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Discovery and Understanding with the SKA
J. M. Cordes and the International SKA Science Working Group October 3, 2006 Version 1.03

Executive Summary
The Square Kilometre Array will be a premier instrument for discovery owing to its continuous coverage of a wide range of radio frequencies combined with unprecedented high sensitivity, wide field of view, multiple-scale angular resolution, and highly flexible sampling of the time domain. In this document we summarize the planned capabilities of the SKA as defined by key science areas that drive the specifications. We characterize the SKA as a discovery instrument, both for known and unknown classes of astrophysical sources. Finally we summarize the unique and complementary aspects of the SKA with respect to other large-scale instruments that are being planned across the electromagnetic spectrum and also for non-photonic detection.

Introduction
The SKA will transform our understanding of the universe on all scales of space and time. Science goals envisioned for it target fundamental aspects of our universe, such as the nature of the mysterious dark energy that is accelerating the universe's expansion, and the properties of gravity around black holes. The rich complexity we see all around us -- a cosmic web of galaxy clusters, each containing hundreds of billions of stars around many of which planets have formed as prospective venues for life -- is also awaiting study and understanding with the SKA working in concert with other instruments. Known classes of sources, such as gamma-ray burst afterglows, will be detected in such large numbers that they will become routine tools for studying the intergalactic and interstellar media (ISM, IGM). And there is the discovery of the as-yet unknown in the universe. The SKA will open up new realms of parameter space in which entirely new classes of sources will be discovered. In this document, we highlight the SKA as a platform for discovery and a tool for understanding the universe and the complex phenomena we find within it. In the following we summarize the broad science areas that the SKA will address in ? I and the requirements on the SKA that are needed to achieve the science goals. In ? II we discuss the capabilities of the SKA from a parameter space point of view and in ? III we outline summarize the types of discovery that are relevant to the SKA, with some emphasis on sources of transient radio emission. We point out in ? IV the importance of data management protocols and systems that will be needed to enable the discovery process. Finally, in ? V we discuss aspects in which the SKA is entirely unique or complementary with other instruments in achieving its science goals.

I. Key Science Areas and Exploration of the Unknown
Five primary science areas have been defined by the internationally constituted Science Working Group that address fundamental questions on the forefront of physics, astrophysics and astrobiology. 1 Much of the science entails massive sky surveys that will be challenging both technologically and logistically. Together they drive the specifications for the SKA 2 . A provisional Reference Design3 suggests a possible implementation of these specifications with aperture (phased) arrays at low frequencices and an array consisting of a large number of small diameter dishes (LNSD) at higher frequencies. Figure 1 shows schematically the frequency ranges demanded by the key pro jects. The Dark Ages: The structure of the universe prior to and during the formation of galaxies can be probed uniquely at radio wavelengths. The 21cm line from hydrogen will be used to map cosmic structure both in space and time (via the redshift) and is a powerful complement to the cosmic microwave background (CMB), which provides a single snapshot of the universe when it was about 300,000 yr old. The 21 cm line, observed at redshifted frequencies above and possibly below the FM band, will sample structures that were in the process of forming clusters of galaxies at redshifts of 6 to 15 or even higher, culminating in the Epoch of Reionization when the formerly atomic universe became the plasma universe. The agents of ionization -- the first stars and black holes -- will also be probed with the SKA through mapping of redshifted carbon monoxide and through high-resolution mapping of active galactic nuclei at high redshifts. Figure 2 shows simulated temperature fluctuations in hydrogen emission and absorption associated with the turning on of ionizing sources. Galaxy Evolution/Dark Energy: The unparalleled sensitivity of the SKA, combined with its extremely large instantaneous field of view, permits ground-breaking cosmic surveys. Reasonable models indicate that, in a year of operation, the SKA can map 109 HI galaxies across the entire visible sky to redshift z 1.5, providing
1 The SKA science case is presented in Science with the Square Kilometre Array, eds: C. Carilli and S. Rawlings, New Astronomy Reviews, Vol. 48, Elsevier, 2004 2 SKA Memo 45, SKA Science Requirements: Version 2, 2004 http://www.skatelescop e.org/pages/page astronom.htm 3 SKA Memo 69, Reference Design for the SKA, 2006


2

Fig. 1.-- Frequency ranges asso ciated with the five science areas identified for the Square Kilometre Array, demonstrating the nominal 0.1 to 25 GHz range sp ecified in the Reference Design (see text).

Fig. 2.-- Simulations of 21 cm hyp erfine radiation at high redshifts, showing temp erature flucutations and the growth of structures (Furlanetto & Briggs 2004).

the premier measurement of the clustering power spectrum: accurately delineating acoustic oscillations and the `turnover'. HI detections provide full 3D positional information without separate spectroscopy observations, as with optical surveys. In addition, a radio continuum survey will quantify the cosmic shear distortion of 10 10 galaxies with a precisely-known point-spread function, determining the power spectrum of dark matter and its


3 growth as a function of cosmic epoch. These experiments will provide exquisite information on the properties of dark energy. Furthermore, additional cosmological constraints will follow from the late-time Integrated Sachs Wolfe effect, and precise geometrical measurements of the distance scale using strong gravitational lensing and studies of extragalactic water masers. CO surveys with the SKA can measure gas at redshifts z > 3.6 providing an important counterpart to high-redshift hydrogen at and before the Epoch of Reionization. Figure 3 shows the detectability of CO and of continuum emission with the SKA and ALMA.

0.001 z=2 5 EVLA 8

0.0001

ALMA

SKA JWST

Fig. 3.-- Plots - one for line (left) and one for continuum (right) sensitivity versus the exp ected SED of a high z star forming galaxy with a luminosity 1/10 that of arp 220 - this would b e typical of Lyman break galaxies or Lyman alpha galaxies.

The Magnetic Universe: The structure and evolution of magnetic fields are topics that thread many of the most important issues in astrophysics today, from galaxy formation to star and planet formation. However, our knowledge of dynamo mechanisms and the cosmic evolution of magnetic fields is at best cursory. The SKA can rectify this by allowing Faraday tomography of polarized synchrotron radiation in our Galaxy and in other galaxies and clusters and large scale surveys of the Faraday rotation of sources at cosmological distances. Variations in sign of the Faraday rotation will reveal model-independent magnetic topologies in galaxies and in the IGM. As an inverse problem, the electron density and magnetic field can be deconvolved with more model dependence to gain a three dimensional picture of the magnetic field as a function of redshift. Probing Strong-Field Gravity with Pulsars and Black Holes: Pulsars are exquisite clocks -- owing to their spins -- that can be used for space-time cartography around massive ob jects, such as other neutron stars and black holes. They also serve as test masses that respond to very long wavelength gravitational waves. Thirdly, their pulses are excellent probes of the gas and magnetic fields through which they must propagate to reach us. The SKA will yield a (nearly) complete census of pulsars in the Milky Way, from which the Galaxy's spiral structure can be defined and turbulence in the magnetized plasma will be mapped on scales from parsecs to hundreds of kilometres. Of greater importance is the guaranteed discovery of rare binary systems -- pulsars with other neutron stars and black holes as companions -- that serve as laboratories for gravity. The most prominent target is the center of our galaxy, where a dense star cluster orbits the massive black hole, Sgr A* (3 з 10 6 M ). The SKA's sensitivity at high frequencies is required to combat the intense radio-wave scattering that quenches the pulsed emission from pulsars in the star cluster. Discovered pulsars will be monitored as they orbit Sgr A*; those with favorable alignments will probe the space-time around the black hole arbitrarily closely to the last stable orbit and thus provide quantitative measures of the gravity in the strong field regime. Many of the millisecond pulsars found with the SKA will comprise a pulsar timing array for detection of low-frequency gravitational waves (nHz). Successful detection of gravitational waves will complement terrestrial and space-based detectors -- such as LIGO, VIRGO and LISA -- by covering a much lower-frequency band of gravitational waves. Finally, pulsars in other galaxies will be detectable with the SKA: out to a few Mpc in periodicity searches and perhaps as far as the Virgo cluster for detection of giant pulses like those from the Crab pulsar. The Cradle of Life: Based on a sample of one (the Earth, its biosphere, and ourselves) we know that planets can provide the constituents for life and the environments needed to jump start and evolve life. However, we have only an incomplete inventory of organic molecules in the interstellar medium that may be important for triggering


4

Fig. 4.-- Left: An image of M51 that is a sup erp osition of optical (red), radio continuum (blue) and p olarization (green) with + symb ols corresp onding to SKA-detectable background p oint sources that follow a standard log N - log S distribution and would provide a rotationmeasure grid for probing the magnetic field co existent with thermal, ionized gas in the galaxy. RM-grid results can b e combined with p olarization imaging of synchrotron radiation to further mo del the magnetic field in M51. Right: Cumulative Rotation Measures vs. time, showing the huge increase in lines of sight measured with the 10% SKA and with the full SKA.

SKA: 1.4 GHz/400 MHz/1024 T/G = 0.25 Jy

600 s

Fig. 5.-- Left: Simulated pulsar survey results for the SKA, assuming it has all-sky coverage at 1 to 2 GHz. In practice, the SKA may have 80% sky coverage. Blue p oints represent the 104 pulsar detections. Yellow symb ols represent the 1604 known pulsars in the ATNF/Jo drell pulsar catalog with distance estimates. The survey yield is based on a 600-s dwell time p er sky p osition and a standard search analysis for disp ersed and p erio dic signals. The simulation do es not include the recently discovered "rotating radio transients" whose numb ers might double those seen here. Right: survey yield for canonical pulsars (blue), those with p erio ds from 30 ms to 5 s with magnetic fields 10 12 G, millisecond pulsars (red) and relativistic binaries (yellow). Note that the left-hand scale applies to canonical pulsars and the right-hand scale to MSPs and binaries; the numb er of binary pulsars has b een multiplied by 10. MSPs and NS-NS binaries provide extraordinary opp ortunities for measuring low-frequency gravitational waves and for testing General Relativity, resp ectively. The imp ortance of Large scale surveys therefore lies in the discovery of such ob jects for their role as gravitational lab oratories and as new to ols for astrophysics.

the first stages of life. The SKA will provide such an inventory through its broad frequency coverage and its ability to survey large regions of the sky at high sensitivity. Many stages lie between the initial collapse of molecular cloud regions and the formation of stable planetary systems that include planets in habitable zones around stars: formation of massive dust and gas disks, agglomeration of planetesimals, growth of planets from the planetesimals, and a final clearing of the debris disks left behind. With the SKA's planned high-frequency and high-angular resolution (0.1 mas), specific protoplanetary disks can be observed as Earth-sized protoplanets carve paths in their feeding zones in the disk. Movies of this process can be made using the SKA's high-resolution imaging capability. Finally, the enormous sensitivity of the SKA provides the means for plausible detection of deliberate or leakage signals from other civilizations. Television from civilizations on planets orbiting nearby stars is detectable, should complex life be prolific in the Milky Way. Other signals, such as those from powerful, monochromatic radars that


5 we use for planetary studies, are detectable across a significant portion of the Milky Way. The beauty of the SKA is that, while it addresses specific key science areas and thus will answer important questions that we pose now, it will have the flexibility to address evolved versions of these questions in the future and entirely new questions that are spawned by the old ones. Very importantly, the SKA will increase the coverage of parameter or phase space by many orders of magnitude, making it a powerful instrument for the discovery of ob jects and phenomena that we do not yet know. This leads to a sixth key science area: Exploration of the Unknown: As an instrument that will better probe the domains of astrophysical and astrobiological sources by many orders of magnitude, the SKA will discover entirely new kinds of ob jects. The chapter "The Exploration of the Unknown" in the SKA science book (Wilkinson et al. 2004) identifies the key variables that underlie each of the long list of fundamental discoveries that have been made in radio astronomy. One might think that all of the key variables have been identified and probed with existing telescopes. This is far from being the case because the so-defined parameter space has been investigated only in very compartamentalized subvolumes. What the SKA offers is a chance for a much more thorough sampling of parameter space combined with incredible sensitivity. An obvious axis of discovery is the time domain and the prospects for detecting counterparts to classes of sources we already know about (e.g. Gamma-ray bursts, flare stars, AGNs) but also surprise discoveries such as unexpected signals from other civilizations, evaporating black holes, etc.

I I. Increasing Discovery Space by Many Orders of Magnitude
The current Reference Design for the SKA specifies coverage of the 0.1 to 25 GHz frequency range with three kinds of receptors to cover three bands: 0.1 to 0.3 GHz with dipoles, parabolic dishes and focal plane arrays in the mid-range 0.3 to about 2 GHz, and dishes with broadband, single-pixel feeds in the high band from 1 to 25 GHz (the implied overlap with the mid-range is intentional because the implementation may be different for the two bands). The revolutionary asp ect of the SKA is the combination of a huge b o ost in sensitivity across all three bands, wide field of view (FoV) for survey throughput, and the ability to sample with high resolutions the time, frequency and spatial domains. Many of the high priority science areas for the SKA require high-throughput surveys, leading to array configuration and FoV requirements as given in the specifications document (SKA Memo 45). In the mid-range band, massive surveys will be conducted for galaxies using the HI hyperfine line at 21 cm and in the continuum for studies of dark energy, dark matter, and Faraday rotation measurements. High-yield surveys of L galaxies will be made to redshifts of up to about 2. These require both high sensitivity and also wide field of view in the 0.5 to 1.4 GHz range. Sampling the time domain to employ pulsars as tools for studying gravity and to discover transients, including orphan gamma-ray burst afterglows to levels 100 times fainter than at present, also requires wide FoV to provide long dwell times on large swaths of solid angle. A more detailed inventory of the tremendous survey capability will be given later. The diverse requirements for sampling the sky with high time and frequency resolutions are depicted in Figures 6-8, which also delineate how astrophysical sources and processes fill the "phase space" defined by these resolution parameters. The Angular Domain: Angular scales include the sizes of AGNs, which are as small as 100 Еas in direct interferometry but also include compact intra-day variable (IDV) sources that are inferred to be just a few зЕas in size using the resolving power of interstellar scintillation. Pulsar magnetospheres can be probed in similar ways to the sub-Еas level. A deep survey for 21-cm HI in 108 - 109 galaxies requires the combination of 1 as resolution and very wide survey FoV, 40 to 100 deg2 . On larger scales, studies of magnetic fields in the Galaxy and in the IGM require a broad range of angular resolution. The Epoch of Reionization signal in HI provides the means for measuring structure evolution prior to and during early galaxy formation. The relevant scales are depicted in Figure 6. The Time Domain: The time domain is shown in Figure 7. Under close scrutiny, most compact sources are time variable. Radio techniques have been used to discover emission events down to nano-second scales and exploit transient emissions to study the energetics of sources (GRB afterglows) and use interstellar scintillation to probe source sizes of compact sources (pulsars and GRB afterglows). From the standpoint of populations of transient sources, however, it is also clear that the time-variable radio sky is very poorly characterized. This owes to the fact that existing large radio telescopes have small FoV so that blind surveys for transients have covered only a small fraction of the overall parameter space. To adequately characterize the transient sky, the product P = AT must be large enough to detect a fair sample given the intensity, sky density, and event rate, where A is the collecting area, is the instantaneous solid angle, and T is the dwell time. With a single pixel instrument, A = 2 , so P = 2 T . At cm wavelengths, multiple-pixelsystems have been used with Npix = 13 (Parkes multibeam surveys) and Npix = 7 (ALFA at Arecibo). Subarrays that analyze different sky regions do not alter P . The SKA is proposed to have Npix in the hundreds at about 1 GHz and below, thus increasing the throughput for transient searches enormously. The Frequency Domain: Natural sources demand spectral resolution as small as a few hundred Hz over a spectral domain of many GHz. For SETI, the search for extraterrestrial intelligence, signals of Hz bandwidth or less are often sought.


6

Fig. 6.-- Angular scales relevant to sources, surveys and scintillation that will b e prob ed with the SKA. Coherent radiation from pulsar magnetospheres and hyp er-compact AGNs can b e prob ed using the high sensitivity and time-frequency sampling of the SKA combined with the resolving p ower of interstellar scintillation.

Fig. 7.-- Time scales relevant to sources, surveys and scintillation.

Fig. 8.-- Frequency resolutions relevant to sources, surveys and scintillation.

I I I. Types of Discovery
As we know, there are known knowns. There are things we know we know. We also know there are known unknowns. That is to say we know there are some things we do not know. But there are also unknown unknowns, the ones we don't know we don't know --- D. Rumsfeld (2002)


7 The SKA will be a discovery instrument of both known classes of ob jects and new ob jects in new classes. Many aspects of the key science pro jects involve large-scale surveys of known types of ob jects that primarily are used as tracers of cosmic evolution, of their environments or of intervening media, or of spacetime itself. However, at one time, most of these ob jects were themselves unknown. A conservative stance, consistent with the Copernican principle, 4 is to expect discoveries of new classes of ob ject. New ob jects in known classes: With known classes of ob jects, the payoff from the SKA is a combination of the large survey yields and the likelihood that rare members of that yield will be especially useful. Examples include: 1. Near-Earth asteroids approaching from the sunward direction and Kuiper-belt ob jects with low albedo. < 2. HI in galaxies to z 2 for studies of dark energy and dark matter and of galaxy evolution. 3. Giant relic galaxies that emit at low frequencies with low-surface brightness and provide information on the evolution of supermassive black holes in galactic nuclei. 4. Magnetized Galactic ob jects 5. Pulsars in the Galactic disk and globular clusters to identify millisecond pulsars and relativistic binary pulsars to probe gravity. 6. Pulsars in the Galactic center that can be used to probe the environment and space time around the massive black hole, Sgr A*. 7. Faraday rotation measures (RMs) toward distant galaxies (active or star-forming) to allow tomographic delineation of cosmic magnetic fields and to exploit galaxies seen as Faraday silhouettes against polarized backgrounds. 8. High-z CO in transitions and redshifts that complement ALMA in quantifying star and element formation vs. cosmological epoch. 9. Giant pulses from extragalactic pulsars analogous to those seen from the Crab pulsar and a handful of other young and millisecond pulsars; these can probe the nearby IGM through propagation effects that alter the pulses (dispersion, scattering and Faraday rotation). Targeted known phenomena: Similarly, there are processes that occur or have occurred that we can detect and analyze through appropriate imaging, spectroscopic and time-domain measurements: 1. 2. 3. 4. 5. The EoR signal from structure formation as it appears both spatially and in the spectral domain. Magnetic fields and dynamo action in the first galaxies and clusters. Weak magnetic fields in galaxy halos, in clusters and in the Cosmic Web, including primordial magnetic fields. Detecting protoplanets in disks as they evolve during the planet formation process. Detecting coherent radio emission from extrasolar planets analogous to radiation seen from solar-system ob jects.

New Classes of Sources and Phenomena Based on Known Physics, Biology, etc: 1. Transient sources of many kinds have been identified (e.g. Figure 10). Mild extrapolations from the physics of known sources suggests that plausible detections may be made from extrasolar planets (through mechanisms other than solar-system type), extraterrestrial intelligence (at minimum, leakage signals analogous to what we transmit), prompt GRB emission that is coherent similar to that seen from pulsars (for both hypernovae and mergers of compact stars), and black hole evaporation. 2. Coherent sources tend to be prominent at low frequencies and thus may emerge as new classes. 3. Radio-loud, gamma-ray quiet GRBs: orphan afterglows seen in the radio without corresponding high-energy radiation would better our understanding of relativistic beaming and environmental effects in cosmic explosions. 4. Reconnection regions in the ISM and magnetic fields in the IGM, including large magnetic filaments in the Cosmic Web. 5. Sources with high circular polarization. 6. ETI (non-transient). The Totally Unexp ected! Finally, we can expect the truly unexpected, some categories of which are: 1. 2. 3. 4. 5. 6.
4

Clusters of magnetic monopoles, probed with Faraday rotation and distinguished through consistency with Spectral lines from dark-energy/dark-matter particles. New kinds of stars (strange, quark). Manifestations of higher dimensions. New physics. ETI technological activity (not signals).

ЗB = 0.

I.e., we do not live at a sp ecial time with resp ect to our study of the universe.


8

Survey Figure of Merit
High sensitivity and wide field of view together boost the SKA's survey capabilities by many orders of magnitude compared to existing instruments. In Appendix A we derive a figure of merit that is related to the volume surveyed. The survey volume is proportional to the FoM taken to some power that depends on how the survey is conducted. 5 We define FoM B (Ae /Tsys )2 where = total instantaneous solid angle, B = bandwidth, Ae = total effective area of array, and Tsys = system temperature. We use Ae = NFoV NA 2 NFoV NA -2 to arrive at the expression (Eq. A4) given in the Appendix; implicitly assumed is that signal processing and survey analysis is of the full primary beam of an individual reflector (which we call the FoV). Table 1 lists the FoM at 1.4 GHz along with input data for the SKA and a number of other telescopes. Figure 9 shows the figure of merit plotted against frequency for the SKA as compared to other radio telescopes.
TABLE 1 Figure of Merit at 1.4 GHz for Nominal Parameters Instrument N N B Tsys log10 (Ae ) log10 (FoM) (GHz) (K) (m2 ) (m2 K-2 GHz-1 ) 0.2 0.2 0.2 0.4 0.3 0.2 0.8 0.3 30 30 30 27 30 20 20 21 5.74 5.74 4.74 4.46 4.46 3.97 3.74 3.28 5.7 6.7 3.6 0.92 1.5 2.1 0.67 0.91

FoV

A

SKA SKA + FPA SKA Phase I Arecib o Arecib o+ALFA EVLA GBT Parkes+MB

1 5000 48 5000 1 500 1 1 7 1 1 27 1 1 13 1

The Transient Radio Sky: The SKA as A Radio Synoptic Survey Telescop e
Unlike the high-energy sky that has been probed with wide-field detectors in X-rays and -rays, leading to discoveries of gamma-ray bursts and afterglows and bursters of various kinds, the transient radio sky is unexplored in any systematic way. In spite of this, a wide variety of radio transients has been identified, as shown in Figure 10, which shows a twodimensional phase space for the transient radio sky. The SKA can cover unprecedentedly large areas of sky while also probing the full domain defined in the figure. Figure 10 has axes chosen because they allow lines of constant brightness temperature to be plotted. Further details can be seen in the chapter "The Dynamic Radio Sky" in the SKA science case (Cordes et al. 2004) Two main points emerge from considering this figure: 1. Known transients already cover a huge range of parameter space, indicating that natural sources populate a large volume. 2. There are also empty areas in the plot; do these signify the patchiness in the way nature populates the phase space or do they signify a proportionate number of new source classes that remain to be discovered? Nature appears to abhor a vacuum, even in phase space, so we expect the latter case to apply: many new discoveries await! Using this subspace as an example, we could approach the question "How many new source classes are there?" in two ways. First, we could simply scale up from the portion of phase space that has been probed to the total volume available. Alternatively, we could list types of ob jects that exist or are thought to exist and then speculate on whether they ever would be detectable in some part of the phase space. The occurrence of several source classes relies on the generation of coherent radiation. If not for that, very compact sources would never be detectable. Fortunately they do generate coherent radiation and thus are detectable. Are there other ob jects that might emit coherent radiation? In this way we might generate a list of possible discoveries to be made. To illustrate the large return to be expected with wide-field sampling over a wide-range of time scales, three recent discoveries come to mind. First is a transient in the Galactic center, GCRT J1745-3009 which appeared in images made with the VLA with approximately hour-like variability. Its nature is not yet known. Pulsar-related discoveries include the rotating radio transients ("RRATs"), which are most likely radio-pulsar-like neutron stars that are triggered through processes we have not yet identified, and the quasi-periodic bursting pulsar, B1931+24, which has a quasi-period of 40 days and is in the on state for only 20% of the time. Recently, a magnetar discovered in 2003 with the X-ray Timing Explorer was identified as a very strong periodic source (5.54 s) about one year after a large burst increased its X-ray flux by a factor of one hundred.
5

While different survey strategies lead to different volumes, they involve the same combination of parameters.


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Fig. 9.-- Survey figure of merit for the SKA with and without multiple-pixel receivers. Also shown is a curve for the "Phase I" SKA, which is assumed here to have 10% of b oth the sensitivity and numb er of antennas and to extend from 0.3 to 10 GHz. The curve applies to a single-pixel system; for clarity we do not show a Phase I curve with fo cal plane array, but the enhancement would b e similar to that shown for the full SKA. For other telescop es, single pixel systems are considered except for the 7-b eam ALFA system at Arecib o and the 13-b eam system on the Parkes telescop e. The figure of merit is related to the spatial volume that can b e surveyed in a fixed amount of time, as describ ed in App endix A. The huge increase in figure of merit for the SKA results from the assumed combination of large collecting area and wide field of view. Note that if only a fraction fc 1 of the collecting area is used for a survey, the figure of merit is reduced prop ortionately. Alternatively, if each antenna is outfitted with a multiple pixel fo cal-plane-array receiver, the figure of merit increases substantially, as shown. The fo cal plane array sp ecifications were obtained from SKA Memo 69, referred to earlier, which assumes a frequency range of 0.1 to 25 GHz for the SKA, p ossibly extended down to 0.06 GHz, as shown here.

The time scales associated with these discoveries -- variability time scales that range from tens of milliseconds to months -- are very difficult to sample with low sensitivity, single-pixel instruments. A measure of phase space coverage for transients is the number of "cells" that cover the angular, frequency and time domains. In general the search domain is a total solid angle , a frequency range B = max - min and a time range T = tmax - tmin . If a source emits only one event with characteristic time and frequency scales t and with unity time-bandwidth product, t = 1, the number of cells to be searched is Ncells B T with cell sizes b t in order to identify the event and assuming there is adequate sensitivity. For sources that emit multiple events with event rate, Rt , fewer cells are needed to detect the source. For continuum sources -- those that have smooth spectra and are not strongly modulated in time -- the number of cells to be surveyed is , (1) Ncells,cont = b where b is the resolution in solid angle. For sources with natural spectral lines that are time invariant, we have / = V /c, where V is the effective range of Doppler velocities (which will be smaller than the actual range for, e.g., maser sources) and if we are searching for spectral lines with a flat prior over a frequency range [ min , max ], the number of cells is max c Ncells,line = ln . (2) b V min For pulsars, which are continuum sources with characteristic time durations t that repeat periodically in many cas