Dormant BH Binaries with Luminous Companions

• Dormant BH-LC systems are detached binaries where inactive black holes orbit luminous stars without active accretion, offering insights into BH formation channels.
• Detection methods such as ellipsoidal photometry, astrometry, and spectroscopy enable precise mass and orbital parameter measurements of these elusive systems.
• Recent surveys like OGLE, Gaia DR3, and TESS combined with population synthesis models offer strong constraints on binary evolution and SN physics.

Dormant black hole binaries with luminous companions (dBH-LC) are detached stellar binaries in which a non-accreting, non-interacting black hole orbits a luminous, normal star. Unlike traditional X-ray binaries, these systems exhibit no persistent accretion-powered emission, rendering the black hole effectively dormant. Their paper provides critical constraints on black hole formation channels, binary evolutionary physics, and the mapping from progenitor metallicity and mass to black hole properties, exploiting the luminous companion as a tracer of system age and chemical enrichment. Recent large-scale time-domain and astrometric surveys, including OGLE, Gaia DR3, and TESS, have yielded both candidate and confirmed dBH-LC systems, stimulating the development of rigorous observational and population-synthesis frameworks.

1. Identification Techniques: Photometry, Astrometry, and Spectroscopy

dBH-LC detection methodologies fall into three principal categories: photometric variability, astrometric reflex motion, and spectroscopic orbital solutions.

• Ellipsoidal-variation photometry identifies Roche-lobe–filling luminous primaries showing twice-per-orbit amplitude modulations, with the observed second-harmonic amplitude $A_2$ tightly constraining the mass ratio $q = M_2/M_1$ for assumed maximal fill-out and inclination (Gomel et al., 2021, Gomel et al., 2021). The “modified minimum mass ratio” (mMMR) formalism provides a lower bound on $q$ given $A_2$, allowing tree-level candidate selection for compact-object companions.
• Astrometric detection employs the angular semi-major axis of the luminous companion's motion, typically extracted from Gaia’s Thiele-Innes parameters, to estimate the unseen mass via the mass function

$$f(M) = \frac{(M_2 \sin i)^3}{(M_1 + M_2)^2} = \frac{P K^3}{2\pi G}$$

(Shahaf et al., 2019, Andrews et al., 2022).

• Spectroscopic confirmation hinges on multi-epoch radial-velocity measurements of the LF, often yielding mass functions sufficient to declare $M_2 > 3\,M_\odot$, or employing emission line diagnostics (e.g., He II line tracking) in systems such as MWC 656 (Casares et al., 2014).

Table: Example detection techniques and their applications

Technique	Observable	Targeted Surveys
Ellipsoidal Phot.	$A_2$, $m_\mathrm{MMR}$	OGLE, TESS, Gaia
Astrometric Binary	$a_0$, $f(M)$	Gaia DR3, Hipparcos
Spectroscopic Orbit	$K$, emission lines	UVES, FEROS, VLT

2. Recent Survey Results: Candidate Yields and Confirmed Systems

Population-synthesis models and survey analyses predict that dBH-LCs are numerous but difficult to identify unambiguously due to overwhelming contamination by binary stars, triples, or contact systems.

• OGLE-IV Bulge survey: out of 10,956 short-period ellipsoidal variables ($P < 2.5$ d), 136 candidates ($\sim$1.2%) meet the mMMR$>$1 criterion (Gomel et al., 2021). Most are main-sequence primaries with inferred $M_2 \gtrsim 1.5\,M_\odot$; only spectroscopic follow-up can confirm compact-object status.
• Gaia DR3: Astrometric binaries yield lower confidence samples, with single confirmed dBH-LCs (Gaia BH1, BH2) and $\sim$1–4 candidates for $M_2 \gtrsim 3\,M_\odot$ (El-Badry et al., 2023, Shikauchi et al., 2023). Population models simulate yields from a few to several hundred depending on assumptions regarding binary formation, common-envelope (CE) efficiency, SN fallback, and natal kicks (Chawla et al., 2021, Yalinewich et al., 2018, Chawla et al., 2023).
• MWC 656 represents the first spectroscopically confirmed dBH-LC: $M_1=10$–$16\,M_\odot$, $M_2=3.8$–$6.9\,M_\odot$, $P=60.37$ d, $e=0.10$; X-ray non-detections agree with radiatively inefficient accretion (Casares et al., 2014).

3. Population Synthesis Frameworks and Physical Dependencies

Binary population synthesis codes (COSMIC, BSE/SSE) incorporate initial stellar and binary distributions, Galactic star formation and metallicity histories, CE ejection physics parameterized via $\alpha_{\rm CE}$, and natal kick prescriptions (fallback-modulated Maxwellian or direct collapse).

• The shape and amplitude of the BH mass function, companion-star distribution, and orbital periods depend sensitively on the adopted SN engine (rapid/delayed), CE efficiency, and kick magnitudes (Chawla et al., 2023, Chawla et al., 2021).
• Rapid SN engines yield a 3–5\,$M_\odot$ BH mass gap, whereas delayed engines fill the gap; CE efficiency shifts the population towards shorter orbits and modulates the period–companion mass relation (Shikauchi et al., 2023).
• Observational comparisons of detected ($P$, $e$) correlations trace the presence or absence of natal kicks; mass–height correlations ($M_{\rm BH}$, $|z|$) relate to SN remnant prescriptions (Shikauchi et al., 2023).

4. Variability, Contamination, and Candidate Vetting

The principal challenge in isolating bona fide dBH-LCs is the prevalence of contact binaries and hierarchical triples mimicking the same photometric or astrometric signals.

• Recent OGLE analyses (Kapusta et al., 20 Jan 2024) show that spectral energy distribution (SED) fits and matching to single-star models typically favor non-compact companions, or reveal contact/overcontact configurations capable of reproducing modulation amplitudes and RV semi-amplitudes; only high-resolution multi-epoch spectroscopy can test the compact-object hypothesis conclusively.
• Triple-star configurations, such as NGC 2004 #115, can be unambiguously resolved through combined ellipsoidal amplitude modeling, reflection-effect photometry, and multi-body RV analysis, demonstrating the necessity of synchronous multi-modal data (El-Badry et al., 2021).

5. Physical Parameter Distributions and Galactic Demographics

Quantitative predictions from population synthesis and survey data show that the dBH-LC population is likely dominated by wide ($P\sim50$ d–10 yr), mildly eccentric systems, with compact-object masses peaking near $7$–$12\,M_\odot$ and luminous companions $0.5$–$3\,M_\odot$ (Yalinewich et al., 2018, Shikauchi et al., 2023, Chawla et al., 2021).

• Space densities of dBH-LCs are predicted to exceed those of accreting X-ray binaries by an order of magnitude (El-Badry et al., 2023).
• The period–eccentricity distributions are modulated by natal kicks and CE physics; the absence or reversal of correlations provides direct measurement of binary formation physics.

6. Role of Radiatively Inefficient Accretion and Multiwavelength Constraints

Confirmed dBH-LCs such as MWC 656 (Casares et al., 2014) and Gaia BH2 (El-Badry et al., 2023) exhibit deep X-ray and radio non-detections even at periastron, ruling out standard Bondi-accretion scenarios and supporting a regime in which only a small fraction of the wind capture rate reaches the horizon ($$\dot{M}_{\rm horizon} \sim 10^{-3} \dot{M}_{\rm BHL}$$), with strong mass-loss/convection in the accretion flow (El-Badry et al., 2023). This sets stringent limits on the detectability of non-interacting BHs and guides the interpretation of dormant status.

7. Future Prospects: Large-Scale Surveys, Follow-up, and Astrophysical Impact

Combining broad time-domain photometry (Gaia, TESS), astrometry, and spectroscopic resources (e.g., Gaia RVS, ground-based high-resolution instruments) enables multi-modal vetting of dBH-LC candidates. Population synthesis models suggest that hundreds of dBH-LCs could be identified in the next decade; follow-up will yield precise BH mass measurements, orbital parameters, and metallicities, providing tight empirical constraints on SN physics, CE evolution, and kick distributions (Chawla et al., 2021, Chawla et al., 2023). The systematic paper of these dormant populations will close the loop between massive-star and compact-object demographics, anchoring the evolutionary pathways of high-mass binaries across cosmic history.