The Observed Mass Distribution of Galactic Black Hole LMXBs Is Biased against Massive Black Holes

Black hole (BH) X-ray binaries are systems in which a BH accretes mass from a companion star. Typically, a distinction is made between low- and high-mass X-ray binaries on the basis of the mass of the donor star in the binary. In this paper, we focus on low-mass X-ray binaries (LMXBs), excluding BH X-ray binaries with O- and early B-type donor stars. When the accretion rate through the disk is large, these systems show up as bright X-ray sources. When the mass flow rate through the disk decreases, the systems go (back) to quiescence. During the quiescent phase, the mass donor or companion star can be detected in the optical and/or near-infrared (NIR). Such observations can be used to determine the mass of the BH (for a review and detailed explanation of the methods involved, see Casares & Jonker 2014).

The observed BH mass distribution in these LMXBs (Özel et al. 2010; Farr et al. 2011) has an apparent lack of BHs in the mass range of 2–5 M_⊙ (the so-called mass gap; Bailyn et al. 1998), and BHs more massive than ≈15 M_⊙ are also not observed. Recently, the mass of the BH in the high-mass X-ray binary Cyg X-1 was adjusted upward to 21.2 ± 2.2 M_⊙ (Miller-Jones et al. 2021), making this the heaviest stellar-mass BH with an electromagnetically measured mass. In some mass determinations, a systematic error is introduced by assuming that the accretion disk light is not contributing to the optical light. Properly accounting for this may remove the apparent lack of BHs in LMXBs in the 2–5 M_⊙ range (e.g., Kreidberg et al. 2012). Depending on the assumed BH kick properties, microlensing mass determinations of single BH lenses may also cast doubt on the presence of the mass gap (Wyrzykowski & Mandel 2020).

The detection of gravitational waves (GWs) by the Laser Interferometer Gravitational Wave Observatory (LIGO; Aasi et al. 2015) and the Virgo interferometer (Acernese et al. 2015) from binary BH mergers (e.g., Abbott et al. 2016a, 2016b, 2019, 2021) revealed the existence of BHs more massive than the stellar-mass BHs previously detected in X-ray binaries. The current record holder is the detection of a BH merger product with a mass of ≈150 M_⊙, where the BH component masses were ${85}_{-14}^{+21}$ and ${66}_{-18}^{+17}{M}_{\odot }$ (Abbott et al. 2020). While some of the BHs involved in binary BH mergers are inferred to have masses in the range electromagnetically observed for stellar-mass BHs, many are considerably larger (Abbott et al. 2021). It is likely that the different binary evolution histories of binary BH merger progenitors and the BH X-ray binaries (especially for the LMXB systems) are an important factor in these different mass distributions (e.g., Perna et al. 2019; Schneider et al. 2021); however, some aspects of the BH formation process may be relevant to both groups of systems.

Stellar-mass BHs can form out of massive stars in two different ways (Fryer & Kalogera 2001); hence, their initial spatial distribution is expected to be correlated to that of massive star formation. For a sufficiently massive progenitor, BHs may form by direct collapse. Observational evidence for this comes from the disappearance of red supergiant stars without evidence of a supernova (Reynolds et al. 2015)—though a faint (NIR) transient may appear (Adams et al. 2017)—and from the zero peculiar velocity of some BH X-ray binaries, such as Cyg X-1 (Mirabel & Rodrigues 2003; Reid et al. 2011), although we note that the peculiar velocity is not a quantity conserved with time (see, e.g., Miller-Jones et al. 2009b). Alternatively, if a supernova explosion is not sufficiently energetic to unbind the complete stellar envelope, fallback of material onto the proto–neutron star formed in the explosion can create a BH (Chevalier 1989; Wong et al. 2014; Chan 2018).

Given that most O stars are formed in binaries (Sana et al. 2012) or higher-order multiples (Moe & Di Stefano 2017), and given that both the accreting BHs and those found through GW merger events are in binaries, we summarize here some important aspects of compact object formation on the space velocities of ensuing BHs, as that influences their observed spatial distribution. First, if one star in a binary explodes in a supernova, leading to impulsive mass loss from the binary system, a Blaauw kick will be imparted on the system, regardless of the type of compact object formed during the supernova event (Blaauw 1961). This Blaauw kick is directed in the orbital plane of the binary.

The BH formation may also be accompanied by natal kicks, powered by the mechanisms that have been proposed to explain the high peculiar velocities of some neutron stars (e.g., Verbunt et al. 2017). Natal kicks from anisotropic neutrino emission are thought to occur regardless of BH formation mechanism, while kicks related to asymmetric mass ejection (or, relatedly, asymmetric mass fallback) can only occur for the fallback channel of BH formation. In principle, hydrodynamical kicks from asymmetries in the supernova ejecta can accelerate a nascent BH to similarly high velocities as observed in neutron stars (Janka 2013). Kicks from neutrino asymmetries, conversely, impart roughly the same momentum to the BH as they do in cases of neutron star formation (Janka 2013) and therefore produce kick velocities that are sensitive to the final compact remnant mass.

Because of the lack of (significant) mass loss, direct-collapse BHs are not subject to Blaauw or ejecta kicks, though in principle, they might still undergo kicks from neutrino anisotropy; as direct-collapse BHs are usually thought to be larger in mass than fallback BHs (e.g., Fryer 1999), this may introduce a mass dependence into the natal kick distribution, with the largest kicks going to the lowest-mass BHs (e.g., Fryer et al. 2012).

LMXBs have long been recognized as a valuable probe of the BH mass distribution (if dynamical mass measurements are obtained), because the mass of the BH will not change appreciably due to gas accretion (as the mass of the secondary is low). LMXBs can also be used to study natal kick physics. Many BH LMXB formation models involve a supernova, and hence the Blaauw and/or natal kick will be imparted on the system and/or BH in the binary (see Tauris & van den Heuvel 2006 for a review). ⁶ As a result, the distribution of LMXB altitudes above and below the Galactic plane will encode their natal kick distribution, so long as they formed in the disk of the Milky Way. Note that the space velocity of old LMXB systems could well have received some component of peculiar velocity through nonaxisymmetric forces experienced on their orbits through the Galaxy by scattering from the potentials of spiral arms or interstellar molecular clouds during the time between the BH formation and the system becoming active as an X-ray binary (Wielen 1977). Estimates of the velocity dispersion of the thin disk population show that it is approximately 40–43 km s⁻¹ for K0–M5 late-type stars (Dehnen & Binney 1998; Mignard 2000), indicating that this effect needs to be taken into account (e.g., such as was done to determine the peculiar space velocity of V404 Cyg; Miller-Jones et al. 2009b).

Initially, it was thought that most BHs would quickly be kicked out of globular clusters, although a few could remain (Kulkarni et al. 1993). However, recent findings of actively accreting and quiescent candidate BH X-ray binaries in both Galactic and extragalactic globular clusters, as well as the detection of binary BH mergers through GW radiation, has led to a renewed interest in the possibility of clusters retaining BHs. Maccarone et al. (2007) provided evidence for an accreting BH in an extragalactic globular cluster associated with the Virgo elliptical galaxy NGC 4472. Quiescent candidate BH LMXBs were identified in globular clusters around the Milky Way. Typically, radio and X-ray luminosity and radio spectral index measurements were used to argue for a candidate quiescent BH LMXB (in M22, Strader et al. 2012; M62, Chomiuk et al. 2013; 47 Tuc, Miller-Jones et al. 2015; M10, Shishkovsky et al. 2018; and Terzan 5, Urquhart et al. 2020).

If a sizable number of BHs are indeed retained by globular clusters, the high stellar density and large interaction rate could lead to the formation of BHs with a binary companion. A significant fraction of these systems will be ejected from the globular cluster through interactions with stars. The evolution of such a binary could imply that it becomes a BH LMXB. This can occur for systems that are either retained or ejected by globular clusters (e.g., Giesler et al. 2018; Kremer et al. 2018). Dynamical evidence for the presence of two or even three BHs in the globular cluster NGC 3201 was presented by Giesers et al. (2018, 2019).

In this paper, we investigate whether the samples of confirmed and candidate BH LMXBs suffer from selection effects by studying their spatial distributions. We exclude the Galactic BH high-mass X-ray binaries Cyg X-1 (Miller-Jones et al. 2021) and MWC 656 (Casares et al. 2014) from our analysis because the BHs in those systems formed recently (as the young age of the mass donor star testifies). The current high metallicity in the Galaxy probably precludes the formation of the most massive stellar-mass BH (e.g., see Vink et al. 2021 for the role of stellar metallicity and remnant mass). However, the BH LMXBs that have late-type mass donors may have formed billions of years ago, when the metallicity was lower. Hence, we cannot exclude that the precursors of the BHs in LMXBs could have formed massive stellar-mass BHs such as found through GW events by the LIGO-Virgo collaboration. In Section 2, we discuss the existing Galactic BH LMXB sample and analyze its spatial distribution. In Section 3, we discuss the implications of this distribution for source selection effects and BH LMXB formation channels. We conclude in Section 4.

We use the sample of confirmed BH LMXBs listed in Casares & Jonker (2014). Table 1 provides basic information on the sources, including distances and mass measurements that are updated with respect to the abovementioned work. In addition to those sources, we included four additional systems with recent (dynamical) mass measurements; Swift J1357.2−0933, MAXI J1820+070, MAXI J1659−152, and MAXI J1305−704. Note that a few of these dynamically confirmed BH LMXBs have mass determinations that do not formally rule out a neutron star nature of the compact object; i.e., the mass determination is consistent with a compact object mass of <3 M_⊙. This includes GX 339−4, 4U 1543−47, and perhaps GRO J0422+32. Nevertheless, we classify these systems as BHs here because the radio and X-ray spectral and timing properties of these sources are best described if they host a BH. In this respect, it is interesting to note that none of the candidate BH LMXBs where a dynamical mass was determined turned out to have a best-fit mass of 1.4–2 M_⊙ (all confirmed BH LMXBs used to be candidate BH LMXBs before their dynamical mass was determined, of course).

Table 1. The Name, Orbital Period P_orb, BH Mass, Distance d, Galactocentric Distance d_GC, and Absolute Distance to the Galactic Plane ∣z∣ for the Sample of Galactic BH LMXBs with a Dynamical Mass Measurement Sorted by Decreasing Orbital Period from Top to Bottom

No.	Name	Porb	Mass	d	dGC	∣z∣	Mass/Distance
		(days)	(M⊙)	(kpc)	(kpc)	(pc)	Reference
1	GRS 1915+105	33.85(0.16)	12.4 ± 2.0	8.6${}_{-1.6}^{+2}$	${6.5}_{-0.6}^{+1.0}$	30 ± 8	[1, 2]/[1]
2	V404 Cyg	6.47129(7)	9${}_{-0.6}^{+0.2}$	2.39 ± 0.14	7.80 ± 0.01	82 ± 5	[3]/[4]
3	XTE J1819−2525 d	2.81730(1)	6.4 ± 0.6	6.2 ± 0.7	${2.2}_{-0.62}^{+0.55}$	515 ± 60	[30]/[30]
4	GRO J1655−40	2.62168(14)	6.6 ± 0.5	3.2 ± 0.2	5.13±0.18	140 ± 10	[5]/[6]
5	Ginga 1354−645 c	2.54451(8)	>7 a	${25}_{0}^{+10}$	21 ± 9.5	${1220}_{-0}^{+500}$	[7]/[7]
6	GX 339−4	1.7587(5)	5.9 ± 3.6	9 ± 4	${3.95}_{-0.6}^{+2.2}$	680 ± 300	[8]/[8]
7	XTE J1550−564	1.542033(2)	9.1 ± 0.6	4.4 ± 0.5	${5.14}_{-0.21}^{+0.25}$	140 ± 15	[9]/[9]
8	4U 1543−47	1.123(8)	5.1 ± 2.7	7.5 ± 0.5	${4.04}_{-0.02}^{+0.08}$	710 ± 45	[21]/[11]
9	MAXI J1820+070	0.68549(1)	7.0 ± 0.6	2.96 ± 0.33	6.1 ± 0.2	525 ± 60	[23]/[24]
10	H1705−250	0.5213(13)	6.4 ± 1.5	8.6 ± 2.0	${1.94}_{-0.5}^{+0.9}$	1400 ± 300	[10]/[11]
11	Ginga 1124−684	0.432606(3)	11.0${}_{-1.4}^{+2.1}$	5.0 ± 0.7	${7.54}_{-0.11}^{+0.17}$	600 ± 100	[12]/[12]
12	MAXI J1305−704	0.394(4)	${8.9}_{-1.0}^{+1.5}$	${7.5}_{-1.4}^{+1.8}$	${7.4}_{-0.5}^{+0.8}$	1000 ± 225	[27]/[27]
13	Ginga 2000+250	0.3440873(2)	7.2 ± 1.7	2.7 ± 0.7	${7.35}_{-0.06}^{+0.12}$	135 ± 35	[10]/[11]
14	1A 0620−00	0.32301405(1)	5.86 ± 0.24	1.6 ± 0.4	9.56 ± 0.36	175 ± 45	[13]/[14]
15	XTE J1650−500	0.3205(7)	5.65 ± 1.65	2.6 ± 0.7	5.86 ± 0.58	150 ± 40	[15]/[16]
16	GRS 1009−45	0.285206(14)	>3.6 a	5.7 ± 0.7	9.46 ± 0.36	930 ± 110	[17]/[11]
17	XTE J1859+226	0.274(2)	>5.4 a	6.3 ± 1.7	${6.82}_{-0.18}^{+0.58}$	950 ± 250	[18]/[19]
18	GRO J0422+32	0.2121600(2)	4 ± 1 b	2.75 ± 0.25	10.8 ± 0.2	560 ± 50	[20]/[11]
19	XTE J1118+480	0.1699339(2)	7.55 ± 0.65	1.8 ± 0.6	9.1 ± 0.35	1600 ± 500	[22]/[11]
20	Swift J1357.2−0933	0.11(4)	12.4 ± 3.6	8 ± 1 e	${7.67}_{-0.41}^{+0.51}$	6130 ± 770	[28, 29]/[29]
21	MAXI J1659−152	0.10058(19)	5.4 ± 2.1	6 ± 2	${3}_{-0.6}^{+1.5}$	1700 ± 570	[25]/[26]

Notes.

^a Lower limit to the BH mass. ^b BH mass uncertain; see Casares & Jonker (2014) for a discussion. ^c Also referred to as BW Cir. ^d Also referred to as V4641 Sgr. ^e The formal distance estimate is >6.7 kpc; we took 8 ± 1 kpc for the calculation of d_GC and ∣z∣.

References: [1] Reid et al. (2014), [2] Steeghs et al. (2013), [3] Khargharia et al. (2010), [4] Miller-Jones et al. (2009a), [5] Shahbaz (2003), [6] Hjellming & Rupen (1995), [7] Casares et al. (2009), [8] Heida et al. (2017), [9] Orosz et al. (2011), [10] Casares & Jonker (2014), [11] Jonker & Nelemans (2004), [12] Wu et al. (2016), [13] van Grunsven et al. (2017), [14] Gandhi et al. (2019), [15] Orosz et al. (2004), [16] Homan et al. (2006), [17] Filippenko et al. (1999), [18] Corral-Santana et al. (2011), [19] Hynes et al. (2002), [20] Gelino & Harrison (2003), [21] Orosz et al. (1998), [22] Khargharia et al. (2013), [23] Torres et al. (2020), [24] Atri et al. (2020), [25] Torres et al. (2021), [26] Jonker et al. (2012), [27] Mata Sánchez et al. (2021), [28] Casares (2016), [29] Mata Sánchez et al. (2015), [30] MacDonald et al. (2014).

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For Swift J1357.2−0933, Mata Sánchez et al. (2015) constrained the BH mass using optical observations of the FWHM of the Hα emission line and the correlation between the FWHM and the semiamplitude of the radial velocity of the mass donor star (Casares 2015). The BH mass determination was further refined by Casares (2016). For MAXI J1820+070, we used the mass measurement of Torres et al. (2019, 2020) and the distance determination of 2.96 ± 0.33 kpc obtained through the radio parallax measurement by Atri et al. (2020). For MAXI J1659−152, we use the (approximate) dynamical mass measurement from Torres et al. (2021). For the distance to this source, we adopt the value of 6 ± 2 kpc from Jonker et al. (2012). However, our conclusions would be unchanged if we had used the value of 8.6 ± 3.7 kpc reported by Kuulkers et al. (2013). For MAXI J1305−704, we use the recently derived mass and distance estimate from Mata Sánchez et al. (2021).

For all sources, the equatorial coordinates and the distance d are used to calculate the absolute value of the distance to the plane,∣z∣, and the distance to the Galactic center, d_GC, using the python astropy:SkyCoord routine. For the calculation, we took 8.15 kpc for the Sun–Galactic center distance and 5.5 pc for the height of the Sun above the plane following Reid et al. (2019).

In the left panel of Figure 1, we show the BH mass versus ∣z∣, and in the right panel, we show the BH d_GC versus ∣z∣ for both the dynamically confirmed BH LMXBs and the known candidate BH LMXBs—those systems that display characteristics during transient outbursts typically also seen in dynamically confirmed BH X-ray transients (cf. Corral-Santana et al. 2016; see Table 2). The thick black line in this figure is at three times the scale height of 19–20 pc for massive stars observed in current star-forming regions with d_GC ≲ 8 kpc (Urquhart et al. 2014; Reid et al. 2019). As shown by these authors, the Galactic scale height for massive star formation sites increases rapidly for sources with d_GC ≳ 8 kpc to a 1σ value of ≈150 pc at d_GC = 12 kpc. While we draw a straight line at three times the scale height, reaching 450 pc for 12 kpc starting at 8 kpc, the exact way the scale height increases with galactocentric distance for d_GC ≳ 8 kpc is somewhat uncertain and might be slightly different for regions below and above the plane.

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For many of the candidate BH LMXBs, the distance is often not well known due to the fact that a reliable distance measurement in BH LMXBs often (though not exclusively; see, e.g., Jonker & Nelemans 2004 for details) comes from the spectroscopic detection of the mass donor star. For all BH candidates except MAXI J1348−630, we take d = 8 ± 3 kpc, as this is virtually always consistent with the (uncertain) distance estimates present in the literature for these systems. For MAXI J1348−630, an accurate distance of 2.2 ± 0.6 kpc has been derived by Chauhan et al. (2020) using H i absorption line measurements.

Using as a null hypothesis that all BHs in LMXBs originate in regions where massive stars form, which we generously take to lie within three times the scale height of the massive star-forming regions, the main conclusion from these two plots is that only the confirmed BH LMXB GRS 1915+105 is found at a location close to its origin, i.e., close to the Galactic plane. Poisson statistics shows that to observe such a configuration, where one source is found in the region of origin out of the 21 sources, by chance is negligible. Similarly, only about four candidate BH LMXBs are at ∣z∣ < 60 pc, excluding the sources in the bulge region with d_GC < 3–5 kpc. Here the 3 or 5 kpc depends on what we take as limit for the boxy/peanut-shaped bulge (Portail et al. 2015; Wegg et al. 2015; and see Shen & Zheng 2020 for a recent review).

Next, we compare the ∣z∣ distribution of the confirmed BH LMXBs with that of the candidate BH LMXBs using a two-sample Kolmogorov–Smirnov (K-S) test. For both the confirmed and the candidate BH LMXBs, we simulated 10⁴ distributions where we take a random ∣z∣ value from the range of possible ∣z∣ values in the 1σ uncertainty range for each source. While the hypothesis that the two ∣z∣ distributions are drawn from the same parent population has a low mean probability of being true (the mean p-value of the 10⁴ samples is 0.05), this p-value does not rule out this possibility at a high confidence level. Similarly, we also compare the two distributions in d_GC. A two-sample K-S test shows that the hypothesis that the distributions in d_GC are drawn from the same parent population has a low mean probability of being true (p-value = 2 × 10⁻⁴). It can be seen from the right panel in Figure 1 that there are many more candidate BH LMXBs (32) at d_GC ≲ 3 kpc than confirmed BH LMXBs (there are only two such sources: 3 (XTE J1819–2525) and 10 (H1705−250)).

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We combine the sets of dynamically confirmed and candidate BH LMXBs and require d_GC > 3 kpc for both BH and BH candidate sources to avoid systems located in the bulge (see the right panel of Figure 1). This combined data set has 30 systems. We compared the observed ∣z∣ distribution of all (candidate) BH LMXBs with a null-hypothesis distribution that is continuous in 60 pc < ∣z∣ < 2000 pc. To do so, we compare the ∣z∣ distribution of the combined systems with the distributions of the same number of systems randomly drawn from a distribution with a uniform probability of having a value in the range 60 pc < ∣z∣ < 2000 pc. As described above, we draw from the range of possible ∣z∣ values afforded by the 1σ uncertainties in the ∣z∣ determination for each source, BH and BH candidate alike. We repeat the whole procedure 10⁴ times and subsequently determine the mean value of the two-sample K-S (Smirnov 1948) p-value and the mean value of the two-sample Anderson–Darling (A-D) p-value (Anderson & Darling 1954). Because we take the 1σ uncertainty ranges in ∣z∣ and d_GC into account in these tests, the number of systems varies by one or two for different draws out of the 10⁴. The mean K-S p-value is 4 × 10⁻², whereas that of the A-D test is 1 × 10⁻². The latter number represents a lower limit because, in about 3850 of the 10⁴ cases, the result was capped at the lowest value allowed by the routine (0.001).

Besides these statistical tests, we also calculate the Mann–Whitney (Mann & Whitney 1947) U-statistic. Here the null hypothesis is that for two randomly selected values from the BH ∣z∣ distribution (X) and the simulated distribution of uniform probability for 60 < ∣z∣ < 2000 (Y), the probability of X being greater than Y is equal to the probability of Y being greater than X. This null hypothesis would be true if the two distributions were drawn from the same parent population. The U-statistic has a mean p-value of 6 × 10⁻³. Overall, we conclude that the observed ∣z∣ distribution is inconsistent with being uniform over the 60–2000 pc range.

From the left panel of Figure 1, there is suggestive evidence for the absence of dynamically confirmed BH LMXBs with ∣z∣ between ≈200 and 400 pc. To investigate whether this apparent gap in the ∣z∣ distribution of BH and candidate BH LMXBs is significant, we repeat the statistical tests done above, comparing the observed distribution with a distribution that is uniform in the range 60 pc < ∣z∣ < 2000 pc, except now we enforce the presence of a gap between 200 and 400 pc. The mean K-S p-value is 0.01, and the mean A-D p-value is 4 × 10⁻³ (although again, the latter number represents a lower limit because, in about 6850 of the 10⁴ times, it was capped at the lowest value allowed by the routine of 0.001). The mean U-statistic p-value is 2 × 10⁻³. Comparing these statistics with those assuming a homogeneous distribution in the ∣z∣-direction reveals that a hypothetical distribution with a gap does not lead to higher probabilities that the two distributions are consistent with being the same. Therefore, we conclude that there is no evidence for a gap in the ∣z∣ distribution of the BH and candidate BH LMXBs. Finally, we checked whether this conclusion was altered if we changed the upper bound of the distribution from 2000 to 1200 pc, but it was not.

This section is structured as follows. We will first discuss our main findings on the observed spatial distribution of confirmed and candidate BH LMXBs, comparing their distributions with each other and with the expected distribution assuming that BH LMXBs are formed in the Galactic plane. Next, in Sections 3.2 and 3.3, we investigate whether the prevalent discovery method of (candidate) BH LMXBs implies the presence of potential biases in BH mass. In Section 3.4, we show that the bias affecting the chance for discovery, together with a mass measurement bias for the confirmed BH LXMBs, implies that a selection effect on BH mass exists, assuming they are formed in the Galactic plane. We investigate this assumption in Section 3.5 by turning to an alternative view, where BH LMXBs are formed in globular clusters. We end the discussion by listing additional (proposed) ways of finding BHs in our Milky Way that may (in the future) alleviate some of the existing selection effects (Section 3.6).

3.1. The Observed Spatial Distributions of Confirmed and Candidate BH LMXBs

3.2. Biases in Discovering Candidate BH LMXBs at Low ∣z∣

3.3. Discovery Bias against Long BH LMXB Outburst Recurrence Times

3.4. Discovery Bias Aggravated by a Mass Measurement Bias

3.5. Testing the Assumption that BH LMXBs Form in the Plane: BH LMXBs Originating from Globular Clusters?

3.6. Alternative Ways to Detect Galactic BHs

Since the first direct GW detections in 2015, astronomers have been puzzled by the apparent discrepancy between BH mass distributions measured (i) electromagnetically in LMXBs and (ii) gravitationally via binary BH mergers. For the most extreme cases, such as GW-selected BHs in the pair instability mass gap (e.g., GW190521), there is likely a true physical difference in formation channels between these two populations. However, outside the pair instability mass gap, it remains unclear whether the electromagnetically and GW-selected samples reflect physically different populations or simply different selection effects for two different messengers applied to the same underlying population. This question is of more than academic interest given its connection to long-standing problems in binary evolution, core-collapse supernova physics, and dynamical channels for binary BH assembly, all of which are plausible candidates for creating a real astrophysical difference between BH LMXB and BH–BH mass distributions. The observed difference between these mass distributions could, in principle, be used to probe these problems, but only if said difference is not due to selection effects.

In this paper, we have explored possible selection effects in the electromagnetic determination of BH LMXB masses. In general, examining the spatial distribution of confirmed and candidate BH LMXBs suggests multiple new selection effects that may be shaping their mass distribution. Our main conclusions are the following.

• 1.  
  The Galactic height ∣z∣ distribution of confirmed and candidate BH LMXBs shows a paucity of sources in the region where they are expected to form (i.e., in the regions of massive star formation in the plane). The paucity of even candidate BH LMXBs in the Milky Way plane suggests a strong selection effect in the X-ray discovery of BH LMXBs, likely due to a combination of crowding and absorption at low Galactic heights, combined with an intrinsic lower outburst probability of LMXBs hosting more massive BHs that reside in the plane.
• 2.  
  The confirmed BH LMXBs have a significantly greater distance to the Galactic center than the population of candidate BH LMXBs. This bias can be explained by a different selection effect acting on the optical spectroscopy needed to dynamically confirm a candidate BH LMXB: high levels of dust extinction in the plane and toward the bulge precluding optical BH mass measurements.
• 3.  
  Taken together, both of the above selection effects combine to give the observed distribution of ∣z∣ for confirmed BH LMXBs with dynamical mass measurements. The combination of these two selection effects favors sources that obtained a significant (natal) kick that moved them out of the plane of their origin.
• 4.  
  Although the magnitudes and mechanisms of BH natal kicks are debated, it is generally believed on theoretical grounds that kicks arising from anisotropic neutrino emission will be of "fixed momentum," i.e., will impart larger velocity kicks to compact remnants of smaller mass (e.g., Fryer et al. 2012). Natal kicks due to asymmetric mass ejection may instead be in the "fixed velocity" regime (i.e., similar kick velocities for remnants of different mass), but most models for core-collapse supernovae predict that above a certain BH remnant mass, BHs form through direct collapse without any natal kick from asymmetric ejection (direct-collapse BHs will also not be subject to Blaauw kicks). The selection effects discussed above, which favor X-ray outburst occurrence and probably also detection, and electromagnetic mass measurements in high-∣z∣ BH LMXBs therefore disfavor mass measurement of high-mass BH LMXBs.
• 5.  
  The observed BH LMXB orbital periods disfavor a globular cluster origin for a majority of dynamically confirmed BH LXMB systems. This constraint does not apply to the ≈six shortest orbital period BH LMXBs, for which there is little decisive evidence for or against a globular cluster origin. In addition, the predicted ∣z∣ distribution of BH LMXBs originating in globular clusters is inconsistent with the observed ∣z∣ distribution of the combined population of candidate and confirmed BH LMXBs (although here we ignore the potential contribution of an initial population of globular clusters that has been disrupted).

Current electromagnetic detection and mass measurement techniques appear biased against massive Galactic BH LMXBs, and these selection effects may help explain the discrepancy between BH mass distributions in LMXB and GW samples. However, as we have explored in Section 3.6, future detection or mass determination strategies focused on BH LMXBs residing in the plane of the Galaxy (for instance, mass measurement using the James Webb Space Telescope) may allow the identification of Galactic LMXBs as massive as those found through LIGO/Virgo's GW detections.

P.G.J. acknowledges the Caltech Kingsley distinguished visitor program and the hospitality at Caltech, where this work was initiated. K.K. and N.C.S. gratefully acknowledge support from the Israel Science Foundation (Individual Research Grant 2565/19). K.K. also thanks the Israel Academy of Sciences and Humanities for supporting her work with an IASH Postdoctoral Fellowship. M.A.P.T. acknowledges support via Ramón y Cajal Fellowship RYC-2015-17854 and MINECO grant AYA2017-83216-P. We would like to thank the anonymous referee for comments that improved the paper.

The data and scripts behind the figures are available through Zenodo: 10.5281/zenodo.5515231.