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