Search for subsolar-mass black hole binaries in the second part of Advanced LIGO’s and Advanced Virgo’s third observing run

We describe a search for gravitational waves from compact binaries with at least one component with mass 0 . 2–1 . 0 M (cid:2) and mass ratio q ≥ 0.1 in Advanced Laser Interferometer Gra vitational-Wa ve Observ atory (LIGO) and Adv anced Virgo data collected between 2019 No v ember 1, 15:00 UTC and 2020 March 27, 17:00 UTC . No signals were detected. The most signiﬁcant candidate has a false alarm rate of 0 . 2 yr − 1 . We estimate the sensitivity of our search o v er the entirety of Advanced LIGO’s and Advanced Virgo’s third observing run, and present the most stringent limits to date on the merger rate of binary black holes with at least one subsolar-mass component. We use the upper limits to constrain two ﬁducial scenarios that could produce subsolar-mass black holes: primordial black holes (PBH) and a model of dissipative dark matter. The PBH model uses recent prescriptions for the merger rate of PBH binaries that include a rate suppression factor to ef fecti vely account for PBH early binary disruptions. If the PBHs are monochromatically distributed, we can exclude a dark matter fraction in PBHs f PBH (cid:2) 0 . 6 (at 90 per cent conﬁdence) in the probed subsolar-mass range. Ho we ver, if we allow for broad PBH mass distributions, we are unable to rule out f PBH = 1. F or the dissipativ e model, where the dark matter has chemistry that allows a small fraction to cool and collapse into black holes, we ﬁnd an upper bound f DBH < 10 − 5 on the fraction of atomic dark matter collapsed into black holes.


INTRODUCTION
The Advanced LIGO (Aasi et al. 2015) and Advanced Virgo (Acernese et al. 2015) detectors have completed three observing runs, O1, O2, and O3 (split into O3a and O3b), since the first observation of gravitational waves from a binary black hole (BBH) coalescence (Abbott et al. 2016b).The collected data have been analyzed by the LIGO-Virgo-KAGRA (LVK) Collaboration (Abbott et al. 2020a) in successive versions of the Gravitational Wave Transient Catalog (GWTC; Abbott et al. 2016aAbbott et al. , 2019aAbbott et al. , 2021d,a,b),a,b), which report a total of 90 candidate gravitational-wave (GW) events from the coalescence of compact binary systems with a probability of astrophysical origin > 0.5.Several additional candidates of compact binary signals have also been included in independent catalogs (Nitz et al. 2019a;Magee et al. 2019;Venumadhav et al. 2019Venumadhav et al. , 2020;;Nitz et al. 2019bNitz et al. , 2021b,a;,a;Olsen et al. 2022) after analyzing the publicly released strain data (Abbott et al. 2021e).These detections have revealed features in the population of coalescing objects that revolutionize our previous understanding of astrophysics and stellar evolution (Mandel & Farmer 2022;Spera et al. 2022).The masses of many black holes (BHs) detected in GWs are much larger than those of the BHs observed in X-ray binaries (Bailyn et al. 1998;Ozel et al. 2010;Farr et al. 2011;Fishbach & Kalogera 2022) and some signals, such as GW190521 (Abbott et al. 2020c,f), have primary component masses within the predicted pair-instability mass gap (Woosley 2017;Farmer et al. 2019).On the other side of the mass range are events like GW190425 (Abbott et al. 2020d), whose total mass is substantially larger than any known Galactic neutron star binary (Farrow et al. 2019;Abbott et al. 2020b), and events like GW190814 (Abbott et al. 2020e, 2021f) and GW200210−092254 (Abbott et al. 2021b) that are also atypical due to their highly asymmetric masses and the properties of their light components (Zevin et al. 2020).While open questions remain, GWs have provided a unique census of the population of black holes in binaries in our Universe (Abbott et al. 2021c).
Current models of stellar evolution predict that white dwarfs that end their thermonuclear burning with a mass greater than the Chandrasekhar limit (Chandrasekhar 1931;Chandrasekhar 1935;Suwa et al. 2018;Müller et al. 2019;Ertl et al. 2019) will collapse to form either a neutron star or a supersolar-mass black hole.Since there are no standard astrophysical channels that produce subsolar-mass objects more compact than white dwarfs, the detection of a subsolar-mass (SSM) compact object would indicate the presence of a new formation mechanism alternative to usual stellar evolution.
Given the still-unknown nature of 84% of the matter in the Universe (Aghanim et al. 2020), it is reasonable to consider whether the DM might be composed of, or produce, distinct populations of compact objects.Primordial black holes (PBHs), postulated to form from the collapse of large overdensities in the early Universe (Zel'dovich & Novikov 1967;Hawking 1971;Carr & Hawking 1974;Chapline 1975), are candidates to form at least a fraction of the dark matter (DM) while providing an explanation to several open problems in astrophysics and cosmology (Barrow et al. 1991;Bean & Magueijo 2002;Kashlinsky 2016;Clesse & García-Bellido 2018).Soon after the first BBH coalescence was observed, it was suggested (Bird et al. 2016;Clesse & García-Bellido 2017;Sasaki et al. 2016) that the detected BHs could have a primordial origin.Large primordial fluctuations at small scales generated during inflation can produce PBHs (Carr & Lidsey 1993;Ivanov et al. 1994;Kim & Lee 1996;García-Bellido et al. 1996), though other processes in the early Universe, like bubble nucleation and domain walls (Garriga et al. 2016), cosmic string loops, and scalar field instabilities (Khlopov et al. 1985;Cotner & Kusenko 2017) can also be sources of overdensities that eventually collapse to produce PBHs (Khlopov 2010;Carr et al. 2021b;Carr & Kuhnel 2020;Villanueva-Domingo et al. 2021).The thermal history of the Universe can further enhance the formation of PBH at different scales (Carr et al. 2021a).For example, the quarkhadron (QCD) transition significantly reduces the radiation pressure of the plasma, so that a uniform primordial enhance-ment stretching across the QCD scale will generate a distribution of PBH masses that is sharply peaked around a solar mass (Byrnes et al. 2018) as well as a broader mass distribution at both larger and smaller masses that could explain some of the GW observations (Clesse & Garcia-Bellido 2022;Jedamzik 2021Jedamzik , 2020;;Chen et al. 2022;Juan et al. 2022;Franciolini & Urbano 2022).In particular, GW events in the SSM range could be used to probe mergers involving PBH black holes from a QCD enhanced peak.
Models of particle dark matter can also produce compact objects either from an interaction of dark matter with Standard Model particles, such as boson stars or neutron stars transmuted into black holes due to DM accretion (Dasgupta et al. 2021;Kouvaris et al. 2018;Kouvaris & Tinyakov 2011;de Lavallaz & Fairbairn 2010;Goldman & Nussinov 1989;Bramante & Elahi 2015;Bramante & Linden 2014;Bramante et al. 2018;Takhistov 2018;Takhistov et al. 2021), or directly from the gravitational collapse of dissipative DM (Ryan et al. 2022;Chang et al. 2019;Shandera et al. 2018;Choquette et al. 2019;Latif et al. 2019;D'Amico et al. 2018;Essig et al. 2019;Hippert et al. 2022).DM black holes (DBHs) may form in the late universe if DM has a sufficiently rich particle content to allow dissipation and collapse of DM into compact structures.While these mechanisms generically produce black holes that overlap the standard astrophysical population, under specific assumptions they may also be able to create SSM compact objects.
Searches for compact binaries with at least one component below 1 M⊙ have been carried out using both Initial LIGO (Abbott et al. 2005(Abbott et al. , 2008)), and Advanced LIGO and Advanced Virgo data (Abbott et al. 2018a(Abbott et al. , 2019b(Abbott et al. , 2022;;Nitz & Wang 2021c, 2022, 2021b;Phukon et al. 2021;Nitz & Wang 2021a).No firm detections were reported in any of these analyses.We describe and present the results of the search for the GWs from binary systems with at least one SSM component down to 0.2M⊙, using data from the second part of the third observing run (O3b) in Sec. 2. We find no unambiguous GW candidates.The null result, combined with our previous analysis of the first part of the third observing run (O3a; Abbott et al. 2022), allows us to set in Sec. 3 upper limits on the merger rate of binaries with one SSM component, as function of the chirp mass and in the m1-m2 plane.
These new upper limits on the merger rate can be used to constrain any model that might generate compact objects in the SSM range.As illustrative examples, we derive in Sec. 4 new constraints on two particular scenarios, PBHs and a model of DBHs.For PBH models, we calculate the merger rate of SSM binaries taking into account the early (Hütsi et al. 2021) and late binary formation scenarios (Clesse & Garcia-Bellido 2022;Phukon et al. 2021), and we reevaluate the constraints on PBH DM models with monochromatic (delta-function) and extended mass distributions.We update the PBH merger rate model of previous LVK works ( Abbott et al. 2018bAbbott et al. , 2019cAbbott et al. , 2022) ) with additional physics to allow for binary disruption and find that the constraints on monochromatically distributed PBHs are weakened.We also consider broad PBH mass functions such as those of thermal history scenarios of PBHs and find that they are not significantly constrained in the SSM range by the present LVK data.For DBHs, we constrain a simple atomic dark matter model where DM consists of two oppositely charged dark fermions interacting via a dark photon (Shandera et al. 2018).This model has been estimated to produce a sizeable population of SSM black holes if the heavier of the fermions, X, is more massive than the Standard Model proton (Shandera et al. 2018); the fermion mass range previously probed was 0.66 GeV/c 2 < mX < 8.8 GeV/c 2 (Abbott et al. 2022;Singh et al. 2021).We obtain improved constraints on the fraction of DM in DBHs as a function of the minimum mass of the DBHs.In Sec. 5 we summarize our findings and discuss prospects for Advanced LIGO and Advanced Virgo's fourth observing run.

SEARCH
The SSM search analyzes data collected during O3b, covering the period from 1 November 2019 1500 UTC to 27 March 2020 1700 UTC.The characterization and calibration of data and the non-linear removal of spectral lines follow the same methods as in our O3a analyses (Abbott et al. 2021a(Abbott et al. ,d, 2022)).
The analysis is performed by using three matched-filtering pipelines: GstLAL (Messick et al. 2017;Sachdev et al. 2019;Hanna et al. 2020), MBTA (Aubin et al. 2021) and PyCBC (Allen et al. 2012;Allen 2005;Dal Canton et al. 2014;Usman et al. 2016;Nitz et al. 2017;Davies et al. 2020).These analyses correlate the data with a bank of templates that model the gravitational-wave signals expected from binaries in quasi-circular orbit.All search pipelines use the same template banks and the same setup as for the O3a SSM analysis (Abbott et al. 2022).Templates are generated using the TaylorF2 waveform (Sathyaprakash & Dhurandhar 1991;Blanchet et al. 1995;Poisson 1998;Damour et al. 2001;Mikóczi et al. 2005;Blanchet et al. 2005;Arun et al. 2009;Buonanno et al. 2009;Bohé et al. 2013Bohé et al. , 2015;;Mishra et al. 2016) and include phase terms up to 3.5 post-Newtonian order, but no amplitude corrections.We estimate the GW emission starting at a frequency of 45 Hz to limit the computational cost of the search; we estimate that this reduces the network average signal-to-noise ratio (SNR) by 7%.The template bank was constructed using a geometric placement algorithm (Harry et al. 2014).The bank is designed to recover binaries with (redshifted) primary mass m1 ∈ [0.2, 10 ] M⊙ and secondary mass m2 ∈ [0.2, 1.0 ] M⊙.The lower mass bound is set for consistency with previous searches (Abbott et al. 2018b(Abbott et al. , 2019c(Abbott et al. , 2022) ) and to limit the computational cost of the search.We additionally limit the binary mass ratio, q ≡ m2/m1, with m2 ≤ m1, to range from 0.1 < q < 1.0.We include the effect of spins aligned with the orbital angular momentum.For masses of a binary component larger than 0.5 M⊙ we allow for a dimensionless component spin (χ1,2 = |S1,2|/m 2 1,2 , with S1,2 the angular momentum of the compact objects) up to 0.9, while for compact objects with masses less than or equal to 0.5 M⊙, we limit the maximum dimensionless spin to 0.1.The restriction on component spins is chosen to reduce the computational cost of the analyses (Abbott et al. 2022).We set a minimum match (Owen 1996) of 0.97 to ensure that no more than 10% of astrophysical signals can be missed due to the discrete sampling of the parameter space.
We report in Table 1 the most significant candidates down to the threshold false alarm rate (FAR) of FAR < 2 yr −1 .We do not apply a trials factor to our analysis.We identify only three triggers that pass this threshold in at least one pipeline.
Table 1.The triggers with a FAR < 2 yr −1 in at least one search pipeline.We include the search-measured parameters associated with each candidate: m 1 and m 2 , the redshifted component masses, and χ 1 and χ 2 , the dimensionless component spin.The parameters shown in the table are the ones reported by the search where the trigger is identified with the lowest FAR.H, L, and V denote the Hanford, Livingston, and Virgo interferometers, respectively.The dashes in the "V SNR" column mean that no single-detector trigger was found in Advanced Virgo.The network SNR is computed by adding the SNR of single detector triggers in quadrature.Visual inspection of the data around the time of the triggers indicate no data quality issues that would point to a definitive instrumental origin of the candidates.However, the number of triggers with their estimated FAR is consistent with what we would expect if no astrophysical signal was present in the data, given that the duration of O3b is 0.34 yr and that three pipelines are being used.The most significant candidate has a FAR of 0.2 yr −1 , which assuming a Poisson distribution for the background triggers and an observing time of 0.34 yr, corresponds to a p-value of 6.6%.We conclude that there is no statistically significant evidence for the detection of a GW from a SSM source.

SENSITIVITY AND RATE LIMITS
The absence of significant candidates in O3b allows us to characterize the sensitivity of our search and to set upper limits on the merger rate of such binary systems.We estimate the sensitive volume-time ⟨V T ⟩ over all of O3.We find the sensitivity of each of the three pipelines introduced in Sec. 2 with a common set of simulated signals in real data, generated using the precessing post-Newtonian waveform model SpinTaylorT5 (Ajith 2011), with source component masses sampled from log-uniform distributions with primary masses in range (0.19, 11.0) M⊙ and secondary masses in range (0.19, 1.1) M⊙.The injection's component spins are distributed isotropically with dimensionless spin magnitudes going up to 0.1.The injections are distributed uniformly in comoving volume up to a maximum redshift of z = 0.2, at which the sensitivity of the search has been checked to be negligible.We injected a total of approximately 2 million simulated signals, spaced 15 s apart, spanning all O3.
The sensitivity of each search pipeline is estimated by computing the sensitive volume-time of the search: where ϵ is the efficiency, defined as the ratio of recovered to total injections in the data in the source frame mass bin of interest, T is the analyzed time, and Vinj is the comoving volume at the farthest injected simulation.Each pipeline uses all injections with q > 0.05.We evaluate the uncertainties at 90% confidence interval on the sensitive volume-time estimate (Tiwari 2018) and consider binomial errors on the efficiency ϵ, given by where Ninj are the total injections in the considered mass range.
We use the FAR of the most significant candidate in O3 for each pipeline to estimate the upper limit on the merger rate in accordance with the loudest event statistic formalism (Biswas et al. 2009).The FAR thresholds used were 0.2 yr −1 , 1.4 yr −1 and 0.14 yr −1 (Abbott et al. 2022) for GstLAL, MBTA and PyCBC, respectively.By omitting a trials factor in our analysis, we obtain a conservative upper limit on the sensitive ⟨V T ⟩ of the searches.Though MBTA and PyCBC results use the full injection set, GstLAL analyzed a subset; the uncertainties in ⟨V T ⟩ shown in Fig. 1 are therefore larger for GstLAL.
To lowest order, the inspiral of a binary depends sensitively on the chirp mass of the system (Blanchet 2014), which is defined as M ≡ (m1m2) 3/5 /(m1 + m2) 1/5 .Therefore, we split the population into nine equally spaced chirp mass bins in the range 0.16M⊙ ≤ M ≤ 2.72M⊙ to determine the ⟨V T ⟩ as a function of the chirp mass, shown in Fig. 1.The highest chirp mass bin of this search exhibits a drop in sensitivity as the component masses contained within this bin are beyond the redshifted component masses covered by the template bank (Sec.2).As a consequence, there is a drop in efficiency and smaller ⟨V T ⟩ values in that region.The sensitivity estimates obtained from the analysis of O3a data with the common injection set are consistent with the ones reported in our previous work (Abbott et al. 2022).
The null result from O3 yields ⟨V T ⟩ values approximately 2 times larger than those obtained for O3a, in agreement with the expected increase in observing time.The sensitive hypervolumes of the searches presented in GWTC-3 (Abbott et al. 2021b) for chirp masses of 1.3 M⊙ and 2.3 M⊙ are comparable to those in Fig. 1 even though the mass ratio bounds of the two populations are different.
Given the obtained sensitive volume and the absence of significant detection, one can infer merger rate limits.Treating each bin, i, as a different population, we computed an upper limit on the binary merger rate to 90% confidence (Biswas et al. 2009): We show in Fig. 2 and in Fig. 3 the upper limits on the binary merger rate as function of the chirp mass and in the source m1-m2 plane, respectively.

CONSTRAINTS ON DARK MATTER MODELS
The upper limits that we infer from our null result can generically be used to constrain models that predict an observable population of binaries with at least one SSM component.We connect our results to two possible sources of SSM black holes: PBHs and DBHs.We parameterize our constraints in  terms of the fraction of the dark matter that can be comprised of compact objects under each model.

Primordial Black Holes
The abundance and mass distribution of PBHs depend on the details of their particular formation mechanism.The pri- mordial power spectrum generated during inflation must have sufficiently large fluctuations on small scales for PBHs formation, while keeping the fluctuations small at the scale of the observed cosmic microwave background anisotropies (Cole et al. 2022).This is possible in several two-field models of inflation (Clesse & García-Bellido 2015;Braglia et al. 2020;Zhou et al. 2020;De Luca et al. 2021), single-field models with a non slow-roll regime due to specific features in the inflation dynamics (García-Bellido & Ruiz Morales 2017;Ezquiaga et al. 2018), and by the enhancement of fluctuations at small scales due to quantum diffusion (Pattison et al. 2017;Ezquiaga et al. 2020), which provide recent examples of inflationary scenarios that can produce PBHs in the SSM range.
The probability of matter fluctuations to collapse into PBHs is enhanced by the decrease of the radiation pressure as different particles become non-relativistic along the thermal history of the Universe (Carr et al. 2021a).In particular, a peak around a solar mass is expected due to the QCD transition, although its exact position and height depend on the characteristics of the matter fluctuations at those scales (Byrnes et al. 2018).Furthermore, the probability of bi-nary formation and thus estimates of the event rates depends on the clustering of PBHs and the cluster dynamics.This remains an area of active study (Raidal et al. 2019;Trashorras et al. 2021;Jedamzik 2020).All these uncertainties make our predictions on the DM fraction of PBHs very sensitive to the particular choice of the model parameters (Escrivà et al. 2022;Franciolini et al. 2022).
We update the theoretical merger rate of PBHs used in previous LVK searches (Abbott et al. 2018b(Abbott et al. , 2019c(Abbott et al. , 2022)).We approximate the merger rates of early PBH binaries (EBs) formed in the radiation-dominated era with the approximations provided by Hütsi et al. (2021); Chen & Huang (2018); Ali-Haïmoud et al. (2017) and numerically validated with Nbody simulations in Raidal et al. (2019), where fPBH denotes the DM density fraction made of PBHs and f (m) is the normalized PBH density distribution.We neglect the redshift dependence in the merger rates, since the current generation of ground-based interferometers is only sensitive to BBHs with at least one SSM component at low redshifts.The main difference, compared to the theoretical rates predicted by Sasaki et al. (2016) that were used in previous LVK searches, comes from a rate suppression factor fsup that effectively accounts for PBH binary disruptions by early forming clusters due to Poisson fluctuations in the initial PBH separation, by matter inhomogeneities, and by nearby PBHs (Suyama & Yokoyama 2019;Matsubara et al. 2019).For instance, if PBHs have all the same mass or a strongly peaked mass function and significantly contribute to the dark matter, one gets fsup ≈ 2.3 × 10 −3 f −0.65 PBH , so the merger rates are highly suppressed (Hütsi et al. 2021).As a result, the limits on fPBH are much less stringent than previously estimated.Data from O2 still allow for fPBH = 1 in a scenario where all the PBHs have the same mass.Though monochromatically distributed PBHs are unrealistic, they provide a useful approximation for models with a highly peaked distribution, e.g., as predicted from PBH scenarios with sharp QCD transitions (Carr et al. 2021a).Given the still large uncertainties and possible caveats for the merger rate prescriptions of early binaries, we also considered the case where merger rates entirely come from late PBH binaries (LBs) formed dynamically inside PBH clusters seeded by the above-mentioned Poisson fluctuations that grow in the matter-dominated era and lead to the formation of PBH clusters, following Clesse & Garcia-Bellido (2022); Phukon et al. (2021).This allows us to illustrate the important variations in the PBH limits obtained for different binary formation scenarios.
For a monochromatic PBH mass distribution, we derive new limits on fPBH in the SSM range, shown in Fig. 4, for both EBs and LBs.While the scenario of DM entirely made of PBHs with the same mass was not totally excluded by previous searches, after O3 it becomes strongly disfavored up to 1M⊙, with fPBH < 0.6 around 0.3M⊙ and fPBH < 0.09 at 1M⊙.For LBs only, we do not find yet significant limits, since we do not restrict fPBH to be lower than one.
For unequal mass BBH, the merger rates are more uncertain and model dependent, but one can obtain a limit on an in such a way that it corresponds to the product of f (m2) and f (m1) in a scenario where fPBH ≈ 1.This allows us to establish model-independent limits on PBHs since FPBH encompasses all the uncertainties on the mass distribution and rate suppression, by using the limits shown in Fig. 3 and the rates of Eq. ( 4) but neglecting their variations in individual mass bins.We find that the limits on FPBH is sensitive to the location in the m1-m2 plane.These can be used to constrain fPBH for arbitrary mass functions.For models with fPBH = 1 and a peak above 1M⊙, these restrict the possible distribution of BHs in the SSM range.We find that some representative distributions with QCD-enhanced features (Byrnes et al. 2018;Carr et al. 2021a;De Luca et al. 2021;Jedamzik 2021) become constrained in the range fPBH ≈ (0.1-1).SSM searches are therefore complementary to searches in the solar mass range in order to distinguish PBH mass functions that are viable from those that are more constrained.

Dark black holes
If all or some of the DM has rich enough particle content to dissipate kinetic energy and cool, then compact objects made from DM may form through gravitational collapse of the dark gas (Shandera et al. 2018).The particle content of the DM allows SSM black holes if, for example, there is a cosmologically dominant heavy fermion analogous to the proton but with mass greater than 938 MeV/c 2 .In that case, the Chandrasekhar limit for DM black holes is lower than that for Standard Model matter.Constraints on SSM black holes in mergers then constrain formation channels for DM black holes in the detectable mass range, bounding the total cooling rate (total dissipation) of the dark sector (Singh et al. 2021).
Here we consider a population of DBHs formed within a particular dissipative scenario, the atomic DM model (Ackerman et al. 2009;Kaplan et al. 2010;Feng et al. 2009), with a power-law distribution of masses modeled after observations and simulations of Population III stars (Stacy & Bromm 2013;Greif et al. 2011;Hartwig et al. 2016).We derive the posterior probability for the fraction of dissipative DM that can be in black holes, the lower and upper limits of the DBH mass distribution, and the power-law slope, using the sensitive volume from the SSM search and modelled rates for DBH mergers (Shandera et al. 2018;Singh et al. 2021).The posterior is marginalized over the parameters that characterize the distribution, including the power-law slope and the upper limit of the distribution to obtain the constraints on the fraction of dissipative DM that can be in black holes, fDBH, together with the lower limit of the DBH distribution M DBH min , as done in Singh et al. (2021); Abbott et al. (2021a) previously.
The upper limits on fDBH are shown as a function of M DBH min in Fig. 5. Compared to the results obtained from the SSM search in O3a (Abbott et al. 2022), where the most stringent constraint on fDBH ≲ 0.003%, the limit improves by roughly a factor of 2, which can be directly attributed to the increase in the observing time.We derive the strictest limit on fDBH ≲ 0.0012 − −0.0014% at M DBH min = 1M⊙ across the 3 pipelines.The range of heavy dark fermion masses, mX probed by this search inferred from the Chandrasekhar limit of the fermionic particle progenitors of DBHs, is 1.1 GeV/c 2 < mX < 8.9 GeV/c 2 .
A non-detection provides no information for the model parameter M DBH min < 2 × 10 −2 M⊙ because the searches are not sensitive enough to support distributions with M DBH min in that mass range since we only consider M DBH max = rM DBH min with 2 ≤ r ≤ 1000.We also exclude limits where M DBH min > 1M⊙ because the detection of a SSM DBH would require a mass distribution with M DBH min ≤ 1M⊙.If these limits survive with subsequent searches, the detection of a SSM compact object would directly constrain the particle properties of atomic dark matter.Future searches could potentially rule out regions of the DM parameter space associated with dissipative dark matter.

CONCLUSIONS AND OUTLOOK
We have presented a search for compact binary coalescences with at least one SSM component in data from the second half of the third LVK observing run, O3b.The search did not yield any significant candidates.
The absence of significant candidates enables us to set improved merger-rate limits based on the full O3 dataset.We obtain consistent results with each of the three considered search pipelines.We demonstrate how the new upper limits can be used to constrain two illustrative models: SSM PBHs and DBHs.
We have considered PBH merger rate models that incorporate additional physics relative to previous LVK works and obtained new limits that are less stringent than previous LVK searches for SSM objects.Using these upper limits, the data allow us to exclude equal mass PBHs with a DM fraction smaller than one, in the entire subsolar range probed by the search.More general PBH distributions with extended mass functions remain viable, even for fPBH ≈ 1.Our SSM search therefore provides limits that are complementary to other types of observations such as pulsar timing arrays (De Luca et al. 2021;Chen et al. 2020;Domènech & Pi 2022;Kohri & Terada 2021) and microlensing surveys (Allsman et al. 2001;Tisserand et al. 2007;Wyrzykowski et al. 2011) that can probe or constrain the GW background induced by the density fluctuations at the origin of the formation of SSM PBHs.
For the dissipative dark matter model we consider, bounds on dark matter self-interactions on large scales (Markevitch et al. 2004) already weakly constrain the amount of dark matter that can be efficiently cooling, so only some of the dark matter can have cooled sufficiently to form compact objects (Buckley & DiFranzo 2018;Shandera et al. 2018).
Our analysis here provides the strongest constraint on this fraction so far from a SSM search, finding that no more than fDBH ≈ 10 −5 of atomic dark matter can be collapsed into black holes for distributions that include DBHs in the 0.2-1M⊙ range where the sensitive volume is determined from this search alone.
Given the fundamental physics implications of observing a SSM black hole, it will important to continue this type of search in the next LVK observing runs (Abbott et al. 2020a).Each of the upcoming observing runs will be preceded by detector upgrades, designed to enhance the sensitivity of our ground-based interferometer network and our reach into the Universe.These developments will facilitate either the detection of a SSM compact object or provide tighter constraints on their abundance.

Figure 1 .
Figure1.Sensitive volume-time as a function of the source frame chirp mass in data from O3, obtained through the analysis of the set of common injections (blue triangles with dotted lines, orange circles with dashed lines, and green squares with continuous lines).The statistical errors are evaluated at 90% confidence interval, following Eq.(2) and represented by the shaded areas.

Figure 2 .
Figure2.Merger rate limits as function of the source frame chirp mass of the binary system, in data from the full O3.The dotted, dashed and solid lines represent the 90% confidence limits obtained by GstLAL, MBTA and PyCBC, respectively.

Figure 3 .
Figure 3. Merger rate limits in the source frame m 1 -m 2 plane, in data from the full O3 for the three pipelines.The error bars in each panel are given at the 90% confidence interval, following Eq. 2.

Figure 4 .
Figure 4. Constraints on DM fraction of PBHs, f PBH , for a monochromatic mass function and assuming the merger rates for early PBH binaries from Hütsi et al. (2021) (orange) and late PBH binaries from Phukon et al. (2021) (blue).Shown in black are results for SSM searches in O2 (Abbott et al. 2019b) with and without the rate suppression factor fsup.For the first time, f PBH = 1 for early binaries is excluded in the whole SSM range probed by this search.

Figure 5 .
Figure 5. Constraints on the abundance of DBHs, f DBH , as a function of the lower limit of the DBH mass distribution, M DBH min from O3 data for the 3 search pipelines: GstLAL (dotted), MBTA (dashed) and PyCBC (solid).Constraints from the search for SSM compact objects in O3a data (Abbott et al. 2022) are shown for comparison.