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**Inspiraling Compact Objects: Detection Expectations**

Vicky Kalogera Physics & Astronomy Dept

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**In this talk : Gravitational Waves and Double Neutron Stars**

Meet PSR J : a new strongly relativistic binary pulsar Inspiral Event Rates for NS-NS, BH-NS, BH-BH Precessing Binaries: astrophysical expectations

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**Double Neutron Star Inspiral**

Do they exist ? YES! What kind of signal ? First known NS -NS: radio pulsar PSR B inspiral chirp orbital decay GW emission causes orbital shrinkage leading to higher GW frequency and amplitude PSR B Weisberg & Taylor 03

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**detection rate ~ r3 strength ~ 1/r Dmax for each signal**

Sensitivity to coalescing binaries Dmax for each signal sets limits on the possible detection rate What is the expected detection rate out to Dmax ? Scaling up from the Galactic rate

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**Inspiral Rates for the Milky Way**

Theoretical Estimates Based on models Empirical Estimates Based on radio of binary evolution until binary compact objects form. for NS -NS, BH -NS, and BH -BH pulsar properties and survey selection effects. for NS -NS only

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**Properties of known coalescing DNS pulsars**

Galactic Disk pulsars B B J Burgay et al. 2003 C M15 (NGC 7078)

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**Properties of known coalescing DNS pulsars**

Ps (ms) (ss-1) L400 Ps . Galactic Disk pulsars B x B x J x Burgay et al. 2003 C x M15 (NGC 7078)

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**Properties of known coalescing DNS pulsars**

Ps (ms) (ss-1) L B9 (G) Ps . Galactic Disk pulsars B x B x J x Burgay et al. 2003 C x M15 (NGC 7078)

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**Properties of known coalescing DNS pulsars**

Ps (ms) (ss-1) L B9 (G) d(kpc) Ps . Galactic Disk pulsars B x B x J x Burgay et al. 2003 C x M15 (NGC 7078)

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**Properties of known coalescing DNS pulsars**

Ps (ms) (ss-1) Porb (hr) Ps . Galactic Disk pulsars B x B x J x Burgay et al. 2003 M15 (NGC 7078) C x

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**Properties of known coalescing DNS pulsars**

Ps (ms) (ss-1) Porb (hr) e Ps . Galactic Disk pulsars B x B x J x Burgay et al. 2003 M15 (NGC 7078) C x

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**Properties of known coalescing DNS pulsars**

Ps (ms) (ss-1) Porb (hr) e Mtot ( ) Ps . Mo Galactic Disk pulsars B x (1.39) B x (1.35) J x (1.24) Burgay et al. 2003 M15 (NGC 7078) C x (1.36)

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**Properties of known coalescing DNS pulsars**

c (Myr) sd (Myr) mrg (Myr) (yr-1) Galactic Disk pulsars B º.23 B º.75 J º.9 Burgay et al. 2003 C º.46 M15 (NGC 7078)

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**X Radio Pulsars in NS-NS binaries NS-NS Merger Rate Estimates 3**

Use of observed sample and models for PSR survey selection effects: estimates of total NS- NS number combined with lifetime estimates (Narayan et al. '91; Phinney '91) Dominant sources of rate estimate uncertainties identified: (VK, Narayan, Spergel, Taylor '01) small - number observed sample (2 NS - NS in Galactic field) PSR population dominated by faint objects Robust lower limit for the MW (10-6 per yr) Upward correction factor for faint PSRs: ~ X 3

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**pulsar luminosity function: hard-to-detect pulsars**

(VK, Narayan, Spergel, Taylor '01) NG Nest pulsar luminosity function: ~ L-2 i.e., dominated by faint, hard-to-detect pulsars median 25% small-N sample is: > assumed to be representative of the Galactic population > dominated by bright pulsars, detectable to large distances total pulsar number is underestimated

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**It is possible to assign statistical significance **

Radio Pulsars in NS-NS binaries NS-NS Merger Rate Estimates (Kim, VK, Lorimer 2002) It is possible to assign statistical significance to NS-NS rate estimates with Monte Carlo simulations Bayesian analysis developed to derive the probability density of NS-NS inspiral rate Small number bias and selection effects for faint pulsars are implicitly included in our method.

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Statistical Method Identify sub-populations of PSRs with pulse and orbital properties similar to each of the observed DNS Model each sub-population in the Galaxy with Monte-Carlo generations Luminosity distribution Spatial distribution power-law: f(L) L-p, Lmin < L (Lmin: cut-off luminosity) 2. Pulsar-survey simulation consider selection effects of all pulsar surveys generate ``observed’’ samples

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Statistical Method fill a model galaxy with Ntot pulsars count the number of pulsars observed (Nobs) Earth 3. Derive rate estimate probability distribution P(R)

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**Statistical Analysis pulsars, Nobs follows a Poisson distribution.**

For a given total number of pulsars, Nobs follows a Poisson distribution. We calculate the best-fit value of <Nobs> as a function of Ntot and the probability P(1; Ntot) We use Bayes’ theorem to calculate P(Ntot) and finally P(R) P(Nobs) for PSR B

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**Results: most probable rate Rpeak P(Rtot)**

statistical confidence levels expected GW detection rates

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**Current Rate Predictions**

Burgay et al. 2003, Nature, 426, 531 VK et al. 2004, ApJ Letters, in press 3 NS-NS : a factor of 6-7 rate increase Initial LIGO Adv. LIGO per 1000 yr per yr ref model: peak 95% opt model: peak 95%

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**Results: Rpeak vs model parameters**

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**Current expectations for LIGO II (LIGO I) **

detection rates of inspiral events NS -NS BH -NS BH -BH Dmax (Mpc) (20) (40) (100) Rdet ,000 (1/yr) ( ) (3x ) (4x ) from population synthesis Use empirical NS-NS rates: constrain pop syn models > BH inspiral rates

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**What do/will learn from PSR J0737-3039 ?**

Inspiral detection rates as high as 1 per 1.5 yr (at 95% C.L.) are possible for initial LIGO ! Detection rates in the range per yr are most probable for advanced LIGO VK, Kim, Lorimer, et al. 2004, ApJ Letters, in press NS #2 progenitor is constrained as less massive than ~4.7 Msolar NS #2 kick is constrained to be in excess of 60 km/s and its most probable value is 150 km/s Willems & VK 2003, ApJ Letters, submitted Better confirmation of GR First double pulsar with eclipses ! Lyne et al. 2004, Science, in press constraints on magnetic field and spin orientation pulsar magnetospheres measurement of new relativistic effects ?

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**Parkes MultiBeam survey and acceleration searches**

Assuming that acceleration searches can perfectly correct for any pulse Doppler smearing due to orbital motion… How many coalescing DNS pulsars would we expect the PMB survey to detect ? VK, Kim et al. 2003 < Nobs > = 3.6 N.B. Not every new coalescing DNS pulsar will significantly increase the DNS rates … PMB Nobs

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**Challenges in the near future...**

Technical: achieve target noise level Data analysis: optimal methods for signal retrieval detection of inspiral signal requires: template waveforms and matched filtering techniques

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**Precession and Inspiral Waveforms**

Compact object binaries can precess if spins are of significant magnitude and misaligned with respect to the orbital angular momentum. Precession can modify inspiral waveforms and decrease the detection efficiency of standard non-precession searches. Precession effects are more important for binaries of high mass ratios (BH-NS) and with spin tilt angles of the massive object in excess of ~30°. (Apostolatos 95)

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**Q: What is the origin of spin tilt angles in compact object binaries ?**

BH Mass transfer episodes in binaries tend to align spin and orbital angular momentum vectors. SN + NS kick BH NS Asymmetric supernova explosions can tilt the orbital plane relative to the spin of the non-exploding star.

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**BH-NS binaries are expected to have significant spin tilt angles**

Q: What are the expected spin tilt angles ? > model BH-NS progenitors and SN kick effects VK 2000 BH-NS Grandclement et al. 2003 10 Mo BH 1.4 Mo NS BH-NS binaries are expected to have significant spin tilt angles

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**Precessing inspiral binaries**

Grandclement, VK, Vecchio 2002 Grandclement & VK 2003 Grandclement, Ihm, VK, Belczynski 2003 Buonanno et al. 2003 Pan et al. 2003 Precessing inspiral binaries with non-precessing templates: detection rate decreases Rdet decrease depends on spin magnitude and tilt angle: templates that can mimic the precession effects can increase the detection rate: For a Mo BH-NS binary Maximum BH spin cos(spin tilt angle) cos(spin tilt angle)

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**Expected rates: BH-NS 1.5 -1500 per yr BH-BH 15 -10,000 per yr**

Rate drop expected from astrophysical predictions for spin tilts in BH-NS binaries Grandclement, Ihm, VK, Belczynski 2003 rate drop by 20-30% Expected rates: BH-NS per yr 3x BH-BH 15 -10,000 per yr 4x 3 BH-NS BH-NS BH spin magnitude

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**In the near and distant future ...**

Initial LIGO 3 NS-NS ---> detection possible BH-BH ---> possible detection too Advanced LIGO expected to detect compact object inspiral as well as NS or BH birth events, pulsars, stochastic background past experience from EM: there will be surprises! Laser Interferometry in space: LISA sources at lower frequencies supermassive black holes and background of wide binaries

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