arXiv subjects

K. Belczynski

Publications and source records attributed to K. Belczynski.

At least 19 recordsLinked to original sources

arXiv2024

Common origin for black holes in both high mass X-ray binaries and gravitational-wave sources

Black-hole (BH) high-mass X-ray binary (HMXB) systems are likely to be the progenitors of BH-BH mergers detected by LIGO/Virgo/KAGRA (LVK). Yet merging BHs reach higher masses ($\sim 100M_{\odot}$) than BHs in HMXBs ($\sim 20 M_{\odot}$) and exhibit lower spins ($a_{\rm BH}\lesssim 0.25$ with a larger values tail) than what is often claimed for BHs in HMXBs ($a_{\rm BH}\gtrsim 0.9$). This could suggest that these two classes of systems belong to different populations, but here we show that this may not necessarily be the case. The difference in masses is easily explained as the known HMXB-BHs are in galaxies with relatively high metallicity, so their progenitor stars are subject to strong mass loss from winds, leading to relatively low-mass BH at core collapse. Conversely, LVK is also able to detect BHs from low-metallicity galaxies that produce more massive stellar-origin BHs. The difference in spin is more difficult to explain. Models with efficient angular momentum transport in stellar interiors produce slowly spinning progenitors for both LVK and HMXB BHs. Known HMXBs have orbital periods that are too long for tidal spin-up and are unlikely to have undergone significant accretion spin-up. Instead, we show that the derived value of the BH spin depends strongly on how the HMXB accretion disc emission is modelled. We argue that since Cyg X-1 is never observed in a soft state, the appropriate spectral models must take into account the Comptonisation of the disc photosphere. We show that such models are consistent with low spin values, namely: $a_{\rm BH}\sim 0.1$. This was confirmed by other teams for both Cyg X-1 and LMC X-1 and we show this is also the case for M33 X-7. We conclude that all HMXB BHs can exhibit low spins, in accordance with stellar evolution models. Hence, the observations are consistent with the LVK BHs and HMXB BHs belonging to the same population.

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arXiv2023

The role of stellar expansion on the formation of gravitational wave sources

Massive stars are the progenitors of black holes and neutron stars, the mergers of which can be detected with gravitational waves (GW). The expansion of massive stars is one of the key factors affecting their evolution in close binary systems, but it remains subject to large uncertainties in stellar astrophysics. For population studies and predictions of GW sources, the stellar expansion is often simulated with the analytic formulae from Hurley et al. (2000). These formulae need to be extrapolated for stars beyond 50 solar masses and are often considered outdated. In this work we present five different prescriptions developed from 1D stellar models to constrain the maximum expansion of massive stars. We adopt these prescriptions to investigate how stellar expansion affects mass transfer interactions and in turn the formation of GW sources. We show that limiting radial expansion with updated 1D stellar models, when compared to the use of Hurley et al. (2000) radial expansion formulae, does not significantly affect GW source properties (rates and masses). This is because most mass transfer events leading to GW sources are initialised before the donor star reaches its maximum expansion. The only significant difference was found for the mass distribution of massive binary black hole mergers (total mass > 50 solar masses) formed from stars that may evolve beyond the Humphreys-Davidson limit, whose radial expansion is the most uncertain. We conclude that understanding the expansion of massive stars and the origin of the Humphrey-Davidson limit is a key factor for the study of GW sources.

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arXiv2022

Black hole - neutron star mergers: The first mass gap and kilonovae

Observations of X-ray binaries indicate a dearth of compact objects in the mass range from $\sim 2-5 M_{\odot}$. The existence of this (first mass) gap has been used to discriminate between proposed engines behind core-collapse supernovae. From LIGO/Virgo observations of binary compact remnant masses, several candidate first mass gap objects (either neutron stars (NSs) or black holes (BHs)) were identified during the O3 science run. Motivated by these new observations, we study the formation of BH-NS mergers in the framework of isolated classical binary evolution, using population synthesis methods to evolve large populations of binary stars (Population I and II) across cosmic time. We present results on the NS to BH mass ratios ($q=M_{\rm NS}/M_{\rm BH}$) in merging systems, showing that although systems with a mass ratio as low as $q=0.02$ can exist, typically BH-NS systems form with moderate mass ratios $q=0.1-0.2$. If we adopt a delayed supernova engine, we conclude that $\sim 30\%$ of BH-NS mergers may host at least one compact object in the first mass gap (FMG$^\circ$). Even allowing for uncertainties in the processes behind compact object formation, we expect the fraction of BH-NS systems ejecting mass during the merger to be small (from $\sim 0.6-9\%$). In our reference model, we assume: (i) the formation of compact objects within the FMG, (ii) natal NS/BH kicks decreased by fallback, (iii) low BH spins due to Tayler-Spruit angular momentum transport in massive stars. We find that $\lesssim 1\%$ of BH-NS mergers will have any mass ejection and about the same percentage will produce kilonova bright enough to have a chance of being detected with a large (Subaru-class) $8$m telescope. Interestingly, all these mergers will have both a BH and an NS in the FMG.

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arXiv2022

Testing the presence of a dormant black hole inside HR 6819

HR 6819 was recently reported to be a triple system with a dormant black hole (BH). The inner binary system was defined as a star estimated to be at the end of its main sequence and a dormant BH. As the inner binary is not resolved, the third component may actually just be spatially coinciding with the inner binary. In this study we test whether the system inner binary can be reconstructed using the isolated binary evolution in the Galactic field or through the dynamical evolution within globular star clusters. Our goal is to understand the formation of the HR 6819 inner binary. To simulate the inner binary evolution we assumed that the influence of the third body on the inner binary is negligible. We created synthetic populations of BH main-sequence binaries for the Galactic disc and the Galactic globular clusters to compare to the reported parameters of the HR 6819 inner binary. We have adopted very optimistic input physics, in terms of common envelope evolution and BH formation, for the formation of binaries similar to the reported inner HR 6819 binary. Despite our optimistic assumptions we cannot form systems like the inner HR 6819 binary in globular clusters. Even with our extreme assumptions, the formation of an HR 6819-like binary in the Galactic field population is not expected. We argue that if a dormant BH actually exists in the reported configuration inside HR 6819, its presence cannot easily be explained by our models based on isolated and dynamical binary evolution.

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arXiv2022

Black hole - black hole total merger mass and the origin of LIGO/Virgo sources

The LIGO-Virgo-KAGRA (LVK) Collaboration has reported nearly 100 BH-BH mergers. The LVK provides estimates of rates, masses, effective spins, and redshifts for these mergers. Yet, the formation channel(s) of the mergers remains uncertain. One way to search for a formation site is to contrast properties of detected BH-BH mergers with different models of BH-BH merger formation. Our study is designed to investigate the usefulness of the total BH-BH merger mass and its evolution with redshift in establishing the origin of gravitational-wave sources. We find that the average intrinsic BH-BH total merger mass shows exceptionally different behavior for the models that we adopt for our analysis. In the local universe (z=0) the average merger mass changes from Mtot,int=25Msun for CE binary evolution and open clusters formation channels, to Mtot,int=30Msun for the stable-RLOF binary channel, to Mtot,int=45Msun for the globular cluster channel. These differences are even more pronounced at larger redshifts. However, these differences are diminished when considering LVK O3 detector sensitivity. Comparison with LVK O3 data shows that none of our adopted models can match the data despite large errors on BH-BH masses and redshifts. We emphasize that our conclusions are derived from a small set of 6 models that are subject to numerous known uncertainties. We also note that BH-BH mergers may originate from a mix of several channels and that other (than those adopted here) BH-BH formation channels may exist.

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arXiv2021

VLT/MUSE and ATCA observations of the host galaxy of the short GRB 080905A at z=0.122

Short-GRB progenitors could come in various flavors, depending on the nature of the merging compact stellar objects (including a stellar-mass black hole or not) or depending on their ages (millions or billions of years). At a redshift of z=0.122, the nearly face-on spiral host of the short GRB 080905A is one of the closest short-GRB host galaxies identified so far. This made it a preferred target to explore spatially resolved star-formation and to investigate the afterglow position in the context of its star formation structures. We used VLT/MUSE integral-field unit observations, supplemented by ATCA 5.5/9.0 GHz radio-continuum measurements and publicly available HST data, to study the star-formation activity in the GRB 080905A host galaxy. The MUSE observations reveal that the entire host is characterized by strong line emission. Using the Halpha line flux, we measure for the entire galaxy an SFR of about 1.6 Msun/yr, consistent with its non-detection by ATCA. Several individual star-forming regions are scattered across the host. The most luminous region has a Halpha luminosity that is nearly four times as high as the luminosity of the Tarantula nebula in the Large Magellanic Cloud. Even though star-forming activity can be traced as close to about 3 kpc (in projection) distance to the GRB explosion site, stellar population synthesis calculations show that none of the Halpha-bright star-forming regions is a likely birthplace of the short-GRB progenitor.

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arXiv2021

The Uncertain Future of Massive Binaries Obscures the Origin of LIGO/Virgo Sources

The LIGO/Virgo gravitational--wave observatories have detected 50 BH-BH coalescences. This sample is large enough to have allowed several recent studies to draw conclusions about the branching ratios between isolated binaries versus dense stellar clusters as the origin of double BHs. It has also led to the exciting suggestion that the population is highly likely to contain primordial black holes. Here we demonstrate that such conclusions cannot yet be robust, because of the large current uncertainties in several key aspects of binary stellar evolution. These include the development and survival of a common envelope, the mass and angular momentum loss during binary interactions, mixing in stellar interiors, pair-instability mass loss and supernova outbursts. Using standard tools such as the population synthesis codes StarTrack and COMPAS and the detailed stellar evolution code MESA, we examine as a case study the possible future evolution of Melnick 34, the most massive known binary star system. We show that, despite its well-known orbital architecture, various assumptions regarding stellar and binary physics predict a wide variety of outcomes: from a close BH-BH binary (which would lead to a potentially detectable coalescence), through a wide BH-BH binary (which might be seen in microlensing observations), or a Thorne-Zytkow object, to a complete disruption of both objects by pair-instability supernovae. Thus since the future of massive binaries is inherently uncertain, sound predictions about the properties of BH-BH systems are highly challenging at this time. Consequently, drawing conclusions about the formation channels for the LIGO/Virgo BH-BH merger population is premature.

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arXiv2020

A supernova remnant associated with a nascent black hole low-mass X-ray binary

Energy released when the core of a high-mass star collapses into a black hole often powers an explosion that creates a supernova remnant. Black holes have limited windows of observability, and consequently are rarely identified in association with supernova remnants. Analysing multi-messenger data, we show that MAXI J1535-571 is the black hole produced in the stellar explosion that gave rise to the supernova remnant G323.7-1.0, making it the first case of an association between a black hole low-mass X-ray binary and a supernova remnant. Given this connection, we can infer from our modelling that the progenitor system was a close binary whose primary star had an initial mass of approx. 23-35 solar masses with a companion star about 10 times less massive.

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arXiv2020

The Origin of inequality: isolated formation of a 30+10Msun binary black-hole merger

The LIGO/Virgo collaboration has reported the detection of GW190412, a BH-BH merger with the most unequal masses to date: 24.4-34.7 Msun and 7.4-10.1 Msun (a mass ratio of q=0.21-0.41). Additionally, GW190412's effective spin was estimated to be Xeff=0.14-0.34, with the spin of the primary BH in the range a=0.17-0.59. Based on this and prior detections, about 10 percent of BH-BH mergers have q<0.4. Major BH-BH formation channels tend to produce BH-BH mergers with comparable masses (typically with q>0.5). Here we test whether the classical isolated binary evolution channel can produce mergers resembling GW190412. We show that our standard binary evolution scenario, with the typical assumptions on input physics we have used in the past, produces such mergers (masses and spins). For this particular model of the input physics the overall BH-BH merger rate density in the local Universe (z=0) is: 73.5 Gpc^-3 yr^-1, while for systems with q<0.41 the rate density is: 6.8 Gpc^-3 yr^-1. As GW190412 shows some weak evidence for misaligned spins, we provide distribution of precession parameter in our models and conclude that if among the new LIGO/Virgo detections the evidence of system precession is strong and more than 10 percent of BH-BH mergers have large in-plane spin components (Xp>0.5) then common envelope isolated binary BH-BH formation channel can be excluded as their origin.

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arXiv2020

Orbital period dependent spatial scatter of Galactic Black Hole Transients

There remain significant uncertainties in the origin and evolution of black holes in binary systems, in particular regarding their birth sites and the influence of natal kicks. These are long-standing issues, but their debate has been reinvigorated in the era of gravitational wave detections and the improving precision of astrometric measurements. Using recent and archival characterisation of Galactic black hole X-ray binaries (BHXBs), we report here an apparent anticorrelation between P{orb} (system orbital periods) and scatter in z (elevation above the Galactic plane). The absence of long period sources at high z is not an obvious observational bias, and two possible explanatory scenarios are qualitatively explored: (1) a disc origin for BHXBs followed by natal kicks producing the scatter in z, with only the tightest binaries preferentially surviving strong kicks; (2) a halo origin, with P{orb} shortening through dynamical interactions in globular clusters (GCs). For the latter case, we show a correspondence in z-scatter between BHXBs and the GCs with most compact core radii of <0.1pc. However, the known absence of outbursting BHXB transients within Galactic GCs remains puzzling in this case, in contrast to the multitude of known GC neutron star XRBs. These results provide an interesting observational constraint for any black hole binary evolutionary model to satisfy.

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arXiv2020

Synthetic catalog of black holes in the Milky Way

We present an open-access database which includes a synthetic catalog of black holes in the Milky Way. To calculate evolution of single and binary stars we used updated population synthesis code StarTrack. We applied a new model of star formation history and chemical evolution of Galactic disk, bulge and halo synthesized from observational and theoretical data. We find that at the current moment Milky Way (disk+bulge+halo) contains about 1.2 x 10^8 single black holes with average mass of about 14 Msun and 9.3 x 10^6 BHs in binary systems with average mass of 19 Msun. We present basic statistical properties of BH populations such as distributions of single and binary BH masses, velocities, orbital parameters or numbers of BH binary systems in different evolutionary configurations. We find that the most massive BHs are formed in mergers of binary systems, such as BH-MS, BH+He, BH-BH. The metallicity of stellar population has a significant impact on the final BH mass due to the stellar winds. Therefore the most massive single BH in our simulation, 113 Msun, originates from a merger of a helium star and a black hole in a low metallicity stellar environment in Galactic halo. The most massive BH in binary system is 60 Msun and was also formed in Galactic halo. We constrain that only 0.006% of total Galactic halo mass (including dark matter) could be hidden in the form of stellar origin BHs which are not detectable by current observational surveys. Galactic binary BHs are minority (10% of all Galactic BHs) and most of them are in BH-BH systems. The current Galactic merger rates for two considered common envelope models which are: 3-81 Myr^-1 for BH-BH, 1-9 Myr^-1, for BH-NS and 14-59 Myr^-1 for NS-NS systems. Data files are available at https://bhc.syntheticuniverse.org/.

astro-ph.SR↗

arXiv2020

The evolutionary roads leading to low effective spins, high black hole masses, and O1/O2 rates of LIGO/Virgo binary black holes

All ten LIGO/Virgo binary black hole (BH-BH) coalescences reported from the O1/O2 runs have near zero effective spins. There are only three potential explanations of this fact. If the BH spin magnitudes are large then (i) either both BH spin vectors must be nearly in the orbital plane or (ii) the spin angular momenta of the BHs must be oppositely directed and similar in magnitude. Or, (iii) the BH spin magnitudes are small. We test the third hypothesis within the framework of the classical isolated binary evolution scenario of the BH-BH merger formation. We test three models of angular momentum transport in massive stars: a mildly efficient transport by meridional currents (as employed in the Geneva code), an efficient transport by the Tayler-Spruit magnetic dynamo (as implemented in the MESA code), and a very-efficient transport (as proposed by Fuller et al.) to calculate natal BH spins. We allow for binary evolution to increase the BH spins through accretion and account for the potential spin-up of stars through tidal interactions. Additionally, we update the calculations of the stellar-origin BH masses, include revisions to the history of star formation and to the chemical evolution across cosmic time. We find that we can match simultaneously the observed BH-BH merger rate density, BH masses, and effective spins. Models with efficient angular momentum transport are favored. The updated stellar-mass weighted gas-phase metallicity evolution now used in our models appears to be a key in better reproducing the LIGO/Virgo merger rate estimate. Mass losses during the pair-instability pulsation supernova phase are likely overestimated if the merger GW170729 hosts a BH more massive than 50 Msun. We also estimate rate of BH-NS mergers from recent LIGO/Virgo observations. Our updated models of BH-BH, BH-NS and NS-NS mergers are now publicly available at www.syntheticuniverse.org.

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arXiv2020

The Formation of a 70 Msun Black Hole at High Metallicity

A 70Msun BH was discovered in Milky Way disk in a long period and almost circular detached binary system (LB-1) with a high metallicity 8Msun B star companion. Current consensus on the formation of BHs from high metallicity stars limits the black hole mass to be below 20Msun. Using simple evolutionary model, we show that the formation of a 70Msun BH in high metallicity environment is possible if stellar wind mass loss rates are reduced by factor of 5. As observations indicate, a fraction of massive stars have surface magnetic fields which may quench the wind mass-loss, independently of stellar mass and metallicity. We also computed detailed stellar evolution models and we confirm such a scenario. A non-rotating 85Msun model at Z=0.014 with decreased winds ends up as a 71Msun star prior core-collapse with a 32Msun helium core and a 28Msun CO core. Such star avoids pair-instability pulsation supernova mass loss and may form a 70Msun BH in the direct collapse. Stars that can form such BHs expand to significant size with radius of R>600Rsun, exceeding the size of LB-1 orbit. Therefore, we can explain the formation of BHs upto 70Msun at high metallicity and this result is independent from LB-1. However, if LB-1 hosts a massive BH we are unable to explain how such a binary star system could have formed without invoking some exotic scenarios.

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arXiv2019

On the formation of neutron stars via accretion-induced collapse in binaries

We investigate evolutionary pathways leading to neutron star formation through the collapse of oxygen-neon white dwarf (ONe WD) stars in interacting binaries. We consider (1) non-dynamical mass transfer where an ONe WD approaches the Chandrasekhar mass leading to accretion-induced collapse (AIC) and (2) dynamical timescale merger-induced collapse (MIC) between an ONe WD and another WD. We present rates, delay times, and progenitor properties for two different treatments of common envelope evolution. We show that AIC neutron stars are formed via many different channels and the most dominant channel depends on the adopted common envelope physics. Most AIC and MIC neutron stars are born shortly after star formation, though some have delay times >10 Gyr. The shortest delay time (25-50 Myr) AIC neutron stars have stripped-envelope, compact, helium-burning star donors, though many prompt AIC neutron stars form via wind-accretion from an asymptotic giant branch star. The longest delay time AIC neutron stars, which may be observed as young milli-second pulsars among globular clusters, have a red giant or main sequence donor at the time of NS formation and will eventually evolve into NS + helium WD binaries. We discuss AIC & MIC binaries as potential gravitational wave sources for LISA. Neutron stars created via AIC undergo a LMXB phase, offering an electromagnetic counterpart for those shortest orbital period sources that LISA could identify. The formation of neutron stars from interacting WDs in binaries is likely to be a key mechanism for the production of LIGO/Virgo gravitational wave sources (NS-NS and BH-NS mergers) in globular clusters.

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arXiv2019

Remnants and ejecta of thermonuclear electron-capture supernovae: Constraining oxygen-neon deflagrations in high-density white dwarfs

(Abridged) The explosion mechanism of electron-capture supernovae (ECSNe) remains equivocal. We attempt to constrain the explosion mechanism (neutron-star-forming implosion or thermonuclear explosion) and the frequency of occurrence of ECSNe using nucleosynthesis simulations of the latter scenario, population synthesis, the solar abundance distribution, pre-solar meteoritic oxide grain isotopic ratio measurements and the white dwarf mass-radius relation. Tracer particles from 3d hydrodynamic simulations were post-processed with a large nuclear reaction network in order to determine the complete compositional state of the bound ONeFe remnant and the ejecta, and population synthesis simulations were performed in order to estimate the ECSN rate with respect to the CCSN rate. The 3d deflagration simulations drastically overproduce the neutron-rich isotopes $^{48}$Ca, $^{50}$Ti, $^{54}$Cr, $^{60}$Fe and several of the Zn isotopes relative to their solar abundances. Using the solar abundance distribution as our constraint, we place an upper limit on the frequency of thermonuclear ECSNe as 1$-$3~\% the frequency at which core-collapse supernovae (FeCCSNe) occur. This is on par with or 1~dex lower than the estimates for ECSNe from single stars. The upper limit from the yields is also in relatively good agreement with the predictions from our population synthesis simulations. The $^{54}$Cr/$^{52}$Cr and $^{50}$Ti/$^{48}$Ti isotopic ratios in the ejecta are a near-perfect match with recent measurements of extreme pre-solar meteoritc oxide grains, and $^{53}$Cr/$^{52}$Cr can also be matched if the ejecta condenses before mixing with the interstellar medium. Theoretical mass-radius relations for the bound ONeFe WD remnants of these explosions are apparently consistent with several observational WD candidates.

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arXiv2018

Binary neutron star formation and the origin of GW170817

The first neutron star-neutron star merger was detected in by LIGO/Virgo in a galaxy in which the majority of star formation was taking place a long time ago (11 Gyr). LIGO/Virgo estimated that local cosmic NS-NS merger rate is 110-3840 Gpc^-3 yr^-1. Only some extreme evolutionary models can generate NS-NS merger rates in old host galaxies consistent with the LIGO/Virgo estimate. However, we show that these models generate rates exceeding empirical Galactic NS-NS merger rates based on the large population of Milky Way NS-NS binaries. Typically, current evolutionary models produce NS-NS merger rates that are consistent with the Milky Way empirical rates. However, these models generate local cosmic NS-NS merger rate in old host galaxies that are below the LIGO/Virgo estimate. The reason behind this tension is the predicted delay time distribution between star formation and NS-NS mergers that favors short delays. Evolutionary models produce a generic steep power-law NS-NS delay time distribution. This limits NS-NS merger rates in old host galaxies. However, we show that such distribution is consistent with observations of Galactic NS-NS binaries; 50% of which show very long merger times (much longer than Hubble time). Once model distributions are convolved with continuous prolonged (10 Gyr) star formation in the Galactic disk, then 20-70% (depending on a model) of the predicted NS-NS population has very long current Galactic merger times. Although NS-NS binaries are formed predominantly with short delay times, many of short delay time systems merge and do not make it to the present, while long delay time systems survive and contribute to the current Galactic NS-NS population. This study highlights the tension between the current evolutionary predictions and the observation of the first NS-NS merger in an old host galaxy.

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arXiv2018

Impact of inter-correlated initial binary parameters on double black hole and neutron star mergers

The distributions of the initial main-sequence binary parameters are one of the key ingredients in obtaining evolutionary predictions for compact binary (BH-BH / BH-NS / NS-NS) merger rates. Until now, such calculations were done under the assumption that initial binary parameter distributions were independent. Here, we implement empirically derived inter-correlated distributions of initial binary parameters primary mass (M1), mass ratio (q), orbital period (P), and eccentricity (e). Unexpectedly, the introduction of inter-correlated initial binary parameters leads to only a small decrease in the predicted merger rates by a factor of 2 $-$ 3 relative to the previously used non-correlated initial distributions. The formation of compact object mergers in the isolated classical binary evolution favors initial binaries with stars of comparable masses (q = 0.5 $-$ 1) at intermediate orbital periods (log P (days) = 2 $-$ 4). New distributions slightly shift the mass ratios towards smaller values with respect to the previously used flat q distribution, which is the dominant effect decreasing the rates. New orbital periods only negligibly increase the number of progenitors. Additionally, we discuss the uncertainty of merger rate predictions associated with possible variations of the massive-star initial mass function (IMF). We argue that evolutionary calculations should be normalized to a star formation rate (SFR) that is obtained from the observed amount of UV light at wavelength 1500Å (SFR indicator). In this case, contrary to recent reports, the uncertainty of the IMF does not affect the rates by more than a factor of 2. Any change to the IMF slope for massive stars requires a change of SFR in a way that counteracts the impact of IMF variations on the merger rates. In contrast, we suggest that the uncertainty in cosmic SFR at low metallicity can be a significant factor at play.

astro-ph.HE↗

arXiv2018

MOCCA-SURVEY Database I: Assessing GW kick retention fractions for BH-BH mergers in globular clusters

Anisotropy of gravitational wave (GW) emission results in a net momentum gained by the black hole (BH) merger product, leading to a recoil velocity up to $\sim10^3\text{ km s}^{-1}$, which may kick it out of a globular cluster (GC). We estimate GW kick retention fractions of merger products assuming different models for BH spin magnitude and orientation (MS0 - random, MS1 - spin as a function of mass and metalicity, MS2 - constant value of $0.5$). We check how they depend on BH-BH merger time and properties of the cluster. We analyze the implications of GW kick retention fractions on intermediate massive BH (IMBH) formation by repeated mergers in a GC. We also calculate final spin of the merger product, and investigate how it correlates with effective spin of the binary. We used data from MOCCA (MOnte Carlo Cluster simulAtor) GC simulations to get a realistic sample of BH-BH mergers, assigned each BH spin value according to a studied model, and calculated recoil velocity and final spin based on most recent theoretical formulas. We discovered that for physically motivated models, GW kick retention fractions are about $30\%$ and display small dependence on assumptions about spin, but are much more prone to cluster properties. In particular, we discovered a strong dependence of GW kick retention fractions on cluster density. We also show that GW kick retention fractions are high in final life stages of the cluster, but low at the beginning. Finally, we derive formulas connecting final spin with effective spin for primordial binaries, and with maximal effective spin for dynamical binaries.

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