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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

The Origin of the Doppler Flip in HD 100546: A Large-scale Spiral Arm Generated by an Inner Binary Companion

Companions at subarcsecond separation from young stars are difficult to image. However, their presence can be inferred from the perturbations they create in the dust and gas of protoplanetary disks. Here we present a new interpretation of SPHERE polarized observations that reveal the previously detected inner spiral in the disk of HD 100546. The spiral coincides with a newly detected 12 CO inner spiral and the previously reported CO emission Doppler flip, which has been interpreted as the signature of an embedded protoplanet. Comparisons with hydrodynamical models indicate that this Doppler flip is instead the kinematic counterpart of the spiral, which is likely generated by an inner companion inside the disk cavity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The population of hot subdwarf stars studied with Gaia: IV. Catalogues of hot subluminous stars based on Gaia EDR3

In light of substantial new discoveries of hot subdwarfs by ongoing spectroscopic surveys and the availability of the Gaia mission Early Data Release 3 (EDR3), we compiled new releases of two catalogues of hot subluminous stars: The data release 3 (DR3) catalogue of the known hot subdwarf stars contains 6616 unique sources and provides multi-band photometry, and astrometry from Gaia EDR3 as well as classifications based on spectroscopy and colours. This is an increase of 742 objects over the DR2 catalogue. This new catalogue provides atmospheric parameters for 3087 stars and radial velocities for 2791 stars from the literature. In addition, we have updated the Gaia Data Release 2 (DR2) catalogue of hot subluminous stars using the improved accuracy of the Gaia EDR3 data set together with updated quality and selection criteria to produce the Gaia EDR3 catalogue of 61 585 hot subluminous stars, representing an increase of 21 785 objects. Furthermore, the improvements in Gaia EDR3 astrometry and photometry compared to Gaia DR2 have enabled us to define more sophisticated selection functions. In particular, we improved hot subluminous star detection in the crowded regions of the Galactic plane as well as in the direction of the Magellanic Clouds by including sources with close apparent neighbours but with flux levels that dominate the neighbourhood.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Astrophysical and Theoretical Physics Implications from Multimessenger Neutron Star Observations

Here, the Neutron Star Interior Composition Explorer (NICER) recently measured the mass and equatorial radius of the isolated neutron star PSR J0030+0451. We use these measurements to infer the moment of inertia, the quadrupole moment, and the surface eccentricity of an isolated neutron star for the first time, using relations between these quantities that are insensitive to the unknown equation of state of supranuclear matter. We also use these results to forecast the moment of inertia of neutron star A in the double pulsar binary J0737-3039, a quantity anticipated to be directly measured in the coming decade with radio observations. Combining this information with the measurement of the tidal Love number with LIGO/Virgo observations, we propose and implement the first theory-agnostic and equation-of-state-insensitive test of general relativity. Specializing these constraints to a particular modified theory, we find that consistency with general relativity places the most stringent constraint on gravitational parity violation to date, surpassing all other previously reported bounds by 7 orders of magnitude and opens the path for a future test of general relativity with multimessenger neutron star observations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Radial velocity variability and the evolution of hot subdwarf stars

Hot subdwarf stars represent a late and peculiar stage in the evolution of low-mass stars, since they are likely formed by close binary interactions. In this work, we perform a radial velocity (RV) variability study of a sample of 646 hot subdwarfs with multi-epoch radial velocities based on spectra from Sloan Digital Sky Survey (SDSS) and Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST). The atmospheric parameters and RVs were taken from the literature. For stars with archival spectra but without literature values, we determined the parameters by fitting model atmospheres. In addition, we redetermined the atmospheric parameters and RVs for all the He-enriched sdO/Bs. This broad sample allowed us to study RV-variability as a function of the location in theT eff - log g- and T eff - log n (He)/n (H) diagrams in a statistically significant way. We used the fraction of RV-variable stars and the distribution of the maximum RV variations ΔRV max as diagnostics. Both indicators turned out to be quite inhomogeneous across the studied parameter ranges. A striking feature is the completely dissimilar behaviour of He-poor and He-rich hot subdwarfs. While the former have a high fraction of close binaries, almost no significant RV variations could be detected for the latter. This has led us to the conclusion that there is likely no evolutionary connection between these subtypes. On the other hand, intermediate He-rich- and extreme He-rich sdOB/Os are more likely to be related. Furthermore, we conclude that the vast majority of this population is formed via one or several binary merger channels. Hot subdwarfs with temperatures cooler than ~24 000 K tend to show fewer and smaller RV-variations. These objects might constitute a new subpopulation of binaries with longer periods and late-type or compact companions. The RV-variability properties of the extreme horizontal branch (EHB) and corresponding post-EHB populations of the He-poor hot subdwarfs match and confirm the predicted evolutionary connection between them. Stars found below the canonical EHB at somewhat higher surface gravities show large RV variations and a high RV variability fraction. These properties are consistent with most of them being low-mass EHB stars or progenitors of low-mass helium white dwarfs in close binaries.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A Radial-velocity Search for Binary RR Lyrae Variables

We report 272 radial velocities for 19 RR Lyrae variables. For most of the stars we have radial velocities for the complete pulsation cycle. These data are used to determine robust center-of-mass radial velocities that have been compared to values from the literature in a search for evidence of binary systems. Center-of-mass velocities were determined for each star using Fourier Series and template fits to the radial velocities. Our center-of-mass velocities have uncertainties from ±0.16 km s{sup −1} to ±2.5 km s{sup −1}, with a mean uncertainty of ±0.92 km s{sup −1}. We combined our center-of-mass velocities with values from the literature to look for deviations from the mean center-of-mass velocity of each star. Fifteen RR Lyrae show no evidence of binary motion (BK And, CI And, Z CVn, DM Cyg, BK Dra, RR Gem, XX Hya, SZ Leo, BX Leo, TT Lyn, CN Lyr, TU Per, U Tri, RV UMa, and AV Vir). In most cases this conclusion is reached due to the sporadic sampling of the center-of-mass velocities over time. Three RR Lyrae show suspicious variation in the center-of-mass velocities that may indicate binary motion but do not prove it (SS Leo, ST Leo, and AO Peg). TU UMa was observed by us near a predicted periastron passage (at 0.14 in orbital phase) but the absence of additional center-of-mass velocities near periastron makes the binary detection, based on radial velocities alone, uncertain. Two stars in our sample show Hγ emission in phases 0.9–1.0: SS Leo and TU UMa.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

The K2 M67 Study: Precise Mass for a Turnoff Star in the Old Open Cluster M67

We present a study of the bright detached eclipsing main-sequence binary WOCS 11028 (Sanders 617) in the open cluster M67. Although the binary has only one eclipse per orbital cycle, we show that the masses of the stars can be derived very precisely thanks to a strong constraint on the orbital inclination: M {sub A} = 1.222 ± 0.006M {sub ⊙} and M {sub B} = 0.909 ± 0.004M {sub ⊙}. We use a spectral energy distribution fitting method to derive characteristics of the component stars in lieu of the precise radii that would normally be derived from a doubly eclipsing binary. The deconvolution of the SEDs reveals that the brighter component of the binary is at the faint turnoff point for the cluster—a distinct evolutionary point that occurs after the convective core has been established and while the star is in the middle of its movement toward lower surface temperatures, before the so-called hook at the end of the main sequence. The measurements are in distinct disagreement with evolution models at solar metallicity: higher metal abundances are needed to reproduce the characteristics of WOCS 11028 A. We discuss the changes to model physics that are likely to be needed to address the discrepancies. The clearest conclusions are that diffusion is probably necessary to reconcile spectroscopic abundances of M67 stars with the need for higher metallicity models and that reduced strength convective overshooting is occurring for stars at the turnoff. At super-solar bulk metallicity, various indicators agree on a cluster age between about 3.5 and 4.0 Gyr.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Heavy-element production in a compact object merger observed by JWST

The mergers of binary compact objects such as neutron stars and black holes are of central interest to several areas of astrophysics, including as the progenitors of gamma-ray bursts (GRBs), sources of high-frequency gravitational waves (GWs) and likely production sites for heavy-element nucleosynthesis by means of rapid neutron capture (the r -process). Here we present observations of the exceptionally bright GRB 230307A. We show that GRB 230307A belongs to the class of long-duration GRBs associated with compact object mergers and contains a kilonova similar to AT2017gfo, associated with the GW merger GW170817. We obtained James Webb Space Telescope (JWST) mid-infrared imaging and spectroscopy 29 and 61 days after the burst. The spectroscopy shows an emission line at 2.15 microns, which we interpret as tellurium (atomic mass A = 130) and a very red source, emitting most of its light in the mid-infrared owing to the production of lanthanides. These observations demonstrate that nucleosynthesis in GRBs can create r -process elements across a broad atomic mass range and play a central role in heavy-element nucleosynthesis across the Universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

LAMOST Time-Domain survey: first results of four K2 plates

From Oct. 2019 to Apr. 2020, LAMOST performed a time-domain (TD) spectroscopic survey of four K2 plates with both low- and medium-resolution observations. The low-resolution spectroscopic survey acquired 282 exposures ( ≈ 46.6 h) over 25 nights, yielding a total of about 767 000 spectra, and the medium-resolution survey took 177 exposures ( ≈ 49.1 h) over 27 nights, collecting about 478 000 spectra. More than 70%/50% of low-resolution/medium-resolution spectra have signal-to-noise ratio higher than 10. We determine stellar parameters (e.g., T eff , log g, [Fe/H]) and radial velocity (RV) with different methods, including LASP, DD-Payne and SLAM. In general, these parameter estimations from different methods show good agreement, and the stellar parameter values are consistent with those of APOGEE. We use the Gaia DR2 RV values to calculate a median RV zero point (RVZP) for each spectrograph exposure by exposure, and the RVZP-corrected RVs agree well with the APOGEE data. The stellar evolutionary and spectroscopic masses are estimated based on the stellar parameters, multi-band magnitudes, distances and extinction values. Finally, we construct a binary catalog including about 2700 candidates by analyzing their light curves, fitting the RV data, calculating the binarity parameters from medium-resolution spectra and cross-matching the spatially resolved binary catalog from Gaia EDR3. In conclusion, the LAMOST TD survey is expected to represent a breakthrough in various scientific topics, such as binary systems, stellar activity, stellar pulsation, etc.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

TYC 2990-127-1: An Algol-type SB2 binary system of subgiant and red giant with a probable ongoing mass-transfer

ABSTRACT We present a study of the spectroscopic binary TYC 2990-127-1 from the LAMOST survey. We use full-spectrum fitting to derive radial velocities and spectral parameters. The high mass ratio indicates that the system underwent mass transfer in the past. We compute the orbital solution and find that it is a very close sub-giant/red giant pair on circular orbit, slightly inclined to the sky-plane. Fitting of the TESS photometrical data confirms this and suggests an inclination of i ∼ 39.8°. The light curve and spectrum around Hα show signs of irregular variability, which supports ongoing mass transfer. The binary evolution simulations suggest that the binary may experience non-conservative mass transfer with accretion efficiency 0.3, and the binary will enter into common envelope (CE) phase in the subsequent evolution. The remnant product after the ejection of CE may be a detached double helium white dwarf (He WD) or a merger.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Outflowing photoionized plasma in Circinus X-1 using the high-resolution X-ray spectrometer Resolve onboard XRISM and the radiative transfer code cloudy

High-resolution X-ray spectroscopy is a key to understanding the mass inflow and outflow of compact objects. Spectral lines carry information about the ionization, density, and velocity structures through their intensity ratios and profiles. They are formed in non-local thermodynamic equilibrium conditions under the intense radiation field from the compact objects; thus radiative transfer (RT) calculation is a requisite for proper interpretations. We present such a study for a low-mass X-ray binary, Circinus X-1, from which the P Cygni profile was discovered using the X-ray grating spectrometer onboard Chandra. We observed the source using the X-ray microcalorimeter onboard XRISM at an orbital phase of 0.93–0.97 and revealed many spectral features unidentified before: the higher series transitions ($n{\rightarrow }1$; $n>2$) of highly ionized (H- and He-like) S, Ca, Ar, and Fe in emission and absorption, the Fe K$\alpha$ and K$\beta$ inner-shell excitation absorption of mildly ionized (O- to Li-like) Fe, and resolved fine-structure level transitions in the Fe Ly$\alpha$ and He$\alpha$ complexes. They blend with each other at different velocity shifts on top of apparently variable continuum emission that changed its flux by an order of magnitude within a 70 ks telescope time. Despite such complexity in the observed spectra, most of them can be explained by a simple model consisting of the photoionized plasma outflowing at $\sim$300 km s$^{-1}$ and the variable blocking material in the line of sight of the incident continuum emission from the accretion disk. We demonstrate this with the aid of the RT code cloudy for the line ratio diagnostics and spectral fitting. We further constrain the physical parameters of the outflow and argue that the outflow is launched close to the outer edge of the accretion disk and can be driven radiatively by being assisted by the line force calculated using the RT simulation.

X-rays: binaries↗
DOE OSTI2024

Annual IC Progress Report

The goal of this project is to computationally investigate the progenitors of astrophysical gamma-ray bursts (GRB), the most extreme explosions in the universe across length and time scales. We have developed a cutting-edge, code-bridging approach to exploring the physics behind these luminous events to test the hypothesis that GRBs with electromagnetic radio emission originate from massive star (MS) and black hole (BH) binary systems. Our multi-scale, multi-physics theoretical framework for GRBs is based on solving well-defined and testable hydrodynamics problems associated with the dynamical evolution of the system. We solve stages of the evolution in a tractable way with a suite of well-developed state-of-the-art computational tools that include the stellar evolution code MESA, the general relativistic magnetohydrodynamics (GRMHD) code Athena++, and the binary black hole (BBH) population synthesis code COSMIC, as well as a number of self-written python post-processing tools.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Multiwavelength Observation Campaign of the TeV Gamma-Ray Binary HESS J0632 + 057 with NuSTAR, VERITAS, MDM, and Swift

HESS J0632+057 belongs to a rare subclass of binary systems that emit gamma rays above 100 GeV. It stands out for its distinctive high-energy light curve, which features a sharp "primary" peak and broader "secondary" peak. We present the results of contemporaneous observations by NuSTAR and VERITAS during the secondary peak between 2019 December and 2020 February, when the orbital phase (Φ) is between 0.55 and 0.75. NuSTAR detected X-ray spectral evolution, while VERITAS detected TeV emission. We fit a leptonic wind-collision model to the multiwavelength spectra data obtained over the four NuSTAR and VERITAS observations, constraining the pulsar spin-down luminosity and the magnetization parameter at the shock. Despite long-term monitoring of the source from 2019 October to 2020 March, the MDM observatory did not detect significant variation in Hα and Hβ line equivalent widths, an expected signature of Be-disk interaction with the pulsar. Furthermore, fitting folded Swift-XRT light-curve data with an intrabinary shock model constrained the orbital parameters, suggesting two orbital phases (at Φ D = 0.13 and 0.37), where the pulsar crosses the Be-disk, as well as phases for the periastron (Φ 0 = 0.30) and inferior conjunction (Φ IFC = 0.75). The broadband X-ray spectra with Swift-XRT and NuSTAR allowed us to measure a higher neutral hydrogen column density at one of the predicted disk-passing phases.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

XRISM spectroscopy on orbital modulation of Fe Ly α lines in Cygnus X-3

To understand physical processes such as mass transfer and binary evolution in X-ray binaries, the orbital parameters of the system are fundamental and crucial information. Cygnus X-3 is a high-mass X-ray binary composed of a compact object of unknown nature and a Wolf–Rayet star, which is of great interest in the context of wind-fed mass accretion and binary evolution. Here we present XRISM/Resolve high-resolution spectroscopy, focusing on the Fe Ly$\alpha$ lines when the source was in its hypersoft state. We perform an orbital phase-resolved spectral analysis of the lines to study the orbital modulation of the emission and absorption lines. It is found that the emission lines reflect the orbital motion of the compact object whose estimated velocity amplitude is $430^{+150}_{-140}$ km s$^{-1}$, while the absorption lines show a variation that can be interpreted as originating from the stellar wind. We discuss possible mass ranges for the binary components using the mass function with the estimated value of the velocity amplitude in this work, combined with the relation between the mass-loss rate and the orbital period derivative and the empirical mass and mass-loss rate relation for Galactic Wolf–Rayet stars. They are constrained to be (1.3–5.1) and (9.3–12) M$_\odot$, respectively, for the assumed inclination angle of $i =25^\circ$, and become more relaxed, (1.3–24) and (9.3–16) M$_\odot$, for $i = 35^\circ$. Thus, it remains unclear whether the system harbors a black hole or a neutron star.

X-rays: binaries↗
DOE OSTI2020

WIYN Open Cluster Study LXXIX. M48 (NGC 2548) I. Radial Velocities, Rotational Velocities, and Metallicities of Stars in the Open Cluster M48 (NGC 2548)

WIYN/Hydra spectra (R ∼ 13,500, signal-to-noise pixel{sup −1} = 50–1000) of a 400 Å region around Li 6708 Å are used to determine radial and rotational velocities for 287 photometrically selected candidate members of the open cluster M48. The sample ranges from turnoff A stars to late-K dwarfs and eight giants. We combine our V {sub RAD} measurements and power spectrum analysis with parallax and proper motion data from Gaia DR2 to evaluate membership and multiplicity. We classify 152 stars as single cluster members, 11 as binary members, 16 as members of uncertain multiplicity, 56 as single nonmembers, 28 as single “likely” nonmembers, two as single “likely” members, one as a binary “likely” member, five as binary nonmembers, 10 as “likely” members of uncertain multiplicity, three as nonmembers of uncertain multiplicity, and three as “likely” nonmembers of uncertain multiplicity. From a subsample of 95 single members, we derive V {sub RAD} = 8.512 ± 0.087 km s{sup −1} (σ {sub μ}, and σ = 0.848 km s{sup −1}). Using 16 isolated Fe I lines for a subsample of 99 single members (that have σ{sub T{sub e{sub f{sub f}}}}<75 K (from 10 colors from UBVRI), v sin i < 25 km s{sup −1}, and well-behaved Fe I lines), [Fe/H]{sub M48} = −0.063 ± 0.007 dex (σ {sub μ}). [Fe/H] is independent of T {sub eff} over an unprecedentedly large range of 2500 K. The minimum cluster binary fraction is 11%–21%. M48 exhibits a clear but modest broadening of the main-sequence turnoff, and there is no correlation between color and v sin i.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

High-velocity CP2 stars in the Galactic halo

The second subclass of chemically peculiar stars, the CP2 stars, are early-type stars exhibiting anomalous abundances with variable line strengths possibly also accompanied by photometric variability that typically belong to the Galactic disk. However, a small fraction of these objects were recently found to be located far from the Galactic plane and are thought to belong to the Galactic halo, which is unexpected for this class of objects. Our study investigates the halo membership of the proposed halo CP2 star candidates based on their velocities and Galactic orbits, to determine their points of origin. In addition, we searched for further halo CP2 star candidates using an as-yet-unpublished sample of CP stars. Our analysis relied on the astrometry from the early third Gaia data release and radial velocities based on the spectroscopy from LAMOST and SDSS, which was also employed in spectral classification. The light variability of the confirmed CP2 stars in our sample was analyzed using data from the ZTF and ATLAS surveys. After filtering our initial sample using kinematic and spectroscopic criteria, we identified six CP2 stars with kinematical properties consistent with a halo membership. The orbits of these stars are in agreement with an origin in the Galactic disk where they were probably ejected through dynamical interactions or in the binary supernova scenario, making them the first runaway CP2 stars known.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Unexpected Short-period Variability in Dwarf Carbon Stars from the Zwicky Transient Facility

Dwarf carbon (dC) stars, main-sequence stars showing carbon molecular bands, are enriched by mass transfer from a previous asymptotic-giant-branch (AGB) companion, which has since evolved to a white dwarf. While previous studies have found radial-velocity variations for large samples of dCs, there are still relatively few dC orbital periods in the literature and no dC eclipsing binaries have yet been found. Here, we analyze photometric light curves from DR5 of the Zwicky Transient Facility for a sample of 944 dC stars. From these light curves, we identify 34 periodically variable dC stars. Remarkably, of the periodic dCs, 82% have periods less than two days. We also provide spectroscopic follow-up for four of these periodic systems, measuring radial velocity variations in three of them. Short-period dCs are almost certainly post-common-envelope binary systems, because the periodicity is most likely related to the orbital period, with tidally locked rotation and photometric modulation on the dC either from spots or from ellipsoidal variations. We discuss evolutionary scenarios that these binaries may have taken to accrete sufficient C-rich material while avoiding truncation of the thermally pulsing AGB phase needed to provide such material in the first place. We compare these dCs to common-envelope models to show that dC stars probably cannot accrete enough C-rich material during the common-envelope phase, suggesting another mechanism like wind-Roche lobe overflow is necessary. The periodic dCs in this paper represent a prime sample for spectroscopic follow-up and for comparison to future models of wind-Roche lobe overflow mass transfer.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Physical Nature of the Eclipsing δ Scuti Star AO Serpentis

We present the absolute properties of the eclipsing binary AO Ser with a pulsating component from our BV photometric and high-resolution spectroscopic observations, which were performed between 2017 April and May. The radial velocities (RVs) for both components were measured, and the effective temperature and projected rotational velocity of the primary star were determined to be T eff,1 = 8,820 ± 62 K and v 1 sini 1 = 90 ± 18 km s -1 , respectively, by comparing the observed spectrum with the Kurucz models. The accurate fundamental parameters of AO Ser were determined by a simultaneous analysis of the light and RV curves. The masses and radii of the primary and secondary components are M 1 = 2.55 ± 0.09 M ⊙ and R 1 = 1.64 ± 0.02 R ⊙ and M 2 = 0.49 ± 0.02 M ⊙ and R 2 = 1.38 ± 0.02 R ⊙ , respectively. Multiple frequency analyses for the eclipse-subtracted light residuals were conducted. As a result, we detected two frequencies of f 1 = 21.852 days -1 and f 2 = 23.484 days -1 . The evolutionary position on the HR diagram and the pulsational characteristics indicate that the primary star is a δ Sct pulsator with a radial fundamental mode. On the other hand, the relatively evolved secondary is oversized for its own mass.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The role of supernova convection for the lower mass gap in the isolated binary formation of gravitational wave sources

ABSTRACT Understanding the astrophysical phenomena involving compact objects requires an insight about the engine behind the core-collapse supernovae (SNe) and the fate of the stellar collapse of massive stars. In particular, this insight is crucial in developing an understanding of the origin and formation channels of the growing populations of the detected black hole–black hole, black hole–neutron star, and neutron star–neutron star mergers. The time-scale of convection growth may have a large effect on the strength of SN explosion and therefore also on the mass distribution of stellar remnants. We adopt new formulas for the relation between the pre-SN star properties and their remnants and check how they impact the population of double compact object (DCO) mergers formed via the isolated binary evolution. The new formulas give one the ability to test a wide spectrum of assumptions on the convection growth time. In particular, the different variants allow for a smooth transition between having a deep mass gap and a remnant mass distribution filled by massive neutron stars and low-mass black holes. We present the distribution of masses, mass ratios, and the local merger rate densities of DCO for the different variants of new formulas and test them together with different approaches to other highly uncertain processes. We find that the mass distribution of DCO mergers is sensitive to the adopted assumption on the SN convection growth time-scale up to $m_1+m_2 \lesssim 35 \, \mathrm{M}_{\odot }$. Between the two extreme tested variants the probability of compact object formation within the mass gap may differ by up to approximately two orders of magnitude.

79 ASTRONOMY AND ASTROPHYSICS↗