A New Relativistic Binary Pulsar: Gravitational Wave Detection and Neutron Star Formation Vicky Kalogera Physics & Astronomy Dept with Chunglee Kim (NU) Duncan Lorimer (Manchester) Bart Willems (NU)

In this talk : In this talk : Gravitational Waves and Double Neutron Stars Gravitational Waves and Double Neutron Stars Meet PSR J : Meet PSR J : a new strongly relativistic binary pulsar Inspiral Event Rates Inspiral Event Rates for NS-NS, BH-NS, BH-BH for NS-NS, BH-NS, BH-BH Supernovae and NS-NS Formation Supernovae and NS-NS Formation

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

Sensitivity to coalescing binaries What is the expected detection rate out to D max ? Scaling up from the Galactic rate detection rate ~ r 3 strength ~ 1/r D max for each signal sets limits on the possible detection rate

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

Properties of known coalescing DNS pulsars B B C M15 (NGC 7078) Galactic Disk pulsars J Burgay et al. 2003

Properties of known coalescing DNS pulsars B x B x J x C x M15 (NGC 7078) Galactic Disk pulsars P s (ms) (ss -1 ) L 400 PsPs. Burgay et al. 2003

Properties of known coalescing DNS pulsars B x B x J x C x M15 (NGC 7078) Galactic Disk pulsars P s (ms) (ss -1 ) L 400 B 9 (G) PsPs. Burgay et al. 2003

Properties of known coalescing DNS pulsars B x B x J x C x M15 (NGC 7078) Galactic Disk pulsars P s (ms) (ss -1 ) L 400 B 9 (G) d(kpc) PsPs. Burgay et al. 2003

Properties of known coalescing DNS pulsars M15 (NGC 7078) Galactic Disk pulsars B x B x J x P s (ms) (ss -1 ) P orb (hr) PsPs C x Burgay et al. 2003

Properties of known coalescing DNS pulsars M15 (NGC 7078) Galactic Disk pulsars B x B x J x P s (ms) (ss -1 ) P orb (hr) e PsPs C x Burgay et al. 2003

Properties of known coalescing DNS pulsars M15 (NGC 7078) Galactic Disk pulsars B x (1.39) B x (1.35) J x (1.24) P s (ms) (ss -1 ) P orb (hr) e M tot ( ) PsPs. MoMo C x (1.36) Burgay et al. 2003

Properties of known coalescing DNS pulsars B º.23 B º.75 J º C º.46 M15 (NGC 7078) Galactic Disk pulsars  c (Myr)  sd (Myr)  mrg (Myr) (yr -1 )  · Burgay et al. 2003

Radio Pulsars in NS-NS binaries NS-NS Merger Rate Estimates 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

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 pulsar luminosity function: ~ L -2 i.e., dominated by faint, hard-to-detect pulsars NGNG N est median 25% (VK, Narayan, Spergel, Taylor '01)

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.

Statistical Method pulse and orbital properties similar to each of the observed DNS 1.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  Luminosity distribution Spatial distribution  Spatial distribution power-law: f(L)  L -p, L min < L (L min : cut-off luminosity) 2. Pulsar-survey simulation  consider selection effects of all pulsar surveys  consider selection effects of all pulsar surveys  generate ``observed’’ samples  generate ``observed’’ samples

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

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

Results: P(R tot ) most probable rate R peak statistical confidence levels expected GW detection rates

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

Results: R peak vs model parameters

Current expectations for LIGO II (LIGO I) detection rates of inspiral events NS -NS BH -NS BH -BH D max (Mpc) (20) (40) (100) R det ,000 (1/yr) ( ) (3x ) (4x ) from population synthesis Use empirical NS-NS rates:constrain pop syn models > BH inspiral rates

NS-NS Formation Channel from Tauris & van den Heuvel 2003 How was PSR J formed ? current properties constrain NS #2 formation process:  NS kick  NS progenitor

Willems & VK 2003 X X X X orbital period (hr)eccentricity Evolve the system backwards in time…  GR evolution back to post-SN #2 properties: N.B. time since SN #2 can be set equal to > the spin-down age from maximum spin-up: ~100Myr (Arzoumanian et al. 2001) < embargoed info! > the characteristic age of NS #2 (~55Myr)

Willems & VK 2003 Evolve the system backwards in time…  Constraints on pre-SN #2 properties: post-SN orbit must contain pre-SN position (in circular orbit): A (1-e) < A o < A (1+e)

Willems & VK 2003 Evolve the system backwards in time…  Constraints on pre-SN #2 properties: post-SN orbit must contain pre-SN position (in circular orbit): A (1-e) < A o < A (1+e) NS #2 progenitor: helium star to avoid mass transfer: A o > A min = R HE max / r L

Willems & VK 2003 Evolve the system backwards in time…  Constraints on pre-SN #2 properties: post-SN orbit must contain pre-SN position (in circular orbit): A (1-e) < A o < A (1+e) NS #2 progenitor: helium star to avoid mass transfer: A o > A min = R HE max / r L to satisfy post-SN masses, a, e: M o < M max = f(V k ) M o > 20 M solar V k > 1200 km/s unlikely …

Willems & VK 2003 Evolve the system backwards in time…  Constraints on pre-SN #2 properties -  allow for mass transfer from the He star: post-SN orbit must contain pre-SN position (in circular orbit): A (1-e) < A o < A (1+e)

Willems & VK 2003 Evolve the system backwards in time…  Constraints on pre-SN #2 properties -  allow for mass transfer from the He star: post-SN orbit must contain pre-SN position (in circular orbit): A (1-e) < A o < A (1+e) to form a NS: M o > 2.2 M solar Habets 1986

Willems & VK 2003 Evolve the system backwards in time…  Constraints on pre-SN #2 properties -  allow for mass transfer from the He star: post-SN orbit must contain pre-SN position (in circular orbit): A (1-e) < A o < A (1+e) to form a NS: M o > 2.2 M solar to avoid a merger: M o < 3.5 M PSR Ivanova et al Habets 1986

Willems & VK 2003 Evolve the system backwards in time…  Constraints on pre-SN #2 properties -  allow for mass transfer from the He star: post-SN orbit must contain pre-SN position (in circular orbit): A (1-e) < A o < A (1+e) to form a NS: M o > 2.2 M solar to avoid a merger: M o < 3.5 M PSR to satisfy post-SN masses, a, e: M o < M max = f(V k ) 2.2 < M o < 4.7 M solar V k > 75 km/s Habets 1986 Ivanova et al. 2003

Progenitor and NS kick constraints for the 3 coalescing DNS pulsars B > 100 B > 30 J > 75 A (R o ) e M o (M o ) A o (R o ) V k (km/s) 

What do/will learn from PSR J ? 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 First double pulsar with eclipses ! constraints on magnetic field and spin orientation pulsar magnetospheres measurement of new relativistic effects ? NS #2 progenitor is constrained to be less massive than ~4.7 M solar NS #2 kick is constrained to be in excess of 75 km/s Better confirmation of GR

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 PMB N obs = 3.6 N.B. Not every new coalescing DNS pulsar will significantly increase the DNS rates …

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

IFO Noise Level and Astrophysical Sources Seismic at low freq. Thermal at intermediate freq. Laser shot noise at high freq. Double Compact Objects Inspiral and Coalescence Compact Object Formation Core collapse-Supernovae Spinning Compact Objects Asymmetries-Instabilities Early Universe Fluctuations-Phase Transitions

Statistical Analysis is linearly proportional to the total number of pulsars in a model galaxy (N tot ). as a function of N tot for B as a function of N tot for B =  N tot =  N tot where  is a slope.

Statistical Analysis  We consider each binary system separately by setting (small number bias is implicitly included). (small number bias is implicitly included). Bayes’ theorem Bayes’ theorem P(1; ) P( ) P(N tot ) P(R) Change of variables Change of variables N obs =1 For an Individual binary i, P i (R) = C i 2 R exp(-C i R) P i (R) = C i 2 R exp(-C i R) where C i = combine all P(R) ’s and calculate P(R tot ) and calculate P(R tot ) τ life N tot f b i

Probability Distribution of NS-NS Inspiral Rate Choose PSR space & luminosity distribution power-law constrained from radio pulsar obs. Populate Galaxy with N tot ‘‘ like’’ pulsars same pulsar period, pulse profile, orbital period Simulate PSR survey detection and produce lots of observed samples for a given N tot Distribution of N obs for a given N tot : it is Poisson Calculate P ( 1; N tot ) Use Bayes’ theorem to calculate P(N tot ) --> P(N tot  x f b  N tot  x f b = rate Repeat for each of the other two known NS-NS binaries