Compact object merger rates Richard O’Shaughnessy Vicky Kalogera, Chris Belczynski, Chunglee Kim, Tassos Fragos GWDAW-10 Dec 14, 2005

Outline Mergers: GW and GRB sources? Population synthesis and predictions Constrained popsyn for Milky Way Heterogeneous galaxy populations Detection rates for… –LIGO –Gamma-ray bursts

Who looks for compact mergers? GW community: –LIGO source : well-understood, detectable waves –Tests: GR, BH spins, massive binary formation/evolution GRB community: –NS-NS, BH-NS mergers = leading short GRB explanation! –Tests: Detailed merger (hydro/radiation) models [some x- ray flares], massive binary formation/evolution, star formation in different galaxy hosts,…

Direct constraints? Milky way NS-NS –Kim, Kalogera, and Lorimer 2004 Universe NS-(NS/BH): [GRBs] –Ando (2004), Guetta and Piran (2005)Ando (2004)Guetta and Piran (2005) Nakar, Gal-Yan, Fox (2005), …Nakar, Gal-Yan, Fox (2005) –Need luminosity function!

Population synthesis –Evolve random population: Monte Carlo over initial conditions Follow binary evolution (w/o interactions) –Uncertainties: parameterize Intrinsic: –…supernova kicks, CE efficiency, wind strength, … –Fundamental uncertainty … so do many times with many choices Uncertain conditions: –Metallicity –IMF slope fix assumptions…

Heterogeneity? Idealized model: FractionZIMF Spirals80%Z O = 0.02Kroupa Ellipticals20%0.5-2x Z O ~Salpeter

Population synthesis results log(t/Myr) BH-BH (elliptical conditions) Mass efficiency e,BH-NS ~ 3.8 x /M O Merger time distribution log( )

Population synthesis results log(t/Myr) BH-BH (spiral conditions) Mass efficiency e,BH-NS ~ 1.6 x /M O Merger time distribution log( )

Population synthesis results log(t/Myr) BH-NS (elliptical conditions) Mass efficiency e,BH-NS ~ 1.3 x /M O Merger time distribution log( )

Population synthesis results log(t/Myr) BH-NS (spiral conditions) Mass efficiency s,BH-NS ~ 3.7 x /M O Merger time distribution log( )

Population synthesis results log(t/Myr) NS-NS (elliptical conditions) Mass efficiency e,NS-NS ~ 1.5 x /M O Merger time distribution log( )

Population synthesis results log(t/Myr) NS-NS (spiral conditions) Mass efficiency s, NS-NS ~ /M O Merger time distribution log( )

Population synthesis results Key points: –Elliptical conditions = flatter IMF = higher mass efficiency ( 10x - 50 x) –Many progenitors long-lived Fraction of merging systems with t mgr >100 Myr dominates Fairly independent of popsyn assumptions ….except NS-NS (under spiral conditions)

Population synthesis predictions ….but to use them for any galaxy, need + star formation history + specific type (elliptical/spiral)

Population synthesis predictions Example: MW galaxy dM * /dt=3.5 M O /yr, spiral conditions (Kroupa IMF) = 2.5 / Myr = 21 / Myr = 5.9/ Myr [O’Shaughnessy et al ApJ ]O’Shaughnessy et al ApJ

Outline Mergers: GW and GRB sources? Population synthesis and predictions Constrained popsyn for Milky Way Heterogeneous galaxy populations Detection rates for… –LIGO –Gamma-ray bursts

Constrain Population Synthesis? Find consistent models which match observations –…only if selection effects well understood (NOT GRBs) Use only them to make predictions Practical problems: –Sparse sampling for detailed models –Strong constraints Partial solution:  Fits  Resampling..can’t address all questions (=no M spectrum, …)

Observational Constraints Supernovae rates: SN I b/c SN II log (R yr) Cappellaro et al AA (1999)

Observational Constraints Observed NS-NS: …not w/ new binary (yet) …small changes expected Wide Merging log (R yr) O’Shaughnessy et al ApJ

Observational Constraints Observed WD-NS: Eccentric Merging log (R yr) Kim et al ApJ ApJ Kim et al astro-ph/ astro-ph/

Constrained results Constrained merger rates: BH-BHBH-NS NS-NS

Outline Mergers: GW and GRB sources? Population synthesis and predictions Constrained popsyn for Milky Way Heterogeneous galaxy populations Detection rates for… –LIGO –Gamma-ray bursts

Heterogeneous populations Tricky! Need: –Statistics of IMF, SFR history, and Z over mass bins [e.g., Heavens et al XXX, extended] –SFR history consistency with other methods: Merger trees Overall SFR of universe so no systematic biases…

Heterogeneous populations Idealized heterogeneity FractionZIMF Spirals80%Z O = 0.02Kroupa Ellipticals20%0.5-2x Z O ~Salpeter

Heterogeneous populations Idealized heterogeneity Time-varying fraction –Ellipticals only for z>z crit –Spirals only for z<z crit

Outline Mergers: GW and GRB sources? Population synthesis and predictions Constrained popsyn for Milky Way Heterogeneous galaxy populations Detection rates for… –LIGO –Gamma-ray bursts

Star formation history Peaks near z~1 Porciani and Madau’s SFR 1 [cf. Heavens; XXX] z M O /yr/Mpc 3

Merger volume density BH-NS … not using constrained popsyn (yet) Transition at z=1 Transition at z=2

Merger volume density NS-NS … not using constrained popsyn (yet) Transition at z=1 Transition at z=2

Detection rates? Don’t have all we need: –Generally: Heterogeneous star formation model! Use constrained popsyn –GW Binary chirp mass spectrum –GRB Luminosity function

Detection rates? Don’t have all we need: –Generally: Heterogeneous star formation model! Use constrained popsyn –GW Binary chirp mass spectrum –GRB Luminosity function Coming soon!

Present and future Present: –Models pass more tests in Milky way –Heterogeneity on large scales matters for detection Future: –Using understood objects: New ns, more possible; Better SN rate (Sloan?) More constraints to be used/found –GRBs?: Need: rates, LFs, … Better statistics in ~ 1 yr

Bonus: Understanding GRB Evidence Explain –Long progenitor lifetimes –Association with ellipticals allowed –Significant offsets likely (except NS-NS)

Belczynski, Bulik, and Rudak (2002)