ec ≈ 280 MeV → ionization • Photons ≳ 100 MeV → electromagnetic cascades ≲ 100 MeV → Compton/Thomson scattering (3) Birth of a dark star Thermal evolution of Pop III protostar m = 100 GeV Must be cool to contract 104 〈σv〉 = 3×10-26 cm3/s m = 100 GeV 〈σv〉 = 3×10-26 cm3/s COOLING DOMINATES 103 HEATING DOMINATES gas temperature [K] gas temperature 102 gas number density [cm-3] (3) Birth of a dark star Spolyar, Freese, Gondolo 2008 Dark matter that can form dark stars Almost all thermal dark matter particles Gondolo, Huh, Kim,Scopel 2010 Exceptions: resonant annihilation, co-annihilation, neutrinophilic dark matter below ~50 GeV 0 10 20 30 40 50 60 70 2.5¥10-5 2.5¥10-5 2.0¥10-5 2.0¥10-5 p-waves 1.5¥10-5 1.5¥10-5 Q f Thresh 1.0¥10-5 1.0¥10-5 olds Coannih - - ilations 0.5¥10 5 0.5¥10 5 NO DARK STAR 0 0 Resonances 0 10 20 30 40 50 60 70 m GeV NO DARK STAR ⌫⌫¯,⌫⌫¯H W,L ⌫⌫¯Z ! Neutralino Neutrinophilic 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 2008 Spolyar, Bodenheimer, Freese, Gondolo 2009 Life of a dark star Sequence of polytropes with gas and dark matter accretion Spolyar, Bodenheimer, Freese, Gondolo 2009 Mature Dark Star (stalls for ~5x105 yr) Young Dark Star (first ~104 yr) Life of a dark star Sequence of polytropes with gas and dark matter accretion Spolyar, Bodenheimer, Freese, Gondolo 2009 Main Sequence Star Kelvin-Helmholtz Contraction Mature Dark Star (stalls for ~5x105 yr) Young Dark Star (first ~104 yr) Life of a dark star Sequence of polytropes with gas and dark matter accretion Spolyar, Bodenheimer, Freese, Gondolo 2009 Main Sequence Star Kelvin-Helmholtz Contraction Mature Dark Star (stalls for ~5x105 yr) Young Dark Star (first ~104 yr) Life of a dark star Spolyar, Bodenheimer, Freese, Gondolo 2009 6 7 For 0.2-1 Myr, dark stars are massive (200-1000 M⊙), bright (10 -10 L⊙), 4 and cold (Teff~10 K). Pair-instability region is avoided because core density is small (10-7-10 g/cm3). Mass accretion is not stopped by feedback because ionizing UV radiation is negligible. The dark star phase ends onto Zero Age Main Sequence stars that are 6 7 5 massive (500-1000 M⊙), bright (10 -10 L⊙), and hot (Teff~10 K). 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 Quasars from dark stars? An old problem: quasars form too early 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⨀ 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? nuclear energy generation rate is not negligible; CNO-cyclehydrogenburningisindeed 3. DependenceExtended on the gas capture masstaking accretion place ratesand in the central appropriate part. The stars evolve ongas the main accretion-sequence track over arate few give dark million years, with their luminosity increasing with mass. Fig.2 also shows the central The stellarstars evolution that for models can withtemperature constant solve gas massand the density accretion ashigh-redshift already a function shows of several stellar mass, for quasar B and Bd models. formation problem. interesting features. Fig. 1 shows the evolution of mass and radius for the accreting stars We find that the fate of the stars depends importantly on the accretion rate. The DM without (upper panel) and with (lower panel) DM annihilationheating. annihilation supplies an extra energy to support a star against gravitational contraction, and thus the star consumesUmeda, less hydrogen Yoshida, per unit time, Nomoto, with its lifetime Tsuruta, prolonged. The Sasaki, Ohkubo 2009 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 JHEP00(2009)000 accretion are also shown. In many cases, the final stellarJHEP00(2009)000 massislargerthan1000M!. JHEP00(2009)000 Figure 3: Final mass and luminosity for various models. Models A(d), B(d), C(d) are the same −5 −1 as in Fig.1. Models D, Y, F, and G are the cases with the accretion rate M˙ =10 M"yr ,rates in [33], [31], and [34], respectively. Lower case letters ‘d’inthemodelnames,suchasDd,indicateFigure 4: The evolution of Model Bd after the DM density is reduced by a factor of 0.3 when the M , M Figure 1: Stellar mass - radius evolutionthat for the each fiducial model. dark The matter upper and annihilationlower panels energy show is includestellard. mass Models is M=12 and000 Md!.TheupperpanelshowsthecentralHemassfractionasafunct use the rates ion of central density. Vertical lines with numbers indicate the time to collapse. At first, hydrogen burning the models without and with the DM annihilationin [31] with energy, a cut resp off atectively.M =300 TheM model".InthemodelsCd names for 3andFd 3, the dark matter capture M˙ −2, −3, −4M −1 ×takes place and× helium mass fraction increases from 0.5 to 1.0in17Myr.Afterthebeginningof =10 10 10 "yr cases are A,rate B, C, is enhanced and Ad, Bd, by Cd, a factor for the of cases 3 than without the models and with Cd and Fd, respectively. The solid straight line the DM heating, respectively. He-burning the star collapses only in 3 days. The middle panelshowstheenergygenerationrateat represents the Eddington Luminosity. The mass range boundethe centerdbythedottedlines,labeledPISN, by DM annihilation and nuclear burning. The nuclear energy generation rate becomes shows the mass range in which the stars explode as pair-instanegativebility (as supernovaeshown by the and dashed do line) not after form entering the (He)photo-dissociationregion.Inthe The adopted constant gas mass accretion rates are, M˙ =10−2 (Model A, Ad), 10−3 (B, massive BHs. The models with arrows are “stalling”, or, theibottomrcentraltemperaturesaredecreasing. panel the dashed line shows the central density - temperature trajectory. The thick solid −4 M −1 Bd), and 10 (C, Cd) " yr ,forwithoutandwithDM(fortheletterswithoutandwithTherefore, their mass may increase further. line indicates that the star is unstable above this line. −3 −1 The most interesting is Model Bd, the case withtheM photosphere,˙ =10 M that!yr may locate(see Figs. far above 1, 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, –4– only the reliable observational data will be the total luminosity of the star, which correlates –6– –10– No extended capture Once the dark star contracts to the Zero Age Main Sequence, the supply of dark matter ends. Sivertsson, Gondolo 2010 Original dark matter density 8 7 Sivertsson & Gondolo, 2010 -7 Sivertsson & Gondolo, 2010 1.8⋅10 10 7 1.6⋅10 with scattering -8 without scattering 10 7 On the throat of death , the 1.4⋅10 10-9 7 dark star burns all of the dark ] 1.2 10 ] ⋅ 3 ! -10 107 10 Dark matter density after matter it can get. 6 8⋅10 10-11 Kelvin-Helmholtz contraction Density [g/cm Luminosity [L 6 6⋅10 10-12 6 4⋅10 -13 The rest of the dark matter 6 10 t = 0.40 Myr 2⋅10 t = 0.28 Myr stays in orbit out of reach of 0 10-14 12 12 12 12 13 13 0 0.1 0.2 0.3 0.4 0.5 0.6 0 2⋅10 4⋅10 6⋅10 8⋅10 10 1.2⋅10 the dead dark star. Time [Myr] Radius [cm] FIG. 3: The time evolution of the dark star luminosity from FIG. 5: The densityRadius profile of of the dark dark matter star around after the star WIMP-WIMP annihilations. The top solid (red) line includes just before (dotted blue line) and just after (solid red line) WIMP-nucleon scattering in addition to annihilation; the bot- the Kelvin-HelmholtzKelvin-Helmholtz contraction at the contraction end of the dark star tom dashed (blue) line does not include scattering. phase (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 is 1 Sivertsson & Gondolo, 2010 × 13 ] 4.2 10 cm, about four times the length of the horizontal ! axis. 0.1 the total mass of WIMPs on orbits crossing the star) is plotted as a function of time. The three lines illustrate 0.01 the effect of the stellar evolution as well as that of scat- tering and annihilation. The top (solid red) line is similar to the curve in Fig. 2, and includes just the gravitational 0.001 response of the WIMPs to the star and neither scatter- no annihilation annihilation only ing nor annihilation. It shows that the mere contrac- + scattering tion of the star already makes it a much smaller target Total mass of WIMPs crossing the star [M 0.0001 for WIMP capture, by about one order of magnitude in 0 0.1 0.2 0.3 0.4 0.5 0.6 the accessible mass. Annihilation reduces the number of Time [Myr] WIMPs that cross the star (green dotted line), as anni- hilation removes WIMPs from the system. The inclusion FIG. 4: The dark matter mass accessible to the star as a function of time. In other words, the total mass of the WIMPs of scattering reduces this number further, which might on orbits intersecting the star at the different stellar evolution at first not seem obvious. The reason is that WIMPs on stages. The dotted (blue) line includes both WIMP scattering orbits not crossing the star cannot scatter in the star. and annihilation. The dashed (green) line includes WIMP Hence the total mass of WIMPs on orbits crossing the annihilation but no scattering. The solid (red) line includes star can never increase due to scattering. Furthermore, neither scattering nor annihilation. scattering puts WIMPs onto lower energy orbits, making them more vulnerable to annihilation. Thus the num- ber of WIMPs in stellar contact is further reduced (see but at a much smaller rate; in the case we study, the anni- Fig. 4). As discussed in Section IV, our Monte-Carlo only hilation after contraction is suppressed by (very roughly) includes WIMPs from the inner 1 percent of the NFW about 15 orders of magnitude (five orders of magnitude halo scale radius rs,butWIMPsfromregionsfurtherout coming from the change in stellar volume and two times do not contribute significantly to the annihilation rate in- five orders of magnitude coming from the decrease in den- side the dark star. sity due to annihilation and scattering, extracted from From the Monte-Carlo one can also extract the dark Fig. 5 below). matter density profile around the formed star. This is When WIMPs scatter, they lose energy, go on smaller shown in Fig. 5 for two different times, just before and orbits, and spend more time near the center of the star just after the KH contraction (blue dotted line and red where the density is higher and the annihilation faster. solid line, respectively). The solid red line is for the time Both annihilation and scattering remove WIMPs from 0.4 Myr, which is just after nuclear burning has started. orbits that cross the star. This is illustrated in Fig. 4, The blue dotted line shows the time 0.28 Myr, which is where the mass of dark matter accessible to the star (i.e. just before the star contracts enough for scattering to Supermassive dark stars? Perhaps some dark stars become much more massive (107 vs 102 11 7 M⨀) and much brighter (10 vs 10 L⨀) Freese, Ilie, Spolyar, Valluri, Bodenheimer 2010 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). Figure 1: Hertzsprung-Russell diagram for dark stars for accretion rate M˙ = −3 10 M"/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 product −39 2 of scattering cross section times ambient WIMP density σcρ¯χ =10 cm 1013GeV/cm3. Also labeled are stellar masses reached by the DS on its way× 5 to becoming supermassive. The final DS mass was taken to be 1.5 10 M" (the baryonic mass inside the initial halo), but could vary from halo× to halo, depending on the specifics of the halo mergers. 29 Dark stars, reionization and the CMB 7 1.0 1.0 ] EC ] EC ii ii (Extreme Capture) (Extreme Capture) 0.8 0.8 tDSP = 150 Myr tDSP = 500 Myr 0.6 fDS =1 0.6 fDS =1 fDS =0.9 fDS =0.9 fDS =0.8 fDS =0.8 0.4 0.4 Dark stars and reionizationfDS =0.6 fDS =0.6 fDS =0.3 fDS =0.3 fDS =0.1 fDS =0.1 A0. 2dark star phase can delay reionization0.2 fDS =0 fDS =0 Hydrogen Ionization Fraction [H Hydrogen Ionization Fraction [H Scott, Venkatesan, Roebber, Gondolo, Pierpaoli, Holder 2011 0.0 0.0 6 8 10 12 14 16 18 20 6 8 10 12 14 16 18 20 8 With capture Redshift z ScottWith et al. extended captureRedshift z 1.0 1.0 1.0 1.0 ] ] ] EC MC ] EC MC ii ii ii ii (Extreme Capture) (Extreme Capture) (Meager Capture) (Meager Capture) 0.8 0.8 0.8 fDS =0.6 0.8 fDS =1 tDSNMS =3Myr tDSNMS =6Myr 0.6 tDSP = 500 Myr 0.6 tDSP = 500 Myr 0.6 tDSP = 150 Myr 0.6 tDSP = 150 Myr tDSP = 50 Myr fDS =1 tDSP = 50 Myr 0.4 0.4 f =0.8 tDSP = 15 Myr DS tDSP = 15 Myr fDS =1 f =0.6 tDSP =5Myr DS tDSP =5Myr 0.4 fDS =0.6 0.4 PopII+III only fDS =0.3 PopII+III only 0.2 fDS =0.1 0.2 fDS =0.1 Hydrogen Ionization Fraction [H Hydrogen Ionization Fraction [H Hydrogen Ionization Fraction [H fDS =0 Hydrogen Ionization Fraction [H fDS =0 0.2 0.2 0.0 0.0 6 11.0 8 11.2 10 11.4 12 11.6 14 11.8 1612.0 1812.2 2012.4 6 11.0 8 11.2 10 11.4 12 11.6 1411.8 1612.0 1812.2 2012.4 RedshiftRedshiftz z RedshiftRedshiftz z FIG.F 1.—IG. 2.— Ionization Ionization histories histories of a of Universe a Universe containing containing dark dark or stars, semi-dark in the stellar meager populations, capture (MC) in thescenario, extreme where capture dark (EC) stars effectively scenario, where receive dark a small stars extension live extendedto their lives main-sequence as cool, diffuse lifetimes. objects. Here TheWithout two weplot panels the compare fraction capture, historiesof hydrogen forno differentin HeffectII as dark a function staron fractions ofreionization. redshift.fDS, Top where panels dark compare stars live histories in the DSNMS for different phase dark for star close to fractionsthe maximumfDS, in situations time allowed where by dark core stars hydrogen live a long depletion time in (t theDSNMS DSP= phase 3 and ( 6tDSP Myr).= 150 Longer Myr DSNMS and 500 Myr). lifetimes Bottom and larger panels dark compare star fractions histories lead for different to small increasesDSP lifetimes,in the in speed situations of reionization where dark (note stars the make zoomed up a substantial axes relative fraction to Fig. of1). the Non-dark mass budget aspects of the of the first calculations population ofare stars as described ( fDS =0. for6 and Fig. 1).1. Longer-lived and more numerous 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 not form 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 of dark 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 themselves later die and get1.0 replaced by newborn Pop II stars. 1.0 ] PopII+III only ] EC and fDS =0.9 - 1, or tDSP = 500 Myr and fDS 0.75, would site trend relative to the EC cases. This is because QDSNMS > ii & ii be ruled out at face value if we were to(f compareDS = 0) directly with QPop III, so extending the DSNMS phase(Extreme and Capture) increasing the 0.8 0.8 the WMAP7 limit that zreion =9.4-11.8. Similarly, one might fraction of baryons contained in it causestDSP reionization= 150 Myr to hap- 4 also conclude that many models with low ft?fesc =1and10 f are pen more quickly than with only a normal Pop III IMF. DSP ⇥ DS f =1 3 DS ⌧ f?fesc =5 10 ruled out for producing zreion and e exceeding the upper⇥ limit Again, as expected the effects increase with increasing fDS 0.6 2 0.6 of the WMAP7 error band. Whilst this is indeedf?fesc =2 true10 when and tDSNMS. The reason the MC scenario has a much smaller ⇥ 4 f? fesc =0.005 as we assume here, such limits are not really ro- effect on reionization than the EC scenariof?fesc =1 is that10 its dura- ⇥ bust to variations in astrophysical parameters. We discuss in- tion is already much more strongly constrained, in3 this case f f =5 10 ? esc ⇥ tegrated optical0.4 depths and corresponding constraints in more by the fusion-burning0.4 timescale of core hydrogen2 during the f f =2 10 detail in the following section. DSNMS phase. ? esc ⇥ For the meager capture (MC) scenario, the effects are less In Fig. 3 we show the impact of varying the product of the dramatic; in0.2 Fig. 2 we show a zoomed-in section of the full astrophysical0.2 parameters f? and fesc from our canonical value history of reionization, for a few combinations of fDS and the of f? fesc = 0.005 to the extreme values of 0.02 ( f? = 0.1, fesc = Hydrogen Ionization Fraction [H Hydrogen Ionization Fraction [H -4 DSNMS lifetime tDSNMS. Here, increasing fDS and tDSNMS 0.2) or 10 ( f? = fesc = 0.01). We give the resulting reioniza- results in progressively earlier reionization, the exact oppo- tion histories both for a standard Pop III without dark stars, 0.0 0.0 6 8 10 12 14 16 18 20 6 8 10 12 14 16 18 20 Redshift z Redshift z FIG. 3.— Impacts of varying astrophysical parameters upon the reionization history of a Universe containing no dark stars (left), and one containing EC dark stars 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 escape fraction fesc. The variation of astrophysical parameters induces a similar change in the reionization history of the Universe to dark stars (left), but has a slightly reduced 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, but also 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, The results we present here agree broadly with those of we see that within this range of astrophysical uncertainties, a Schleicher et al. (2009), but the correspondence is not imme- large range of reionization histories is possible. Indeed, in the diately obvious. Schleicher et al. considered reionization from most extreme cases, dark stars have a similar magnitude effect ‘MS-dominated’ (main sequence), and ‘CD’ (capture domi- as the variation of astrophysical parameters. This degeneracy nated) dark stars, roughly corresponding to our own MC and is unfortunate, but not unexpected; substantial uncertainty ex- EC scenarios, respectively. They investigated the case where ists in reionization models at present, even before introduc- fDS = 1, showing that the higher ionizing photon fluxes of the ing the possibility of stellar populations including dark stars. DSNMS phase hasten reionization, whereas the lower fluxes Hearteningly however, the impact of the astrophysical uncer- of the DSP phase delay it. This is in good agreement with tainties is reduced in situations where dark stars play a sig- what we show here, and earlier predictions by Yoon et al. nificant role, as can be seen by comparing the two panels of (2008). Where we differ from Schleicher et al.’s analysis is in Fig. 3. our atmospheric modeling (we use actual model atmospheres Dark stars, reionization and the CMB 11 0 0 1 . 1 . ⌧e =0.07 e 10 ⌧e ⌧ 8 =0 10 .08 Scott0 . et al. 0 . ⌧ 8 DS e =0 f 0 . .09 DS f 6 Planck 1 ,14months 0 . ) ) 0.12 WMAP 1 , 7 years 08 0.12 WMAP 1 , 7 years z z 6 0 . ( ⌧ ( e e e =0 0 . ⌧ Planck 1 , 14 months ⌧ Planck 1 , 14 months .10 4 0.10 0 . fDS =0 0.10 fDS =0 fDS =0.1 fDS =0.1 4 WMAP 1 ,7years 06 0 . 0 . 2 fDS =0.3 fDS =0.3 Dark star fraction 0.08 0 . 0.08 fDS =0.6 Integrated optical depth fDS =0.6 fDS =0.8 2 fDS =0.8 Dark star fraction 0.06 0.06 0 . 0 fDS =0100.9 200 300 400 500 fDS =0.9 fDS =1 fDS =1 Dark starsDSP lifetime andtDSP (Myr) the CMB 0.04 0.04 FIG. 5.— Contours of equal integratedEC CMB optical depth to z = 1090 in the 0 100 200EC 300 400 500 EC scenario, as a function of fDS and tDSP. Here we performed the interpola- tionA0. 02 ondark the optical star depths inphase Table 1 using(Extreme can two-dimensional Capture) affect exponential the ten-cosmic0.02 microwaveDSP lifetime background(ExtremetDSP Capture)(Myr) sion splines (Renka 1996b), based on a Delauney triangulation (Renka 1996a) tDSP = 150 Myr tDSP = 500 Myr andThomson-Scattering Optical Depth an iterative determination of the appropriate tension factors. Longer life- Thomson-Scattering Optical Depth Scott, Venkatesan, Roebber,FIG. 7.— Gondolo, Implied 1 Pierpaoli,detection/exclusion Holder regions in2011 the fDS–tDSP plane times and larger dark star fractions generically lead to smaller integrated op- for EC dark stars, based on the integrated optical depth to last scattering ob- tical depths;0 the slight5 upturn at large10 tDSP in the15⌧e =0.08 and20 0.09 contours served0 by WMAP75 (Komatsu10 et al. 2011).15 We also show20 projected Planck is an artifact of the interpolation. constraints (Colombo et al. 2009), assuming that the same central value Redshift z Redshift z With capture With(⌧e =0extended.088) is measured capture by Planck as by WMAP7. To guide the eye, the depth of shading is proportional to the likelihood of each parameter com- bination. For a product f? fesc =0.005 of the star-formation efficiency and UV photon escape fraction, parameter combinations outside the red WMAP ) ) 0.12 WMAP 1 , 7 years ) 0.12 WMAP 1 , 7 years z z 0.110 z shaded region are excluded at greater than 1 by existing data. Combinations ( ( ( e e e outside the shaded blue region will be excludable at better than 1 by Planck. ⌧ ⌧ Planck 1 , 14 months ⌧ Planck 1 , 14 months Note however that variations in f? fesc will shift these regions substantially; 0.10 PopII+III only MC 0.refer10 to discussionsPopII+III only in the final paragraph of Sec. 6.1 and in Sec. 6.3. The tDSP =5Myr (Meager Capture) same interpolationtDSP =5Myr methods were employed in this figure as in Fig. 5; the 0.105 slight upturn of the boundaries of the Planck region at large tDSP is again an tDSP = 15 Myr tDSNMS =6Myr tDSP = 15 Myr 0.08 0.artifact08 of the interpolation. tDSP = 50 Myr tDSP = 50 Myr WMAP 1 , 7 years tDSP = 150 Myr visible thantDSP = in 150 the Myr EE spectra. We also do not show power Planck 1 , 14 months 0.06 0.spectra06 for the MC or NC cases, as they show little deviation 0.100 tDSP = 500 Myr tDSP = 500 Myr fDS =1 in general from the standard Pop III+II case. fDS =0.8 0.04 0.04 fDS =0.6 6.3. Astrophysical uncertainties and implications for EC parameters ofEC reionization models 0.095 fDS =0.3 (Extreme Capture) (Extreme Capture) 0.02 fDS =0.1 0.02 In Fig. 9 we show the impacts of varying astrophysical pa- fDS =0.f6DS =0 rameters upon CMB observables.fDS =1 Here we give the variations Thomson-Scattering Optical Depth Thomson-Scattering Optical Depth Thomson-Scattering Optical Depth in optical depth and EE polarization resulting from the same 0 10 5 12 1014 16 15 18 20 20 variations0 of 5 f? fesc as in10 Fig. 3.15 For EE spectra,20 we nor- malize to the corresponding curve with default astrophysical RedshiftRedshiftz z Redshift z parameters in each case; i.e. to the standard f? fesc =0.005 FIG. 4.—FIG. Evolution 6.— Evolution of the of lookback the lookback optical optical depth from depth the from present the present day to redshift day to z accordingPop III+II to Eq. spectrum6, for EC dark for stars the offDS varying= 0curves, lifetimes and abundances. to the fDS = 1, Theseredshift curves,z andaccording the corresponding to Eq. 6, for dark MC stellar dark stars populations, with the correspond maximum allowedto the reionizationtDSP histories= 150 Myr,presentedf? f inesc Fig.=01..005 Larger spectrum dark star for fractions the curves and more where extended lifetimes reionize later, producingWithout smaller optical depths.capture, For comparison, no effect we show on the WMAP7the CMB. measured 1 band (Komatsu et al. 2011) for the DSNMS lifetime (tDSNMS = 6 Myr). These curves, and the corresponding fDS = 1, tDSP = 150 Myr. Comparing with Figs. 4 and 8, we see opticaldark depth stellar to the populations, surface of correspond last scattering, to the and reionization the corresponding histories errorpresented band in expected from Planck (Colombo et al. 2009), assuming it measures the same centralthe value. right Whilst panel of these Fig. strictly2. In the correspond MC scenario, to a redshift earlierz reionization1090, the caused optical by depth curvesagain have that largely variations begun to plateau in the by astrophysicalz 20 anyway. parameters within ⇠ ⇠ increasing values of fDS results in a slight increase in optical depth. We also reasonable ranges can have similar effects (both in strength steadshow of the WMAP7 simple and hydrogen Planck 1 detection/prediction reionization model bands, included as per Fig. in4. Note slightand difference character) in the to treatment variations of in He theIII darkhere star and parameters. in Sec. 6.1 Al- CAMB,the zoomed-in our modified axes relative version to Fig. uses4. the H ionization fractions has athough negligible this impact means thatupon the integrated impact of optical dark stars depths. on the CMB is presented in Sec. 5 as the basis for its reionization calcula- Invery Fig. difficult8 we plot to EE unambiguously polarization disentanglespectra for the from same existing EC the- tions.optical We include depth, contributions the EE spectrum to the would total nonetheless electron fraction provide a casesoretical as illustrated uncertainties in Figs. in1 reionizationand 4. The spectra modeling, are itnormal- also serves fromcomplementary H II, He II and (albeit He III weak)with the statistical assumptions handle stated via which ear- to izedas to a the clear corresponding indication that EE the spectrum potential obtained effect of in dark the starsstan- upon lier,increase as well as the a power residual of electron full parameter fraction. scans As in to the exclude stan- such dard CMBfDS = observables 0, Pop III+II affected scenario, by in reionization order to investigate could be quite the sig- darddark CAMB star reionizationmodels. calculation, we assume that elec- abilitynificant. of CMB experiments to distinguish dark stars from trons fromWe do He notII track show those TT or from TE spectra H II, and for model the EC contribu- scenario, as standardIn reionization. some cases, itTo is this possible end, we that also specific plot the regions uncer- of the tionsthey from exhibit He III lesswith striking a smoothed deviations step function from the centered corresponding at taintyreionization on the normalization parameter due space to that cosmic are variance, ruled out and in standard the z 3spectra.5. We of take the standardthe residual Pop electron III+II scenario fraction at after low multipolesrecom- l combinationPop III+II-only of cosmic scenarios variance by and the total current readout WMAP7 noise ex- (or pro- bination⇠ to be x =2.1 10-4, based on the output of REC- pected across the 70, 100 and 143 GHz channels in the first (large angulare scales)⇥ than the EE curves do. We do point out jected Planck) data, are reopened by the possibility of having FASThowever within that CAMB. the TT Using and CAMB’sTE spectra highest exhibit accuracy damping set- at large 14 monthsdark stars. of Planck For example, operation Fig. (Colombo9 reveals et that al. 2009 the extreme). Large cases ting, we calculated the temperature (TT), polarization (EE) parts of the parameter space are distinguishable from f =0-4 l due to the changing optical depth, which is more clearly of varying astrophysical parameters ( f? fesc =0.02 orDS 10 ) are and cross (TE) power spectra, as well as integrated optical in a cosmic-variance-limited experiment, and a number of the depths. We checked that the optical depths computed with more extreme scenarios are even detectable by Planck at bet- CAMB agree to within their stated numerical accuracy with ter than 1 . Although essentially all such models may be dis- those from Eq. 6 (as presented in Table 1), and verified that the favored anyway by Planck’s measurement of the integrated Dark stars and the CMB A dark star phase can affect the cosmic microwave background Scott, Venkatesan, Roebber, Gondolo, Pierpaoli, Holder 2011 Dark stars, reionizationWith and the CMBextended capture 11 0 0 1 . 1 . ⌧e =0.07 e 10 WMAP7 excludes⌧ the region ⌧ e 8 =0 .08 0 . 0 . ⌧ 8 DS e =0 f outside the red band 0 . .09 DS f 6 Planck 1 ,14months 0 . 08 6 ⌧ 0 . e =0 0 . .10 4 Planck0 . will probe the blue band 4 WMAP 1 ,7years 06 0 . 0 . 2 Dark star fraction 0 . Integrated optical depth 2 Dark star fraction 0 . 0 100Star 200formation300 efficiency400 500 and UV DSPphoton lifetime escapetDSP (Myr) rate shift these FIG. 5.— Contours ofregions equal integrated substantially. CMB optical depth to z = 1090 in the 0 100 200 300 400 500 EC 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- DSP lifetime tDSP (Myr) sion splines (Renka 1996b), based on a Delauney triangulation (Renka 1996a) and an iterative determination of the appropriate tension factors. Longer life- FIG. 7.— Implied 1 detection/exclusion regions in the fDS–tDSP plane times and larger dark star fractions generically lead to smaller integrated op- for EC dark stars, based on the integrated optical depth to last scattering ob- tical depths; the slight upturn at large tDSP in the ⌧e =0.08 and 0.09 contours served by WMAP7 (Komatsu et al. 2011). We also show projected Planck is an artifact of the interpolation. constraints (Colombo et al. 2009), assuming that the same central value (⌧e =0.088) is measured by Planck as by WMAP7. To guide the eye, the depth of shading is proportional to the likelihood of each parameter com- bination. For a product f? fesc =0.005 of the star-formation efficiency and UV photon escape fraction, parameter combinations outside the red WMAP ) z 0.110 shaded region are excluded at greater than 1 by existing data. Combinations ( e outside 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; MC refer to discussions in the final paragraph of Sec. 6.1 and in Sec. 6.3. The (Meager Capture) same interpolation methods were employed in this figure as in Fig. 5; the 0.105 slight upturn of the boundaries of the Planck region at large tDSP is again an tDSNMS =6Myr artifact of the interpolation. WMAP 1 , 7 years visible than in the EE spectra. We also do not show power Planck 1 , 14 months 0.100 spectra for the MC or NC cases, as they show little deviation fDS =1 in general from the standard Pop III+II case. fDS =0.8 fDS =0.6 6.3. Astrophysical uncertainties and implications for parameters of reionization models 0.095 fDS =0.3 fDS =0.1 In Fig. 9 we show the impacts of varying astrophysical pa- fDS =0 rameters upon CMB observables. Here we give the variations Thomson-Scattering Optical Depth in optical depth and EE polarization resulting from the same 10 12 14 16 18 20 variations of f? fesc as in Fig. 3. For EE spectra, we nor- malize to the corresponding curve with default astrophysical Redshift z parameters in each case; i.e. to the standard f? fesc =0.005 FIG. 6.— Evolution of the lookback optical depth from the present day to Pop III+II spectrum for the fDS = 0 curves, and to the fDS = 1, redshift z according to Eq. 6, for MC dark stars with the maximum allowed tDSP = 150 Myr, f? fesc =0.005 spectrum for the curves where DSNMS lifetime (tDSNMS = 6 Myr). These curves, and the corresponding fDS = 1, tDSP = 150 Myr. Comparing with Figs. 4 and 8, we see dark stellar populations, correspond to the reionization histories presented in the right panel of Fig. 2. In the MC scenario, earlier reionization caused by again that variations in the astrophysical parameters within increasing values of fDS results in a slight increase in optical depth. We also reasonable ranges can have similar effects (both in strength show WMAP7 and Planck 1 detection/prediction bands, as per Fig. 4. Note and character) to variations in the dark star parameters. Al- the zoomed-in axes relative to Fig. 4. though this means that the impact of dark stars on the CMB is very difficult to unambiguously disentangle from existing the- optical depth, the EE spectrum would nonetheless provide a oretical uncertainties in reionization modeling, it also serves complementary (albeit weak) statistical handle via which to as a clear indication that the potential effect of dark stars upon increase the power of full parameter scans to exclude such CMB observables affected by reionization could be quite sig- dark star models. nificant. We do not show TT or TE spectra for the EC scenario, as In some cases, it is possible that specific regions of the they exhibit less striking deviations from the corresponding reionization parameter space that are ruled out in standard spectra of the standard Pop III+II scenario at low multipoles l Pop III+II-only scenarios by the current WMAP7 (or pro- (large angular scales) than the EE curves do. We do point out jected Planck) data, are reopened by the possibility of having however that the TT and TE spectra exhibit damping at large dark stars. For example, Fig. 9 reveals that the extreme cases -4 l due to the changing optical depth, which is more clearly of varying astrophysical parameters ( f? fesc =0.02 or 10 ) are Finding dark stars with JWST Dark stars at redshift z~6-15 are too dim to be detected, but.... Idea: Dark stars may become supermassive Freese et al 2010 Figure 3: Black body spectra of two dark stars formedFigure via 4: extende Similard adiabatic to Fig. 3 for dark stars formed “with capture”. Left panel: 5 5 6 contraction (“without capture”) for mχ=100 GeV.1.7 Left10 panel:M! 1.SMDS7 10 formedM! in 10 M! halo (mχ = 50Gev). Right panel: 6 7 × 7 8 × 8 SMDS in a 10 M! halo. Right panel: 1.5 10 M1.7! SMDS10 M in! 10SMDSM! formedhalo. in 10 M! halo (mχ =100Gev). The black body flux is shown at z = 15 (formation× × redshift) and at z =10 and 5 (see line legends) assuming that the dark star survives till the lower redshifts. Blue dashes show sensitivity limit and bandwidth of NIRCam 2µ (R=4) while the green dashes show the sensitivity limit and band width ofthe NIRCam 3.5µ (R=4) band. The upper and lower dashes show the sensitivity limits after exposure times of 104s, 106s respectively. The sensitivity of MIRI (10µ, R=5) is shown for exposure time of 106s (orange dash). All sensitivities are computed assuming a S/N=10. The red vertical lines show the location of the 1216A˚ line redshifted from the rest-frame wavelength of the star at each of the three redshifts. The observed flux to the left of the vertical lines will decrease relative to the black curves depending on the model assumed for IGM absorption up to the redshift of reionization. 32 31 Finding dark stars with JWST Dark stars at redshift z~6-15 are too dim to be detected, but.... Idea: Use a magnifying lens Zackrisson et al 2010 Finding dark stars with JWST Dark stars at redshift z~6-15 are too dim to be detected, but.... Idea: Use a magnifying lens Zackrisson et al 2010 Detectable with JWST via gravitational lens magnification ~100 6 Finding dark starsZackrisson with the JWST et al. 9 z = 6 6 z = 10 (purple lines). The three20 rows of panels in Fig. 4 corre- 20 spond to the cosmic populationa) III star formation histo- b) ries with standard LW (top row), reduced LW (middle 4 25 25 row) and no LW feedback (bottom row). The different Star clusters Dark stars markers within each panel indicate the AB-magnitudes 2 Galaxies and numbers of dark stars30 atJWST redshifts detectionz limits=10(triangle), 30 JWST detection limits z =15(star)andz =20(square). 277 AGNs − m AB In general, long dark35 starx100 lifetimes τ imply larger num- 0 AB 35 m m 200 bers of dark stars at detectable brightnesses. In the m case of the 690 M!, T40eff =7500Kdarkstar(rightcol- −2 40MW stars umn), considerable numbers (≥ 10) of dark stars are ex- Brown dwarfs pected to be sufficiently bright for detection (at 5σ after 45 −4 45 3.6 × 105 s) in the high-magnification regionsDark star of MACSspectra J0717.5+3745 at z ≈ 10–11, provided that their lifetimes 8 50 −6 50 are ≈ 5 × 10 yrs. This holds regardless0 0.5 of which of1 the 1.5 −2 −1 0 0 10.5 2 1 3 4 1.5 log ! (micron) m log−m ! (micron) three feedback scenarios is adopted. For the10 reduced LW 356 10444 and no LW feedbackFig. 2.— The models, predicted significant apparent AB dark magnitudes stars are of dark starsFig. at 5.—z =6(a)andz =10(b), asm a356 function− m444 of centralm200 wavelength− m277 of the 7 The JWST/NIRCam vs. expected evenJWST if broadband the lifetime filters. is closerEach solid to lineτ =10 correspondsyrs. to a sepacoloursrate dark of Te starff < model10000 from K dark Table stars 1. These at z lines=10(redstarsym- have been colour-coded according to the effective temperatures6 of the dark stars: Teff ≤ 8000 K (red), 8000 K Dark Stars are stars made of ordinary matter that shine thanks to the annihilation of dark matter. The first stars to form in the universe may have been powered by dark matter annihilation instead of nuclear fusion. • Explain chemical elements in old halo stars • Explain origin of supermassive black holes in early quasars Artist’s impression