Cosmological supernovae as neutrino and gravitational wave sources

Günter Sigl, Astroparticules et Cosmologie, ParisData analysis workshop, Paris, November 15, 2006

Cosmological supernovae as neutrino and gravitational wave sources mHz gravitational wave background from inspiral of compact objects embedded in AGN accretion discs.

Astrophysical Gravitational WaveBackgrounds

Günter SiglAPC (Astroparticule et Cosmologie), Université Paris 7and GReCO, Institut d’Astrophysique de Paris, CNRShttp://www2.iap.fr/users/sigl/homepage.html


Individual and Diffuse Signals

Thecharacteristic GW amplitudehc(f ) for singleevents is related to theenergyemitted per frequency interval, (dEgw=df )(f )

h2c(f ) =

2(1+z)2

¼2

1d2

L

dEgw

df[f (1+z)] ;

where dL is the luminosity distance.

The signal to noise ratio (SNR) of an individual event is de ned by

SNR2 =

Z f max

f min

dlnfh2

c(f )f Sn

;

where Sn(f ) is the detectors noisebudget.

In termsof cosmology jdt=dzj = [(1+z)H (z)]¡ 1 and an event rateper comovingvolume R(z), the time-averaged GW energy density per logarithmic frequencyinterval is

d½gw

dlnf(f ) =

Z 1

0dz

R(z)1+z

¯¯¯¯dtdz

¯¯¯¯f z

dEgw

df(f z) :


Event rates and Duty Cycles

The duty cycle is given by multiplying the integrand with the coherence timescale (1+z)tcoh[(1+ z)f ]:

Duty cycle'Z 1

0dzR(z)

4¼r2(z)tcoh[(1+z)f ]H (z)

:

The event rateas seen from Earth is

¡ =

Z 1

0dz

R(z)1+z

dVdz =

Z 1

0dzR(z)

4¼r2(z)(1+z)H (z)

:

with r(z) the comoving coordinate, dr = (1+ z)dt.


Onion structure of a supernova

Convection, turbulence

Janka, Mueller


Supernovae as Neutrino and Gravitational Wave Sources

Anisotropic mass motion and neutrino emission in collapse of massive starsleads to gravitational wave emission. At low frequencies anisotropic neutrinoemission of luminosity Lν(t) and anisotropy q(t) dominates and leads to thedimensionless strain at distance D

Dt

tqtLtdD

Gth )()(

2)( N

Individual supernovae (SN) in our Galaxy can give prominent signals inneutrinos in Super-Kamiokande, Amanda, ICECUBE, Uno… and ingravitational waves in Virgo/EGO, LIGO…, but are rare events.

However, backgrounds from cosmological SN may soon be detectableby gadolinium upgrade of Super-K in neutrinos and by gravitational wavedetectors such as the Big Bang Observatory (BBO).


Illustration for a particular rotating core collapse model by Mueller et al.,Astrophys. J. 603 (2004) 221.

time dependent q

average< q>» 0:45%

Fully 2D, axisymmetric rotating 15M ¯ progenitor, » 3£ 10¡ 9M ¯ released inGW during simulation


However, note dependence on progenitor model

average< q>» 3£ 10¡ 5

Fully 2D, axisymmetricnon-rotatingnakedproto-neutronstar, » 1:6£10¡ 10M ¯released in GW during simulation


SN rate

neutrino spectragravitational wave spectra

+simulations

+ very massive PopIII starsat z≥15future input from SWIFT…

ordinary SN

≥100Msun PopIII


=>diffuse neutrino spectra

stochastic gravitational wave backgroundAndo and Sato, astro-ph/0410061 Buonanno, Sigl, Raffelt, Janka, Mueller,

Phys.Rev.D 72 (2005) 084001


At low frequency gravitational wave spectrum always dominated by anisotropicneutrino emission. At high frequency f > 100 Hz convective mass motiondominates.

Note that simulations stop after ~250 msec, during which only about 1/6 of thetotal 3x1053 erg in neutrinos radiated during cooling phase has been emitted Possible enhancement factors in the GW amplitude between ~√6 and ~6(bands in previous figure)

Red vs blue band are different type II SN redshift evolutions


The rate of ordinary supernovae is R ~ 1/sec. For Pop III events related toa few hundred solar mass stars the rate RIII is related to the fraction ofbaryons converted into Pop III stars fIII by

3

1

10 s 2.0 III

III

fR

If metals are released, fIII has to be <10-5.However, there are speculations that an observed infrared background exesscould be explained by efficient Pop III formation correponding to fIII ~ 0.1.Metallicity constraints in this case must be circumvented by fall into black hole.

For events with rate R and processes that loose phase coherence after onecycle, at frequencies f < R the signal becomes « stochastic », or « gaussian »,i.e. more than one event is « on » at any given time. Individual events are alsounresolvable at such frequencies because SNR < 1.


Uncertainties in star formation rates at high redshift

reionization


By using more optimistic SFR, Sandick et al, Phys.Rev.D 73 (2006) 104024obtain more optimistic estimates


Compare this with upper limits, sensitivities, and cosmological predictions

Giovannini

BBO

BBO correlated

SN and PopIII

By the way: Accelerated expansion could decrease conventional inflationsignal by factor 100 ! This makes astrophysical sources more important.


Sensitivities of existing and future ground-based gravitational wave detectors(uncorrelated)


Active Galactic Nuclei as Photon andGravitational Wave Sources

The bolometric luminosity Lbol of an AGN with central black hole of massM is related to the accretion rate Lacc and the Eddington rate LEdd by

of which a fraction fX is in X-rays between 2 and 10 keV, LX = fX Lbol.

Assume that a fraction fco of accretion is in the form of compact objectsof typical mass m ~ 100 Msun. These objects release a fraction α ~ 0.2 oftheir mass m in gravitational waves during inspiral to the last stable orbit:

Thus, from the observed X-ray luminosity function dn/dLX for AGNs, wecan compute the cosmological gravitational wave background.

Lgw » ´gwf coLacc »´gwf co

fX ´emLX :

Lbol » ´emLacc » f EddLEdd » 1:25£ 1038f Edd

µMM¯

¶ergs¡ 1


For ΩSMBH = fraction of critical density in SMBHs, Ωacc = fraction of criticaldensity in accreted gas, ΩX = fraction of critical density of X-rays in the2-10 keV band, facc = fraction of SMBH mass due to accreted gas, fobsc =fraction of obscured emission ~ 0.3, one has

facc ΩSMBH ~ (1 – ηem) Ωacc

ΩX ~ <(1+z)-1> fobsc fX ηem Ωacc

Since ΩX/ΩSMBH ~ 1.3x10-3, <(1+z)-1> ~ 0.4 from AGN evolution data, oneobtains the condition

fobsc facc fX ηem ~ 3x10-3

Observations suggest that ηem is not much smaller than 0.1, and thatSMBH build-up is dominated by accretion facc ~ 1 and NOT by mergersfX ~ 0.1: bolometric emission dominated by infrared.This will be our standard case.


The universalphoton spectrum


AGN+galaxy clusters

unobscured

Compton thin

Compton thick

Diffuse X-ray background

Comastri, Gilli, Hasinger. astro-ph/0604523


The X-ray background between ~1 and ~100 keV is explained by AGNs.

X-ray luminosity function


SNR of a 100M ¯ object spirallinginto central black holes of various masses.

107 M ¯

106 M ¯

105 M ¯

Individual events

Sigl, Schnittman, Buonanno, astro-ph/0610680


fX = 0.03, ηem = 0.2, (infrared emission dominated, solid line)facc = 1, fco = 0.01, black hole spin a/M = 0.95, for which ηgw ~ 0.2

Time-averagedtotal signal

Confusion noise

Noise induced bysubtractingresolvable eventswith SNR > 15

dR =f co

f X

1Egw

dndlnLX

dLX

where Egw=gravitational wave release per event,goverened by GR


The duty factor is the event rate times the time tcoh ~ f/(df/dt) ~ f -8/3 spentemitting at frequency f.

Below a few milli-Hertz > 1 event contributes at any given time and the signalis gaussian. At higher frequencies one would see individual events at final stages

of inspiral. These events also have sufficient SNR to be resolved.



The observable total (solid) and resolvable (dashed) chirp rateas function of frequency f.



The rate of individual events can thus be approximated by

¡ (f ) ' 102

µf co

0:01

¶ µ102 M ¯

m

¶y¡ 1 for f < 5£ 10¡ 3 Hz

in this scenario. The duration of such a typical event would be

tcoh(f ) ' 0:2µ

102 M¯

m

¶ µ10¡ 3 Hz

f

¶8=3

yr :

Individual eventscould thusbefollowed through frequency spacewith thechar-acteristic frequency evolution for coalescence.Thebackground becomes gaussian (duty cycle > 1) for

f . f gauss ' 2£ 10¡ 3

µf co

0:01

¶3=8 µ102 M ¯

m

¶3=4

Hz:

At frequencies a factor 5-10 lower, thebackground becomes confusion noise.


Conclusions1

1.) There is a deep connection between neutrino and gravitational wave emission by collapsing massive stars. Both signals have good chances to be seen by future experiments.

2.) Such astrophysical backgrounds could partially mask the inflationary background in the BBO (~0.1 Hz) frequency range. In the ground based frequency range ~100 Hz, these backgrounds would only be detectable by the most advanced third generation detectors.

3.) The supernova type II background is gaussian below ~1 Hz, however the neutron star phase transition background would be pop-corn type.


Conclusions2

4.) The accretion powering Active Galactic Nuclei give rise to electromagnetic emission from the infrared to γ-rays and at the same time to gravitational waves from inspiral of compact objects.

5.) If > 1% of the accreted matter fueling AGNs is in form of compact objects, a continuous background detectable by LISA results below 1 mHz. If the typical compact object masses are > 10 solar masses, individual inspirals should be resolvable above a few mHz with a rate of a few hundred per year.

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Cosmological supernovae as neutrino and gravitational wave sources