[Pafgbt] PAF beam spacing on the GBT for a pulsar survey

[Rick Fisher]

Hi Paul,

Do we want to maximize the integral of (G/T)^2, or should the pulsar 
population as a function of flux density be factored in?  If completeness 
is an issue, a steeper log(N)-log(S) curve would favor closer spacings 
since more pulsars would be discovered near the sensitivity limit.  This 
would be particularly true for new pulsars.

I realize that PALFA uses interlaced pointings to fill in closer spacings, 
but their "47 pointings to cover one square degree" still implies -3 dB 
crossings (assuming 3.3 arcmin HPBW).

Rick

On Tue, 13 Apr 2010, Paul Demorest wrote:

> Hi Rick,
>
> There is a nice picture of the ALFA beam shape at the top of this page:
>
> http://www2.naic.edu/alfa/gen_info/info_obs.shtml
>
> maybe you've seen this already, but the beams are widely spaced, crossing at 
> about -6dB.  They get -3dB spacing in the actual survey by filling in the 
> holes with multiple pointings.
>
> To determine an optimal beam spacing (for a given array+telescope) I think we 
> want to maximize the integral of (G/T)^2 over the field of view.  That should 
> result in the highest possible survey speed.  Then we should check the 
> figures we used for the comparison with PMB and Efflesburg surveys and see if 
> any claims need to be revised.
>
> I'd guess the survey speed goes down by a factor of ~2 vs ideal fully-spaced 
> beams, but maybe the optimization could make this only ~1.5 or so?
>
> -Paul
>
> On Tue, 13 Apr 2010, Rick Fisher wrote:
>
>>  In writing an MRI proposal for the construction of a PAF for the GBT we've
>>  run into a conundrum that we should have anticipated much earlier. Any
>>  thoughts on the following will be appreciated.
>>
>>  The problem is that the "plate scale" (linear feed offset distance per
>>  angular beam offset in HPBWs) is roughly twice as large on the GBT as it
>>  is on the 20-meter telescope where we have done our PAF tests.  Hence, our
>>  19-element array can accommodate only half as many HPBW offsets as the
>>  20-meter before the focal spot loses significant power off the edge of the
>>  array.  The attached plot calculated by Karl Warnick shows
>>  Tsys/aperture_efficiency as a function of beam offset for the GBT. Going
>>  to 37 elements (or even more) is something that we clearly want to do in
>>  the long run, but it's a big step up in all aspects of the array system
>>  (Dewar size, number of receiver channels, real-time beamformer size,
>>  etc.).
>>
>>  I am wondering if the best strategy for this proposal will be to stay with
>>  the 19-element array as the next logical step and to form 7 beams on the
>>  GBT with the 6 outer beams spaced about 0.6 HPBW from the center beam.
>>  This is essentially Nyquist spacing, but it is different from the strategy
>>  used in the Arecibo PALFA survey.
>>
>>  The PALFA web site says that they are using 47, 7-beam pointings to cover
>>  one square degree of sky.  This would imply that their beams cross at
>>  about the 3-dB level, which means that most of the sky is covered with
>>  sensitivity considerably below peak beam sensitivity.  If we use 0.5 or
>>  0.6 HPBW spacing we won't cover as much sky in beam areas, but the
>>  relative average sensitivity within this area will be considerably higher.
>>  Does this sound like a reasonable enough trade-off to justify putting a
>>  19-element array on the GBT as the first science instrument?
>>
>>  Rick
>
>