Constraining properties of asymmetric dark matter candidates from gravitational-wave observations

2025-09-29 0 0 3.26MB 18 页 10玖币

侵权投诉

Constraining properties of asymmetric dark matter candidates from

gravitational-wave observations

Divya Singh ,1, ∗Anuradha Gupta ,2Emanuele Berti ,3Sanjay Reddy ,4and B. S. Sathyaprakash 1, 5, 6

1Institute for Gravitation and the Cosmos, Department of Physics,

Pennsylvania State University, University Park, PA, 16802, USA

2Department of Physics and Astronomy, The University of Mississippi, University MS 38677, USA

3Department of Physics and Astronomy, Johns Hopkins University,

3400 N. Charles Street, Baltimore, Maryland, 21218, USA

4Institute for Nuclear Theory, University of Washington, Seattle, WA USA

5Department of Astronomy & Astrophysics, Pennsylvania State University, University Park, PA, 16802, USA

6School of Physics and Astronomy, Cardiﬀ University, Cardiﬀ, UK, CF24 3AA

The accumulation of certain types of dark matter particles in neutron star cores due to accretion

over long timescales can lead to the formation of a mini black hole. In this scenario, the neutron star

is destabilized and implodes to form a black hole without signiﬁcantly increasing its mass. When this

process occurs in neutron stars in coalescing binaries, one or both stars might be converted to a black

hole before they merge. Thus, in the mass range of ∼1–2 M,the Universe might contain three

distinct populations of compact binaries: one containing only neutron stars, the second population

of only black holes, and a third, mixed population consisting of a neutron star and a black hole.

However, it is unlikely to have a mixed population as the various timescales allow for both neutron

stars to remain or collapse within a short timescale. In this paper, we explore the capability of

future gravitational-wave detector networks, including upgrades of Advanced LIGO and Virgo, and

new facilities such as the Cosmic Explorer and Einstein Telescope (XG network), to discriminate

between diﬀerent populations by measuring the eﬀective tidal deformability of the binary, which

is zero for binary black holes but nonzero for binary neutron stars. Furthermore, we show that

observing the relative abundances of the diﬀerent populations can be used to infer the timescale for

neutron stars to implode into black holes, and in turn, provide constraints on the particle nature of

dark matter. The XG network will infer the implosion timescale to within an accuracy of 0.01 Gyr

at 90% credible interval and determine the dark matter mass and interaction cross section to within

a factor of 2 GeV and 10 cm−2, respectively.

Keywords: Gravitational Waves; Astrophysics, Black Holes, Star Clusters, Dark Matter

I. INTRODUCTION AND BACKGROUND

The origin and properties of dark matter (DM) have

been long-standing problems in fundamental physics and

cosmology. Astronomical observations have increasingly

provided evidence for a non-baryonic component of mat-

ter that either does not interact electromagnetically

with baryons or has a negligibly small interaction cross-

section. Consequently, the presence of DM is inferred due

to its gravitational eﬀect on baryonic matter. Laboratory

experiments to detect DM particles from their weak in-

teraction with baryons have so far produced null results,

as have the observations of decay products that would

result from the annihilation of certain types of DM par-

ticles. Although there are a few plausible DM candidates

in the Standard Model, theoretical insight into what they

might be in theories beyond the Standard Model is plenti-

ful and not very constraining. Currently, there is an eﬀort

to look for DM over sixty orders of magnitude in mass,

with candidates ranging from wave-like [1] and particle

DM [2] to macroscopic objects such as primordial black

holes (BHs) [3].

∗dus960@psu.edu

Observations of gravitational waves (GWs) by the

Laser Interferometer Gravitational-Wave Observatory

(LIGO) and Virgo over the past seven years [4–6] have

opened up a new avenue for exploring DM. On the one

hand, detecting BHs of unusually large masses (compared

to astrophysical BHs observed until then) could hint at

their primordial origin [7]. This remains a possibility, al-

though several astrophysical models can account for the

broad range of BH masses detected by LIGO and Virgo

(see, e.g., [8,9]). The search for GWs from sub-solar

mass BHs has so far been unsuccessful, severely con-

straining the fraction of total DM content in primordial

BHs [10,11]. If the Universe has no primordial BHs with

masses of O(10 M), XG detectors can set upper limit

on their abundance as a fraction of DM energy density

as low as fPBH ∼ O(10−5), about two orders of magni-

tude lower than current upper limits in this mass range;

if instead fPBH &10−4, future GW observations would

exclude fPBH = 0 at the 95% credible interval [12]. The

minimum testable abundance as a fraction of DM energy

density depends on the primordial BH mass, and can be

as low as fPBH ∼ O(10−10)(see e.g. Fig. 5 of [13]).

An alternative way to constrain the presence of DM

would be to look for its gravitational drag on the orbits

of BHs and neutron stars (NSs) [14–24]. Additionally, the

presence of an axionic cloud around BHs could extract

arXiv:2210.15739v1 [gr-qc] 27 Oct 2022

FIG. 1. Two plausible scenarios for the formation of BHs by imploding NSs without signiﬁcantly changing their mass. In the

ﬁrst scenario, DM particles accumulate, thermalize and form a self-gravitating object, which collapses to a BH if the number

of DM particles exceeds the Chandrasekhar limit. In the second scenario, when a suﬃciently large number of DM particles

accumulates, a Bose-Einstein condensate (BEC) could form under favorable conditions and then collapse to a BH. Once a BH

is assembled at the core, it can grow by accretion of NS matter, eventually leading to the implosion of the NS. The BH forms

over a shorter timescale through BEC formation for DM particles of mass mχ≤2×104GeV. Therefore, we show the timescales

with mχ= 2 ×104GeV for the channel where the BH forms without a BEC (blue), and with mχ= 1 GeV for the BEC channel

(green), assuming a scattering cross-section σχ= 2 ×10−45cm−2and ambient dark matter density ρχ= 1 GeV/cm3.

the rotational energy from BHs, thereby aﬀecting the

spin distribution of BHs or producing continuous GWs

from newly formed BHs [25,26]. Several authors have

explored the prospect of making such observations [27–

30]. In fact, next-generation ground-based GW observa-

tories, with the prospect of detecting several binary black

hole (BBH) inspiral events each year with large signal-to-

noise-ratios (SNRs), could observe dozens of post-merger

axionic signals [31], conﬁrming or constraining bosons in

the mass range ∼[7 ×10−14,2×10−11]eV [32].

In this paper, we explore the accumulation of bosonic

DM in NS cores that could eventually form a stable,

mini-BH, grow by Bondi-Hoyle accretion and eventually

lead NSs to implode and form BHs, without signiﬁcantly

changing their mass. Two plausible scenarios are de-

scribed in Fig. 1. These mechanisms could be particu-

larly eﬃcient in regions of large DM densities, such as

the central cores of large galaxies. It has been suggested

that the lack of a sizeable population of pulsars in the

core of the Milky Way, where the density of DM is ex-

pected to be particularly high, is because most of them

have imploded to form BHs [33]. While this explanation

might not be the root cause of why the Galactic center is

deﬁcient of pulsars, future GW observations could test if

the implosion mechanism operates in NSs, as described

below.

The timescale tc(ρχ, mχ, σχ)over which the accumula-

tion of DM eventually makes NSs implode to form BHs

depends on the DM density ρχin the neighborhood of

NSs, its mass mχ, and its interaction cross-section with

hadrons σχ.NSs that live for a time longer than tcwill

get converted to BHs, and those that live for a shorter

duration won’t. Although isolated NSs can last forever,

those in a merging binary would only live for a time td,

called the delay time, before they inspiral and merge to ei-

ther form (rarely) supermassive NSs or (frequently) BHs.

The delay time depends on the companion masses, and

the periapsis and eccentricity of the binary at the time

when it ﬁrst forms. The delay time, therefore, is not

the same for all binary neutron stars (BNSs). Instead,

the NS binary population is characterized by a certain

delay-time distribution P(td).

The probability distribution P(td)is not well known,

but it is often assumed to scale like P(td)∝1/td[34–38].

The fraction of the population for which td> tcwill be

converted to BHs and the rest will remain as NSs. For the

population of mergers detected with a suﬃciently large

SNR, GW observations can determine the fraction of the

BNS population that has been converted to BBHs. This

fraction, if nonzero, can be used to infer the implosion

timescale tc(ρχ, mχ, σχ)and hence constrain the param-

eter space of local DM density, DM mass, and interac-

tion cross-section. If the population does not contain any

BBHs, then it will be possible to set limits on the very

same quantities.

It is quite possible, although unlikely, that BHs in the

mass range of NSs of 1–3 Mare produced by stellar

evolution or, alternatively, they could be primordial in

origin [39,40]. The current consensus is that massive

stars up to ∼23 Mleave behind NSs of masses in the

range 1.2–2.0 Mat the end of their lives, while more

massive stars are likely to leave behind a BH of mass

greater than about ∼5M[41–45]. Although the pri-

mordial Universe could produce BHs in the mass range

of NSs, they should also produce sub-solar mass BHs.

A detection of sub-solar mass BHs could hint at the

early-Universe origin of BHs with NS masses. Moreover,

primordial BHs are expected to have small spin magni-

tudes if they do not increase their spin by coherent ac-

cretion [46], while BHs formed from imploding NSs could

have nonzero spins (see, e.g., [47,48]). Consequently, it

might be possible to discriminate between the two pop-

ulations from their spin distributions [49]. Another pro-

posal to distinguish primordial BHs from astrophysical

compact objects is to use their mass distribution and the

redshift evolution of the merger rates by using LVK and

A+ detections of the stochastic GW background [50],

and possibly (in the future) Cosmic Explorer and Ein-

stein Telescope observations of the stochastic background

produced by sub-solar mass compact objects [51].

The above argument assumes that either both NSs will

implode, or neither does. If the time diﬀerence between

the formation of the two NSs is large compared to the

delay time td, then it is possible that only one of the NSs

gets converted to a BH, but not its companion. However,

this scenario is likely to be very rare.

The complex evolutionary process leading to NS for-

mation is not completely understood, but stellar evolu-

tion models broadly suggest that NSs form from pro-

genitors whose mass Mlies in the range 8M.M.

23 M[45]. The lifetime of such progenitor stars in the

main-sequence, which varies as 10(M/M)−2.5Gyr [52],

would be in the range 4–55 Myr. The heavier compan-

ion would evolve through the main sequence ﬁrst to form

a NS, followed by the lighter progenitor after a delay

∆tMS.Assuming that the progenitors are drawn from

FIG. 2. The fraction of BBH and NSBH binaries formed from

the implosion of one or both NSs, compared to the fraction of

BNS systems as a function of the implosion time-scale tc. As

a function of tcthe NSBH fraction remains negligibly small

and can be ignored.

the Salpeter mass function, i.e., P(m)∝m−2.3[53], we

ﬁnd that ∆tMS has a median value of ∼14 Myr, which

is smaller than the smallest delay time tmin

d= 20 Myr

that we will be using in this work, and likely much

smaller than the implosion timescale tc,which could be

as large as billions of years. A speciﬁc binary with delay

time tdwill be seen as a BBH if tc< td,as a BNS if

tc> td+ ∆tMS, or as a neutron star-black hole (NSBH)

system otherwise. In Fig. 2we plot the three fractions,

and we see that the NSBH population constitutes at best

about 6% of the total, and only over a small range of val-

ues of tc.Consequently, we can safely assume that either

both NSs in a binary would implode to form BHs, or

neither would.

Observations of GWs could potentially discriminate

the BBH population from that of BNSs. In the ﬁnal

moments before a BNS coalesces, each star experiences

the tidal ﬁeld of its companion, inducing a time-varying

quadrupole deformation and associated emission of GWs.

This is a high-order post-Newtonian eﬀect – technically

a ﬁfth post-Newtonian eﬀect or a (v/c)10 correction in

the orbital phase evolution of the binary, where vis the

orbital speed and cis the speed of light [54,55] – which

becomes important before the two NSs merge with each

other, and will be absent in the case of BBHs [56–59].

Thus, by measuring the tidal polarizability, often referred

to as the eﬀective tidal deformability, it will be possible

to ascertain the fraction of the two populations. It will

not be possible to measure tidal deformability with suﬃ-

ciently good accuracy for the entire observed population,

but only for a fraction with suﬃciently large SNR. In this

paper we explore the sensitivity of future ground-based

GW detectors to constrain the properties of a class of

DM particles that can accumulate in NS cores and cause

implosion, given suﬃciently large time.

The rest of the paper is organized as follows. In Sec. II,

we recall how tidal eﬀects are encoded in GWs from

BNSs. In Sec. III we introduce the various GW detector

networks and the waveform model used in this study, and

compute the accuracy with which the tidal deformability

of a BNS can be measured using the Fisher matrix for-

malism. This will be followed by a computation in Sec. IV

of the relative rates of BBHs and BNSs, as a function of

the unknown implosion timescale tcneeded to form this

novel population of BBHs. It turns out that the most

important hyperparameter needed in the computation of

relative rates is the implosion timescale tc.Thus, from

the measured relative rates we can infer the implosion

timescale, as shown in Sec. V. In Sec. VI, we discuss the

physics of implosion from DM accretion and the various

timescales involved in the problem, from accumulation of

DM particles to form a mini-BH, through self-gravitation

with or without the formation of a Bose-Einstein conden-

sate, its growth, and the ﬁnal implosion of the NS (cf.

Fig. 1). In Sec. VII we derive the constraints that can

be placed on DM particles if the proposed analysis does

not ﬁnd a single BBH event in the mass range of 1–3

M(which would imply that the implosion timescale is

larger than the Hubble time) and obtain the properties

of bosonic DM particles assuming a collapse time of 1

Gyr. In Sec. VIII we brieﬂy summarize our ﬁndings, as

well as our plans to apply this technique to the known

population of LIGO-Virgo binary mergers for a number

of implosion scenarios and diﬀerent DM candidates.

II. TIDAL INTERACTION TO DISTINGUISH

BINARY NEUTRON STARS FROM BINARY

BLACK HOLES

In this Section we will discuss how to distinguish BNS

mergers from BBH mergers using GW observations. An

important diﬀerence in the GWs from the coalescence of

BBH and BNS systems is that waves from BNS mergers

have imprinted in them the tidal interaction between the

two bodies, while BBH mergers will have no such signa-

ture [56,60]. Additionally, while BBH mergers leave be-

hind a BH remnant, BNS mergers could either promptly

form a BH or leave behind a long-lived NS remnant with

neutron-rich relativistic ejecta and a thermonuclear ﬁre-

ball. In this work, we will only consider the tidal interac-

tion between the two bodies during the adiabatic inspiral

regime. A merger accompanied by an electromagnetic af-

terglow essentially rules out a BBH merger.

A. Tidal deformability

A massive body produces a tidal ﬁeld. The deforma-

tion induced by the tidal ﬁeld on other bodies can be ex-

pressed as a multipole expansion, the quadrupole being

the dominant multipole. Consider a spherically symmet-

ric NS of radius Rin the tidal ﬁeld Eij of its companion

NS. The quadrupole deformation Qij induced in the star

is related to the tidal ﬁeld via the tidal deformability as

Qij =−λEij ,(1)

where λ≡ − 2

3Gk2R5, R is the star’s radius, and k2is

the dimensionless tidal Love number. The tidal Love

number, which measures a body’s rigidity, depends on

the equation of state (EOS) of the NS via its compactness

C≡Gm/(c2R),where mis the mass of the star [61]. For

NS equations of state considered in this paper, we have

k2∼0.1[62].

In a binary system of stars orbiting each other the

above quadrupole deformation is a function of time,

which generates gravitational radiation, modifying the

emitted signal at the ﬁfth post-Newtonian order, induc-

ing a (v/c)10 correction to the dynamics of the sys-

tem beyond the dominant quadrupole radiation reac-

tion. In other words, the tidal interaction dissipates addi-

tional orbital energy into GWs, thus changing the orbital

phase evolution of the waves at (v/c)10 order beyond the

quadrupole. This modiﬁcation is signiﬁcant in the ﬁnal

few cycles of the inspiral and coalescence of a binary, and

can be detected if the signal is observed with a high SNR.

The tidal deformability λhas dimensions of kg m2s2,

but what appears in the post-Newtonian dynamics is the

dimensionless tidal deformability, deﬁned by

Λ≡c10λ

G4m5=2

3k2C−5.(2)

As mentioned before, the Love number k2generally de-

creases with increasing compactness, thus the tidal de-

formability falls of steeper than C−5.For candidate equa-

tions of state of NSs Λdecreases with the NS’s mass

and varies over the range ∼[100,4000] for NS masses

in the range 1.1-1.5 Mconsidered in this study (see,

e.g., Fig. 1 of Ref. [63]), the smallest values correspond-

ing to largest NS masses and softer equations of state,

and largest values corresponding to smallest masses and

stiﬀer equations of state. For BHs, Λ=0[56–58]: this is

the key to distinguishing BBH mergers from NSBH and

BNS mergers [64–66].

B. Tidal signature in neutron-star binary signal

The GWs produced by BNSs are accurately described

by post-Newtonian theory. We assume NSs have negligi-

bly small spins and are on quasi-circular orbits. These are

reasonable assumptions, as companions in Galactic dou-

ble NS systems have negligible spins (based on Ref. [67],

see also Fig. 2.17 of Ref. [68]) and gravitational radiation

back reaction causes orbital eccentricity to decay more

rapidly compared to the orbital separation [69]. In the

Fourier domain, the strain amplitude ˜

h(f)measured by

an interferometric GW detector in response to an inci-

dent BNS signal on a quasi-circular orbit is given by:

f˜

h(f) = A(f)eiψPP (f)+iψTidal (f),(3)

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

Constrainingpropertiesofasymmetricdarkmattercandidatesfromgravitational-waveobservationsDivyaSingh,1,AnuradhaGupta,2EmanueleBerti,3SanjayReddy,4andB.S.Sathyaprakash1,5,61InstituteforGravitationandtheCosmos,DepartmentofPhysics,PennsylvaniaStateUniversity,UniversityPark,PA,16802,USA2DepartmentofPhysi...

展开>> 收起<<

Constraining properties of asymmetric dark matter candidates from gravitational-wave observations.pdf

共18页,预览4页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Constraining properties of asymmetric dark matter candidates from gravitational-wave observations

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: