Detections of gravitational waves are now starting to probe the mass distribution of stellar mass black holes (BHs). Robust predictions from stellar models are needed to interpret these. Theory ...predicts the existence of a gap in the BH mass distribution because of pair-instability supernovae. The maximum BH mass below the gap is the result of pulsational mass loss. We evolve massive helium stars through their late hydrodynamical phases of evolution using the open-source MESA stellar evolution code. We find that the location of the lower edge of the mass gap at 45 is remarkably robust against variations in the metallicity ( 3 ), the treatment of internal mixing ( 1 ), and stellar wind mass loss ( 4 ), making it the most robust predictor for the final stages of the evolution of massive stars. The reason is that the onset of the instability is dictated by the near-final core mass, which in turn sets the resulting BH mass. However, varying the reaction rate within its 1 uncertainties shifts the location of the gap between 40 and 56 . We provide updated analytic fits for population synthesis simulations. Our results imply that the detection of merging BHs can provide constraints on nuclear astrophysics. Furthermore, the robustness against metallicity suggests that there is a universal maximum for the location of the lower edge of the gap, which is insensitive to the formation environment and redshift for first-generation BHs. This is promising for the possibility to use the location of the gap as a "standard siren" across the universe.
A new index for standardising groundwater level time series and characterising groundwater droughts, the Standardised Groundwater level Index (SGI), is described. The SGI builds on the Standardised ...Precipitation Index (SPI) to account for differences in the form and characteristics of groundwater level and precipitation time series. The SGI is estimated using a non-parametric normal scores transform of groundwater level data for each calendar month. These monthly estimates are then merged to form a continuous index. The SGI has been calculated for 14 relatively long, up to 103 yr, groundwater level hydrographs from a variety of aquifers and compared with SPI for the same sites. The relationship between SGI and SPI is site specific and the SPI accumulation period which leads to the strongest correlation between SGI and SPI, q sub(max), varies between sites. However, there is a consistent positive linear correlation between a measure of the range of significant autocorrelation in the SGI series, m sub(max), and q sub(max) across all sites. Given this correlation between SGI m sub(max) and SPI q sub(max), and given that periods of low values of SGI can be shown to coincide with previously independently documented droughts, SGI is taken to be a robust and meaningful index of groundwater drought. The maximum length of groundwater droughts defined by SGI is an increasing function of m sub(max), meaning that relatively long groundwater droughts are generally more prevalent at sites where SGI has a relatively long autocorrelation range. Based on correlations between m sub(max), average unsaturated zone thickness and aquifer hydraulic diffusivity, the source of autocorrelation in SGI is inferred to be dependent on dominant aquifer flow and storage characteristics. For fractured aquifers, such as the Cretaceous Chalk, autocorrelation in SGI is inferred to be primarily related to autocorrelation in the recharge time series, while in granular aquifers, such as the Permo-Triassic sandstones, autocorrelation in SGI is inferred to be primarily a function of intrinsic saturated flow and storage properties of aquifer. These results highlight the need to take into account the hydrogeological context of groundwater monitoring sites when designing and interpreting data from groundwater drought monitoring networks.
ABSTRACT
During the first three observing runs of the Advanced gravitational-wave detector network, the LIGO/Virgo collaboration detected several black hole binary (BHBH) mergers. As the population ...of detected BHBH mergers grows, it will become possible to constrain different channels for their formation. Here we consider the chemically homogeneous evolution (CHE) channel in close binaries, by performing population synthesis simulations that combine realistic binary models with detailed cosmological calculations of the chemical and star-formation history of the Universe. This allows us to constrain population properties, as well as cosmological and aLIGO/aVirgo detection rates of BHBH mergers formed through this pathway. We predict a BHBH merger rate at redshift zero of $5.8 \textrm {Gpc}^{-3} \textrm {yr}^{-1}$ through the CHE channel, to be compared with aLIGO/aVirgo’s measured rate of ${53.2}_{-28.2}^{+55.8} \text{Gpc}^{-3}\text{yr}^{-1}$, and find that eventual merger systems have BH masses in the range $17{-}43 \,\textrm {M}_{\odot }$ below the pair-instability supernova (PISN) gap, and ${\gt}124 \textrm {M}_{\odot }$ above the PISN gap. We investigate effects of momentum kicks during black hole formation, and calculate cosmological and magnitude limited PISN rates. We also study the effects of high-redshift deviations in the star formation rate. We find that momentum kicks tend to increase delay times of BHBH systems, and our magnitude limited PISN rate estimates indicate that current deep surveys should be able to detect such events. Lastly, we find that our cosmological merger rate estimates change by at most ${\sim}8{{\ \rm per\ cent}}$ for mild deviations of the star formation rate in the early Universe, and by up to ${\sim}40\,\text{per cent}$ for extreme deviations.
A large number of extremely low-mass helium white dwarfs (ELM WDs) have been discovered in recent years. The majority of them are found in close binary systems suggesting they are formed either ...through a common-envelope phase or via stable mass transfer in a low-mass X-ray binary (LMXB) or a cataclysmic variable (CV) system. Here, we investigate the formation of these objects through the LMXB channel with emphasis on the proto-WD evolution in environments with different metallicities. We study for the first time the combined effects of rotational mixing and element diffusion (e.g. gravitational settling, thermal and chemical diffusion) on the evolution of proto-WDs and on the cooling properties of the resulting WDs. We present state-of-the-art binary stellar evolution models computed with MESA for metallicities of Z = 0.02, 0.01, 0.001 and 0.0002, producing WDs with masses between ~ 0.16−0.45 M⊙. Our results confirm that element diffusion plays a significant role in the evolution of proto-WDs that experience hydrogen shell flashes. The occurrence of these flashes produces a clear dichotomy in the cooling timescales of ELM WDs, which has important consequences e.g. for the age determination of binary millisecond pulsars. In addition, we confirm that the threshold mass at which this dichotomy occurs depends on metallicity. Rotational mixing is found to counteract the effect of gravitational settling in the surface layers of young, bloated ELM proto-WDs and therefore plays a key role in determining their surface chemical abundances, i.e. the observed presence of metals in their atmospheres. We predict that these proto-WDs have helium-rich envelopes through a significant part of their lifetime. This is of great importance as helium is a crucial ingredient in the driving of the κ-mechanism suggested for the newly observed ELM proto-WD pulsators. However, we find that the number of hydrogen shell flashes and, as a result, the hydrogen envelope mass at the beginning of the cooling track, are not influenced significantly by rotational mixing. In addition to being dependent on proto-WD mass and metallicity, the hydrogen envelope mass of the newly formed proto-WDs depends on whether or not the donor star experiences a temporary contraction when the H-burning shell crosses the hydrogen discontinuity left behind by the convective envelope. The hydrogen envelope at detachment, although small compared to the total mass of the WD, contains enough angular momentum such that the spin frequency of the resulting WD on the cooling track is well above the orbital frequency.
Magnetic fields in upper main-sequence stars, white dwarfs and neutron stars are known to persist for time-scales comparable to their lifetimes. From a theoretical perspective this is problematic, as ...it can be shown that simple magnetic field configurations are always unstable. In non-barotropic stars, stable stratification allows for a much wider range of magnetic field structures than in barotropic stars, and helps stabilize them by making it harder to induce radial displacements. Recent simulations by Braithwaite and collaborators have shown that, in stably stratified stars, random initial magnetic fields evolve into nearly axisymmetric configurations with both poloidal and toroidal components, which then remain stable for some time. It is desirable to provide an analytic study of the stability of such fields. We write an explicit expression for a plausible equilibrium structure of an axially symmetric magnetic field with both poloidal and toroidal components of adjustable strengths, in a non-barotropic, non-rotating, fluid star, and study its stability using the energy principle. We construct a displacement field that should be a reasonable approximation to the most unstable mode of a toroidal field, and confirm Braithwaite's result that a given toroidal field can be stabilized by a poloidal field containing much less energy than the former, as given through the condition E
pol/E
tor 2aE
tor/E
grav, where E
pol and E
tor are the energies of the poloidal and toroidal fields, respectively, and E
grav is the gravitational binding energy of the star. We find that a 7.4 for main-sequence stars, and a ∼ 200 for neutron stars. Since E
pol/E
grav < 1, we conclude that the energy of the toroidal field can be substantially larger than that of the poloidal field, which is consistent with the speculation that the toroidal field is the main reservoir powering magnetar activity. The deformation of a neutron star caused by the hidden toroidal field can also cause emission of gravitational waves.
ABSTRACT
Gravitational-wave detections are now probing the black hole (BH) mass distribution, including the predicted pair-instability mass gap. These data require robust quantitative predictions, ...which are challenging to obtain. The most massive BH progenitors experience episodic mass ejections on time-scales shorter than the convective turnover time-scale. This invalidates the steady-state assumption on which the classic mixing length theory relies. We compare the final BH masses computed with two different versions of the stellar evolutionary code $\tt{MESA}$: (i) using the default implementation of Paxton et al. (2018) and (ii) solving an additional equation accounting for the time-scale for convective deceleration. In the second grid, where stronger convection develops during the pulses and carries part of the energy, we find weaker pulses. This leads to lower amounts of mass being ejected and thus higher final BH masses of up to ∼$5\, \mathrm{M}_\odot$. The differences are much smaller for the progenitors that determine the maximum mass of BHs below the gap. This prediction is robust at $M_{\rm BH, max}\simeq 48\, \mathrm{M}_\odot$, at least within the idealized context of this study. This is an encouraging indication that current models are robust enough for comparison with the present-day gravitational-wave detections. However, the large differences between individual models emphasize the importance of improving the treatment of convection in stellar models, especially in the light of the data anticipated from the third generation of gravitational-wave detectors.
Context.
The intriguing binary
LS V +22 25
(LB-1) has drawn much attention following claims of it being a single-lined spectroscopic binary with a 79-day orbit comprising a B-type star and a ≈70
M
⊙
...black hole – the most massive stellar black hole reported to date. Subsequent studies demonstrated a lack of evidence for a companion of such great mass. Recent analyses have implied that the primary star is a stripped He-rich star with peculiar sub-solar abundances of heavy elements, such as Mg and Fe. However, the nature of the secondary, which was proposed to be a black hole, a neutron star, or a main sequence star, remains unknown.
Aims.
Based on 26 newly acquired spectroscopic observations secured with the HERMES and FEROS spectrographs covering the orbit of the system, we perform an orbital analysis and spectral disentangling of LB-1 to elucidate the nature of the system.
Methods.
To derive the radial velocity semi-amplitude
K
2
of the secondary and extract the spectra of the two components, we used two independent disentangling methods: the shift-and-add technique and Fourier disentangling with FDBinary. We used atmosphere models to constrain the surface properties and abundances.
Results.
Our disentangling and spectral analysis shows that LB-1 contains two components of comparable brightness in the optical. The narrow-lined primary, which we estimate to contribute ≈55% in the optical, has spectral properties that suggest that it is a stripped star: it has a small spectroscopic mass (≈1
M
⊙
) for a B-type star and it is He- and N-rich. Unlike previous reports, the abundances of heavy elements are found to be solar. The “hidden” secondary, which contributes about 45% of the optical flux, is a rapidly rotating (
v
sin
i
≈ 300 km s
−1
) B3 V star with a decretion disk – a Be star. As a result of its rapid rotation and dilution, the photospheric absorption lines of the secondary are not readily apparent in the individual observations. We measure a semi-amplitude for this star of
K
2
= 11.2 ± 1.0 km s
−1
and adopting a mass of
M
2
= 7 ± 2
M
⊙
typical for B3 V stars, we derive an orbital mass for the stripped primary of
M
1
= 1.5 ± 0.4
M
⊙
. The orbital inclination of 39 ± 4° implies a near-critical rotation for the Be secondary (
v
eq
≈ 470 km s
−1
).
Conclusions.
LB-1 does not contain a compact object. Instead, it is a rare Be binary system consisting of a stripped star (the former mass donor) and a Be star rotating at near its critical velocity (the former mass accretor). This system is a clear example that binary interactions play a decisive role in the production of rapid stellar rotators and Be stars.
Present and upcoming time-domain astronomy efforts, in part driven by gravitational-wave follow-up campaigns, will unveil a variety of rare explosive transients in the sky. Here, we focus on ...pulsational pair-instability evolution, which can result in signatures that are observable with electromagnetic and gravitational waves. We simulated grids of bare helium stars to characterize the resulting black hole (BH) masses together with the ejecta composition, velocity, and thermal state. We find that the stars do not react “elastically” to the thermonuclear ignition in the core: there is not a one-to-one correspondence between pair-instability driven ignition and mass ejections, which causes ambiguity as to what is an observable pulse. In agreement with previous studies, we find that for initial helium core masses of 37.5
M
⊙
≲
M
He, init
≲ 41
M
⊙
, corresponding to carbon-oxygen core masses 27.5
M
⊙
≲
M
CO
≲ 30.1
M
⊙
, the explosions are not strong enough to affect the surface. With increasing initial helium core mass, they become progressively stronger causing first large radial expansion (41
M
⊙
≲
M
He, init
≲ 42
M
⊙
, corresponding to 30.1
M
⊙
≲
M
CO
≲ 30.8
M
⊙
) and, finally, also mass ejection episodes (for
M
He, init
≳ 42
M
⊙
, or
M
CO
≳ 30.8
M
⊙
). The lowest mass helium core to be fully disrupted in a pair-instability supernova is
M
He, init
≃ 80
M
⊙
, corresponding to
M
CO
≃ 55
M
⊙
. Models with
M
He, init
≳ 200
M
⊙
(
M
CO
≳ 114
M
⊙
) reach the photodisintegration regime, resulting in BHs with masses of
M
BH
≳ 125
M
⊙
. Although this is currently considered unlikely, if BHs from these models form via (weak) explosions, the previously-ejected material might be hit by the blast wave and convert kinetic energy into observable electromagnetic radiation. We characterize the hydrogen-free circumstellar material from the pulsational pair-instability of helium cores by simply assuming that the ejecta maintain a constant velocity after ejection. We find that our models produce helium-rich ejecta with mass of 10
−3
M
⊙
≲
M
CSM
≲ 40
M
⊙
, the larger values corresponding to the more massive progenitor stars. These ejecta are typically launched at a few thousand km s
−1
and reach distances of ∼10
12
− 10
15
cm before the core-collapse of the star. The delays between mass ejection events and the final collapse span a wide and mass-dependent range (from subhour to 10
4
years), and the shells ejected can also collide with each other, powering supernova impostor events before the final core-collapse. The range of properties we find suggests a possible connection with (some) type Ibn supernovae.
Context. It is now well established that the majority of massive stars reside in multiple systems. However, the effect of multiplicity is not sufficiently understood, resulting in a plethora of ...uncertainties about the end stages of massive-star evolution. In order to investigate these uncertainties, it is useful to study massive stars just before their demise. Classical Wolf-Rayet stars represent the final end stages of stars at the upper-mass end. The multiplicity fraction of these stars was reported to be ∼0.4 in the Galaxy but no correction for observational biases has been attempted. Aims. The aim of this study is to conduct a homogeneous radial-velocity survey of a magnitude-limited (V ≤ 12) sample of Galactic Wolf-Rayet stars to derive their bias-corrected multiplicity properties. The present paper focuses on 12 northern Galactic carbon-rich (WC) Wolf-Rayet stars observable with the 1.2 m Mercator telescope on the island of La Palma. Methods. We homogeneously measured relative radial velocities (RVs) for carbon-rich Wolf-Rayet stars using cross-correlation. Variations in the derived RVs were used to flag binary candidates. We investigated probable orbital configurations and provide a first correction of observational biases through Monte-Carlo simulations. Results. Of the 12 northern Galactic WC stars in our sample, seven show peak-to-peak RV variations larger than 10 km s−1, which we adopt as our detection threshold. This results in an observed spectroscopic multiplicity fraction of 0.58 with a binomial error of 0.14. In our campaign, we find a clear lack of short-period (P < ∼100 d), indicating that a large number of Galactic WC binaries likely reside in long-period systems. Finally, our simulations show that at the 10% significance level, the intrinsic multiplicity fraction of the Galactic WC population is at least 0.72.
Context. The recently detected gravitational wave signals (GW150914 and GW151226) of the merger event of a pair of relatively massive stellar-mass black holes (BHs) calls for an investigation of the ...formation of such progenitor systems in general. Aims. We analyse the common-envelope (CE) stage of the traditional formation channel in binaries where the first-formed compact object undergoes an in-spiral inside the envelope of its evolved companion star and ejects the envelope in this process. Methods. We calculated envelope binding energies of donor stars with initial masses between 4 and 115M sub(middot in circle) for metallicities of Z= Z sub(Milky Way) = Z sub(middot in circle)/ 2 and Z= Z sub(middot in circle)/ 50, and derived minimum masses of in-spiralling objects needed to eject these envelopes. Results. In addition to producing double white dwarf and double neutron star binaries, CE evolution may also produce massive BH-BH systems with individual BH component masses of up to ~50 - 60M sub(middot in circle), in particular for donor stars evolved to giants beyond the Hertzsprung gap. However, the physics of envelope ejection of massive stars remains uncertain. We discuss the applicability of the energy-budget formalism, the location of the bifurcation point, the recombination energy, and the accretion energy during in-spiral as possible energy sources, and also comment on the effect of inflated helium cores. Conclusions. Massive stars in a wide range of metallicities and with initial masses of up to at least 115M sub(middot in circle) may shed their envelopes and survive CE evolution, depending on their initial orbital parameters, similarly to the situation for intermediate- and low-mass stars with degenerate cores. In addition to being dependent on stellar radius, the envelope binding energies and lambda-values also depend on the applied convective core-overshooting parameter, whereas these structure parameters are basically independent of metallicity for stars with initial masses below 60M sub(middot in circle). Metal-rich stars > or = 60M sub(middot in circle) become luminous blue variables and do not evolve to reach the red giant stage. We conclude that based on stellar structure calculations, and in the view of the usual simple energy budget analysis, events like GW150914 and GW151226 might be produced by the CE channel. Calculations of post-CE orbital separations, however, and thus the estimated LIGO detection rates, remain highly uncertain.
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