No X-Rays or Radio from the Nearest Black Holes and Implications for Future Searches

Astrometry from the Gaia mission was recently used to discover the two nearest known stellar-mass black holes (BHs), Gaia BH1 and Gaia BH2. These objects are among the first stellar-mass BHs not discovered via X-rays or gravitational waves. Both systems contain ∼1 M ⊙ stars in wide orbits (a ≈ 1.4 au, 4.96 au) around ∼9 M ⊙ BHs, with both stars (solar-type main sequence star, red giant) well within their Roche lobes in Gaia BH1 and BH2, respectively. However, the BHs are still expected to accrete stellar winds, leading to potentially detectable X-ray or radio emission. Here, we report observations of both systems with the Chandra X-ray Observatory, the Very Large Array (for Gaia BH1) and MeerKAT (for Gaia BH2). We did not detect either system, leading to X-ray upper limits of L X < 9.4 × 1028 and L X < 4.0 × 1029 erg s−1 and radio upper limits of L r < 1.6 × 1025 and L r < 1.0 × 1026 erg s−1 for Gaia BH1 and BH2, respectively. For Gaia BH2, the non-detection implies that the accretion rate near the horizon is much lower than the Bondi rate, consistent with recent models for hot accretion flows. We discuss implications of these non-detections for broader BH searches, concluding that it is unlikely that isolated BHs will be detected via interstellar medium accretion in the near future. We also calculate evolutionary models for the binaries’ future evolution using Modules for Experiments in Stellar Astrophysics, and find that Gaia BH1 will be visible as a symbiotic BH X-ray binary for 5–50 Myr. Since no symbiotic BH X-ray binaries are known, this implies either that fewer than ∼104 Gaia BH1-like binaries exist in the Milky Way, or that they are common but have evaded detection.


INTRODUCTION
Understanding the full demographics of the stellarmass black hole (BH) population provides key insights into stellar and galactic evolution.BHs are created by the deaths of some stars with initial masses M * ≳ 20M ⊙ .Precisely which stars form BHs, and which leave behind neutron stars or no remnant at all, is uncertain (e.g.O'Connor & Ott 2011;Sukhbold et al. 2016;Laplace et al. 2021).The Milky Way has formed ∼ 10 11 stars in its lifetime, and the stellar initial mass function (IMF; e.g.Salpeter 1955) dictates that the number of massive stars that have formed, died, and left behind a BH stands at ∼ 10 7 − 10 8 (e.g.Sweeney et al. 2022).
Most (≳ 70%) of these massive stars exist with a binary companion, with triple and higher order systems also being common (Kobulnicky & Fryer 2007;Sana et al. 2012;Moe & Di Stefano 2017).However, the binary fraction of BHs is unknown.Virtually all known or suspected stellar-mass BHs today are in close binaries, in which a stellar companion to a BH is close enough that the BH is accreting significant quantities of gas from it, and the accretion flow produces observable emission across the electromagnetic spectrum.∼20 dynamically confirmed BHs exist in X-ray binaries, ∼50 X-ray sources are suspected to contain a BH based on their X-ray properties (e.g.McClintock & Remillard 2006;Corral-Santana et al. 2016), and a few X-ray quiet binaries have been reported in which a BH is suspected on dynamical grounds.Just one isolated BH candidate has been discovered via microlensing (Sahu et al. 2022;Lam et al. 2022;Mróz et al. 2022).
In X-ray bright systems, a BH accretes material from a close companion through stable Roche lobe overflow or stellar winds (e.g.McClintock & Remillard 2006).These systems are called X-ray binaries (XRBs), and are often placed into three distinct spectral/temporal states: 1) the high/soft state, where the system is X-ray bright (L X ∼ L Edd ) and dominated by thermal emission from the accretion disk, 2) the low/hard state, where the system is less X-ray luminous (L X ∼ 10 −2 L Edd ) and dominated by power-law emission, and the 3) quiescent state, where the system is very faint (L X ≲ 10 −3 L Edd ) and still dominated by power-law emission (e.g.McClintock & Remillard 2006).All BH XRBs have been discovered in either a persistent high/soft state or through transient X-ray nova (outburst) events (e.g.Corral-Santana et al. 2016).X-ray novae are caused by a sudden increase of mass transfer onto the BH, which leads to a dramatic increase in X-ray luminosity from quiescence (e.g.Mc-Clintock & Remillard 2006).All-sky X-ray monitors (e.g.MAXI, Swift/BAT; Matsuoka et al. 2009;Burrows et al. 2005) have been effective at discovering BH candidates from their X-ray novae across the entire Milky Way for those whose luminosities approach L Edd , and out to a few kpc for those that reach ∼ 10 −2 L Edd (e.g.Corral-Santana et al. 2016).However, the recurrence timescale of these outbursts is under strong debate, and so the total number of BH XRBs in the Galaxy is still quite uncertain (Tanaka & Shibazaki 1996;Maccarone et al. 2022;Mori et al. 2022).
In the last few years, a handful of BHs orbited by luminous stars have been discovered in wider orbits (Giesers et al. 2018;Shenar et al. 2022;El-Badry et al. 2023a,b).These systems are still outnumbered by XRBs, but this is likely a consequence of the very different selection functions of X-ray and optical searches.The few wide systems discovered so far likely represent the tip of a substantial iceberg.In this paper, we focus on Gaia BH1 and BH2, the newest and nearest of these systems.Precision astrometry from the third data release of the Gaia mission (DR3) enabled their discovery, and optical high-resolution spectroscopy confirmed their nature.Gaia BH1 and BH2 are systems with a BH in an orbit with a sun-like main-sequence star, and a red giant likely in its first ascent of the giant branch, respectively.These systems are unique in currently being the BH binaries with the longest known orbital periods (186 days, 1277 days), largest binary separations (a =1.4 AU, 4.96 AU), and also the closest to Earth (480 pc, 1.16 kpc).
Since both sun-like stars and red giants have stellar winds (e.g.Parker 1958;Faulkner & Iben 1966), we asked: can we see evidence of wind accretion in Gaia BH1 and BH2?In Section 2, we describe our observations and calculate upper limits for both Gaia BH1 and BH2 based on X-ray data from Chandra/ACIS-S, and radio data from the Very Large Array (VLA) and MeerKAT.In Section 3, we show that under the assumption of Bondi-Hoyle-Littleton (BHL) accretion, we should have seen X-rays and radio from Gaia BH2.We argue that a lack thereof signals that radiatively inefficient accretion is responsible for reduced accretion rates and the subsequent lack of multiwavelength emission.Finally, in Section 4, we explore the prospects of detecting wind accretion onto BHs using rates and efficiencies assuming inefficient accretion flow, either through a red giant companion or from the interstellar medium (ISM).We show that surveys such as SRG/eROSITA and pointed observations from Chandra are at best sensitive to 1) BHs accreting from ∼ 100R ⊙ red giants and 2) BHs accreting from high density (n ≳ 10 3 cm −3 ) H 2 regions while traveling at very low (≲ 5 km/s) speeds.Finally, we present MESA models for the future evolution of both systems and their expected X-ray luminosities.Based on these models and the lack of detections of symbiotic BH XRBs from all-sky surveys, we conclude that at most ∼ 10 4 systems similar to either Gaia BH1 or BH2 exist in the Milky Way, unless a substantial population of symbiotic BH XRBs have evaded detection so far.

X-Ray
We observed Gaia BH1 with the Chandra X-ray Observatory (ObsID: 27524; PI: Rodriguez) using the Advanced CCD Imaging Spectrometer (ACIS; Garmire et al. 2003) on 31 October 2022 (UT) for a cumulative time of 21.89 ks (sum of two observations: 12.13 ks and 9.76 ks).The ACIS-S instrument was used in pointing mode, chosen over ACIS-I for its slight sensitivity advantage.The observations were taken about 9 days before apastron, when the separation between the BH and star was ≈2.01 AU.
We observed Gaia BH2 for 20ks with Chandra on 2023 January 25 (proposal ID 23208881; PI: El-Badry).We also used the ACIS-S configuration, with a spatial resolution of about 1 arcsec.The observations were timed to occur near the periastron passage, when the separation between the BH and the star was ≈ 2.47 AU.
The X-ray images of both sources are shown in Figure 1.We first ran the chandra repro tool to reprocess the observations; this creates a new bad pixel file and de-streaks the event file.Since the observation of Gaia BH1 was split into two, we then ran the reproject obs tool to merge both observations with respect to a common World Coordinate System (WCS).We then performed aperture photometry at the optical positions of Gaia BH1 and BH2 in the reprocessed event files using the srcflux tool.We detect no significant flux at the location of either system and obtain a background count rate of (2.0 × 10 −4 , 1.5 × 10 −4 cts s −1 ), for Gaia BH1 and BH2 respectively.
In order to convert to unabsorbed flux, we assume a power-law spectrum with index of 2, and calculate the Galactic hydrogen column density using the relation from Güver & Özel (2009) and the value of A V from Green et al. (2019); Lallement et al. (2022) -A V = 0.93 ± 0.1, 0.62 ± 0.1 for BH1, BH2, respectively.Using the PIMMS tool, we calculate a background (1σ) unabsorbed X-ray flux of F X = 3.6 × 10 −15 erg s −1 cm −2 (BH1) and F X = 2.6 × 10 −15 erg s −1 cm −2 (BH2) in the 0.5-7 keV energy range.With the Gaia distances, we can calculate 3σ upper limits on flux and luminosity, which we present in Table 1.

Radio
We observed Gaia BH1 for 4 hr with the Very Large Array (VLA) in C band (4-8 GHz) in the "C" configuration on 2022 November 27-28 (DDT 22B-294; PI: Cendes).At this time, Gaia BH1 was 17 days past apastron, and the separation between the BH and star was ≈1.98 AU.Data was calibrated using the Common Astronomy Software Applications (CASA) software using standard flux and gain calibrators.We measured the flux density using the imtool package within pwkit (Williams et al. 2017) at the location of Gaia BH1.The RMS at the source's position is 3.4 µJy, and we present flux and luminosity 3σ upper limits in Table 1.
We observed Gaia BH2 for 4 hr with the MeerKAT radio telescope in L band (0.86-1.71GHz) on 2023 January 13 (DDT-20230103-YC01; PI: Cendes), when the separation between the BH and the star was ≈ 2.54 AU.We used the flux calibrator J1939-6342 and the gain calibrator J1424-4913, and used the calibrated images obtained via the SARAO Science Data Processor (SDP)4 for our analysis.We measured the flux density using the imtool package within pwkit (Williams et al. 2017) at the location of Gaia BH2.The RMS at the source's position is 17 µJy, and we present flux and luminosity 3σ upper limits in Table 1.
We show cutouts of all X-ray and radio images in Figure 1.No significant source of flux is detected at the position of Gaia BH1 or BH2 in either X-rays or radio.

X-ray Estimates
We first calculate the X-ray luminosity expected if the BHs accrete their companion stars' winds at the Bondi-Hoyle-Littleton (BHL) rate: where d sep is the separation between the star and BH (which varies as a function of position along the orbit in an elliptical orbit), M BH is the mass of the BH, ρ is the density of accreted material, Ṁwind is the mass loss rate of the donor, c s is the sound speed, v is the relative velocity between the BH and the accreted material, and v wind is the wind speed.We note that the second equality assumes the relative velocity between the BH and accreted material (i.e. the wind speed) greatly exceeds the sound speed.We assume that a fraction η of the accreted rest mass is converted to X-rays, leading to an observable X-ray flux: where d is the distance to the system from Earth.We are left with an X-ray flux that depends on three unknown physical quantities: Ṁwind , the mass loss rate of the donor star due to winds, v wind , the wind speed, and η, the radiative efficiency of accretion.It is important to note that η may vary with accretion rate, or with other properties of the accretion flow.
The donor star in Gaia BH1 is a main-sequence Sunlike star (G dwarf), while the donor in Gaia BH2 is a lower red giant (R ∼ 8 R ⊙ ).Since the donor in Gaia BH1 closely resembles the Sun, and abundance measurements point to it being ≳ 4 Gyr old, we adopt a solar mass loss rate: Ṁwind ≈ 2 × 10 −14 M ⊙ yr −1 (Wang 1998).Gaia BH2, however, hosts a red giant donor star, which has a mass loss rate strongly dependent on stellar properties.We adopt a simple estimate for its mass loss rate from Reimers (1975): where β R is a scaling parameter for the mass loss rate.We set β R = 0.1, following empirical estimates for red giant branch stars (Reimers 1975;Choi et al. 2016).We approximate the wind speed as the escape velocity times a scaling parameter, β wind :  We can then write a scaling relation for Equation 2, assuming fiducial values for Gaia BH1: and Equations 3 and 4 can be substituted in for Gaia BH2.We plot the expected X-ray flux from Gaia BH1 and BH2 for a range of possible wind speeds and accretion efficiencies in Figure 2.
Figure 2 shows that a 20 ks Chandra observation should only be able to detect Gaia BH1 if accretion were radiatively efficient (η ≳ 0.01, depending on wind speed).Due to the high wind speed and low mass loss rate, Gaia BH1 is nowhere near its Eddington luminosity and should not experience radiatively efficient accretion.Indeed, no X-rays are detected from Gaia BH1, which supports this prediction.
Because of the much stronger wind expected for Gaia BH2, it should have approximately 100 times the Xray flux of Gaia BH1 under the assumption of BHL accretion.This is despite Gaia BH2 being over twice as distant as Gaia BH1.Remarkably, Gaia BH2 would be within the detection threshold of a 20 ks Chandra ACIS observation for any values of η X ≳ 10 −4 .This also applies for any wind slower than the escape velocity (β w < 1), which is to be expected as the wind slows down farther from the star.Figure 2 shows that a 20 ks Chandra observation should be able to detect Gaia BH2 down to the case of radiatively inefficient flow: η ≳ 3 × 10 −3 if the wind speed is the escape velocity and η ≳ 10 −4 if the wind slows by the time it escapes from the star and reaches the BH.However, no X-rays were detected from Gaia BH2, indicating that the radiative efficiency is η < 3 × 10 −3 .In Figure 2, we show the expected accretion efficiencies (black dots; assuming BHL accretion rates) using the hot accretion flow models of Xie & Yuan (2012), which we will further describe in the following subsection.While these models may not be appropriate for obtaining estimates of accretion efficiency under BHL accretion, the X-ray non-detection of Gaia BH2 shows that reduced accretion rates, not just low efficiency at BHL rates, must be invoked to explain this non-detection.

Evidence of Reduced Accretion Rate and
Inefficient Accretion in Gaia BH2 The nondetection of X-rays in Gaia BH2 can be explained by going back to Equation 5.The two most uncertain parameters in that equation are the accretion rate at the BH event horizon, Ṁ , as well as the accretion efficiency, η.Indeed, the former causes a change in the latter (e.g.Xie & Yuan 2012).We suggest that in Gaia BH2, the X-ray non-detection is due to Ṁ being lower than the BHL assumption, which also leads to a lower radiative efficiency.This has been seen in other highly sub-Eddington accreting BHs such as the Milky Way's supermassive BH, Sgr A * (e.g.Yuan et al. 2003), as well as two stellar mass BHs in LMXBs which have been famously well-studied in quiescence: A0620-00 and V404 Cyg (e.g.Narayan et al. 1996Narayan et al. , 1997)).
In all of these systems, a similar reduction in X-rays is seen, and explained by either advection dominated accretion flows (ADAF), or luminous hot accretion flows (LHAF), both of which fall under the class of hot accretion flows (e.g.Yuan et al. 2012;Xie & Yuan 2012).Most of the energy dissipated by viscosity is stored as entropy rather than being radiated away (e.g. through X-rays).
Models of hot accretion flows lead to a reduced accretion rate near the BH event horizon, with Ṁ ∝ r s , where 0 < s < 1.A general description is presented in Yuan et al. (2012), where it is found that s ≈ 0.5 and that the accretion rate within 10R s (R s being the Schwarzschild radius) is approximate constant.This leads to the following reduction to BHL accretion: where R acc = GM BH /v 2 w is the characteristic radius of accretion.In the case of Gaia BH1, this leads to Ṁ ≈ 0.009 ṀBHL in Gaia BH1 and Ṁ ≈ 0.003 ṀBHL in Gaia BH2.
With a more realistic accretion rate in hand, there is one more correction that we can make, which is to use values of radiative efficiency, η, computed for hot accretion flows by Xie & Yuan (2012).Both accretion rates are highly sub-Eddington: L Edd = 0.1 ṀEdd c 2 =⇒ ṀEdd ≈ 2 × 10 −7 M ⊙ yr −1 for both Gaia BH1 and BH2.
Finally, by substituting both (1) the reduced accretion rate and (2) the corresponding radiative efficiency into Equation 5, we obtain X-ray flux estimates of Gaia BH1 and BH2 to be 10 −22 − 10 −20 erg s −1 cm −2 and 10 −18 − 10 −16 erg s −1 cm −2 , respectively, which we show with cyan curves in Figure 2.This places both systems well under the Chandra detection limit, but may be within the limits of future missions.

Radio Estimates
The empirical Fundamental Plane of black hole activity relates X-ray luminosity, radio luminosity and BH mass of Galactic black holes and their supermassive analogues (Plotkin et al. 2012).By placing BHs on the Fundamental Plane, the physical process behind BH X-ray and radio emission can be understood.We reproduce the most current compilation of hard state Galactic BHs with measured X-ray and radio luminosities (Bahramian et al. 2018;Plotkin et al. 2021) with upper limits of Gaia BH1 and BH2 overplotted in Figure 3.There is a minor correction to convert to the same X-ray energy ranges and radio frequency ranges, which we omit since it is of order unity.
If we assume that the Fundamental Plane holds for our systems, and our assumptions of reduced accretion rate and inefficient accretion flow, we can calculate the expected radio luminosities/fluxes: ∼ 10 21 erg s −1 / ∼ 1 nJy at 5 GHz (BH1) and ∼ 10 23 erg s −1 / ∼ 10 nJy at 5 GHz (BH2).These radio flux densities are well under the projections for future facilities such as the Next Generation Very Large Array (ngVLA; Murphy et al. 2018), so we proceed with a discussion of prospects for finding other BHs in the X-ray.
If no X-ray or radio signatures of accretion are seen from targeted observations of the two nearest known BHs, then what can we expect from blind searches?In the following subsections, we explore the prospects of detecting in the X-ray, (1) wind-accreting BHs in binary systems similar to Gaia BH2, and (2) isolated BHs accreting from the ISM.While other studies have done similar computations in the past (e.g.Agol & Kamionkowski 2002), we incorporate the modern models of inefficient accretion flow and reduced accretion rates (compared to BHL) which we used to explain the X-ray non-detection of Gaia BH2.

Wind Accreting BHs in Binaries
Are wind-accreting binaries like Gaia BH2 detectable by current X-ray missions?From Equations 3, 4 and 5, it is clear that systems with (1) a closer separation or (2) a star with a larger radius will lead to a larger X-ray luminosity.
Since sun-like stars that ascend the red giant branch keep their temperatures roughly constant but swell up to ∼ 100R ⊙ , one could expect systems like this to be strong X-ray emitters.In Figure 4, we show the prospects of finding systems similar to Gaia BH2 from X-ray searches alone.We use Equations 4 and 3, to calculate wind speeds and mass loss rates, and Equations 6 and 7 to calculate efficiency and reduced accretion rate corrections from hot accretion flows, as we did for Gaia BH2.In the top panel of Figure 4, we plot the X-ray flux as a function of orbital period for a system with all other parameters the same as Gaia BH2 (M BH = 9M ⊙ , R * = 8R ⊙ , e = 0.5, d = 1.16 kpc), and observed at periastron.
Even if a Gaia BH2-like system (i.e. a BH and an 8R ⊙ giant) were in a shorter period orbit, it would not be detectable before filling its Roche lobe (P orb ≈ 30 days).At this point, an accretion disk could form, which could lead to higher radiative efficiency and/or outbursts that could lead to the system being more easily detectable in X-rays.Such calculations are the subject of Section 5, where we explore the prospects of detecting systems similar to Gaia BH1 and BH2 when filling their Roche lobes.
In the bottom panel of Figure 4, we plot the X-ray flux as a function of orbital period for a system that could resemble what Gaia BH2 will look like in 100 Myr, when the red giant reaches the tip of the red giant branch (M BH = 9M ⊙ , R * = 100R ⊙ , e = 0.5).We plot the Xray flux for a system at 1, 2, and 4 kpc.Such a system would fill its Roche lobe at P orb ∼ 10 3 days, but systems in the range of P orb ∼ 10 3 − 10 4 days are detectable by Chandra out to a few kpc, depending on the exact orbital period.In Figure 4 and following figures, we adopt Even if Gaia BH2-like system had a shorter orbital period, it would not be detectable in X-rays before filling its Roche lobe (gray shaded area).Bottom: A BH in a binary with a tip of the red giant branch star (R * ∼ 100R⊙) can be bright enough in X-rays for the system to be detectable before the star fills its Roche lobe (P orb ≈ 10 3 − 10 4 days).
a Chandra flux limit of 7 × 10 −15 erg s −1 cm −2 , approximately corresponding to the 3σ flux limits presented in this paper in a 20 ks exposure, We also show a flux limit of 5×10 −14 erg s −1 cm −2 from a single all-sky scan of the SRG/eROSITA mission -eRASS1 is the name of the first all sky scan, though co-adds of multiple scans go deeper (Sunyaev et al. 2021;Predehl et al. 2021).This means that wind-accreting BHs in binaries could be detectable in X-rays before the donor stars fill their Roche lobes.However, this is only the case for appreciable eccentricities e ≳ 0.5.Circular orbits (as might be more likely for R * ∼ 100R ⊙ donors), would lead to a 75% decease in flux, pushing the limits of Chandra.

BHs Accreting from the ISM
Figure 5.A BH accreting from the ISM in an H2 region is detectable by current X-ray missions out to a few kpc.However, given that the nearest BH, Gaia BH1, is 480 pc away, it is unlikely to find BHs much nearer than that.With that in mind, the plot above shows that the prospects for detecting BHs accreting from the CNM or any lower density ISM phase are slim to none with current capabilities.
We compute the observed X-ray flux from a BH accreting from the ISM.This could be either an isolated BH or a BH in a binary or higher-order system, as long as it is accreting from the ISM.Previous works assumed a BHL accretion rate (e.g.Agol & Kamionkowski 2002), whereas we use the corrected accretion rates and efficiencies from Yuan et al. (2012) and Xie & Yuan (2012), respectively, as supported by the non-detection of Gaia BH2.
The ISM is made up of at least 5 phases, ordered from most to least dense: gravitationally bound giant molecular clouds (GMCs) made up of molecular hydrogen, diffuse H 2 regions, the cold neutral medium (CNM), warm neutral medium (WNM), and warm ionized medium (WIM) (e.g.Draine 2011).All phases of the ISM have been found to be roughly in pressure equilibrium (i.e.ρ × T = constant).Given that sound speed in a medium is proportional to the square root of temperature: c s ∝ √ T , from Equation 1, it is already clear that ISM-accreting BHs will be more X-ray bright when passing through the densest regions of the ISM.
We calculate the expected X-ray flux due to a BH accreting from an H 2 region (n ≈ 10 3 cm −3 , T ≈ 30 K) and from the CNM (n ≈ 30 cm −3 , T ≈ 100 K).We take ρ = m p n and calculate the sound speed as c s = k B T /m p .We then use the left hand sides of Equations 1 and 2 and additionally incorporate the hot accretion flow corrections to the accretion rate (Equation 6) and accretion efficiency (Equation 7).We plot the X-ray flux as a function of distance for a BH accreting from the ISM in Figure 5.We present curves for a BH accreting from an H 2 region and the CNM, for BH space velocities of 5 km/s and 50 km/s.We do not plot curves for higher velocities since the flux levels are reduced dramatically.In other words, isolated BHs with space velocities that exceed 50 km/s are virtually impossible to detect by current X-ray capabilities.While a few isolated BHs within 100 pc may be detectable as faint X-ray sources, it would be difficult to distinguish them from other astrophysical sources at larger distances.
Figure 5 shows that a very slow-moving BH (v = 10 km/s) can be detectable if passing through a highdensity H 2 region.Such systems are detectable out to ∼ 2 kpc in eRASS1, and ∼ 5 kpc in a 20 ks Chandra pointing.We note that Figure 5 makes the propsects of finding such systems deceptively promising, given the low volume fillin factors of H 2 regions.Furthermore, the high column density of hydrogen in H 2 regions is likely to reduce the flux by an appreciable amount, further challenging the prospects of detection.
Given the above calculations for single systems, how many ISM-accreting BHs can be found in the Milky Way? From Equation 1 and Figure 5, it is clear that that ṀBHL ∝ v −3 BH scaling relation makes the X-ray flux of BHs dramatically decrease given a slight increase in BH space velocity.Currently, the velocity distribution of BHs in binaries is unknown, both due to low-number statistics (only ∼ 20 systems are dynamically confirmed) (Corral-Santana et al. 2016;Atri et al. 2019) and due to selection effects in samples of detectable BHs.It is still uncertain if BHs are born with kicks (e.g.Stevenson 2022;Kimball et al. 2023).Furthermore, because there are only a few known BHs in wide binaries and one candidate isolated BH from microlensing, we must assume a velocity distribution.
To investigate an optimistic scenario, we assume the space velocity of ISM-accreting BHs is uniformly distributed between 10 and 50 km/s.We assume that 10 8 BHs are distributed axisymmetrically throughout the Milky Way, exponentially in cylindrical h and s coordinates with characterstic scales of 410 pc and 1 kpc, respectively (e.g.van Paradijs & White 1995).We then use the filling factor of each component of the ISM (H 2 region: 0.05%, CNM: 1%, WMN: 30%) to calculate the total number of BHs passing through each region (e.g.Draine 2011).We present the resulting distributions in Figure 6.Based on those results, virtually no ISMaccreting BHs are detectable in eRASS1, but ∼ 10 could be detectable in 20 ks Chandra observations of all H 2 regions.However, this number is almost certainly inflated due to the effects of a high column density in H 2 regions and our uncertain assumptions on the BH velocity distribution.It appears improbable to detect X-rays from ISM-accreting BHs passing through the CNM or WMN, given current capabilities.

FUTURE EVOLUTION OF GAIA BLACK HOLES AND DETECTION AS SYMBIOTIC BH XRBS
We use the expected future evolution of Gaia BH1 and BH2 to understand how common these systems could be in the Milky Way.The discovery paper of Gaia BH1 used the properties of the Gaia DR3 astrometric sample to infer that ∼ 40, 000 BH1-like systems should exist (El-Badry et al. 2023a).To constrain the population size, we take a different approach and evolve the Gaia BH1 and BH2 systems using Modules for Experiments in Stellar Astrophysics (MESA; Paxton et al. 2011Paxton et al. , 2013Paxton et al. , 2015Paxton et al. , 2018)).The donor star in Gaia BH1 will become a red giant in a few Gyr, and will ultimately fill its Roche lobe near the tip of the first giant branch.The donor star in Gaia BH2 is already a red giant, and will swell enough to fill its Roche lobe in ∼ 100 Myr at the tip of the asymptotic giant branch (AGB).We show their locations in the HR diagram today and during RLOF in Figure 7.We look for the timescales in their evolution when the systems could be visible as symbiotic BH Figure 7. Gaia BH1 will fill its Roche lobe near the tip of its first giant branch in a few Gyr.Gaia BH2 will do so near the tip of the AGB in ∼ 100 Myr.Leading up to this stage, both systems will likely be detectable as symbiotic BH XRBs, yet no such systems have been confirmed to date.
XRBs (i.e. a BH accreting from a red giant filling or nearly filling its Roche lobe).
In the top panels of Figure 8, we show the BH mass loss rates ( Ṁ ) of the donor star in the Gaia BH1 and BH2 systems for approximately 500 Myr and 10 Myr before Roche lobe overflow (RLOF), respectively.The bottom panels of Figure 8 zoom in and show where RLOF begins.Before RLOF, wind accretion takes place.For low mass loss rates ( Ṁ ≲ 10 −2 ṀEdd, BH ), the BH accretion rate could be much lower than the donor mass loss rate (as we explain through most of this paper).However, for mass loss rates that approach the Eddington accretion rate of the BH and certainly during RLOF, the two should be nearly equal (e.g.Ritter 1988).It is also worth noting that after RLOF, the donor star will have been stripped of its atmosphere, and the orbit of both systems will expand.The orbital period will increase from 186 days to ≈850 days in Gaia BH1 and from 1277 days to ≈2000 days in Gaia BH2.
In the top panels of Figure 8, we then shade the region where the accretion rate exceeds 10 −2 ṀEdd , where we expect the accretion rate is high enough to lead to frequent outbursts that could be observed by all-sky Xray monitors.This accretion rate corresponds to the X-ray lumionsities at which both currently known symbiotic XRBs (albeit with neutron star accretors) have been seen to outburst (e.g.Kuranov & Postnov 2015;Yungelson et al. 2019).We define the timescale during which the Gaia BH systems are seen as symbiotic XRBs as τ SymXRB , which in Gaia BH1 lasts ≈ 50 Myr and in Gaia BH2 lasts ≈ 2 Myr.X-ray monitors such as the Swift Burst Alert Trigger (BAT) (Burrows et al. 2005) and MAXI (Matsuoka et al. 2009) have similar sensitivities of ∼100 mCrab (10 −9 erg s −1 cm −2 ) for ∼min long exposures.This means that these monitors are sensitive to essentially all L X ∼ L Edd bursts in the Galaxy, and sensitive to bursts L X ≳ 10 −2 L Edd out to a few kpc.
Both Gaia BH1 and BH2 undergo a very short phase where Ṁ ≳ ṀEdd (Gaia BH1 exceeds ṀEdd by a factor of 10, while BH2 reaches factors of 10 2 − 10 3 ).Centaurus X-3 is an example of such a system, where extended periods of low X-ray flux have been observed in a pulsar high mass X-ray binary accreting near the Eddington rate.It has been postulated that at the highest accretion rates, matter gathers at the innermost regions of the accretion disk and absorbs the X-rays, leading to extended lows (Schreier et al. 1976).However, this system is still X-ray bright for the majority of the time and detectable by all-sky X-ray monitors.Our models show that Gaia BH1 will be in such a phase for ∼ 5 Myr, and BH2 for ∼ 0.2 Myr.In both cases, this phase lasts for ≈10% the duration of the evolution when the systems are in the symbiotic XRB phase (i.e.accretion is sub-Eddington and is due to winds rather than Roche lobe overflow).
In order to estimate an upper limit on the number of similar systems in the Milky Way, we assume a detection efficiency, ε detect , for all-sky X-ray monitors and take the lifetime of ∼ 1M ⊙ stars divided by the time during which these systems are visible as symbiotic BH XRBs: In the case where we use the short-lived phase where the donors are Roche lobe overflowing, the above becomes: During the last ∼50 years, all-sky X-ray surveys have been sensitive to X-ray bursts from such systems, but no symbiotic BH XRBs have been discovered.From Uhuru (Forman et al. 1978) to MAXI, it is highly unlikely that the brightest X-ray bursts have been missed.From Equation 9, even if we assume a 10% efficiency (ε detect = 0.1) of all-sky X-ray monitors in detecting such systems, this places Gaia BH1-like systems at N ≲ 2 × 10 3 and BH2-like systems at N ≲ 2 × 10 4 in our galaxy.If we assume that systems are only detectable during RLOF, the corresponding limits are N ≲ 2 × 10 4 and N ≲ 2 × 10 5 .
There is at least one candidate symbiotic XRB proposed to host a BH, IGR J17454-2919 (Paizis et al. 2015).The most accurate Chandra localization of the X-ray source coincides with a red giant (K-to M-type), while the X-ray burst properties of the system do not securely point to either a NS or BH accretor.Ongoing work is being conducted to determine the nature of this system.A handful of symbiotic XRBs hosting NSs have been detected as X-ray sources even though the donors have not yet overflowed their Roche lobes (e.g.Hinkle et al. 2006;Masetti et al. 2007;Bozzo et al. 2018;Hinkle et al. 2019;De et al. 2022).That being said, the radiative efficiencies of accreting NSs are likely to be larger than those of BHs (e.g.Garcia et al. 2001), and the accretion rate above which BH symbiotic XRTs are likely to be recognized as such is uncertain.

DISCUSSION AND CONCLUSIONS
We have analyzed X-ray and radio observations of the two nearest known BHs: Gaia BH1 and BH2.For both sources, we only detect upper limits in both the X-ray and radio.Due to the relatively strong, low-velocity winds from the red giant in Gaia BH2, BHL accretion predicts that we should have seen X-rays from the system.We interpret our non-detection as a sign of reduced accretion rates as seen in hot accretion flows, and an ensuing lower radiative efficiency than predicted by BHL accretion.We found that these hot accretion flow corrections lead to X-ray (and radio) fluxes well below the limit of current facilities.
We then used the corrected accretion rates and efficiencies to compute the observed flux from a BH accreting from a R * ∼ 100R ⊙ red giant (i.e.what Gaia BH2 will become in 100 Myr).We found that a relatively nearby system (d ≲4 kpc) of that type could be detectable in X-rays before filling its Roche lobe.
We then extended our calculations to wind-accreting BHs passing through the ISM.We found that the only plausible scenario for detecting such a system would be to have a very slowly moving (v ≲ 10 km/s) BH passing through a dense (n ≳ 10 3 cm −3 ) H 2 region.Current technologies rule out the possibility of detecting an ISMaccreting BH passing through the CNM or any lower density phase of the ISM, even with generous assumptions about BH velocity and the population distribution.
Finally, we produced MESA models of the future evolution of Gaia BH1 and BH2.We predict that the accretion rate in Gaia BH1 will be high enough ( Ṁ ∼ Figure 8. MESA models around the time when the donors fill their Roche lobes show that Gaia BH1 will be visible as a symbiotic BH XRB for ≈50 Myr, while Ṁ > 10 −2 ṀEdd (upper left) and for ≈5 Myr, while Ṁ ∼ ṀEdd (lower left).Gaia BH2 will be visible as a symbiotic BH XRB for ≈2 Myr, while Ṁ > 10 −2 ṀEdd (upper right) and for ≈0.2 Myr, while Ṁ ∼ ṀEdd (lower right).Because no such systems have been discovered through X-ray bursts, there should be at most ∼ 10 4 Gaia BH1-like systems in the Milky Way, unless outburst timescales of such systems have been underestimated.

−2
ṀEdd ) for the system to be visible as a symbiotic BH XRB for ≈ 50 Myr.The same will be true for Gaia BH2, but only for ≈ 2 Myr.Although the symbiotic BH XRB phase is a relatively short-lived phase in the evolution of these systems, the effective search volume for X-ray bright systems is large.Because all-sky Xray monitors have been sensitive to X-ray bursts in a large part of the Galaxy for the last ≈ 50 yrs, the lack of detected symbiotic BH XRBs would seem to imply an upper limit on the number of Gaia BH1-like systems at N ≲ 10 3 (10 4 assuming 10% detection efficiency), assuming BH + giant systems could be detected anywhere in the galaxy when the BH accretes at a rate Ṁ > 10 −2 ṀEdd .
This limit is somewhat puzzling.El-Badry et al. (2023a) estimated that the effective search volume for Gaia BH1-like systems in Gaia DR3 was only ∼ 3 × 10 6 stars, which would seem to suggest that > 10 4 similar systems should exist in the Milky Way.There are several possible explanations for these apparently inconsistent limits.One is that symbiotic BH XRBs have already been detected by X-ray surveys but have not been rec-ognized as such.This seems plausible particularly for wind-accretion systems, which may not form disks and undergo outbursts.Such systems would appear as relatively faint X-ray sources coincident with red giants.Many such sources exist in the Galactic plane and have never been studied in detail.These consideration suggest that radial velocity follow-up of giants coincident with X-ray sources may be a promising search strategy for symbiotic BH XRBs.
Another possibility is that the detection efficiency of symbiotic BH XRBs is simply very low.This could be the case if they have unstable disks with very long outburst recurrence timescales, as has indeed been proposed (e.g.Deegan et al. 2009).
The next few years show promise for the discovery of many more BH binaries: SRG/eROSITA in Xrays, Gaia through optical astrometry, and the Rubin Legacy Survey of Space and Time (LSST) through optical photometry.X-ray and radio detections (and non-detections) of future systems will provide new clues regarding the nature of accretion around BHs in a wide range of astrophysical scenarios.

Figure 1 .
Figure1.Images of Gaia BH1 (left panels) and Gaia BH2 (right panels) in the X-ray (upper panels) and the radio (lower panels).Both sources were observed for ≈ 20 ks with Chandra/ACIS-S, corresponding to a flux limit of ∼ 5 × 10 −15 .Gaia BH1 was observed with the VLA for ≈4 hrs, and Gaia BH2 was observed with MeerKAT for ≈4 hrs.No significant source of flux is detected at the position of Gaia BH1 or BH2 in either X-rays or radio.

Figure 2 .
Figure2.For all plausible wind speeds under the assumption of BHL accretion (black lines), Chandra should have detected X-rays from Gaia BH1 if the accretion flow were radiatively efficient (η ≳ 0.1; top panel) and from Gaia BH2 if the accretion flow were radiatively inefficient down to η ≳ 10 −4 (bottom panel).Black dots show expected efficiencies from models of hot accretion flows, but assuming the BHL accretion rate.Neither system is detected in X-rays, due to a combination of reduced accretion rates compared to the BHL assumption (cyan lines), and ensuing lower radiative efficiencies (cyan dots).

Figure 3 .
Figure 3. Gaia BH1 and BH2 could lie on the BH "Fundamental Plane".In gray are all measurements of hard state galactic BHs.The dotted line shows the BH fundamental plane from Plotkin et al. (2012) for 10 M⊙ BHs.

Figure 4 .
Figure4.Top: Even if Gaia BH2-like system had a shorter orbital period, it would not be detectable in X-rays before filling its Roche lobe (gray shaded area).Bottom: A BH in a binary with a tip of the red giant branch star (R * ∼ 100R⊙) can be bright enough in X-rays for the system to be detectable before the star fills its Roche lobe (P orb ≈ 10 3 − 10 4 days).

Figure 6 .
Figure6.A simple model assuming a distribution of 10 8 stellar-mass BHs passing through the various phases of the ISM in the Milky Way show that the most X-ray bright will be those passing through low density H2 regions.However, even generous model assumptions suggest that the chances of detecting BHs accreting from the ISM are unlikely after adopting models of hot accretion flows.