Constraining Binary Evolution with Gravitational Wave

Measurements of Chirp MassesTomasz Bulik

CAMK, Warsaw, Poland

Questions

• What do theoretical models tell us about the masses of compact object binaries?

• What can be measured with high frequency gravitational wave detectors?

• What can one learn about stellar evolution from gravitational wave observations?

Single Star Evolution

• Evolutionary code based on Hurley, Pols, Tout (2000)

• Evolution starts at ZAMS and goes through:main sequence, Hertzsprung gap, red giant branch, core helium burning, asymptotic giant branch, helium star main sequence, helium star giant branch

• Evolution ends at formation of: helium white dwarf, carbon-oxygen white dwarf, oxygen-neon white dwarf, neutron star, black hole

Binary evolution

• Effects included in the population synthesis code: wind mass loss (standard, LBV, W-R type), tidal circularisation of binary orbit, magnetic breaking, conservative mass transfer, quasi-dynamic mass transfer, common envelope evolution, rejuvenation, hyper accretion onto compact objects, detailed supernovae treament, fall back and direct black hole formation, gravitational ewave energy loss in compact object binaries

Binary initial parameters

• Salpeter IMF with –2.7 exponent

• Flat mass ratio distribution

• Eccentricity distribution proprtional to e

• Orbital separation flat in log

• Maxwellian kick velocity distribution

Mass distributions - fingerprints

Intrinsic distribution of M

Detection of GW from binaries

• Detection in inspiral phase

• The frequency change and signal depends on the chirp mass only

• Only the chirp mass can be measured in the zero approximation

• Post Newtonian corrections – both masses

What can be observed

• Sampling distance is proportional to chirp mass in power 5/6

• Sampling volume is proprtional to chirp mass in power 2.5 !

• Assume Euclidean space and flat star formation rate history

Observed chirp masses

Is constraning stellar evolution feasible with GW observations?

• Assume that the true stellar evolution goes through a giiven model from our list

• Find the probability with which model A can be rejected with observations of 20, 100, 500 mergers

• Repeat and find the probability that appears in less than 1% of the cases

Cumulative distributions of obs chirp masses

Significance of the test

Conclusions

• The distribution of masses of compact objects is a very sensitive function of stellar evolution

• The observed binaries will be dominated by BHBH mergers

• Most parameters can be constrained with about 100 merger observations