MMA Memo. No. 243
Report of the Antenna Size Committee Meeting
Bryan Butler, Bob Brown - NRAO
Leo Blitz, Jack Welch - UCBerkeley
John Carlstrom - UChicago
Dave Woody - OVRO
Ed Churchwell - UWMadison
May 4, 1999
Homogeneous array designs (antennas of common size) are currently
preferred over heterogeneous designs (antennas of different sizes,
e.g., 8 and 15 meters) for the combination MMA/LSA (hereafter referred
to as the ALMA - Atacama Large Millimeter Array). Given that
preference, it remains to be decided exactly which antenna diameter
will yield the ``best'' ALMA. In an attempt to address this problem,
a committee met in Berkeley on November 4, 1998. This report is a
description of discussions which took place during that meeting and
some subsequent analysis by the members of the committee.
It is not the intent of this memo to provide the answer to the
question of which antenna diameter to use, but merely to point out
and describe the arguments which should provide a framework within
which a decision on antenna diameter can be made in an informed manner.
These arguments include scientific, technical, and cost drivers for the
ALMA.
The ALMA will be the principal instrument for astronomy at millimeter
and submillimeter wavelengths in the first part of the next century.
As such, it must be useful for much, if not all, of the future science
that is planned for these wavelengths. These programs will impact all
of astronomy. They include characterizing our solar system and the
sun, understanding the birth of stars and planets, the late evolution
of stars and their envelopes, the physical and chemical evolution of
the ISM and stellar content of our galaxy and those nearby, and the
evolution of the universe from the earliest times. For many of these
programs, observations will need to be made, not only with high
resolution, but also over very large fields (minutes of arc or more).
It is clear that there is a class of objects which will be observed by
the ALMA with single pointings. Such objects include some solar system
bodies (NEA's and KBO's, e.g.), O stars and their associated winds, the
photospheres of giant stars, observations of the very inner portions
(including protostellar and protoplanetary disks) of star formation
regions, and observations of the high z universe. For the high z
observations, one is likely to mosaic first to form a finder map in
the continuum, where the sensitivity of the array is already extremely
high and one can detect L* galaxies at any z. One would then image
each galaxy in line emission with one pointing each (with a field of
several 10's of kpc at z>1, one pointing per galaxy will be
sufficient).
Two areas which are of particular current interest are star formation
and the study of high red shift galaxies. Sites of star formation are
the Myers and Benson cores many of which contain IRAS sources,
evidently Young Stellar Objects. Recent interferometer surveys of a
number of such cores by Looney and colleagues (ApJ, in press) have
found that these typically contain multiple YSO's. Indeed, out of
nine objects studied, all show multiple YSO's. Although there is a
bias in the survey toward brighter sources, nine out of nine is a good
statistic, and it is clear that star formation in small clusters must
be an important way in which it happens. The clumps are isolated, and
the processes appear approximately coeval in each clump. The YSO's
have disks, adjacent envelopes, and overall envelopes. Understanding
the formation process requires mapping the entire clump with its
contents at the highest resolution. Clump sizes are typically .05 to
.2 pc, which correspond to fields of one to several arcminutes. A
recent image of HL Tau in 
CO(1-0) made with the BIMA array plus
single antenna data for the short spacings from the NRAO 12-m shows
that there is much to learn from the study of large fields with high
resolution. In this 200
diameter field, there is a
clearly expanding bubble approximately centered on XZ Tau which
dominates the kinematics of the region. Even larger fields are being
mosaiced with interferometer resolutions. A recent map in the NGC 1333
cloud covers a region which is 6
by 8 in size,
showing the structure of many bipolar flows with resolutions of a few
arcseconds.
Observation of galaxies in the early universe is also an important
area. Much of the exciting recent work has been focused on infrared
galaxies at moderate red shift and lensed galaxies at z up to nearly
5. These have small angular extents and can be observed in a single
pointing. On the other hand, the future may well be in the study of
such regions as the Hubble Deep Field. In this field, approximately
2.5 in diameter, there are 3000 galaxies with a large range of
red shifts. The mean separation is about 2.4. The
spacing for 10% of the galaxies is about 8, and for
1% it is 25. One could imagine making a mosaic of
the region at modest resolution (a few arcseconds) and then returning
to image a number of interesting targets with single pointings.
Although a long integration of the HST was required to obtain this
striking image, the NGST with excellent detectors operating in the
near-IR with a larger mirror is expected to be at least 100 times
faster than the HST. Thus, deep fields of many objects in many
directions will be available in a few hours observation with the NGST,
and the expected field size is 4 arcminutes. We should anticipate that
this instrument may drive much of the science that will be interesting
with the millimeter wave array. Another example of this point is the
Eagle Nebula, imaged with the HST, which has been recently mapped at a
few seconds resolution in both CO(1-0) and CO(2-1) by
Mark Pound. The combination of the excellent optical image and the
kinematic and density data that can be obtained with the interferometer
array shows the importance of the combined study.
In the nearer neighborhood of our galaxy, interferometer images of the
interacting galaxies NGC 6670 and Arp 293 cover fields of 1-2
arcminutes. Grand design spirals, such as M51 and NGC 5194 are
extended over regions of several arcminutes.
Even closer to home, images of the envelopes of carbon stars, very old
stars destined soon to transform into planetary nebulae, reveal large
structures. An example is the star CIT6 which, at a distance of about
200 pc, shows an outer envelope that is at least 100
in diameter. It has a core-halo structure. Studies of the whole
envelope are important in the understanding of the overall lifetimes of
such objects. Measurements of isotopic ratios as a function of radius
may reveal the history of the rapid nuclear chemistry that is expected
to be in progress in these old stars.
Very large structures also include comets, the sun and moon, and whole
molecular clouds. The planets, though not quite so large, will
nevertheless have to be mosaiced at all but the longest wavelengths of
the ALMA.
Larger antennas will force interferometric observations of the CMB to
higher angular scales, i.e., higher 
. It is unlikely that ALMA
total power observing (single dish mode) will be stable enough to
recover the low data from mosaicing techniques with sufficient
sensitivity, at least not without a considerable investment, and so
ALMA CMB observations will focus on higher angular scale CMB
observations (higher ). Current CMB studies, however, are
focused on much larger angular scales, and it is expected that most of
this work will be done by the time ALMA is comissioned. ALMA operating
at 1 cm will be most sensitive to 
5000 to 10,000 for 8 to 15 m
antennas where most of the CMB anisotropy is caused by secondary
effects such as patchy reionization or the Sunyaev Zel'dovich effect
from galaxy clusters and filamentary structures. For these
observations the smaller telescopes are strongly preferred, although
the larger diameter will still provide useful data.
Since it is clear that both single pointing observations (which want
optimized) and mosaiced observations (which want ND
optimized) will be undertaken with the ALMA, and we might envision
that the division between the two may be roughly equal, we would like
to be able to do both types of observations as well as possible. It
therefore seems reasonable to investigate what the minimum desired
values are for the quantities ND and .
Present spectroscopic observations of high redshift objects are
limited to those extremely bright (ultraluminous) galaxies, even such
galaxies where the observed line flux density is boosted through
gravitational lensing. The ALMA goal for spectroscopic studies of the
early universe is to be able to image normal galaxies, L* galaxies or
galaxies such as the Milky Way. Let us use the goal to be able to
detect the Milky Way spectroscopically at redshifts greater than one as
a means to set a requirement on for the array. At cosmological
redshifts the 10 kpc disk of the Milky Way is much smaller than the
primary beam so is the parameter we need to optimize.
The following sensitivity discussion is derived from the 1998 SPIE
paper ``Technical Specification of the Millimeter Array'' by R.L.
Brown; it is available via the MMA www library.
The flux density sensitivity, or rms noise in flux density units, is
where 
is the aperture efficiency, 
is the
correlator quantization efficiency, 
is the number of
simultaneously sampled polarizations, and 
is a gridding
parameter that we shall set equal to unity. Now simplify this by
setting 
, and 
. For
spectroscopic observations of extragalactic observations we'll use a
velocity channel width 
and write 
. We can then simplify the above expression for 
to
The aperture efficiency is:
which for the goals of the ALMA (
m, 
)
takes the values shown in table 1 over the range of
frequencies planned for the initial ALMA.
We refer 
to a point outside the terrestial atmosphere and
compute it as:
where 
is the fraction of the antenna power that is
received in the forward direction (i.e., the fraction that is on the
sky in the main lobe and all the forward sidelobes), 
is the
effective atmospheric temperature and 
is the temperature onto
which the spillover falls. The terms of represent the
contributions from the receiver, the sky, the ``antenna'', and the CMB.
We assume that 
where 
is the ambient
surface temperature. We assume that 
(Bevis et al. 1992), which has been verified to be a fairly accurate
representation of the effective atmospheric temperature by comparison
to detailed atmospheric emission models. We assume = 269 K,
the average surface temperature at the Chajnantor site. For simplicity
we will not correct temperatures to radiation temperature by the Planck
function.
The goal for the MMA SIS receivers is that they be image separating
receivers with a receiver temperature in the chosen sideband (i.e., the
SSB noise temperature) of 6 times the photon limit. The unwanted
sideband is terminated at 4K. This gives:
For the second two terms we adopt the MMA antenna goal of
, i.e., 95% of the received power comes from the
forward direction. We will compute at an airmass of 1.3
(50
elevation) and use for the frequency dependent optical
depths on the Chajnantor site the opacities produced by a model
atmosphere for the site which has 1.5 mm of precipitable water. Note
that the opacities produced by this model agree very well with those
measured by Matsuo et al. (1998).
The terms in the equation above, along with the resultant
are shown in table 2. Note that these numbers
agree very well with those of Jewell and Mangum (1997) when a common
set of assumptions is used.
We can now combine the results for together with the
equation for above to compute the spectral sensitivity of
the ALMA:
where the second line follows from the first by using a spectral
bandwidth of 75 km/s and an integration time of 6 hours. Note that
and (75km/s; 6h) both include the aperture
efficiency. We tabulate these quantities as a function of frequency in
Table 3.
If we wish to detect spectral line emission in a galaxy that is
similar to the Milky Way but at redshifts of one or greater then the
most obvious candidate to observe is CO. The total CO luminosity of
the Milky Way in the 1-0 transition has been estimated by Solomon and
Rivolo (1989). This luminosity agrees roughly with the CO luminosities
seen in the higher transitions by COBE (Bennett et al. 1994; Wright
et al. 1991). Note that COBE also measured emission from neutral and
ionized carbon (CI and CII) and ionized nitrogen (NII). We presume
here that the desire is to measure the neutral species, so concentrate
on CO. Given the luminosity of the CO 1-0 transition, we can
calculate the expected received flux density in any transition as (see
e.g. Solomon et al. 1992):
is the flux density in Jy, 
is the CO luminosity in
K km/s pc
, 
is the rest frequency of the transition in
GHz, 
is the ``luminosity distance'' in Mpc, and 
is the rest line width in km/s. The luminosity distance can be written
(Weinberg 1972):
We use 
K km/s pc for the 1-0 transition,
which is slightly larger than that in Solomon and Rivolo (they give
), but is consistent with the COBE results. We then
modify the luminosity as a function of transition and redshift according
to a model which accounts for the proper radiative transfer given the
higher background temperature at higher z, and assuming that 90% of
the CO is in clouds similar to our galactic dark clouds and 10% is in
regions similar to strong PDR's (H. Liszt provided this calculation).
We assume 
, 
, and the intrinsic
width of the lines is 
km/s (Solomon et al. 1997).
We can then calculate, given any array collecting area, the maximum
z to which any of the transitions of CO (we calculate up to 8-7) can
be detected by that array. We demand a 4-sigma detection in a 75 km/s
channel in 6 hours of integration. With these requirements, and the
additional requirement that at least 3 transitions must be observable,
the following relationship between collecting area and maximum
detectable z is derived:
Thus, to reach z=2, an of 6800 m is required. This is
satisfied with an array of 68 10-m antennas or 47 12-m antennas.
We point out, however, that reducing to 6400 (64 10-m or
45 12-m antennas) allows for a 
of 1.9, essentially the same
as z=2. Of course, larger values of are always desirable, as
they would allow us to resolve the line flux density into more pixels
(higher angular or spectral resolution) or image to higher S/N more
quickly.
We note finally that lines of CI, and redshifted lines of NII and CII
will also be observable and will provide important probes of the IMF
and the Lyman continuum luminosity from the most luminous stars in
early galaxies. However, because so little is know about the
luminosity of these lines as a function of redshift in galaxies of
differing Hubble type we have not used them here to help us place
limits on the needed of the array.
Guilloteau (1996) presents an argument on the minimum desirable value
of . We duplicate that argument here, with updated numbers,
and a slightly different formulation for the noise flux density.
The noise flux density of an interferometric array is given by:
where is the system temperature, 
is the
total system efficiency (including aperture efficiency, correlator
(quantization) efficiency, and any other efficiency factors),
A is the physical antenna area, 
is the number of baselines
(
for large N), 
is the
total bandwidth over all polarizations observed simultaneously, and
is the total on-source time.
If we assume that the fluctuations that we are to observe are
imposed on a background brightness temperature for which the
Rayleigh-Jeans approximation is appropriate, then the noise flux
density is related to the brightness temperature fluctuations
(
) via:
where 
is the solid angle of the synthesized beam. For
an image which is restored with a circular gaussian of width 
(e.g., the result of CLEAN or relatives), this solid angle is given by:
for maximum baseline 
at wavelength 
.
Making all of the appropriate substitutions, and assuming that
the total system efficiency is about 0.7, we end up with:
Note that this is nearly identical to equation 2 of Guilloteau
(1996) (substitute 
, and 
).
Now, consider an observation of the gas distribution and kinematics in
a protoplanetary disk. A velocity resolution of 0.3 km/s might be
desired, implying 
kHz per polarization at a center
frequency of 110 GHz. Assume 2 polarizations, and assume that we have
24 hours of on-source time, implying 
s. Assume also
a maximum baseline of 3 km. This leaves us:
For an observation near 110 GHz, the system temperature during
median conditions is 
K (see Table 2),
leaving:
Given a desired of 1 K, which should be sufficient to
image marginally optically thick lines, we then have the criterion:
For an observation near 230 GHz, we have for median conditions
K, leaving (remembering that the bandwidth is
now a factor of 2 larger for the same velocity resolution):
For 
, this gives a brightness temperature sensitivity
of 
1.2 K. Thus, it seems that 
is a good goal
to attempt to reach, from both the high z and the protoplanetary
disk observation arguments. This is satisfied with an array of 64 10-m
antennas, or 45 12-m antennas.
Holdaway (1998) assesses the ability of the MMA to provide precision
imaging in all the array configurations and at all the frequency bands
planned for the MMA. Here the consideration for imaging is the ability
of the instrument to achieve good coverage of the (u,v)-plane. Morita
and others have emphasized that excellent imaging, imaging limited by
dynamic range, can be achieved when 50% of the (u,v)-cells are filled.
Morita calls this quantity FOCC, the ``fraction of occupied cells.''
It is calculated by simulating (u,v)-points taken in short integrations
by the array in a particular configuration and gridding them onto the
Fourier plane with a cellsize equal to the antenna diameter. The
fractional area of the gridded (u,v)-plane out to the diameter of the
longest array baselines that is filled by observations is the quantity
FOCC. Clearly, FOCC is a function of hour angle that asympotically
approaches a value of one.
For the three shorter MMA configurations-the compact array(s), the
240-m and 860-m arrays, the MMA achieves FOCC=0.5 in less than two
hours of observations. But for the longest array, the 3000-m diameter
A-array, FOCC=0.5 can be realized only with 8 hours of hour-angle
tracking. Such long tracks can only be obtained at the expense of
observations being made well off the meridian at increasingly low
elevation angles. At low elevation the sensitivity is compromised by
the increasing atmospheric contribution to the system temperature
making the weights of the (u,v)-points so obtained very low. This
compromises the fidelity of the image and reduces its signal-to-noise.
The situation worsens at higher frequencies where the atmospheric
contribution to is larger. The ALMA, however, should have
a sufficiently large number of antennas such that FOCC=0.5 can be
achieved even in the highest resolution 3000-m array with suitably
short hour-angle tracks taken near the meridian where the sensitivity
always remains high.
In Figure 2 of Holdaway (1998), the FOCC as a function of hour angle
for the 3 longer MMA configurations is shown. As hour angle
increases all these curves asympotically approach one as an increasing
number of the gridded (u,v)-cells are sampled redundantly. However, as
Holdaway notes, the non-redundant FOCC (i.e., the FOCC for
``snapshots'') for each of the arrays is approximately proportional to
where is the maximum baseline length in the array. ``Hence,
to achieve optimal Fourier plane coverage, one wants to optimize the
so-called 'collecting length' ND'' (Holdaway 1998).
The function that is plotted in Figure 2 of Holdwaway (1998) for FOCC
as a function of hour angle for the 3000-m array has the form
where h is the hour angle and we've explicitly used = 3000.
To achieve the precision imaging for which FOCC
0.5 is the figure
of merit using an array of given collecting length (ND) will require
observations made out to the hour angle limits shown in
Table 4.
As noted above, observations taken at large hour angles will be given
low weight in the imaging owing to the increase in system temperature
at low elevation. To avoid corrupting the image with such low weight
points, let us restrict our observations to hour angles such that the
lowest weight points are reduced from those on the meridian by no more
than 
. Let us also retain the opportunity to do such imaging
in the submm. Then in median meteorological conditions on the
Chajnantor site (Figure 4b of Holdaway [1998]) we conclude that we
need to observe out to a limiting hour angle range of no more than
approximately h=2.0.
With the restriction that h<2 hours, we can return to
Table 4 above and conclude that the specification for the
``collecting length'' ND for the ALMA needs to be approximately
560. A joint array of 56 10-m antennas or 47 12-m antennas
will satisfy this specification.
- 1.
-
It is clear that there will be single pointed observations done
with the ALMA. These observations want optimized.
- 2.
-
It is also clear that a significant fraction of observations with
the ALMA will involve mosaicing. In particular, some fields which
have traditionally been considered single pointing fields will
require mosaicing for correct interpretation (e.g., star formation
regions). These observations want ND optimized.
- 3.
-
A vast majority of the science considered so far could be done with
any size antenna from 8-m to 15-m, given that it meets
specifications (including surface, pointing, and total power
capability).
- 4.
-
ND should be
560 m if possible.
- 5.
-
should be 6400 m if possible.
In this section, we consider technical considerations influencing the
decision on antenna diameter. These include antenna design and
construction issues, antenna performance issues (e.g. calibration of
several flavors), and other related issues (e.g., number of receivers).
It appears clear that meeting the required telescope specifications
(including pointing, surface rms, and slew rate) could be done
relatively easily for an 8-m antenna. With a traditionally designed
10-m telescope, meeting these specifications will be difficult. A
traditionally designed 12-m telescope will probably not meet the design
specifications. Because of this, it seems counterproductive to keep
modifying a traditional design to meet the specifications. Rather, it
seems better to start from the ground up with designs that avoid the
difficulties encountered by the more traditional designs. When
starting from the ground up with well understood, but admittedly
untested, designs, it seems that the specifiations could be easily met
at 10-m and likely met at 12-m. At 12-m, however, there would be very
little margin for error or manufacturability, i.e., no design
contingency. It seems unlikely that a 15-m design of any type will
meet the design specifications. Discussions of various designs and
attempts to meet the specifications exist in the MMA memo series
(Plathner 1999; Plathner et al. 1999; Anderson 1999; Woody and Lamb
1999; Lugten et al. 1999).
As the antenna diameter decreases, the number of antennas will
increase, thereby increasing the total number of all related items:
receivers, amplifiers, LO's, etc... It has been perceived by some that
the maintenance of large numbers of such systems will be impractical at
best, and fail at worst. It seems, given the large number of systems
now being considered for any of the reasonable antenna diameters, that
this is less of an issue. There will be large numbers of systems in
any case, and we must figure out how to deal with that.
With smaller diameters, and more antennas, the size of the correlator
also increases (quite rapidly). The size of the correlator should
certainly be of concern, but it seems that it will not limit in any
fundamental way the number of antennas up to some reasonable limit
(which NRAO engineers estimate to be of order 100 or more).
While the larger antennas may have slightly more room in the receiver
cabin, the difference does not favor any antenna size strongly.
It is important to realize that blind pointing at 1/30 of a beam is not
necessary. Only offset pointing with that accuracy is needed. While
it is true that large submm telescopes such as the CSO and JCMT have
not achieved this dead recogning specification, they do, in fact, meet
the offset pointing specification. The argument has been made in the
past that larger dishes imply that a weaker pointing calibrator can be
used, implying that the pointing calibrator will be closer for larger
antennas. This is in fact true, but makes little difference. The
difference in distance to a pointing calibrator for 10-m or 12-m
antennas is much less than a degree. Therefore, the difference in the
quality of the derived pointing solution should be very small.
Also, since offset pointing is envisioned to occur only every 15
minutes or so, the small difference in time to go an extra 0.1 degree
or so on the sky is negligible.
The argument has been made that larger antenna diameter means that
a calibrator of smaller flux density can be used for secondary
calibration. Again, this is true, but makes little practical
difference, since it just means that the angular distance to a usable
calibrator increases by some very small value (M. Holdaway estimates
that this difference is 0.15 deg for 10-m vs. 12-m antennas).
While anomalous refraction will be a nuisance (and perhaps worse)
to deal with, it seems that this effect has no particularly strong
bearing on the antenna size discussion. This is because the errors
caused by this atmospheric phenomena are essentially random, and
thus are less important than constant pointing offsets (see e.g.,
Holdaway and Woody 1999; Holdaway 1997).
It has been suggested that larger dishes could simply be
under-illuminated at the higher frequencies, in order to essentially
relax some of the antenna specifications. This does not seem to be
a good alternative, and should be discouraged.
Measurement of short spacings (all the way to the zero spacing) is
absolutely critical for the success of the science to be done with
the ALMA. Cornwell et al. (1993) have argued that it is more desirable
to have these short spacings measured by the antennas of the array
themselves, rather than a larger central element. The specification
that the antennas of the ALMA have very sensitive total power
capability is perceived to be possibly hard to achieve, and of great
import.
In order to be able to satisfy the fast switching requirement for the
ALMA antennas, the antennas will be driven with large accelerations.
In order for these accelerations to not excite resonant modes in the
antennas, we would like the lowest resonant frequency to be as high
as possible. It becomes increasingly difficult to avoid this problem
as the diameter of the antenna increases. This does not seem to be
an overriding consideration in the decision on antenna diameter, but
must be considered nonetheless.
When driving the antennas for the fast switching, large amounts of
power will be necessary to drive the motors. Larger antennas require
more power, as the required torque scales roughly as 
. However,
this does not seem to be an overriding consideration, as large amounts
of power will be consumed in any case with the large numbers of
antennas now being considered for the ALMA.
Given the above points, it seems that the largest antenna which should
be considered is of order 12-m. It is not thought that larger antennas
can be constructed which will meet the demanding specifications. Of
the 8-m, 10-m, and 12-m diameter antennas, it is clear that the 8-m and
10-m can be designed, and most likely constructed, to meet the
specifications. The 12-m is somewhat riskier. The issue is then the
tradeoff between the risk of not meeting the specifications with the
12-m antenna vs. the problems associated with large numbers of
elements/receivers/etc...
In this section, we attempt to summarize the costing information that
we presently have available for the MMA and to extend that information
to assemble an estimate for the cost of the instrument as augmented by
the merger with the LSA project (to form the ALMA). The costing
estimates in all areas are incomplete and they are likely to remain
uncertain through the completion of the Design and Development phase of
the project. The uncertainties we've attempted to accommodate by use
of contingencies assigned, separately, to each major area of the
project. The contingencies will be a permanent part of the project
management, although not necessarily at the magnitudes used here.
Nevertheless it is important to emphasize at the outset that one should
not be tempted to 'spend' the contingency; the contingency is a real
cost item not to be regarded differently than the cost of antennas,
receivers or any hardware part of the array. Clearly as we make
progress in designing the instruments, and defining how all the various
pieces of the instrument will be built in production, the contingency
can be reduced and the money ``saved'' in this way can be reallocated
within the project. However at each step in the project we need to
acknowledge the uncertainty in our cost estimates, and associate a cost
with that uncertainty: this is the role of contingency. At the moment
the cost estimates in many areas are not reliable and we need to budget
contingency to cover that uncertainty.
The cost estimate will be greatly refined over the next few months, in
particular by means of a proper 'roll up' of the costs defined through
the work breakdown structure of the entire project. At the moment
that's not available. Hence the effort below is our own attempt at
costing-it is not an 'official' MMA project estimate, it is not the
NRAO estimate or the NSF estimate. Rather it is used to help us
understand the distribution of costs within a project like the MMA and
to guide the merger discussions in the near future.
We will divide the array tasks to be costed into the following eleven
categories:
- 1.
- Site
- 2.
- Antennas
- 3.
- Transporter
- 4.
- Electronics at the antennas
- 5.
- Central electronics
- 6.
- Correlator
- 7.
- Monitor and Control
- 8.
- Computing
- 9.
- System Engineering
- 10.
- Management
- 11.
- Long Baselines (the 10 km array)
A cost equation is parameterized in terms of the number of antennas in
the array, N, the diameter of each of those antennas, D, and the
number of frequency bands, 
.
We use the term ``site'' to refer to activities on the Chajnantor site
itself and for those functions to be located at the array Operations
Support Facility (OSF) near the village of San Pedro de Atacama. In
both these locations the costs come from a very large number of civil
works tasks - roads, power and power distribution, water, buildings and
so forth. This information and the associated costs are being compiled
now in collaboration with engineering and construction firms in Chile.
Refined numbers should be available very soon. Note that the
Chajnantor costs include the antenna foundations, and all the site
civil works. We use 15% contingency on all of these items. Our
current best estimate of these costs can be expressed as:
Chajnantor site: $[13.0 + 0.325 N]M
OSF: $5.3M
Contingency: $[0.15 (18.3 + 0.325 N)]M
Site Total: $[21.045 + 0.37375 N]M
The best costing information we have is for a 10-m antenna which we
believe in production will cost about $2.0M. We assume that the cost
of antennas of other diameters scales from the 10-m cost with the 2.5
power of the diameter. We include in the antenna cost the cost of
shipping and installation in Chile and for this purpose we adopt a
figure of $75k for each 10-m antenna. Larger antennas will be more
costly to ship and handle so we scale this latter cost by the square of
the diameter. Finally, the antenna cost is very uncertain and will
remain so until we have signed the contract for the production run of
antennas and verified that the manufacturer can indeed deliver
production antennas that meet the specifications. For this reason we
adopt 30% contingency for the 10-m antenna and scale that uncertainty
with antenna diameter (i.e., a larger contingency for larger antennas).
This gives the antenna cost equation and the equation for antenna
contingency as:
Antennas: $[0.0063 
]M
Contingency: $[0.0063 
]M
Antennas Total : $[
]M
We assume that one transporter will be needed for each 15 antennas and
each will cost $600k. We use 15% contingency, leaving:
Transporter: $[0.04 N]M
Contingency: $[0.04 N (0.15)]M
Transporter Total : $[0.046 N]M
We assume that each antenna has one 4K cryogenic dewar that costs
$100k. We use $75k for the cost of IF switching and monitor/control
circuitry. We use $20k for the LO required at the antenna for each
frequency band and use $75k for each (dual polarization) frequency
band including the cost of the control and IF instrumentation. Finally
we use 30% as the contingency for this item to reflect the unavoidable
uncertainty associated with instrumentation such as this which will be
built in-house. This gives:
Antenna Electronics: $[
]M
Contingency: $[
]M
Antenna Electronics Total:
$[
]M
For the MMA the parameter is 9. We will use this number below
but remember that it enters here explicitly and could be changed if
that is desired.
This includes the interface electronics to each antenna and the IF
processing of 16 Ghz of returned bandwidth from each antenna. We use
15% contingency, leaving:
Central Electronics: $[0.150 N]M
Contingency: $[0.0225 N]M
Central Electronics Total: $[0.1725 N]M
A conceptual design for the MMA correlator exists and has been costed.
This was done for the 40 element MMA. We adopt 20% contingency for
that correlator and scale the contingency with N for larger
correlators such that the contingency doubles with N=80. This gives:
Correlator: $[
]M
Contingency: $[
]M
Correlator Total: $[
]M
The costs for M/C are costs associated with the number of antenna
stations (foundations). We assume that the 5 MMA arrays out to 3000m
use a total of 4N stations assuming that many of the stations can be
used for more than one array. We associate $50k costs with each
station and use 15% contingency:
Monitor and Control: $[0.20 N]M
Contingency: $[0.03 N]M
Monitor and Control Total: $[0.23 N]M
This is a level of effort task with a large contingency. We assume it
requires 50 work-years at a cost of $100k for each work-year and add
to that $5M in array computing equipment to be purchased over the
construction phase of the project. We use 25% contingency on the lot.
None of this depends in any significant way on N or D. So, we
have:
Computing: $10M
Contingency: $2.5M
Computing Total: $12.5M
We use a total of 20 work-years for the system engineer and his or her
staff and cost that at $100k per person year. Contingency will be 15%.
None of this depends in any significant way on N or D. So, we have:
System Engineering: $2.0M
Contingency: $0.3M
System Engineering Total: $2.3M
We assume 50 work-years at $100k per year and add to that the project
travel and communications budget of $5M over the construction phase of
the project. The contingency will be 15%. None of this depends in
any significant way on N or D. So, we have:
Management $10M
Contingency: $0.15M
Management Total: $11.5M
The 30,000 m circumference of this array needs to be connected with
salt-stabilized roads (not asphalt), it needs power cable, IF and
communications cables, power transformers etc. This leaves:
Long Baselines: $[1.8 + 0.115 N]M
Contingency: $[(1.8 + 0.115 N)(0.15)]M
Long Baselines Total: $[2.07 + 0.13225 N]M
We cost spares at 5% of the cost of items 2-7 above, and 2.5% of item
8. Spares will not be provided in other areas.
The antenna diameter D appears only in the antenna cost term. We
will therefore compute below the ``base costs'', contingency for the
``base costs'' and spares also for the ``base costs'' of the array
as a function of N without the antenna term. After that we will cost
the antennas as a function of N and D and then finally combine all
the costs. Table 5 shows the base costs as a function of
N. We will separately account for the contingency in each of these
categories; the result is presented in Table 6.
Finally, to complete the base cost without antennas we present in
Table 7 the costs budgeted for spares.
Now we examine the antenna costs as a function of N and D. Here we
separate the cost of procuring and shipping/delivering the antennas
from the costs being carried as contingency and the costs allocated to
spares. All of this information is compiled in Table 8 for
antennas of diameter 8-m, 10-m, and 12-m.
In Table 9 we accumulate all the costs for arrays of 8-m,
10-m, 12-m and 15-m antennas.
To interpret all these tables we explore two cases: assume that we knew
today that we had available to us total funding for the project from
all sources of $350M or $400M and that we were to be held to that
funding amount (i.e., we will not allow cost overruns). In that case
we would feel reasonably confident signing up to build, with these
constraints, any of the arrays with the parameters listed below in
Tables 10 or 11.
We point out here that in an entirely independent assesment of cost vs
size and number of antennas, numbers were derived which are so close to
those shown in tables 10 and 11 as to be
indistinguishable (D. Woody, 1998). This adds confidence that we have
performed the costing estimate properly.
We point out finally that the total construction cost for an ALMA with
64 12-m antennas using the above costing numbers would be $520M.
Considering all of the issues outlined above, it seems apparent that
arrays of antennas with either 10-m or 12-m diameters should be
considered at this point. The 15-m designs (even assuming that they
could meet the specifications) do not meet the minimum desirable ND
requirement and the 8-m designs do not meet the minimum
requirement.
In order to make a decision between 10-m and 12-m antenna diameter at
this point in time, it seems that there are two classes of questions
that we need to resolve:
- 1.
- What do we hope to achieve with the array in the long term,
and how much risk are we willing to assume to achieve it?
- 2.
- What is the proper course for us to pursue jointly in the
near term?
The first question has to do with where we place our emphasis and how
we weigh the risk. What the tables above show us is that if we build
an array of 12-m antennas we maximize our collecting area at the
expense of a 10% reduction in our imaging sensitivity ND. On
the other hand, if we build an array of 10-m antennas we maximize our
imaging sensitivity at the expense of a 10% reduction in our
point source sensitivity. Where is the balance here? Is either
design acceptable in terms of the science we hope to achieve?
Now consider the risk: the risk that the as-delivered antenna will not
meet the specifications is greater for the larger antennas. If we miss
the specifications for pointing, surface accuracy, and slew rate, then
we are going to increasingly compromise our ability to image well in
the submillimeter (where the primary beam is smallest and the surface
errors - the sidelobes - are fractionally greater). How important is
good imaging in the submillimeter? How do we weigh the risk of
compromising submillimeter imaging against the gain of a 10% increase
in collecting area by going to 12-m antennas?
It seems extremely difficult to answer these questions because we don't
know how to assess the risk that a contractor can deliver the antennas
to specifications. This brings us to the second question we've listed
above, how to we proceed in the near term? Let us examine our
resources. From the MMA we have enough money to contract for a 10-m
prototype antenna but not enough to procure a 12-m prototype antenna.
In Europe we may have enough for a prototype antenna but only if that
becomes the overriding emphasis of the D&D work in Europe. However,
if we combine the MMA and European resources we have several options:
- We have enough money to procure a prototype of a single
12-m antenna
-
- We have enough money to commission complete design
work from two antenna manufacturers and enough to procure a
prototype antenna of 10-m diameter (and perhaps of 12-m
diameter)
The MMA NSF advisory committee has supported the concept of keeping
competition in the antenna procurement process as long as possible in
order for us to have the most leverage over the antenna manufacturers.
For this reason they like the idea of funding two designs. If we did
this, one option we would have would be to support design work from a
commercial manufacturer on development of the innovative antenna design
that David Woody and James Lamb have been working on that extends many
of Dietmar Plathner's ideas. Is this a reasonable way to proceed, fund
two designs, one of which we define, and then make a judgement as to
what we build as a prototype? In this scenario, we could also consider
funding one of the designs internally, leaving open the possibility
that NRAO may eventually become its own prime contractor on the antenna
construction.
If we agree that there is a real risk that an antenna manufacturer can
deliver (as opposed to design) an antenna that meets our
specifications, and if we agree that this risk is a concern, and hence
that a prototype antenna is absolutely necessary, does it follow that
the proper prototype to build is then 10-m thinking that if the
contractor can't meet those specifications he surely can't meet the
12-m specifications (and it's affordable in the D&D budget we have)?
Again, the point of this manuscript is not to provide one single answer
to the question of which antenna diameter to use, but merely to point
out and describe the arguments which should provide a framework within
which a decision on antenna diameter can be made in an informed manner.
T.Anderson, Feasibility Study for a 12 m Submillimeter Antenna,
MMA Memo 253, 1999
Bennett, C.L., and 11 others, Morphology of the Interstellar
Cooling Lines Detected by COBE, Ap. J., 434, 587-598, 1994
Bevis, M., S. Businger, T.A. Herring, C. Rocken, R.A. Anthes,
and R.H. Ware, GPS meteorology: Remote Sensing of Atmospheric
Water Vapor using the Global Positioning System, JGR, 97,
15787-15801, 1992
Guilloteau, S., Large Southern Array: Feasibility, in Science
With Large Millimetre Arrays, ed. P.A. Shaver, Springer, 1995
Holdaway, M.A., and D.P. Woody, Yet Another Look at Anomalous
Refraction, MMA Memo 223, 1998
Holdaway, M.A., Hour Angle Ranges for configuration Optimization,
MMA Memo 201, 1998
Holdaway, M.A., Effects of Pointing Errors on Mosaic Images with
8m, 12m, and 15m Dishes, MMA Memo 178, 1997
Jewell, P.R., and J.G. Mangum, System Temperatures, Single Versus
Double Sideband Operation, and Optimum Receiver Performance,
MMA Memo 170, 1997
Lugten, J., J. Kingsley, J. Cheng, V. Gasho, and M. Fleming,
A 10-m Antenna Design for the Millimeter Array, MMA Memo 240, 1999
Plathner, D., A 12m Telescope for the MMA-LSA Project, MMA Memo
259, 1999
Plathner, D., M. Bremer, and J. Delannoy, The 15m (12.8m)
Telescopes for the MMA/LSA Project, MMA Memo 254, 1999
Solomon, P.M., and A.R. Rivolo, A Face-On View of the First
Galactic Quadrant in Molecular Clouds, Ap. J., 339,
919-925, 1989
Solomon, P.M., D. Downes, and S.J.E. Radford, Warm Molecular
Gas in the Primeval Galaxy IRAS 10214+4724, Ap. J., 398,
L29-L32, 1992
Solomon, P.M., D. Downes, S.J.E. Radford, and J.W. Barrett, The
Molecular Interstellar Medium in Ultraluminous Infrared Galaxies,
Ap. J., 478, 144-161, 1997
Weinberg, S., Gravitation and Cosmology: Principles and
Applications of the General Theory of Relativity, Wiley, 1972
Woody, D.P., and J.W. Lamb, A Design for a Precision 10-m
Sub-Millimeter Antenna, MMA Memo 241, 1999
Wright, E.L., and 21 others, Preliminary Spectral Observations of
the Galaxy with a 7 Beam by the Cosmic Background
Explorer (COBE), Ap. J., 381, 200-209, 1991
Bryan Butler
Tue May 4 11:31:45 MDT 1999
m) 
