[Pafgbt] pulsar search metric

[Walter Brisken]

Hi Rick,

I don't understand how source count statistics enters at all -- that might 
help estimate the total number of pulsars to be detected for a given 
observation, but that shouldn't factor into hardware design.  It should 
factor into search strategy (e.g., depth vs. breadth) but hopefully the 
hardware is not being specifically designed for a single survey.  To me 
the right metric to design to is sky coverage per time to reach a target 
sensitivity.

There may be secondary criteria to consider though that are not described 
by the standard survey speed metrics.  One is the on source time to reach 
the target sensitivity.  Pulsar searching experts should correct me if I 
am wrong, but I believe there are significant gains to be had in reaching 
the target sensitivity as quickly as possible.  Things like computational 
costs grow quickly with longer observations, especially when acceleration 
searching is needed.  Detectability of single pulses improves with higher 
instantaneous sensitivity, and the ability to take advantage of 
scintillation maxima to get below the search threshhold increases (and I 
think this is a case where log(N) - log(S) does actually enter, but only 
the slope of the distribution).  Also there may be an advantage from 
the RFI avoidance perspective.  Are there any ways in which a longer time 
series has any advangate in searching (assuming same sensitivity)?

I think for all-sky seaching the beam spacing is not really a critical 
parameter, except perhaps in planning for tiling of patterns on the sky.

-Walter


On Tue, 2 Mar 2010, Rick Fisher wrote:

> 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
>> 
>> 
>