Astronomical Requirements for the Millimeter Array Correlator
Michael P. Rupen
National Radio Astronomy Observatory
Socorro, NM 87801
Debra S. Shepherd
California Institute of Technology
Department of Astronomy
Pasadena, CA 91125
&
M.C.H. Wright
Radio Astronomy Laboratory
University of California
Berkeley, CA 94720
February 1998
Abstract:
Taking full advantage of the sensitivity and flexibility of the Millimeter
Array (MMA) will require an impressive correlator. The signals from
40 telescopes (possibly as many as 128, if major foreign collaborations
materialize) must be correlated over bandwidths of at
least 2 GHz, and preferably 8 GHz, per polarization, producing 
of (bandwidth times polarizations). This should be split amongst at least 4,
and preferably 8, independently-tunable baseband pairs. There should
be 500-1000 channels (with two polarization products each) over the full
8 GHz, and one should be able to trade bandwidth for channels in a fairly
flexible way. Standard
sustainable integration times of 0.1 second are required, with sustainable
integration times of 
being highly
desirable. This gives a required sustainable data rate of at least
250 million visibilities per second. The spectral dynamic range,
measured either as the accuracy of continuum subtraction or the ratio of
the peak to the spectral sidelobes of a narrow signal,
must be 
.
The prospect of a collaborative
project with international partners leaves several of the most important
correlator requirements uncertain.
This memorandum aims to set forth the astronomical requirements for the
correlator of the proposed Millimeter Array (MMA). The current working
design for that correlator is described in MMA Memorandum 166
(Escoffier 1997) and MMA Memorandum 194 (Rupen & Escoffier 1998),
the latter of which also discusses the limits on the expansion of that
design. Here we step back to ask what astronomers would
like to be able to do with the instrument, and what requirements those
desires set for the correlator. The emphasis is naturally on the more
challenging projects, those which push the correlator to its limits; at the
same time we try to specify a reasonable minimal as well as the ``dream''
correlator. The underlying philosophy is that the correlator should not rule
out plausible experiments which would otherwise be allowed by the design.
Obviously not all of these experiments will be doable when the MMA first
opens; but if the VLA experience is any guide, the original correlator will
remain in use for many decades following first light.
To avoid confusing what is intended primarily as a scientific discussion,
and to restrict the length of an already-lengthy document, we defer
consideration of cost equations and other practical matters of correlator
design to a later memorandum. Similarly, we do not here compare the requested
to the current design specifications.
We use the same terminology as MMA Memo 194. The numbers given here
are for reference only, to make a somewhat confusing discussion more
concrete, and are based on the current notional design of the MMA system.
- Channel: the resolution element of frequency; also referred
to as a spectral point. A channel may be have associated single, dual
(XX & YY), or full (all Stokes) polarization correlator products.
We have tried to be careful to state specifically which is required in each
instance: e.g., 4000 channels dual polarization, which means 4000
frequency elements with two polarization products each. Other authors
sometimes refer to this as ``8000 channels''; here 8000 channels always
means 8000 chunks which do not overlap in frequency.
In this notation, the total number of complex correlator products is
the number of channels times the number of Stokes parameters required for
each channel (4000 channels dual polarization corresponds to 8000 complex
correlator products).
- IF: abbreviation for ``intermediate frequency''; a terribly
confusing term we try to avoid, as it is used to mean so many different
things. Insofar as it must be used, an IF is a wire coming out of a
receiver package. In the current design for the MMA, each wire carries an
8 GHz bandwidth. There is provision for switching halves of the IFs (that
is, a 4 GHz bandwidth) independently, and each half is sometimes called an
IF. The current plan has a total of 16 GHz being sent down from each
antenna to the correlator, for a total of 4 independent (4 GHz) IFs.
- Baseband (BB): the signal presented to a sampler. In the MMA
case, each BB has a bandwidth of 2 GHz or less, and can be flexibly
positioned within an IF band, or switched between IFs. The canonical
design has 4 pairs of basebands, with the two basebands of each pair
having the same frequency but different (linear) polarizations.
We often refer to `independently-tunable' basebands or baseband pairs.
This is intended to mean, ``capable of being tuned to different frequencies,
with reasonable flexibility.'' There could be some restrictions on which
exact frequencies are possible, and the LO chains for the BBs need not be
totally independent (e.g. they might share a first LO or some such). The
MMA will require much more flexible tuning than the VLA; for the correlator
this doesn't matter, and discussion of the LO system, tuning capabilities,
and the like, is outside the scope of this document.
In this parlance the VLA currently has two 50 MHz BB pairs.
- Total bandwidth: in this memo, the total bandwidth is the total
frequency coverage, NOT the total frequency coverage times the
number of correlator products. Again the required polarization
products will usually be stated explicitly; for instance, an observation
covering 230-232 GHz with all four Stokes parameters recorded simultaneously
will be referred to as ``2 GHz full polarization.''
- Correlator: one source of confusion is the dividing line between the
correlator and the other electronics systems. Here we do not maintain a
rigorous distinction, but have generally drawn the line at the samplers.
The correlators takes as input the sampled signal from each antenna, and
gives as output spectra (either frequency or lag) for each baseline and
polarization product. There have been many discussions about how much
processing is done within the correlator itself, with the tendency being
to do as little as possible; so for instance resampling or smoothing the
spectra, either in frequency or in time, will probably be done after
the correlator.
We assume throughout that the MMA will eventually observe through all
atmospheric windows between 
GHz and 
GHz, although it will
probably not be equipped with all of the requisite receivers initially.
For concreteness we also assume that linear polarizations (X and Y) are
recorded.
The lower limit to the number of antennas is set by the desire for
excellent `snapshot' uv-coverage. Snapshot observations are of more
importance to the MMA than to other interferometers
for several reasons. First, the atmosphere at millimeter and submillimeter
wavelengths is highly variable both in opacity and in phase coherence, and one
wishes both to take advantage of brief periods of exceptionally fine weather,
and to image large regions on the sky rapidly to minimize systematic effects
across the resulting maps. This becomes progressively more important at higher
frequencies. Second, the MMA's excellent sensitivity makes very
short observations attractive, if the instantaneous uv-coverage is good
enough to ensure accurate images. Finally, mosaics are expected to become
rather common with the MMA, given the small primary beams at these
frequencies; the quality of those mosaics will be set in part by the
consistency and completeness of the uv-coverage of each pointing. The
second and third of these points were quantified in Cornwell, Holdaway, and
Uson (1993) and further elaborated in a series of MMA memoranda by Holdaway
and others (Holdaway 1990, 1992; Holdaway & Foster 1994; Wright 1997).
All three desiderata considered together led
to the design goal of 40 antennas for the MMA (cf. the original MMA
proposal to the NSF [1990]).
Another, less strong argument for a large number of antennas is
the desire for multiple subarrays, each with very good mapping capabilities.
This is discussed further below (§3.7).
More significant are the recent discussions between NRAO, ESO, and Japan's
NAO concerning possible partnership(s),
which would result in a much larger array. The most recent
European proposal (Downes et al. 1997b) suggests 
dishes, set by the desire to maximize collecting area while minimizing the
number of antennas, subject to the constraint that the antennas maintain
excellent performance for mosaicing and for high frequency work. The
complexity of the correlator itself, and the resulting data rates, are the
main arguments for minimizing the number of dishes. On the other hand, it is
clearly easier to build superb small dishes than superb big ones, and
alternative suggestions range from 
to
dishes. Since we will probably not know until at
least the end of 1999 whether ESO and/or NAO will actually fund the
proposed joint project, the number of telescopes could be a factor two lower
than suggested here. So the bottom line is that the MMA correlator should be
able to handle at least 40 antennas, and perhaps as many as 80-128 if these
major foreign partnerships materialize.
Unfortunately the number of antennas is not something that can
readily be changed in the correlator at some later date; see MMA Memo
194. If we are to have e.g. 80 telescopes eventually it is far preferable to
design the correlator to handle them from the start.
Of course a correlator which can handle more telescopes than are actually
built would allow the addition of further dishes after the completion of the
original project (cf. Downes et al. 1997b).
Many observations will benefit from the widest possible bandwidths.
For continuum experiments this is important mainly for sensitivity, and
so will directly affect virtually all such observations.
Projects for which sensitivity
is paramount, even for the ``maximal'' combined US and European array,
cover every area of millimeter astronomy: the detection of proto-Jupiters in
other solar systems; high-resolution dust mapping around young stellar
objects (YSOs); the observation of pulsar emission at wavelengths which
minimize the effects of dispersion; the search for dust emission in
high-redshift galaxies and proto-galaxies; and so on and on. Sensitivity
becomes progressively more important at higher frequencies, as the atmospheric
contribution leads to higher and higher system temperatures; and at higher
resolutions, since the same total flux is spread over a larger number of
synthesized beams. Some of the most interesting science expected to come from
the MMA depends on high-resolution, low-noise images. The importance
of wide bandwidths in achieving the desired sensitivity cannot be stressed
enough.
Wide-band continuum observations will also provide accurate
single-band ``colours'' (spectral indices). While a few narrow basebands
spread across the band might suffice for bright sources (the Sun, the planets,
Sgr A
, M87), wider bandwidth (e.g., 1 GHz) `chunks' spread over a
receiver's frequency window would allow similar analysis of more standard
sources, in particular the measurement of thermal dust temperatures in
Galactic YSOs and extragalactic disks.
The above argues for a wide continuum bandwidth using dual polarization
for sensitivity. Full polarization imaging is also important, primarily for
stellar emission, dust polarization mapping, Faraday rotation observations,
and planetary work (where the polarization fraction is of order 1%). The
signals are expected to be quite faint, but the results will be well worth the
effort, particularly in mapping the magnetic fields in molecular clouds and
accretion disks.
A number of spectral line experiments also require or benefit from
wide bandwidths.
- Pressure-broadened planetary lines can be up to 3 GHz
across. In general one would like to measure a line-free
continuum at the same time as well.
- Solar radio recombination lines are expected to be broad
and shallow, requiring total bandwidths of 1 to 2 GHz.
- YSO outflows could cover up to 600 km/s (full-width at zero
intensity, FWZI), including the extremely-high-velocity CO `bullets' in
sources like HH111. This corresponds
to
at 850 GHz, the highest frequency proposed for the
MMA. Adding a reasonable area for continuum subtraction brings this to
total bandwidth.
- Radio recombination lines in ultracompact H II regions may
be up to 250 km/s broad, for the most energetic ionized outflows.
Observing H, He, and C recombination lines at once adds another
150 km/s; adding a bit for baseline determination brings the total to
, or 1.6 GHz at 850 GHz.
- Large-scale surveys of Galactic gas need to cover
total bandwidth, allowing for the full range of
Galactic rotation. However, it seems unlikely that these will be carried
out at the highest frequencies, so the total required bandwidth is more
modest, 0.7 GHz at 345 GHz.
- Radio recombination lines arising from narrow line regions of
active galactic nuclei (including Sgr A) require
a total velocity coverage of at least 1500 km/s, or
at
850 GHz. These high-frequency lines, observed at high resolution with high
sensitivity, are expected to prove very interesting in constraining
models of the dense gas surrounding AGNs (Anantharamaiah 1997, priv.
comm.).
- Surveying a galaxy cluster covering
in
CO J=2-1 at 230 GHz, expected to be the most sensitive transition for
such searches, requires 8 GHz total bandwidth. Higher frequency
transitions would demand even wider bandwidths. Of course the full
bandwidth need not be observed simultaneously.
- Spectral line surveys in general, either local (Galactic) or at
high redshifts, benefit from the widest possible bandwidths. For
example, 8 GHz at 45 GHz covers CO J=1-0 emission from redshifts of
1.5 to 2.1. Again such surveys could be carried out by time-sharing
among several frequency settings.
Most of these experiments would involve dual polarization for sensitivity. The
case for full polarization wide-band spectral line measurements is much less
clear, confined to Zeeman splitting observations of masers covering a wide
range of velocities; however this could easily be done in a series of frequency
settings, and will probably be a rare enough project that the additional
time required will not be an issue.
In sum, a bandwidth of 2 GHz, producing two correlator polarization
products (XX & YY), is necessary for a wide variety of spectral line
experiments. Observations of pressure-broadened planetary lines and radio
recombination lines associated with the Sun or AGNs require double that
bandwidth (4 GHz with two polarization products) to fit the line into a single
frequency setting, while the very broadest of such lines at the highest
frequencies might require up to 5 GHz. For continuum observations sensitivity
demands the widest bandwidths possible. A large number of experiments would
also benefit from the ability to sacrifice polarization products for
bandwidth; most experiments not involving linear polarization measurements
would prefer to cover, e.g., 16 GHz producing only the parallel-hand (XX,
YY) polarization products, to always getting full Stokes information but
only over 8 GHz. In any event the correlator should match the rest of the
instrument in allowing the maximum bandwidth permitted through the receivers,
backends, etc; with the current systems design, with 
sent to the
correlator from each antenna, this would imply all four polarization
products for an 8 GHz bandwidth.
The highest frequency resolution needed for the MMA is set by the
possibility of future millimetric bistatic radar observations of solar system
objects, which would require a few hundred 
channels. Apart
from this the highest velocity resolution required is 
(2-5 kHz at 30 GHz), needed for a wide variety of
experiments: measuring wind velocities on Venus; sampling thermal and/or
dynamical line widths of comets, planetary satellites, protostellar disks,
and dark cloud cores; finding and characterizing the structure of narrow
absorption lines; and measuring magnetic field strengths via Zeeman
splitting (of order 1 Hz splitting per microGauss). SETI observations would
benefit from 1 Hz or even finer resolution (J. Tarter 1997, priv. comm.),
but this should not be allowed to drive the correlator
design.1
At the other end of the scale, very wide channels are desirable primarily
to reduce the data rate and the total data volume produced by an experiment.
Most continuum observers would be happy with as few as one channel per
baseband pair, corresponding (in the current design) to 1-2 GHz channels.
However, there are a number of constraints on how wide a channel is actually
usable:
- Bandwidth smearing: Assuming one wishes to lose at most 5%\
in sensitivity at the half-power point of the primary beam due to
bandwidth smearing, the frequency resolution must be better than
(see, e.g., Rupen 1997a), where the parameters used are those appropriate
to the smallest proposed configuration and the highest proposed
observing frequency. These parameters give the largest channel width one
might ever wish to use; even for the most extended proposed
configuration (10km) at the lowest observing frequency (30 GHz), the
required frequency resolution is only 24 MHz. Clearly this is not much
of a constraint.
- Delay errors: Delay errors will cause phase slopes across the
band; the corresponding decorrelation across a channel should not be too
large. 5% decorrelation seems a reasonable limit (high dynamic range
observations will use more channels), corresponding to about
across a single channel. At the VLA, the delays seem to be stable to
about 1 nsec, arguing for 50 MHz channels. At OVRO, using analog delay
lines, the phase errors due to delay errors are negligible over a full
1 GHz (Woody, priv. comm.). In part this comes down to how often one
wishes to reset the delays; a very rough guess for the MMA might be
a drift of 5-10 picoseconds per hour, or 5-10 times worse than that
in a week (Clark 1997, priv. comm.). This would imply channels a few
hundred to a few thousand MHz wide.
- Instrumental structure in the bandpass: The receiver and
signal transmission will themselves introduce gain and phase errors
which one would like to calibrate out even for continuum experiments.
Since the RF and IF components will all be very broad band there should
be no instrumental structure on frequency scales less than a few hundred
MHz.
This suggests that the broadest practicable channels will be 
wide. Of course for a lag correlator this number is not very important
for the design.
Finally, between these two extremes one must be able to choose frequency
resolution (and bandwidth) in geometric (factor two or whatever is convenient)
intervals; preferably these choices could be made independently for each
baseband or baseband pair.
There are two main arguments for having as many baseband pairs as
possible. First, to the extent that each baseband may be positioned
independently in frequency, more basebands imply more flexibility in
observing several lines or several `chunks' of continuum within a single
band. Second, to zeroth order the size of a lag correlator goes inversely as
the number of basebands, since one can use proportionately fewer lags to
cover the same total bandwidth with a given frequency resolution (see e.g.
MMA Memo 194). Of course there are counter-arguments which
suggest a smaller number of basebands. Astronomically, it is difficult to
keep consistent calibration between different basebands, particularly for
single-dish data; this implies that the maximum bandwidth of a baseband
should roughly match the width of the broadest lines that would regularly be
observed. From considerations like those in §3.2 above, this probably
corresponds to 1-2 GHz per baseband. Practically, correlators with many
basebands (e.g., the analogue correlator at the 12m) have not been terribly
successful, and the ideal number of basebands from an engineering point of
view is a subject of current debate. That debate however is outside the scope
of the present paper, which purports to concentrate on astronomical needs,
and the remainder of this subsection is addressed to the question of how
many independently-tunable basebands are necessary to allow the observer to
take good advantage of the capabilities of the MMA.
For continuum work one wants a number of baseband pairs for two reasons:
first, to allow one to position individual `chunks' of continuum bandwidth to
avoid strong lines, atmospheric contamination, and strong interference; and
second, to allow single-band spectral index (or colour temperature) mapping.
Four independently-tunable baseband pairs is probably the maximum necessary
for these sorts of experiments. Note that each BB
pair will be made up of a number of channels (see the next section), so
while one would want to avoid broad interfering lines, narrow ones are not a
problem, since the contaminating lines can simply be deleted from the
data set.
Line experiments in general benefit from having as many BB pairs as
possible, as this maximizes the observing efficiency by allowing many lines
(as well as the continuum) to be observed at once. This is particularly
important at high frequencies and for the larger array configurations, since
one wishes to take the best advantage of periods of good phase stability,
low wind conditions, and/or low opacity. For similar reasons very long
integrations, which may be quite common (Evans et al. 1995),
should also be
carried out simultaneously in as many lines as possible. That many
interesting lines are available is very clear; for instance, Schilke et
al. (1997) found an average of 26 reasonably strong lines per GHz in the
350 GHz window towards Orion K-L. Obvious choices for multi-line studies
include a set of different isotopes and transitions of a single
molecule, which could easily add up to 8 or more lines in a single band.
Many experiments require, or would benefit greatly from, simultaneous wide
and narrow bandwidths; measuring accurate line-to-continuum ratios,
referencing the phase of a line to a strong continuum or vice versa,
observing a single line at multiple velocity resolutions (e.g., observing
both a protostellar disk and the associated outflow at the same time), and
`piggy-back' surveys (e.g., doing a pencil-beam survey for CO while
mapping the emission in a nearby galaxy) are all examples of
observations of this type.
Finally, VLBI observations using the MMA would benefit from having
the same flexibility as the VLBA system provides, i.e. 8
independently-tunable basebands.
Based on the above considerations, the ideal correlator would allow for a
minimum of 4 BB pairs, and preferably 8. Note that this is one
of the aspects of the correlator which is modular - it would be relatively
easy to add more basebands later (MMA Memo 194).
At least one of these BB pairs should have a maximum bandwidth of at least
1-2 GHz, and together they should of
course span the full bandwidth discussed in §3.2.
Insofar as possible, since even broader lines will be observed occasionally,
and perforce be split amongst several basebands,
one should be able to join these basebands together smoothly over
frequency, with little loss in sensitivity and minimal systematic errors.
The bandwidth and channelization of each baseband (or, at a minimum, each
baseband pair) should be set independently, allowing e.g. one BB pair to
cover 1 GHz with 100 channels while another covers 10 MHz with 1000
channels.
Multibeam feeds, if used, would represent an additional complication,
as presumably one would want to correlate all the beams from one telescope
with the corresponding beams from all others. To first order this would be
similar to having additional (sets of) BBs. This should probably not drive
the initial correlator design.
A number of experiments benefit from a large number of channels; many of
these involve wide (several GHz) total bandwidths. Among the most obvious are:
- Mapping molecular clouds: The maximum linewidth for a molecular
cloud (ignoring outflows) might be about 50 km/s, while protostellar disks
embedded in such clouds benefit from velocity resolutions as high as
50 m/s. Blind searches for such disks, looking through the entire
velocity range of the cloud, could then be done with
channels
per BB pair; the total number of channels would then be 4000-8000
spread over the 4-8 BB pairs (see above). Similar desiderata
obtain for mapping the Zeeman splitting in a cloud, for which
one wants spectral resolutions of order 
. Note however that
for most of these experiments the total bandwidth would only be about
0.14 GHz, even when observing at 850 GHz; assuming one can trade
bandwidth for channels in at least a proportional rate (i.e. half the
bandwidth implies twice the number of channels), 4000-8000 channels
in 0.14 GHz corresponds to only 70-140 channels over 8 GHz.
- Searching for molecular clouds in ellipticals and AGNs:
Several nearby dwarf ellipticals have CO emission with total linewidths
of only a few km/s (e.g., Wiklind and Rydbek 1986),
corresponding to a single molecular cloud;
some have also been observed with very patchy dust emission, implying
that their interstellar media (ISM) may consist mainly of small,
independent clumps of gas. Similarly, HI absorption observations of
AGNs (e.g. van Gorkom et al. 1989) often show fairly narrow lines,
or lines with significant substructure. Searching for such
narrow lines in a giant elliptical requires a velocity resolution of order
1 km/s (to match the linewidth of a single cloud) over 2000 km/s
(the dynamical width of the elliptical), implying of order 2000 channels,
spread over 2.3 GHz at 345 GHz, or 5.7 GHz at 850 GHz (the highest
operating frequency of the array). Again, if one can trade bandwidth
for channels, this corresponds to 575-1425 channels spread over 8 GHz.
- An unbiased search for CO in galaxy clusters: An unbiased
230 GHz search for CO in a galaxy cluster would require covering
at 10 km/s resolution, implying about
1000 channels spread over 8 GHz. This will however be an unusual
experiment, as the array, even with the largest areas
currently under consideration, will not be sensitive enough to make such
searches fruitful for other than the closest clusters.
- Imaging the primary beam: The most extended configuration
suggested for the MMA stretches to
km baselines. Following the
discussion in Rupen (1997a), making an image covering the full primary
beam at the highest available resolution, with at most 5% sensitivity
lost to bandwidth smearing, would require
Here 
is the maximum baseline, 
is the dish diameter,
is the total bandwidth observed, and 
is the observing
frequency. Note that this mode may be much more common than is the case
for the VLA, since the primary beam is much smaller, and since many
high-resolution experiments will also demand quite long observations
(implying that sacrificing sensitivity in the outer part of the
primary beam will be more painful).
- NGC 4258: to cover the millimeter analogues of the masers in
NGC 4258, all in one observation, would require three IFs, one
wide for the components near systemic velocity,
and two of 
each for the outliers. With 0.1 km/s
channels this would give a total of 9000 channels, which could be single
polarization, spread over 2.6 GHz at 850 GHz (corresponding to
channels spread over 8 GHz). Although such
an unusual source should not be allowed to drive the correlator design,
it's heartening that its requirements are not much more stringent than
those for the more common experiments already discussed.
- Spectral line surveys: Numerous single-dish line surveys have
been done of active star-forming regions (e.g., Schilke's review in
Shaver 1996); the availability
of high spectral resolution over wide bandwidths would allow astronomers
to harness the sensitivity of the MMA to do similar experiments, but
at much higher angular resolution, examining the spatial distribution
of (potentially) 100s of lines at a time. For instance, Schilke et
al. (1997) found an average of 26 fairly strong lines (by MMA
standards) per GHz in the 350 GHz atmospheric window in Orion KL; this
implies some 200 lines over 8 GHz,
which one would like to image at high spectral resolution both to follow
dynamical structures and to separate the lines (and measure their
frequencies) as well as possible. Schilke et al.'s observations
were done at 1 MHz resolution, i.e. 1000 channels per GHz. Doing a
similar experiment over 8 GHz in a single observation would then require
perhaps 4000 channels; of course one could observe instead by
time-sharing among somewhat narrower bandwidths.
- Extragalactic absorption lines: Both Galactic and
extragalactic molecular absorption lines can have widths below 1 km/s
(see e.g. the reviews by Wiklind & Combes and Lucas in Shaver 1996).
Many experiments (e.g. looking for intervening galaxies towards
background quasars) involve searching for these narrow lines at unknown
redshifts, and hence benefit from covering as wide a band as possible
at high spectral resolution. 8 GHz corresponds to some 80,000 km/s at
30 GHz, the lowest operating frequency of the array; ideally one would
observe this with 0.5 km/s resolution, to match the expected line
widths, implying 160,000 channels. A more reasonable project would
use
channels, with follow-up observations to
``zoom in'' on any unresolved lines.
- Unbiased searches for high-redshift CO: Here one wants to
cover the full available bandwidth at
resolution. This corresponds to 1000 channels per
GHz at 30 GHz, the lowest frequency proposed for the array (
for
CO J=1-0). Once again one would prefer to cover as wide a bandwidth as
possible in one observation, but time-sharing between frequencies is
certainly an option.
Apart from line surveys and the like (most of which would benefit from as
many as 1000 channels per GHz), and assuming that one can trade
bandwidth for channels in a fairly flexible fashion, all of these experiments
correspond to having 500-1000 channels spread over 8 GHz.
Since most of these projects are limited by sensitivity,
dual polarization is essential. Only Zeeman splitting and maser
observations would benefit from both the maximum number of channels and full
polarization products, and we could probably get by with only half as many
channels when asking for full polarization information. Line surveys of
course could use as many channels spread over as wide a bandwidth as is
practicable, but they should probably not drive the correlator design.
It seems unlikely that any reasonable experiment would demand many
more channels over a narrower bandwidth; although the sensitivity of the
instrument would support this, the intrinsic linewidths are broad enough
that much higher resolution does not seem necessary. The obvious exception
would be SETI searches, which benefit from very high resolution over the
broadest possible bandwidth; again this should probably not be allowed to
drive the correlator design, though it should be allowed if it is not
terribly costly.
We note that Escoffier's current (1997) correlator design would
give 512 channels over an 8 GHz bandwidth for each of two polarization
products (e.g., XX & YY) (see MMA Memo 194), nicely matching
the above (independently derived) astronomical specification.
The shortest astronomically interesting integration period for the MMA
is the subject of a lengthy discussion in MMA Memorandum 192 (Rupen
1997b). The conclusions of that memo were:
- On-the-fly total power observations require writing
out autocorrelation spectra every few milliseconds. A hard limit of
is set by the desire for good
atmospheric subtraction up to 350 GHz.
- Pulsar observations need time resolutions as high as
, but only the phased array (vector sum) output must be
written out. Note that while the data would have to be gated on these
timescales, they may not actually need to be dumped this frequently;
see MMA Memo 192.
- Surveys of large regions are the most challenging interferometric
observations: a minimum dump time of more than about 100 msec will make
mapping objects like the Magellanic Clouds, the Cepheus Cloud, and the
Virgo Cluster virtually impossible. Ideally one would like dump times
of order to allow mapping these
large sources in a finite amount of time.
- A variety of other experiments, most significantly the need to
avoid significant decorrelation due to phase variation during an
integration, demand integration times as short as 100 msec.
On the other end of the scale, the enormous data rate coming from an
instrument with at least 40 telescopes and several thousand spectral
channels argues for the availability of much longer integrations, up to
perhaps some 10s of seconds or longer. The limit here will be
the phase wind due to the electronics and the atmosphere, which (at the
higher frequencies) may often be so fast that long integrations would
require on-line phase correction, which would add significantly to the
complexity of the correlator. At low frequencies (30 GHz)
integrations of 30 seconds or longer will often be fine. This is discussed
further in §3.9.
Subarrays will be much more important for the MMA than for the VLA or
other existing interferometers, for a wide variety of reasons.
- Multifrequency capability: Some observations would benefit
from the ability to observe in several bands at once. For example,
solar flares vary rapidly enough
that one wants to track their behavior at several widely-spaced
frequencies, at identical times. Atmospheric studies (e.g. measuring
the opacity at the same time at different wavelengths) could similarly
benefit from simultaneous multi-frequency data. Also, subarrays
will be essential if only some of the antennas are equipped with certain
receivers, which will undoubtedly be the case for some time while the
array is gradually fitted out with all frequency bands.
- Calibration: It may be useful to devote some
subset (as many as half, in some proposals) of the antennas to
continuous calibration measurements, at one or more frequencies. For
phases the benefits of looking at a calibrator all the time are obvious;
for amplitudes one might wish to monitor the opacity and/or the
gain on short timescales through tipping scans or other measurements at
one or more wavelengths. These sort of schemes
would require at least two and possibly more subarrays.
- Mapping large areas: As discussed in MMA Memo 192, there
are a number of very large sources (the Magellanic Clouds, nearby
clusters, etc.) which are bright enough that the time needed to map them
is set primarily by the dump time of the correlator. Splitting the MMA
into M subarrays would shorten the mapping time by the same factor.
For solar system sources, particularly the Sun, one needs to map areas
much larger than the primary beam as fast as possible, either because
of intrinsic variability (e.g., solar flares, planetary weather), or
because the orientation of the object studied changes rapidly with
time (due for instance to rotation). Obviously these considerations
become more important for bigger dish diameters and longer dump times.
- Fast-response observations: Some objects need to be observed
as rapidly after some trigger as possible, but may either be very
bright, so the full array is not required, or have only a very poorly
known position, requiring multiple subarrays to allow a rapid search of
the entire region. Stealing only a few telescopes may also be
more palatable than completely disrupting the regular observation in
progress when a target-of-opportunity proposal is triggered, and would
certainly allow more continuous time coverage than is typically
possible at existing interferometers. Examples of interesting,
potentially-bright and rapidly variable sources include gamma-ray
bursts, novae, supernovae, variable stars undergoing outbursts, and
lensed stars.
- Lower data rates: Splitting the array into M subarrays
reduces the total number of baselines, and hence the data rate,
by roughly the same factor. This may be a
significant consideration for experiments that require large numbers
of channels but can live with the lower sensitivity (which goes
down by the same factor), and for observations (like large surveys)
which require very short dump times. This tradeoff may in fact be
essential in the early years of operation, when the storage media may not
be able to keep up with the full data rate of the correlator.
- VLBI: The MMA will be in great demand as the most sensitive
element in millimetric VLBI arrays. As with the VLA one will often
wish to support such experiments without giving up the entire array;
even a third of the MMA would still give significant collecting area,
particularly if the European/American collaboration materializes.
- Inhomogeneous arrays: Although out of favour at the moment,
if the MMA does eventually include a variety of dish sizes, it may
be useful for some experiments to be able to split the array into
subarrays each of which is composed solely of telescopes with a single
dish size.
- Single-dish observations: It is quite likely that part of the
array will be devoted to single-dish work, either occasionally or
frequently. In this case one must be able to handle the situation where
those antennas are pointing in different directions and observing at
different frequencies than the remainder of the array; at times one may
even wish to have, say, 10 individual telescopes all observing different
things. This isn't quite the same as a regular subarray but the
correlator should be able to handle the resulting data.
- `Faking' big dish diameters: One might occasionally wish to
phase up a number of subarrays and correlate the result, either to slow
down the data rate or to allow the use of fainter calibrators. To make
this mode useful would require perhaps 10-30 subarrays each consisting
of 3-10 antennas, as well as the correlation of the outputs of those
subarrays (see MMA Memo 165 (Thompson et al. 1997).
More generally, given the superb sensitivity of the array and the large number
of telescopes (up to 128), many interesting projects will be so easy that it
makes sense to allow for multiple subarrays. The correlator should allow
for at least 4, and preferably 6-8, independent subarrays. This requirement
is especially important if there are more than 
antennas, and if the
collecting area is much more than 
. These subarrays should be
as fully independent as possible; in particular, it would be very helpful to
be able to specify different dump times, baseband bandwidths, and
channelizations for each subarray.
Total power measurements will be much more important than for centimeter
interferometers, and require higher accuracy. Mostly this is because the
primary beam will be small, and many sources will require mosaicing;
single-dish observations will be needed to fill in the central hole in the
uv-plane. There are various arguments that the MMA itself should provide
its own short-spacing information, rather than relying on other dishes as
most current interferometers do. The MMA will be the premiere
millimeter telescope in the world, and as such is expected to be observing
almost continuously, with high sensitivity, covering large areas of the sky.
The corresponding single-dish measurements will have to match the MMA
observations in both quantity and quality, over the entire spectral window
covered by the MMA. It would be unreasonable to rely on any other instrument
for this sort of vital support; nor are there any international,
publicly-available instruments capable of providing it. Further, a
series of studies (e.g., Emerson 1990) have shown that the MMA telescopes
themselves can be used quite handily to fill in the missing short spacings,
without any need for larger dishes. Finally, there is a
software/post-processing advantage to having a `standard' source for total
power data, rather than allowing for a wide variety of possible instruments;
one could optimize the (automatic?) routines for mosaicing and the like, for
the case of MMA single-dish data.
The correlator must therefore be prepared to handle total power
measurements from all MMA dishes simultaneously,2 or at least from all dishes equipped to produce
such data.3 The single-dish data
should be allowed at least the same
number of channels, bandwidths, etc. as provided for the interferometric
data. A number of special observing modes must be supported as well:
- On-the-fly mapping: Much more efficient that standard
``point and shoot'' mapping, particularly for big, bright sources.
May be useful or necessary for removing the atmosphere.
Requires dump times for the autocorrelations as short as
. Useful for both line and
continuum work.
- Beam switching: Standard method for removing the atmosphere.
Requires labeling data as ON or OFF, on short (
)
timescales, or (more likely) storing the changing position; this would
of course also imply short dump times. May involve a nutating
subreflector.
- Frequency switching: Useful for subtracting the atmosphere in
spectral line work when there is no obvious off-source position for
beam-switching.
Requires labeling data as ON or OFF, on short ()
timescales, or (more likely) storing the changing central frequency.
- Multi-beam feeds: While these are becoming common on
single-dish telescopes, and the idea of SCUBA-type arrays on 40 JCMTs
sitting on the Altacama plateau is almost unbearably attractive, it's
not clear whether the MMA telescopes will ever have or need multi-beam
feeds. If they do, the correlator must be able to support multiple
feeds off a single dish. The number of pixels per telescope might
easily approach 100 (cf. SCUBA, with 91 at
). Presumably
one would only equip a small number of dishes with such multi-beam
arrays, but this has not yet been discussed.
Although it would seem easiest to use the same correlator for the auto- and
the cross-correlations, there is no strong reason that the same correlator
must handle both.
Finally, one must distinguish between spectroscopy and continuum total
power data.4
One may well want to do both at the same time (usually to be
able to subtract the line emission from the continuum), but they are quite
different things. One does single dish spectroscopy with the usual
autocorrelations, with level controls etc. used in the same way as one does
for interferometry; but this may either destroy or severely injure the
absolute amplitudes used for continuum measurements. The current plan is to
do continuum single dish measurements based on detectors located in the
antennas, far ahead of all the stuff that might bother the gain stability.
This detector system would then be well outside the correlator.
Operating at very high frequencies requires monitoring the atmosphere
on short timescales. There are two issues: correcting the amplitudes for
atmospheric opacity fluctuations, and maintaining phase coherence. Based
on the extensive site testing database and atmospheric transmission models,
Holdaway (1998; in prep.) concludes that short timescale (i.e., 30 seconds)
amplitude fluctuations will typically be only a few percent rms at 650 GHz.
On longer time scales (600 seconds) amplitude fluctuations rise to about
10% rms at 650 GHz. This implies that opacity corrections need only be
calibrated out on time scales of 30 seconds or longer. Similar modelling
gives atmospheric coherence times at 650 GHz of 
seconds for median
weather conditions and 90% coherence (<1 second for 98% coherence),
rising to longer than 10 seconds (90% coherence; about 3 seconds for 98%\
coherence) during the best 20% of the weather, which is presumably when
most high-frequency work will be carried out. There is thus little need
to make phase corrections on time scales less than about a second. Other
simple arguments give similar time scales. For instance, assuming peak wind
speeds aloft of 10 m/s, a given atmospheric perturbation will cross an
antenna in 
; it seems unlikely that one
will be able to sensibly correct phases any faster than that. It is also
questionable whether one could measure the phase any more frequently than
this.
So, at the highest frequencies one might want to correct the phase every
second or so, and the amplitude every 30 seconds. This implies that all
statistics related to the atmospheric phase - radiometric measurements of the
water line, opacities, wind velocities, temperatures, on-site water vapor
measurements, pressure - together with pointing information, must be written
out with the data, on that timescale.5 This basically increases
the size of the output data set and the corresponding data volume, without
requiring much of the correlator. However, integrations which are longer
than about a second at high frequencies may require on-line corrections
to the phase,6 to avoid
decorrelation within an integration period. This is a major issue, because
such corrections may be complicated, and because long integrations would be
very helpful in reducing both the data rate and the total volume of data
which has to be stored on disk and eventually analyzed. Such on-line
corrections would make the correlator significantly more complicated. One
option would be to have the correlator always produce a data stream with
a maximum integration time of one second, and allocate a special-purpose
processor to do the corrections and average the data in time after the
correlation. Unfortunately that processor would have itself to be fairly
complex. This is an area which needs further study fairly quickly.
The term ``spectral dynamic range'' (SDR) is used to mean at least three
different things:
- 1.
- The ratio of the peak continuum signal to the root-mean-squared
(rms) noise in a continuum-subtracted image. A high SDR in this sense
corresponds to having a very flat frequency response.
- 2.
- The ratio of the peak continuum signal to the accuracy with
which one can measure a very deep absorption line. A high SDR in this
sense corresponds to correctly measuring a very wide range in
correlation coefficient.
- 3.
- The ratio of the peak of a narrow (in frequency) signal to its
spectral sidelobes. A high SDR in this sense corresponds to very little
cross-talk between frequency channels.
The MMA, especially in the larger versions suggested for the collaboration
with the Europeans, will be a very sensitive instrument, with noise levels at
230 GHz in one minute as low as 
in the continuum and
(
, for the smallest configuration) in a 0.2 km/s
channel. One will often be looking for weak signals in the presence of
strong confusing sources, either continuum or line (e.g., masers), requiring
a high SDR potentially in all three senses.
- 1.
- Flatness: the ratio of the continuum brightness to the
noise level in a channel map will often need to be as high as
and for many experiments 
or higher in observations of faint
lines on top of very bright continuum sources. Examples include
rarefied species near bright YSOs, H II regions, and the like;
radio recombination lines in ionized outflows; and searches for faint
absorption lines against very bright AGNs.
- 2.
- Absorption: This is probably the least important type of
SDR to an astronomer, as it limits the accuracy of a measurement rather
than the possibility of a detection. The cases where this would matter
a great deal are probably limited to searches for faint substructure in
high-opacity lines, for instance searching for very weak emission
superposed on very strong absorption. Probably one would like to be
able to believe 1% variations in highly opaque lines, but it seems
unlikely that even higher accuracy would regularly be required.
- 3.
- Spectral sidelobes: the desired limit on the leakage of a
strong signal in one channel into other channels in the same baseband, is
set primarily by deep observations of emission in line wings of sources
with very bright emission at the line center. Examples include many of
the most interesting objects in the sky: planetary absorption lines
(e.g. Gurwell 1996); molecular outflows (e.g. Yu & Chernin 1997
[VLA 1623/CO], Cernicharo & Reipurth 1996 [HH111/CO]); YSOs (e.g.,
Hogerheijde et al. 1997 [T Tauri/HCO
], Olmi et al. 1996
[G10.47+0.03/CH
CN]); star forming regions (e.g. Wink et al. 1994
[W3(OH)], Shepherd, Churchwell, & Wilner 1997 [ON2]); stars (e.g.,
Dayal & Bieging 1995 [IRC+10216]); and even external galaxies (e.g.
Shen & Lo 1995 [M82], Sofue & Irwin 1992 [NGC 3079]).
In all these cases the line centers peak at some 10s of Kelvin, while the
rms noise in one minute on source might be a few milliKelvin (for the
most compact configuration). This neglects even more difficult cases,
such as looking for thermal emission around masers, searching for faint
(rarefied?) species in the same BB as stronger lines, planetary
radar experiments (where the strong zero-velocity return signal creates
a problem similar to the maser case), and observations (at the lower
frequencies at least) in the presence of strong radio frequency
interference. This suggests that will be desired fairly often,
and may not be that unusual a requirement.
Of course, achieving these levels is not purely a correlator problem;
at the VLA we almost always Hanning smooth the raw spectra to beat down
the spectral sidelobes, and (so long as one has enough bits) one can do
this or more sophisticated apodisation after the correlator. The
discussion here refers to the SDR after such apodisation.
Although it is not clear how to relate image quality to the correlator
design, for completeness it may be worth mentioning the dynamic range (peak
to off-source rms noise level) MMA images will achieve. With noise levels
as in the last section and taking 10 hours as a reasonable long integration,
one expects dynamic ranges of
-
for a few special sources - planets, masers, strong AGNs;
- a few to 10 times for many sources - including continuum
and strong line emission from young stellar objects, AGB stars, H II
regions, the Galactic center, and less impressive AGNs;
-
fairly routinely, in many cases in only a few minutes of
integration.
The above dynamic ranges assume the joint US+European project with a collecting
area of 
; for the MMA alone (
) they should
be reduced by a factor 
.
Such excellent images will be useful scientifically in many contexts,
ranging from searching for extragalactic counterjets at frequencies where
the core is not so bright as to limit the imaging, to looking for
proto-Jupiters around main sequence stars, to mapping faint, extended gas
around young stellar objects. Most of these projects require not simply
high dynamic range, but high on-source accuracy as well, with peak on-source
errors of 1% being a good target (cf. Cornwell, Holdaway, and Uson 1993).
Nothing in the correlator should prohibit making such high-quality images.
Another kind of dynamic range relates to the total range of data within
a single uv-data set - the ratio of the peak short-spacing flux to the rms
noise on the longest baseline. This is in some ways a more difficult
number to derive, since it involves comparing the integrated flux density of
a source to the rms noise in an integration period. Probably the brightest
sources for which one might achieve thermal noise on the longest baselines
are the planets, with brightness temperatures of 200-300 K (for Jupiter and
Venus). The flux density measured on the shortest baseline would then be
of order
where is the telescope diameter. With a noise level between 5 and
20 mJy on a single baseline in 1 second for frequencies up to about 230 GHz,
the peak ratio of flux density on the shortest baseline to rms noise on the
longest baseline would be of order .
Although radio frequency interference (RFI) has not in the past been much
of a problem for millimeter interferometers, RFI has been increasing even at
the high frequencies used by the MMA, and will certainly be an issue for at
least the lower observing bands by the time it is built. Currently the main
frequency allocations above 30 GHz have been to satellites, with a few
areas in Q band going to stratospheric balloons and automobile radar
systems. Little
use has yet been made of the frequency space already allocated, but
some important features are already clear. First, most services proposing
to operate at these high frequencies do so because they need fairly wide
bandwidths. This implies that typical RFI signals will be at least a few MHz
wide. Second, at millimeter wavelengths it is more difficult to
generate high transmitter power, while high gain beams require only small
antennas. Thus one would expect most transmissions to be highly beamed at
specific areas. Most importantly, the sidelobe levels of radio astronomy
antennas are likely to have similar gain to those at centimeter
wavelengths, i.e. of order 10 dB for those near the main beam and order
0.1 dB at angles greater than about 50 degrees from the main beam. Since
the collecting area for a given gain is proportional to wavelength
squared, the sidelobe sensitivity to interference decreases with
increasing frequency.7 This leads to the third point, that the bulk of the worrisome
interference will come from satellite downlinks. Since those satellites are
likely to surround the globe, we will not escape their transmissions however
remote the observatory site.
If the satellite downlinks use time multiplexing like IRIDIUM,
they will transmit in brief bursts (IRIDIUM uses 4.5 msec packets) which we
may be able to flag if the signal can be recognized and discarded on
timescales. Such time-sharing may not be very common however,
since most satellite allocations are designated specifically as
space-to-Earth or Earth-to-space, whereas IRIDIUM takes advantage of an
unusual secondary uplink allocation within a primary downlink band.
While the RFI situation is currently fairly benign, we cannot afford to be
complacent. At the VLA the bulk of the interference above 
is internally generated, due mostly to the LO systems (the 100-200 MHz
`birdies'). This should be avoided if at all possible at the MMA; it will
do us little good to have clear skies if we bring with us our own headlights.
Further, although no allocations have yet been made above 300 GHz,
those are to be discussed in the 1999 World Radiocommunications Conference.
In addition to the major requirements discussed above, the correlator
must allow for a number of more specific constraints:
- Fast telescope motions: Slew speeds of order
,
and the correspondingly fast dump times, will require rapid updates to
the correlator model.8
In the (common) fast switching case there may be
savings because one is switching between only two positions, but OTF (or
even `point and shoot') maps will be more challenging. Unlike the VLA,
the MMA will often be pointing at significantly different positions
during adjacent integration periods (dump times).
- Rapid frequency switching: several experiments would benefit
from rapid frequency switching within a single band, though the
availability of more than the minimal 4 BB pairs would take care of most
cases. More important and more difficult is the problem of
phase-referencing one band to another, e.g. to take advantage of a strong
maser transition. In this case one might want to switch between frequency
bands in a few seconds (for the more extreme examples).
Whether this mode should be considered vital, and how often it might be
used, will be discussed in an upcoming memo on phase calibration
(Holdaway et al., in prep.).
- Maximum baseline: Many of the most interesting MMA observations
require high resolution, between several 10s of milliarcseconds and an
arcsecond. Examples are legion, including e.g. searches for proto-Jupiters
(or tell-tale gaps in disks) around YSOs, imaging of stellar
photospheres, and resolving AGN accretion disks out to Virgo and beyond.
The desired resolution corresponds to baselines ranging from a few to 10s
of kilometers, with 10km being the maximum currently discussed. The
correlator should therefore allow for baselines up to 10km long. Although
it is unlikely
that the initial array will include such long baselines, the existence of
prospective international partners specifically interested in such
high-resolution experiments is a strong argument for allowing for this
capability from the start. Even longer baselines have occasionally been
discussed in the context of major international partners.
- Phased-array output: For some types of experiments, most
notably gated pulsar and VLBI observations, one wishes to phase up the
array in real time and write out the summed data. For VLBI one wants
the raw summed data, not averaged over time; for pulsars one can average
down (see Gating, below).
- Gating: Pulsars are very weak (but detectable; Kramer et
al. 1997) at MMA frequencies; writing out the (phased array) correlator
output in time bins sufficient to phase resolve the pulse profile would
therefore be useful in increasing the signal-to-noise of their emission.
This sort of gating in time would also be useful for on-line RFI
excision, particularly of periodic interference. Various flux
calibration schemes (measurements of ON/OFF loads and the like) might
benefit as well from the availability of multiple data streams.
The required time resolution for pulsars would be a tenth of a millisecond
or better, and one might want to employ 10 or 20
different time bins across the
msec pulse, to sample the pulse
profile. RFI may require time samples as fine as 
(IRIDIUM for instance pulses with a 45 msec period, and its individual
data packets are a tenth as long).
- Burst mode: Some objects (e.g. solar flares) vary so rapidly
that it might be advantageous to write out partial data at a much higher
rate than normally allowed. One might also consider trading baselines
for time resolution, for instance for large scale surveys limited by
total observing time rather than sensitivity, at least during the early
days of the instrument. A special burst mode is probably not necessary
if dump times of some 10s of milliseconds are considered `standard' (see
§3.6).
- The Sun and Other Bright Sources:9 The Sun is an example of a source which dominates the
system temperature; during bursts, that system temperature will vary
dramatically. Similarly other sources contribute significantly to the
system temperature (e.g., planets), and there too
will vary
somewhat as the source wobbles around in the primary beam of each
antenna. That variation must be monitored and the visibility data
corrected. This affects the correlator because its power inputs may
not be held at constant and optimum levels. The consequent
less-than-optimum performance is probably not a big issue, as this
should affect only a small number of sources.
From the above discussion, the main requirements for the MMA correlator
are as follows:
- Number of antennas:
: at least 40 for
good imaging, up to 80-128 if we can afford more collecting area but
don't want huge dishes.
- Maximum bandwidth: There are several obvious break points for
this.
with two polarization products,
corresponding to 
of (bandwidth times polarization
products), for a wide variety of spectral line experiments.
with two polarization products for
pressure-broadened planetary lines and wide RRLs.
with full (4) polarization products to
match the maximum bandwidth sent down from each antenna in the current
systems design.
- As wide as possible to maximum continuum sensitivity and
the efficiency of spectral line surveys.
- Frequency resolution: 10 Hz - 100 MHz, with the ability
to select in factors of two or something similarly flexible. A few to
10 Hz is needed (but only over a few hundred channels) for bistatic
radar; other experiments require only 2 kHz
resolution, for sampling thermal/dynamical linewidths of low-mass
systems (comets, YSOs, dense cores, etc.), resolving molecular absorption
lines, and Zeeman splitting. SETI searches on the other hand would
benefit from 0.1 - 1 Hz resolution, over as wide a band as
possible, but this should not be permitted to drive the correlator
design. The lowest interesting resolution is that
corresponding to features in the bandpass, due to poor delay settings
or to the RF/IF systems themselves. One wants this low resolution
for continuum experiments, to keep the data rate down as much as possible.
- Number of basebands: 4-8 independently-tunable baseband
pairs. Desirable for flexibility in placement of continuum
bandwidth (for spectral index studies, and to avoid atmospheric emission
and RFI) and choice of multiple line transitions. This last is crucial
to the MMA, not so much because its lack would disallow vital
experiments, but because observing several lines
at once is a far more efficient use of the instrument.
- Number of channels: 500-1000 (with dual polarization
products) spread over 8 GHz, desirable for a wide variety of line
experiments, ranging from searching for molecular clouds in elliptical
galaxies, to imaging the entire primary beam with negligible sensitivity
losses due to bandwidth smearing. Spectral line surveys and unbiased
line searches could benefit from as many as 1000 channels per GHz
over the entire band, but these can be carried out by time-multiplexing
amongst several frequency settings; it is however interesting to note
that there is no obvious experiment which would benefit greatly from
more than this number of channels. These numbers assume that one
can trade bandwidth for frequency in a fairly flexible way, i.e. obtain
more channels across a narrower bandwidth.
- Dump times:
- Autocorrelation spectra:
, to
allow good atmospheric subtraction during on-the-fly measurements at
350 GHz
- Phased-array data:
for pulsar work
- Interferometric data:
to allow
surveys of large regions on the sky. This requirement, if it must
be relaxed, should at least be kept below 100 msec, to avoid
significant decorrelation due to phase variation.
- Max. dump time: 10 seconds or longer, if one can
hold the phase steady during that time. Without active phase
correction the maximum dump time would probably be about 1 second.
- Subarrays: at least 4; prefer 6-8. Desirable
for many reasons, most importantly
for flux/phase calibration, to speed up mapping large areas,
to lower the data rate, and to allow the use of part of the array for
single-dish measurements. More important if there are more telescopes
and for larger total collecting areas.
- Total power measurements: must be fully supported for
taking data similar to those from the interferometer. Vital for
flux calibration and mosaicing.
- Ancillary data: must record a variety of weather,
telescope, and related information with the visibilities. Important
primarily for calibration (phase, flux, and pointing) and flagging.
- Spectral dynamic range:
, for
many projects (weak lines near strong thermal sources (stars, YSOs, H II
regions), faint line wings, etc.). Conveniently this numerical
requirement is roughly the same for both the flatness of the frequency
response and the limit on spectral sidelobes.
- RFI excision: allow for very strong, transient signals;
possibly employ on-line flagging and masking, particularly for the longer
integration times. May require flexible, programmable on-line
flagging.
- Maximum baseline: 10 km, to allow eventual resolutions
of a few milliarcseconds. Might be even longer if a major foreign
collaboration materializes.
As the astute reader will have noticed, several areas of these correlator
specifications would benefit from more careful study. While the need for
ancillary data (§3.9) is obvious, whether it would be useful to
apply any calibration derived therefrom on-line is not. Although doing this
in the correlator would significantly complicate the design, the prospect of
averaging down the data before writing them out is very attractive. Perhaps
one could employ an intermediate, real-time processor directly after
correlation to do some simple calibration and flagging before the data are
written to disk. Similarly the
maximum channel width is important in limiting the output rate, but will
be determined by the accuracy of the delay settings and the frequency
characteristics of the LO and related systems.
By far the largest source of uncertainty however is the possibility of
significant foreign partners. If either the European LSA or the Japanese
LMSA does
in fact merge with the MMA, the budget will grow considerably, and a rather
different instrument will result. This uncertainty is reflected in several
areas of the correlator specifications. The most obvious is the number of
antennas, which might go from 40 to a hundred or more. This together with
the larger collecting area leads to a desire for more subarrays and more
stringent dynamic range limits. Larger antennas have smaller primary beams,
which make one want shorter integrations to allow mapping a given sky area
in the same total time. Some of the joint proposals, particularly the
Japanese, also push for longer baselines.
The MMA correlator will be an impressive and complex instrument. Assuming
100 MHz channels and 1 second integrations, the minimum data rate for a
full-bandwidth, 8 GHz continuum experiment will be
visibilities per second.
For an 8000-channel line observation using 0.1 second integrations this
jumps up by a factor of 1000. By contrast the VLA produces at most
3,300 visibilities per second, the VLBA about 3.3 million.10 A standard
figure of merit (or at least size!) for a correlator is the number of
multiplications per second, computed as 
. Using the requirements given above, the
proposed MMA weighs in at
multiplies per second, compared to 
for the current VLA,
and 
for the VLBA and the GBT.
The MMA will be a great leap forward for millimeter astronomy, much as the
VLA was for radio astronomy in the '70s. Almost 30 years later the VLA is
limited primarily by its original correlator, which both restricts the total
bandwidth and severely constrains the number of channels one can use to
cover that bandwidth. Unless the budgetary process changes significantly we
can expect the initial MMA correlator to be similarly long-lived. We are
designing this instrument therefore not for the 1990s, nor yet for first
light in 2005 or beyond, but for the maturity of the instrument 40 years
hence. What seems ambitious now may by then seem merely prudent.
We are very grateful to the many people who carefully reviewed this
document, to wit: Tim Bastian, John Benson, Bryan Butler, Barry Clark,
Larry D'Addario, Ray Escoffier, and Craig Walker. In addition, Dan Merteley
and Greg Taylor commented on the RFI discussion, as Chris Carilli did on the
sections on calibration. Finally, Ray Escoffier was infinitely patient and
helpful in answering a huge number of MPR's questions about correlators.
#1
=1cm=1 #1
Those of the following which were not cited explicitly are useful references
either on millimeter array science in general, or on correlator design
issues in particular.
Cernicharo, J. & Reipurth, B. 1996, ApJ (Letters) 460, L57.
Churchwell, E. et al. 1997, MMA Advisory Committee Report,
November 1997.
Clark, B.G. 1992, MMA Memo No. 85: Some Remarks on MMA System
Design.
Cornwell, T.J., Holdaway, M.A., and Uson, J.M. 1993, A& A 271,
697.
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The translation was initiated by Kate Weatherall on Tue Feb 17 13:40:41 MST 1998
- ...design.
- Although radio frequency interference (RFI) can be quite
narrow, most services operating at these high frequencies do so because they
need broad bandwidths, a few MHz or more. High spectral resolution is
therefore not needed for finding and excising interference signals (see
§3.11). An exception is internally-generated interference, which tends to
be quite narrow; hopefully the MMA will try to avoid the kind of internal
emissions which currently plague the VLA.
- ...simultaneously,
- One might be able
to simply define a small number of single-dish subarrays and use those,
rather than recording data from all MMA dishes at once. But it is more
efficient to time-multiplex by using the full array consecutively for
interferometric and single dish measurements, because the number of
interferometric baselines goes as the number of antennas squared; and it is
quite possible that a non-negligible fraction of the array's time may have to
be used for single-dish observations (as much as 10-25%, for large-scale
mosaics; see MMA Memo 128, Holdaway & Rupen 1995). The use of the
MMA antennas for single dish observations clearly needs much more attention
than it has yet received.
- ...data.
- Some have proposed outfitting only a subset of the full
array with special single-dish equipment, such as nutating subreflectors, total
power continuum detectors, and multi-beam feeds.
- ...data.
- This paragraph is taken almost verbatim from an email
from Barry Clark (30 December 1997). Thanks Barry!
- ...timescale.
- Of course, current
interferometers often do not provide this sort of information. But the high
operating frequencies of the MMA, together with the availability of
sophisticated algorithms (currently under development; T. Cornwell 1998,
priv. comm.) which explicitly take these data into account when imaging,
make this information much more important for the MMA than for existing
telescopes.
- ...phase,
- Amplitude corrections can be made on much longer
timescales (C. Carilli 1998, priv. comm.).
- ...frequency.
- Thanks to Dick Thompson for making this
point.
- ...model.
- The correlator model refers to the model
of the telescope geometry and atmosphere used during correlation.
- ...Sources:
- With thanks as always
to Tim Bastian.
- ...3.3 million.
- Note
that the VLBA correlator is currently limited by disk write times to
actually writing out only 64,000 visibilities per second.
Kate Weatherall
Tue Feb 17 13:40:41 MST 1998