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 .23 B .75 J C .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 ) 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