#### Transcript Population synthesis view of gravitational waves - Astro-PF

Binary population synthesis implications for gravitational wave sources with Dorota Gondek-Rosińska Krzyś Belczyński Bronek Rudak Tomasz Bulik CAMK Questions What are the expected rates? How uncertain the rates are? What are the properties of the sources? Are the methods credible? Binary compact objects Only few coalescing NSNS known: Hulse-Taylor PSR1913+16, t=300 Myrs B1534+12, t=2700 Myrs B2127+11C, t=220 Myrs Binary Pulsar J0737 – 3039, t=80 Myrs BHNS? BHBH? Rate estimate Method I: observations 1 N V Use real data Selection effects Very low or even zero statistics Large uncertainty RATES – METHOD 1 Find the galactic density of coalescing sources from the model Obtain galactic merger rate Extrapolate from the Galaxy further out: Scale by: mass density? galaxy density? blue luminosity? Supernovae rate density? The result is dominated by a single object: J0737-3039!! Kalogera etal 2004 Rate estimate Method II: binary population synthesis Binary evolution Formation of NS i BH binaries Dependence on the parametrization Unknowns in the stellar evolution Population synthesis -single stars ● Numerical models ● Helium stars ● Evolutionary times ● Radii ● Internal structure: mass and radius of the core ● Convection ● Winds Binary evolution Mass transfers Rejuvenation Supernovae and orbits Masses of BH i NS Orbit changes - circularization Parameter study: many models Simulations Initial masses Mass ratios Orbits A chosen parameter set Typically we evolve 106 binaries An example of a binary leading to formation of a coalescing binary BH-BH: Parameter study Initial conditions: m, q, a ,e Mass transfers: mass loss, ang momentum loss and mass transfer Compact object masses Supernovae explosions: kick velocities Metallicity , winds Standard model Evolutionary times Short lived NSNS are not observable as pulsars Chirp mass distribution Detection Inspiral phase: Amplitude and frequency depend on chirp mass: M (m1m2 ) (m1 m2 ) 3/ 5 chirp Signal to noise: 1 ( S / N ) M chirp R 5/ 6 Sampling volume: V M 5/ 2 chirp 1/ 5 From simulations to rates Requirements: 1. model of the detector, signal to noise, sampling volume 2. normalisation Simulation to rates: normalisation Galactic supernova rate, Galactic blue luminosity + blue luminosity density in the local Universe: Coalescence rate ~ blue luminosity Star formation rate history + initial mass function + evolutionary times: Calculate the coalescence rate as a function of z Assumptions: Star formation rate: What was it at large z? Does it correspond to the local SFR a few Gyrs ago? Cosmological model (0.3, 0.7) and H=65 km/s/Mpc Initial mass function (M ) M M av fs Needed to convert from SFR mass to number of stars formed We do not simulate all the stars only a small fraction that may produce compact object binaries Results (1 z) M chirp is observed Uncertainty in rate Star formation historyA factor of 10 IMF – shape and range Together a factor of at least 30 Stellar evolution model A factor of 10 Non-stationary noise RATES – METHOD 1 Find the galactic density of coalescing sources from the model Obtain galactic merger rate Extrapolate from the Galaxy further out: Scale by: mass density? galaxy density? blue luminosity? Supernovae rate density? The result is dominated by a single object: J0737-3039!! Kalogera etal 2004 METHOD 1+2 Population synthesis predicts ratios What types of objects were used for Method 1? Long lived NSNS binaries Observed NSNS population dominated by the short lived objects Observed objects dominated by BHBH Number of “observed” binaries ________________________________ = Number of “observed” long lived NSNS ● BHBH – have higher chirp mass ● BHBH have longer coalescing times 200 (from 10 to 1000) This brings the expected VIRGO rate to 1-60 per year! Such an estimate leans on a single object..... PSR J0737-3039 Seeing this : Imagine THIS ! Expected object types ● NSNS ● BHNS ● BHBH Population of observed objects in the mass vs mass ratio space BHBH binaries NSNS binaries BHNS binaries SHOULD YOU BELIEVE IN ANY OF THIS? Observed masses of pulsars The initial-final mass relation depends on the estimate of the mass of the core, and on numerical simulations of supernovae explosions. Some uncertainty may cancel out if one considers mass ratios not masses themselves The intrinsic mass ratio distribution: burst star formation, all stars contained in a box. T> 100 Myrs Simulated radio pulsars: Observability proportional to lifetime. Constant SFR. Assume that one sees objects in a volume limited sample, eg. Galaxy. Sample is dominated by long lived objects. Typical mass ratio shifted upwards. Gravitational waves: Constant SFR. A flux limited sample. Low mass ratio objects have larger chirp masses. Long libed pulsars are a small fraction of all systems Summary Uncertainty of rates is huge First object: BHBH with similar masses NSNS binaries –less than 5-10% Important to consider no equal mass neutron star binaries. What next? ● Binaries in globular clusters, different formation channels, three body interactions ● Population 3 binaries ● ? Resonant detectors Requirements: mass, ccooling, specified frequency bands, strongly directional AURIGA, EXPLORER, NAUTILUS First detection attempts r 10 16 cm J. Weber – the 1960-ies Sensitivity Narrow bands corresponding to resonant frequencies of the bar Interferometers Michelsona-Morley design Noise: seismic, therma, quantum (shot) Czułość LIGO Gravitational wave sources .. hD Requirements: mass asymmetry, size Frequencies: 10 to 1000Hz Msun f 2200 Hz M Gravitational waves Predicted by the General Relativity Theory Binary pulsars: Indirect observations of gravitational waves Weak field approximation PSR 1913+16 Present and future detectors Resonant: bars and spheres Typical frequencies: around 1kHz, but in a narrow band Interferometric: LIGO, VIRGO, TAMA300, GEO600 Typical frequencies: 50 – 5000 Hz – wide bands LISA 0.001 – 0.1 Hz Astronomical objects Pulsars Supernovae Binary coalescences Interferometers Parameter D 4 N 2 D Cosmological parameters Hubble constant Omega B B A A Non stationary noise A B Stellar evolution A: B: Chirp mass versus evolutionary time Three phases of coalescence “inspiral” - until the marginally stable orbit “merger” - unitl formation of horizon “ringdown” - black hole rotation and oscillations Slow tightening Star on ZAMS z3 z2 z 0 z1 Detection A compact object binary is formed Coalescence Rate Formation at z3: fs F ( M chirp , z , t ) SFR( z ) ( M chirp M i chirp ) (t t i ) NM av Coalescence rate at z1 f ( M chirp , z ) dt ' F (M chirp , z f ( z , t ' ), t ' ) Observed rate: R 4 V ( M chirp ) dV dz f ( M chirp , z ) dz 1 z Rates are very uncertain. Can observations in GW be useful for astronomy? Consider not the rates but the ratios of the rates! •BHBH to NSNS etc. •Distribution of observed chirp masses Weakly depends on normalisation. Distribution of observed chirp mass Simple toy model: Constant SFR ● Euclidean space ● BHBH are dominant! Dependence: On cosmological model On star formation rate On stellar binary evolution We can use the Kolmogorov-Smirnov test to compare different distributions Parameter D – cumulative distribution distance. Two example detectors: A: 100Mpc i B: 1Gpc for NSNS Stellar evolution