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

TLDR: In this article, the authors proposed three models of angular momentum transport in massive stars: a mildly efficient transport by meridional currents, an efficient transport implemented in the MESA code, and a very efficient transport to calculate natal BH spins.

Abstract: All ten LIGO/Virgo binary black hole (BH-BH) coalescences reported following the O1/O2 runs have near-zero effective spins. There are only three potential explanations for this. 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. Then there is also the possibility that (iii) the BH spin magnitudes are small. We consider 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, including revisions to the history of star formation and to the chemical evolution across cosmic time. We find that we can simultaneously match the observed BH-BH merger rate density and BH masses and BH-BH 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 key for obtaining an improved reproduction of the LIGO/Virgo merger rate estimate. Mass losses during the pair-instability pulsation supernova phase are likely to be overestimated if the merger GW170729 hosts a BH more massive than 50âMâS. We also estimate rates of black hole-neutron star (BH-NS) mergers from recent LIGO/Virgo observations. If, in fact. angular momentum transport in massive stars is efficient, then any (electromagnetic or gravitational wave) observation of a rapidly spinning BH would indicate either a very effective tidal spin up of the progenitor star (homogeneous evolution, high-mass X-ray binary formation through case A mass transfer, or a spin-up of a Wolf-Rayet star in a close binary by a close companion), significant mass accretion by the hole, or a BH formation through the merger of two or more BHs (in a dense stellar cluster). (Less)

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Table 3. continued.

Fig. 26. Intrinsic merger rate distribution as a function of primary black hole mass MBH1 (top) and binary mass ratio MBH2/MBH1 of BH-BH mergers (bottom) for different StarTrack model choices. The gray bands show the 90% confidence limits on the populations inferred in Abbott et al. (2019a) using the phenomenological Model B.

Fig. 27. Cumulative density functions (CDFs) of four StarTrackmodels versus effective spins χeff . Solid color lines correspond to χeff CDF of detectable events for each model. The black line shows the χeff CDF of median likelihoods of the O1/O2 LVC events, and the gray region bounds CDFs of the 5th and 95th percentiles of the likelihoods from LVC parameter estimation. In the corresponding colored shaded regions, we show the 90% range of 5000 mock observed CDFs under each model. To generate a mock observed CDF, we draw 10 χeff values from the detected population under a given model and add random Gaussian noise with σ = 0.05, which is approximately the uncertainty in χeff likelihoods from the events of GWTC-1 (we resample any samples with |χeff | > 1 after adding noise).

Fig. 11. Merger rate density of BH-BH mergers for various assumptions about the common envelope and BH natal kicks. The possibility of development and survival of the CE phase with a Hertzsprung gap donor, increases the low-redshift BH-BH merger rate density by ∼1 order of magnitude: compare models M30.A and M30.B (a similar effect is found for other models). Natal kicks tend to decrease the BH-BH merger rate density by ∼1.5 order of magnitude: from fall-back attenuated natal kicks (almost no BH natal kicks: model M30.B) to full scale BH natal kicks (as high as observed for Galactic single pulsars: model M33.B). We note that the degeneracy between the tested input physics; by applying high natal kicks we can bring model M30.A down to agree with the LIGO/Virgo estimate, or by allowing for HG CE we can bring models M35.B and M33.B up to also match the LIGO/Virgo constraint.

Fig. 12. Merger rate density of NS-NS, BH-NS and BH-BH mergers for model M30. For comparison, we show LIGO/Virgo O1/O2 constraints on merger rate densities. While actual estimates are available for the BH-BH and NS-NS mergers, only an upper limit is available for the BH-NS mergers from O1/O2 data (but see Appendix A.9). We note that the presented merger rate densities are consistent with the LIGO/Virgo estimates.

Fig. 10. Merger rate density of BH-BH mergers from Population I/II stars. We employ models M10.B and M30.B to illustrate the effects of our assumptions on the star formation rate and cosmic metallicity evolution on the BH-BH mergers. LIGO/Virgo O1/O2 constraint on the BH-BH merger rate in local Universe is also shown. We note that the decrease of the BH-BH merger rate density at low-redshift (from old to new models) is due to the average metallicity of stars at any given redshift in old models, as it is much lower than the average metallicity of stars in new models (see Sect. 3.2 for details).

Frequently asked questions

Q1. What have the authors contributed in "Evolutionary roads leading to low effective spins, high black hole masses, and o1/o2 rates for ligo/virgo binary black holes" ?

The authors consider the third hypothesis within the framework of the classical isolated binary evolution scenario of the BH-BH merger formation. The authors 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. The authors allow for binary evolution to increase the BH spins through accretion and account for the potential spin-up of stars through tidal interactions. The authors find that they can simultaneously match the observed BH-BH merger rate density and BH masses and BH-BH effective spins. 

Q2. What are the future works mentioned in the paper "Evolutionary roads leading to low effective spins, high black hole masses, and o1/o2 rates for ligo/virgo binary black holes" ?

The values of BH spins may distinguish these two possibilities. If, however, such a BH is found to have a large spin as expected from consecutive BH mergers, then its presence will point to formation in a dense stellar environment ( e. g., globular cluster ). If individual BH masses are in fact as high as LIGO/Virgo reports for the most likely values from O1/O2 run ( e. g., 50. 6 M for GW170729 ) then the authors can already exclude strong mass ejection during the PPSN. 

Q3. How can a dense stellar environment be induced to merge?

In dense stellar environments, even binaries that are initially too wide to inspiral via gravitational radiation in a Hubble time can be hardened and induced to merge by binary-single and binarybinary interactions. 

Q4. What are the main reasons why their binary evolution models have many parameters?

While their binary evolution models have many parameters, because of the limited role of accretion on the BH spin, very few parameters have more impact on the χeff distribution than the physics the authors have described above. 

Q5. How do the authors generate a mock observed CDF?

To generate a mock observed CDF, the authors draw 10 χeff values from the detected population under a given model and add random Gaussian noise with σ = 0.05, which is approximately the uncertainty in χeff likelihoods from the events of GWTC-1 (we resample any samples with |χeff | > 1 after adding noise). 

Q6. What is the reason why the SFRD was not tested for WR stars?

it was only tested for initially non-spinning WR stars, and therefore did not take into account the fact that for inefficient angular momentum transport and high initial stellar rotation, WR stars can be born with high spins. 

Q7. What is the spin-down of the core in non-magnetic models?

In non-magnetic models, spin-down of the core is weak anyway and models still end up with relatively large spin values, aspin: 0.25 to maximum spin (see Table A.1). 

Q8. How many km s1 initial rotation speeds does a binary model give?

Depending on a mass and stellar structure of a model, this gives a range of 250−450 km s−1 initial rotation speeds at the equator (see Tables A.1 and A.2). 

Q9. What is the significant fraction of BH-WR binaries found on orbits smaller than?

In their evolution, a small, but significant fraction (∼20−30%; see Figs. 19 and 20) of the BH-WR/WR-BH/WR-WR binaries are found on orbits smaller than ∼10−20 R (orbital periods Porb < 1.3 d) for which the tides are expected to be effective for WR stars (Kushnir et al. 

Q10. What are the two groups of models that tend to produce shallower power-law distributions?

In the second group the authors show models that tend to produce shallower power-law distributions (∝M−2.4): M10.B (old Z(z) relation with standard stellar winds and restrictive CE treatment), M50.A (new Z(z) relation with 30% reduced stellar winds and optimistic CE), and M50.B (new Z(z) relation with 30% reduced stellar winds and restrictive CE).