Low-mass X-ray Binary Systems Research Articles

Estimation of the accuracy of methods for determining component masses for low-mass X-ray binary systems

Modern modeling of the population of low-mass X-ray binary systems containing black holes applying standard assumptions leads to a lack of agreement between the modeled and observed mass distributions for the optical components, with the observed masses being lower. This makes the task of estimating the systematic errors in the derived component masses due to imperfect models relevant. To estimate the influence of systematic errors in the derived masses of stars in X-ray binary systems, we considered two approximations for the tidally deformed star in a Roche model. Approximating the star as a sphere with a volume equal to that of the Roche lobe leads to slight overestimation of the equatorial rotational velocity V rot sin i, and hence to slight underestimation of the mass ratio q = M x /M v . Approximating the star as a flat, circular disk with constant local line profiles and a linear limb-darkening law (a classical rotational broadeningmodel) is an appreciably cruder approach, and leads to overestimation of V rot sin i by about 20%. In the case of high values of q = M x /M v , this approximation leads to substantial underestimation of the mass ratio q, which can reach several tens of percent. The mass of the optical star is overestimated by a factor of 1.5 in this case, while the mass of the black hole is changed only slightly. Since most estimates of component mass ratios for X-ray binary systems are carried out using a classical rotational broadening model for the lines, this leads to the need for appreciable corrections to (reductions of) previously published masses for the optical stars, which enhances the contradiction with the standard evolutionary scenario for low-mass X-ray binaries containing black holes.

Study of the reflection spectrum of the LMXB 4U 1702-429

The source 4U 1702-429 (Ara X-1) is a low-mass X-ray binary system hosting a neutron star. Albeit the source is quite bright ( $\sim10^{37}$ erg s$^{-1}$) its broadband spectrum has never been studied. Neither dips nor eclipses have been observed in the light curve suggesting that its inclination angle is smaller than 60$^{\circ}$.We analysed the broadband spectrum of 4U 1702-429 in the 0.3-60 keV energy range, using XMM-Newton and INTEGRAL data, to constrain its Compton reflection component if it is present. After excluding the three time intervals in which three type-I X-ray bursts occurred, we fitted the joint XMM-Newton and INTEGRAL spectra obtained from simultaneous observations. A broad emission line at 6.7 keV and two absorption edges at 0.87 and 8.82 keV were detected. We found that a self-consistent reflection model fits the 0.3-60 keV spectrum well. The broadband continuum is composed of an emission component originating from the inner region of the accretion disc, a Comptonised direct emission coming from a corona with an electron temperature of $2.63 \pm 0.06$ keV and an optical depth $\tau=13.6 \pm 0.2$, and, finally, a reflection component. The best-fit indicates that the broad emission line and the absorption edge at 8.82 keV, both associated with the presence of \ion{Fe}{xxv} ions, are produced by reflection in the region above the disc with a ionisation parameter of $Log(\xi) \simeq 2.7$. We have inferred that the inner radius, where the broad emission line originates, is $64^{+52}_{-15}$ km, and the inner radius of the accretion disc is $39^{+6}_{-8}$ km. (Abridged)

New orbital ephemerides for the dipping source 4U 1323-619: constraining the distance to the source

4U 1323-619 is a low mass X-ray binary system that shows type I X-ray bursts and dips. The most accurate estimation of the orbital period is 2.941923(36) hrs and a distance from the source that is lower than 11 kpc has been proposed. We aim to obtain the orbital ephemeris, the orbital period of the system, as well as its derivative to compare the observed luminosity with that predicted by the theory of secular evolution. We took the advantage of about 26 years of X-ray data and grouped the selected observations when close in time. We folded the light curves and used the timing technique, obtaining 12 dip arrival times. We fit the delays of the dip arrival times both with a linear and a quadratic function. We locate 4U 1323-619 within a circular area centred at RA (J2000)= 201.6543\degree and DEC (J2000)= -62.1358\degree with an associated error of 0.0002\degree, and confirm the detection of the IR counterpart already discussed in literature. We estimate an orbital period of P=2.9419156(6) hrs compatible with the estimations that are present in the literature, but with an accuracy ten times higher. We also obtain a constraint on the orbital period derivative for the first time, estimating $\dot{P}=(8\pm 13)\times 10^{-12}$ s/s. Assuming that the companion star is in thermal equilibrium in the lower main sequence, and is a neutron star of 1.4 M$_{\odot}$, we infer a mass of 0.28$\pm$0.03 M$_{\odot}$ for the companion star. Assuming a distance of 10 kpc, we obtained a luminosity of (4.3$\pm$0.5)$\times 10^{36}$ erg s$^{-1}$, which is not in agreement with what is predicted by the theory of secular evolution. Using a 3D extinction map of the K$_{s}$ radiation in our Galaxy, we obtain a distance of 4.2$^{+0.8}_{-0.7}$ kpc at 68\% confidence level. (Abridged)

Observational constraints on neutron star masses and radii

Precise and reliable measurements of the masses and radii of neutron stars with a variety of masses would provide valuable guidance for improving models of the properties of cold matter with densities above the saturation density of nuclear matter. Several different approaches for measuring the masses and radii of neutron stars have been tried or proposed, including analyzing the X-ray fluxes and spectra of the emission from neutron stars in quiescent low-mass X-ray binary systems and thermonuclear burst sources; fitting the energy-dependent X-ray waveforms of rotation-powered millisecond pulsars, burst oscillations with millisecond periods, and accretion-powered millisecond pulsars; and modeling the gravitational radiation waveforms of coalescing double neutron star and neutron star -- black hole binary systems. We describe the strengths and weaknesses of these approaches, most of which currently have substantial systematic errors, and discuss the prospects for decreasing the systematic errors in each method.

Fundamental frequencies in the Schwarzschild Spacetime

We consider the Keplerian, radial and vertical fundamental frequencies in the Schwarzschild spacetime to study the so-called kilohertz quasi-periodic oscillations from low-mass X-ray binary systems. We show that, within the Relativistic Precession Model, the interpretation of observed kilohertz quasi-periodic oscillations in terms of the fundamental frequencies of test particles in the Schwarzschild spacetime, allows one to infer the total mass $M$ of the central object, the internal $R_{in}$ and external $R_{ex}$ radii of accretion disks, and innermost stable circular orbits $r_{ISCO}$ for test particles in a low-mass X-ray binary system. By constructing the relation between the upper and lower frequencies and exploiting the quasi-periodic oscillation data of the Z and Atoll sources we perform the non-linear model fit analysis and estimate the mass of the central object. Knowing the value of the mass we calculate the internal $R_{in}$ and external $R_{ex}$ radii of accretion disks and show that they are larger than $r_{ISCO}$, what was expected.

RADIO IMAGING OBSERVATIONS OF PSR J1023+0038 IN AN LMXB STATE

The transitional millisecond pulsar binary system PSR J1023+0038 re-entered an accreting state in 2013 June, in which it bears many similarities to low-mass X-ray binaries (LMXBs) in quiescence or near-quiescence. At a distance of just 1.37 kpc, PSR J1023+0038 offers an unsurpassed ability to study low-level accretion onto a highly-magnetized compact object. We have monitored PSR J1023+0038 intensively using radio imaging with the Karl G. Jansky Very Large Array, the European VLBI Network and LOFAR, seeing rapidly variable, flat spectrum emission that persists over a period of 6 months. The flat spectrum and variability are indicative of synchrotron emission originating in an outflow from the system, most likely in the form of a compact, partially self-absorbed jet, as is seen in LMXBs at higher accretion rates. The radio brightness, however, greatly exceeds extrapolations made from observations of more vigorously accreting neutron star LMXB systems. We postulate that PSR J1023+0038 is undergoing radiatively inefficient 'propeller-mode' accretion, with the jet carrying away a dominant fraction of the liberated accretion luminosity. We confirm that the enhanced gamma-ray emission seen in PSR J1023+0038 since it re-entered an accreting state has been maintained; the increased gamma-ray emission in this state can also potentially be associated with propeller-mode accretion. Similar accretion modes can be invoked to explain the radio and X-ray properties of the other two known transitional millisecond pulsar systems XSS J12270-4859 and PSR J1824-2452I (M28I), suggesting that radiatively inefficient accretion may be an ubiquitous phenomenon amongst (at least one class of) neutron star binaries at low accretion rates.

Taking into account the effects of component proximity on the spectral-line profiles of stars in low-mass X-ray binary systems

An exact calculation of CaI λ6439 A absorption profiles in the spectra of optical stars in low-mass X-ray binary systems is carried out. The calculations are used to revise a formula relating the rotational broadening of lines and the component-mass ratio. In the case of modest (substantial) X-ray heating, failure to take into account the tidal-rotational deformation of the figure of the star leads to overestimation (underestimation) of the mass of the relativistic object. The radial-velocity curves of optical stars are modeled for binary systems with various parameters and X-ray heating powers kx; corresponding tables ofK corrections are presented. Refined values for the component-mass ratio q = 23 ± 1, black-hole mass Mx = 8.4 ± 0.5, and optical-star mass Mv = 0.36 ± 0.07 for the GS 2023+338 (V404 Cyg) system are presented.

A possible cyclotron resonance scattering feature near 0.7 keV in X1822-371

Context. The source X1822-371 is a low-mass X-ray binary system (LMXB) viewed at a high inclination angle. It hosts a neutron star with a spin period of ~0.59 s, and recently, the spin period derivative was estimated to be (−2.43 ± 0.05) × 10-12 s/s.

IDENTIFICATION OF THE HIGH-ENERGY GAMMA-RAY SOURCE 3FGL J1544.6–1125 AS A TRANSITIONAL MILLISECOND PULSAR BINARY IN AN ACCRETING STATE

We present X-ray, ultraviolet, and optical observations of 1RXS J154439.4-112820, the most probable counterpart of the unassociated Fermi LAT source 3FGL J1544.6-1125. The optical data reveal rapid variability, which is a feature of accreting systems. The X-rays exhibit large-amplitude variations in the form of fast switching (within ~10 s) between two distinct flux levels that differ by a factor of $\approx$10. The detailed optical and X-ray behavior is virtually identical to that seen in the accretion-disk-dominated states of the transitional millisecond pulsar binaries PSR J1023+0038 and XSS J12270-4859, which are also associated with $\gamma$-ray sources. Based on the available observational evidence, we conclude that 1RXS J154439.4-112820 and 3FGL J1544.6-1125 are the same object, with the X-rays arising from intermittent low-luminosity accretion onto a millisecond pulsar and the $\gamma$-rays originating from an accretion-driven outflow. 1RXS J154439.4-112820 is only the fourth $\gamma$-ray emitting low-mass X-ray binary system to be identified and is likely to sporadically undergo transformations to a non-accreting rotation-powered pulsar system.

New possible class of neutron stars: hot and fast non-accreting rotators

A new class of neutron stars (NSs) -- hot rapidly rotating non-accreting NSs, which we propose to call HOFNARs (HOt and Fast Non-Accreting Rotators) or "hot widows" (in analogy with "black widow" pulsars) -- is suggested. We argue that such stars should originate from the low-mass X-ray binaries (LMXBs) provided that they were unstable with respect to excitation of $r$-modes at the end of accretion epoch (when their low-mass companions ceased to fill the Roche lobe). High temperature of "hot widows"/HOFNARs is maintained by $r$-mode dissipation rather than by accretion. We analyse observational properties of "hot widows"/HOFNARs and demonstrate that these objects form a specific separate class of neutron stars. In particular, some of the most stable X-ray sources among the candidates to quiescent LMXB systems (qLMXBs), can, in fact, belong to that new class. We formulate observational criteria which allow to distinguish "hot widows"/HOFNARs from qLMXB systems, and argue that available observations of X-ray sources 47 Tuc X5 and X7 satisfy (or, at least, do not contradict) these criteria. In addition, we discuss indirect evidences in favor of "hot widows"/HOFNARs existence, following from the analysis of observations and predictions of population synthesis theories. If that new class of NSs does exist, it would prove the possibility to emit gravitational waves by mass-current multipole. Various applications of our results, such as prospects for constraining superdense matter properties with hot widows"/HOFNARs, are analyzed.

NuSTAROBSERVATIONS OF THE STATE TRANSITION OF MILLISECOND PULSAR BINARY PSR J1023+0038

We report NuSTAR observations of the millisecond pulsar - low mass X-ray binary (LMXB) transition system PSR J1023+0038 from June and October 2013, before and after the formation of an accretion disk around the neutron star. Between June 10-12, a few days to two weeks before the radio disappearance of the pulsar, the 3-79 keV X-ray spectrum was well fit by a simple power law with a photon index of Gamma=1.17 +/-0.08 (at 90% confidence) with a 3-79 keV luminosity of 7.4+/-0.4 x 10^32 erg/s. Significant orbital modulation was observed with a modulation fraction of 36+/-10%. During the October 19-21 observation, the spectrum is described by a softer power law (Gamma=1.66+/-0.06) with an average luminosity of 5.8+/-0.2 x 10^33 erg/s and a peak luminosity of ~1.2 x 10^34 erg/s observed during a flare. No significant orbital modulation was detected. The spectral observations are consistent with previous and current multi-wavelength observations and show the hard X-ray power law extending to 79 keV without a spectral break. Sharp edged, flat bottomed `dips' are observed with widths between 30-1000 s and ingress and egress time-scales of 30-60 s. No change in hardness ratio was observed during the dips. Consecutive dip separations are log-normal in distribution with a typical separation of approximately 400 s. These dips are distinct from dipping activity observed in LMXBs. We compare and contrast these dips to observations of dips and state changes in the similar transition systems PSR J1824-2452I and XSS J1227.0-4859 and discuss possible interpretations based on the transitions in the inner disk.

A STATE CHANGE IN THE MISSING LINK BINARY PULSAR SYSTEM PSR J1023+0038

We present radio, X-ray, and gamma-ray observations which reveal that the binary millisecond pulsar / low-mass X-ray binary transition system PSR J1023+0038 has undergone a transformation in state. Whereas until recently the system harbored a bright millisecond radio pulsar, the radio pulsations at frequencies between 300 to 5000 MHz have now become undetectable. Concurrent with this radio disappearance, the gamma-ray flux of the system has quintupled. We conclude that, though the radio pulsar is currently not detectable, the pulsar mechanism is still active and the pulsar wind, as well as a newly formed accretion disk, are together providing the necessary conditions to create the gamma-ray increase. The system is the first example of a transient, compact, low-mass gamma-ray binary and will continue to provide an exceptional test bed for better understanding the formation of millisecond pulsars as well as accretion onto neutron stars in general.

A Statistical Study of the Mass Distribution of Neutron Stars

By reviewing the methods of mass measurements of neutron stars in four different kinds of systems, i.e., the high-mass X-ray binaries (HMXBs), low-mass X-ray binaries (LMXBs), double neutron star systems (DNSs) and neutron star-white dwarf (NS-WD) binary systems, we have collected the orbital parameters of 40 systems. By using the boot-strap method and the Monte-Carlo method, we have rebuilt the likelihood probability curves of the measured masses of 46 neutron stars. The statistical analysis of the simulation results shows that the masses of neutron stars in the X-ray neutron star systems and those in the radio pulsar systems exhibit different distributions. Besides, the Bayes statistics of these four different kind systems yields the most-probable probability density distributions of these four kind systems to be (1.340 ± 0.230)M8, (1, 505 ± 0.125)M8,(1.335 ± 0.055)M8 and (1.495 ± 0.225)M8, respectively. It is noteworthy that the masses of neutron stars in the HMXB and DNS systems are smaller than those in the other two kind systems by approximately 0.16M8. This result is consistent with the theoretical model of the pulsar to be accelerated to the millisecond order of magnitude via accretion of approximately 0.2M8. If the HMXBs and LMXBs are respectively taken to be the precursors of the BNS and NS-WD systems, then the influence of the accretion effect on the masses of neutron stars in the HMXB systems should be exceedingly small. Their mass distributions should be very close to the initial one during the formation of neutron stars. As for the LMXB and NS-WD systems, they should have already under- gone the process of suffcient accretion, hence there arises rather large deviation from the initial mass distribution.

A state change in the low-mass X-ray binary XSS J12270−4859

Millisecond radio pulsars acquire their rapid rotation rates through mass and angular momentum transfer in a low-mass X-ray binary system. Recent studies of PSR J1824-2452I and PSR J1023+0038 have observationally demonstrated this link, and they have also shown that such systems can repeatedly transition back-and-forth between the radio millisecond pulsar and low-mass X-ray binary states. This also suggests that a fraction of such systems are not newly born radio millisecond pulsars but are rather suspended in a back-and-forth state switching phase, perhaps for giga-years. XSS J12270-4859 has been previously suggested to be a low-mass X-ray binary, and until recently the only such system to be seen at MeV-GeV energies. We present radio, optical and X-ray observations that offer compelling evidence that XSS J12270-4859 is a low-mass X-ray binary which transitioned to a radio millisecond pulsar state between 2012 November 14 and 2012 December 21. Though radio pulsations remain to be detected, we use optical and X-ray photometry/spectroscopy to show that the system has undergone a sudden dimming and no longer shows evidence for an accretion disk. The optical observations constrain the orbital period to 6.913+-0.002 hr.

Orbital motion and quasi-quantized disk around rotating neutron stars

In accreting neutron star (NS) low-mass X-ray binary (LMXB) systems, NS accretes material from its low-mass companion via a Keplerian disk. In a viscous accretion disk, inflows orbit the NS and spiral in due to dissipative processes, such as the viscous process and collisions of elements. The dynamics of accretion flows in the inner region of an accretion disk is significantly affected by the rotation of NS. The rotation makes NS, thus the spacetime metric, deviate from the originally spherical symmetry, and leads to gravitational quadrupole, on one hand. On the other hand, a rotating NS drags the local inertial frame in its vicinity, which is known as the rotational frame-dragging effect. In this paper, we investigate the orbital motion of accretion flows of accreting NS/LMXBs and demonstrate that the rotational effects of NS result in a band of quasi-quantized structure in the inner region of the accretion disk, which is different, in nature, from the scenario in the strong gravity of black hole arising from the resonance for frequencies related to epicyclic and orbital motions. We also demonstrate that such a disk structure may account for frequencies seen in X-ray variability, such as quasi-periodic oscillations (QPOs), and can be a potential promising tool for the investigation of photon polarization.

The puzzling symbiotic X-ray system 4U1700+24

Symbiotic X-ray binaries form a subclass of low-mass X-ray binary systems consisting of a neutron star accreting material from a red giant donor star via stellar wind or Roche lobe overflow. Only a few confirmed members are currently known; 4U 1700+24 is a good candidate as it is a relatively bright X-ray object, possibly associated with the late-type star V934 Her. We analysed the archive {\it XMM}-Newton and Swift/XRT observations of 4U 1700+24 in order to have a uniform high-energy ($0.3-10$ keV) view of the source. We confirmed the existence of a red-shifted O VIII Ly-$\alpha$ transition (already observed in the 2002 {\it XMM}-Newton data) in the high-resolution spectra collected via the RGS instruments. The red-shift of the line is found in all the analysed observations and, on average, it was estimated to be $\simeq 0.009$. We also observed a modulation of the centroid energy of the line on short time scales (a few days) and discuss the observations in the framework of different scenarios. If the modulation is due to the gravitational red-shift of the neutron star, it might arise from a sudden re-organization of the emitting $X$-ray matter on the scale of a few hundreds of km. Alternatively, we are witnessing a uni-polar jet of matter (with typical velocity of $1000-4000$ km s$^{-1}$) possibly emitted by the neutron star in an almost face-on system. The second possibility seems to be required by the apparent lack of any modulation in the observed $X$-ray light curve. We also note also that the low-resolution spectra (both {\it XMM}-Newton and Swift/XRT in the $0.3-10$ keV band) show the existence of a black body radiation emitted by a region (possibly associated with the neutron star polar cap) with typical size from a few tens to hundreds of meters. The size of this spot-like region reduces as the overall luminosity of 4U 1700+24 decreases.

ABeppoSAXandXMM-Newtonspectral study of 4U 1735-44

Low-mass X-ray binary systems consist of a neutron star and a main-sequence companion star. The compact object accretes matter via Roche-lobe overflow, which leads to an accretion disk. In addition to a broad-band continuum emission of a thermal component and a Comptonization part, evidence for a broad iron K{\alpha} line is found in several sources. Some of them show an asymmetric line profile as well, which could originate from relativistic effects. To understand the spectral behavior of the system 4U 1735-44, we study the broad-band spectrum and especially the iron line feature between 6.4 and 6.97 keV. The shape of the line allows one to determine the region where the line is produced. Together with the continuum models, a geometrical model of the source can be proposed. Furthermore, the effects of pile-up in the XMM-Newton observation are investigated. We analyzed data obtained with the X-ray satellites BeppoSAX and XMM-Newton. The XMM-Newton data were analyzed, specifically taking into account pile-up effects. With the help of the data of these two satellites, we performed a detailed spectral study in an energy range from 0.2-24 keV. During the observations, the source was in the so-called banana state of an atoll source. Fitting the BeppoSAX data, we found line features that we were able to model with a reflection model, whereas the continuum was modeled with a combination of a thermal component and a Comptonization part. The analysis of the XMM-Newton data gave evidence for a broad but not asymmetric iron line. We found no broadening or asymmetry of the line because of pile-up.

Evolution of low-mass X-ray binaries: dependence on the mass of the compact object

We perform numerical calculations to simulate the evolution of low-mass X-ray binary systems. For the accreting compact object we consider the initial mass of 1.4, 10, 20, 100, 200, 500 and 1000 M⊙, corresponding to neutron stars (NSs), stellar-mass black holes (BHs) and intermediate-mass BHs. Mass transfer in these binaries is driven by nuclear evolution of the donors and/or orbital angular momentum loss due to magnetic braking and gravitational wave radiation. For the different systems, we determine their bifurcation periods Pbif that separate the formation of converging systems from the diverging ones, and show that Pbif changes from ∼ 1 d to ≳ 3 d for a 1 M⊙ donor star, with increasing initial accretor mass from 1.4 to 1000 M⊙. This means that the dominant mechanism of orbital angular momentum loss changes from magnetic braking to gravitational radiation. As an illustration we compare the evolution of binaries consisting of a secondary star of 1 M⊙ at a fixed initial period of 2 d. In the case of the NS or stellar-mass BH accretor, the system evolves to a well-detached He white dwarf-neutron star/black hole pair, but it evolves to an ultra-compact binary if the compact object is an intermediate-mass BH. Thus the binary evolution heavily depends upon the mass of the compact object. However, we show that the final orbital period-white dwarf mass relation found for NS low-mass X-ray binaries is fairly insensitive to the initial mass of the accreting star, even if it is an intermediate-mass BH.

POSSIBLE DETECTION OF AN EMISSION CYCLOTRON RESONANCE SCATTERING FEATURE FROM THE ACCRETION-POWERED PULSAR 4U 1626–67

We present analysis of 4U 1626-67, a 7.7 s pulsar in a low-mass X-ray binary system, observed with the hard X-ray detector of the Japanese X-ray satellite Suzaku in March 2006 for a net exposure of \sim88 ks. The source was detected at an average 10-60 keV flux of \sim4 x10^-10 erg cm^-2 s^-1. The phase-averaged spectrum is reproduced well by combining a negative and positive power-law times exponential cutoff (NPEX) model modified at \sim 37 keV by a cyclotron resonance scattering feature (CRSF). The phase-resolved analysis shows that the spectra at the bright phases are well fit by the NPEX with CRSF model. On the other hand, the spectrum in the dim phase lacks the NPEX high-energy cutoff component, and the CRSF can be reproduced by either an emission or an absorption profile. When fitting the dim phase spectrum with the NPEX plus Gaussian model, we find that the feature is better described in terms of an emission rather than an absorption profile. The statistical significance of this result, evaluated by means of an F-test, is between 2.91 x 10^-3 and 1.53 x 10^-5, taking into account the systematic errors in the background evaluation of HXD-PIN. We find that, the emission profile is more feasible than the absorption one for comparing the physical parameters in other phases. Therefore, we have possibly detected an emission line at the cyclotron resonance energy in the dim phase.

THE MASS DISTRIBUTION OF STELLAR-MASS BLACK HOLES

We perform a Bayesian analysis of the mass distribution of stellar-mass black holes using the observed masses of 15 low-mass X-ray binary systems undergoing Roche lobe overflow and five high-mass, wind-fed X-ray binary systems. Using Markov Chain Monte Carlo calculations, we model the mass distribution both parametrically---as a power law, exponential, gaussian, combination of two gaussians, or log-normal distribution---and non-parametrically---as histograms with varying numbers of bins. We provide confidence bounds on the shape of the mass distribution in the context of each model and compare the models with each other by calculating their relative Bayesian evidence as supported by the measurements, taking into account the number of degrees of freedom of each model. The mass distribution of the low-mass systems is best fit by a power-law, while the distribution of the combined sample is best fit by the exponential model. We examine the existence of a "gap" between the most massive neutron stars and the least massive black holes by considering the value, M_1%, of the 1% quantile from each black hole mass distribution as the lower bound of black hole masses. The best model (the power law) fitted to the low-mass systems has a distribution of lower-bounds with M_1% > 4.3 Msun with 90% confidence, while the best model (the exponential) fitted to all 20 systems has M_1% > 4.5 Msun with 90% confidence. We conclude that our sample of black hole masses provides strong evidence of a gap between the maximum neutron star mass and the lower bound on black hole masses. Our results on the low-mass sample are in qualitative agreement with those of Ozel, et al (2010).