The origin of pulsating ultra-luminous X-ray sources: Low- and intermediate-mass X-ray binaries containing neutron star accretors

Ultra-luminous X-ray sources (ULXs) are those X-ray sources located away from the centre of their host galaxy with luminosities exceeding the Eddington limit of a stellar-mass black hole ($L_X>10^{39}\;{\rm erg\,s}^{-1}$). The discovery of X-ray pulsations in some of these objects (e.g. M82~X-2) suggests that a certain fraction of the ULX population may have a neutron star accretor. We present systematic modelling of low- and intermediate-mass X-ray binaries (LMXBs and IMXBs; donor-star mass range $0.92$--$8.0$~M$_{\odot}$ and neutron-star accretors) to explain the formation of this sub-population of ULXs. Using MESA, we explored the allowed initial parameter space of binary systems consisting of a neutron star and a low- or intermediate-mass donor star that could explain the observed properties of ULXs. Our simulations take into account beaming effects, stellar rotation, general angular momentum losses, and a detailed and self-consistent calculation of the mass-transfer rate. We study the conditions that lead to dynamical stability of these systems, which depends strongly on the response of the donor star to mass loss. Using two values for the initial neutron star mass ($1.3$~M$_{\odot}$ and $2.0$~M$_{\odot}$), we present two sets of mass-transfer calculation grids. We find that LMXBs/IMXBs can produce NS-ULXs with typical time-averaged isotropic-equivalent X-ray luminosities of $10^{39}$--$10^{41}\;{\rm erg\,s}^{-1}$ on a timescale up to $\sim\!1.0\;{\rm Myr}$ for the lower luminosities. We also estimate their likelihood of detection, the types of white-dwarf remnants left behind by the donors, and the total amount of mass accreted by the neutron stars. We also compare our results to the observed pulsating ULXs. Our results suggest that a large subset of the observed pulsating ULX population can be explained by LMXBs/IMXBs undergoing a super-Eddington mass-transfer phase.Comment: 19 pages, 13 figures, Accepted by A&A. Parameter space was increased to include low-mass XRBs and corresponding changes made to the text (including the title) and figures 4, 6-11. Changed axes for figures 1 and 2. Fixed typos and updated references. Added arguments about why spin period is not an accurate reflection of mass accretion rate in the introductio

X-ray luminosity function of high-mass X-ray binaries: Studying the signatures of different physical processes using detailed binary evolution calculations

The ever-expanding observational sample of X-ray binaries (XRBs) makes them excellent laboratories for constraining binary evolution theory. Such constraints can be obtained by studying the effects of various physical assumptions on synthetic X-ray luminosity functions (XLFs) and comparing to observed XLFs. In this work, we focus on high-mass XRBs (HMXBs) and study the effects on the XLF of various, poorly-constrained assumptions regarding physical processes such as the common-envelope phase, the core-collapse, and wind-fed accretion. We use the new binary population synthesis code POSYDON, which employs extensive pre-computed grids of detailed stellar structure and binary evolution models, to simulate the evolution of binaries. We generate 96 synthetic XRB populations corresponding to different combinations of model assumptions. The generated HMXB XLFs are feature-rich, deviating from the commonly assumed single-power law. We find a break in our synthetic XLF at luminosity $\sim 10^{38}$ erg s$^{-1}$, similar to observed XLFs. However, we find also a general overabundance of XRBs (up to a factor of $\sim$10 for certain model parameter combinations) driven primarily by XRBs with black hole accretors. Assumptions about the transient behavior of Be-XRBs, asymmetric supernova kicks, and common-envelope physics can significantly affect the shape and normalization of our synthetic XLFs. We find that less well-studied assumptions regarding the circularization of the orbit at the onset of Roche-lobe overflow and criteria for the formation of an X-ray emitting accretion disk around wind-accreting black holes can also impact our synthetic XLFs. Our study reveals the importance of large-scale parameter studies, highlighting the power of XRBs in constraining binary evolution theory.Comment: 31 pages, 32 figures, Accepted by A&A. Fixed typos and updated references. Referee's comments were addresse

Active Learning for Computationally Efficient Distribution of Binary Evolution Simulations

Binary stars undergo a variety of interactions and evolutionary phases, critical for predicting and explaining observed properties. Binary population synthesis with full stellar-structure and evolution simulations are computationally expensive requiring a large number of mass-transfer sequences. The recently developed binary population synthesis code POSYDON incorporates grids of MESA binary star simulations which are then interpolated to model large-scale populations of massive binaries. The traditional method of computing a high-density rectilinear grid of simulations is not scalable for higher-dimension grids, accounting for a range of metallicities, rotation, and eccentricity. We present a new active learning algorithm, psy-cris, which uses machine learning in the data-gathering process to adaptively and iteratively select targeted simulations to run, resulting in a custom, high-performance training set. We test psy-cris on a toy problem and find the resulting training sets require fewer simulations for accurate classification and regression than either regular or randomly sampled grids. We further apply psy-cris to the target problem of building a dynamic grid of MESA simulations, and we demonstrate that, even without fine tuning, a simulation set of only $\sim 1/4$ the size of a rectilinear grid is sufficient to achieve the same classification accuracy. We anticipate further gains when algorithmic parameters are optimized for the targeted application. We find that optimizing for classification only may lead to performance losses in regression, and vice versa. Lowering the computational cost of producing grids will enable future versions of POSYDON to cover more input parameters while preserving interpolation accuracies.Comment: 20 pages (16 main text), 10 figures, submitted to Ap

A Black Hole Kicked At Birth: MAXI J1305-704

When a compact object is formed in a binary, any mass lost during core collapse will impart a kick on the binary's center of mass. Asymmetries in this mass loss would impart an additional natal kick on the remnant black hole or neutron star, whether it was formed in a binary or in isolation. While it is well established that neutron stars receive natal kicks upon formation, it is unclear whether black holes do as well. Here, we consider the low-mass X-ray binary MAXI J1305-704, which has been reported to have a space velocity $\gtrsim$ 200 km/s. In addition to integrating its trajectory to infer its velocity upon formation of its black hole, we reconstruct its evolutionary history, accounting for recent estimates of its period, black hole mass, mass ratio, and donor effective temperature from photometric and spectroscopic observations. We find that if MAXI J1305-704 formed via isolated binary evolution in the thick Galactic disk, then its black hole received a natal kick of at least 70 km/s with 95\% confidence.Comment: To be submitted; 9 pages, 5 figure

The impact of mass-transfer physics on the observable properties of field binary black hole populations

We study the impact of mass-transfer physics on the observable properties of binary black hole populations formed through isolated binary evolution. We investigate the impact of mass-accretion efficiency onto compact objects and common-envelope efficiency on the observed distributions of $\chi_{eff}$, $M_{chirp}$ and $q$. We find that low common envelope efficiency translates to tighter orbits post common envelope and therefore more tidally spun up second-born black holes. However, these systems have short merger timescales and are only marginally detectable by current gravitational-waves detectors as they form and merge at high redshifts ($z\sim 2$), outside current detector horizons. Assuming Eddington-limited accretion efficiency and that the first-born black hole is formed with a negligible spin, we find that all non-zero $\chi_{eff}$ systems in the detectable population can come only from the common envelope channel as the stable mass-transfer channel cannot shrink the orbits enough for efficient tidal spin-up to take place. We find the local rate density ($z\simeq 0.01$) for the common envelope channel is in the range $\sim 17-113~Gpc^{-3}yr^{-1}$ considering a range of $\alpha_{CE} \in [0.2,5.0]$ while for the stable mass transfer channel the rate density is $\sim 25~Gpc^{-3}yr^{-1}$. The latter drops by two orders of magnitude if the mass accretion onto the black hole is not Eddington limited because conservative mass transfer does not shrink the orbit as efficiently as non-conservative mass transfer does. Finally, using GWTC-2 events, we constrain the lower bound of branching fraction from other formation channels in the detected population to be $\sim 0.2$. Assuming all remaining events to be formed through either stable mass transfer or common envelope channels, we find moderate to strong evidence in favour of models with inefficient common envelopes.Comment: 26 pages, 13 figures, accepted for publication in A&

Investigating the Lower Mass Gap with Low Mass X-ray Binary Population Synthesis

Mass measurements from low-mass black hole X-ray binaries (LMXBs) and radio pulsars have been used to identify a gap between the most massive neutron stars (NSs) and the least massive black holes (BHs). BH mass measurements in LMXBs are typically only possible for transient systems: outburst periods enable detection via all-sky X-ray monitors, while quiescent periods enable radial-velocity measurements of the low-mass donor. We quantitatively study selection biases due to the requirement of transient behavior for BH mass measurements. Using rapid population synthesis simulations (COSMIC), detailed binary stellar-evolution models (MESA), and the disk instability model of transient behavior, we demonstrate that transient-LMXB selection effects introduce observational biases, and can suppress mass-gap BHs in the observed sample. However, we find a population of transient LMXBs with mass-gap BHs form through accretion-induced collapse of a NS during the LMXB phase, which is inconsistent with observations. These results are robust against variations of binary evolution prescriptions. The significance of this accretion-induced collapse population depends upon the maximum NS birth mass $M_\mathrm{ NS, birth-max}$. To reflect the observed dearth of low-mass BHs, COSMIC and MESA models favor $M_\mathrm{ NS, birth-max} \lesssim2M_{\odot}$. In the absence of further observational biases against LMXBs with mass-gap BHs, our results indicate the need for additional physics connected to the modeling of LMXB formation and evolution.Comment: 21 pages, accepted to Ap

POSYDON: A General-Purpose Population Synthesis Code with Detailed Binary-Evolution Simulations

Most massive stars are members of a binary or a higher-order stellar systems, where the presence of a binary companion can decisively alter their evolution via binary interactions. Interacting binaries are also important astrophysical laboratories for the study of compact objects. Binary population synthesis studies have been used extensively over the last two decades to interpret observations of compact-object binaries and to decipher the physical processes that lead to their formation. Here, we present POSYDON, a novel, binary population synthesis code that incorporates full stellar-structure and binary-evolution modeling, using the MESA code, throughout the whole evolution of the binaries. The use of POSYDON enables the self-consistent treatment of physical processes in stellar and binary evolution, including: realistic mass-transfer calculations and assessment of stability, internal angular-momentum transport and tides, stellar core sizes, mass-transfer rates and orbital periods. This paper describes the detailed methodology and implementation of POSYDON, including the assumed physics of stellar- and binary-evolution, the extensive grids of detailed single- and binary-star models, the post-processing, classification and interpolation methods we developed for use with the grids, and the treatment of evolutionary phases that are not based on pre-calculated grids. The first version of POSYDON targets binaries with massive primary stars (potential progenitors of neutron stars or black holes) at solar metallicity.Comment: 60 pages, 33 figures, 8 tables, referee's comments addressed. The code and the accompanying documentations and data products are available at https:\\posydon.or

Formation and evolution of X-ray binaries: Exploring Ultra-luminous X-ray Sources

X-ray binaries (XRBs) are some of the brightest X-ray sources in the Universe. The emission from XRBs is produced by the transfer of material from a star onto a compact object serving as its companion. The brightest of XRBs are ultra-luminous X-ray sources (ULXs), with X-ray luminosities greater than 1039 erg s-1 (which is about the Eddington limit of a 10Msun black hole). Observations of coherent X-ray pulsations in a subset of ULXs indicate the presence of an accreting neutron star. Considering that the Eddington limit of a neutron star is ~1038 erg s-1, it makes these pulsating ULXs highly super-Eddington. This thesis aims at studying the formation and evolution of ULXs, and by extension XRBs as a whole. We investigate ULXs in the form of XRBs undergoing super-Eddington mass-transfer phases and include super-Eddington disc models to help explain their luminosities. In doing so, we also investigate the stability of mass transfer in XRBs and formulate a method of constraining the mass-transfer stability in semi-detached binaries, using the overflow from the second Lagrange point as a constraint. We study the demographic of ULX populations at different ages of stellar populations, and the effect of different assumptions of accretion physics on ULXs. In order to carry out these studies, we used population synthesis techniques in combination with detailed stellar and binary evolutionary calculations. Given the uncertainties that currently exist in our understanding of binary interactions and assumptions that need to be made for evolutionary phases (for instance, the efficiency in the common-envelope phase), we carried out a parameter study with the aim of constraining the said physics. We base our studies of ULX populations on the results of the parameter study and draw conclusions from the inferred information, finding that observations of ULXs could be used to constrain the treatment of kicks in binaries and that NS-ULXs are almost always geometrically beamed whereas BH-ULXs are beamed in ~50% of the cases. Future studies, including a wider range of metallicities, will aid us better in our understanding of sources like ULXs that are more abundant in sub-solar metallicities. </p

BMI does not accurately predict overweight in Asian Indians in northern India

Asian Indians are at high risk for the development of atherosclerosis and related complications, possibly initiated by higher body fat (BF). The present study attempted to establish appropriate cut-off levels of the BMI for defining overweight, considering percentage BF in healthy Asian Indians in northern India as the standard. A total of 123 healthy volunteers (eighty-six males aged 18–75 years and thirty-seven females aged 20–69 years) participated in the study. Clinical examination and anthropometric measurements were performed, and percentage BF was calculated. BMI for males was 21·4 (SD 3·7) KG/M2 AND FOR FEMALES WAS 23·3 (sd 5·5) kg/m2. Percentage BF was 21·3 (sd 7·6) in males and 35·4 (sd 5·0) in females. A comparison of BF data among Caucasians, Blacks, Polynesians and Asian ethnic groups (e.g. immigrant Chinese) revealed conspicuous differences. Receiver operating characteristic (ROC) curve analysis showed a low sensitivity and negative predictive value of the conventional cut-off value of the BMI (25 kg/m2) in identifying subjects with overweight as compared to the cut-off value based on percentage BF (males >25, females >30). This observation is particularly obvious in females, resulting in substantial misclassification. Based on the ROC curve, a lower cut-off value of the BMI (21·5 kg/m2 for males and 19·0 kg/m2 for females) displayed the optimal sensitivity and specificity, and less misclassification in identification of subjects with high percentage BF. Furthermore, a novel obesity variable, BF:BMI, was tested and should prove useful for interethnic comparison of body composition. In the northern Indian population, the conventional cut-off level of the BMI underestimates overweight and obesity when percentage BF is used as the standard to define overweight. These preliminary findings, if confirmed in a larger number of subjects and with the use of instruments having a higher accuracy of BF assessment, would be crucial for planning and the prevention and treatment of various obesity-related metabolic diseases in the Asian Indian population