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Compact Object Merger Rates Predictions & Constraints

Explore the merger rates of compact objects such as neutron stars and black holes with uncertainties analyzed through Monte Carlo simulations. The study focuses on the Milky Way's population density of spirals, local star formation rates, and delay time distributions of mergers. Discover how assumptions on star formation, prompt mergers, and birth conditions impact the estimated merger rates. The study also evaluates the contributions of spiral and elliptical galaxies to high-mass progenitors and refines the merger rate predictions based on different scenarios.

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Compact Object Merger Rates Predictions & Constraints

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  1. Compact object merger rates Predictions Constraints (including short GRBs) Richard O’Shaughnessy Vicky Kalogera Northwestern University LSC, March 21, 2006 work in progress! LIGO-G060157-00-Z

  2. Results (2005) Key: NS-NS BH-NS BH-BH • LIGO rates: INITIAL ADVANCED -1 -1 LIGO-G060157-00-Z

  3. Method (2005) • Based on Milky Way(well understood: history, population, …) + density of spirals • Rates/MW (now): - <RBH-BH>= 1.8 / Myr * 4+1 --> 1.8 x 10-8/ Mpc3/yr - <RBH-NS>=5 / Myr * 4+1 --> 5 x 10-8 / Mpc3/yr - <RNS-NS>= 16 / Myr *(4.4)+1 --> 16 x10-8 / Mpc3/yr Key: NS-NS BH-NS BH-BH Uncertainties Monte carlo over plausible astrophysical assumptions log10 (R/yr/MWEG) LIGO-G060157-00-Z

  4. Method (2005) • Other contributions?: • Prompt mergers ( << 1400 Myr ~ universe age) • Spirals dominate local SFR / blue light PSR name Ps (ms) Pb (hr) e life (Myr) B1913+16 59.03 7.752 0.617 365 B1534+12 37.90 10.1 0.274 2700 J0737-3039A 22.70 2.45 0.088 185 J1756-2251 28.46 7.67 0.181 2.0 C. Kim (talk 2005) ROS et al (2005) Reason why NG used (in inspiral analysis interpretation) LIGO-G060157-00-Z

  5. Key assumptions (2005) Extrapolation Universe all like Milky Way • Steady star formation • Prompt mergers dominate • Spiral-like birth conditions (IMF) LIGO-G060157-00-Z

  6. Refinements Star formation history: • Previous estimate: • Observed history: • Estimate 3x too high (locally) • Past ~ 20x present 20x …are mergers “prompt enough?” 3x LIGO-G060157-00-Z

  7. Refinements Delay time distribution : • Delay time = merger time - birth time Sample distribution (model-dependent) + 1/t works well [long times] … over a specific range + some prompt/instant log10(t/Myr) P(<t) dP/dt ~ 1/t LIGO-G060157-00-Z

  8. Refinements Delay time distribution : • Delay time = merger time - birth time Sample distribution (model-dependent) + 1/t works well [long times] … over a specific range + some prompt/instant Recent vs ancient contribution? dRate ~ (d/dt) dt/t ancient star formation important… LIGO-G060157-00-Z

  9. Refinements Heterogeneity • Spirals • Young • Hard to make high M stars • Ellipticals • Old • Easier to make high M stars 2-4x IMF log Ellipticals: atleast2-4x more high-mass progenitors LIGO-G060157-00-Z

  10. Refinements Scorecard: old vs young IMF : up x 3 SFR : up x 10 Delay: down x 10 ---------------------------- Net : up x ~ 3 Summary (usually) • Steady star formation • Wrong….early dominates • Prompt mergers dominate • Wrong…long delays dominate • Spiral-like birth conditions (IMF) • Wrong…ellipticals dominate LIGO-G060157-00-Z

  11. Revised results? Merger rates (/volume) versus redshift: …sample result Key ‘Reference’ Spirals Ellipticals log LIGO-G060157-00-Z log

  12. Observations: Short GRBs Review • Many seen (gamma-ray) [detection rate 1/(2-3 months)] … many missed (too faint) • Afterglows & assocations • Variety, includes OLD • Offsets (!) • Weak afterglows [low-density] …not SN • Beaming? Merger model (BH-NS, NS-NS) consistent LIGO-G060157-00-Z

  13. Observations: Short GRBs • ‘Experimental’ rates: • Conservative : (~what is seen) RGRB,low ~ 3x10-8/Mpc3/yr = ~ expected [spirals alone] • Optimistic?: (correct for faint and off-axis) RGRB,high~ RGRB,low (Lcut/Lmin) fb ~ RGRB,low(~100) x (~3) ~ 1x 10-5 / Mpc3/yr would be almost visible by initial LIGO …runs into problems (run out of SN) LIGO-G060157-00-Z

  14. Applying experimental constraints I:N(<P) [H] • Matching: SFR history + (homogeneous) + delay time distribution (try a few) + intrinsic LF (try a few) = guess FIT TO OBSERVED Results: rate ~ O(0.1-10 / Gpc3/yr) [depends on model] Guetta and Piran 2005/6 Ando 2004 LIGO-G060157-00-Z

  15. Applying experimental constraints III:N(<P) + observed ‘z’ • Method: • Previous • + match z distrib • + limit faint end [Tanvir et al 2005] • Odd claims: • 1/t excluded (!?) [what is tmin?] • 6 Gyr lifetime preferred? Results No beaming: 10/Gpc3/yr Beaming, faint: 105/Gpc3/yr (~x30) (~ 3x103) Nakar et al 2005 LIGO-G060157-00-Z

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