[mmaimcal] stretched E and D arrays

[Mark Holdaway]

Dear All,

I am changing my comments made at yesterday's Img/Cal meeting.
After reviewing Old MMA Memo 155, I see that the E configuration
(and pretty much the D as well) have little sensitivity loss
due to shadowing between dec +20 and -70, which is very similar
to Memo 155's D1 array, which went from +24 to -72.

So, I take back what I said about this configuration's shadowing
performance.

This points to another problem, though: both the E and the D
configurations (D array shadowing is very similar for both the
Donut and the Spiral arrays) will need to have at least one
more hybrid configuration to permit far Dec observing, unless
we decide we can tolerate the shadowing and the highly elongated
beams.

Quantitatively:

E array transit observing:
(Note: the situation degrades rather smoothly as we go off transit)

dec	%baselines	% sensitivity
	remaining	remaining

+50	.04		.2
+40	.28		.53
+30	.61		.78

-70	.77		.88
-80	.45		.67


D (spiral) array transit observing
(D donit is a bit worse)

dec	%baselines	% sensitivity
	remaining	remaining

+50	.56		.75
+40	.69		.83
+30	.80		.89

-70	.88		0.94
-80	.71		0.84


-------------------------------------------------------------

For the loss in sensitivity, we can do a simple cost-benefit analysis,
trading the capital investment for more antenna stations and time lost in
moving antennas against the cost of the sensitivity lost (considering the
fraction of time ALMA would observe in each DEC range in the two compact
arrays). To come up with a cost of the sensitivity that is lost due to
shadowing, we could take the capital cost of the ALMA, add to it its
lifetime of operating costs, and divide by its lifetime to get a cost per
unit time.

This cost-benefit analysis would not address any losses to the scientist
for not having a circular beam, which is more difficult to assess
(unless we were take a brute force solution such as to taper the (u,v)
coverage to have the same maximum extent in all directions).

For the compact spiral configurations, there are antenna pads everywhere,
so the only costs in going to stretched configurations will be logistical
(ie, paying for the antenna moves) and lost observing time.  To some
extent, we will need to move those antennas out ANYWAY (though the order
may be different, and we may endup moving some back in, too).  It seems
pretty clear to me, without doing the math, that making stretched
E and even D configurations is a big win for the Spiral array case.
For the donut array case, there would be more cost in stations, so I won't
make such a confident guess for it.

Just taking observational density as proportional to sky area,

D array loses 4% of its integrated sensitivity to shadowing (assuming
here that all is transit observations; it will be higher for more
realistic cases),

and E array loses 11% of its integrated sensitivity.

Lets say we are in E array 17% of the time, in D array 17%.
Also, lets say ALMA is $600M + $20M * 20 yrs = $1 Billion.

So, the lower limit to the cost of the shadowed sensitivity, over the
lifetime of the ALMA, is

E:   .17 * .11  * $1 Billion   =    $18.7 Million

D:   .17 * .04  * $1 Billion   =    $ 6.8   Million

Which I think is well worth saving by dealing with the
logistical issues of the hybrid arrays.
Again, this doesn't consider the additional benefit of having more
circular beams, or the cost of any addition infrastructure,
lost observing time due to the moves, etc.


On the other hand, the loss is only $1.3  Million per year, small
compared to the operating budget.




	-Mark