Compact object merger rates

Richard O’ShaughnessyVicky 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)

Nakar, Gal-Yan, Fox (2005), …

– Need luminosity function!

Population synthesis

– Evolve random population:Monte Carlo over initial conditionsFollow 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:

Fraction Z IMF

Spirals 80% ZO = 0.02 Kroupa

Ellipticals 20% 0.5-2x ZO ~Salpeter

Population synthesis results

log(t/Myr) log(t/Myr)

• BH-NS (elliptical conditions)

Mass efficiency

e,BH-NS~ 1.3 x 10-2/MO

Merger time distributionlog()

Population synthesis results

log(t/Myr) log(t/Myr)

• BH-NS (spiral conditions)

Mass efficiency

s,BH-NS ~ 3.7 x 10-4/MO

Merger time distribution log()

Population synthesis results

log(t/Myr) log(t/Myr)

• NS-NS (elliptical conditions)

Mass efficiency

e,NS-NS ~ 1.5 x 10-2/MO

Merger time distribution log()

Population synthesis results

log(t/Myr) log(t/Myr)

• NS-NS (spiral conditions)

Mass efficiency

s, NS-NS ~ 10-3/MO

Merger time distributionlog()

Population synthesis results

• Key points:– Elliptical conditions =

flatter IMF =

higher mass efficiency ( 10x - 50 x)

– Many progenitors long-livedFraction of merging systems with tmgr>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 galaxydM*/dt=3.5 MO/yr , spiral conditions (Kroupa IMF)

<Rbh> = 2.5 / Myr

<Rns> = 21 / Myr

<Rbh-ns>= 5.9/ Myr [O’Shaughnessy et al ApJ 633 1076]

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:FitsResampling

..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 351 459 (1999)

Observational Constraints

• Observed NS-NS:

…not w/ new binary (yet)

…small changes expected

Wide

Merging

log (R yr)

O’Shaughnessy et al ApJ 633 1076

Observational Constraints

• Observed WD-NS:

Eccentric

Merging

log (R yr)

Kim et al ApJ 616 1109Kim et al astro-ph/0408247

Constrained results

• Constrained merger rates:

BH-BH BH-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 universeso no systematic biases…

Heterogeneous populations

• Idealized heterogeneity

Fraction Z IMF

Spirals 80% ZO = 0.02 Kroupa

Ellipticals 20% 0.5-2x ZO ~Salpeter

Heterogeneous populations

• Idealized heterogeneity

• Time-varying fraction– Ellipticals only for z>zcrit

– Spirals only for z<zcrit

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

MO/y

r/M

pc3

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)