23 Jan 2006
Dear Scott et al,
I have been through all Ryan & Scott's plots of dD/D
(http://gmunu.mit.edu/LIST/) and dOmega/arcmin
(http://gmunu.mit.edu/rlang/skypos.html), judging the medians by eye.
[Note that the files seemed to be moving as I viewed them, so they
may all be in the LIST place by now!).
My conclusions are
There is surprisingly little dependence on the noise slope below 10^{-4}
Hz except for the M1~10^(6.5-7) Msun cases 7 and 14 days before.
For the sources expected to dominate the rates (numbers are for
Sesana/Madau models; I also indicate model-dependence):
[comoving search volume for flat universe is dOmega*D_M^3 (dD_M/D_M)=
dOmega (1+z)D_A^2D_L (dD_L/D_L). The space density of bright galaxies
is around 0.003Mpc^{-3} -cf astro-ph/0302543, and of AGN (L_X>1e42 erg/s)
around 0.0001Mpc^{-3} -cf astro-ph/0506118].
So final search volumes larger than ~3e4 comoving Mpc^3 will require
luck and going through signatures of gw-induced electromagnetic
variability with a fine-tooth comb to identify the host.
LSST and Schmidts have ~5-7 degree=300-420' fields. Larger
sqrt(dOmega) would mean that the variability data would not be
obtainable.
Note also that the sqrt(dOmega) and search vols given below are medians.
25% of sources have values larger by about 3 and 27, respectively.
The correct requirement should be that the semi-major axis of the
25%-worse position error ellipse be less than the telescope field ~400'.
LISA Short quiet Short louder
[expect a few of these in 3y; robust since these BH observationally known]
1e7/1e6, z=1, end
dD/D 0.004 0.01 0.01
sqrt(dOmega)/' 15 30 30
search vol 2800 28000 28000 comoving Mpc^3
1e7/3e6, z=1, end
dD/D 0.004 0.015 0.015
sqrt(dOmega)/' 15 30 40
search vol 2800 42000 76000 comoving Mpc^3
1e7/3e6, z=1, 7 days, white noise
dD/D 0.04 0.1 0.15 all 5x worse w/ noise 2
sqrt(dOmega)/' 150 300 400 all 3x worse w/ noise 2
search vol 2.8e6 2.8e7 7.6e7 comoving Mpc^3
1e7/3e6, z=1, 14 days
dD/D no useful info..............
sqrt(dOmega)/' no useful info..............
[expect ~1 of these in 3y; model-dep since these BH numbers unmeasured]
3e5/1e5, z=1, end
dD/D 0.001 0.002 0.003
sqrt(dOmega)/' 5 10 10
search vol 77 600 900 comoving Mpc^3
[expect ~15 of these in 3y; model-dep since these BH numbers unmeasured;
could be several times higher or lower depending on occupation fraction
of seed BH and accretion growth history]
1e6-1e5, z=5, end
dD/D 0.02 0.03 0.03
sqrt(dOmega)/' 30 100 100
search vol 7.6e5 1.2e7 1.2e7 comoving Mpc^3
1e6/3e5, z=5, end
dD/D 0.02 0.04 0.04
sqrt(dOmega)/' 50 100 150
search vol 2.1e6 1.7e7 3.8e7 comoving Mpc^3
Preliminary conclusion:
2Gm arms for LISA preclude identifying the host galaxies of the
guaranteed, high S/N merging SMBH, increasing search volumes over
LISA by around 10. There is only modest difference
between 9 and 15pm/rtHz noise cases for the 2Gm arms.
Further actions for Scott/Ryan:
1. Can you generate a table like mine above with real (as opposed to `by
eye' medians, and also <25% worse levels)?
2. For the telescopes' field of view, it is the semi-major axis of
the Omega ellipse that matters, not sqrt(dOmega). Can you list that
as well?
3. Do you have unprocessed "4 or 7 days before" runs for the cases listed
above without them? If so can they be processed?
Action item for Neil/Scott:
By what factor should the dD/D and sqrt(dOmega) values computed
by Scott's sky-average source/noise be increased to account for
real source positions and sky-variations of noise?
Action item for Curt:
Any news on the systematic error due to template mismatch?
Action item for Michele:
Any news on the factor by which dD/D and sqrt(dOmega) should be
increased to account for finite SNR and failure of the Fisher matrix
approach?
Action item for all:
Comments/conclusions...
Cheers,
Sterl
On Fri, 13 Jan 2006, Scott A. Hughes wrote:
>
>
> 2. What further data are high priority for you? Variations on this
> theme for which data exists are:
> --- One additional LISA variant (2 Gm, 15 pm/rtHz). Results for
> this configuration could be added to these plots, though they are
> likely to get rather busy.
> --- Different redshifts (we have z = 1, 3, 5).
> --- Different reddening models [white all the way down; reddened by
> f^(-1/2); reddened by f^(-1)].
> --- Errors prior to merger: in at least some cases, we have measures
> of these errors 7 days prior to merger and 14 days prior. In
> some cases, particularly at z = 3 & 5, the SNRs are so low at
> this point that the Fisher matrix doesn't invert nicely; we
> looked at 4 days prior for some of these cases.
>
> Let me know what's interesting. I'll try to generate more plots over
> the weekend and put them up at http://gmunu.mit.edu/LIST
>
> cheers,
>
> scott