[mmaimcal] Bob Brown message re: science vs. cost

[Al Wootten]

Folks-
I forward this for you comments.  -Al (enjoying a nor'easter).

From: Robert Brown <rbrown at NRAO.EDU>
To: guillote <guillote at iram.fr>, awootten at NRAO.EDU
CC: rkurz at eso.org, mrafal at NRAO.EDU
Subject: ALMA Science vs Cost
Date: Tue, 18 Apr 2000 09:58:30 -0400

Stephane, Al:

As you know, one of the things the NSF management (Bob Eisenstein) has
been asking for is a simple display of ALMA Science as a function of
cost.  He says he needs this in order to make the case for NSF
committing to half the $552M cost.  The argument is to be made to the
NSF Director's office, and hence has to be simple enough that a
biologist, a business man and a lawyer can understand it.

As you also know, I've struggled with this request for the last few
months.  Two problems.  (1) "Science" isn't simply parameterized by
cost; and (2) if we try and illustrate specific science (e.g. detect
high-z galaxies) as a function of the capability of the array we run
into the "when is enough, enough questions"--that is, if a large array
will allow us to detect 100 galaxies in 100 hours, why can't we use a
small array and detect 100 galaxies in 100 days?  We can't win these
arguments, especially not when we are talking to bureaucrats not
scientists.

My approach has been to search for a characterization of the 'science
performance' of ALMA that, when plotted as a function of cost, tends to
an asymptote, it 'saturates'.  Then we can argue that if we spend enough
money to get close to that asymptote we've gotten all the science we can
get for the money spent.  But if we spend 75% (say) of the money
required to get close to that asymptote we get *much* less than 75% of
the science.  The function that I found that does this is the imaging
performance measured in terms of image dynamic range and image fidelity.

Here's the argument:  ALMA is an image maker, a camera.  All science
done with ALMA will be done with images.  The quality of the science is
directly related to the quality of the ALMA images, and the quality of
the images can be quantified by cost.

Here's the approach:  I'm using the same argument as in ALMA memo 243 to
justify the ND required for ALMA.  I start with ALMA memo 201 and note
that image quality as measured by 'dynamic range' and 'image fidelity
index' are related to the fraction of occupied uv-cells, Focc.  I got
from Morita his results quantitively relating Dynamic Range and Image
Fidelity to Focc--I used the curves for natural weights.  Then I used
Holdaway's results (Memo 201) to compute Focc as a function of the hour
angle range of the observaton.  All this was done for the array with
maximum baseline 4500 m, the array that gives 0."1 resolution at 1 mm.
So now I have Focc as a function of HA and I use Morita's curves to turn
this into relations between Dynamic Range and Image Fidelity as a
function of HA.  What I find is that we can get high DR and Image
Fidelity with an array of modest ND if we can observe over a large HA
range; or we can get that same DR and Image Fidelity with an array of
large ND observing over only a small HA range.  Next I note that the HA
available at Chajnantor for any particular source depends on source
declination.  Therefore, for sources of limited HA availability
(equatorial and northern sources) we need an array of large ND in order
to get good imaging.  I can then plot the imaging quality, the DR and
Image Fidelity, as a function of sky coverage and this plot has an
asymptotic shape:  For the 64 element ALMA (ND=768) we can make images
of high DR and high Image Fidelity over the entire sky accessible from
the site.  If we step down to arrays of lower ND the sky coverage over
which we can make good images decreases.  Finally I turned "ND" into
cost using our cost parameterization and I believe this plot is what Mr.
Eisenstein is looking for.

I put this argument into vu-graph form in a highly over-simplified way
for the NSF.  I would certainly welcome any comments you'd care to make
on it.  The vu-graphs are available at

http://www.cv.nrao.edu/~cwhite/almansf.html

There are 19 vu-graphs in this package, numbers 15 and 16 are the cost
plots I refer to above (the others are used to describe synthesis
astronomy and make the image-quality=science correspondence in, I know,
a simplified and imprecise way).

Finally, it occurred to me that there is one other way of making this
same science-vs-cost argument that sticks closer to the science.  That
is to plot the cumulative fraction of mass in the universe, that is in
galaxies, that can be studied with ALMA.  Here the idea would be to use
the mass function of galaxies, dN(M)/dM (or get this function from
dN(L)/dL with some M/L assumption), together with some assumption about
the mean dust-mass/total-mass in galaxies, compute the detectability of
the dust and infer the total mass being studied.  As a cumulative plot
this will asymptotically tend to 100% of the galaxy mass in the
universe, but it will rise quickly because most of the mass is in the
most-massive galaxies.  Perhaps someone in the science group would like
to have a run at producing such a plot; if so it would be helpful.

Regards,
    Bob



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