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Evolution of Primordial Stars Powered by Dark Matter Annihilation up to the Main-Sequence Stage

May 2011
The Astrophysical Journal 736(1)

DOI:10.1088/0004-637X/736/1/58

Authors:

Shingo Hirano

Kanagawa University

Hideyuki Umeda

The University of Tokyo

Naoki Yoshida

The University of Tokyo

Primordial stars formed in the early universe are thought to be hosted by compact dark matter (DM) halos. If DM consists of weakly interacting massive particles (WIMPs), such stars may be powered by DM annihilation during the early phases of their evolution. We study the pre-main-sequence evolution of the primordial star using a detailed stellar evolution code under the assumption that the annihilation of adiabatically contracted WIMP DM within the star provides sufficient energy to sustain the stellar equilibrium. We follow the evolution of accreting stars using several gas mass accretion rates derived from cosmological simulations. We show that the stellar mass becomes very large, up to 900-1000 M ☉ when the star reaches the main-sequence phase for a reasonable set of model parameters such as DM particle mass and the annihilation cross section. During the dark star phase, the star expands by over a thousand solar radii, while the surface temperature remains below 104 K. The energy generated by nuclear reactions is not dominant during this phase. We also study models with different gas mass accretion rates and the DM particle masses. All our models for different DM particle masses pass the dark star phase. The final mass of the dark stars is essentially unchanged for DM mass of m χ ≤ 10 GeV. Gravitational collapse of the massive dark stars will leave massive black holes with mass as large as 1000 M ☉ in the early universe.

Gas mass accretion rates adopted in our stellar evolution calculations. "G-rate" is the accretion rate of Eq. 3. We adopt three rates 1.0, 0.5 and 0.2× G-rate. The other two lines are the rates adopted in Spolyar et al. (2009), for comparison.

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arXiv:1105.1255v1 [astro-ph.CO] 6 May 2011

Evolution of Primordial Stars Powered by Dark Matter

Annihilation up to the Main-Sequence Stage

Shingo Hirano

Department of Astronomy, School of Science, University of Tokyo, Hongo Tokyo 113-0033, Japan

hirano@astron.s.u-tokyo.ac.jp

Hideyuki Umeda

Department of Astronomy, School of Science, University of Tokyo, Hongo Tokyo 113-0033, Japan

umeda@astron.s.u-tokyo.ac.jp

and

Naoki Yoshida

IPMU, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan

naoki.yoshida@ipmu.jp

ABSTRACT

Primordial stars formed in the early universe are thought to be hosted by compact dark matter

(DM) halos. If DM consists of Weakly Interacting Massive Particles (WIMPs), such stars may

be powered by DM annihilation during the early phases of their evolutions. We study the pre-

main sequence evolutions of the primordial star using a detailed stellar evolution code under the

assumption that the annihilation of adiabatically contracted WIMPs DM within the star provides

a suﬃcient energy to sustain the stellar equilibrium. We follow the evolution of accreting stars

using several gas mass accretion rates derived from cosmological simulations. We show that the

stellar mass becomes very large, up to 900 −1000 M⊙when the star reaches the main-sequence

phase for a reasonable set of model parameters such as DM particle mass and the annihilation

cross section. During the dark star phase, the star expands over a thousand solar-radii, while

the surface temperature remains below 104K. The energy generated by nuclear reactions is not

dominant during this phase. We also study models with diﬀerent gas mass accretion rates and

the DM particle masses. All our models for diﬀerent DM particle masses pass the dark star

phase. The ﬁnal mass of the dark stars is essentially unchanged for DM mass of mχ≤10 GeV.

Gravitational collapse of the massive dark stars will leave massive black holes with mass as large

as 1000 M⊙in the early universe.

Subject headings: cosmology: ﬁrst stars — cosmology: dark matter — stars: evolution

1. Introduction

The ﬁrst stars in the universe may have con-

tributed early cosmic reionization and may have

also enriched the inter-galactic medium with

heavy elements such as carbon, oxygen and iron

(see, e.g. Bromm et al. (2009) for a review). Fu-

ture observations of the distant universe will ex-

ploit large ground-based and space-borne tele-

scopes such as James Webb Space Telescope and

Thirty Meter Telescope to answer the important

questions of how and when the ﬁrst stars were

formed and how they aﬀected the subsequent evo-

lution of the universe.

Recent theoretical studies based on cosmolog-

ical simulations suggest that the ﬁrst stars are

formed in dark matter (DM) halos with mass

105−106M⊙at z∼20 −30 (Tegmark et al.

1997; Yoshida et al. 2003). In such a cosmological

“minihalo”, the gas cools and condenses by molec-

ular hydrogen cooling to form a star-forming gas

cloud. The gravitationally unstable cloud further

contracts, and ﬁnally a proto-star is born inside

it (Omukai & Nishi 1998; Yoshida et al. 2008). A

unique characteristic of primordial star formation

in the standard cold dark matter model is that the

star and its parent gas cloud are embedded at the

center of the host dark halo. Thus the formation

and evolution of primordial stars may be much af-

fected by DM dynamically.

The nature of DM remains still unknown, but

the best candidates are thought to be Weakly

Interacting Massive Particles, WIMPs. WIMP

DM such as neutralinos must have a large self-

annihilation cross-section in order to be a dom-

inant component of DM in the present-day uni-

verse. DM annihilation produces an enormous

amount of energy, essentially equal to the rest

mass energy of the annihilated DM particles. If

DM density can be very large in a primordial gas

cloud and in a primordial star, the annihilation

energy would act as an eﬃcient heat input. DM

annihilation could even supply suﬃcient energy to

support self-gravitation of a star. This is indeed

a recently proposed new stellar phase, in which

stars are powered by DM annihilation energy in-

stead of that of the nuclear fusion (Spolyar et al.

2008). Hereafter we call such a star “dark star”.

Spolyar et al. (2008) suggest that, in a collaps-

ing primordial gas cloud, DM annihilation heating

can win over the radiative cooling, eﬀectively halts

further collapse of the cloud. Natarajan et al.

(2009) study the evolution of the DM density pro-

ﬁle during the ﬁrst star formation using cosmolog-

ical simulations. They show that the DM density

proﬁle indeed becomes very steep, as much as ex-

pected by adiabatic contraction models.

There have been many previous studies on dark

stars. While most of them assume constant stel-

lar mass models (Iocco et al. 2008; Taoso et al.

2008; Yoon et al. 2008). Spolyar et al. (2009)

and Umeda et al. (2009) study dark star evolu-

tion with gas mass accretion. By using an ap-

proximated stellar structure model, Spolyar et al.

(2009) follow dark star evolutions with adiabati-

cally contracted DM (ACDM). They show that the

ﬁnal stellar mass becomes as large as 1000 M⊙.

Umeda et al. (2009) perform detailed, dynami-

cally self-consistent stellar evolution calculations

up to gravitational core-collapse. They show that

the ﬁnal mass can be as large as 104−5M⊙or

more, if the star captures DM eﬃciently. However,

the DM capture rate itself is uncertain because it

depends on the unknown DM-baryon scattering

cross section and also on the ambient DM density

during the dark star evolution. Thus the proposed

formation of inter-mediate massive black holes ap-

pears to occur only in very particular cases.

An attractive feature of the dark star models is

that the possibility for the birth of massive stars,

and black holes (BHs) as the end of such stars, in

the early universe. Super-massive BHs (SMBHs)

existed already at z∼6, when the age of the uni-

verse is less than one billion years old, but the for-

mation mechanism of such early SMBHs remains

unknown. Gravitational collapse of a very massive

dark star might provide a solution to this prob-

lem. We explore a possibility that the ﬁrst stars

formed in DM halos can become very massive by

being powered by DM annihilation. To this end,

it is important to determine the ﬁnal state of the

dark star phase exactly, and to determine the ﬁnal

stellar mass.

In this paper, we study the evolution of an ac-

creting dark star using a detailed stellar evolu-

tion code as in Umeda et al. (2009) but with the

ACDM annihilation. We calculate the density pro-

ﬁle of ACDM using an analytical method and de-

termine the DM annihilation rate. We then follow

the evolution of the dark star which grows in mass

by gas accretion. The dark star model has two pa-

rameters eﬀectively; the gas mass accretion rate

and DM particle mass. We calculate several mod-

els with diﬀerent set of parameters and investigate

the eﬀects on the ﬁnal stellar mass. Especially, we

clarify the eﬀect of the diﬀerent mass accretion

rates, which were not explicitly shown in a similar

work by Spolyar et al. (2009).

The rest of the paper is organized as follows. In

section 2, we introduce our numerical calculation

and explain how we implement DM annihilation

in the stellar evolution. Sec. 3 shows the results

of our dark star models and we discuss the impli-

cations in Sec. 4. We give our concluding remarks

in Sec. 5.

2. Method

We use a stellar evolution code with gas

mass accretion developed by Ohkubo et al. (2006,

2009); Umeda et al. (2009). We implement en-

ergy generation by DM annihilation rate in the

code in the following manner. We consider a

primordial (proto-)star embedded at the cen-

ter of a small mass DM halos. The DM den-

sity proﬁle, ρχ, is calculated using the analyt-

ical method of Blumenthal et al. (1986); when

the primordial gas cools and collapses, DM par-

ticles are also “dragged” into the gravitational

potential well. The adiabatic contraction model

uses an adiabatic invariant. For spherically dis-

tributed DM and baryons with a total mass of

M(R) = Mgas(R) + MDM (R), an adiabatic invari-

ant is

M(R)R=const. (1)

Freese et al. (2009) compared the diﬀerence of DM

density proﬁle calculated using this method and a

more accurate method developed by Young (1980).

They conclude that the diﬀerence is not more than

a factor of two.

We have performed direct numerical simula-

tions of early structure formation to check the

accuracy of this analytical method. To this end

we have used the parallel N-body/Smoothed Par-

ticle Hydrodynamics (SPH) solver GADGET-2

(Springel 2005) in its version suitably adopted

to follow radiative cooling processes at very high

densities (Yoshida et al. 2006). We have found

that the DM density calculated by Blumenthal’s

method is indeed in good agreement with the re-

sult of our direct numerical simulations. Figure 1

compares the results from the analytic model and

the simulations. Details will be presented else-

where (Hirano et al., in preparation). We note

that, although these two results agree very well,

conﬁrming the validity of the analytic model, the

simulations do not resolve the DM density down

to length scales of astronomical units. Because the

gas density proﬁle itself evolves in a self-similar

manner (Omukai & Nishi 1998), we assume that

the DM continue to contract adiabatically and the

evolution of DM density can be calculated by Blu-

menthal’s method.

In this work, we only consider the DM den-

sity evolution based on adiabatic contraction. In

principle, DM annihilation can occur even more

eﬃciently in the star by capture. If the den-

sity of the stellar core increases enough to scat-

ter and trap DM particles, the DM particles can

rapidly sink toward the center, to self-annihilate

eﬃciently. During the dark star phase, however,

the eﬀect of DM capture is unimportant because

the star has expanded extremely and the gas den-

sity is low.

Suppose a “cloud” of DM particles contract

from a radial position Rpre to Rnew , and the to-

tal mass distribution changes from Mpre(R) to

Mnew(R). Then the following relation holds dur-

ing adiabatic contraction:

Mnew(Rnew )Rnew =Mpre (Rpre)Rpre .(2)

The “new” DM density proﬁle can be simply cal-

culated from the above equation. Note that, in our

case, the gas distribution also changes because of

the gas accretion onto the central primordial pro-

tostar. We model the gas mass accretion rate in

a simple parameterized form as a function of the

stellar mass. We use the accretion rate calculated

by cosmological simulations of Gao et al. (2007).

They found a large variation of accretion rates.

In particular, the accretion rates for rotationally

supported disks are typically smaller than for the

other cases. As our ﬁducial model, we choose the

accretion rate of their R5 run, which is well de-

scribed as a power-law

dT= 0.18 ×M−0.6M⊙yrs−1.(3)

Hereafter we call this rate “G-rate” (see Figure 2).

The rate is for a cosmological halo forming from

a very high-σpeak, and is slightly larger than

that adopted in a previous work (Spolyar et al.

2009). We also run models with three diﬀerent

accretion rates 1.0,0.5,0.2×G-rate. The inter-

mediate value, 0.5×G-rate, is close to that used in

Spolyar et al. (2009). We use this model to com-

pare with their result.

The energy generation rate of DM annihilation

is given by

QDM =hσviρ2

mχ

GeV cm−3s−1(4)

where hσviis the DM self-annihilation rate in

units of cm3s−1, and mχis the DM parti-

cle mass in units of GeV = 109electron volt

(e.g. Bertone et al. (2005)). Notice that eﬀec-

tively only the ratio, hσvi/mχ, determines the

net energy generation rate. We vary the DM

particle mass as a model parameter as mχ=

1,10,20,50,100 and 200 GeV, while ﬁxing

hσviconstant. Spolyar et al. (2008) calculate the

critical transition gas density above which most

of the DM annihilation energy is absorbed inside

the core. The critical density is smaller than the

stellar density with the WIMP mass 1 GeV to 10

TeV, and thus we assume that the released en-

ergy from DM annihilation quickly thermalize the

star. Through the self-annihilation process, DM

changes into multiple species including neutrinos,

which escape away from the star and the cloud.

We assume that about one third of DM annihila-

tion energy is carried away from the star, and thus

the eﬀective energy generation rate is (2/3)QDM

(see, e.g. Spolyar et al. (2008)).

All our calculations start from a protostar with

M∼10 M⊙. As the initial condition, we calcu-

late an equilibrium stellar structure for this mass,

including DM annihilation energy. In order to

apply the Blumenthal’s method for the adiabatic

contraction calculation, we need the gas density

proﬁle outside the star. We use the result in the

cosmological simulation of Gao et al. (2007) which

shows the gas density ρscales with distance ras

ρgas ∝r−2.3. Within an integration time step, the

accreted gas is added to the stellar mass and DM

annihilation energy is re-calculated. Because the

DM density increases extremely within the central

star due to adiabatic contraction, the DM annihi-

lation rate at the outside of the star is relatively

small than inside. Thus we consider the eﬀect of

DM annihilation inside the star only. We stop

the calculation when the star contracts to be suf-

ﬁciently compact and the stellar surface tempera-

ture reaches 105K. The dark star phase ends well

before entering this regime. Afterwards the star

is expected to settle quickly on the main-sequence

phase, mainly powered by nuclear reactions. In

this study, we do not include nuclear reactions for

our dark star models, because the nuclear reac-

tions are ineﬀective owing to the low temperature

inside the star during the dark star phase.

In the next section, we ﬁrst show the results

from the run with a ﬁducial set of parameter val-

ues. We call this model “base model”. The pa-

rameters of our base model are a power-law gas

mass accretion rate 1.0×G-rate, mχ= 100 GeV

and hσvi= 3 ×10−26 cm3s−1. We will also show

the results of models which adopt diﬀerent values

for these two parameters.

3. Results

3.1. Base model

Figure 3 shows the evolution of the dark star in

the Hertzsprung-Russell (HR) diagram. The ac-

creting star grows constantly in mass. In the HR

diagram, the star moves upward and then turns

to the left (higher temperature). The solid line is

for our dark star model, whereas the dashed line is

for a standard Population III model (without DM

annihilation energy; no-DM model, Umeda et al.

(2009)). Symbols indicate the times when the stel-

lar mass is M= 100,200,600,800 and 1000 M⊙.

Clearly the dark star model moves on a very diﬀer-

ent path from that of the no-DM model, showing

a signiﬁcant eﬀect of the DM annihilation energy.

In the no-DM model, the star contracts gravita-

tionally and becomes hot quickly until the ﬁrst

symbol (100 M⊙). The dark star, on the other

hand, has essentially the same eﬀective tempera-

ture because DM annihilation energy prevents the

star from gravitational contraction. When the no-

DM star reaches ∼100 M⊙, it expands, and turns

to the lower temperature side in the HR diagram.

There, the hydrogen burning becomes eﬀective to

supply energy to stop the contraction and the star

expands slightly. Subsequently the star lands on

the main-sequence phase.

Contrastingly, the dark star remains “cool”

while it is powered by DM annihilation. This is

because the DM annihilation energy (Eq. 4) is in-

dependent of the stellar temperature. Even if the

stellar interior remains at low temperatures, DM

annihilation can produce enough energy to sustain

the stellar structure. As long as this condition is

met, the star cannot contract while still grows in

mass by accretion. Interestingly, by the time when

the dark star reaches main-sequence, the stellar

mass is already ∼1000 M⊙, which is much larger

than the no-DM case (100 −200 M⊙).

Figure 4 shows the evolution of the DM mass

inside the star and its time derivative. The left

panel shows the total DM mass inside the star,

whereas the right panel shows the ratio of the rate

of DM annihilation in mass to the rate of DM mass

increase (within the star) owing to adiabatic con-

traction:

dMDM

dt 



annihilationdMDM

dt 



contraction

.(5)

In Figure 4, we show the results for an additional

model in which the depletion of DM in the star is

not taken into account. Although this case might

appear unrealistic, it is useful to see when DM

depletion becomes substantial. The solid line rep-

resents our “base model” while the dashed line

shows the result of the no-depletion case. Up to

M∼200 −300 M⊙, there is almost no diﬀer-

ence between the two cases. At M > 300M⊙,

however, DM depletion becomes signiﬁcant and

then the total DM mass actually starts decreas-

ing. The evolution thereafter is interesting. The

DM “fuel” inside the star runs short to sustain

the star. The star stops expanding, the gas den-

sity increases more eﬃciently, and then DM den-

sity also increases again. Then DM annihilation

consumes rapidly the DM fuel inside the star. Fi-

nally, the DM annihilation energy cannot sustain

the star, marking the end of the dark star phase.

The star collapses and will eventually reach the

main-sequence phase.

Figure 5 shows the radial proﬁles for various

quantities of gas (left) and DM (right) when the

stellar mass is M= 200 (solid lines), 800 (dashed

lines) and 1000 M⊙(dotted lines) respectively.

The horizontal axis is the radial distance from the

stellar center divided by the stellar radius.

The top panels show the evolution of gas den-

sity and DM density. Between M= 200 to

800 M⊙, the star has an extended structure and

the central density does not increase much. The

DM density increases by adiabatic contraction but

actually decreases slightly at the inner most part

owing to annihilation. At the ﬁnal contraction

phase (M= 800 to 1000 M⊙), both the gas den-

sity and the DM density increase substantially.

The middle panels show the evolution of en-

closed mass of gas and DM. Although the gas mass

proﬁle stays roughly unchanged, the DM mass de-

creases dramatically during the ﬁnal phase from

M= 800 to 1000 M⊙. Note that the horizontal

axis in the plots shows a normalized radius R/R∗.

The stellar radius R∗itself changes signiﬁcantly

over the plotted range of evolutionary stages. Be-

cause the dark star phase ends with the runaway

burning of DM inside of the star, the total amount

of DM when M= 1000 M⊙is already very small.

The bottom-left panel shows the DM annihi-

lation rate and the bottom-right panel shows the

total luminosity generated by the DM annihilation

within the radius. These panels show the energy

generating eﬃciency from the DM annihilation.

Again, we see that the annihilation rate is low in-

side the star at the ﬁnal stage M= 1000 M⊙and

the enclosed DM luminosity at the stellar surface

(at log10Radius/R∗= 0) is smaller than in the ear-

lier phases. The stellar mass increases by gas ac-

cretion but the DM energy supply decreases; this

causes the star to contract.

Figure 6 shows the evolution of some basic stel-

lar quantities which characterize the dark star. We

compare the results of our base model (solid lines)

with those of no-DM model (dashed lines) and of

no-depletion model (dotted lines). Until the star

grows to M∼200 −300 M⊙, the base model and

the no-depletion model appear very similar, show-

ing again that DM depletion is negligible in early

phases. After the star grows to ∼300M⊙, we see

small but appreciable diﬀerences between the base

model and the no-depletion model. As has been

shown in Figure 4, DM is consumed by annihila-

tion inside the star whereas the supply by adia-

batic contraction is slow owing to the small gas

mass accretion rate. As the star becomes more

massive, it needs more DM to produce necessary

energy to sustain gravitational equilibrium. When

the DM supply becomes insuﬃcient, this quasi-

stable dark star phase cannot be sustained. It oc-

curs at M∼600 M⊙for the base model. The

stellar properties, however, do not change imme-

diately until up to M∼900 M⊙. At around

M≥900 M⊙, the DM inside the star burns out

rapidly, the star begins to collapse, and the central

temperature increases rapidly. Finally the central

temperature reaches 107−108K, the nuclear burn-

ing will soon start, and the star will eventually

land on the main-sequence.

Table 1 summarizes the basic stellar proper-

ties at several characteristic phases. Note that the

elapsed time diﬀerence (the right column) is large

between 800 and 1000 M⊙. The dark star phase

continues for about ∼0.2 Myr. Throughout the

run, the DM mass is very small compared with the

stellar gas mass. Dark stars can be sustained by

the DM of only 0.1% of their total mass M∗.

3.2. The eﬀect of gas mass accretion rate

We now explore a few parameter spaces. Our

dark star model has essentially two parameters,

the gas mass accretion rate and the DM particle

mass. First, we examine the eﬀect of the gas mass

accretion rate. We adopt three accretion rates,

1.0,0.5,and 0.2×G-rate (Figure 2). “G-rate”

is the gas accretion rate in our base model (Eq.

3). In general, less DM is attracted toward the

star for smaller gas accretion rates. We consider

only smaller accretion rates than G-rate because

it seems reasonable to assume that various proto-

stellar feedback eﬀects, such as ionizing radiation

from the star, can only reduce the gas mass accre-

tion rate.

Figure 7 shows the stellar evolution for the

three models with diﬀerent accretion rates in the

HR diagram. Initially, the stars are puﬀy, cool and

evolve along virtually the same path. Tables 2 and

3 show the basic stellar properties when the mod-

els with the reduced accretion rates reach the end

of the stable phase where Teﬀ = 104K, and where

Teﬀ = 105K, respectively. The latter phase is the

end of our calculations. As is expected naively, the

ﬁnal stellar mass is smaller for lower gas accretion

rates, but the period of the dark star phase is actu-

ally longer. In the reduced accretion models, the

star needs a longer time to reach the same stel-

lar mass. Then the DM density inside the star is

smaller because the gas contraction is slow. Con-

sequently, the star with a smaller gas accretion

rate ends the dark star phase and begins to con-

tract when its mass is smaller than in the base

model.

Figures 8 and 9 show clearly the eﬀect of re-

ducing the accretion rate. There are essentially

no diﬀerences among the three models when the

stellar mass is small. The DM fuel inside the star

increases very similarly (Fig. 8a) because the rate

of DM decrease to DM increase is very small (Fig.

8b). For the smallest accretion rate, the dark star

ends when the stellar mass reaches ∼500 M⊙.

Overall, the lower the accretion rate is, the smaller

the DM mass is inside the star. The dark star

phase lasts longer but ends at lower masses.

3.3. The eﬀect of DM particle mass

Finally, we study models with diﬀerent DM par-

ticle masses. We adopt the base accretion rate of

1.0×G-rate which is larger than those adopted in

Spolyar et al. (2009) (see Figure 2). so our results

are slightly diﬀerent from theirs, especially for a

small DM particle mass case. We discuss this issue

later in this section.

We run six models with mχ= 1,10,20,50,100

and 200 GeV. Note that, from Eq. 4, the DM

annihilation energy is inversely proportional to

mχ. Thus the characteristic features of dark stars

appear strongly in runs with small DM masses.

Figures 10, 11 and 12 show the results for the

ﬁve models. For smaller DM particle masses, the

DM annihilation rate is large, and thus the star

expands more and the temperature and density in

the star are lower. The period of the dark star

phase is also prolonged for smaller mχ, and the

ﬁnal stellar mass gets larger than our base model.

Tables 4 and 5 list the basic properties of the

stars when the surface temperature Teﬀ reaches

104K and 105K, respectively. The ﬁnal stellar

mass M∗diﬀers by about a factor of two among

the ﬁve models; M∗= 776 to 1370 GeV in Ta-

ble 5. The overall trend is as describe above,

but the lightest particle model is worth describ-

ing more in detail. When the star enters main-

sequence, the stellar mass in mχ= 1 GeV model

is similar to that of 10 GeV model, although it

has 10 times larger DM energy generation rate.

The reason is that the DM burning rate is too

large in mχ= 1 GeV model. When the DM con-

sumption rate exceeds the DM supply by adia-

batic contraction (see discussion in Sec. 3.1), the

star runs out of the DM fuel and begins to con-

tract. The DM consumption becomes even more

eﬃcient then. This ﬁnal “runaway” phase takes

place faster in 1 GeV model than in 10 GeV model.

Consequently, the star lands on the main-sequence

early in 1 GeV model (see the last column of Table

5 which gives the elapsed time).

Interestingly, the mχ= 1 GeV model predicts

the most luminous star, reaching L∼some 107L⊙

at the peak (Fig. 12). The extremely high lumi-

nosity is, however, still smaller than the upper-

limit given by the Eddington Luminosity LEDD:

LEDD =4πcGM∗

κ(6)

where the opacity κdetermines essentially the crit-

ical luminosity. Figure 13 shows the ratio of the

energy generation rate of DM annihilation (“lu-

minosity”) to the Eddington luminosity for our

ﬁve models with diﬀerent DM particle masses.

The ratio stays always less than unity, even for

1 GeV model. During the dark star phase (Teﬀ <

10,000K), the opacity κat lower temperatures is

mainly contributed by H−ion which has a small

value.

4. Discussion

4.1. Dark Star Models

We compare our results with those of previous

works. Unlike previous studies (e.g., Spolyar et al.

(2009)), we solve full radiative transfer and follow

self-consistently the stellar structure and its evo-

lution. A direct comparison can be made with the

results of Table 2 in Spolyar et al. (2009) (here-

after “SP09”), by using the result of our 0.5×G-

rate model (see Sec. 3.2; hereafter “05G”). The

other model parameters are set to be the same,

mχ= 100 GeV and hσvi= 3 ×10−26 cm3s−1, ex-

cept for the gas mass accretion rate. The gas mass

accretion rates in these two models (Figure 2) are

almost the same at M∗>100 M⊙, which is the

main period of the dark star phase. The results

of 05G and SP09 are roughly similar; in stellar

radius, luminosity and other quantities, the diﬀer-

ences are less than 20% at M∗= 106 M⊙(the ﬁrst

line in SP09), and remain within a factor of two

at later stages. During calculation, 05G model

has a slightly expanded structure and is some-

what cooler than SP09 model. On the other hand,

the diﬀerence of the central temperature is rela-

tively large between the two models. The value

in 05G becomes lower than in SP09 especially at

the ﬁnal stages; at M∗= 716,756,779 M⊙,

Tcen = 2.4,9.3,132 (106)K in 05G whereas

Tcen = 15,78,280 (106)K in SP09. Because of

the lower central temperature, nuclear burning is

unimportant in our calculations.

4.2. Possible Range of WIMP DM mass

The WIMP mass signiﬁcantly aﬀect the dura-

tion of the dark star phase because the DM an-

nihilation energy is inversely proportional to the

WIMP mass mχ, as can be seen in Eq. 4. We

have already shown the eﬀect in Section 3.3 for

a typical DM mass range, from 1 to 200 GeV.

However, in supersymmetric particle physics mod-

els, the WIMP DM mass may be 10 TeV or even

greater. To estimate the evolutionary path of dark

star models with heavier WIMPs, we have run our

no-depletion model for two larger WIMP masses,

mχ= 1 and 10 TeV. Figure 14a and 14b show

the result. At the beginning of the calculation

with M≃15M⊙, all the models are in the dark

star phase and on the Hayashi-line in the H-R di-

agram. The left panel of Fig. 14 shows that, at

this phase, all models have Teﬀ ≃103.7K. For mχ

= 10 TeV, the Pop.III star leaves the dark star

phase early. Because annihilation rate is small for

a large WIMP mass, the stellar mass at the end of

the dark star phase remains small.

All the dark star models are on Teﬀ ≃103.7K

line at ﬁrst (see also Fig. 10) and leave the

line gradually as mass-accretion continues. To

quantify the evolution, we deﬁne two charac-

teristic stellar masses, M3.8and M4.0, the stel-

lar masses at which the surface temperature

reaches Teﬀ ≃103.8and 104.0K. The former

indicate the phase where the star deviates from

the Hayashi-line. The later indicates when a

star ends the stable dark star phase. The re-

sult is, M3.8= (1145,821,402,74,26) M⊙

and M4.0= (1349,1325,821,270,50) M⊙for

mχ= (1,10,100 GeV,1,10 TeV), respectively.

We conclude that Pop.III stars with a large WIMP

mass up to 10 TeV can path through the dark star

phase, although the duration of this phase are very

short. The ﬁnal stellar masses are small for the

dark stars with most massive WIMPs.

Note that we have used no-depletion models

here for simplicity, because dark matter depletion

eﬀect is small for the early stages of the dark star

evolution. If we take the DM depletion into ac-

count, a dark star ends the stable phase earlier

and above two quantities M3.8and M4.0become

smaller.

5. Conclusion

We have studied the pre-main-sequence evolu-

tion of dark stars by following the self-consistent

stellar evolution. We have suitably modiﬁed the

code to incorporate the energy generation from

spherically distributed DM.

Our base model with mχ= 100 GeV and

dM/dT = 1.0×G-rate M⊙yrs−1shows the char-

acteristic features of the dark star phase; the large

DM annihilation energy expands the star, making

the star to be in gravitational equilibrium. The

lower temperature is one of the peculiar proper-

ties of the dark star. This stable phase continues

until the energy supply from DM annihilation be-

comes insuﬃcient to maintain the stable structure.

Finally, the star collapses rapidly and reaches the

main-sequence phase. At this point, the stellar

mass has grown up to M∼900 −1000 M⊙.

Such features in dark star phase are all consistent

with the ﬁndings of previous works of Iocco et al.

(2008); Spolyar et al. (2009) who employed much

simpler stellar models.

The dark star model has eﬀectively two param-

eters. One of them is the gas mass accretion rate

which determines the evolution of the gas and

DM distribution. Cosmological simulations pre-

dict a variety of gas accretion rates. For a small

accretion rate, the period of the dark star phase

increases whereas the ﬁnal stellar mass decreases

M∼500 M⊙. Note however that the mass is still

larger than the standard Pop III (no-DM) case

(100 −200 M⊙). Another parameter is the DM

particle mass which determines the energy gen-

eration rate. For a small DM particle mass, the

period of dark star phase becomes longer and the

ﬁnal stellar mass becomes larger (see Table 5).

All models pass through the dark star phase

and this phase is maintained by a little DM fuel

which is less than 0.1 % of the stellar mass. If

the ﬁrst stars in the universe have undergone such

phase, there are exotic stars which are cool and

massive in the early universe.

Formation of very massive dark stars has an

important implication. Such stars eventually col-

lapse gravitationally, to form massive black holes

with masses as large as 1000 M⊙. The rem-

nant black holes can also grow by accretion or

by mergers to seed super-massive black holes.

The exotic feature of dark star’s appearance, lu-

minous and cool, may be able to use as the

powerful clue to search such stars. Our cal-

culations show that ﬁrst stars can grow to be

dark stars with luminosity ∼few 107L⊙at

most and they will not be detectable by JWST.

However, Freese et al. (2010) estimate for super-

massive dark stars (SMDSs) and such very mas-

sive and bright stars (about 109−11 L⊙) can be de-

tected by JWST. Sandick et al. (2010) argue that

dark star remnants might survive to the present

day in the Milky Way, leaving γ-ray signatures

from DM annihilation.

In future work, we will include the nuclear re-

action to calculate the ﬁrst star evolution from

the dark star phase to the main-sequence phase

completely. It would be also interesting to include

capture of DM particles. Once the stars have con-

tracted and stop growing in mass, there will be

no more DM supplied by adiabatic contraction.

However, DM particle may still be captured by

the star. Previous studies showed that this pro-

cess can make the star back in the dark star phase

again. We will explore the eﬀect of DM capture

and make a complete evolutionary model of the

ﬁrst stars with DM annihilation.

This work was supported by the Grants-in-Aid

for Scientiﬁc Research (20041005, 20105004) from

the MEXT of Japan and the Grants-in-Aid for

Young Scientists (S) 20674003 by the Japan So-

ciety for the Promotion of Science, and support

from World Premier International Research Cen-

ter Initiative (WPI Initiative), MEXT, Japan.

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This 2-column preprint was prepared with the AAS L

macros v5.2.

0.01

0.1

100

1000

10000

100000

0.01 0.1 1 10 100 1000

ρDM [GeV cm-3]

Radius [pc]

Initial

Simulation

Blumenthal

Fig. 1.— Dark matter density proﬁle calculated by an adiabatic contraction model. The solid and dashed

lines are calculated directly from our cosmological N-body simulation, whereas the dotted line is calculated

from the initial proﬁle data using the analytical method of Blumenthal et al. (1986). The dashed and dotted

proﬁles agree remarkably well.

0.0001

0.001

0.01

0.1

1 10 100 1000

dM/dT [M⊙ yrs-1]

Mass [M⊙]

Tan, McKee (2004)

O’shea, Norman (2007)

1.0 × G-rate

0.5 × G-rate

0.2 × G-rate

Fig. 2.— Gas mass accretion rates adopted in our stellar evolution calculations. “G-rate” is the accretion

rate of Eq. 3. We adopt three rates 1.0,0.5 and 0.2×G-rate. The other two lines are the rates adopted in

Spolyar et al. (2009), for comparison.

3.63.844.24.44.64.855.2

Log10 L [L⊙]

Log10 Teff [K]

100M

800M

1000M

100M

Base model

No-DM model

Fig. 3.— Hertzsprung-Russell (HR) diagram for our base model. Symbols indicate the stellar mass of

M= 100,200,600,800 and 1000 M⊙. The solid line is for the dark star model (“base model”), whereas

the dashed line is for the standard Pop III model (no-DM model of Umeda et al. (2009)).

0.1

0.2

0.3

0.4

0.5

0.6

10 100 1000

MDM [M⊙]

Mass [M⊙]

Base model

No-depletion

-4

-3

-2

-1

10 100 1000

log10 dMdTann/dMdTcon

Mass [M⊙]

Fig. 4.— DM mass inside the star (left panel) and the DM consumption rate by the annihilation (right

panel) as a function of stellar mass. We normalize the DM consumption rate dMDM /dt|annihilation by the

DM mass supply by adiabatic contraction dMDM /dt|contraction. The solid line is for the dark star model

(“base model”), whereas the dotted line is for no-depletion model.

-8 -6 -4 -2 0 2 4 6

log10 ρGas [GeV cm-3]

log10 Radius/R*

200 M⊙

800 M⊙

1000 M⊙ 5

-8 -6 -4 -2 0 2 4 6

log10 ρDM [GeV cm-3]

log10 Radius/R*

-25

-20

-15

-10

-5

-8 -6 -4 -2 0 2 4 6

log10 MGas [M⊙]

log10 Radius/R*

-25

-20

-15

-10

-5

-8 -6 -4 -2 0 2 4 6

log10 MDM [M⊙]

log10 Radius/R*

-25

-20

-15

-10

-5

-8 -6 -4 -2 0 2 4 6

log10 dMdTann [M⊙ yrs-1]

log10 Radius/R*

-15

-10

-5

-8 -6 -4 -2 0 2 4 6

log10 LDM [L⊙]

log10 Radius/R*

Fig. 5.— Radial proﬁles of various quantities for our base model when the stellar masses are M= 200,800

and 1000 M⊙. In all the panels, the horizontal axis shows the ratio of radial distance normalized to the

stellar radius (see Table 1). Top panels show the gas and DM density proﬁles. The middle panels show

the gas and DM enclosed mass. The bottom panels show DM annihilation rate and DM luminosity from

annihilation.

Base model

No-DM model

no-depletion

R [R⊙]

-7

-5

-3

-1

0 200 400 600 8001000

ρcen [g cm-3]

Mass [M⊙]

L [L⊙]

Teff [K]

200 400 600 8001000

Tcen [K]

Mass [M⊙]

Fig. 6.— Evolution of basic stellar quantities. The horizontal axis indicates the stellar mass. The vertical

axis shows, respectively, the stellar radius, the central gas density, the luminosity , the surface temperature

and the central temperature in the logarithm scales. The solid line is for the base model, the dashed line is

for no-DM model and the dotted line is for no-depletion model.

5.5

6.5

7.5

3.63.844.24.44.64.85

Log10 L [L⊙]

Log10 Teff [K]

1.0 × G-rate

0.5 × G-rate

0.2 × G-rate

Fig. 7.— HR diagram for models with three accretion rates, 1.0,0.5 and 0.2×G-rate, shown in Figure 2.

0.05

0.1

0.15

0.2

0.25

0.3

0.35

10 100 1000

MDM [M⊙]

Mass [M⊙]

1.0 × G-rate

0.5 × G-rate

0.2 × G-rate

-4

-3

-2

-1

10 100 1000

log10 dMdTann/dMdTcon

Mass [M⊙]

Fig. 8.— DM mass and the DM consumption rate by the annihilation as a function of stellar mass for three

accretion rates models, as in Figure 4.

1.0 × G-rate

0.5 × G-rate

0.2 × G-rate

R [R⊙]

-7

-5

-3

-1

0 200 400 600 8001000

ρcen [g cm-3]

Mass [M⊙]

L [L⊙]

Teff [K]

200 400 600 8001000

Tcen [K]

Mass [M⊙]

Fig. 9.— Evolution of basic stellar quantities for dark star models with reduced accretion rates. All vertical

axes are plotted in logarithm scale. The plotted quantities are the same as in Figure 6.

5.5

6.5

7.5

8.5

3.63.844.24.44.64.85

Log10 L [L⊙]

Log10 Teff [K]

1GeV

10GeV

20GeV

50GeV

100GeV

200GeV

No-DM

Fig. 10.— HR diagram for models with variation of DM particle masses. Each lines show models with

DM particle masses mχ= 1,10,20,50,100,200 GeV and the no-DM model (the same as in Figure 3),

respectively.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10 100 1000

MDM [M⊙]

Mass [M⊙]

1GeV

10GeV

20GeV

50GeV

100GeV

200GeV

-4

-3

-2

-1

10 100 1000

log10 dMdTann/dMdTcon

Mass [M⊙]

Fig. 11.— DM mass and the DM consumption rate by the annihilation for the variation of DM particle

masses, as the same plot of Figure 4.

1GeV

10GeV

20GeV

50GeV

100GeV

200GeV

R [R⊙]

-8

-6

-4

-2

0 500 1000 1500

ρcen [g cm-3]

Mass [M⊙]

L [L⊙]

Teff [K]

500 1000 1500

Tcen [K]

Mass [M⊙]

Fig. 12.— Evolution of stellar values for dark star models with parameters of DM particle masses. All

vertical axes are plotted in logarithm scale. As for Figure 6, but for diﬀerent DM particle masses.

10-5

10-4

10-3

10-2

10-1

10 100 1000

LDM/LEDD

Mass [M⊙]

1GeV

10GeV

20GeV

100GeV

200GeV

-2.5

-2

-1.5

-1

-0.5

10 100 1000

log10 κ

Mass [M⊙]

Fig. 13.— We plot the ratio of DM annihilation luminosity to Eddington luminosity (left) and the opacity

at photosphere as a function of stellar mass (right) for diﬀerent DM particle masses. In all the models, the

luminosity ratio stays less than unity.

3.6

3.7

3.8

3.9

4.1

4.2

4.3

4.4

0 50 100 150 200

Log10 Teff [K]

M [M⊙]

100[GeV]

1[TeV]

10[TeV]

2.2

2.4

2.6

2.8

3.2

3.4

0 50 100 150 200

Log10 R [R⊙]

M [M⊙]

Fig. 14.— Stellar values of no-depletion models with large WIMP mass mχ= 100 GeV,1 and 10 TeV.

Left panel shows the evolutions of the stellar surface temperature and right panel shows ones of the stellar

radius. All models are on the dark star phases at ﬁrst.

Table 1

Stellar properties for the “base model” calculation

M∗[M⊙]R∗[R⊙]L∗[L⊙]Teﬀ [K] Tcen [K] MDM [M⊙]t[Myr]

200 1.51E3 1.83E6 5.49E3 4.69E5 0.166 0.017

600 1.51E3 6.98E6 7.67E3 9.33E5 0.313 0.097

800 1.19E3 1.08E7 9.65E3 1.42E6 0.287 0.153

1000 21.98 3.24E7 9.33E4 9.25E7 3.75E-4 0.218

Note.—We tabulate the main results for the base dark star model at stellar

masses, M= 200,600,800 and 1000 M⊙. The columns show, from left to right,

the stellar radius, luminosity, surface temperature, central temperature, DM mass

inside the star, and the time elapsed from the beginning of the calculation.

Table 2

Stellar properties for three accretion models at Teﬀ = 104K

Accretion Rate M∗[M⊙]R∗[R⊙]L∗[L⊙]Teﬀ [K] Tcen [K] MDM [M⊙]t[Myr]

1.0 ×G-rate 821 1.14E3 1.15E7 1.00E4 1.51E6 0.277 0.160

0.5 ×G-rate 682 9.87E2 8.67E6 1.00E4 1.56E6 0.205 0.237

0.2 ×G-rate 492 7.87E2 5.55E6 1.00E4 1.63E6 0.125 0.351

Note.—Stellar properties for three accretion models when the stellar surface temperature reaches

Teﬀ = 104K. After this phase, the star begins to run out the DM fuel and begins to gravitationally

contract.

Table 3

Stellar properties for three accretion models at Teﬀ = 105K

Accretion Rate M∗[M⊙]R∗[R⊙]L∗[L⊙]Teﬀ [K] Tcen [K] MDM [M⊙]t[Myr]

1.0 ×G-rate 1002 19.27 3.32E7 1.00E5 1.07E8 2.43E-4 0.220

0.5 ×G-rate 775 16.55 2.43E7 1.00E5 1.08E8 1.46E-4 0.291

0.2 ×G-rate 534 13.44 1.62E7 1.00E5 1.09E8 7.65E-5 0.401

Note.—Stellar properties for three accretion models when the stellar surface temperature reaches

Teﬀ = 105K. By this phase, the star has contracted suﬃciently and the density and temperature

has risen up enough to start the hydrogen burning. In this point, the star is not supported by DM

annihilation energy, so we stop the calculation.

Table 4

Stellar properties for some DM mass models at Teﬀ = 104K

mχ[GeV] M∗[M⊙]R∗[R⊙]L∗[L⊙]Teﬀ [K] Tcen [K] MDM [M⊙]t[Myr]

1 1349 1.82E3 2.92E7 1.00E4 1.11E7 0.096 0.354

10 1325 1.59E3 2.23E7 1.00E4 1.33E6 0.254 0.344

20 1214 1.51E3 2.02E7 1.00E4 1.42E6 0.297 0.298

50 1009 1.32E3 1.55E7 1.00E4 1.46E6 0.307 0.222

100 821 1.14E3 1.15E7 1.00E4 1.51E6 0.277 0.160

200 536 8.76E2 6.81E6 1.00E4 1.47E6 0.198 0.081

Note.—Stellar properties for DM mass variation models when stellar surface temperature

reaches Teﬀ = 104K; the end of the stable dark star phase and the start of transformation into

main-sequence star.

Table 5

Stellar properties for some DM mass models at Teﬀ = 105K

mχ[GeV] M∗[M⊙]R∗[R⊙]L∗[L⊙]Teﬀ [K] Tcen [K] MDM [M⊙]t[Myr]

1 1370 23.86 5.03E7 1.00E5 2.49E8 3.47E-6 0.362

10 1381 23.32 4.83E7 1.00E5 1.07E8 4.96E-5 0.367

20 1295 22.45 4.48E7 1.00E5 1.07E8 8.92E-5 0.333

50 1138 20.85 3.86E7 1.00E5 1.07E8 1.59E-4 0.269

100 1002 19.27 3.32E7 1.00E5 1.07E8 2.43E-4 0.220

200 776 18.91 3.16E7 1.00E5 9.95E7 3.88E-4 0.146

Note.—Stellar properties for DM mass variation models when stellar surface temperature

reaches Teﬀ = 105K; the end of calculation.

Impact of Sub-MeV Dark Matter on the Cooling of Pulsating White Dwarfs

Preprint

Full-text available

Nov 2024

In our galaxy, white dwarfs inevitably undergo scattering and capture processes with the interstellar diffuse dark matter. The captured dark matter forms a dark halo that eventually evaporates or annihilates. Theoretical pulsation modes and observations of pulsating white dwarfs provide predictions about their evolution. This motivates us to study the impact of sub-MeV interstellar dark matter on the cooling processes of white dwarfs. In this work, we consider the collisions between dark matter and relativistic degenerate electrons inside white dwarfs, numerically calculating the energy input and output results from scattering, capture, evaporation, and annihilation processes. Based on observational data from G117-B15, we conclude that the maximum cooling luminosity of the interstellar sub-MeV dark matter is approximately

10^{22} \, \text{erg}/\text{s}

, which is insufficient to provide an effective cooling mechanism for white dwarfs. Finally, if future observations detect a pulsating white dwarf in the Galactic center, the potential sensitivity of this scenario could extend to the region

10^{-3}\,\text{MeV} < m_\chi < 10 \, \text{MeV}

and

6.02 \times 10^{-38}\,\text{cm}^2 > \sigma_0 \geq 1.5 \times 10^{40} \, \text{cm}^2

Detectability of Supermassive Dark Stars with the Roman Space Telescope

Article

Full-text available

Apr 2024

Supermassive dark stars (SMDS) are luminous stellar objects formed in the early Universe at redshift z ∼ 10–20, made primarily of hydrogen and helium, yet powered by dark matter. We examine the capabilities of the Roman Space Telescope (RST), and find it able to identify ∼10 ⁶ M ⊙ SMDSs at redshifts up to z ≃ 14. With a gravitational lensing factor of μ ∼ 100, RST could identify SMDS as small as ∼10 ⁴ M ⊙ at z ∼ 12 with ∼10 ⁶ s exposure. Differentiating SMDSs from early galaxies containing zero metallicity stars at similar redshifts requires spectral, photometric, and morphological comparisons. With only RST, the differentiation of SMDS, particularly those formed via adiabatic contraction with M ≳ 10 ⁵ M ⊙ and lensed by μ ≳ 100, is possible due to their distinct photometric signatures from the first galaxies. Those formed via dark matter capture can be differentiated only by image morphology: i.e., point object (SMDSs) versus extended object (sufficiently magnified galaxies). By additionally employing James Webb Space Telescope (JWST) spectroscopy, we can identify the He ii λ 1640 absorption line, a smoking gun for SMDS detection. Although RST does not cover the required wavelength band (for z emi ≳ 10), JWST does; hence, the two can be used in tandem to identify SMDS. The detection of SMDS would confirm a new type of star powered by dark matter and may shed light on the origins of the supermassive black holes powering bright quasars observed at z ≳ 6.

The first fireworks: A roadmap to Population III stars during the Epoch of Reionization through Pair-Instability Supernovae

Article

Full-text available

Nov 2023
MON NOT R ASTRON SOC

With the launch of JWST and other scheduled missions aimed at probing the distant Universe, we are entering a new promising era for high-z astronomy. One of our main goals is the detection of the first population of stars (Population III or Pop III stars), and models suggest that Pop III star formation is allowed well into the Epoch of Reionization (EoR), rendering this an attainable achievement. In this paper, we focus on our chance of detecting massive Pop IIIs at the moment of their death as Pair-Instability Supernovae (PISNe). We estimate the probability of discovering PISNe during the EoR in galaxies with different stellar masses (7.5 ≤ Log(M⋆/M⊙) ≤ 10.5) from six dustyGadget simulations of 50h−1 cMpc per side. We further assess the expected number of PISNe in surveys with JWST/NIRCam and Roman/WFI. On average, less than one PISN is expected in all examined JWST fields at z ≃ 8 with Δz = 1, and O(1) PISN may be found in a ∼1 deg2 Roman field in the best-case scenario, although different assumptions on the Pop III IMF and/or Pop III star-formation efficiency can decrease this number substantially. Including the contribution from unresolved low-mass halos holds the potential for increased discoveries. JWST/NIRCam and Roman/WFI allow the detection of massive-progenitor (∼250 M⊙) PISNe throughout all the optimal F200W-F356W, F277W-F444W, and F158-F213 colors. PISNe are also predominantly located at the outskirts of their hosting haloes, facilitating the disentangling of underlying stellar emission thanks to the spatial-resolution capabilities of the instruments.

Detectability of Supermassive Dark Stars with the Roman Space Telescope

Preprint

Full-text available

Jun 2023

The first bright objects to form in the Universe at redshift

z \sim 10-20

might have been Dark Stars, made primarily of hydrogen and helium but powered by dark matter. In this study, we investigate the detectability of Supermassive Dark Stars (SMDS) by the Roman Space Telescope. RST will be able to detect SMDSs at redshifts as high as

z\simeq 14

. In cases with gravitational lensing factors of

\mu\sim 100

, RST will be able to find SMDS as small as

\sim10^4 M_{\odot}

z\sim 12

with

\sim 10^6

s of exposure. To differentiate SMDS from early galaxies containing zero metallicity stars at similar redshifts, we compare their spectra, photometry in RST bands, color indexes and image morphology. With RST alone, the differentiation is possible only for limited cases: SMDS formed via "adiabatic contraction" (DM pulled into the star via gravity alone) with

M\gtrsim 10^5M_{\odot}

and lensed by

\mu\gtrsim 30

have distinct photometric signatures from those of the first galaxies. For SMDSs formed via "dark matter capture," their spectra are degenerate to those of many galaxies with little to no nebular emission. Thus with RST alone, the only way to tell them apart from first galaxies would be via image morphology: i.e. point object (SMDSs) vs. extended object (sufficiently magnified galaxies). However, if the same objects are further examined by JWST spectroscopy, a "smoking gun" for detection of SMDS is the HeII

\lambda

1640 absorption line. While RST does not cover the wavelength band required to find this line (for

z_{\rm emi}\gtrsim 10

), JWST does. Hence the two detectors can be used together in identifying SMDS. The confirmed detection of any SMDSs will provide evidence for a new type of star, powered by dark matter. Moreover, such massive stars can also be natural progenitors of the supermassive black holes powering the extremely bright quasars observed at

z\gtrsim 6

The first fireworks: A roadmap to Population III stars during the Epoch of Reionization through Pair Instability Supernovae

Preprint

Full-text available

Jun 2023

7.5 \leq \mathrm{Log}(M_\star/\mathrm{M_\odot}) \leq 10.5

) from six dustyGadget simulations of

50h^{-1}

cMpc per side. We further assess the expected number of PISNe in surveys with JWST/NIRCam and Roman/WFI. On average, less than one PISN is expected in all examined JWST fields, while

\simeq 1.5 \, \eta_\mathrm{III}

PISNe may be found in a

\sim 1

deg

^2

Roman field, with potential for increased discoveries when considering more optimistic choices for the Pop III initial mass function and formation efficiency

\eta_\mathrm{III}

, and when including the contribution of coarsely-resolved environments. JWST/NIRCam and Roman/WFI allow the detection of massive-progenitor (

\sim 250

\mathrm{M_\odot}

) PISNe throughout all the optimal F200W-F356W, F277W-F444W, and F158-F213 colors. PISNe are also predominantly located at the outskirts of their hosting haloes, facilitating the disentangling of underlying stellar emission thanks to the spatial-resolution capabilities of the instruments.

Formation of the First Stars and Black Holes

Article

Full-text available

Apr 2020
SPACE SCI REV

We review the current status of knowledge concerning the early phases of star formation during cosmic dawn. This includes the first generations of stars forming in the lowest mass dark matter halos in which cooling and condensation of gas with primordial composition is possible at very high redshift (

z > 20

), namely metal-free Population III stars, and the first generation of massive black holes forming at such early epochs, the so-called black hole seeds. The formation of black hole seeds as end states of the collapse of Population III stars, or via direct collapse scenarios, is discussed. In particular, special emphasis is given to the physics of supermassive stars as potential precursors of direct collapse black holes, in light of recent results of stellar evolution models, and of numerical simulations of the early stages of galaxy formation. Furthermore, we discuss the role of the cosmic radiation produced by the early generation of stars and black holes at high redshift in the process of reionization.

Formation of the first stars and black holes

Preprint

Mar 2020

z > 20

Formation of the first stars

Preprint

Jul 2018

Ralf S. Klessen

From studying the cosmic microwave background, we know our Universe started out very simple. It was by and large homogeneous and isotropic, with small fluctuations that can be described by linear perturbation theory. In stark contrast, the Universe today is highly structured on a vast range of length and mass scales. In the evolution towards increasing complexity, the formation of the first stars marks a primary transition event. The first generation of stars, the so-called Population III (or Pop. III) build up from truly metal-free primordial gas. They have long been thought to live short, solitary lives, with only one massive star forming per halo. However, in recent years this simple picture has undergone substantial revision, and we now understand that stellar birth in the early Universe is subject to the same complexity as star formation at present days. In this chapter, I review the current state of the field. I begin by introducing the basics concepts of star-formation theory and by discussing the typical environment in which Pop. III stars are thought to form. Then I argue that the accretion disk that builds up in the center of a halo is likely to fragment, resulting in the formation of a cluster of stars with a wide range of masses, and I speculate about how this process may be influenced by stellar feedback, the presence of magnetic fields, the energy input from dark matter annihilation, and the occurrence of large- scale streaming velocities between baryons and dark matter. Finally, I discuss direct and indirect constraints on Pop. III star formation from high-redshift observations and from the search for extremely metal-poor stars in the Milky Way and its satellites.

Double dark-matter admixed neutron star

Article

Full-text available

Jul 2018
INT J MOD PHYS D

Zeinab Rezaei

The dark matter in neutron stars can exist from the lifetime of the progenitor or captured by this compact object. The properties of dark matter entered the neutron stars through each step could be different from each other. Here, we investigate the structure of neutron stars which are influenced by the dark matter in two processes. Applying a generalization of two-fluid formalism to three-fluid one and the equation of state from the rotational curves of galaxies, we explore the structure of double dark-matter admixed neutron stars. The behavior of the neutron and dark matter portions for these stars is considered. In addition, the influence of the dark matter equations of state on the stars with different contributions of visible and dark matter is studied. The gravitational redshift of these stars in different cases of dark matter equations of state is investigated.

The First Stars: Formation, Properties, and Impact

Article

Jun 2023

The first generation of stars, often called Population III (or Pop III), form from metal-free primordial gas at redshifts z ∼ 30 and below. They dominate the cosmic star-formation history until z ∼ 15–20, at which point the formation of metal-enriched Population II stars takes over. We review current theoretical models for the formation, properties, and impact of Pop III stars and discuss existing and future observational constraints. Key takeaways from this review include the following: ▪ Primordial gas is highly susceptible to fragmentation and Pop III stars form as members of small clusters with a logarithmically flat mass function. ▪ Feedback from massive Pop III stars plays a central role in regulating subsequent star formation, but major uncertainties remain regarding its immediate impact. ▪ In extreme conditions, supermassive Pop III stars can form, reaching masses of several 10 ⁵ M ⊙ . Their remnants may be the seeds of the supermassive black holes observed in high-redshift quasars. ▪ Direct observations of Pop III stars in the early Universe remain extremely challenging. Indirect constraints from the global 21-cm signal or gravitational waves are more promising. ▪ Stellar archeological surveys allow us to constrain both the low-mass and the high-mass ends of the Pop III mass distribution. Observations suggest that most massive Pop III stars end their lives as core-collapse supernovae rather than as pair-instability supernovae. Expected final online publication date for the Annual Review of Astronomy and Astrophysics, Volume 61 is August 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

The formation of the first stars and galaxies

Article

Full-text available

May 2009

Observations made using large ground-based and space-borne telescopes have probed cosmic history all the way from the present-day to a time when the Universe was less than a tenth of its present age. Earlier on lies the remaining frontier, where the first stars, galaxies, and massive black holes formed. They fundamentally transformed the early Universe by endowing it with the first sources of light and chemical elements beyond the primordial hydrogen and helium produced in the Big Bang. The interplay of theory and upcoming observations promises to answer the key open questions in this emerging field.

Supermassive Dark Stars: Detectable in JWST

Article

Full-text available

Jun 2010

The first phase of stellar evolution in the history of the universe may be dark stars (DSs), powered by dark matter (DM) heating rather than by nuclear fusion. Weakly interacting massive particles (WIMPs), which may be their own antipartners, collect inside the first stars and annihilate to produce a heat source that can power the stars for millions to billions of years. In this paper, we show that these objects can grow to be supermassive dark stars (SMDSs) with masses (105-107) M ☉. The growth continues as long as DM heating persists, since DSs are large and cool (surface temperature 5 × 104 K) and do not emit enough ionizing photons to prevent further accretion of baryons onto the star. The DM may be provided by two mechanisms: (1) gravitational attraction of DM particles on a variety of orbits not previously considered and (2) capture of WIMPs due to elastic scattering. Once the DM fuel is exhausted, the SMDS becomes a heavy main-sequence star; these stars eventually collapse to form massive black holes (BHs) that may provide seeds for supermassive BHs in the universe. SMDSs are very bright, with luminosities exceeding (109-1011) L ☉. We demonstrate that for several reasonable parameters, these objects will be detectable with the James Webb Space Telescope. Such an observational discovery would confirm the existence of a new phase of stellar evolution powered by DM.

Core-Collapse Very Massive Stars: Evolution, Explosion, and Nucleosynthesis of Population III 500-1000 M☉ Stars

Article

Jul 2006

We calculate evolution, collapse, explosion, and nucleosynthesis of Population III very massive stars with 500 and 1000 Msolar. Presupernova evolution is calculated in spherical symmetry. Collapse and explosion are calculated by a two-dimensional code, based on the bipolar jet models. We compare the results of nucleosynthesis with the abundance patterns of intracluster matter, hot gases in M82, and extremely metal-poor stars in the Galactic halo. It was found that both 500 and 1000 Msolar models enter the region of pair instability but continue to undergo core collapse. In the presupernova stage, silicon-burning regions occupy a large fraction, more than 20% of the total mass. For moderately aspherical explosions, the patterns of nucleosynthesis match the observational data of both the intracluster medium and M82. Our results suggest that explosions of Population III core-collapse very massive stars contribute significantly to the chemical evolution of gases in clusters of galaxies. For Galactic halo stars our [O/Fe] ratios are smaller than the observational abundances. However, our proposed scenario is naturally consistent with this outcome. The final black hole masses are ~230 and ~500 Msolar for the 500 and 1000 Msolar models, respectively. This result may support the view that Population III very massive stars are responsible for the origin of intermediate-mass black holes, which were recently reported to be discovered.

cosmological simulation code GADGET

Article

Dec 2005
MON NOT R ASTRON SOC

Volker Springel

We discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the `tree' method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different time-steps. Individual and adaptive short-range time-steps may also be employed. The domain decomposition used in the parallelization algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 1010 dark matter particles, reaching a homogeneous spatial dynamic range of 105 per dimension in a three-dimensional box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community.

Numerical models of star clusters with a central black hole. I - Adiabatic models

Article

Nov 1980

Young P. J.

Numerical models of star clusters containing a massive black hole are computed for the case of a black hole which grows adiabatically in the cluster center. The growth of the hole is assumed to be at a rate longer than the cluster dynamical time scale but shorter than the relaxation time scale. The angular momentum and radial action of each star in the cluster are conserved during the adiabatic variations. This leads to the invariance of the distribution function in (E, J) space which is used to facilitate the numerical calculations. A power-law density cusp forms near the black hole. When the hole has grown to exceed the core mass of the cluster, this cusp joins smoothly onto the isothermal density law.

How Small Were The First Cosmological Objects?

Article

Jan 2009

The minimum mass that a virialized gas cloud must have in order to be able to cool in a Hubble time is computed, using a detailed treatment of the chemistry of molecular hydrogen. With a simple model for halo profiles, we reduce the problem to that of numerically integrating a system of chemical equations. The results agree well with numerically expensive three-dimensional simulations, and our approach has the advantage of being able to explore large regions of parameter space rapidly. The minimum baryonic mass Mb is found to be strongly redshift dependent, dropping from 106 M☉ at z ~ 15 to 5 × 103 M☉ at z ~ 100 as molecular cooling becomes effective. For z 100, Mb rises again, as cosmic microwave background photons inhibit H2 formation through the H- channel. Finally, for z 200, the H+2 channel for H2 formation becomes effective, driving Mb down toward Mb ~ 103 M☉. With a standard cold dark matter power spectrum with σ8 = 0.7, this implies that a fraction 10-3 of all baryons may have formed luminous objects by z = 30, which could be sufficient to reheat the universe.

Early Black Hole Formation by Accretion of Gas and Dark Matter

Article

Aug 2009
J COSMOL ASTROPART P

We propose a model in which intermediate-mass black holes (IMBHs) with mass of ~10000 Msun are formed in early dark matter halos. We carry out detailed stellar evolution calculations for accreting primordial stars including annihilation energy of dark matter particles. We follow the stellar core evolution consistently up to gravitational collapse. We show that very massive stars, as massive as 10000 Msun, can be formed in an early dark matter halo. Such stars are extremely bright with Log L/Lsun > 8.2. They gravitationally collapse to form IMBHs. These black holes could have seeded the formation of early super-massive blackholes.

Formation of Primordial Stars in a ΛCDM Universe

Article

Dec 2008

We study the formation of the first generation of stars in the standard cold dark matter model. We use a very high resolution cosmological hydrodynamic simulation that achieves a dynamic range of ~1010 in length scale. With accurate treatment of atomic and molecular physics, including the effect of molecular line opacities and cooling by collision-induced continuum emission, it allows us to study the chemothermal evolution of primordial gas clouds to densities up to ρ ~ 2 × 10-8 g cm-3 (nH ~ 1016 cm-3) without assuming any a priori equation of state, an improvement of 6 orders of magnitude over previous three-dimensional calculations. We study the evolution of a primordial star-forming gas cloud in the cosmological simulation in detail. The cloud core becomes marginally unstable against chemothermal instability when the gas cooling rate is increased owing to three-body molecule formation. However, since the core is already compact at that point, runaway cooling simply leads to fast condensation to form a single protostellar seed. During the final dynamical collapse, small angular momentum material collapses faster than the rest of the gas and selectively sinks inward. Consequently, the central regions have little specific angular momentum, and rotation does not halt collapse. We, for the first time, obtain an accurate gas mass accretion rate within a 10 M☉ innermost region around the protostar. We carry out protostellar evolution calculations using the obtained accretion rate. The resulting mass of the first star when it reaches the zero-age main sequence is MZAMS ~ 100 M☉, and less (60 M☉) for substantially reduced accretion rates.

Contraction of dark matter galactic halos due to baryonic infall

Article

Feb 1986

Varied evidence suggests that galaxies consist of roughly 10 percent baryonic matter by mass and that baryons sink dissipatively by about a factor of 10 in. radius during galaxy formation. It is shown that such infall strongly perturbs the underlying dark matter distribution, pulling it inward and creating cores that are considerably smaller and denser than would have evolved without dissipation. Any discontinuity between the baryonic and dark matter mass distributions is smoothed out by the coupled motions of the two components. If dark halos have large core radii in the absence of dissipation, the above infall scenario yields rotation curves that are flat over large distances, in agreement with observations of spiral galaxies. Such large dissipationless cores may plausibly result from large internal kinetic energy in protogalaxies at maximum expansion, perhaps as a result of subclustering, tidal effects, or anisotropic collapse.

The first generation of stars in the Λ cold dark matter cosmology

Article

Jun 2007

We have performed a large set of high-resolution cosmological simulations using smoothed particle hydrodynamics to study the formation of the first luminous objects in the Lambda cold dark matter cosmology. We follow the collapse of primordial gas clouds in eight early structures and document the scatter in the properties of the first star-forming clouds. Our first objects span formation redshifts from z∼ 10 to ∼50 and cover an order of magnitude in halo mass. We find that the physical properties of the central star-forming clouds are very similar in all of the simulated objects despite significant differences in formation redshift and environment. This suggests that the formation path of the first stars is largely independent of the collapse redshift; the physical properties of the clouds have little correlation with spin, mass or assembly history of the host halo. The collapse of protostellar objects at higher redshifts progresses much more rapidly due to the higher densities, which accelerates the formation of molecular hydrogen, enhances initial cooling and shortens the dynamical time-scales. The mass of the star-forming clouds cover a broad range, from a few hundred to a few thousand solar masses, and exhibit various morphologies: some have disc-like structures which are nearly rotational supported; others form flattened spheroids; still others form bars. All of them develop a single protostellar ‘seed’ which does not fragment into multiple objects up to the moment that the central gas becomes optically thick to H2 cooling lines. At this time, the instantaneous mass accretion rate on to the centre varies significantly from object to object, with disc-like structures having the smallest mass accretion rates. The formation epoch and properties of the star-forming clouds are sensitive to the values of cosmological parameters.

Evolution of Primordial Stars Powered by Dark Matter Annihilation up to the Main-Sequence Stage

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