Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.naic.edu/~astro/frontiers/ska_ds.pdf Дата изменения: Wed Dec 19 22:13:36 2007 Дата индексирования: Tue Oct 2 05:30:30 2012 Кодировка: ISO8859-5 Поисковые слова: gamma-ray burst

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.


9

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 cases but are sporadic in others (RRATs), the number of required cells is 1 Ncells ,PSR = . (3) b Rt t Finally, ETI sources that may be both narrowband and pulsed require 1 max - min (4) Ncells,ETI = b Rt t


10

IDV

ISS ISS

GRB

Type II

Type III UVCeti

ADLeo BD LP944-20

Jup DAM

Fig. 10.-- The time-luminosity phase space for radio transients. A log-log plot of the pro duct of p eak flux S in Jy and the square of the distance D in kp c vs. the pro duct of frequency in GHz and pulse width W in s. Lines of constant brightness temp erature T = S D 2 /2k ( W )2 are shown, where k is Boltzmann's constant. Points are shown for the `nano-giant' pulses detected from the Crab (Hankins et al. 2003), giant pulses detected from the Crab pulsar and a few millisecond pulsars, and single pulses from other pulsars. Several of the recently discovered "rotating radio transients" (RRATs; McLaughlin et al. 2006) are shown, along with the Galactic center transient source, GCRT J1745-3009 (Hyman et al. 2006) and the recently rep orted strong bursting from the magnetar XTE J1810-197 (Camilo et al. 2006), illustrating the fact that empty regions of the W - Spk D 2 plane may b e p opulated with sources not yet discovered. Points are also shown for Jovian and solar bursts, flares from stars, a brown dwarf, OH masers, and AGNs. The regions lab eled `coherent' and `incoherent' are separated by the canonical 1012 K limit from the inverse Compton effect. Arrows p ointing to the right for the GRB and IDV p oints indicate that interstellar scintillation (ISS) implies smaller brightness temp eratures than if characteristic variation times are used to estimate the brightness temp erature.

Transient Blind Survey Sp eed and Sensitivity
Detailed aspects of sky surveys are presented elsewhere. Basically, the duration of transient signals along with distribution of source populations determines whether a staring or a scanning strategy should be used. To emphasize tremendous survey capacity for the SKA, we consider here a raster-scanning approach, which is also proposed for Large Synoptic Survey Telescope that will operate at optical wavelengths and will survey the sky every few days. For the SKA operating with NFoV independent fields of view and Nsa subarrays (i.e. the collecting area divided subarrays that each survey an independent part of the sky), the survey rate is N =
FoV

the the the into (5)

Nsa T1

FoV

10

-1.65

deg2 s

-1

N T
1,100

FoV

N

sa

(

GHz

D12 )

2

,
12

where T1 102 T1,100 is the integration time per sky position in seconds and D = 12 m D meters. The time to survey a sky area total is then, if a fraction fsky is surveyed, T
survey

is the antenna diameter in (6)

=

N

T1 survey T1,100 (fsky /0.8) 17.2 days 2. Nsa FoV FoV NFoV Nsa (GHz D12 )

With a nominal 100 s integration per sky position, the minimum detectable flux density, taking into account only radiometer noise but requiring detections at the m = 10 level, is S
min

5.5 ЕJy T

sys,30

Nsa D

2 12

(B

GHz 1,100

T

)

-1/2

m 10

f c NA 5000

-1

.

(7)


11 The coefficient in this expression is for 5000 antennas, a 30K system temperature, and 1 GHz bandwidth. As is evident, a deep survey of the visible sky (80% of the total) can be done about every two weeks using nominal parameters at = 1 GHz and can be done even faster at lower frequencies or if multiple fields of view are employed. The detection level 6 Еs is sufficient to detect GRB afterglows at levels that are about з20 fainter than at present with the VLA. More importantly, GRB afterglows will be detected in blind SKA surveys rather than being triggered by detections with high energy satellites. And, of course, an SKA survey will be unbiased and complete with respect to al l classes of transient sources. An SKA transient survey will parallel that proposed for the LSST. However, the classes of transients that will be detected in the radio and optical bands are already known to be different in many ways, particularly given the prominence of sources of coherent radiation at low frequencies. Nonetheless there are areas of overlap (e.g. supernovae) and the LSST and SKA surveys can be cross-compared for both coincidences and anti-coincidences. Such comparisons can be done contemporaneously for the portion of the SKA that has been built during LSST's lifetime and also after the fact for sources that display both quiescent and bursting states.

IV. Enabling Discovery: Virtual Observatory Tools
The SKA will provide data products at a rate that will dwarf those seen for telescopes today and of other telescopes now in the planning process, such as the Large Synoptic Survey Telescope (LSST) that will operate at optical wavelengths. As such, processing for particular key science goals needs to be efficient and robust. At the same time, however, tools are needed that allow exploration of the data for as-yet unidentified signal classes from celestial sources. These tools must also sift through the myriad of interference generated both at electromagnetic frequencies and by instrumentation. Data adaptive methods must clearly play a role.

V. Unique and Complementary Aspects of the SKA
Essentially all telescopes are built for discovery. Their construction is also motivated to follow up on discoveries through various analyses that lead to a better understanding of the universe we live in. In this regard the SKA provides unique capabilities that surpass those operating in other wavelength regimes for some target areas. For other science goals, the SKA plays a complementary role that is needed in order to fully understand what is going on. Finally, there are areas where the primary survey or observation is in a non-radio band but for which the SKA plays an important supporting role. Table 2 summarizes how the SKA addresses key science questions or activities and compares the SKA with other telescopes now being planned. A more complete discussion of SKA complementarity and uniqueness is in the document "Science with the Square Kilometre Array: Uniqueness and Complementarity." Some brief comments follow on particular key science areas for the SKA: 1. Ep o ch of Reionization: LOFAR and MWA EoR/HI signal which will inform follow-on work vide unique information about the first ionizing information about the EoR will be provided by will pave the way by providing, hopefully, first detections of the with the SKA and its design. HI Imaging of EoR structure will prostructures via the mapping of epoch into redshift. Complementary WMAP, Planck, and spectroscopy of high-z AGNs.

2. CO and Star Formation at High Z: IR and sub-mm surveys of high-z galaxies. JWST. ALMA together with the SKA will provide a complete picture of the CO universe and its implications for element formation vs. cosmic epoch. The SKA will detect low-level, redshifted CO lines that are out of ALMA's frequency range. 3. Dark Energy: As the report of the Dark Energy Task Force describes 6 , the SKA can play a ma jor role in studies of dark energy in the fourth stage of program of studies that has already begun: "Stage IV comprises a Large Survey Telescope (LST), and/or the Square Kilometer Array (SKA), and/or a Joint Dark Energy (Space) Mission (JDEM)." Characterization of dark energy includes estimation of the equation of state parameter, w = P /, which is -1 for a cosmological constant. Large-scale surveys of N sources will yield determinations of w and its derivative dw/dz with precisions proportional to N -1/2 . While programs in the optical and radio play out, it also seems likely that a thorough understanding of DE will require the full arsenal of pan-chromatic surveys. An SKA survey has a particular advantage over an optical survey with LST in that radio redshifts will be provided for all 10 9 galaxies detected. 4. Magnetic Universe: There is no real competitor for measurements of polarized synchrotron radiation and its Faraday rotation. Synchrotron emission dominates the radio continuum from cosmic sources and thus provides a signal detectable to very high redshift. Degrees of polarization are much higher at radio wavelengths than in any other spectral range. Faraday rotation, being an integral effect, allows detection of very weak magnetic fields. Planck and Auger will provide important supporting roles in mapping the Faraday-free polarized sky and in measuring magnetic fields in the local IGM, respectively.
6

http://www-astro-theory.fnal.gov/events/detf.p df


12

TABLE 2 SKA Science and Complementarity with Other Ventures

Fundamental Question Or Activity What is Dark Energy?

SKA

SKA Advantage

Complement

Comment

LSST, SNAP lab oratory exp eriments What is Dark Matter? 1010 sources, LSST 108 sources lab oratory exp eriments Was Einstein Right? sustained precision timing, IR orbits around Sgr A* (ELT/GMT/TMT) ab out Gravity? strong field lensing LISA NS plunge into BH + ringdown LIGO I I merger detection, GAIA > Reionization: when and how? tomography of neutral IGM (15 > z 6) direct observation of IGM prior to and CMB: Planck LOFAR, PaST, MWA first stars: high-z CO at birth of first OIR luminous ob jects ALMA (CO) = pathfinders first AGNs JWST (senses first luminous ob jects) Structure formation massive surveys of galaxies, AGNs high angular resolution (no confusion) LSST Evolution of Cosmic Magnetism RM grid (107 sources), Faraday tomography, direction and strength of B, Planck, Auger, NeXT, ALMA, B in first galaxies and in IGM; no extinction XEUS, Constellation-X X-rays provide n e p olarization imaging, high-z synchr. sources sensitivity to small B зelectron density SDSS, JWST < < Using Gravitation Waves as to ols millisecond pulsar timing array 10-9 10-6 Hz gravitational waves LIGO/LISA: 10-5 Hz f 1 kHz SMBH mergers, cosmic strings Black Hole Masses and Spins timing of Sgr A* pulsars high-f mitigates scattering, LISA long time-frame (decades) masers around AGNs 3D velo cities Matter in Extreme States submillisecond NS detection or limits strong statistical significance GLAST and follow-ons masses of 100s of NS, p ossibly BH delineate mass range of NS vs. spin extreme magnetic fields massive survey Acceleration mechanisms high-energy cosmic rays: large sampling area GLAST LOFAR, LWA, MWA atmospheric coherent bursts, lunar neutrinos = pathfinders How do Planets Form? Molecules for Life Search for Extraterrestrial Intelligence (SETI) synoptic images of gaps in disks deep survey of massive molecules targeted and blind surveys high-resolution imaging (mas) broad frequency coverage, sensitivity full coverage of water hole TV from nearest stars, stongest radars across Milky Way wide field of view, long dwells ALMA, CCAT, ELT/GMT/TMT JWST ALMA ATA

massive galaxy survey standard ro d weak lensing survey, rotation curves of large sample compact star binaries (100s), compact orbits around Sgr A*

109 sources = w 1%

The Transient Sky

inventory of transient radio sky, GRB afterglows in blind surveys, lo cal IGM from giant pulses, extrasolar planet flares

LOFAR, LWA, MWA, LSST GLAST


13 5. Gravity and Pulsars: Pulsar studies with SKA will be highly complementary with an all-sky survey with GLAST, which will provide complementary studies of beaming in rotation-driven pulsars and complete Galactic censuses of pulsars and other manifestations of neutron stars, such as magnetars. SKA may provide the first direct detection of gravitational waves. Whether it or LIGO-II does, SKA studies will provide unique information about the gravitational-wave background at nano-Hz frequencies. It also will provide opportunities for testing gravity in the strong field regime through timing measurements of compact relativistic binaries and also of pulsars orbiting the Galaxy's central black hole, Sgr A*. The extent of strong gravity can be arbitrarily large for ray paths that approach the last stable photon orbit around a black hole companion. LISA and perhaps LIGO-II in the end will supplant the SKA in using gravitational waves as astrophysical tools for studying the plunge and ringdown of neutron stars falling into black holes. However, LISA may not come on line until well after the SKA comes on line. 6. Protoplanetary and Debris Disks: Other instruments -- JWST, the ELTs and ALMA -- are needed along with the SKA to develop a thorough understanding of disk types, jets produced by disks and their co-evolution with planet formation. 7. SETI: Historically, SETI has largely been done in the radio but recent work explores pulsed laser signals in the optical and the IR. However, exploration of radio bands is a reasonable path to take because SKA will be able to detect "leakage" signals like those our civilization transmits at distances that encompass a large number of solar-type stars. 8. The Transient Universe: Blind surveys are a main goal of LSST to explore the optical transient sky. As discussed previously, the SKA can provide an equally rich and exciting view of the radio transient sky on time scales similar to those probed by LSST. The radio sky is known to be rich on sub-second time scales that correspond uniquely to coherent radio emissions from compact sources, including relativistic stellar ob jects, planets, and stellar flare emission. Gamma-ray burst afterglows with the SKA can be detected in all-sky surveys without a high-energy trigger 100 times fainter than with the VLA. 9. Near Earth Ob jects: Discovery of NEOs is a primary goal for LSST and related instruments. Orbit determination is far better with the SKA in concert with a radar transmitter than with optical or infrared monitoring.

REFERENCES Camilo, F. 2006, Transient Pulsed Radio Emission from a Magnetar Cordes, J. M., T. J. W. Lazio & McLaughlin, M. A. 2004, The Dynamic Radio Sky, New Astronomy Reviews, 48, 1459 Furlanetto, S. R., & Briggs, F. H. 2004, New Astronomy Review, 48, 1039 Hankins, T. H. et al. 2003, Nanosecond Radio Bursts from Strong Plasma Turbulence in the Crab Pulsar, Nature, 422, 141 Harwit, M. 1981, Cosmic Discovery, New York: Basic Bo oks Hyman, S. D. et al. 2006, A New Radio Detection of the Transient Bursting Source GCRT J1745-3009, Astrophysical Journal, 639, 348 McLaughlin, M. A. et al. 2006, Transient Radio Bursts from Rotating Neutron Stars, Nature, 439, 817 Paydarfar, D. & Schwartz, W. J. 2001, An Algorithm for Discovery, Science, 292, 13 Wilkinson, P. N., Kellermann, K. I., Ekers, R. D., Cordes, J. M., Lazio, T. J. W. 2004, The Exploration of the Unknown, New Astronomy Reviews, 48, 1551


14
APPENDIX

A. Metrics
Etendue: Often the "etendue" -- the product A -- is used as a figure of merit for a telescope, a large value signifying that the field of view of the telescope exceeds the diffraction limit associated with a single pixel, for which A pix 2 . While informative for comparing telescopes that measure the same emission process from a class of sources, this metric is not useful for comparing surveys made with telescopes operating at different wavelengths that may sample the same population of sources but with different tracers. For example, the etendue values for radio arrays such as the EVLA, A = 104.1 m2 deg2 , or the SKA, A = 106 m2 deg2 , are enormously larger than that of an optical survey telescope, such as the Large Synoptic Survey Telescope (LSST), A = 102.5 m2 deg2 . However, a far better metric is the number of sources detected in a given sky region. The bottom-line metric for a survey is the rate at which members of a particular source population are detected. This rate depends on the depth (distance reached) of a survey, the time needed to detect an ob ject with a given luminosity, and instantaneous sky coverage. Detection rates of known sources: In large-scale surveys, the source detection rate is a clear figure of merit because the larger the number, the more successful the survey. For a given luminosity density L , distance, emission solid angle, and detection threshold, I,min , the integration time for detection is . With a field of view FOV and source number density ns , the number of sources detected per unit time is ns Vmax Nd = ns L
3/2



FOV

B

3/4



1/4 S 3/2 sys

.
3/2

(A1)

where B is the bandwidth and Ssys is the SEFD. For a source population with a wide range of luminosities, ns L would be replaced by an appropriate integral. This figure of merit emphasizes the importance of having a large instantaneous field of view and we can compare different telescopes by taking the ratio of Nd , in which case the source properties scale out. Another approach is to consider two broad types of survey. For fixed total solid angle and fixed total time for the survey, the maximum distance Dmax reached depends on the integration time per pointing and thus depends on the FoV; the volume surveyed is V
survey

(N

FoV fc

NA A e B )

3/4

/T

3/2 sys

,

(A2)

where NFoV is the number of independent fields of view and fc NA is the number of antennas (out of a total NA ) that that can be used in a particular survey (owing to baseline constraints). A fundamental assumption here is that the survey is done over the entire FoV of an individual antenna, for which FoV Ae 1 = 2 , where Ae 1 is the effective area of a single antenna. If, instead, we hold the total time fixed and Dmax fixed, we obtain a different expression, V
survey

N

FoV fc

NA Ae B /T

2 sys

.

(A3)

In both of these cases and for Eq. A1, the same combination of parameters appears (but taken to different powers). Therefore we take as a figure of merit, FoM = N
FoV fc NA 2 2 Tsys

Ae B

.

(A4)

This same figure of merit follows by simply defining it as proportional to the survey speed, i / , where i = NFoV FoV is the instantaneous solid angle that is sampled and is the integration time needed to reach a minimum detectable flux density. SKA Memo 66 presents a comparison of survey speeds for the SKA and other instruments. 7 For clarity, we note that survey volume is not necessarily proportional to the chosen figure of merit, but in general is proportional to FoMx . For the two cases considered above, we have x = 2/3 or 1. Phase-space volumes surveyed: To date, surveys have covered little of the phase space, . The SKA will increase the volume surveyed by orders of magnitude. Where are the sweet spots in that are likely to yield the greatest payoffs? Or are all volumes equally populated? Do we quantify the volume linearly or (as Harwit did) logarithmically? This metric is useful for comparing the coverage of phase space by different radio telescopes. Sampling of sp ecific source p opulations: This metric assesses performance based on how a given instrument samples members of a source class with known properties (e.g. canonical pulsars, HI in L* galaxies, etc.).
7 SKA Memo 66, Relative Sensitivities of the SKA and Other Current or Near-Future Instruments, 2005, D. Jones, http://www.skatelescop e.org/pages/page astronom.htm


15

B. Axes of Discovery: Delineating Parameter Space
The goal is to identify the axes and extent of an appropriate parameter space and then to define metrics for coverage of the space. We can then demonstrate how the SKA will drastically increase our coverage. A key issue is how nature populates the parameter space. We have partial knowledge of this but the greatest interest is in those things not yet discovered: a chicken and egg problem. Harwit in Cosmic Discovery estimated the fraction of ob jects discovered by considering the rate of rediscovery when new instruments were built that pushed on one or more axes. His analysis was therefore multiwavelength in nature and also considered non-electromagnetic information carriers (e.g. cosmic rays, neutrinos and gravitational waves). Our approach will focus on radio discovery space while keeping in mind multidisciplinary aspects of source populations. We take an approach that is similar to but diverges from that of Harwit. His Table 1.2 lists parameters that characterize an elementary astronomical observation. We extend the dimensionality of the phase space according to measurements that are under our control. To define the phase or parameter space, we need to consider both the resolution and the extent of each axis. The properties of astrophysical sources of course map into this measurement space. Let the Stokes parameter vector be S = col(I , Q, U, V ). Then define measurement space as the set P = {t, , , t, , } , (B2) where the first three elements are axes for time, frequency, and direction (solid angle) and the following three are the corresponding resolutions.8 The Stokes vector is a function of P : S = S (P ). We define observational phase space as = {S (P ), P }. Sources in the universe have complex dependences on the various parameters and thus show structure in parameter space. E.g. the luminosity function, spectrum and spatial distribution of a source population link I , , and . Time axis: Transients define how the time axis needs to be covered. The fastest known events are the "nano-giant" pulses from the Crab pulsar which are up to 1 Mjy in amplitude with t 1 ns widths. Event rates per source, the density of sources on the sky, and the luminosity distribution all determine how the time axis should be covered. Frequency axis: Spectral lines (with widths determined by velocity spreads and, where applicable, maser gain) need to be resolved. Frequency coverage needs to be continuous though not necessarily simultaneously. A blind survey for spectral lines has not yet been done. Spectral line transients might include maser transients (examples known) and ETI signals. Angular coverage: The angular axis (which is itself two-dimensional) covers the entire sky but with a pixelization that accomodates the dynamic range of source sizes, which is large. The most compact sources are 1. 2. 3. 4. common AGNs: 0.1 - 1 mas; accessible through VLBI techniques. IDV sources: 1 - 10 Еas; accessible through scintillation techniques. GRB afterglow sources: 1 Еas; scintillation. < pulsar magnetospheres: 0.1 Еas; scintillation. (B3) (B1)

The SKA will need to map angular scales from a few tenths of a mas on up and, through appropriate sampling of the frequency-time plane, allow the angular resolving power of interstellar scintillations to be exploited. Astrometry requires VLB resolution for extragalactic maser studies and pulsar parallaxes, among other pro jects. In survey mode, the SKA will be used to cover either the entire sky or the Galactic plane, depending on survey goals. Sensitivity and Phase Space Coverage: The luminosities of sources tie together most of the other axes. Let L = luminosity density (erg s-1 Hz-1 ) for a source assuming isotropic emission. The maximum distance that the source could be detected is D
max

=

L 4 S,min

1/2

,

(B4)

8 We might also have included the p osition vector x of the observer; we leave this implicit. Multiple site measurements for interferometry, coincidence tests, and excision of radio frequency interference require consideration of x, but these are really just details of how we op erationally characterize the sky in terms of the phase space.


16 where S,min is the minimum detectable flux density, which is strongly dependent on P as well as on telescope size and on source properties. For other Stokes parameters, equivalent expresssions may be written down. To assess coverage of phase space, we need to compare Dmax with the distance range for the target population of ob jects and take into account 13 the luminosity function of the population. Equivalently, we can consider the maximum volume surveyed, V max = 3 Dmax , and the volume occupied by the population. These quantities of course are dependent on time, frequency, location on the sky, etc. Astrophysical source prop erties that map into phase space: Source attributes are: 1. luminosity density (L ), 2. beaming of the radiation, expressed as a solid angle into which L is radiated, s , with no preferred beaming direction. 3. spatial distribution expressed as a number density vs. and distance (or redshift); 4. polarization state (which we could characterize through a luminosity density Stokes vector, but for now let's just include polarization as here); 5. characteristic time scale W and event rate R for repetitive sources. E.g. GRBs have W seconds and R 0. Pulsars have R = P -1 and RW 0.03. Steady sources correspond to RW = 1. We therefore define the set of astrophysical source parameters as A = {L , s , n(, D), pol, R, W } . (B5) For some populations, D might be sensibly replaced with redshift, z . Other source attributes could be included, such as space velocity, which can contribute to the discovery process via the proper motion of asteroids and comets, but these aren't particular relevant for a discussion of radio discovery. The mapping from source parameters to observational phase space is thus A Propagation Effects: Radio waves are strongly affected by plasma propagation effects, including dispersion, refraction, and multipath scattering, which alter the distribution of S in the frequency-time plane (dispersive arrival times, pulse broadening, spectral broadening, intensity scintillations) and broaden sources in angle. Gravitational lensing affects all sources through weak and strong lensing, which are time variable but frequency independent (except in instances where plasma and gravitational affects are coupled). Propagation effects may be subsumed in source properties A. Priors: To assess the prospects for discovery, we need to consider how source populations are distributed in P and whether currently empty subvolumes in P of equal importance. Coverage: What coverage of P has been done and can be done with the SKA? Radio surveys to date have covered the entire sky (or nearly so), but only for steady -- not transient -- sources. Transients have been searched over small solid-angle ranges or towards specific targets. The large-scale sky surveys that have been done have been rather shallow, down to 1 mJy whereas deep field studies reveal the existence of sources a thousand times fainter. Existing telescopes have covered sub-regions of P but only very sparsely and with low sensitivity. The innovation of the SKA lies in two primary axes: sensitivity a factor of 10 to 100 greater than with existing instruments and wide field of view. These two factors will allow signficant coverage of the parameter space that has been neglected so far, especially for the transient radio sky, and it will allow very sensitive, massive surveys of both the polarized and the unpolarized universe.