Constraining ultralight vector dark matter with the Parkes Pulsar Timing Array second data release Yu-Mei Wu1 2 3Zu-Cheng Chen4 5yQing-Guo Huang1 3 2zXingjiang Zhu5xN. D. Ramesh Bhat6Yi

2025-04-27 0 0 644.09KB 9 页 10玖币

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Constraining ultralight vector dark matter with the Parkes Pulsar Timing Array

second data release

Yu-Mei Wu,1, 2, 3, ∗Zu-Cheng Chen,4, 5, †Qing-Guo Huang,1, 3, 2, ‡Xingjiang Zhu,5, §N. D. Ramesh Bhat,6Yi

Feng,7George Hobbs,8Richard N. Manchester,8Christopher J. Russell,9and R. M. Shannon10, 11

1School of Fundamental Physics and Mathematical Sciences,

Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China

2School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing 100049, China

3CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics,

Chinese Academy of Sciences, Beijing 100190, China

4Department of Astronomy, Beijing Normal University, Beijing 100875, China

5Advanced Institute of Natural Sciences, Beijing Normal University, Zhuhai 519087, China

6International Centre for Radio Astronomy Research, Curtin University, Bentley, WA 6102, Australia

7Research Center for Intelligent Computing Platforms, Zhejiang Laboratory, Hangzhou 311100, China

8Australia Telescope National Facility, CSIRO Astronomy and Space Science, P.O. Box 76, Epping, NSW 1710, Australia

9CSIRO Scientiﬁc Computing, Australian Technology Park,

Locked Bag 9013, Alexandria, NSW 1435, Australia

10Centre for Astrophysics and Supercomputing, Swinburne University of Technology, Hawthorn, VIC, 3122 Australia

11Australian Research Council Centre of Excellence in Graviational Wave Discovery (OzGrav)

Composed of ultralight bosons, fuzzy dark matter provides an intriguing solution to challenges

that the standard cold dark matter model encounters on sub-galactic scales. The ultralight dark

matter with mass m∼10−23eV will induce a periodic oscillation in gravitational potentials with a

frequency in the nanohertz band, leading to observable eﬀects in the arrival times of radio pulses

from pulsars. Unlike scalar dark matter, pulsar timing signals induced by the vector dark matter

are dependent on the oscillation direction of the vector ﬁelds. In this work, we search for ultralight

vector dark matter in the mass range of [2 ×10−24,2×10−22 ]eV through its gravitational eﬀect

in the Parkes Pulsar Timing Array (PPTA) second data release. Since no statistically signiﬁcant

detection is made, we place 95% upper limits on the local dark matter density as ρVF .5 GeV/cm3

for m.10−23 eV. As no preferred direction is found for the vector dark matter, these constraints

are comparable to those given by the scalar dark matter search with an earlier 12-year data set of

PPTA.

I. INTRODUCTION

Numerous astrophysical observations, such as galaxy

rotational curves [1,2], velocity dispersions [3], and grav-

itational lensing [4] reveal the existence of invisible mat-

ter, the so-called dark matter. In combination with ob-

servational evidence of the Universe’s accelerating expan-

sion, the standard Lambda Cold Dark Matter (ΛCDM)

cosmological model has been established. Precision anal-

yses of the cosmic microwave background show that dark

matter constitutes 26% of the total energy density of the

present-day universe [5].

The cold dark matter paradigm has achieved great

success in describing the structure of galaxies on large

scales [6–8], but it is met with puzzling discrepancies be-

tween the predictions and observations of galaxies and

their clustering on small scales. For example, the N-body

simulations based on the cold dark matter model show

a much steeper central density proﬁle in the dark mat-

ter halos than that inferred from the galaxy rotational

∗wuyumei@itp.ac.cn

†Corresponding author: zucheng.chen@bnu.edu.cn

‡Corresponding author: huangqg@itp.ac.cn

§Corresponding author: zhuxj@bnu.edu.cn

curves (the “core-cusp problem” [9,10]). The predicted

number of subhalos with decreasing mass grows much

more steeply than what is observed around galaxies (the

“missing-satellites problem” [11,12]).

Because of the diﬃculty in solving the small-scale prob-

lems as well as the null result in searching for traditional

cold dark matter candidates, e.g., weakly interactive mas-

sive particles [13], alternative paradigms for dark matter

have been proposed. These include the warm dark mat-

ter [14] and fuzzy dark matter [15].

The term “fuzzy dark matter” often refers to ultralight

scalar particles with a mass around m∼10−22 eV. Such

a dark matter scenario can get the correct relic abun-

dance through the misalignment mechanism similar to

that of axions [16]; that is, when the initial value of the

scalar ﬁeld is away from its potential minimum, the ﬁeld

is condensed during inﬂation when its mass is smaller

than the Hubble scale, and then starts a coherent oscilla-

tion as a non-relativistic matter at a later epoch. Fuzzy

dark matter makes the same large-scale structure pre-

dictions as ΛCDM, but the particle’s large de Broglie

wavelength, λ∼kpc, suppresses the structure on small

scales and thus explains well the corresponding smaller-

scale observational phenomena [17].

Besides the scalar particle, a naturally light vector bo-

son predicted in string-inspired models with compactiﬁed

extra dimensions [18] can also act as a good fuzzy dark

arXiv:2210.03880v1 [astro-ph.CO] 8 Oct 2022

matter candidate. There are several mechanisms to pro-

duce vector dark matter with the correct relic abundance,

such as the misalignment mechanism [19,20], quantum

ﬂuctuations during inﬂation [21,22], and decay of a net-

work of global cosmic strings [23]. Because of their diﬀer-

ent spins, if the dark matter is assumed to have interac-

tion with Standard Model, scalar and vector ﬁelds couple

with Standard Model particles in ways which lead to dif-

ferent observable phenomena. For example, if the vector

dark matter particle is a U(1)B(“B” refers to baryon )

or U(1)B−L(“L” refers to lepton) gauge boson, the so-

called “dark photon” would interact with ordinary mat-

ter [24], then it can be detected with gravitational-wave

interferometers because it exerts forces on test masses

and results in displacements [25,26]; it can also be de-

tected with binary pulsar systems via its eﬀects on the

secular dynamics of binary systems [27,28]. Such a gauge

eﬀect is not applicable to scalar dark matter [29].

In addition to unknown interaction with the Standard

Model, pure gravitational eﬀects of fuzzy dark matter can

also lead to observable results and help distinguish the

scalar and vector dark matter. The dark matter ﬁeld with

ultralight mass has a wave nature with the oscillating fre-

quency of fdm =mc2/h = 2.4×10−9(mc2/10−23eV) Hz.

Such a coherently oscillating ﬁeld leads to periodic os-

cillations in the gravitational potentials and further in-

duces periodic signals with the frequency on the order of

nanohertz [22,30], which falls into the sensitive range of

the pulsar timing arrays (PTAs). A PTA consists of sta-

ble millisecond pulsars for which times of arrival (ToAs)

of radio pulses are monitored with high precision over

a course of years to decades [31–33]. Any unmodelled

signal will induce timing residues, which represent the

diﬀerence between the measured and predicted ToAs.

In contrast to the ultralight scalar dark matter, the

timing residuals caused by the ultralight vector dark mat-

ter are dependent on the oscillation direction of the vec-

tor ﬁelds [22,30]. Several previous works have used PTA

data to search for ultralight scalar dark matter [34–36].

In a recent work [37], a search was performed for the

dark photon dark matter in the PPTA second data re-

lease (DR2) based on the gauge eﬀect. This resulted in

upper limits on the coupling strength between dark pho-

tons and ordinary matter, assuming that all dark matter

is composed of ultralight dark photons. In this work,

we search for ultralight vector dark matter in the mass

range of [2 ×10−24,2×10−22 ]eV in the PPTA DR2 data

set based on the gravitational eﬀect without assuming its

interaction with Standard Model particles.

This paper is organized as follows. In Sec. II we de-

scribe the observable pulsar timing eﬀects induced by

vector dark matter. In Sec. III we provide details of our

data analysis. We present the results and conclusions in

Sec. IV. In the following sections, we set c=~= 1.

II. GRAVITATIONAL EFFECT FROM VECTOR

DARK MATTER

In this section, we ﬁrst introduce the timing residuals

caused by the gravitational eﬀect from the ultralight vec-

tor dark matter in the Galaxy; a more detailed derivation

can be found in Ref. [22].

Assuming no coupling between the ultralight particles

and any other ﬁelds, we take the action for a free vector

ﬁeld Aµwith mass mas,

S=Zd4x√−g−1

4Fµν Fµν −1

2m2AµAµ,(1)

where gis the determinant of the metric gµν and Fµν =

∂µAν−∂νAµ. On Galactic scales, the cosmic expan-

sion is negligible and the background is approximately

Minkowski. The energy-momentum tensor carried by the

vector dark matter induces perturbations into the metric

which, in the Newtonian gauge, can be written as

ds2=ηµν dxµdxν−2Φ(t, x)dt2+ 2Ψ(t, x)δij dxidxj

+hij (t, x)dxidxj,(2)

where ηµν = diag(−1,+1,+1,+1) is the background

Minkowski metric, Φ and Ψ are gravitational potentials,

and hij describes the traceless spatial metric perturba-

tions. hij is absent in the scalar-ﬁeld case and demon-

strates the anisotropy induced by additional degrees of

freedom in vector ﬁelds.

With a huge occupation number, the vector ﬁeld can

be described as a classical wave with a monochromatic

frequency determined by its mass. This is a good ap-

proximation because the characteristic speed of the dark

matter is non-relativistic v∼10−3. During inﬂation,

only the longitudinal mode of the vector ﬁelds survives

[21], so the equation of motion of the vector ﬁeld is

given by the component in the oscillating direction ˆ

(sin θcos φ, sin θsin φ, cos θ),

Aˆ

k(t, x) = A(x) cos(mt +α(x)).(3)

The vector ﬁelds contribute a time-independent energy

density

ρVF(x) = 1

2m2A2(x),(4)

and an anisotropic oscillating pressure which leads to os-

cillating gravitational potentials. By solving the photon

geodesic equation from the pulsar to the Earth under

the metric Eq. (2), it is found that the metric perturba-

tions that give rise to the observable eﬀects in PTAs are

from the spatial components (see the Appendix of [22]).

Furthermore, splitting the potential Ψ into a dominant

time-independent part and an oscillating part and solv-

ing the linear Einstein equation by neglecting the spatial

gradient of the oscillating part (which is suppressed by

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ConstrainingultralightvectordarkmatterwiththeParkesPulsarTimingArrayseconddatareleaseYu-MeiWu,1,2,3,Zu-ChengChen,4,5,yQing-GuoHuang,1,3,2,zXingjiangZhu,5,xN.D.RameshBhat,6YiFeng,7GeorgeHobbs,8RichardN.Manchester,8ChristopherJ.Russell,9andR.M.Shannon10,111SchoolofFundamentalPhysicsandMathematicalSci...

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