Supermassive black hole detection

1
Are there potential complementarities between
LISA and pulsar timing?
Matthew Pitkin, James Clark, Martin Hendry, Ik
Siong Heng, Chris Messenger, Jennifer Toher,
Graham Woan University of Glasgow,
matthew_at_astro.gla.ac.uk


Supermassive black hole detection
A major source of strong gravitational wave (GW)
signals in LISA will the inspiral and ring-down
of merging supermassive black holes (SMBHs) at
cosmological distances. Inspirals should be seen
for SMBH with masses up to a few 108 M?, with
more massive systems merging before they enter
the LISA band, but observable in their ring-down
phase. Such systems can potentially be observed
with signal-to-noise ratios of hundreds allowing
the waveform to be precisely parameterised. For
such events observed in LISA we consider what
complementary information could be gained by
looking for the same signal in pulsar timing data.
The LISA strain spectral density curve (pink)
with estimates of source strength for SMBH
coalescences and ring-downs at z1, where e is
the mass conversion efficiency.
Pulsar timing
Many pulsars are very precise clocks. The
residuals in their timing are a potential way to
probe the low frequency GW spectrum1. Residuals
contain noise from signal processing and the
intrinsic instability of the pulsar. A search
called the Parkes Pulsar Timing Array2 (PPTA)
aims to time tens of the most stable pulsars with
precisions of around 100 ns. In the future with
the Square Kilometre Array (SKA) there is the
potential to be able to time thousands of pulsars
with 10 ns precision. There have already been
efforts to search for a GW background3, and
individual systems4, of SMBH inspirals in
pulsar timing data. Pulsar timing residuals
contain two components of a GW signal the part
passing the Earth (which will be correlated
between all pulsar observations) and the part
passing the pulsar as it emitted the pulses now
being observed. The signal amplitude will depend
on the angular separation between the GW source
and the pulsar - sources along the pulsar
line-of-sight producing no residual. The timing
residual will increase with source period.
The gravitational wave background in timing
residuals from a population of SMBH systems
characterised by dt 10-16(f/yr-1)-5/3 secs5
Pulsar distance measurements
For the very well constrained inspiral signals
seen in LISA the equivalent waveform in the
pulsar timing data can be constructed such that
the only unknown is the distance to the pulsar. A
single parameter space search is simple, although
even with small uncertainties on several source
parameters we could still perform an MCMC search
with relative ease. This provides a way of
getting pulsar distances independently of the
galactic electron density distribution model used
in dispersion measure distance estimates, which
can have large uncertainties. If we assume that a
pulsars timing residual is dominated by the GW
background of SMBHs then individual strong events
observed by LISA would allow very accurate
measurements of pulsar distances for hundreds of
data points over a few years. However, more
realistic situations need to be considered. For a
simulated two 5x108 M? system at z1, with the
source and pulsar perpendicular, timing residual
accuracies of around 5 ns would be needed to get
the pulsar distance to of order 20. To obtain
distances with 20 error, using potentially
obtainable timing accuracies of 10 and 100 ns
requires such a system to be 1000 and 100 Mpc
away respectively. Such high mass systems
inspirals are likely to be rare, or may only be
seen as ring-downs in LISA, so lower mass systems
would need to be even closer to give decent
pulsar distance estimates. We have assumed
observing a single pulsar, but the SKA should
observe many thousands of stable pulsars, so a
global fit using the data from many pulsars and
fitting for all there distances could allow us to
dig much deeper into the noise where more
realistic signals would lie.
Ring-down signals as triggers
The ring-down of SMBH mergers offer better event
rates in LISA for high mass systems, due to
higher frequency and visibility to larger
distances. However, LISA will be unable to obtain
information about the inspiral phase. This offers
the opportunity for pulsar timing observations to
provide information on the unseen part of the
merger. Constraints on the system parameter
space, and the time of coalescence seen in LISA
gives a trigger with which to search in pulsar
timing data. Unfortunately the ring-down does not
provide information on the sources position
making the parameter space more difficult. Again
a global fit using the data from multiple pulsar
observations could allow the reconstruction of
the inspiral and would also allow the position of
the source to be recovered.
1 Detweiler, Ap. J. 234, 1100 (1979) 2
Manchester, Ch. J. A. S. 6, S2 (2006) 3 Jenet
et al, Ap. J. 653, 1571 (2006) 4 Jenet et al,
Ap. J. 606, 799 (2004) 5 Jaffe and Backer, Ap.
J. 538, 616 (2003)