This is the combined text of two messages from Chris Fassnacht.
Gentlemen,
Here are some thoughts I've had about lens studies with the EVLA.
The focus is on the possibility of conducting a large survey
for lenses with the goal of substantially increasing the number of
known lenses. If you believe all the extrapolations, then the time
required for the survey is extreme. I have added some caveats and
further thoughts about such a survey at the end. All calculations
should be taken with a grain of salt; please let me know if you find
any mistakes. Also, please feel free to forward this to any other
interested parties. Comments and corrections are appreciated.
Ciao,
Chris
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First of all, why do we want to search for more lenses?
1. To improve the lensing statistics for use in constraining
Lambda. The statistical errors associated
with the relatively small number of lenses found in various
surveys are large enough to make distinguishing between
different cosmologies difficult, although the situation
is improving.
2. To find more lenses that can be used for H_0 determinations.
3. To study galaxy evolution. Lensing provides a nearly
model independent method of measuring galaxy masses and
may be the best way to determine masses accurately for
galaxies at moderate redshifts. With a large number of lens
systems spread over a decent range in redshift, the evolution
of, say, mass-to-light ratios can be studied.
4. To study the mass function of lensing galaxies.
5. And so on...
How does the upgrade help?
1. Increased sensitivity allows many more sources to be examined
for signs of lensing. Radio surveys for lenses tend to be much
better than optical surveys because lenses are not lost due to
extinction or bad seeing.
2. Better angular resolution allows us to search for systems with
lower-mass lensing galaxies.
Assumption -- Survey conducted with A+ configuration
I have assumed that the search for lenses will be conducted with the
A+ array at a relatively high frequency. My bias, coming from the
CLASS survey, is that the most effective method for finding lenses is to
search among flat-spectrum objects for which lensing geometries are easy
to recognize. Observing at high frequency (say 5 GHz) means that
emission from the compact core is starting to dominate; observing
at the high angular resolution provided by A+ additionally resolves
out a lot of the extended emission that might confuse the issue.
Thus, a 5 GHz A+ survey should have VERY clean statistics in terms
of lensing rates.
Sensitivity and survey limits
From Rick's sensitivity charts for the A+ array, I calculate that
rms noise levels in a 20 sec integration (the choice of integration
time will be discussed below) in the 4-8 GHz band are
~50 microJy.
Our experience with the CLASS survey was that the typical snapshot
image, for 30 sec integrations, had an rms noise level of about
twice the expected thermal noise. So, assuming that the same holds
and assuming a 5-"sigma" detection threshold, we should be able to
credibly detect point sources down to ~0.5 mJy in the 20 sec snapshots.
Surface number density of flat-spectrum sources
To estimate the number density of sources, I have used the
relation from Langston et al. (1990, ApJ, 353, 34). For sources
with a 5 GHz flux density < 15 mJy, their relation is:
n (>S) = 0.019 +/- 0.004 (S (mJy))^{-0.93} sources/sq. arcmin
For S=0.5 mJy this gives n (>S) = 0.036 sources/sq. arcmin.
We want flat-spectrum sources. Assume that ~10% of sources
at this flux density are core-dominated (e.g. Wall & Jackson, 1997,
MNRAS, 290, L17), giving a flat-spectrum number density of
3.6x10^{-3} sources/sq. arcmin.
Survey area
Assuming a lensing rate similar to that observed in CLASS,
~100,000 sources would have to be surveyed in order to increase the
number of radio lens systems by an order of magnitude,
I assume that this lens search would have to be conducted as a
blind survey, due to a lack of catalogs of sources at these
flux densities. Given the above number density of flat-spectrum
sources, ~8000 sq. degrees would have to be surveyed in order
to observe ~100,000 sources.
Depth vs. area
As pointed out in the NVSS paper (Condon et al. 1998), if the
cumulative density of sources is n (>S) proportional to S^{-beta}
then the rate of source detection is approximately
t^{(beta - 2)/2} where t is the integration time. This allows
you to weigh the trade offs between going deeper and covering
more area. For beta = 0.93 you lose by going deeper. It is
better to spend the observing time making shallow observations and
to cover a greater area.
Estimated time
In order to save time, a lens survey could be conducted using offset
cards rather than source cards, in a manner similar to the NVSS.
Integration times would have to be an integral multiple of 10 sec,
and slewing times would be ~8 sec. I have assumed 20 sec integrations,
giving 30 sec total per field, including slewing. I have also
assumed that uniform sensitivity is important, and thus an observing
pattern similar to that used in the NVSS would be used (a hexagonal
pattern with grid size of Delta = ~theta_P / sqrt(2), where theta_P
is the primary beam size). The problem here is the decrease of the primary
beam size with increasing frequency. The NVSS achieved uniform coverage
with ~7 pointings per square degree. At 5 GHz, you need ~100 pointings
per square degree. For an 8000 sq. degree survey with 30 sec integration
per pointing, this would require ~7000 - 8000 hr (~300 - 350 d).
Caveats
1. You would do much better (time-wise) if you could do pointed
observations rather than a survey. This requires deep enough surveys
at other frequencies or with other telescopes to generate the
appropriate catalogs.
2. The lensing rate may be lower than that in CLASS due to the change
in slope of the luminosity function at S_5 ~ 30 mJy.
3. On the other hand, the lensing rate may be higher than that in CLASS if
there are a lot of small-separation lenses that the CLASS observations
did not resolve.
4. The estimated time above is for a factor of 10 increase in the
number of lenses. Going for a factor of 5 increase would still
substantially improve the lensing statistics, and the time
requirement would be reduced. If the survey was split over several
seasons of observing, the time required might not seem so
unreasonable.
5. The high angular resolution of the A+ array might make observing
at frequencies lower than 5 GHz reasonable because much of the
extended emission from the survey sources would be resolved out.
At a lower observing frequency, the increase in the primary beam
size would help to substantially reduce the observing time.
6. The time needed for calibration observations have not been factored
into the time estimate.
Chris
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