[Pafgbt] pulsar search metric

[Rick Fisher]

Hi Paul,

Thanks for the run down on sensitivity.  Right now I'm thinking very 
primitively about things like how far apart to form the beams and what the 
effects of lower sensitivity of outer beams might be.  My intuition is 
that a 1 dB or even 0.5 dB degradation in outer beam aperture efficiency 
hurts pretty significantly in terms of new pulsar count, but I'd like to 
quantify this.  Scattering, duty cycle, etc. are backend design issues 
that we'll need to deal with separately.  I have the ATNF pulsar catalog 
from which I can generate a log(N) - log(S) relationship, and I'll see how 
far I can go with that.

Rick

On Tue, 2 Mar 2010, Paul Demorest wrote:

>
> 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
>
>