New Frontiers in Solar Physics:

Broadband Imaging Spectroscopy with the Frequency Agile Solar Radio Telescope

Prepared by:
T.S. Bastian (NRAO), D.E. Gary (NJIT), and S.M. White (UMd)
Introduction
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The Sun is an ordinary star made extraordinary by virtue of its close proximity. Despite its stature as an ordinary star it confronts us with a large number of problems that demand a fundamental understanding of an importance well beyond the Sun itself, for it is often against our understanding of the Sun that we measure our understanding of stars and other astrophysical objects and processes. Outstanding problems in solar physics include (1) the magnetic dynamo and the solar cycle; (2) the solar atmosphere and solar wind; and (3) solar energetic phenomena. Related problems include those associated with the impact of the Sun on the Earth and near-Earth environment, problems which have practical consequences for life on Earth and in space.  Radio observations play an important role in our understanding of all of these phenomena.
 
Background

Historically, exploration of radio emission from the Sun has proceeded along two, orthogonal lines: imaging observations and spectroscopy. Imaging observations have been performed at discrete frequencies with interferometric arrays for many years. Spatially unresolved broadband spectroscopy has been pursued using a number fixed-frequency polarimeters while high-resolution spectroscopy has exploited swept-frequency or broadband digital spectrographs. The capabilities and frequency coverage of instruments that are currently used for solar observations are summarized in Appendix A.

In order to fully exploit the diagnostic potential of radio emission from the Sun, both imaging and spectroscopy must be obtained simultaneously.  A consensus exists among the international solar radio community, as expressed at an NSF/NASA supported Solar Radio Telescope Workshop held in San Juan Capistrano in 1995, that it is possible, highly desirable, and timely to construct an advanced, solar-dedicated radiotelescope designed to perform broadband, high--spatial--resolution imaging-spectroscopy.  This consensus is reflected by the broader community in the report of the NRC/SSB  Task Group on Ground-based Solar Research: in their four recommendations regarding facilities, the task group recommended pursuing "exploratory development of a high-resolution frequency-agile solar radio telescope (FASR)".
 
The Frequency Agile Solar Radiotelescope

The Frequency-Agile Solar Radiotelescope (FASR) represents a major advance over existing facilities.  The FASR is a solar-dedicated radio telescope designed to produce high-quality images of the Sun and solar phenomena over a core frequency range of 0.3-30 GHz. It is designed to do so with sufficient angular, spectral, and temporal resolution to fully exploit radio emission from the Sun as a diagnostic of the wide variety of physical processes which occur there.  As a broadband, imaging spectrometer, the FASR will be a versatile and unique instrument producing unique observables. These will be exploited to address a broad science program. FASR will be extremely flexible, allowing it to carry out basic research programs in addition to providing, on a routine basis, a number of unique data products of interest to the solar forecasting and space weather, geomagnetic, ionospheric, and aeronomy communities.

We now discuss the science themes and goals addressed by the FASR, the science requirements of the instrument, and the main design considerations.
 
Science with the FASR

The decimeter through centimeter wavelength range offers a rich variety of diagnostic tools with which to address a broad program of solar physics. FASR is designed to exploit these diagnostic tools. The following list outlines the three broad themes to be addressed by FASR:

With its unique and comprehensive capabilities the FASR also has tremendous potential for new discoveries and unanticipated uses of the data it produces.

In the remainder of this section, we discuss each of these science themes and the associated goals in greater detail. Before doing so, however, it is worth making a brief digression to remind readers of the radio emission mechanisms relevant to the Sun.
 
Emission Mechanisms

For most astrophysical objects, continuum emission in the decimeter to centimeter wavelength range is due to incoherent synchrotron and/or free-free radiation. Emission in spectral lines is also available for study, notably HI, radio recombination lines, and molecular lines (e.g., OH, H2O, SiO, etc.). The temperatures, densities, and magnetic field strengths encountered on the Sun are such that spectral lines play no role. There is no HI; nor are molecular lines available. Radio recombination lines of H and other ions are rendered undetectable by pressure and/or Zeeman broadening. Furthermore, polarimetric techniques are limited. Strong differential Faraday rotation washes out any linearly polarized component in most cases (but perhaps not all).

Nevertheless, the radio spectrum at decimeter and centimeter wavelengths is rich in diagnostic potential. Because two of the natural frequencies of the solar atmosphere -- the electron plasma frequency and the electron cyclotron frequency -- are often of the same order as the radio frequency in which observations are made, additional emission mechanisms are available for study which are not encountered in other astrophysical contexts.  Three distinct radio emission mechanisms are widespread in the solar atmosphere and are commonly available for diagnosing physical conditions in the source:

Several other emission mechanisms may play important roles  on the Sun and offer additional diagnostics. These include the cyclotron maser (Melrose & Dulk 1982), radiation from electron accelerated in strong DC electric fields (Tajima et al. 1990), and transition radiation resulting from the interaction of electrons with small scale turbulence (Fleischman & Kahler 1992). One, two, or even more of these emission mechanisms may occur simultaneously on the Sun. An example is shown in Figure 1.
 
 
Figure 1
Full-disk 17 GHz images of the Sun made with the Nobeyama radioheliograph.  The brightest feature in the total intensity image (Stokes I, left panel) is a set of post--flare loops on the east limb in which the radio emission is produced by a mixture of optically thin bremstrahlung from 2 x 107 K plasma, and gyrosynchrotron emission from electrons accelerated to energies of hundreds of keV.Just to the south of the flare, and probably associated with it, a prominence can be seen erupting off the east limb, a consequence of a CME.  The prominence (8000 K) emits bremsstrahlung, but is opticallythick.  Closer to the center of the Sun lies an active region containing several bright, circularly polarized (Stokes V; right panel) features, the result of gyroresonance emission. Such emission at 17 GHz requires magnetic fields of at least 1500 G in the solar corona. FASR will make images with spatial resolution (up to 14 times) better than this image at all frequencies above 2 GHz.

The major advance offered by the FASR is time-resolved, broadband, imaging-spectroscopy. It represents orders-of-magnitude improvement over any radio facility currently available for solar studies.  The FASR will produce high-spatial-resolution images with excellent dynamic range and fidelity, and with sufficient spectral and temporal resolution to enable us to measure the radiation spectrum and its evolution in time at each point in the field of view. In so doing it will enable full exploitation of the many radiative diagnostics available.  We now return to the science themes that the FASR is designed to address.
 
Transient Energetic Phenomena

Transient energetic phenomena on the Sun include flares, coronal mass ejections (CMEs), and filament or prominence eruptions. Flares involve the catastrophic release of energy in the low corona. Plasma is heated and particles are accelerated to relativistic energies on short time scales. A large flare may require the acceleration of ~1037 electrons s-1 to energies >20 keV for periods of tens of seconds (Miller et al. 1998). CMEs involve the destabilization and expulsion of a significant portion of the corona. CMEs are now recognized to be the primary drivers of interplanetary disturbances and geomagnetic effects. A filament is ejected from the Sun as part of the destabilization process that produces CMEs.
 
 
Figure 2
Example of the time evolution of a flaring source at cm-l.  The contours represent 4.9 GHz (l=6.1 cm) VLA observations of the M8.7 flare in AR 5528 studied by Bastian & Kiplinger (1991). The greyscale image shows the Ha emission, characterized by two ribbons. Large Sunspots are seen to the NW. a) In the early phase of the flare, the region containing the strongest magnetic fields emits; b) The magnetically conjugate footpoint then emits; c) The 4.9 GHz emission bridges the magnetic neutral line; d) The entire 4.9 GHz source is optically thick near the time of the flare maximum and the location of maximum radio brightness lies between the magnetic footpoints.

The study of flares offers one of the best available means of observing energy storage, energy release, particle acceleration, wave-particle interaction and particle transport in an astrophysical plasma in detail and under a variety of conditions. Similary, the study of CMEs yields insights into the destabilization of MHD structures, the formation of MHD shocks, shock acceleration of electrons and ions, and the impact of shocks and energetic particles on the IPM and the near-Earth environment.

The FASR will, for the first time, allow full exploitation of microwave/decimetric emission for flare studies. Moreover, it will provide an integrated view of the role of coherent burst emissions at decimeter wavelengths and the incoherent gyrosynchotron emission at centimeter wavelengths. The possibilities are numerous and exciting:
 
Location and properties of the energy release site
Work over the past decade, in large part at radio wavelengths, has demonstrated that energy release in solar flares is fundamentally a fragmentary process.  Multitudes of type III and reverse drift type III bursts--resulting from bidirectional electron beams--accompany the impulsive phase of energy release in many flares (Aschwanden et al. 1995).  The decimetric type III bursts are believed to be intimately related to the primary energy release (Figure 3), with each beam perhaps corresponding to an elementary energy release event. While spectroscopic observations of classical and reverse-drift type IIIs during flares have been performed, they have rarely been imaged directly at decimeter wavelengths, and then only at fixed frequencies (Figure 4). The most interesting information is the energy release site, the location where the type III and reverse-drift type III is initiated. Since this could be at any frequency over the decimetric range (but most typically in the 500-1000 MHz range), this can only be done with a broadband telescopesuch as FASR.  Furthermore, broadband imaging spectroscopy will allow the trajectories of both upward and downward electron beams to be traced out in the flaring volume. The trajectory mapping will provide the means of identifying the location of the energy release, the electron number density in the energy release site, and will trace out the density along the electron beam trajectory. These measurements will place important, new, and unique constraints on the location and physical properties of the energy release site, on the relevant magnetic topology, and on the nature of the energy release process itself.
 

Figure 3
Cartoon of a flare model suggesting a global view of acceleration and ablation processes in the context of density measurements by coherent radio bursts and SXR emission.  The pannel on the right illustrates a radio spectrogram (dynamic spectrum) with bursts indicated schematically. The acceleration site is located in a low-density cusp from where electron beams are accelerated in upward (m-l type III) and downward (reverse-slope bursts) directions. (from Aschwanden & Benz 1997).

 
Figure 4
An example of a type U burst observed by the VLA. A type U burst is a type III burst in a closed magnetic loop. Spectrographic records from the PHOENIX spectrometer (ETH/Zurich) show that the VLA, imaging the burst at 1446 MHz on 13 August 1989, sampled the frequency corresponding to the apex of a magnetic loop anchored in the active region. The magnetic field lines shown are the result of a potential field extrapolation using the magnetogram (color) as a boundary condition (from Aschwanden et al. 1992).
Magnetic field in the flaring volume
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Microwave emission in flares is due to incoherent gyrosynchrotron emission from electrons with energies of several 10s of keV to several MeV that have been injected into coronal magnetic loops.  The peak spectral frequency npk at a given location depends sensitively on the local magnetic field strength and the angle between the line of sight and the local magnetic field vector. It typically occurs between 5-15 GHz. Joint observations of npk and the source polarization will allow the magnetic field strength and orientation to be inferred for the flaring source as a function of time. Additional and independent constraints are available on the magnetic field. An example is the use of timing comparisons between HXR and microwave emissions which ``calibrate'' the harmonic of the emitting electrons as a function of location in the source and hence, the magnetic field (Bastian 1999). No other techniques are available for this purpose.
 
Electron acceleration and transport
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The microwave spectrum is a powerful diagnostic of the details of the emitting distribution of energetic electrons.  The optically thin part of the spectrum is sensitive to the details of the electron distribution function, including high energy cutoffs and anisotropies. It is also worth pointing out that, due to the dispersive properties of coronal magnetic loops (Bastian, Benz, & Gary 1998), the relative timing of temporal features at different frequencies offers an additional diagnostic of acceleration and transport (Figure 5). In particular, joint microwave/HXR observations can be used to determine the roles of Coulomb collisions and wave-particle interactions (e.g., whistler waves) to pitch-angle scattering and electron acceleration in flares. Although space based HXR imagers will provide images of the nonthermal HXR emission from < 10 keV to MeV energies in the near future (the HESSI SMEX), these emissions originate from precipitation points, where fast electrons impact the dense atmosphere at the foot points of flaring magnetic loops. In contrast, the FASR will image emission whenever and wherever energetic electrons are present in the flaring volume.
 
 
 
Figure 5
An example of the time variation of the Nobeyama 17 GHz brightness compared to the HXR count rate as measured by BATSE/CGRO for a simple magnetic loop.  The panels to the left show a 17 GHz map at the time of the flare maximum. Light curve B shows Stokes I near the loop top. Light curve A shows Stokes V at the right-circularly polarized footpoint; Light curve C shows the absolute value of Stokes V for the left-circularly polarized footpoint.  See Bastian, Benz, & Gary (1998).
Chromospheric ablation
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Electrons accelerated to high energies can stream along the coronal magnetic field to the chromosphere if their pitch angle is sufficiently small. There, they collide with the relatively dense, cold, plasma and produce HXR emission via nonthermal bremsstrahlung. The electrons are thermalized and heat the chromospheric plasma which is ablated into the corona where it emits copious SXRs.  In addition to diagnosing the magnetic field and the details of the energetic electron population, spatially and spectrally resolved radio observations over a broad frequency range offer a means of probing the changing density of the ambient plasma due to chromospheric ablation. Razin suppression depends on the density of the ambient plasma and the local magnetic field strength. Since the magnetic field will be constrained by other means, the ambient density may be inferred as a function of position and time during the courseof a flare. An alternate and independent means of probing chromospheric ablation is to exploit the interaction of reverse-slope type IIIdm bursts with the ablated material (see Aschwanden & Benz 1995).
 
CME detection
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Coronal mass ejections have become the main focus of studies of space weather and the near--Earth space environment. Bastian & Gary (1997) have shown that FASR will likely be able to detect the thermal bremsstrahlung from CMEs at decimetric wavelengths.  The advantages of CME detection at radio wavelengths are: i) there is no occulting disk, so earth-directed CMEs will be detected; ii) CMEs will be detected in their nascent stages of development and can be directly associated with structures such as filament channel arcades; iii) unlike SXR and white-light observations, observations at radio wavelengths are sensitive to both thermal free-free emission from CMEs and possible nonthermal constituents.  Owing to its frequency agility the FASR could provide a comprehensive observational picture of CMEs and associated phenomena over a wide frequency range.
 
The Nature and Evolution of Coronal Magnetic Fields
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One of the strengths of solar radio astronomy is that it is the only practical technique by which magnetic fields in the solar corona can be measured directly. This measurement utilizes the fact that gyroresonance emission renders the corona optically thick in regions of strong magnetic field, and at a given frequency the radio emission arises in a very thin layer of constant magnetic field strength in the corona.  Quantitative knowledge of coronal magnetic fields is crucial to virtually all solar physics above the photosphere, including the structure and evolution of active regions, flares, filaments, and coronal mass ejections.  The measurement of magnetic fields in the photosphere using optical and infrared lines is a well-developed technique, and in the absence of routine measurements of coronal magnetic fields, considerable resources are devoted to extrapolating the observed surface magnetic field distribution into the upper chromosphere and corona under the assumption that it is potential or force-free.  An example of such a force-free magnetic field extrapolation is shown in Figure 6. These extrapolations are difficult, depend sensitively on measurements at the photospheric level, and rely on assumptions that need to be more thoroughly tested.

Radio observations provide the means of both directly and indirectly measuring magnetic fields in the corona. However, such measurements require a broadband imaging capability. The FASR provides that capability.
 
Coronal magnetography in active regions
Active regions are those regions on the Sun where magnetic fields have bouyantly emerged through the photospheric surface into the corona. Their photospheric signature is sunspots, but their true nature is revealed by observations in EUV, SXR, and radio emission: active regions are complex and evolving magnetic structures composed of magnetic loops containing hot plasma. As their name implies, flares and other forms of solar activity occur in active regions.

Radio observations provide the only means by which coronal magnetic field strengths >100 G can be measured above the chromosphere. The magnitude of the magnetic field can be obtained rather directly at the base of the corona by exploiting the break in the spectrum of thermal gyroresonance emission where the electron temperature drops to sub-coronal values. However, the FASR will, in addition, enable us to constrain the vector magnetic field and its evolution in active regions. Figure 6 shows how gyroresonance emission at different frequencies arises on nested surfaces of constant magnetic field.  The particular isogauss level at which the corona is rendered optically thick to gyroresonance absorption depends on the magnetionic mode of the radiation (ordinary or extraordinary) and the orientation of the field. The dense spectral coverage provided by the FASR provides complete sampling of the coronal volume over active regions. Dense spectral coverage translates into continuous magnetic field strength coverage.  When coupled with extrapolation techniques FASR observations provide the means of performing three-dimensional coronal magnetography where the magnetic field strength exceeds approximately 100 G.
 

Figure 6
A perspective view of a complex sunspot group (7 May 1991) in optical continuum is shown with field lines extrapolated into the corona using a nonlinear force-free extrapolation by Z. Mikic. The three surfaces are the calculated gyroresonant surfaces in the corona that will dominate the radio opacity at each of three radio frequencies: 5 GHz (B = 600 G), 8 GHz (B = 950 G) and 11 GHz (B = 1300 G). (Produced by Jeongwoo Lee/NJIT.)
Use of mode coupling properties
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Another unique capability provided by the FASR is the means of constraining the magnetic field topology above active regions using the mode coupling properties of the radio radiation.  When radio radiation traverses a magnetic field wherein the longitudinal field component changes sign, the polarization of the radiation may reverse, depending on whether the coupling between the ordinary and extraordinary modes is strong or weak.  As seen in projection against the Sun by a distant observer, the line which demarcates the reversal in the sense of circular polarization is called the ``depolarization strip'' (e.g., Bandiera 1982). Using the frequency agility of the FASR, a ``depolarization sheet'' can be deduced above active regions over the frequency range where circularly polarized emission is present, thereby providing additional constraints on the nature of magnetic fields in the solar corona.

Measurements of the magnetic field in and above active regions will provide critical new insights into the temporal evolution of coronal magnetic fields, the role of currents in the corona, and the storage and release of magnetic energy. In addition to providing critical inputs to the important problem of the nature and evolution of coronal magnetic fields, these measurements will likely have practical utility as well. We return to this point in Section 3.
 
The Solar Atmosphere

Our understanding of the solar atmosphere has undergone significant changes of perspective over the years. All have been driven by observational advances. With the discovery of a high temperature corona in 1930s, and later the solar wind in the 1960s, a great deal of work has been devoted to understanding the nature of the nonradiative mechanism(s) required to sustain both phenomena. Early theories of the solar atmosphere were spherically or azimuthally symmetric. One of the most important lessons of the Skylab mission in the early-1970's was that the corona is far from symmetric -- it is highly structured by the magnetic field, as well as by density and temperature gradients, on a wide variety of scales. More recently, the SXT on board the Yohkoh satellite has revealed that, in addition, the solar corona is highly dynamic. It is constantly changing on time scales of seconds to minutes, hours, days, and years. Coupled with progress at radio, UV, and optical wavelengths, it is now appreciated that the entire solar atmosphere -- from the photosphere to the corona, and out into the solar wind -- is a highly structured and restless entity.

The FASR can make significant contributions to our understanding of the structure, dynamics, and energetics of the solar atmosphere.
 
Coronal heating
One of the fundamental questions in solar physics is how the solar corona maintains its high temperature of several million Kelvin above a surface with a temperature of 6000 K.  The power needed to maintain the corona above an active region against radiation and conduction losses is >1028 erg s-1 (Shimizu 1995).  The leading theoretical ideas for how the corona is heated is either some form of resonant wave heating (e.g., Ofman, Klimchuk, & Davila 1998 ) or ``nanoflares'' (Parker 1988), although there exist many other models. The FASR will provide observational inputs with which to test these, and other types of model.

Wave heating models make specific predictions of where and on what time scales energy deposition occurs in coronal magnetic loops. The FASR will provide a detailed history of the temperature, density, and magnetic field in coronal loops in active regions, from which the rate of energy deposition can be calculated as a function of position and time.

The role of "nanoflares" -- tiny, flare-like releases of energy from small magnetic reconnection events -- depends critically on the rate at which such events occur.  Numerous studies have shown that X-ray events ranging over as much as five orders of magnitude in energy, from 1027 to 1032erg, form a single powerlaw with slope 1.5-1.6.  Smaller events cannot be energetically significant relative to the larger events unless the rate distribution at lower energies becomes significantly steeper. It is therefore of critical importance to characterize the distribution and energy content of the smallest energy release events on the Sun.

Recent observational work in this area at radio wavelengths has been promising.  Using broadband, total power measurements, Gary, Hartl, & Shimizu (1997) established that the 1027 erg SXR events in active regions studied by Shimizu (1995) are accompanied by nonthermal electrons; i.e., they are flare-like.  Even events that are near the limit of visibility for the {\sl Yohkoh} SXT typically have radio counterparts that are easily detectable in total power by small non--imaging radio telescopes. High-quality imaging will lower the flux limit one achieves in microwaves by orders of magnitude.  For example, Gopalswamy et al. (1994) have demonstrated this with the VLA by detecting transient events over the penumbra of a large sunspot with total energies much above Parker's (1988) canonical nanoflare value of 1024 ergs. Recently Benz & Krucker (1999), using multiband VLA and SoHO EIT and MDI data, have show that even tiny transient events in the quiet chromospheric network are, in fact, flare-like.

To date, the observations have been insufficient to determine the contibution of these tiny flare-like events to the coronal heating energy budget. The counting statistics and frequency coverage have been inadequate. The FASR will greatly improve on previous work by providing vastly better frequency coverage and a sensitivity comparable to the VLA.  The study of microflares with FASR will be aided by the instrument's flexibility, which will allow the data to be treated in an optimum way for a given goal.  For example, spatial, spectral, and/or time resolution can be traded off for sensitivity at the data analysis stage.  This and the instrument's full-Sun capability should allow FASR to obtain accurate counting statistics on the occurrence rate of these events, and to determine whether that rate increases greatly enough at low energies to heat the corona.
 
 

Figure 7
Temporal evolution of network flares observed in SXR and radio emission on 20 Feb 1995. The image at the top shows the region observed in SXRs; the inset shows its location on the solar disk. Enhanced emission is dark. The locations of network flares are indicated by boxes. The plots below show the temporal variations of the SXR flux in the Al.1 and AlMg filters, and the 2 cm radio emission for the different network flares. (from Krucker et al. 1997)
Structure and dynamics of the chromosphere
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In weak-magnetic-field regions, thermal gyroresonance emission is negligible and the radio emission is largely due to thermal free-free emission [As noted in the previous section, however, there is evidence, that tiny, transient radio events in the chromospheric network may be flare-like and magnetic in origin (see Figure 7; Krucker et al. 1997; Benz & Krucker 1999)].  Small magnetic elements may therefore contribute a transient nonthermal component to the thermal background emission.}.  Microwave radiation is formed under conditions of LTE and the source function is therefore Planckian. For microwave observations the Rayleigh-Jeans approximation is valid and the observed intensity is linearly proportional to the kinetic temperature of the emitting material for optically thick sources (in contrast with lines in the visible and UV). The optical depth is  proportionsal to n2n2 T 1.5-- by varying the frequency n one samples the thermal state of optically thick plasma at heights ranging from the mid-chromosphere to the low-corona. The broadband imaging capability of the FASR will be exploited to probe the thermal structure of the solar atmosphere in active regions, the quiet Sun, and coronal holes, as well as in filaments and prominences.

The chromosphere will be a particularly interesting target for the FASR. In recent years it has become evident that the prevailing semi-empirical chromospheric models, largely based on non-LTE UV/EUV line and IR/submm/mm continuum observations and computed under the assumption of hydrostatic equilibrium, are in stark disagreement with observations in bands of carbon monoxide (CO) and with microwave observations. In particular, observations of the CO molecule near 4.7mm show that the low-chromosphere contains a substantial amount of cool (3800~K) material leading to the view that the chromosphere is fundamentally bifurcated between cool and hot material (e.g., Ayres & Rabin 1996).  Accurate broadband microwave (1-18 GHz) spectroscopy of the quiet Sun (Zirin, Baumert, & Hurford 1991) convincingly demonstrates that the prevailing semi-empirical models include an over-abundance of warm chromospheric material (Bastian, Dulk,  & Leblanc 1996).

These developments have caused the solar community to begin to re-think the solar chromosphere.  Schematic multi-component models have been proposed which emphasize the pervasive cool component in the solar atmosphere (e.g., Ayres & Rabin 1996). Another approach has recognized that chromospheric dynamics play a critical role in understanding the structure of the chromosphere (Carlsson & Stein 1995).  Testing of modern chromospheric models require spatially and temporally resolved observations of the thermal state of the chromosphere on the relevant spatial and temporal scales.

The FASR design will allow us to sample the thermal structure of the chromosphere down to the height where Te~ 8000 K. The sensitivity of the FASR, as presently conceived, will allow us to study the time variability of the thermal structure of the solar chromosphere in a single frequency band on a timescale ~1 min (TB ~ 100 K). Over a period of several hours, the FASR will provide high quality maps of the mean thermal state of the chromosphere over its entire frequency range.  FASR observations will therefore provide a comprehensive specification of the thermal structure of the chromosphere---in coronal holes, quiet regions, enhanced network, plages---as an input for modern models of the inhomogeneous and dynamic chromosphere.
 
 

Figure 8
View of a quiet region near the center of the solar disk on 12 July 1996. The left panel shows the longitudinal component of the photospheric magnetic field as observed by SoHO/MDI. The contours represent radio intensities emitted by the chromosphere and transition region as observed by the VLA (yellow = 2 cm, green = 3.6 cm, blue = 6 cm). The right panel shows the coronal emission measure in the 1.1-1.9 106 K temperature range as derived from SoHO/EIT Fe IX/X and Fe XII lines. The contours are as before. (from Benz & Krucker 1999)
Synoptic Measurements and Solar Forecasting
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The Sun occupies a unique position in astronomy and astrophysics because it has a direct impact on life on Earth and in space (although, on rare occasions comets or asteroids do too!).  Aside from the obvious fact that the Sun makes life on Earth possible, it is the vagaries of the Sun's activity cycle that may cause climatic change (the Thames froze during the Maunder minimum in the late-17th C.). Moreover, as we have come to rely on both ground and space based technologies for the distribution of electrical power, oil and gas (pipelines), communications, etc., in recent decades we have become more vulnerable to disruptions by transient phenomena on the Sun (flares, CMEs). Longterm studies of solar activity and both short- and longterm forecasting of solar activity are therefore of pressing interest.

The solar 10.7 cm flux has been used for many years as a proxy indicator of solar activity due to its close correlation with other diagnostics such as sunspot number and area, the emission in Lyb, Mg II, and EUV fluxes, and the total solar irradiance. The 10.7 cm flux remains the solar measurement in highest demand amongst the space weather community. However, Schmahl & Kundu (1997) have shown that multi-radio-frequency measurements can be combined to yield superior proxies for both sunspots and irradiance. FASR will provide well-calibrated multifrequency observations suitable for exploiting such diagnostics, but one can envision many other synoptic studies with an instrument like the FASR. For example, with high-resolution, spatially resolved maps at each frequency, synoptic studies of the gyroresonance component of the radio emission and hence, the coronal magnetic field, could be performed.  Such observations require accurate and stable calibration over long periods of time. FASR will achieve this by calibrating against cosmic standards.

FASR is designed to be flexible enough to carry out a wide variety of research programs requiring specialized data, but in addition it will carry out a strong synoptic role and produce certain data products that will be available in real-time or near real-time. The forecasting community, ionospheric physicists, aeronomists and other interested parties will be free to download these products as they become available.  Examples of such data products include the following:
 

Instrument Requirements
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The science program described above places a large number of specific demands on the instrument.  The goal is to design and build an instrument that fully exploits solar decimeter and microwave emission as a diagnostic of physical processes on the Sun. To this end, a number of instrumental requirements have been identified:

  1. Imaging: Radio emission on the Sun must be imaged with high dynamic range, fidelity, and angular resolution, with good sensitivity to both compact and extended sources of emission, instantaneously. A dynamic range >1000:1 and an angular resolution of 1" at a frequency of 20 GHz are considered reasonable goals.
  2. Broadband spectroscopy: Spectral coverage over a core frequency range of 0.3-30 GHz is required. Excellent sampling of the solar visibility function is needed at all frequencies. Matched resolution at selected frequencies is highly desirable.
  3. Polarimetry: Dual polarization observations are required. The polarization correlations required to form all four Stokes parameters are not needed. Normally, only Stokes I and V need be recorded. However, the means of performing the polarization correlations required for Stokes Q and U should be included.
  4. High time resolution: Spectra must be acquired at a rate sufficient to resolve the time scale on which phenomena of interest evolve. At centimeter wavelengths a full spectrum (3-30 GHz) must be obtained in <1 sec. At decimeter wavelengths, the requirement is more demanding: 0.1 sec on a routine basis, with even higher rates over restricted bandwidths as required.
  5. Large field of view: In the interest of maximizing observing efficiency and in matching the capabilities of existing full disk spectrographs and imagers at other wavelengths, a full disk imaging capability is desired over a significant portion of the spectral range of the instrument.
  6. Good absolute positional accuracy: Instruments in most wavelength bands now possess an angular resolution ranging from less than 1 arcsec to several arcsec. Quantitative cross-comparisons of FASR observations with those in other wavelength regimes will require precise knowledge of absolute source positions.
  7. Easy access by the solar community: As a operational requirement, the instrument should not place the burden of data reduction on the user. Most of the calibration and data reduction should be performed on-site and a wide variety of data products should be made available for immediate and open use by the community at large.
A Strawman Design
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High-angular-resolution imaging at radio wavelengths requires an instrument that employs Fourier synthesis imaging using an interferometric array of antennas.  We therefore take as our starting point the assumption that the FASR will be an array of antennas.  The number and size of the antennas, the antenna feeds, the analog signal transmission, digitization, correlation, and post-processing are all important issues that require careful consideration.  We begin with some discussion of the optimum array configuration, antenna number, and antenna size, and then briefly consider additional issues mentioned above. For analog signal processings, both a conservative approach, modeled after the OVRO solar array, and a more radical approach are outlined.
 
Antenna configuration
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A Fourier synthesis telescope measures the Fourier transform of the radio brightness distribution, the so-called visibility function.  The sampling of the visibility function is determined by the cross-correlation function of the antenna locations in the array. The point spread function (PSF) of the array is the inverse Fourier transform of the sampling function.  The criteria by which antenna configurations are assessed depend on the imaging problem at hand. For a two-dimensional array of finite extent, uniform sampling in the Fourier, or uv, plane yields both the highest angular resolution and the best signal to noise ratio (Keto 1997). Hence, a commonly employed criterion for assessing general purpose astronomical array configurations has been uniformity of sampling in the \uv\ plane. However, additional criteria often come into play. In the case of the VLA (Napier, Thompson, \& Ekers 1983), reconfigurability, scalability, and a practical means of accomplishing both led designers to choose a "Y" configuration of three linear arrays of nine antennas each.  The distance of each antenna from the center of the array along each arm is given by a power law, d = c na, where n = 1,2,3, ... 9, yielding a nonuniform, centrally-condensed sampling function.

The FASR is a special-purpose instrument best served by other considerations. It will observe the Sun at a large number of frequencies between 0.3-30 GHz with a fixed array configuration.  The range of spatial scales present in solar radio emission -- from <1" up to the solar diameter of about 2000" more than three orders of magnitude -- must be extremely well-sampled.  By comparison, the ratio of the maximum to minimum spatial frequencies sampled by a given configuration of the VLA is 40.  Many phenomena of interest occur on very short time scales. The snapshot imaging capabilities of the array, and hence the instantaneous uvcoverage, must therefore be excellent.  Finally, for precise cross-comparisons between frequencies, matched PSFs are highly desirable at selected frequencies.

We choose a distribution of antennas that samples the required range of spatial scales while at the same time providing i) similar sampling densities at each frequency and ii) embedded matched configurations at certain frequencies.  We choose antenna spacings according to an exponential law, s = c an , n = 1,2,3, ..., N, where N is the number of antennas on each arm. The distance of an antenna from the center of the array is then d = cSan.  The spatial frequency sampled by an antenna baseline b is b(n/c); the sampling function therefore scales with frequency.  Sampling in the radial direction in the uv plane can therefore be improved by sampling over a limited spectral bandwidth, a technique referred to as "frequency synthesis" (Bastian 1989, Conway et al. 1990, Komm et al 1997).  The proposed configuration lends itself naturally to frequency synthesis: for example, if a = 1.5, sampling over a bandwidth of 50% yields complete sampling in the radial direction.  Furthermore, for all frequency pairs with a ratio of n1 /n2 = 1.5m, m an integer, the uv coverage is identical for the two frequencies over most of the uv plane, thereby yielding identical PSFs.  The array is "self-similar" in this sense (Bastian et al. 1998). The basic point is illustrated in Figure 9for a linear array of seven antennas where a = 1.5 and c = 3.
 

Figure 9
Illustration of a self-similar array configuration. For a linear array of  7 antennas, the 21 antenna spacings are distributed as on the bottom row for a frequency no. If we discard spacings involving the inner antenna at and compare the no distribution to those resulting from the same array at 1.5no, this time discarding spacings involving the outer antenna, the distributions are identical. The same applies for any two frequencies in the ratio 1.5m, discarding m antennas in each case.

 While frequency synthesis can fill in the uv coverage in the radial direction essentially instantaneously, no such technique is available for further improving the instantaneous azimuthal coverage. One must rely on either Earth rotation aperture synthesis or large numbers of antennas. The FASR will rely on both. The use of approximately 100 antennas will provide nearly 5000 baselines.  Examples of the imaging properties of a self-similar array composed of many antennas are shown in Appendix B.
 
Antenna Size

Competing factors play a role in the choice of antenna size.  The desire for full--disk imaging at most frequencies implies the use of small antenna elements.  For example, let us suppose that we must observe the full disk of the Sun to a frequency of 15 GHz. This implies an antenna size of roughly 2 m.  On the other hand, the need for good absolute fluxes and positions implies a need for astronomical calibration; i.e., referencing solar visibility measurements to sidereal sources with accurately known positions and fluxes. This requires good sensitivity which, in turn, implies a need for larger, more sensitive antennas. Two possible approaches are:

  1. The array could composed of many 2~m antennas and one or more large (20-25 m) antennas.  The large antenna(s) would be used to calibrate the small ones against sidereal sources. The construction of one or more new 25 m antennas would be prohibitively expensive. An affordable alternative is to refurbish existing antennas.
  2. The FASR could be a homogeneous array of larger antennas: the use of 4-5 m antennas, for example, would be sufficient to calibrate the instrument. The penalty one pays is in the reduced FOV at high frequencies.
At present we favor the latter approach. Full disk coverage will be available to a frequency of  ~7 GHz for a 5 m antenna, a frequency that is near the spectral maximum of most flares.  We note that an array of larger dishes is significantly more sensitive (Appendix B) at higher frequencies, and for a fixed number of antennas the smaller field of view permits better image fidelity. Full disk imaging at high frequencies can be recovered via mosaicing techniques, which are well understood, as the need arises.
 
Front ends and feeds
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The front ends (feeds, low-noise amplifiers (LNAs), and mixers) must be very broadband. The USAF SRBL telescope design employs a log-periodic spiral feed sensitive to the 1-18 GHz range while the OVRO solar array employs both spiral feeds and log-periodic linear feeds in a hybrid scheme that maximizes sensitivity while allowing circular polarization measurements.  These instruments both employ 0.1-18 GHz FET preamplifiers with a room-temperature noise figure of 2.3 dB, and 1-18 GHz mixer/preamps.

For the FASR, log-periodic crossed-dipole feeds, or some variant, may be employed. A hybrid network (or networks) will insert a l/4 phase shift to convert from the X and Y linearly polarized signals to R and L circularly polarized signals.  The feeds, LNAs, and mixer/preamps will need extremely large bandwidths or else switchable, separate signal paths for frequency sub-ranges.
 
Analog signal processing

Conventionally, the input radio frequency (RF) at each antenna is converted to an intermediate frequency (IF) by mixing it with a local oscillator (LO) signal slaved to a master oscillator. These operations take place at the antenna and the IF is then transmitted to a central location for further processing. Within such a scheme, the requirement of high time resolution might appear to impose severe demands on the system.  However, the entire spectrum need not be sampled instantaneously, and the frequency resolution and rate at which spectra are acquired depends on the phenomenon of interest. The high flux levels from the Sun allow fast sampling with good signal to noise.  Thus one option is to assume that the total frequency range will be divided into sections of width Dn that will be sampled sequentially; i.e., that frequency multiplexing will be performed.

A conservative approach to solve this problem is to use the scheme employed currently at the OVRO Solar Array.  To cover the broad frequency range (0.3-30 GHz), the FASR would require ~60 separate tunings for a modest IF bandwidth Dn = 500 MHz.  The science requirement calls for the entire microwave spectrum to be covered in <1 s. Thus, the required tuning, phase lock, and data acquisition must occur in ~15 msec, for each frequency sampled.  This requirement is, of course, relaxed when two or more IF pairs are used. With four IF pairs, data acquisition at a given frequency could occur in 60 msec. The sample time used at the OVRO Solar Array is 20 msec,  so this approach is clearly feasible. We note that the observing efficiency could be  further increased by using two sets of LOs and phase lock systems in each receiver. This redundancy would allow data to be taken at one frequency while phase lock is being acquired for the next sample.

A more radical, but technologically more interesting, alternative to that outlined above is to simply transmit the entire RF segment of 0.3--30 GHz from the antennas to a central location. This approach would obviate the need for LOs, mixers, and phase-lock loops in each antenna as well as the distribution of reference signals to all antennas. The advantage of this approach is that the amount of equipment in the field is greatly reduced. Components at the antenna would be limited to a quadrature hybrid, a single amplifier, a noise calibration source, and a broadband optical transmitter.  All signal processing could be confined to a central location, thereby simplifying maintenance, testing, and possible refinements and upgrades to the instrument. However, a careful evaluation of the potential effects of strong, narrow-band RFI in gain compression will have to be performed.
 
Data transmission

Optical fibers will be used to transmit data to and from the antennas. Optical fibers are inherently broadband and are immune to radiofrequency interference (RFI). The length of optical fiber runs in the FASR are modest. For an angular resolution of  1"at 20 GHz, a maximum antenna baseline of  about 3 km is needed. The transmission losses will therefore be small. Optical fiber data transmission systems are currently in use at a number of existing or planned sites (e.g., the Australia Telescope and the Nobeyama Radioheliograph).

A disadvantage of optical fibers at present is the relatively low dynamic range imposed by optical-to-electrical and electrical-to-optical converters. The input signal is expected frequently to exceed that typical of quiet Sun conditions by 10 dB during flares.  Exceptional events may elevate the input signal to 20, or even 30 dB, above quiet Sun levels. Some means of automatic level control is therefore necessary in the antenna front ends, irrespective of what type of analog signal processing is adopted.  Optical fiber data transmission is used at the Nobeyama Radioheliograph; a single switched 10 dB attenuator was found to be sufficient to avoid dynamic range problems in the data transmission. The additional problem of exposure to RFI may be partially controlled through the use of notch filters at frequencies of the strongest and most persistent interference.
 
Digital signal processing

At a central location the analog signals from the antennas will be further processed. If the signal has not already been mixed to baseband, it will be done at this point. The signal must then be digitized, corrected for delay, and correlated. To avoid bandwidth smearing, the IF must be coarsely channelized.  This may be done in one of two ways: 1) The analog data can first pass through a filter bank.  Each channel may then be digitized, corrected for delay, and correlated in a continuum correlator. 2) The IF signal can be digitized, corrected for delay, and then sent to a lag correlator. The former places fewer demands on the signal processing. The delay tolerances are modest and the sampling rates would be relatively low. It may be, however, that a hybrid solution involving both coarse channelization and a lag correlator will be optimum. If the entire RF spectrum is transmitted from the antennas to a central location, the details of signal processing may also differ.

Regardless of the details of its architecture, the correlator itself will likely perform one-bit, two-level sampling. The advantage of one-bit sampling is that it is immune to variations in the input signal levels, thus eliminating the need for tight control of the correlator inputs (as needed for two-bit, three- and four-level sampling, for example). One-bit correlation produces a correlation coefficient that must be multiplied by the system temperature to recover the correlated brightness on each baseline. Hence, a means of measuring the system temperature must be employed. One possible scheme is to monitor total power with a square-law detector and to monitor slow gain variations by injecting a broadband calibration signal in the RF with a switching cycle compatible with the data sampling scheme adopted.

The data volume will be large, but not extreme by today's standards. With approximately 5000 baselines and dual polarization the data rate would be 10 Mbyte/sec for a frequency resolution of  about 3% and a time resolution of 1 sec over the 3-30 GHz range. For the specifications in the table, this rate jumps by a factor of 25 to 250 Mbyte/sec. While these rates are large, they are not large compared to the MMA or the VLA Upgrade. In practice, they will likely be much smaller. High data rates need only be produced during active phenomena. And because active phenomena which evolve quickly are compact, it is not necessary to correlate all antennas on these short time scales. For decimeter bursts, for example, it may well be sufficient to correlate only 1/3 of the antennas, thereby relaxing the data rate by an order of magnitude. Realistically, then, data rates are anticipated to be in the range of a few to a few tens of  Mbyte/sec.

FASR Specifications

Frequency range 0.3-30 GHz
Frequency resolution ~3%, 3-30 GHz
~1%, 0.3-3 GHz
Time resolution <1 s, 3-30 GHz
<0.1 s, 0.3-3 GHz
Antenna size 2-5 m
Number of antennas ~100
Number of Baselines ~5000
Polarization Dual
Number IF pairs 4-8
Angular resolution 20/n9 arcsec
Field of view 1125/n9D arcmin
Data processing and data products
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As a fixed-configuration, solar-dedicated instrument, many of the data calibration, reduction, and archiving tasks can be automated.  It is anticipated that the instrument will produce a large number of data products of great value to the research and space environment forecasting communities (Section 3).

Of course, many research projects will require complete and detailed analyses of the data. For example, flare studies will require deconvolved maps for every frequency and integration time. These reductions will be largely automated, but will likely be performed off line and then archived. Users will be able to access the archive in a flexible way. Sophisticated users may wish to work with raw data. The means will be provided to do so.
 
 
User Community

A major emphasis will be placed on making FASR data as widely and as easily accessible as possible in processed-image form (i.e., calibrated and deconvolved). Generally, FASR will be used in a fixed configuration with standard operating procedures to produce a standard set of data. The excellent imaging and spatial resolution will allow the radio images and spectra to be used in much the same way as optical or soft X-ray imaging data are used today--the user will obtain data products that in many cases can be used for science without having to be concerned that they were produced with a Fourier synthesis telescope. Because of this, we expect that the user-base for FASR will be much broader than the traditional group of radioexperts, and the data will be used by the entire solar and solar-terrestrial communities. For example, it will be possible for a hard X-ray astronomer, using an automated web-based server, to request FASR images for a given event from the general database, and receive fully calibrated and optimally reconstructed images for direct comparison with hard X-ray images.

Special-purpose experiments and/or data{processing can be performed by users in a customized environment. Groups or individuals who currently use the VLA for solar work (existing at NRAO, New Jersey Institute of Technology, U. Maryland, Catholic U., Tufts, Smithsonian Astrophysical Observatory, Lockheed-Martin, UC-Berkeley, Zurich, Potsdam, Naval Research Laboratory, Ioannina, Florence, and Meudon) can be expected to make FASR their instrument of choice, and to design specific observing sequences which make use of the flexibility of the instrument to do targeted research of particular interest. Additional software for post-analysis of processed images and spectra will be made available in the IDL package, which has become the standard tool for analysis of solar data.  We anticipate that the FASR will have a completely open data policy. Current developments in mass-storage devices should make it feasible for us to keep FASR data available on-line for automated access by the processing software. We expect that by making retrieval of fully processed images as easy as possible we can make the usage of FASR data straightforward for anyone in the solar and solar/terrestrial physics communities.
 
The FASR Consortium

FASR is presently conceived to be a joint project between the New Jersey Institute of Technology, Lucent Technologies (formerly Bell Labs) and the NRAO, with individual participation from Maryland and Berkeley. Additional participation is quite possible, including foreign partners.  The NJIT Center for Solar Research is the managing partner of both the Big Bear Solar Observatory and the OVRO solar array, formerly managed by Caltech with H. Zirin as the Director. It is likely that the OVRO solar array (Dale Gary of NJIT, Director) will serve as the test bed for the D&D phase of the FASR project, and possibly as the site of the telescope itself. Lucent Technologies has agreed, with the approval of the Executive Director of the Physical Sciences Research Division, William Brinkman, to participate in the project with the help of Louis Lanzerotti (Distinguished Member of the Technical Staff in the Physical Sciences and Engineering Division) and Anthony Tyson (Optical Physics Research section).  Lucent is interested in "tangential research collaborations" which lead to innovative ideas, and specifically for FASR they will provide technical support in microelectronics, broadband fiberoptic communications, and possibly in high-speed computing/data links. NRAO will provide funded support where needed--e.g., receivers, mixers, correlator--with Tim Bastian coordinating NRAO activities.

Summary

The FASR is the first instrument of its kind. It is designed to take advantage of the unique observational opportunities presented by radio emission on the Sun. The FASR is designed to exploit these opportunities to attack a broad science program: understanding energy release, particle acceleration, and particle transport, and shocks through studies of transient energetic phenomena; understanding the nature and evolution of coronal magnetic fields through direct and indirect measurements; understanding the nature of the chromosphere and corona in three dimensions, coronal heating, the origins of the solar wind, and the structure and evolution of filaments. The FASR will provide unique and important insights into these fundamental problems, and make numerous unforeseen discoveries.
 
Appendix A - Brief descriptions of selected instruments

In the table below we summarize the capabilities of radio instruments around the world that spend all, or a large fraction of the time, observing the Sun.  It should be noted, however, that several general purpose, non-solar instruments have been extremely important to the solar physics community.

The VLA has been the workhorse instrument for solar radiophysics in the U.S. It supports observations in the 74 and 327 MHz bands, as well as the 1.4, 4.9, 8.4, 15, 22.5, and 43 GHz bands. The array of 27 antennas can be placed in four standard configurations of differing size. The most compact configuration (D array) has a maximum baseline of 1 km; the largest configuration (A array) has a maximum baseline of 35.4 km. The C and D arrays have been most useful for solar work. The best time resolution available is 200 msec (continuum).

At millimeter wavelengths, interferometric observations of flares have been made by the Berkeley, Illinois, Maryland Array (BIMA) at Hatcreek, California, at a wavelength of 3 mm since in 1989 (White & Kundu 1992). With the recent upgrade of BIMA to a nine-element, 2D array, \mml\ imaging is now possible (e.g., Silva et al 1996).  Several other instruments have been used on an occassional basis for solar work. These include the WSRT, CSO, OVRO mm array, Arecibo, and Haystack. The GMRT has also recently been used to observe the Sun.
 

Observatory
Country
Ang. Res.
Frequencies
Type
Gauribidanur India 5' 40 - 150 MHz 2D mapping
Nancay  France arcmin  150 - 450 MHz 2D mapping
RATAN-600* Russia 240"-15" 1 - 20 GHz  fan beam
OVRO USA 90"-5" 1 - 18 GHz 2D mapping, frequency agile
Siberian SRT Russia 20" 6 GHz 2D mapping/fan beam
Nobeyama  Japan 15", 8" 17,  34 GHz 2D mapping

Itapetinga* Brazil 2' 48 GHz Single dish multibeam
SST Argentina 3', 1' 212, 410 GHz Single dish
Metsahovi* Finland 4', 1' 22, 37, 90 GHz Single dish

Bruny Island Australia - 3 - 20 MHz Spectrograph
Izmiran Russia - 25 - 260 MHz Spectrograph
Ondrejov Czech Rep - 0.8 - 4.5 Spectrograph
Tremsdorf Germany - 40 - 800 Spectrograph
ETH Switzerland - 0.1 - 8 GHz Spectrograph
Espiunica Portugal - 150 - 650 MHz Spectrograph
Nancay France - 10 - 40 MHz Spectrograph
Culgoora Australia - 18 - 1800 MHz Spectrograph
Hiraiso Japan - 25 - 2500 MHz  Spectrograph
ARTEMIS Greece - 100 - 469 MHz Spectrograph
Beijing China - 0.7 - 7.3 GHz Spectrograph
DRAO Canada - 2.8 GHz polarimeter
Cracow Poland - 410-1450 MHz 6 polarimeters
Nobeyama Japan - 1-86 GHz 7 polarimeters
Hiraiso Japan - 200, 500, 2800 3 polarimeters
SRBL USA - 0.4 - 15 GHz Frequency agile

 
 
Figure 10
Comparative display of the frequency coverage of selected  instruments. Those in the U.S. are above the dashed line. Single dishes are marked with an asterisk. Solar-dedicated instruments are colored orange; non-solar-dedicated instruments are blue.

 
 
Figure 11
Comparative display of the angular resolution of  selected instruments. Solar-dedicated instruments are colored orange; non-solar-dedicated instruments are blue.
Appendix B - Sensitivity estimates
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The sensitivity of the FASR is determined by the usual factors -- aperture size, aperture efficiency, correlator efficiency, and the system temperature -- and one additional factor: the Sun itself. When pointing at the Sun, the antenna temperature far exceeds the system  temperature. Rough estimates of the instrument sensitivity are given in  graphical form for a single baseline/single correlation as a function of frequency for antenna sizes of 2 m and 5 m. In the case of the Sun, estimates include cases where small to large flares are superposed on the quiet Sun background.
 
 

Figure 12
Flux sensitivity of the FASR on a single baseline for a single correlation: a) on the Sun for 1 sec; b) on a calibrator source for 1 min. The sensitivity of 2 m antennas is shown in blue and that of 5~m antennas is shown in red. Note that 1 sfu = 104 Jy.  The solid line in panel (a) represents the quiet Sun (using the QS model of Zirin, Baumert, & Hurford (1991). The dashed lines represent weak, moderate, and strong flares.

 
Figure 13
The brightness temperature sensitivity of a 100 antenna array in 1 sec. The array of 2~m antennas is indicated with blue whereas the array of 5~m antennas is indicated in red. Note that the array of 5 m antennas is more sensitive to quiet Sun emission at high frequencies.
Appendix C - Imaging example
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In this appendix we show that a self-similar array can plausibly image complex structure over a wide range of scales and at a wide range of frequencies. We use a simple 88 antenna configuration as shown in Figure 14. The number 88 was chosen because the maximum number that AIPS can accomodate is 90 at present.  For the purposes of this simple demonstration, a 512 x 512 image was selected, 2'' x 2'' per pixel. The FOV is therefore 17'. Figure 15 shows dirty snapshot maps of the test image at 2, 5, 10, and 20 GHz. One has no trouble recognizing the essential features. By way of comparison, snapshot maps of the test image are also produced using the VLA C configuration at the same frequencies (Figure 16). Deconvolution presents no difficulties (Figure 17). We emphasize that the configuration shown is for the purposes of illustration only.
 
 

Figure 14
An example of a self-similar array configuration containing 88 antennas and its corresponding snapshot uv coverage. The coverage shown is for a fequency of 1 GHz.

 
 
Figure 15
An example of snapshot ``maps'' of a test image using an 88 antenna self-similar array configuration. It does very well over a decade in frequency.

 
 
Figure 16
Comparison maps obtained by making snapshot ``maps'' of the test image using the uv coverage provided by the VLA C configuration.

 
 
Figure 17
The sampling of the array shown in Figure 14  is sufficient that deconvolution of the maps shown in Figure 15 is straightforward. Note, however, that these simple examples do not include thermal noise.