1 Gravitational waves from short Gamma-Ray Bursts Dafne Guetta (Rome Obs.) In collaboration with Luigi Stella

2 LIGO and VIRGO and their advanced versions. Merging binary systems containing two collapsed objects: DNS, BH-NS and BH-BH, emit most of their binding energy in gravitational waves (GW), they are prime targets for LIGO and VIRGO and their advanced versions. Horizons LIGO: 20 Mpc, 40 Mpc and 100 Mpc advanced LIGO: 300 Mpc, 650 Mpc, 1.6 Gpc merger rateFundamental: the number of events, we should know the merger rate DNSs BH-NS (NeSCO) are thought to be the sources of Short GRBs (SHBs) DNSs sources of Short GRBSs

3 Two possible NeSCO binaries formation mechanisms: 1. Primordial NeSCO systems 1.NeSCO can form from massive binaries surviving two SN explosions: Primordial NeSCO systems Population synthesis calculations (Belczynski et al. 2002, 2006) show that they merge in small time  ~ 0.1 Gyr  SHBs follow closely SFR NeSCO binaries MODELS

4 Dynamically formed DNS. 2. NeSCO systems can be formed through dynamical interactions in the core of globular clusters. NS (BH) captures a non degenerate star forming a binary system. The binary exchange interaction with a single NS and form a DNS or a BH-NS: Dynamically formed DNS. High probability exchange during core collapse  ~ CC time ~ Hubble time (Grindlay et al. 2006)  more low-z SHBs respect to SFR as detected (Guetta and Piran 05, 06, Hopman et al. 06, Salvaterra et al. 07)

5 DNSs merging

6 DNSs primordial merging rates Estimates based on observed DNS systems containing at least a radio pulsar, these were reevaluated by the discovery of PSR J selection effects (Kalogera 2004) R~ /Myr  one event every 10 years for VIRGO, LIGO, one event every 2 days for LIGO II. Estimates based on population synthesis studies (Belczynski et al. 2001) give a similar rate. If the number density of galaxies /Mpc 3, the merger rate is /Gpc 3 /yr BH-NS and BH-BH are 1% and 0.1 % of DNSs (Belczynski et al. 2007)

7 Short Gamma-Ray Bursts (SHBs) Bursts that last less than 2 sec Bursts that last less than 2 sec SHBs are harder than long bursts and comprise 1/4 and 1/10 of the BATSE and Swift samplesSHBs are harder than long bursts and comprise 1/4 and 1/10 of the BATSE and Swift samples Swift first determination of SHBs afterglows and host galaxies Swift first determination of SHBs afterglows and host galaxies First detemination of the redshift ~ 9 bursts First detemination of the redshift ~ 9 bursts First indication of beaming. First indication of beaming.

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9 Progenitor of SHBs merging of NeSCO binaries

10 Swift: First short GRB afterglows n From the data: The observed short bursts are significantly nearer than the observed long ones. n THIS WAS EXPECTED….. n n short = 0.39  0.02 while long = 0.29  0.01 ( Guetta & Piran 2005, Guetta, Piran & Waxman 2004 ) n n Different BATSE sensitivity is not enough. Delayed SFR distribution needed!!

11 DNSs rates from SHBs rates If NeSCOs are SHBs sources, we can infer the NeSCOs rate (GW event rate) from the SHBs rate (Guetta & Piran 2005, 2006; Nakar et al. 2006) Derive the SHBs rate by fitting the peak flux distribution for both models (primordial and dynamical) Derive the SHBs rate by fitting the peak flux distribution for both models (primordial and dynamical) By using recent estimates of the beaming factor By using recent estimates of the beaming factor Possibility that LF extends to low values Possibility that LF extends to low values Contribution of dynamically formed NeSCO binaries to the SHB and GW event rate.Contribution of dynamically formed NeSCO binaries to the SHB and GW event rate.

12 Rates from Flux n N(>F) Number of bursts with flux >F  Rate as a function of z Luminosity function n(z) Rate as a function of z  (L)  Luminosity function {

13 Rates from Flux n Number of bursts with flux >F n Rate as a function of z n Luminosity function n Maximal redshift for detection of a burst with a luminosity L given the detector’s sensitivity P.

14 Time lag p(  )~1/  – probability for a time lag  for primordial (Belcynski et al 2007) Convolution of SFR with the merg. time distribution More bursts at low z p(  )~p(  dyn for dynamically formed (Hopman et al 2006) p(  dyn 1/  SFR

15 Constraints on  (L) The method (Schmidt 1999) SHB follow NS-NS formation rate p(  )  1/  SHB follow NS-NS formation rate p(  )  1/  p(  )= p(  ) dyn p(  )= p(  ) dyn  1 ~  2 ~100 Sample of 194 bursts detected by BATSE Fitting the logN-logS the best fit values for , , L * and the local rate  0 can be found

16 Best Fit Values Model L * [10 51 erg/sec]   0 Gpc -3 yr -1 SF2-1/  SF2-p(  ) dyn In the dynamical model, the rate is higher!! Better sources of GW

17 Effect of the cutoffs Increasing  2 does not add a significant number of bursts, does not change the result Increasing  2 does not add a significant number of bursts, does not change the result Increasing  1 increase the overall rate as the luminosity function increase with increasing  1 Increasing  1 increase the overall rate as the luminosity function increase with increasing  1 0(1)0(1)0(1)0(1) Most of these Low Luminous (LL) bursts cannot be detected unless they are nearby but they should exist as there is evidence in long bursts. GRB (L~10 46 erg/sec) GRB (L~10 46 erg/sec) GRB (L~10 48 erg/sec)

18 Luminosity function and Rates ~10 /Gpc 3 /yr  80 mergers /Myr Galaxy* *with beaming L*~ erg/sec Comparable to the estimated rate of mergers (e.g Kalogera 04) Number density of galaxies is /Mpc 3

19 Luminosity function and Rates ~10 4 /Gpc 3 /yr  8  10 4 mergers /Myr Galaxy Nakar, Gal-Yam, Fox 05, Nakar, Gal-Yam, Fox 05, L*~ erg/sec Weakly constrained by current detectors See also Tanvir 05

20 Jet breaks in short bursts and rates In short bursts few evidences of jet break in and f b -1 ~50 (Fox et al. 2005) Other evidences in f b -1 ~3000 (Stratta et al. 2007) 50<f b -1 <3000 taking f b -1 ~100 R~  0 f b -1 ~130 (400)/Gpc 3 /yr For primordial (dynamical) models. This rate is compares well with the lower end of the range for primordial DNSs mergers /Gpc 3 /yr

21 Observed redshift distribution Dynamical model fit better the data KS ~ 0.6 but primordial cannot be excluded Bimodal origin of SHBs: low-z from GC-DNSs high-z from primordial

22 LIGO Livingston Observatory Laser Interferometer GW-Observatory

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24 Prospects for GW detections Local rate of SHBs has implications for the # of GW events that can be detected. NeSCO systems formed in GCs may improve the chances of detecting GW signals because: Local rate of SHBs has implications for the # of GW events that can be detected. NeSCO systems formed in GCs may improve the chances of detecting GW signals because: 1. Local SHB rate dominated by dynamically formed NeSCO 2. The incidence of BH-NS binaries formed in GC is higher than that formed in the field and the horizon of GW interferometers to BH-NS is larger than DNSs

25 For a beaming factor ~ 100 we expect 1/238 yr (LIGO) and 14/yr (advanced LIGO) for primordial modelFor a beaming factor ~ 100 we expect 1/238 yr (LIGO) and 14/yr (advanced LIGO) for primordial model 1/9 yr (LIGO), 360/yr (advanced LIGO) for dynamical model. 1/9 yr (LIGO), 360/yr (advanced LIGO) for dynamical model. Number of detectable GW events  ~1 Advanced LIGO and 3x10 -4 LIGO g b g b incidence of BH-NS systems among NeSCO progenitors of SBHs ~0.01 prim. ~1 dyn. 8