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Prospects for gravitational wave detection with forthcoming Pulsar Timing Arrays
Alberto Sesana CGWP at PennState
Alberto Vecchio Marta Volonteri Carlo Nicola Colacino University of Birmingham University of Michigan RMKI Budapest
STScI 3/30/2009


OUTLINE
> PTAs and MBHBs > GWs and PTAs: unresolved background > GWs and PTAs: resolvable sources


HIERARCHICAL GALAXY FORMATION...

From De Lucia et al. 2006


MBH- bulge relations: co-evolution of MBHs and galaxies


MBH- bulge relations: co-evolution of MBHs and galaxies



During galaxy mergers, MBHBs will Inevitably form!


SMBHs DYNAMICS
1. dynamical friction (Lacey & Cole 1993, Colpi et al. 2000)

from the interaction between the DM halos to the formation of the BH binary
determined by the global distribution of matter

efficient only for major mergers against mass stripping
2. binary hardening (Quinlan 1996, Miloslavljevic & Merritt 2001, Sesana et al. 2007)

3 bodies interactions between the binary and the surrounding stars
the binding energy of the BHs is larger than the thermal energy of the stars

the SMBHs create a stellar density core ejecting the background stars
3. emission of gravitational waves (Peters 1964)

takes over at subparsec scales
leads the binary to coalescence


THE GRAVITATIONAL WAVE SPECTRUM


Pulsar Timing Arrays

Intensity

Pulsar Earth Time


The GW passage cause a modulation of the MSP frequency

The residual in the time of arrival of the pulse is the integral of the frequency modulation over time

R~h/f


The GW passage cause a modulation of the MSP frequency

The residual in the time of arrival of the pulse is the integral of the frequency modulation over time

R~h/f


Theory of GW background from SMBHs
Consider a class of sources with differential number density d2n/dzdM emitting an energy spectrum dE/dlnf

For MBHBs dN/dlnff 8

/3

Phinney 2001, Jaffe & Backer 2003, Wyithe & Loeb 2003, Sesana et al. 2004, Enoki et al. 2004


Modelling the SMBH population
SEMIANALYTICAL MERGER TREES:
> We follow backwards the merger hierarchy by means of EPS Monte Carlo merger tree > The semianalytic code follows the accretion and the dynamical history of BHs in every single branch of the tree

MILLENNIUM RUN:
> SPH numerical simulations of the halo hierarchy > Semianalytical models for galaxy formation and evolution > We extract catalogues of merging galaxies and we populate them with sensible MBH prescriptions



Theoretical background >
Sensitivity in the frequency range 109107 Hz >Signal dominated by MBHBs with masses >108 M at z<2

>Probe the MBHB merger rate at low redshift >Constrain the local MBH mass function? >Is insensitive to the seed BH population


Simulated Montecarlo signal

is not smooth at all significantly deviate from the 2/3 slope


Expeceted background level
Sesana, Vecchio & Colacino 2008, MNRAS, 390, 192

Three parameter fit to the background


Resolvable sources
>Nearby and/or massive binaries could rise above the background >We quantify their statistics and the typical induced residuals to asses required timing precision for detection


The typical situation...


Cumulative number of sources...
Sesana, Vecchio & Volonteri, MNRAS, in press

>a total timing precision of 550 ns is required to detect an individual resolvable MBHB >Uncertainties depend on the MBHhost relation and MBH accretion route during mergers


Uncertainties


Source distributions
Probe MBHs at lowtomedium redshift 0.1
Probe very massive systems mass > 108 solar masses


Caveats....
We considered here only circular binaries....
binaries may be highly eccentric hardening in stellar background > eccentricity grows hardening in a gaseous disk> who knows.... each system then emits a whole spectrum of harmonics may have interesting signatures on both the background global shape, and on the characteristics of individually resolvable sources.

We supposed that binaries loose orbital energy by means of gravitational wave emission only....
extremely inefficient at low frequencies an effective shrinking mechanism (timescale ~106 yr) may cause the suppression of the low frequency background


Examples, eccentric bursts....


Summary
> Future PTAs will detect the unresolved MBHB background > The background spectrum can be fitted by a double power law with a break around 10-8 Hz > A timing precision between 5-50 ns should guarantee the detection of at least one individual MBHB



...HIERARCHICAL MBH FORMATION
GENERAL FRAMEWORK:
> We follow backwards the merger hierarchy by means of EPS Monte Carlo merger tree > Halo density profile: DM: NFW Baryons: SIS The semianalytic code follows the accretion and the dynamical history of BHs in every single branch of the tree The adopted threshold for density peaks hosting a seed ensures an occupation fraction of order unity

(Volonteri, Haardt & Madau 2003)
Z=0

During galaxy mergers,
MBHBs will Inevitably form!

Z=20

today for halos more massive than Binary merger trees starting at z=20 In a CDM cosmology 11 10 M


COALESCENCE RATE

To support a steady merger rate
millions of wide (in the PTA window) MBHBs must exist at any time!


A simple sampling issue


Numbers
Sesana, Vecchio & Volonteri 2008, arXiv:0809.3412

With a 10ns precision 1to5 MBHBs can be individually resolved


Directly from genetal relativity
Every accelerating mass distribution with nonzero quadrupole momentum emits GWs!

Perturbed Minkowski metric tensor :

Perturbation perpendicular to the wave propagation direction

A MBHB is a perfect candidate for GW emission!


SIMPLE EXAMPLE (ongoing experiment)


SIMPLE EXAMPLE (ongoing experiment)



Unexpected and phenomenon

still unexplained