# Bosenovae with Quadratically-Coupled Scalars in Quantum Sensing Experiments

Jason Arakawa<EMAIL_ADDRESS>Department of Physics and Astronomy,
University of Delaware, Newark, Delaware 19716, USA  International Center for
Quantum-field Measurement Systems for Studies of the Universe and Particles
(QUP), KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan  Muhammad H. Zaheer
<EMAIL_ADDRESS>Department of Physics and Astronomy, University of Delaware,
Newark, Delaware 19716, USA  Joshua Eby<EMAIL_ADDRESS>The Oskar
Klein Centre, Department of Physics, Stockholm University, 10691 Stockholm,
Sweden  Kavli Institute for the Physics and Mathematics of the Universe (WPI),
The University of Tokyo Institutes for Advanced Study, The University of
Tokyo, Kashiwa, Chiba 277-8583, Japan Volodymyr Takhistov
<EMAIL_ADDRESS>International Center for Quantum-field Measurement
Systems for Studies of the Universe and Particles (QUP), KEK, 1-1 Oho,
Tsukuba, Ibaraki 305-0801, Japan  Theory Center, Institute of Particle and
Nuclear Studies, High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan  Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho,
Tsukuba, Ibaraki 305-0801, Japan  Kavli Institute for the Physics and
Mathematics of the Universe (WPI), The University of Tokyo Institutes for
Advanced Study, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
Marianna S. Safronova<EMAIL_ADDRESS>Department of Physics and Astronomy,
University of Delaware, Newark, Delaware 19716, USA  Joint Quantum Institute,
National Institute of Standards and Technology and the University of Maryland,
College Park, Maryland 20742, USA

###### Abstract

Ultralight dark matter (ULDM) particles of mass $m_{\phi}\lesssim 1~{}{\rm
eV}$ can form boson stars in DM halos. Collapse of boson stars leads to
explosive bosenova emission of copious relativistic ULDM particles. In this
work, we analyze sensitivity of terrestrial and space-based experiments to
detect such relativistic scalar ULDM particles interacting through quadratic
couplings with Standard Model constituents, including electrons, photons and
gluons. We highlight key differences with searches for linear ULDM couplings.
Screening of ULDM with quadratic couplings near the surface of the Earth can
significantly impact observations in terrestrial experiments, motivating
future space-based experiments. We demonstrate excellent ULDM discovery
prospects, especially for quantum sensors, which can probe quadratic couplings
orders below existing constraints by detecting bosenova events in the ULDM
mass range $10^{-23}\,{\rm eV}\lesssim m_{\phi}\lesssim 10^{-5}\,{\rm eV}$. We
also report updated constraints on quadratic couplings of ULDM in case it
comprises cold DM.

††preprint: KEK-QUP-2024-0002, KEK-TH-2599, KEK-Cosmo-0338, IPMU24-0004

##  I Introduction

The predominant constituent of matter in the Universe, contributing $\sim$85%,
resides in mysterious dark matter (DM) (see e.g. Ref. Cooley:2022ufh  for an
overview). Despite decades of efforts, DM continues to evade direct detection
aiming to detect DM energy depositions in experiments due to non-gravitational
DM interactions. Significant attention has been devoted to exploring weakly
interacting massive particles, which have typical masses in the range of $\sim
1$ GeV – 100 TeV (see e.g. Ref. Roszkowski:2017nbc ; Schumann:2019eaa  for
reviews). A well-motivated class of DM that has been less studied is
ultralight dark matter (ULDM) ULDM , having mass of $m_{\phi}\lesssim 1\,{\rm
eV}$. With such small constituent masses, the DM is characterised by very
large occupation numbers and behaves like a coherent classical wave (e.g.
Hu:2000ke ; Hui:2016ltb ). The associated direct DM detection signatures are
also distinct.

In the case of scalar ULDM, direct couplings with the Standard Model (SM) can
lead to the variation of fundamental constants, such as the fine-structure
constant $\alpha$. The experimental program searching for scalar ULDM has
particularly benefited from variety of approaches based on high-precision
instruments ULDM ; Antypas:2022asj ; adams2023axion , such as atomic clocks
Beloy:2020tgz ; Filzinger:2023zrs ; Sherrill:2023zah ; 2022PhRvL.129x1301K ;
Hees:2016gop ; Arvanitaki:2014faa ; Aharony:2019iad ; Banerjee:2023bjc ;
SrOH2021 ; Zhang:2022ewz ; Zaheer:2023ulf , optical cavities Kennedy:2020bac ;
Tretiak:2022ndx ; Campbell:2020fvq ; Geraci:2018fax , spectroscopy
Oswald:2021vtc ; VanTilburg:2015oza , mechanical resonators Branca:2016rez ;
Arvanitaki:2015iga ; Manley:2019vxy , optical interferometers Savalle:2020vgz
; Aiello:2021wlp ; Vermeulen:2021epa ; Fukusumi:2023kqd , atom interferometers
Badurina:2021rgt ; 2021QS&T….6d4003A , tests of the equivalence principle (EP)
Hees:2018fpg ; Berge:2017ovy , and fifth force searches Fischbach:1996eq ;
Adelberger:2003zx ; Murata:2014nra  whose complementary sensitivities span and
cover a wide ULDM mass range.

ULDM can form gravitationally-bound boson stars Kaup:1968zz ; Ruffini:1969qy ;
Colpi:1986ye  through both gravitational interactions Levkov:2018kau ;
Chen:2020cef  and the self-interactions of the ULDM field Kirkpatrick:2020fwd
; Chen:2021oot ; Kirkpatrick:2021wwz . In the presence of attractive self-
interactions, the boson star is expected to become unstable once it reaches a
critical mass. This occurs when the density of the boson star increases enough
for the ULDM self-interactions to destablize the previously-established
hydrostatic equilibrium between the boson star’s gravitational and the
gradient energy Chavanis:2011zi ; Chavanis:2011zm ; Eby:2014fya .
Subsequently, the boson star collapses and, due to the same self-interactions,
explodes in a bosenova event, copiously emitting relativistic ULDM scalars
Eby:2016cnq ; Levkov:2016rkk ; Helfer:2016ljl ; Eby:2017xrr . Due to wave-
spreading of relativistic scalar bursts in-flight away from the source the
signal can persist for a significant time, even months to years, as it
traverses terrestrial or space-based experiments Eby:2021ece . In previous
work Arakawa:2023gyq , we explored transient signals from bosenovae,
establishing prospects for enhanced reach in case of dilatonic ULDM couplings
to SM present at first order in the effective field theory (EFT) description.
Some of us also have explored prospects for detection of bosenovae from axion
stars Eby:2021ece . Complementary, relativistic particles originating from
historic bosenova events can contribute to diffuse background with distinct
observable signatures Eby:2024mhd .

In this work we explore the detection prospects for bosenovae focusing on
quadratic couplings of ULDM to the SM. Quadratic couplings could dominate over
linear ULDM couplings in scenarios with additional symmetries, such as a
$\mathbb{Z}_{2}$ symmetry under which ULDM $\phi$ field is odd. This is
readily realized for axions, which transform as a pseudoscalar field under
parity symmetry. As a consequence, axion-like fields including the QCD axion
generically possess quadratic couplings without corresponding linear
“dilatonic” coupling Kim:2022ype ; Beadle:2023flm ; Kim:2023pvt . In contrast
to the analysis of observational bosenova signatures with linear ULDM
couplings to SM Arakawa:2023gyq , quadratic interactions posses additional
phenomenological consequences such as screening of the field in the presence
of matter density Hees:2018fpg .

The paper is organized as follows. First, in Sec. II we describe the EFT
characterizing the ULDM-SM interactions, as well as the self-interaction
coupling. Then, in Sec. III we give an overview of boson stars and bosenovae
which provide the astrophysical signal. Next, in Sec. IV we give an outline of
the detection methods for bosenovae and experimental sensitivities. In Sec. V
we describe implications of our results. We conclude in Sec. VI.

##  II Theoretical Model

###  II.1 Effective interactions

A real scalar field $\phi$ can be generally characterized by a Lagrangian

$\displaystyle\mathcal{L}_{\phi}$
$\displaystyle=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m_{\phi}^{2}\phi^{2}+\frac{\lambda}{4!}\phi^{4}+...$
(1)

where $m_{\phi}$ is the field’s mass and $\lambda$ is the self-interaction
coupling, and the $[\dots]$ indicate possible terms with higher powers of
$\phi$. Here, we consider $\phi$ to constitute ULDM with mass
$m_{\phi}\lesssim{\rm eV}$, and treat $|\lambda|\ll 1$ as a free parameter
that depends on the underlying theory. We focus on parameter space
$\lambda>0$, denoting attractive self-interactions between $\phi$
particles111This is also motivated by some theoretical considerations, see
e.g. Fan:2016rda .. In Sec. II.3 we discuss various constraints on $\lambda$.

Couplings of $\phi$ to the SM, and as a consequence their optimal methods for
detection, will depend on the symmetries such as parity of the model. Axions
and axion-like particles more generally (see e.g. adams2023axion ) are
typically parity-odd, which implies derivative couplings to SM fields. On the
other hand, parity-even fields (see e.g. Antypas:2022asj ) have different
interactions with SM fields. As we discuss below, this leads to distinct
detection prospects and promising search strategies.

We can generally characterize the possible dilatonic-type (i.e. parity-even)
couplings of $\phi$ to the SM by their EFT Lagrangian contributions

$\displaystyle\mathcal{L}_{\text{int}}=\sum_{n,i}d^{(n)}_{i}\bigg{(}\frac{\sqrt{4\pi}\,\phi}{M_{\text{pl}}}\bigg{)}^{n}\mathcal{O}^{i}_{\text{SM}}~{},$
(2)

where $M_{\text{pl}}=1.2\times 10^{19}\,{\rm GeV}$ is the Planck mass and
${\mathcal{O}}_{\rm SM}^{i}$ are dimension-four SM operators labeled by index
$i$. In this parametrization the $d_{i}^{(n)}$ couplings are dimensionless.
Throughout, we will focus on scalars with quadratic $\propto\phi^{2}$
interactions with SM constituents, corresponding to Eq. (2) with $n=2$. In
particular we consider

$\displaystyle\mathcal{L}_{\text{int}}\supset$
$\displaystyle~{}\frac{4\pi\,\phi^{2}}{M_{\text{pl}}^{2}}\bigg{(}d_{m_{e}}^{(2)}m_{e}\overline{e}e-\frac{d_{e}^{(2)}}{4}F_{\mu\nu}F^{\mu\nu}$
$\displaystyle-\frac{d_{g}^{(2)}\beta(g_{s})}{2g_{s}}G_{\mu\nu}^{a}G^{a\mu\nu}\bigg{)}~{},$
(3)

where $d_{m_{e}}^{(2)}$, $d_{e}^{(2)}$ and $d_{g}^{(2)}$ are couplings of
$\phi^{2}$ to SM, $F_{\mu\nu}$ is the electromagnetic field strength tensor,
$G_{\mu\nu}^{a}$ is the quantum chromodynamics (QCD) field strength tensor,
and $e$ is the electron field with mass $m_{e}$. The gluon interactions depend
on the ratio $\beta(g_{s})/g_{s}$ of the QCD beta function to the strong
coupling.

In the presence of the couplings described in Eq. (II.1), classical
oscillations of the ULDM field at frequency of order $m_{\phi}$ lead to
oscillations of the fundamental constants, $m_{e}/m_{p}$ (electron-to-proton
mass ratio), $\alpha$ (fine structure constant), and $m_{q}/\Lambda_{\rm QCD}$
(ratio of quark mass to QCD scale), respectively. As we discuss, this allows
for unique opportunities to search for their manifestations in quantum sensing
experiments. Typically, such searches focus on detecting local DM abundance in
the vicinity of Earth, which is expected to have an energy density of order
$\rho_{\rm DM}\simeq 0.4\,{\rm GeV/cm}^{3}$ Read:2014qva . However, burst
emissions of relativistic ULDM arising from Galactic transient sources
establish novel and unique complementary observational targets Eby:2021ece ;
Arakawa:2023gyq . Previously Arakawa:2023gyq , we analyzed the detection
prospects for ULDM with linear $\propto\phi$ interactions with the SM
constituents, corresponding to $n=1$ case in Eq. (2). In this study, we
analyze the signatures and detection prospects for ULDM scalars with quadratic
SM couplings.

###  II.2 Screening

Figure 1: A pictorial representation of the Earth screening a ULDM wave,
analogous to typical finite width barrier problems in quantum mechanics. Due
to the quadratic $\phi-$SM coupling, the Earth represents a potential barrier,
whose height is equivalent to $V_{\rm
barrier}\equiv\sum_{i}8\pi\,d_{i}^{(2)}\rho_{i}/(m_{\phi}M_{\text{pl}}^{2})$.
If the DM has kinetic energy greater than the height of the potential barrier,
the DM will primarily reflect off the barrier, with an exponentially
suppressed profile inside the Earth.

A distinct consequence of quadratic ULDM couplings to SM is the screening of
$\phi$ fields, arising from an increase in their effective masses in the
presence of large densities of SM fields in various environments Hees:2018fpg
. These effects can lead to significantly decreased sensitivities to such
interactions in cases where critical screening occurs. In particular, for ULDM
couplings proportional to $\phi^{2}$ the presence of SM fields modifies the
effective mass of $\phi$ as

$\displaystyle m_{\rm eff,\phi}^{2}=m_{\phi}^{2}+\Delta m_{{\rm
eff},\phi}^{2}=m_{\phi}^{2}+\sum_{i}\frac{8\pi\,d_{i}^{(2)}\langle\mathcal{O}_{\rm
SM}^{i}\rangle}{M_{\text{pl}}^{2}}~{},$ (4)

where

$\langle\mathcal{O}_{\rm SM}^{i}\rangle\equiv\rho_{i}=\langle
m_{e}\bar{e}e\rangle,~{}\langle-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}\rangle,~{}\langle-\frac{\beta(g_{s})}{2g_{s}}G^{a}_{\mu\nu}G^{a\mu\nu}\rangle$
(5)

are the expectation values of the SM operators in the presence of electron,
photon and gluon SM fields, which represent the energy density of those fields
in a medium. In environments with sufficiently dense SM matter, such as the
Earth, the effective mass of traversing $\phi$ can become greater than its
total energy. This leads to an exponentially decaying field profile inside,
such as in case of the Earth. As we illustrate in Fig. 1, the considered
system can be also viewed akin to a quantum mechanical potential barrier of
finite width whose potential energy is larger than the particle’s kinetic
energy, where the transmission probability of the field in those regions
becomes significantly suppressed. In this case, the potential barrier height
is governed by the change in effective mass between different regions, Eq.
(4).

The critical coupling above which the field $\phi$ becomes exponentially
screened depends on the density of the environment of interest, and for
terrestrial experiments particularly relevant is that of Earth. In the case
where $d_{i}^{(2)}>0$, the characteristic critical coupling is given by

$\displaystyle d_{i}^{(2),\,{\rm
crit}}=M_{\text{pl}}^{2}\frac{1/R^{2}+E_{\phi}^{2}-m_{\phi}^{2}}{8\pi\rho_{i}}\,,$
(6)

where $E_{\phi}=\sqrt{p_{\phi}^{2}+m_{\phi}^{2}}$ is the total energy of
$\phi$ and $R$ is the radius of the Earth, which plays the role of the
potential-barrier width. For terrestrial experiments, the SM energy density
$\rho_{i}\simeq 10^{-4}\rho_{\oplus},10^{-3}\rho_{\oplus},\rho_{\oplus}$ for
the electron, photon, and gluon coupling respectively222These fractions can be
derived from a semi-empirical formula for the distribution of mass and energy
in atoms composing the Earth; see e.g. krane1991introductory ., where
$\rho_{\oplus}\simeq 1-10\,{\rm g/cm}^{3}$ is of order the mass density of
Earth. This sets an upper limit on the coupling that can be probed, for
example, for the gluon coupling it is approximately $d_{g}^{(2),{\rm
crit}}\simeq 10^{8}$ for $m_{\phi}\lesssim 10^{-14}\,{\rm eV}$. The constraint
weakens at larger $m_{\phi}$, due to the finite-size effect becoming
subdominant, i.e. when $E_{\phi}^{2}-m_{\phi}^{2}\equiv p_{\phi}^{2}>1/R^{2}$
in Eq. (6). Analogously, there also exists critical coupling associated with
the dense medium of the experimental apparatus itself. However, it corresponds
to a significantly larger values of the dilatonic coupling. Thus, high-
precision space-based experiments sensitive to smaller couplings that are
unaffected by dense terrestrial environments, are advantageous for probing
broader parameter space of ULDM couplings.

We note that dilatonic ULDM couplings with an opposite, negative, sign can in
principle also appear. This is a more complicated situation with rich
phenomenology, where higher-order effects are expected to be prominent and is
beyond the scope of the present study. Here, we only discuss positive sign
interactions and leave a thorough general investigation of other scenarios for
future work Arakawa_2024 .

###  II.3 Constraints on self-interaction coupling $\lambda$

####  II.3.1 Observational constraints

There are a number of observational constraints on ULDM, which we summarize
below and represent quantitatively in Fig. 3. First, we consider those that
arise purely from gravitational interactions and depend only on the mass
$m_{\phi}$.

  * •

Lyman–$\alpha$: ULDM fields can have significant de Broglie wavelengths that
are relevant on astrophysical scales. Their presence can suppress cosmic
structure growth below certain scales. Observations of the matter power
spectrum using Lyman-$\alpha$ forest neutral hydrogen absorption seen in high-
redshift quasar spectra imply that Irsic:2017yje ; Rogers:2020ltq

$m_{\phi}\gtrsim 10^{-21}\,{\rm eV}\,.$ (7)

  * •

Ultrafaint dwarf (UFD) galaxies: wave-like fluctuations in the ULDM density
field can induce anomalous heating of stellar populations Hui:2016ltb ;
Church:2018sro ; Bar-Or:2018pxz ; Bar-Or:2020tys . Observations of velocity
dispersions in cold UFD galaxies suggest that Dalal:2022rmp

$m_{\phi}\gtrsim 10^{-19}\,{\rm eV}\,.$ (8)

Note that this constraint depends on various assumptions, including that the
DM in the outer regions of considered galaxies is not tidally stripped by
galaxy mergers or encounters (see e.g. DuttaChowdhury:2023qxg ) and that boson
star formation inside does not diminish heating effects. See Ref.
Zupancic:2023qgj  for further discussion.

Additionally, there are variety of observational constraints that depend on
the ULDM self-interaction coupling $\lambda$.

  * •

Bullet Cluster: the distribution of matter in the colliding Bullet Cluster of
galaxies constrains the size of the DM self-interaction cross section
Markevitch:2003at , for ULDM giving

$\lambda\lesssim 10^{-38}\left(\frac{m_{\phi}}{10^{-18}\,{\rm
eV}}\right)^{3/2}\,.$ (9)

  * •

Structure formation: sizable attractive (repulsive) ULDM self-couplings can
lead to enhancement (suppression) of the matter power spectrum on
astrophysical and cosmological scales (e.g. Li:2013nal ; Fan:2016rda ).
Observations on scales of $\mathcal{O}(\textrm{Mpc})$ imply Cembranos:2018ulm

$\lambda\lesssim 3\times 10^{-79}\left(\frac{m_{\phi}}{10^{-18}\,{\rm
eV}}\right)^{4}\,.$ (10)

Such constraints can become even stronger if the growth of structure begins
earlier than the epoch of matter-radiation equality Budker:2023sex .

  * •

Black-hole superradiance (BHSR): rotating black holes can spin down by
copiously generating ULDM particles in a gravitational-atom-like cloud
configuration. Observations of rapidly spinning black holes can thus constrain
existence of such ULDM fields. Astrophysical stellar-mass black holes can
constrain ULDM in the mass range $2\times 10^{-13}\,{\rm eV}\lesssim
m_{\phi}\lesssim 3\times 10^{-12}\,{\rm eV}$ Arvanitaki:2010sy ;
Arvanitaki:2015iga ; Arvanitaki:2016qwi ; Baryakhtar:2020gao , whereas
supermassive black holes are sensitive to $3\times 10^{-21}\,{\rm eV}\lesssim
m_{\phi}\lesssim 2\times 10^{-17}\,{\rm eV}$ Unal:2020jiy . Sizable ULDM self-
interactions can quench the growth of superradiant instability and particle
generation Baryakhtar:2020gao ; Branco:2023frw , alleviating the constraints
when

$|\lambda|\gtrsim 10^{-84}\left(\frac{m_{\phi}}{10^{-18}\,{\rm
eV}}\right)^{5/2}~{}.$ (11)

We stress that the BHSR constraints depend sensitively on challenging
astrophysical measurements and accurate determination of black hole spins,
with high degree of uncertainty.

More detailed discussion of these constraints can be found in Ref.
Arakawa:2023gyq , and references therein. In our sensitivity estimates, we use
the following benchmark for the self-coupling:

$\displaystyle\lambda_{\text{b}}=\displaystyle
10^{-90}\bigg{(}\frac{m_{\phi}}{5\times 10^{-21}\,{\rm eV}}\bigg{)}^{4}\,,$
(12)

which is indicated by a black dashed line in Fig. 3. Given the challenges and
uncertainties associated with establishing robust BHSR bounds, we do not
include them in $\lambda_{b}$ here. In Appendix A (see black dotted line in
Fig. 3) we present results for an alternative analysis with a discontinuous
$\lambda$ benchmark, which is taken to satisfy the expected BHSR limits.

####  II.3.2 Naturalness

The overall $\phi^{4}$ self-interaction in Eq. (1) is generated not only by
the bare parameter $\lambda_{0}$, which originates in the high-energy (UV)
potential of $\phi$, but also by the $\phi$-SM couplings with contributions
arising at loop level; the relevant diagrams at one-loop level are shown in
Fig. 2. We can outline a limitation on $\lambda$ motivated by naturalness,
i.e. by requiring that contributions due to $\phi$-SM interactions at one-loop
level are not significantly greater than the effective coupling $\lambda$,
thus avoiding unnatural cancellation of these contributions with the bare
Lagrangian parameter. We emphasize that the resulting upper limit on $\lambda$
will depend on the unknown dilatonic coupling and more generally does not
constitute a strict bound. Instead, our estimates show a rough guideline for
where the one-loop effects begin to become important.

Figure 2:  One-loop diagrams that generate corrections to ULDM self-
interaction coupling $\lambda$ originating from the quadratic couplings to SM
$d_{m_{e}}^{(2)}$ (top left), $d_{e}^{(2)}$ (top right) and $d_{g}^{(2)}$
(bottom). See Eq. (II.1) of text.

Accounting for the contribution of one-loop diagrams in Fig. 2 at an
ultraviolet (UV) cutoff scale $\Lambda_{\rm UV}$, the quartic coupling scales
as

$\displaystyle\lambda(\Lambda_{\text{UV}})\simeq$
$\displaystyle~{}\lambda(\mu_{0})-\frac{(d^{(2)}_{m_{e}})^{2}m_{e}^{2}}{4\pi^{2}M_{\text{pl}}^{4}}\Lambda_{\text{UV}}^{2}$
$\displaystyle+\frac{(d^{(2)}_{e})^{2}}{8\pi^{2}M_{\text{pl}}^{4}}\Lambda_{\text{UV}}^{4}+\frac{2(d^{(2)}_{g}\beta(g_{s}))^{2}}{\pi^{2}g_{s}^{2}M_{\text{pl}}^{4}}\Lambda_{\text{UV}}^{4}\,,$
(13)

where $\mu_{0}\ll\Lambda_{\rm UV}$ is a reference energy scale. The same
couplings in Eq. (II.1) imply divergent contributions $\delta m_{\phi}^{2}$ to
the the ULDM mass $m_{\phi}$ (see e.g. Craig:2022eqo  for a recent review).
Requiring a “natural” ULDM mass, with corrections being subdominant $\delta
m_{\phi}\lesssim m_{\phi}$, implies

$\displaystyle\Lambda^{m_{e}}_{\text{UV}}$ $\displaystyle\lesssim\frac{2\pi
M_{\text{pl}}m_{\phi}}{m_{e}\sqrt{d_{m_{e}}^{(2)}}}\,,$ (14)
$\displaystyle\Lambda^{e}_{\text{UV}}$
$\displaystyle\lesssim\bigg{(}\frac{8\pi^{2}M_{\text{pl}}^{2}m_{\phi}^{2}}{d_{e}^{(2)}}\bigg{)}^{1/4}\,,$
(15) $\displaystyle\Lambda^{g}_{\text{UV}}$
$\displaystyle\lesssim\bigg{(}\frac{4\pi^{2}M_{\text{pl}}^{2}g_{s}m_{\phi}^{2}}{\beta(g_{s})d_{g}^{(2)}}\bigg{)}^{1/4}\,.$
(16)

Applying these limits to Eq. (II.3.2), the naturalness limits on renormalized
self-couplings are

$\displaystyle\lambda$
$\displaystyle\gtrsim\frac{d^{(2)}_{m_{e}}m_{\phi}^{2}}{M_{\text{pl}}^{2}}\,,$
(17) $\displaystyle\lambda$
$\displaystyle\gtrsim\frac{d^{(2)}_{e}m_{\phi}^{2}}{M_{\text{pl}}^{2}}\,,$
(18) $\displaystyle\lambda$
$\displaystyle\gtrsim\frac{8d^{(2)}_{g}\beta(g_{s})m_{\phi}^{2}}{g_{s}M_{\text{pl}}^{2}}\,.$
(19)

To summarize, a theory with a UV cutoff satisfying Eqs. (14-16) and self-
coupling satisfying Eqs. (17-19) can be considered natural in both its
quadratic (i.e. mass) and quartic (i.e. self-interaction coupling) UV
contributions at one-loop order.

Figure 3: Constraints on ULDM self-interaction $\lambda$ versus mass
$m_{\phi}$. The bounds from the Bullet Cluster (cyan) Markevitch:2003at ,
structure formation (orange) Cembranos:2018ulm , Lyman-$\alpha$ Irsic:2017yje
; Rogers:2020ltq  and ultra-faint dwarf (UFD) galaxies Dalal:2022rmp  (red
vertical thick and dashed lines, respectively), black hole superradiance
Baryakhtar:2020gao ; Unal:2020jiy  (BHSR, brown), as well as the lower bounds
for naturalness arising from $d^{(2)}_{m_{e},e}$ (red), and $d^{(2)}_{g}$
(pink) are shown. The naturalness lines assume benchmark values for the
couplings that are allowed by current experimental observations, as labeled.
We also illustrate the region where critical boson stars would not undergo
bosenova due to general relativistic effects (purple hatched region). The
dashed black line represents the benchmark $\lambda_{b}$ that we choose at
each mass, as given in Eq. (12) and discussed in the Sec. II.3. The dotted
black line shows the benchmark $\lambda_{b}^{\prime}$ we choose when we
consider the BHSR bounds, given in Eq. (30). See text for details.

The constraints from naturalness are shown in Fig. 3 for a benchmark choice of
the dilatonic coupling $d_{i}^{(2)}=10^{-4}$, which is allowed by all current
experimental bounds. We note that dilatonic couplings that are larger than
this are also allowed by experimental constraints at the higher end of the
mass spectrum (see Sec. V for details), and also the dilatonic couplings could
be significantly smaller. The naturalness constraint depends on the choice of
dilatonic coupling linearly, as can be seen from Eqs. (17-19). While we
illustrate constraints from naturalness considerations, we do not consider
them here as strict limits for our choice of benchmark parameter values of
self-interaction coupling $\lambda$.

##  III Boson Stars and Bosenovae

ULDM can form gravitationally-bound objects known as _boson stars_ Kaup:1968zz
; Ruffini:1969qy ; Colpi:1986ye . The most important quantity characterizing a
boson star is its mass $M$, which can grow in astrophysical environments,
through accretion Levkov:2018kau ; Eggemeier:2019jsu ; Chen:2020cef ;
Chan:2022bkz ; Dmitriev:2023ipv  or mergers Mundim:2010hi ; Cotner:2016aaq ;
Schwabe:2016rze ; Eby:2017xaw ; Hertzberg:2020dbk ; Du:2023jxh , until it
reaches a critical value Chavanis:2011zi ; Chavanis:2011zm ; Eby:2014fya

$M_{c}=\frac{10M_{\text{pl}}}{\sqrt{\lambda}}\,,$ (20)

assuming attractive self-interactions $\lambda>0$. Subsequently, the boson
star collapses. In this work, we are interested in transient signals
associated with such events.

Importantly, if $\lambda$ is too small, the corresponding critical radius
$R_{c}\simeq 0.5M_{\text{pl}}\sqrt{\lambda}/m_{\phi}$ of a boson star would be
smaller than its Schwarzschild radius $R_{S}=2M_{c}/M_{\text{pl}}^{2}$. Hence,
we will be interested only in couplings for which the critical radius
satisfies $R_{c}>R_{S}$, which is equivalent to the condition

$\lambda\gtrsim\lambda_{\rm BH}\equiv
40\dfrac{m_{\phi}^{2}}{M_{\text{pl}}^{2}}\,.$ (21)

This limit is illustrated by the shaded purple region in Fig. 3. The benchmark
$\lambda_{b}$ of Eq. (12) can be written as $\lambda_{b}=10\lambda_{\rm BH}$.

When a boson star reaches the critical mass in Eq. (20), it collapses
gravitationally and emits $\mathcal{O}(1)$ of its mass fraction in the form of
semi-relativistic ULDM particles Eby:2016cnq ; Levkov:2016rkk ; Helfer:2016ljl
; Eby:2017xrr . This so-called _bosenova_ emission of energetic particles has
already been established to constitute a novel fruitful source of signatures
that is complementary to the conventional searches for cold DM Eby:2021ece ;
Arakawa:2023gyq .

Key properties of the bosenova emission from a boson star have been obtained
with numerical simulations Levkov:2016rkk . Of interest for our work, the
leading peak of the emission spectrum occurs around particle momentum of
$\bar{k}\simeq 2.4m_{\phi}$ with a spread of $\delta k\simeq m_{\phi}$ (see
also Ref. Eby:2015hyx ; Eby:2017azn ). The total energy emitted in this range
can be estimated as Eby:2021ece ; Arakawa:2023gyq

$\mathcal{E}_{\rm peak}\simeq 10^{3}\frac{m_{\phi}}{\lambda}\,.$ (22)

The emission is expected to be approximately spherically symmetric, and
therefore associated ULDM bursts will travel in spherical waves from the
source to the detector.

After emission, the relativistic ULDM wave will spread in-flight along the
radial direction from the source. We briefly outline the consequences of these
effects below, with a comprehensive discussion given in Ref. Eby:2021ece ;
Arakawa:2023gyq . For emission sources located at astrophysical distances $r$,
the wave spreading spreading in-flight rapidly comes to dominate the intrinsic
burst duration $\delta t_{0}$. This can result in a persistent signal of a
significant duration at detector site

$\delta t\simeq\frac{\delta k}{m_{\phi}}\frac{r}{q^{2}\sqrt{q^{2}+1}}\simeq
0.2\,{\rm year}\left(\frac{r}{\rm pc}\right)\,,$ (23)

where $q\equiv\bar{k}/m_{\phi}\simeq 2.4$ for the bosenova. Eq. (23) indicates
the timescales on which the relativistic bosenova waves can interact in the
detector. Since the signal duration is significantly protracted, one can
benefit from long integration time as the burst passes through the experiment,
as opposed to searching only for a signal from the leading edge of the
wavefront. The typical energy density of a bosenova at the detector site,
taking into account wave spreading in-flight, is given by

$\rho_{*}=\frac{\mathcal{E}_{\rm peak}}{4\pi r^{2}\delta x}\simeq 3\rho_{\rm
DM}\left(\frac{m_{\phi}}{10^{-15}\,{\rm
eV}}\right)\left(\frac{10^{-80}}{\lambda}\right)\left(\frac{\rm
pc}{r}\right)^{3}\,,$ (24)

where $\delta x\simeq\delta t$ is the spatial spread of the wave, and we have
normalized to the background DM density to the local DM density near the
vicinity of Earth $\rho_{\rm DM}\simeq 0.4\,{\rm GeV/cm}^{3}$ (see e.g.
Read:2014qva ).

Another important consequence of the wave spreading is that the momentum modes
in the wave become increasingly separated. Hence, the energy deposited in a
given detector will “chirp” from high to low frequency over timescales $\delta
t$. Although the wave is incoherent at the source, due to this spreading of
momentum modes, at any given time the wavefront depositing energy in the
detector can posses significant degree of coherence. The effective coherence
timescale for the bosenova, after traveling a distance $r$, is given by
Eby:2021ece

$\tau_{*}\simeq\frac{2\pi r}{q^{3}\xi}\simeq 4\times 10^{-3}\,{\rm
year}\left(\frac{r}{\rm pc}\right)\,,$ (25)

where $\xi\equiv m_{\phi}\delta t_{0}\simeq 400$ is linked to the intrinsic
burst duration $\delta t_{0}$ of the emission. This can be compared to the
typical coherence time in the DM signal, $\tau_{\rm DM}\simeq
2\pi/(m_{\phi}v_{\rm vir}^{2})\simeq 10^{7}/m_{\phi}$, where $v_{\rm
vir}\simeq 10^{-3}$ is the virial velocity of the DM.

Combining the results above, for a given direct DM detection experiment we can
relate its sensitivity to a bosenova signal, characterized by the coupling
$d^{(2)}_{i,*}$, to its sensitivity expected for a cold DM signal,
characterized by $d^{(2)}_{i,{\rm DM}}$. The ratio is given by

$\frac{d^{(2)}_{i,*}}{d^{(2)}_{i,{\rm DM}}}\simeq\frac{\rho_{\rm
DM}}{\rho_{*}}\frac{t_{\rm int}^{1/4}{\rm min}\left(\tau_{\rm DM}^{1/4},t_{\rm
int}^{1/4}\right)}{{\rm min}\left((\delta t)^{1/4},t_{\rm
int}^{1/4}\right){\rm min}\left(\tau_{*}^{1/4},t_{\rm int}^{1/4}\right)}\,,$
(26)

where $t_{\rm int}$ is the livetime of the experiment, which we assume to be
$t_{\rm int}=1$ year. Note that both sensitivities should be evaluated at the
same frequency $E_{\phi}$, which will correspond to different $m_{\phi}$
shifted by $\bar{k}/m_{\phi}\simeq\mathcal{O}({\rm few})$ in this case, i.e.
$E_{\phi}\simeq m_{\phi}$ for cold DM and
$E_{\phi}=\sqrt{\bar{k}^{2}+m_{\phi}^{2}}\simeq 2.6\,m_{\phi}$ for the
bosenova peak described above. When Eq. (26) is smaller than unity, a given
experiment can probe couplings with higher sensitivity for a bosenova signal,
if such occurs during the experimental livetime within a distance $r$, than to
the cold DM signal.

The expected rate of bosenovae in the Galaxy is a complex topic worthy of a
dedicated study beyond the scope of the present work. The predictions depend
on variety of considerations including cosmological evolution
Gorghetto:2018myk ; Vaquero:2018tib ; Buschmann:2019icd ; Gorghetto:2020qws ;
Buschmann:2021sdq ; Saikawa:2024bta  and structure formation Schive:2014hza ;
Schive:2014dra ; Mocz:2017wlg ; Schwabe:2020eac ; Nori:2020jzx  for ULDM, as
well as details of boson star formation Levkov:2018kau ; Chen:2020cef ;
Kirkpatrick:2020fwd ; Chen:2021oot ; Kirkpatrick:2021wwz , tidal stripping
Dokuchaev:2017psd ; Kavanagh:2020gcy ; Edwards:2020afl , accretion
Eggemeier:2019jsu ; Chan:2022bkz ; Dmitriev:2023ipv  and mergers Mundim:2010hi
; Cotner:2016aaq ; Schwabe:2016rze ; Eby:2017xaw ; Hertzberg:2020dbk ;
Du:2023jxh , among others. See also Refs. Eby:2021ece ; Arakawa:2023gyq  for
further discussion.

##  IV Detection

###  IV.1 Detection methods

A variety of distinct experiments can sensitively probe variations in
fundamental constants that can result from ULDM interactions with SM,
including the fine-structure constant $\alpha$. We refer to Ref.
Antypas:2022asj  for detailed discussion of experimental probes, and below
summarize the searches which are relevant to our results discussed in Sec. V.

  * •

Atomic, molecular and nuclear clocks: Atomic, molecular, and nuclear energy
levels depend on fundamental constant values, with variations resulting in
observable modification of clock frequency ratios. Comparing ratios between
distinct clocks allows for unique probes of new physics interactions. Clock
that are based on transitions between different electronic configurations are
referred to as “optical” clocks. Microwave clocks are based on transitions
between atomic ground state hyperfine substates. Molecular clocks are based on
various transitions in molecules and molecular ions. All of the clock
comparisons experiments are sensitive to $d_{e}$. Optical clock frequency
ratios are also sensitive to $d_{g}$ via the oscillating nuclear radius
Banerjee:2023bjc . Optical to microwave clock comparisons are sensitive to
$d_{m_{e}}$ and $d_{g}$ in addition to $d_{e}$.

Limits to $d_{m_{e}}$ include 133Cs/87Rb atomic fountain clock frequency ratio
Hees:2016gop , frequency comparison between 171Yb optical lattice clock and
133Cs fountain microwave clock 2022PhRvL.129x1301K , and a comparison of Rb
hyperfine transition with quartz oscillator Zhang:2022ewz .

The limits on $d_{e}$ come from frequency ratio measurements of 27Al+, 171Yb
and 87Sr optical clocks (BACON) Beloy:2020tgz , frequency ratios of the E3
transition in a single-ion 171Yb+ clock with E2 transition in the same ion and
with and 171Yb+ 87Sr optical lattice clock Filzinger:2023zrs , and a dynamical
decoupling demonstration in Sr+ trapped ion clock transition Aharony:2019iad .

The limits on $d_{g}$ come from the 133Cs/87Rb atomic fountain clock frequency
ratio Hees:2016gop , the limits from oscillating nuclear radius effects in
171Yb+ ion clock Banerjee:2023bjc , and 171Yb optical lattice clock and 133Cs
fountain microwave clock comparison 2022PhRvL.129x1301K . A significant
improvement in $d_{m_{e}}$ limits is expected with the SrOH molecular
experiment SrOH2021 . Very high sensitivity to variation of fundamental
constants is expected of nuclear clock 2021Peik , which rely on a nuclear
transition in 229Th, leading to potential orders of magnitude improvement in
$d_{e}$ and $d_{g}$ Antypas:2022asj .

  * •

Optical cavities: Variations of fundamental constants can induce modifications
of physical dimensions of solid objects, which can be observable when sound
waves propagate through objects faster than the relaxation response time.
Effects of ULDM can be sensitively probed by cavity reference frequency
comparisons. H-maser comparison with a Si cavity Kennedy:2020bac  provides
limits to $d_{m_{e}}$ and $d_{g}$, comparison of Cs frequency with a cavity
Tretiak:2022ndx  is sensitive to $d_{m_{e}}$ and $d_{e}$, while frequency
comparisons of strontium optical clock with silicon cavity Kennedy:2020bac ,
and H-maser and sapphire oscillator with quartz oscillator Campbell:2020fvq
are sensitive to $d_{e}$. A proposal for a future cavity experiment
Geraci:2018fax  offers sensitivity to $d_{m_{e}}$ in a different mass range to
the current optical cavity searches.

  * •

Spectroscopy: Variations in fundamental constants due to ULDM-SM couplings
that lead to observable signatures in atomic and molecular spectra are the
basis of clock searches. However, other spectroscopy experiments can also be
used for this purpose. These include molecular spectroscopy of iodine molecule
Oswald:2021vtc , frequency comparisons of 164Dy with quartz oscillator
Zhang:2022ewz , and between two isotopes of dysprosium (Dy/Dy)
VanTilburg:2015oza , which are all sensitive to $d_{e}$.

  * •

Mechanical resonators: Both torsion balances and optical-cavity-based UDM
searches involve the measurement of the deformation of an elastic body (the
mechanical response) produced by a weak force Antypas:2022asj . The
deformation can be amplified by a factor as large as the resonance Q factor if
the body has internal resonances at the ULDM Compton frequency, yielding
massive sensitivity enhancement over a narrow bandwidth.

Results from AURIGA Branca:2016rez  were used to put constraints on ULDM-SM
coupling. Future experiments include DUAL gravitational wave detector
Arvanitaki:2015iga  and compact acoustic resonators composed of superfluid
Helium and crystals (Sapphire, Pillar, Quartz) Manley:2019vxy  sensitive to
both $d_{m_{e}}$ and $d_{e}$.

  * •

Optical interferometers: Modern optical interferometers can operate beyond the
quantum shot-noise limit, thus offering high sensitivity to minute changes in
the optical path length of their arms. Such interferometers have been used to
search for and detect gravitational waves. Variations in fundamental constants
due to ULDM would manifest as changes in electronic modes and lattice spacing
of materials, leading to measurable change in size and refractive index of the
interferometer. Using this principle, DAMNED Savalle:2020vgz , Fermi Holometer
Aiello:2021wlp , GEO 600 Vermeulen:2021epa  and LIGO O3 Fukusumi:2023kqd  have
been used to constrain ULDM couplings to electrons and photons.

  * •

Atom interferometers: Atom interferometers involve splitting of matter waves
and recombining them using coordinated laser pulses. Particularly high
sensitivity can be achieved for large-scale interferometers, prompting
considerations of space-based interferometers. Here, we consider projected
constraints on $d_{m_{e}}$ and $d_{e}$ from terrestrial AION and space-based
AEDGE Badurina:2021rgt , and terrestrial MAGIS 2021QS&T….6d4003A  proposals.

We refer to the searches above as _direct DM (DDM) searches_ due to the nature
of their coupling directly to the DM background (see Sec. IV.2 for details).
In addition to these direct searches, there are searches for ULDM emission or
absorption in physical systems, which are outlined below. As we will explain
in Sec. IV.2, the sensitivity of such probes will scale differently with the
local DM density compared to direct searches.

  * •

Equivalence-principle tests: Ultralight scalars can induce violations in the
Einstein equivalence principle (EP). Torsion balances can measure difference
in forces acting on massive objects, and thus can be used to test EP
violation, such as the E$\ddot{\rm{o}}$t-Wash experiment Hees:2018fpg , which
gives constraints on $d_{m_{e}}$ and $d_{e}$. The space-based MICROSCOPE
experiment tests the same by measuring the difference in accelerations of two
freely-falling objects of differing composition in orbit around the Earth
Berge:2017ovy , and is sensitive to $d_{m_{e}}$, $d_{e}$ and $d_{g}$.

  * •

Fifth-force tests: Scalar coupling to SM fields can lead to Yukawa-type
interaction between matter, modifying Newton’s law of universal gravitation.
Tests of such “fifth forces” can constrain linear ULDM-SM couplings
Fischbach:1996eq ; Murata:2014nra .

  * •

Astrophysical bounds: Massive self-interacting ultralight fields contribute to
the evolution of the matter power spectrum (see our previous work for more
details Arakawa:2023gyq ). We have outlined several astrophysical constraints
on the ULDM parameter space in Sec. II.3. Constraints on photon emissivity in
supernova cores from astrophysical observations can also be used to constrain
ULDM-photon coupling Olive:2007aj .

Figure 4: The sensitivity ratio of a given DM-SM coupling for a burst search
$d_{i,*}$ compared to a DM search $d_{i}$, using Eq. (26), is depicted in the
allowed parameter space $m_{\phi}$ vs $\lambda$. The white dotted line
represents equal sensitivity to bosenova and DM. Two choices for the distance
to the bosenova are illustrated: $r=\rm{pc}$ (left) and $r=\rm{kpc}$ (right).
See Sec. II.3 and Fig. 3 for a discussion of constraints.

###  IV.2 Differences with linear couplings

Comparing to linear interactions, experimental sensitivities to fifth-forces
and equivalence-principle (EP) violation are drastically modified for
quadratic interactions. For linear interactions, long-range forces mediated by
$\phi$ arise at tree-level. However, for quadratic interactions, they are
loop-level processes, and require the exchange of two $\phi$ fields at a
vertex. The long-range effective force between the Earth and each test mass
therefore depends on the background density of dark matter nearby.

To analyze the difference quantitatively, we estimate the acceleration of test
masses near the Earth as

$\displaystyle|\vec{a}|\simeq\tilde{\alpha}(\phi)(\nabla\phi+\vec{v}\dot{\phi})\,,$
(27)

where $\tilde{\alpha}(\phi)\propto\phi$ is a coupling function (for details,
see Refs. Banerjee:2022sqg ; Hees:2018fpg ; Damour:2010rm ; Damour:2010rp ).
The differential acceleration between two test masses is generated by the
gradient of the $\phi$ profile caused by massive nearby objects. EP violation
experiments seek to measure the difference in gravitational acceleration
experienced by test masses with different compositions. In this case, the
central body corresponds to the Earth, which generates a significant gradient.
Because of this, EP tests depend on the $\phi$ background, and there exists an
effective long-range force. However, fifth-force searches, search for a
violation of the inverse square law between two test masses on small scales,
where the gradient in the $\phi$ profile generated by the test masses is
negligible. As a consequence, the fifth force searches rely purely on the
quantum potential, $V_{\phi^{2}}(r)\sim r^{-3}$ Banerjee:2022sqg , leading to
significant suppression of their sensitivity.

The ratio of sensitivities of a given experiment to the dilatonic couplings of
ultralight scalar dark matter to SM fields ($i\in(m_{e},e,g)$) for the
quadratic and linear cases is (see Banerjee:2022sqg )

$\displaystyle\left(\frac{d_{i}^{(2)}}{d_{i}^{(1)}}\right)_{\rm EP}$
$\displaystyle=\frac{M_{\rm Pl}m_{\phi}}{\sqrt{\rho_{\rm DM}}}\,,$ (28)
$\displaystyle\left(\frac{d_{i}^{(2)}}{d_{i}^{(1)}}\right)_{\rm DDM}$
$\displaystyle=2^{3/2}\frac{M_{\rm Pl}m_{\phi}}{\sqrt{\rho_{\rm DM}}}\,,$ (29)

for EP-type and direct dark matter detection experiments. In our results, all
experimental lines scale from the linear case in either of these two ways.
Astrophysical observational bounds due to Lyman-$\alpha$ forest Irsic:2017yje
; Rogers:2020ltq , UFDs Dalal:2022rmp  and supernova constraints on
$\gamma\gamma\to\phi\phi$ Olive:2007aj  are analogous to the case of linear
couplings.

Finally, the quadratic coupling case can induce screening of the field (as
discussed in Sec. II), which is not the case for linear couplings. The
terrestrial experiments are therefore at a disadvantage because they cannot
probe arbitrarily large dilatonic couplings, and must reach sensitivities
beyond the critical dilatonic coupling in Eq. (6). All direct-detection and EP
experiments that are based on the Earth are subject to this screening, which
provides important motivation for future space-based searches.

##  V Results

We find that bosenovae can lead to large enhancements of the ULDM density at
experimental site in a wide range of the parameter space. Our results
complement those of Ref. Arakawa:2023gyq  that analyzed bosenovae signatures
for linear ULDM couplings to SM constituents. However, in our studied case of
quadratic couplings, the signal enhancement is greater than for linear
couplings. This is because the sensitivity reach of quadratic couplings
follows a scaling relation of $d^{(2)}_{i,*}/d^{(2)}_{i,{\rm DM}}\sim\rho_{\rm
DM}/\rho_{*}$, as opposed to $d^{(1)}_{i,*}/d^{(1)}_{i,{\rm
DM}}\sim\sqrt{\rho_{\rm DM}/\rho_{*}}$ for linear couplings Arakawa:2023gyq .
We demonstrate the sensitivity enhancement in the case of a bosenova search
using Eq. (26) for the parameter space of $m_{\phi}-\lambda$ plane in Fig. 4.
The region below the dotted white line indicates $d_{i,*}^{(2)}/d_{i,{\rm
DM}}^{(2)}<1$, implying improved sensitivity to a bosenova search provided
that such a transient event occurs within distance $r$ from detector. We find
that the reach for ULDM dilatonic couplings could be over 10 orders of
magnitude better than that of cold DM in case of a bosenova occurring below
$\lesssim$ kpc of experimental site.

In Figs. 5, 6, and 7, we display the electron ($d^{(2)}_{m_{e}}$), photon
($d_{e}^{(2)}$), and gluon ($d_{g}^{(2)}$) ULDM coupling reach associated with
bosenova events as a function of $E_{\phi}=2.6\,m_{\phi}$, where the energy of
the scalar field is identified with the expected from simulations leading peak
in the emission spectrum from a boson star explosion Levkov:2016rkk . We
showcase results for two benchmark distances between the Earth and the
bosenova of $r=1~{}{\rm pc}$ (dashed black) and $r=1~{}{\rm kpc}$ (dotted
black), considering reference coupling $\lambda$ from Eq. (12). Each figure
displays four panels, separated by the current (left column) and the projected
(right column) experiments, and terrestrial (top row) as well as space-based
(bottom row) experiments. The terrestrial experiments are subject to screening
due to the Earth, demonstrated by the light blue hashed critical screening
region, while the space-based experiments are not. Since the screening by
Earth creates an upper bound on dilatonic couplings able to be probed by
terrestrial experiments, we cut off the black lines if they continue above the
screening region. We also represent the region where BHSR bounds would affect
the results, without taking them into account for our benchmark (see Sec.
II.3). We discuss the results with the BHSR constraints included in App. A.

We note that the astrophysical constraints coming from Lyman-$\alpha$ and
ultra-faint dwarf galaxies (UFDs) described in Sec. II.3 rely on the
assumption that $\phi$ comprises the entirety of the DM abundance. Hence, they
become weaker or even disappear if $\phi$ represents a sub-leading
contribution to the total DM density. The laboratory bounds therefore give
complementary constraints on such mass regions.

Figure 5: Current and projected bounds on $d_{m_{e}}^{(2)}$ from terrestrial
and space-based experiments as a function of $E_{\phi}$. The best bounds for
each mass are depicted by the solid black lines. The dashed and dotted black
lines indicate the potential reach for detection of bosenovae at distances of
$r=$ pc and kpc from the Earth, respectively. We choose $\lambda=\lambda_{b}$
in Eq. (12), as explained in the text. Current experiments consist of various
detector types. The following are terrestrial experiments contributing to
current bounds. Clocks: Frequency comparison between 171Yb optical lattice
clock and 133Cs fountain microwave clock (Yb/Cs) 2022PhRvL.129x1301K ,
comparison between 87Rb hyperfine transition and quartz mechanical oscillator
(Rb/Quartz) Zhang:2022ewz ; Optical cavities: H-maser comparison with a Si
cavity (H/Si) Kennedy:2020bac , comparison between Cs clock and a cavity
(Cs/Cav) Tretiak:2022ndx , and comparison of a H-maser and sapphire oscillator
with a quartz oscillator (H/Quartz/Sapphire) Campbell:2020fvq ; Spectroscopy:
Molecular iodine spectroscopy (I2) Oswald:2021vtc ; Mechanical Oscillators:
Resonant mass detector (AURIGA) Branca:2016rez ; Optical interferometers:
Unequal delay interferometer experiment (DAMNED) Savalle:2020vgz , co-located
Michelson interferometers (Holometer) Aiello:2021wlp , GEO600
Vermeulen:2021epa , LIGO O3 Fukusumi:2023kqd ; and Equivalence-principle
tests: E$\ddot{\rm{o}}$t-Wash Hees:2018fpg . The only current space-based
bound comes from a search for EP violation (MICROSCOPE Berge:2017ovy ). Future
terrestrial experiments include 88Sr+ optical clock and 133Cs fountain atomic
clock comparison Arvanitaki:2014faa , SrOH molecular clock SrOH2021 , optical
cavities Geraci:2018fax , resonant-mass detectors (DUAL Arvanitaki:2015iga ),
other mechanical resonators (Sapphire, Pillar, Quartz and Superfluid Helium
Manley:2019vxy ), and atom interferometery (AION Badurina:2021rgt , MAGIS
2021QS&T….6d4003A ). Future space-based bounds come from atom interferometery
(AEDGE Badurina:2021rgt ). Lyman-$\alpha$ Irsic:2017yje ; Rogers:2020ltq  and
ultra-faint dwarf galaxies (UFDs) Dalal:2022rmp  also constrain ULDM. In cyan,
we show the region of the parameter space critically screened by the Earth, as
discussed in Sec. II.2. Finally, the regions of the parameter space
corresponding to the black hole superradiance (BHSR) bounds Baryakhtar:2020gao
; Unal:2020jiy  are displayed at the bottom of the plots by the arrows. In the
terrestrial plots, we also show the region of parameter space critically
screened by the Earth in cyan. See Sec. II.2 for a detailed discussion of
screening of quadratically-coupled scalars. Figure 6: Current and projected
bounds on $d^{(2)}_{e}$ from terrestrial and space-based experiments as a
function of $E_{\phi}$. The best bounds for each mass are depicted by the
solid black lines. The dashed and dotted black lines indicate the potential
reach for detection of bosenovae at distances of $r=$ pc and kpc from the
Earth, respectively. We choose $\lambda=\lambda_{b}$ in Eq. (12), as explained
in the text. Current experiments consist of various detector types. The
following are terrestrial experiments contributing to current bounds. Clocks:
Frequency ratios of 27Al+, 171Yb and 87Sr optical clocks (BACON) Beloy:2020tgz
, frequency ratios of E2/E3 transitions in a single-ion 171Yb+ clock and Yb+
with 87Sr optical lattice clock (PTB) Filzinger:2023zrs , dual 133Cs/87Rb
atomic fountain clock frequency ratio (Rb/Cs) Hees:2016gop , and dynamical
decoupling in trapped ion clock transition (DD) Aharony:2019iad ; Optical
cavities: Frequency comparisons between Strontium optical clock and Silicon
cavity (Sr/Si) Kennedy:2020bac , atomic spectroscopy in Cesium vapor with
Fabry-Perot cavity locked to laser (Cs/Cav) Tretiak:2022ndx  and frequency
comparison of Hydrogen maser and sapphire oscillator with quartz oscillator
(H/Quartz/Sapphire) Campbell:2020fvq ; Spectroscopy: Spectroscopic experiments
of molecular iodine (I2) Oswald:2021vtc , frequency comparison of 164Dy with
quartz oscillator (Dy/Quartz) Zhang:2022ewz , precision spectroscopy
measurements involving two isotopes of dysprosium (Dy/Dy) VanTilburg:2015oza ;
Mechanical resonators: Resonant mass detector (AURIGA) Branca:2016rez ;
Optical interferometers: Three-arm Mach-Zender interferometer (DAMNED)
Savalle:2020vgz , co-located Michelson interferometers (Holometer)
Aiello:2021wlp , GEO 600 Vermeulen:2021epa  and LIGO O3 Fukusumi:2023kqd ; and
Equivalence-principle tests: Test of equivalence principle violation by
E$\ddot{\rm{o}}$t-Wash Hees:2018fpg . The space-based experimental bound also
comes from an equivalence-principle test: MICROSCOPE Berge:2017ovy . Future
terrestrial experiments include Thorium Nuclear Clock projections
Antypas:2022asj , resonant-mass detectors DUAL Arvanitaki:2015iga , mechanical
resonators (Sapphire, Pillar, Quartz and Superfluid Helium) Manley:2019vxy ,
and atom interferometers AION Badurina:2021rgt  and MAGIS 2021QS&T….6d4003A .
Future space-based bounds come from atom interferometer AEDGE Badurina:2021rgt
. In cyan, we show the region of the parameter space critically screened by
the Earth, as discussed in Sec. II.2. Lyman-$\alpha$ Irsic:2017yje ;
Rogers:2020ltq , ultra-faint dwarf galaxies (UFDs) Dalal:2022rmp , and
Supernova observations Olive:2007aj  also constrain ULDM. Finally, the regions
of the parameter space corresponding to the black hole superradiance (BHSR)
bounds Baryakhtar:2020gao ; Unal:2020jiy  are displayed at the bottom of the
plots by the arrows. In the terrestrial plots, we also show the region of
parameter space critically screened by the Earth in cyan. See Sec. II.2 for a
detailed discussion of screening of quadratically-coupled scalars. Figure 7:
Current and projected bounds on $d^{(2)}_{g}$ from terrestrial and space-based
experiments as a function of $E_{\phi}$. The best bounds for each mass are
depicted by the solid black lines. The dashed and dotted black lines indicate
the potential reach for detection of bosenovae at distances of $r=$ pc and kpc
from the Earth, respectively. We choose $\lambda=\lambda_{b}$ in Eq. (12), as
explained in the text. The terrestrial experiments contributing to current
bounds on $d_{g}^{(2)}$ include Clocks: 171Yb lattice clock - 133Cs microwave
clock comparison (Yb/Cs) 2022PhRvL.129x1301K , frequency comparison in dual
rubidium-caesium cold atom clock (Rb/Cs) Hees:2016gop  and Yb+ ion clock
Banerjee:2023bjc ; and Optical cavities: H-maser comparison with a Si cavity
(H/Si) Kennedy:2020bac ; while space-based current bound comes from
Equivalence-principle tests: MICROSCOPE Berge:2017ovy . Future experiment
projections are for the 229Th nNuclear cClock Antypas:2022asj  and 171Yb+ ion
clock Banerjee:2023bjc . Note: The Nuclear Clock line in previous estimates is
cut off at $10^{-21}~{}\rm eV$, due to the Lyman-$\alpha$ constraint. However,
there is no reason that the experiment cannot be run to search for lower mass
range, as in $\rm Yb^{+}$ experiment. Therefore, we extrapolate linearly to
lower masses. We are not aware of any space-based planned experiments that
will constrain $d^{(2)}_{g}$. In cyan, we show the region of the parameter
space critically screened by the Earth, as discussed in Sec. II.2.
Lyman-$\alpha$ Irsic:2017yje ; Rogers:2020ltq  and ultra-faint dwarf galaxies
(UFDs) Dalal:2022rmp  also constrain ULDM. Finally, the regions of the
parameter space corresponding to the black hole superradiance (BHSR) bounds
Baryakhtar:2020gao ; Unal:2020jiy  are displayed at the bottom of the plots by
the arrows. In the terrestrial plots, we also show the region of parameter
space critically screened by the Earth in cyan. See Sec. II.2 for a detailed
discussion of screening of quadratically-coupled scalars.

##  VI Conclusions

ULDM can form macroscopic long-lived bound boson star configurations. Their
violent bosenova explosions in the presence of attractive ULDM self-
interactions result in copious emissions of relativistic particles. These
transient events provide intriguing novel targets for ULDM searches, with
enhanced densities compared to cold DM at experimental sites that can persist
for months or even years. We find that such sources can increase the reach of
current and future experiments aiming to detect ULDM by many orders of
magnitude across the range of masses $10^{-23}\,{\rm eV}\lesssim
m_{\phi}\lesssim 10^{-5}$ eV. This work initiates further studies that will
explore detectable signatures from distinct transient sources for ULDM.

We observe that phenomenon of screening can significantly diminish ULDM
detection prospects for sizable quadratic couplings to SM. This motivates
further developments of space-based experiments that will avoid screening
associated with the Earth affecting terrestrial experiments. Further, our
analysis highlights that there is a ULDM parameter gap where there are no
existing or planned space-based experiments that are sensitive to the larger
mass range of $m_{\phi}\gtrsim 10^{-10}~{}{\rm eV}$.

## Acknowledgements

We thank Abhishek Banerjee, Gilad Perez, and Yevgeny Stadnik for useful
discussions. This work was supported in part by the NSF QLCI Award OMA -
2016244, NSF Grant PHY-2012068, and the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation program (Grant
Number 856415). JA thanks the International Center for Quantum-field
Measurement Systems for Studies of the Universe and Particles (QUP) for the
warm hospitality and exciting research environment. The work of JE and VT was
supported by the World Premier International Research Center Initiative (WPI),
MEXT, Japan, and by the JSPS KAKENHI Grant Numbers 21H05451 (JE), 21K20366
(JE) and 23K13109 (VT). The work of JE was also supported by the Swedish
Research Council (VR) under grants 2018-03641 and 2019-02337. This research
was supported in part by the INT’s U.S. Department of Energy grant No. DE-
FG02- 00ER41132. This article is also based upon work from COST Action COSMIC
WISPers CA21106, supported by COST (European Cooperation in Science and
Technology).

##  Appendix A Results with Superradiance Bounds

In the main text, our benchmark choice $\lambda=\lambda_{b}$ in Eq. (12) did
not account for the existence of black hole superradiance (BHSR) constraints
from rapidly-rotating black holes, discussed in Sec. II.3. In the presence of
BHSR limits, we can instead use a discontinuous benchmark of the form

$\displaystyle\lambda_{\text{b}}^{\prime}=\begin{cases}\displaystyle 3\times
10^{-73}\bigg{(}\frac{m_{\phi}}{10^{-13}\,{\rm
eV}}\bigg{)}^{6}\,,&\displaystyle 2\times 10^{-13}\lesssim\frac{m_{\phi}}{\rm
eV}\lesssim 3\times 10^{-12}\\\ \\\ \displaystyle
10^{-90}\bigg{(}\frac{m_{\phi}}{5\times 10^{-21}\,{\rm
eV}}\bigg{)}^{4}\,,&\displaystyle 3\times 10^{-21}\lesssim\frac{m_{\phi}}{\rm
eV}\lesssim 2\times 10^{-17}\\\ \\\ \displaystyle
10\,\lambda_{\text{BH}}\,,&{\rm elsewhere}\end{cases}\,.$ (30)

This benchmark traces the BHSR bounds, where applicable, as in the dotted line
in Fig. 3. The two discontinuities arise from observations of stellar-mass
black holes in the range $m_{\phi}\simeq 3\times 10^{-13}-3\times
10^{-12}~{}{\rm eV}$ Baryakhtar:2020gao  and supermassive black holes in the
range $m_{\phi}\simeq 3\times 10^{-21}-2\times 10^{-17}~{}{\rm eV}$
Unal:2020jiy . As with Eq. (12), this benchmark is chosen to illustrate the
maximum detection prospects, since smaller values of $\lambda$ lead to larger
bosenova energy density (see Eq. (24)).

Using the modified benchmark $\lambda_{b}^{\prime}$, we illustrate current and
projected bosenovae bounds on the quadratic scalar-electron, scalar-photon and
scalar-gluon ULDM couplings in Figs. 8, 9 and 10, respectively.

Figure 8: Current and projected bounds on $d_{m_{e}}^{(2)}$ from terrestrial
and space-based experiments as a function of $E_{\phi}$ including BHSR in
$\lambda$ benchmark given in Eq. (30). The strongest limits for each mass are
depicted by the solid black lines. The dashed and dotted black lines indicate
the potential reach for detection of bosenovae at distances of $r=$ pc and kpc
from the Earth, respectively. See Fig. 5 and Sec. IV for details and
references of experimental lines. Figure 9: Current and projected bounds on
$d_{e}^{(2)}$ from terrestrial and space-based experiments as a function of
$E_{\phi}$ including BHSR in $\lambda$ benchmark given in Eq. (30). The
strongest limits for each mass are depicted by the solid black lines. The
dashed and dotted black lines indicate the potential reach for detection of
bosenovae at distances of $r=$ pc and kpc from the Earth, respectively. See
Fig. 6 and Sec. IV for details and references of experimental lines. Figure
10: Current and projected bounds on $d_{g}^{(2)}$ from terrestrial and space-
based experiments as a function of $E_{\phi}$ including BHSR in $\lambda$
benchmark given in Eq. (30). The strongest limits for each mass are depicted
by the solid black lines. The dashed and dotted black lines indicate the
potential reach for detection of bosenovae at distances of $r=$ pc and kpc
from the Earth, respectively. See Fig. 7 and Sec. IV for details and
references of experimental lines.

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