MMA Antenna Diameters--Some Thoughts on the Effect on Science Al Wootten 2 November 1998 Dave had an excellent discussion in his memo of 21 October. To summarize his discussion, he pointed out that while the cost equation for antenna diameter may be useful in the definition of an array project, maximizing scientific return depends on different variables, ones which may be more difficult to define. In a nutshell, as Dave put it, going to bigger antenna sizes lowers the cost curve, increasing the optimum size. The total collecting area grows, but at what cost to the science? With this in mind, I have reviewed the submillimeter science arguments put together by the MAC. I have culled out those experiments which might be impacted the most by using fewer antennas of larger diameters. Then, with reference to MMA Memo No. 178 by Holdaway, I have attempted to determine which measure of image quality would be most applicable to the experiments. Holdaway's Simulations The question is 'How much might imaging performance be compromised by employing larger antennas?' Holdaway addressed this in MMA Memo No. 178, in which he considered the effects of pointing errors on mosaic images with 8m, 12m and 15m antennas. Three measures of imaging quality were evaluated: dynamic range, Median image fidelity and first moment fidelity. The dynamic range between the array of 40 x 8m antennas and 60 x 12m antennas degraded from 250 to 100 at 650 GHz. For an array of 80 x 10m antennas this degradation would have been somewhat less given the models employed, but it might be as much as a factor of two. Median fidelity fell from 22 for the 8m array to about 12 for the 12m array. On Holdaway's plots, this looks fairly linear, so we might guess that for the 10m array fidelity might decline by 25% or so. The first moment fidelity weights brighter parts of the image more heavily; there is little difference in Holdaway's comparison between 8m and 12m antenna arrays, so the difference between 10m and 12m would probably be negligible. Antenna performance affecting image quality * Surface accuracy Since high frequency efficiency decreases rapidly as surface accuracy tolerance is loosened, the penalty for relaxing this specification is foremost a limitation on the submillimeter science. An active surface might help, but since there is little field experience with this on single structures the complexity it introduces seems daunting on an array the size of the MMA or LMA. * Pointing error Dynamic range in maps decreases as tolerance is loosened, especially in the submillimeter. Active devices such as tiltmeters, CFRP reference structures, laser metrology, or thermistor networks might be added; some of these mitigate the errors on existing antennas now. nonetheless, no existing telescope has pointed to the MMA specs. All experience teaches us that pointing evolves, sometimes rapidly, as structures wear. Keeping up with the evolution of many dozens of structures is a daunting task. * Fast switching This is the primary calibration means of the antennas. While water vapor radiometry can achieve some improvement in calibration, few would argue that it can match the improvments which might be achieved through this tested technique. Less capable phase correction probably impacts submillimeter and precision imaging science most severely. A less capable antenna would have a lower resonant frequency, with worse performance in the windy Chajnantor conditions. * Wide field imaging This clearly drives one toward smaller antennas. But at submillimeter wavelengths, the primary beam is already near 10 arcseconds. SCUBA images of galactic objects have taught us that the submillimeter sky is nearly as full of emission as IRAS proved the 100 micron sky to be. Two important areas of science will be compromised by large antennas with less precise imaging performance: the distribution and physics of dust, and the distribution and physics of molecular emission. First we discuss dust in protostars. As the AC pointed out, it offers our best probe of the mass distribution in interstellar structures; the MAC notes the strong case that submillimeter observations are critical to dust study. In a typical Class 0 protostar such as S68N or L483, 75% of the flux lies on scales larger than 10 arcseconds. Existing interferometers offer an advantage in that they penetrate this bright region to offer a detailed picture of the protostellar disk. We might expect the MMA to illustrate how material flows through the envelope into the disk of a forming star. In its report, the MAC stated 'The MMA will be able to provide even higher resolution (than SCUBA) and over large fields of view by fast OTF imaging techniques or mosaicing.' I believe that this goal will be compromised by larger antennas with poorer specifications; quantification of the amount by which they might be compromised will be difficult to estimate. How important are submillimeter mosaics, for instance, compared to mosaicked 1.3mm or 3mm images? One would like a new instrument to test paradigms. One such paradigm is Shu's scenario of star formation, in which an isothermal structure characterized by a r$^-2$ density law undergoes inside out collapse, with the density law of the central collapsing region tending toward r$^-3/2$. For most modeled sources, the expansion wave signalling the onset of collapse moves outward at the local sound speed; it is the zone of demarkation between these two density law regimes. Observationally, it has proven difficult to identify this wave; in most modelling it is chosen so that the model data fits the observed data. Partly, this is because given the collapse timescales and the evolutionary state which we believe Class 0 SED objects are in, this zone lies just at or just below typical single antenna resolution but above typical interferometer resolution, in an outer zone of the envelope where emission at the low frequencies at which these instruments work best is weak. While one might hope that the MMA would be able to overcome this difficulty, identification of this zone might be best accomplished at submillimeter wavelengths, where excellent fidelity in mosaicking would be required. The MAC also identified mapping of variations in dust temperature and emissivity across molecular clouds through comparison of maps at 450, 850 and 1300 microns. This can only be accomplished if the imaging characteristics at the submillimeter frequencies are not compromised; this project will be carried out with more difficulty with larger antenna diameters. Dynamic range and median fidelity are probably the most appropriate measures of image quality. Holdaway's memo suggests that the penalty for employing larger diameter antennas would be on the order of 25-30%. The second major area of compromise is in the excitation studies of molecular lines. While multitransition studies have been a staple of single antennas for many years, few, if any have been published from interferometric images. This is precisely because of the poor spatial frequency sampling properties of existing arrays, a deficiency we have designed the MMA to overcome. Owing to the expected poorer pointing performance at high frequencies of the larger antennas, this important science goal is compromised by increasing antenna diameter. This occurs because, except for certain symmetric top molecules which have lines at several energies juxtaposed in frequency, the lines one wishes to compare to derive temperature or density images of a cloud lie at disparate frequencies. Unless the molecule under scrutiny is a symmetric top molecule limited in emission region by its chemistry, such as CH$_3$CN, multitransition studies cannot be done. Even the slightly asymmetric top molecule H$_2$CO poses challenges--a study by Mangum and Wootten with the OVRO interferometer at 218 GHz compared adjacent lines at 23 (K=0) and 65 K (K=2) above ground--energies identical to those of the oft-used ammonia (1,1) and (2,2) lines at centimeter wavelengths. They found that so much emission was missing--resolved out--in the 30" primary beam in DR21(OH), which lies at several kpc distance, that the temperature map they had sought to determine could not be derived from the data. This problem becomes worse at submillimeter wavelengths. As the MAC pointed out, submillimeter molecular line observations would actually have better sensitivity than observations in the 2mm or 3mm bands, when compared at constant angular resolution. The fixed-resolution imaging necessary to derive phsical conditions and molecular abundances from multi-transition observation and subsequent excitation analyses would be compromised by larger antenna diameters relative to smaller ones. In my experience, the higher excitation transitions arise in compact structures. They also tend to lie at higher frequencies. This suggests to me that first moment fidelity is the most appropriate quantity to gauge image quality; this quantity changed mininally in Holdaway's simulations. Excitation studies would suffer only marginally from increased antenna size. The neutral carbon lines at 492 and 809 GHz have been identified as important targets for MMA imaging. Although emission from these lines is ubiquitous, there is little evidence for emission from very small scale structures (though of course a layer of neutral carbon emission is expected in transition regions, such as photodissociation layers). Larger antenna sizes can be expected to compromise performance in accurate imaging of [CI]. Carbon lines tend to be diffuse, and I would guess that median fidelity would be the best measure of image quality, which might suffer by a few tens of per cent in an array employing larger antennas. The MAC identified several areas of planetary science which would benefit from submillimeter performance of the MMA. Imaging of large planets, difficult or impossible today, would remain compromised in an MMA outfitted with large poorly performing antennas. Although IRAM produced some spectacular results from observations of C/ Hale Bopp, only a few per cent of the flux was recovered. Like young protostars, most of the flux lies in the envelope, the coma. In a comet, the coma material carries important information on how molecules transform when long-frozen bodies begin to evaporate. The MAC found 10m antennas to be only marginally acceptable in terms of available field of view; larger antennas would compromise planetary science. The MAC found that image fidelity, the difference between the image formed by the interferometer and a true image of the source, should be better than 1%. It must be able to achieve this fidelity quickly as planets change during single transits through rotation and evolution of weather patterns. At the highest frequencies, this may translate into a problem for larger telescopes, which require more pointings for mosaicked images of planetary atmospheres on the larger planets. I would guess that images used in cometary science would be best judged by dynamic range and median fidelity, with perhaps several tens of per cent penalty for using larger antennas. Planetary science images will be, in general, strong and probably best measured by first moment fidelity. It would seem that the 1% goal would be adequately addressed by either 10m or 12m antenna diameters. In summary, it appears to me that some critical science experiments would be affected by degradation of perhaps 20-30% in the worst case by employing larger antennas in the array. However, much of the science would be relatively unaffected. I thank Jeff Mangum for useful comments.