Fundamentals of interferometers: LIGO vs LISA.
To this I attempted some feeble humor my remarking that much of LIGO's
cost was in creating the vacuum (and protecting it from shotguns), but those
both came free with launch for LISA.
Cosmological black hole signals on
LISA 5 sigma sky-average noise curves. The noise curves
include Galactic white dwarf noise, partially removed by assuming the
availability of 3 years of data with no `interesting' non-white dwarf
sources active. These are used to define zero power bands at frequencies
at which there are typically a few white dwarfs per frequency bin,
beating and making time-dependent correlated `noise', and to do
direct subraction at higher frequencies, for which
there is a low probability of multiple white dwarfs per Fourier bin.
Superposed are h_c for merging equal mass black holes of the indicated
masses and redshifts (H0=65, Omega_m=0.25, Omega_lambda=0.75 assumed).
Red curves are for the post-newtonian inspiral; blue for the messy
numerical merger part, and the red dot for the post-merger ringdown of
the merged black hole (rapidly rotating even if the pre-merger black holes
are not; the amplitude counts the ringdown as producing the last 3% of
Mc^2.) Assumptions are as in Hughes and Flanagan 1998 PRD 57, 4535.
5+10^(The distance above the noise curve) is the S/N of the signal
as it moves across and e-fold in frequency (except for the ring-down point
which gives the S/N of the whole thud). These S/N have also been
confirmed by the applying the template-matching formalism of
Hughes and Flanagan to the illustrated LISA noise curve, which is
quite similar to Cutler's fit to the noise curve in LISA pre-phase A
graphs (even though these don't specify how white dwarf `noise'
is treated at the frequencies at which it is not gaussian noise).
Notice the detectability of black holes of 3e4 and 1e5 at z=10-100.
Such black holes would represent the same fraction of
the collapsed baryonic structures predicted in fashionable LCDM models as
the observed black holes in galaxies today are of current galaxies.
Contributions to the total LISA `noise'
of the previous plot. Blue: instrumental position and acceleration noise
(a la Pre-phase A, Jul 1998, multiplied by Bender's extra f^{-0.5} below
1e-4 Hz); solid green: Galactic (white dwarf) binary noise (below 1e-3Hz, many
sources per 1/3y frequency bin; above 1e-3Hz, treated as described in
previous caption), merger rate 1/30 y as per Webbink and Han 1998;
dashed green: extragalactic (white dwarf) binary noise.
