Astrophysical Sources of Stochastic Gravitational-Wave Background

Tania Regimbau CNRS/ARTEMIS

GWDAW 12, Boston, Dec. 2008

1LIGO-G070843-00-0

Stochastic Background

2

Cosmological SGWB: signature of the early Universeinflation, cosmic strings, phase transitions…

Astrophysical SGWB: sources since the beginning of stellar activitycompact binaries, supernovae, rotating NSs, core-collapse to NSs or BHs, supermassive BHs…

A stochastic background of gravitational waves (SGWB) has resulted from the superposition of a large number of unresolved sources since the Big Bang.We distinguish between two contributions:

Plan of this talk

3

Spectral properties of Astrophysical Backgrounds (AGBs)

Detection regimes (resolved sources, popcorn, continuous)

Some predictions

Astrophysical constraints with advanced detectors

Spectral properties of AGBs

4

AGB spectra are determined by:

the cosmological model (H0=70 km/s/Mpc, m =0.3, =0.7)

the star formation history

the spectral properties of individual sources dEgw /d

sup

fluence of single sourcessource cosmic rate

( )

3 2 200

max max

maxsup

max

8 ( ) 1( )= ( )

3 4 ( )(1 )

1 for 1where ( )

~ 6 otherwise

ooz gw

gw o o o

ooo

dEG dR zdz

c H dz r z z d

zz

z

Cosmic Star Formation Rate

5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.00

0.05

0.10

0.15

0.20

0.25

h0=0.7

m

Madau & Pozzetti, 2000 Steidel et al., 1999 Blain et al., 1999 Hopkins & Beacom, 2006

R* (

Mo

yr-1 M

pc-3)

z

Detection Regimes

6

The nature of AGBs is charaterized by the duty cycle, the ratio between the average event duration and the time interval between successive events t.

0

(1 ')( ') 1( ) ' where( ') ( ') ( ')

'

o

ozo

o o

zz

D z dz dRt z t z zdz

resolved sources (D <<1): burst data analysis, optimal filtering

popcorn noise (D~1) Maximum Likelihood statistic (Drasco et al. 2003), Probability Event Horizon (Coward et al. 2005)

gaussian stochastic background (D>>1) cross correlation statistic (isotropic/anisotropic)

Models

7

Core collapse supernovae• Neutron star formation: Blair & Ju 1996, Coward et al. 2001-02, Howell et al. 2004, Buonanno et

al. 2005 • Stellar Black Hole formation: Ferrari et al. 1999, de Araujo et al. 2000-04

Neutron stars• tri-axial emission: Regimbau & de F. Pacheco 2001-06

• bar or r-modes: Owen et al. 1998, Ferrari et al. 1999, Regimbau 2001

• phase transitions: Sigl 2006

Stellar Compact Binaries • near coalescence (NS, BH): Regimbau et al. 2006-07 , Coward et al. 2005 (BNS), Howell et al.

2007 (BBH) • low frequency inspiral phase: Ferrari et al. 2002, Farmer & Phinney 2002, Cooray 2004 (WD-NS)

Capture of compact objects by SMBHs : Barack & Cutler 2004

Spectra

8

The shape of AGBs is characterized by:cutoff at the maximal emission frequencymax

maximum which depends on the shape of the SFR and max

often well approximated by power laws at low frequency

10 100 10001E-18

1E-17

1E-16

1E-15

1E-14

1E-13

1E-12

1E-11

1E-10

1E-9

1E-8

de Sitter inflation

slow roll inflation

bar modesMaclauren/Dedekind

r modesSN II: Buonnano et al. astro-ph/0412277

NS phase transitionSigl astro-ph/0602345

magnetars

pulsars

core collapse to BH: ringdown

NS-NSRegimbau et al. gr-qc/07074327

(Hz)

gw

10 100 10001E-63

1E-62

1E-61

1E-60

1E-59

1E-58

1E-57

1E-56

1E-55

1E-54

1E-53

1E-52

1E-51

1E-50

1E-49

(Hz)

ShH

z-1

230

2

3spectal energy density: ( ) ( )

4h o o gw o

HS

Tri-axial Neutron Stars

9

source rate:follows the star formation rate (fast evolution of massive stars)

spectral energy density:

Population synthesis (Regimbau & de F. Pacheco 2000, Faucher-Giguere & Kaspi 2006) :

• initial period: normal distribution with <Po>~250 -300 ms and ~80 -150ms

• magnetic field: log-normal distribution with <log B>~13 G

4 3 23

02 6 2 2

192 with [0;2 / ]

5 singw

dip

dE GIP

d c R B

0 *

*

( )( ) ( )

(1 )

= mass fraction of NS progenitors in the range 8-40 M

( ) = cosmic star formation rate

p

p

dR R z dVz z

dz z dz

R z

Energy density spectrum

10

10 100 1000

1E-18

1E-17

1E-16

1E-15

1E-14

1E-13

B = 1013

G, = 10-6

Pmin

=0.8 ms P

min=0.5 ms

gw

(Hz)

Spectrum from the cosmological population of rotating NSs, assuming initial period and magnetic field distributions derived from population synthesis.

0

4v

Constraints on B*

11

1E11 1E12 1E13 1E141E-7

1E-6

1E-5

1E-4

1E-3

0.01

SNR=1

SNR=5

Excluded region

<Beff

> (Gauss)

1E11 1E12 1E13 1E141E-7

1E-6

1E-5

1E-4

1E-3

0.01

SNR=1

SNR=5

Excluded region

<Beff

> (Gauss)

Constraints given by coaligned and coincident detectors (ex: H1-H2), for T=3 yrs of observation, in the range 10-500 Hz.

Advanced detectors (Ad LIGO sensitivity) 3rd generation detectors (Einstein Telescope)

*2-D projection, assuming the distribution of initial period derived from population synthesis.

Double Neutron Stars

12

Last thousands seconds before the last stable orbit in [10-1500 Hz]: 96% of the energy released.

source rate:

spectral energy density:2/3

1/31 21/3

1 2

( ) with [10 Hz; ]

3 ( )gw

lso

dE m mG

d m m

*0 ( )( ) ( ) ( )

1

= mass fraction of NS progenitors in the range 8-40 M

: fraction of massive binaries formed among all stars

:fraction of massive binaries that remain

c db ns p d d

f

p

b

NS

R t tdR dVz f P t dt z

dz z dz

f

*

bounded after the second supernova

( ) = cosmic star formation rate

( ): probability for a newly formed NS/NS to coalesce in a timescale td d

R z

P t

13

Cosmic coalescence rate

0 1 2 3 4 5 60.00

0.05

0.10

0.15

0.20

star formation rate = 1, =20 Myr = 3/2, =20 Myr = 1/2, =20 Myr = 1, =100 Myr

R* (

MoM

pc-3yr

-1)

z

( ) with minimal delay d d oP t t

Energy density spectrum

14

0.1 1

0.01

0.1

1

10

100

continuous background

resolved sources

popcorn noiseD(z

)

z

10 100 1000

1E-10

1E-9

popcorn noise

resolved sources

gaussian background gw

(Hz)

all sources z >0.26 (popcorn) z >0.52 (continuous)

Spectrum for the three regimes (resolved sources, popcorn noise and gaussian background), assuming a galactic coalescence rate Rmw=3. 10-5 yr-1 and a coalescence time distribution with parameter =1 and 0=20Myr.

Constraints on fb-ns*

15

0.0 0.2 0.4 0.6 0.8 1.0

1E-4

1E-3

0.01

0.1

1

Rmw

=10-5 yr-1

Rmw

=10-6 yr-1

Rmw

=10-4 yr-1

Ad H1L1: Rmw

=4.5 10-4 yr-1

Ad H1H2: Rmw

=2.4 10-5 yr-1

3rd gen. H1L1: Rmw

=4.5 10-6 yr-1

3rd gen. H1H2: Rmw

=1.7 10-6 yr-1

ns

fb

Constraints given on the fractions fb and ns for T= 3 years and SNR=1.

*2D projection, assuming a coalescence time distribution with parameter =1 and 0=20Myr.

Summary and Conclusions

16

Why are AGBs important (and need to be modeled accurately)?

carry information about the star formation history, the statistical properties of source populations. may be a noise for the cosmological background

How do AGBs differ from the CGB (and need specific detection strategies)?

anisotropic in the local universe (directed searches)different regimes: shot noise, popcorn noise and gaussian (maximum likelihood statistic, Drasco et al.; probability event horizon Coward et al.)spectrum characterized by a maximum and a cutoff frequency

Advanced detectors may be able to put interesting constraints

NS ellipticity, magnetic field, initial periodrate of compact binaries….

Extra Slides

17

Sensitivity

18

10 100 1000

1E-24

1E-23

1E-22

1E-21

1E-20

LIGO SDR 4K

EGO

Ad LIGO

h n(f)

f Hz

Magnetars

1919

about 10-20% of the radio pulsar population super-strong crustal magnetic fields (Bdip~1014 – 1016 G) formed by dynamo action

in proto neutron stars with millisecond rotation period P0 ~0.6 – 3 ms (break up limit - convective overturn).

strong magnetic fields can induce significant equatorial deformation

• pure poloidal field (Bonazzola 1996)

The distortion parameter g depends on both the EOS and the geometry of the magnetic field: g~1-10 (non-superconductor), g~100-1000 (type I superconductor), g>1000-10000 (type II superconductor, counter rotating electric current)

• internal field dominated by the toroidal component (Cutler 2002, dall’Osso et al. 2007):

spectral energy density

8 2 24 8 2 2

100 10 45 152

sin3.7 10

4B

R Bg g R I B

GI

4 2 2,16~ 1.6 10 when B t t pB B B

100

37 2 21153 2

2 36 4 2,16 15

3.9 10 (pure poloidal field)1 where ~

7.1 10 (toroidal internal field)

gw

t

g BdE KK K

d I B B

Energy density spectrum

20

10 100 10001E-17

1E-16

1E-15

1E-14

1E-13

1E-12

1E-11

1E-10

1E-9

1E-8

1E-7

1E-6saturation: GW spin-down Beff=10

15G ; g=100

Beff=1016

G ; g=1000

Beff=1017

G ; g=10000

gw

(Hz)10 100 1000

1E-18

1E-17

1E-16

1E-15

1E-14

1E-13

1E-12

1E-11

1E-10

1E-9

1E-8

1E-7

(Hz)

Bt=10

17G B

eff=10

14G

Bt=10

17G B

eff=10

15G

Bt=10

16G B

eff=10

14G

Bt=10

16G B

eff=10

15G

gw

pure poloidal magnetic field toroidal internal magnetic field

Spectrum from the cosmological population of magnetars, assuming an initial period P i =1 ms and a galactic rate Rmw=0.1 per century.

Constraints on g-B

21

10 100 1000 10000

1E14

1E15

1E16

1E17

1E18

SNR=1

normal interior superconductor II or currents

superconductor I

magnetic spindown:

SNR~0.002 I45

-1 RMW;0.1

(g100

B15

)2

GW spindown: SNR~1.5 I

45 R

MW;0.1 (saturation)

<B>AXP

<B>SGR

magnetar limit

Bef

f G

g

If no detection, we can rule out the model of spindown dominated by GW emission

10 100 1000 10000

1E14

1E15

1E16

1E17

1E18

SNR=10

SNR=5

SNR=1

normal interior superconductor II or currents

superconductor I

magnetic spindown:

SNR~0.01 I45

-1 RMW;0.1(g100B15)2

GW spindown: SNR~16 I45 RMW;0.1 (saturation)

<B>AXP

<B>SGR

magnetar limit

Bef

f G

g

Constraints given by coaligned and coincident detectors (H1-H2), for T=3 yrs of observation, , in the range 10-500 Hz.

3rd generation detectors (Einstein Telescope)Advanced detectors (Ad LIGO sensitivity)

Constraints on BtB

22

If no detection, we can rule out the model of spindown dominated by GW emission

Constraints given by coaligned and coincident detectors (ex: H1-H2), for T=3 yrs of observation, in the range 10-500 Hz.

Advanced detectors (Ad LIGO sensitivity) 3rd generation detectors (Einstein Telescope)

1E15 1E16 1E17 1E18

1E14

1E15

1E16

1E17

SNR=1

magnetic spindown:

SNR~0.04 (B16

2/B14

)2

GW spindown (saturation)SNR~1.5

<B>AXP

<B>SGR

magnetar limit

Bef

f (G

)

Bt (G)

1E15 1E16 1E17 1E18

1E14

1E15

1E16

1E17

SNR=5

SNR=10

SNR=1magnetic spindown:

SNR~0.22 I45

3 RMW;0.1

(B16

2/B14

)2

GW spindown (saturation)SNR~16 I

45 R

MW;0.1

<B>AXP

<B>SGR

magnetar limit

Bef

f (G

)

Bt (G)

NS Initial Instabilities

23

source rate:Only the small fraction of NS born fast enough to enter the instability window:

Population synthesis ((Regimbau & de F. Pacheco 2000, Faucher-Giguere & Kaspi 2006) :

• initial period: normal distribution with <Po>~250 -300 ms and ~80 -150ms

spectral energy density:

max

min

0 *

0 0

*

( )( ) ( )

(1 )

= mass fraction of NS progenitors in the range 40-100 M

fraction of newborn NS that enter the instability ( = ( ) )

( ) = cosmic star formation rate

p

p

P

P

dR R z dVz z

dz z dz

g P dP

R z

002

0sup

r-modes: 2

bar-modes: K

MacLauren Dedekind

E EEdE

E E Ed

Instability windows

24

Bar modes:

secular instability: 0.14< <0.27-R=10 km: Po ~0.8-1.1 ms (~2e-5)

-R=12.5 km: Po ~ 1.1-1.6 ms (~3e-5)

R modes:

gwv ,T)

-R=10 km: Po ~0.7-9 ms (~5e-4)

-R=12.5 km: Po ~1-12 ms ~8e-4)

GW emission

viscosity

0.14 0.16 0.18 0.20 0.22 0.24 0.260.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

R=10 km

R=12.5 km

P (m

s)

=T/W

0.076

Energy density spectrum

25

10 10010

-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

R=10 km (shot noise DC<<1) R=12.5 km (shot noise DC<<1) 1% of NS born with P0~1ms (continuous)

gw

(Hz)

10 100 10001E-15

1E-14

1E-13

1E-12

1E-11

1E-10

1E-9

1E-8

(Hz)

gw

R=10 km R=12.5 km 1% of NS born with

max

Bar modes: R modes:

Spectrum from the cosmological population of newborn NSs that enter the bar and r-modes instability windows.

Constraints on

26

Bar modes:

sensitivity H1L1 H1H2

Advanced - 2-5%

3rd gen.

4-10% 0.2-0.5%

Constraints on the fraction of NS that enter the instability window of bar modes and R modes near the Keplerian velocity for T= 3 years and SNR=1-5.

R modes:

Core collapse to BH (ringdown)

272727

source rate:follows the star formation rate (fast evolution of massive stars)

spectral energy density:All the energy is emitted at the same frequency (Thorne, 1987)

2* *

4

( ( )) with (kHz) ~ 13 / (M )

mass of the BH: with ~ 10 20%

efficiency: <7 10

gwc c c

c p

dEM c M M

dM M

0 *

*

( )( ) ( )

(1 )

= mass fraction of NS progenitors in the range 40-100 M

( ) = cosmic star formation rate

p

p

dR R z dVz z

dz z dz

R z

0 500 1000 1500 2000 2500 3000 3500 4000 45000.00E+000

2.00E-009

4.00E-009

6.00E-009

8.00E-009

1.00E-008

1.20E-008

1.40E-008 =7.10-4 Mmin=40 Ms =10% Mmin=40 Ms =20% Mmin=30 Ms =10% Mmin=30 Ms =20%

gw

Hz

Energy density spectrum

28

Spectrum from the cosmological population of newborn distorted BHs. The resulted background is not gaussian but rather a shot noise with a duty cycle DC~0.01.