[Pafgbt] pulsar search metric

[Rick Fisher]

Hi Walter,

Maybe I'm splitting hairs, but I'm trying to determine the effects of loss 
of aperture efficiency in the outer beams formed with the array and the 
optimum beam spacing.  You gain in sky coverage, up to some asymptotic 
value, by spacing the beams farther apart, but you lose aperture 
efficiency as the beams get closer to the edge of the array.  For a given 
array size, what's the best beam spacing, and how many beams is it worth 
forming and processing?

Rick

On Tue, 2 Mar 2010, Walter Brisken wrote:

>
> 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
>> > 
>> > 
>> 
>