[Pafgbt] pulsar search metric

[Paul Demorest]

The usual pulsar sensitivity expression (for a single beam/pointing) is

S_min = (# sigma) * (T_sys/G) / sqrt(2*BW*t_int) * sqrt(W/(P-W))

(see for example the Lorimer and Kramer book.. this eqn is probably given 
in lots of other places as well)

Most of these are just the standard factors.. T_sys needs to include both 
recvr temp and galactic BG sky temp.  P is the pulse period and W is the 
pulse width.  W is really the only complicated thing, it's usually taken 
as a quadrature sum of several terms:

W^2 = W_psr^2 + W_dm^2 + W_inst^2 + W_scat^2

W_psr is the intrinsic pulse width, typically assumed to be 5-10% of P for 
survey planning purposes.  MSPs tend to have a higher duty cycle than slow 
PSRs.

W_dm is the dm smearing, which depends on the frequency resolution, and is 
equal to 8.3us*DM*chan_bw(MHz)/RF(GHz)^3.

W_inst is the instrumental time resolution.

W_scat is ISM scatter broadening.. usually ignored except in special cases 
like galactic center searches.

The sensitivty ends up being a function of pulse period and dispersion 
measure.  To compare searches involving different numbers of beams, fields 
of view, etc, this should probably be converted to telescope time needed 
to cover a certain area to a certain sensitivty or something along those 
lines.

I don't know of a standard way of bringing other factors like data storage 
and computation requirements into a single metric.  Here are a couple SKA 
memos that may or may not be useful:

http://www.skatelescope.org/PDF/memos/105_Memo_Smits.pdf
http://www.skatelescope.org/PDF/memos/97_Memo_Cordes_REVISED.pdf

-Paul

On Mon, 1 Mar 2010, Walter Brisken wrote:

>
> http://xxx.lanl.gov/abs/astro-ph/0304364
>
> This paper discusses searches for "fast transients", i.e., single pulses.
> Possibly not exactly what you want, but I believe it could be generalized
> easily for the case of periodic sources.
>
> On Mon, 1 Mar 2010, Rick Fisher wrote:
>
>> I've been tinkering with metrics for assessing PAF perfomance for pulsar
>> searches.  Are there any published papers or internal reports on the
>> subject?
>>
>> Rick