Matching the feature in the observed binary black hole mass distribution by varying the mass lost in pulsational pair instability supernovae.

David Hendriks 1 , Lieke van Son 2 , Mathieu Renzo 3 , Rob Farmer 4 , Rob Izzard 1

  • 1 University Of Surrey Astrophysics, Guildford
  • 2 Centre for Astrophysics Harvard & Smithsonian, Cambridge
  • 3 Center for Computational Astrophysics Flatiron Institute, New York City
  • 4 Max-Planck-Institut for Astrophysics, Garching

Abstract

The most recent gravitational wave detections hint at a feature in the mass distribution at around 35 solar mass. It is difficult to explain the location of this feature based on our current understanding of binary evolution. Specifically, pulsational pair instability supernovae (PPISN) have been suggested to lead to a feature in the mass distribution, but current models suggest that this should lead to a feature at a higher mass.

We implement our recently updated PPISN prescription in the binary_c population synthesis framework, and generate a distribution of black hole mergers for system that merge at low redshift, using up-to-date redshift dependent metallicity distributions and star formation rate prescriptions. We compare our simulations for the fiducial implementation of the PPISN
with simulations where we take off a variable extra amount of mass for stars that undergo PPISN and study how this variation affects the location of the feature. We also shift the CO core mass requirement for stars to undergo PPISN by some mass as an alternative method to explain the feature.

In this talk I will discuss the possibility of the PPISN mass loss or core mass shift as the cause behind the observed feature at ∼35 Msun, and show how they compare to alternative scenarios.

Introduction

Observations

Recent observations of the LIGO VIRGO KAGRA gravitaional wave observatories start to uncover interesting features and unexpected observations.

Peak at high mass

An interesting feature that has been uncovered in the GTWC3a data release, and reconfirmed in the GWTC3b data release is a peak of black hole masses in the primary mass distribution. The distribution is best fit by a broken power-law + peak model, where the peak is located at  ~35 solar masses. The origin of this peak is as of yet not determined.

Pulsational pair-instability supernovae

A possible cause for a peak in the primary mass distribution of merging black holes is the pulsational pair-instability supernova (PPISN) pile-up. Overall the PPISN mechanism is well understood but there are physical processed that can change the predicted mass loss due to pulses. Generally the peak caused by PPISNe is predicted to be at a higher mass and we aim to study whether variations on the PPISNe induced mass loss can match the observed peak location.

Methods

Simulating isolated binary black hole systems with variations on the pulsational pair-instability prescription

We take our recently developed prescription for PPISNe and introduce two parameters to vary the prescribe mass loss and onset mass for the PPISN. We simulate populations of isolated binary stars and generate binary black hole systems for several variations of our PPISNe prescription.

Convolution with cosmologic metallicity specific starformation rates

We take the results of the population synthesis and convolve the binary black hole systems with up-to-date metallicity specific star formation rates based on the IllustrisTNG simulations (2, 3). We calculate the the rate and mass distribution of binary black hole systems that merge at redshift zero.

References

1: Renzo, Hendriks, van Son 2022

2: van Son et al 2021

3: TNG-project

Results: Effect on instrinsic cosmological supernova event rate

Our variations affect the shape of the mass distribution of merging binary black hole systems, but they can also change the supernova rate (ratio) of the PPISNe and PISNe

Fiducial prediction of SN rates and the effect of shifting the core mass range

Redshift evolution for the rate density (rate per yer per comoving gigaparsec cubed) of several events (transparent, gray, multiple linestyles for gravitational wave merger events, transparent coloured for supernovae events for our fiducial and coloured dash-dotted for supernovae events for ur CO core mass shift variation).

In the left plot we show the intrinsic event rate density of our fiducial model, with gravitational wave merger events in gray and supernova events in color. We additionaly show the variation dataset that is leads to a peak in the primary mass distribution closest to what we observe.

The overall effect of shifting the minimum core mass for stars to undergo PPISNe to lower values leads to an increase in the rate of PPISne and PISNe. In the case of a shift downwards of 15 solar masses, we find that the rate increases with about an order of magnitude compared to our fiducial rate. The ratio of CCSNe to PPISNe is about 2000 to 1 in our fiducial models and about 200 to 1 in the variation of 15 core mass shift.

 

Methods: Schematic overview of variations on the Pulsational pair instability prescription

Top-down approach

Initial (ZAMS) mass vs. final remnant mass for a range of single stars at metallicity 1e-4, showing both prescription variations. The top panel shows the variation with additional mass removal, where the black line indicates final remnant mass using the fiducial implementation of the prescription and the orange dashed line indicates the final remnant mass after when additional mass is removed. The bottom panel shows the core mass shift variation where again the black line indicates the final remnant mass using the fiducial implementation and the orange line indicates the remnant mass when we introduce a shift in the required core mass. In both panels the grey dash-dotted line indicates the pre-SN mass, the blue dash-dotted line indicates the final remnant mass as given by (2). The coloured regions under the curves indicates the supernova mechanism, where the yellow region indicates core collapse (CC), and the pink region indicates PPISN + CC.

In a recent paper (1) we published an updated prescription for PPISNe mass loss, which unlike other prescriptions takes the top-down approach of prescribing am amount of mass loss rather than predicting a fixed remnant mass for the compact object for a given CO core mass.

 

Our approach is more flexible and allows for a different predicted remnant mass for stars with a different He shell mass for a given CO core mass.

Introduction of two extra parameters

We introduce two types of variations in our PPISne prescription that we can vary and try to match with the observed binary black hole distribution and the location of the peak.

We show a schematic overview of the initial-final mass relation for stars at metallicity Z=0.001, as calculated with our new prescription in binary_c. The yellow regions indicate remnants formed through core collapse supernovae (CCSNe) and the pink regions indicate those formed through PPISNe.

The top panel shows our fiducial remnant mass predictions and the extra mass loss variations, as well as the previous implementation for PPISNe mass loss. Introducing extra mass loss only affects the range of stars that would normally undergo PPISN

The bottom panel shows the variations with the downward shift of CO core masses that undergo PPISNe. Here both the CCSNe and the PPISNe regions are affected.

 

References

1: Renzo et al 2022

2: Farmer et al 2019

Results: Primary mass distribution for variations on PPISNe

We calculate the primary mass distribution at redshift zero for merging binary black holes, for our fiducial PPISNe prescription, the variations we introduced in the previous panel, and the previous prescription of (1).

CO core mass shift

Top panel: Merger rate density as a function of primary mass for BBH mergers at z = 0, for the fiducial models (blue, solid), Farmer+19 models (yellow dotted), and the additional mass loss models  (ΔMPPI CO = -5 M☉ green dashed, ΔMPPI CO = -10 M☉ red dash-dotted,  ΔMPPI CO = -15 M☉ magenta dotted) Bottom panel: fraction to total in that bin where the primary black hole formed through PPISN.

The left plot shows primary mass distribution for the fiducial, previous, and CO core mass variations.

Top panel:

Our fiducial distribution has a maximum mass black hole of about 55 solar mass, and peaks at 52 solar mass. The previous prescription of Farmer+19 creates a primary mass distribution with a maximum black hole mass of about 48 solar mass, and it peaks at 40 solar mass.

We see that with the downward shift, the location of the peak shifts downward as well, and the maximum black hole mass formed through isolated binary evolution decreases.

Bottom panel:

For each of the variations the black holes at the upper mass end always form through PPISNe. This is not the case for the Farmer+19 prescription, where we see at maximum a fraction of 0.5 of the black holes formed through PPISNe.

Additional mass loss

References

1: Farmer et al 2019

Conclusions

We have simulation populations of binary stars and convolved the resulting binary black holes with up-to-date star formation rates to calculate the primary mass distribution of merging black holes.

We use a new prescription for PPISN mass loss, which is based on a top-down approach. Moreover, we introduce several variations on this prescription, which we can vary to match the observed peak at 35 solar masses.

We find that by shifting the range of CO core masses that undergo PPISNe downward we can control the location of the peak, but the variation that produces an overdensity at 35 solar masses is not shaped like the observed peak.

Our new top-down approach is sensitive to the amount of He shell mass that envelopes the CO core mass at the moment of PPISN. This will affect the remnant mass distribution, and a next step is to study how sensitive our results are to effects like overshooting.