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Gravitational waves from Gravitational waves from short Gamma-Ray Burstsshort Gamma-Ray Bursts

Dafne GuettaDafne Guetta (Rome Obs.) (Rome Obs.)

In collaboration with Luigi StellaIn collaboration with Luigi Stella

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• 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 LIGO and VIRGO and their advanced versions.and their advanced versions.

• Horizons LIGO: 20 Mpc, 40 Mpc and 100 Mpc advanced LIGO: 300 Mpc, 650 Mpc, 1.6 Gpc

• Fundamental: the number of events, we should know the merger ratemerger rate

• DNSs BH-NS (NeSCO) are thought to be the sources of Short GRBs (SHBs)

DNSs sources of Short GRBSsDNSs sources of Short GRBSs

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Two possible NeSCO binaries formation mechanisms: 1.NeSCO can form from massive binaries surviving two SN explosions: Primordial Primordial NeSCO systems 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 MODELSNeSCO binaries MODELS

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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. 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)

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QuickTime™ e undecompressore Codec YUV420

sono necessari per visualizzare quest'immagine.

DNSs mergingDNSs merging

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DNSs primordial merging rates DNSs primordial merging rates Estimates based on observed DNS systems Estimates based on observed DNS systems

containing at least a radio pulsar, these were containing at least a radio pulsar, these were reevaluated by the discovery of PSR J037-3039 reevaluated by the discovery of PSR J037-3039

selection effects selection effects (Kalogera 2004) (Kalogera 2004) R~80R~80+200+200-60-60/Myr/Myr

one event every 10 years for VIRGO, LIGO, one one event every 10 years for VIRGO, LIGO, one event every 2 days for LIGO II.event every 2 days for LIGO II.

Estimates based on population synthesis studies Estimates based on population synthesis studies (Belczynski et al. 2001)(Belczynski et al. 2001) give a similar rate. give a similar rate.

If the number density of galaxies 10If the number density of galaxies 10-2-2/Mpc/Mpc33, the , the merger rate is merger rate is 800800+200+200

-600-600/Gpc/Gpc33/yr/yr

BH-NS and BH-BH are 1% and 0.1 % BH-NS and BH-BH are 1% and 0.1 % of DNSs of DNSs (Belczynski et al. 2007)(Belczynski et al. 2007)

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

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QuickTime™ e undecompressore TIFF (LZW)

sono necessari per visualizzare quest'immagine.

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Progenitor of SHBs merging of NeSCO binaries Progenitor of SHBs merging of NeSCO binaries

QuickTime™ e undecompressore H.264

sono necessari per visualizzare quest'immagine.

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Swift: First short GRB afterglowsSwift: First short GRB afterglows

From the data: TheFrom the data: The observed observed short bursts are short bursts are significantly nearer than the significantly nearer than the observedobserved long long onesones..

THIS WAS EXPECTED…..THIS WAS EXPECTED….. <V/Vmax>short = 0.390.02 while

<V/Vmax>long = 0.290.01 (Guetta & Piran 2005, Guetta, Piran & Waxman 2004)

Different BATSE sensitivity is not enough. Delayed SFR distribution needed!!

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DNSs rates from SHBs ratesDNSs rates from SHBs rates

If NeSCOs are SHBs sources, we can infer the If NeSCOs are SHBs sources, we can infer the NeSCOs rate (GW event rate) from the SHBs rate NeSCOs rate (GW event rate) from the SHBs rate

(Guetta & Piran 2005, 2006; Nakar et al. 2006)(Guetta & Piran 2005, 2006; Nakar et al. 2006) • Derive the SHBs rate by fitting the peak flux Derive the SHBs rate by fitting the peak flux distribution for both models (primordial and distribution for both models (primordial and dynamical) dynamical) • By using recent estimates of the beaming factorBy using recent estimates of the beaming factor• Possibility that LF extends to low valuesPossibility that LF extends to low values•Contribution of dynamically formed NeSCO Contribution of dynamically formed NeSCO binaries to the SHB and GW event rate.binaries to the SHB and GW event rate.

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Rates from Flux

N(>F) Number of N(>F) Number of bursts with flux >F bursts with flux >F

n(z) Rate as a function of zn(z) Rate as a function of z(L)(L)Luminosity functionLuminosity function{{

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∫∫∞

=>0

),,(

0)()()(

max

LdLzndzFNpFLZ

φ

Rates from Flux

Number of bursts with flux >FNumber of bursts with flux >F Rate as a function of zRate as a function of z Luminosity functionLuminosity function Maximal redshift for detection of a burst with a luminosity Maximal redshift for detection of a burst with a luminosity

L given the detector’s sensitivity P.L given the detector’s sensitivity P.

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Time lagTime lag p(p()~1/)~1/ – –

probability for a probability for a time lag time lag for for primordial primordial

(Belcynski et al 2007)

dpztRznzt

SFR )(])([)()(

0

−= ∫Convolution of SFR with the merg. time distribution Convolution of SFR with the merg. time distribution

More bursts at low z

p(p()~p()~p(dyndyn

for dynamically formed for dynamically formed

(Hopman et al 2006)

p(p(dyndyn

1/1/SFRSFR

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Constraints on (L)

The method (Schmidt 1999)⎪⎩

⎪⎨⎧

Δ<<

<<Δ=Φ

*2

**

*1

**

)/(

/)/()(

LLLLL

LLLLLL

β

α

• SHB follow NS-NS formation rate SHB follow NS-NS formation rate p(p())1/1/• p(p()= p()= p())dyndyn

ΔΔ11~ ~ ΔΔ2 2 ~100 ~100

Sample of 194 bursts detected by BATSE Sample of 194 bursts detected by BATSE

Fitting the logN-logS the best fit values for Fitting the logN-logS the best fit values for , , , , LL** and the local rate and the local rate 00 can be found can be found

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Best Fit ValuesModelModel LL**

[10[1051 51 erg/sec]erg/sec]

00

GpcGpc-3-3yryr-1-1

SF2-1/SF2-1/ 22 0.60.6 22 1.31.3

SF2-p(SF2-p())dyndyn 0.80.8 0.80.8 22 4.04.0

In the dynamical model, the rate is higher!! In the dynamical model, the rate is higher!! Better sources of GW Better sources of GW

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Effect of the cutoffsEffect of the cutoffs• Increasing Increasing ΔΔ22 does not add a significant number does not add a significant number

of bursts, does not change the resultof bursts, does not change the result• Increasing Increasing ΔΔ11 increase increase the overall rate as the the overall rate as the

luminosity function increase with increasing luminosity function increase with increasing ΔΔ11

00((ΔΔ11))

Most of these Low Luminous (LL) bursts cannot Most of these Low Luminous (LL) bursts cannot be detected unless they are nearby but they be detected unless they are nearby but they should exist as there is evidence in long bursts.should exist as there is evidence in long bursts.GRB980425GRB980425 (L~10 (L~104646 erg/sec) erg/sec) GRB060218GRB060218 (L~10(L~104646 erg/sec) erg/sec) GRB031203GRB031203 (L~10 (L~104848 erg/sec) erg/sec)

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Luminosity function and RatesLuminosity function and Rates

~10 /Gpc~10 /Gpc33/yr /yr 80 mergers 80 mergers /Myr Galaxy* /Myr Galaxy* *with beaming *with beaming

L*~2 10L*~2 105050erg/secerg/sec

Comparable to Comparable to the estimated rate the estimated rate of mergers (e.g of mergers (e.g Kalogera 04)Kalogera 04)

Number density of galaxies is 10Number density of galaxies is 10-2-2/Mpc/Mpc33

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Luminosity function and RatesLuminosity function and Rates

~104 /Gpc3/yr 8 104 mergers /Myr Galaxy

Nakar, Gal-Yam, Fox 05,Nakar, Gal-Yam, Fox 05,

L*~2 10L*~2 105050erg/secerg/secWeakly constrained Weakly constrained by current detectorsby current detectors

See also Tanvir 05See also Tanvir 05

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Jet breaks in short bursts and ratesIn short bursts few evidences of jet break in 050709 In short bursts few evidences of jet break in 050709

and 050724 fand 050724 fbb-1-1~50 ~50 (Fox et al. 2005) (Fox et al. 2005)

Other evidences in 061201 fOther evidences in 061201 fbb-1-1~3000~3000 (Stratta et al. 2007)(Stratta et al. 2007)

50<f50<fbb-1-1<3000 taking f<3000 taking fbb

-1-1 ~100 ~100

R~R~00ffbb-1 -1 ~130 (400)/Gpc~130 (400)/Gpc33/yr/yr

For primordial (dynamical) models. This rate is For primordial (dynamical) models. This rate is compares well with the lower end of the range compares well with the lower end of the range

for primordial DNSs mergers 200-2800/Gpcfor primordial DNSs mergers 200-2800/Gpc33/yr/yr

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LdLdz

dV

z

zRzN

L

zPL

GRB

l

log)()1(

)()(

max

min ),(

Φ+

= ∫

Observed redshift distributionObserved redshift distribution

Dynamical model fit better the data Dynamical model fit better the data KS ~ 0.6 but primordial cannot be KS ~ 0.6 but primordial cannot be excludedexcludedBimodal origin of SHBs: low-z from Bimodal origin of SHBs: low-z from GC-DNSs high-z from primordialGC-DNSs high-z from primordial

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LIGO Livingston ObservatoryLIGO Livingston ObservatoryLaser Interferometer GW-ObservatoryLaser Interferometer GW-Observatory

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Prospects for GW detectionsProspects for GW detections

• Local rate of SHBs has implications for the # Local rate of SHBs has implications for the # of GW events that can be detected. NeSCO of GW events that can be detected. NeSCO systems formed in GCs may improve the systems formed in GCs may improve the chances of detecting GW signals because: chances of detecting GW signals because:

1.1. Local SHB rate dominated by dynamically Local SHB rate dominated by dynamically formed NeSCO formed NeSCO

2.2. The incidence of BH-NS binaries formed in The incidence of BH-NS binaries formed in GC is higher than that formed in the field and GC is higher than that formed in the field and the horizon of GW interferometers to BH-NS is the horizon of GW interferometers to BH-NS is larger than DNSslarger than DNSs

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•For a beaming factor ~ 100 we expect 1/238 yr For a beaming factor ~ 100 we expect 1/238 yr (LIGO) and 14/yr (advanced LIGO) for (LIGO) and 14/yr (advanced LIGO) for primordial modelprimordial model• 1/9 yr (LIGO), 360/yr (advanced LIGO) for 1/9 yr (LIGO), 360/yr (advanced LIGO) for dynamical model.dynamical model.

Number of detectable GW events Number of detectable GW events

€

NGW

~ 40ηf −1

b100

⎛

⎝ ⎜

⎞

⎠ ⎟

ρ 0

4Gpc−3yr−1

⎛

⎝ ⎜

⎞

⎠ ⎟

Δ1

100

⎛

⎝ ⎜

⎞

⎠ ⎟α

[(1− gB ) + gB

VBHNS

VDNSs

]yr−1

~1 Advanced LIGO and 3x10~1 Advanced LIGO and 3x10-4-4 LIGO LIGOggb b incidence of BH-NS systems among NeSCO

progenitors of SBHs ~0.01 prim. ~1 dyn.

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