The Square Kilometer Array as a Radio Synoptic Survey Telescope: Widefield Surveys for Transients, Pulsars and ETI Version October 17, 2007

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1 Document: April 4, October 17, 2007 Typeset using L A TEX style emulateapj v. 16/07/00 The Square Kilometer Array as a Radio Synoptic Survey Telescope: Widefield Surveys for Transients, Pulsars and ETI Version October 17, 2007 Jim Cordes, Cornell University ABSTRACT This document explores some of the issues involved in searching for transients, pulsars, and ETI signals with the assumption that steady sources are surveyed at the same time, including spectral lines and continuum from galaxies and AGNs. We present a survey metric that quantifies survey completeness and incorporates time-variable sources with arbitrary durations and event rates. We discuss the role of propagation effects in surveys. Some radio sources are intensely modulated, such as giant pulses from the Crab pulsar with structure as short as 0.4 ns, variations in active galactic nuclei on time scales of days and longer, and GRB afterglows on day to month time scales. Apart from pulsars, we know about such variations from observations that target previously detected sources, as opposed to discovering them via their time variability in blind surveys. The transient or dynamic radio sky is rich enough to make it plausible that blind surveys will discover many sources of both known and unknown types. Schemes for conducting searches are outlined in the context of the Large-N-Small-D concept for the Square Kilometer Array, though they are applicable to aperture array concepts with minimal changes. The particular science addressed is for mid-range frequencies, e.g. 0.3 to 10 GHz. The Square Kilometer Array (SKA), properly designed, can provide the capabilities needed high sensitivity, wide field of view, and flexibility in processing the time and frequency domains to serve as a radio synoptic survey telescope (RSST). An example synoptic cycle is presented that includes different scan rates for extragalactic and Galactic science; it also includes options for non-survey projects and targets of opportunity triggered by other telescopes. Further work is neeeded to confirm that surveys for transients, pulsars and ETI can be done simultaneously with those for steady sources, such as galaxy HI surveys and continuum source surveys, including polarimetry to yield Faraday rotation measures. The example synoptic cycle underscores the need for field-of-view expansion through use of multiple-pixel receivers in order to conduct a large-scale galaxy survey in a reasonable amount of time. In addition, investigation is needed on whether followup monitoring observations, such as pulsar timing, can be encompassed in the survey mode or instead require special pointings outside the survey paradigm. Finally, requirements for calibration and backend processing systems need to be identified. 1

2 Table of Contents 1 Introduction Motivations Assumptions About the SKA Search Domains Types of Analysis The Role of Multipath Propagation: Scintillations, Refraction and Broadening in Angle, Time, and Frequency Pulsars and Magnetars General Pulsar and Magnetar Surveys Galactic Center Survey Globular Cluster Surveys Extragalactic Pulsars and Magnetars Transients Giant Pulse Detection Magnetar Detection Rotating Radio Transients (RRATs) Extragalactic Fast Transients Maximal Giant Pulse Emission from Pulsars and Mergers Gamma-ray Bursts: Afterglows and Prompt Radio Emission Evaporating Black Holes SETI Asteroid/Comet Radars The Radio Synoptic Survey Telescope Figures of Merit for Raster-scan Surveys of Steady Sources Figures of Merit for Raster-scan Surveys of TransientSources Completeness Coefficient of a Transient Survey Trading Field of View and Sensitivity The Synoptic Cycle Requirements for Searching the Full Field of View Sampling the Field of View Search Processing Summary Appendices A General Survey Metrics (including transients) B Matched Filtering: Detection and Estimation C Minimum Detectable Flux Density in Pulsar Surveys D Single-pulse vs. Periodic Pulse Detection for Highly Modulated Pulse Trains E Scattering in the Galactic Center

3 1. introduction Science drivers for the SKA involve surveys on massive scales. These include surveys of steady sources, such as the billion-galaxy survey in HI to study dark energy and galaxy evolution and a Faraday rotation survey of continuum sources to study the evolution of cosmic magnetic fields. Time-variable sources are also a part of the key science case (Carilli and Rawlings 2004) through proposed surveys for pulsars and ETI. There is now growing recognition that the SKA should be geared for deliberate exploration of the unknown, including the time-variable radio sky. This follows from two facts. First, wide-field X-and-γ-ray telescopes have been enormously successful discovery instruments for transient sources. Second, recent discoveries at radio wavelengths have underscored what was already obvious: that the radio sky is equally rich in time-variable sources even though it has not yet been systematically surveyed. In this article, we analyze the requirements for sampling radio transients taking into account the large range of time scales (ns to years) and signal complexity in the time-frequency domain. We explicitly consider pulsars and ETI along with other known types of transients. We also speculate on particular new classes of transients that may fill the overall phase space of amplitude, duration and frequency. Implementation of the SKA for studies of time-variable sources necessarily must consider other proposed applications including the billion-galaxy survey and pointed observations of particular sources, targets of opportunity, etc. which place demands on a significant fraction of the available array time. Consequently, we consider implementation of the SKA as a synoptic survey telescope with which most or all of the proposed surveys are done simultaneously. The advantages for survey throughput and community buy-in are obvious. However, such an implementation places great demands on processing and data-management requirements, some of which are discussed here. 2. motivations While doing massive surveys for time-steady sources, the SKA can also do unprecedented deep surveys for pulsars, transient radio sources, and signals from ETI. To do so places distinct constraints on the configuration and signal-processing capabilities of the SKA, which are discussed in this article. Why search for transients? As Heraclitus might have said, You don t observe the same universe twice, and in modern times we recognize the time domain as an important dimension in the overall phase space of variables that characterizes the observable universe. Examples of transient radio signals are known that range from 0.4 ns and longer in time scale with apparent brightness temperatures from thermal to K. However, compared to the high-energy transient sky, we know next to nothing about the overall constituency of the transient radio sky. A highlighted science area for the SKA is Exploration of the Unknown (Wilkinson et al. 2004), which includes the overall phase space opened up by the SKA and the likely discovery of new classes of objects and phenomena. Another chapter in the SKA science book, The Dynamic Radio Sky (Cordes et al. 2004) discusses the anticipated payoff from an SKA design that combines widefield sampling of the sky with high sensitivity and flexibility in analyzing likely or hypothetical event signatures and time scales. One possibility is coherent emission from extra-solar planets (Lazio et al. 2004) Finally, the SKA Memo Discovery and Understanding with the Square Kilometer Array includes a discussion of radio transients as a primary component of the SKA discovery space. Most known radio transients have been found by making radio observations on targets selected from surveys made at other wavelengths or energies, such as radio afterglows from gamma-ray burst (GRB) sources and the turn-on of periodic radio pulsations from a formerly quiescent magnetar, J (Camilo et al. 2006). Recent exceptions include the discovery of the RRAT population (McLaughlin et al. 2006) and a transient sources in the Galactic-center (GC) direction (Hyman et al. 2006; Bower et al. 2006) found through archived VLA imaging observations of the GC. It is clear that blind surveys of the transient sky will yield new objects and new classes of objects that will serve as laboratories for the basic physics of extreme states of matter as well as inventorying Nature s proclivity for astrophysical complexity. Indeed, Nature is said to abhor a vaccuum, and this appears to be true in parameter space as well as physical space. Why search for more pulsars? Radio pulsars continue to provide unique opportunities for testing theories of gravity, for detecting nano-hz gravitational waves, and for probing states of matter otherwise inaccessible to experimental science. One of the five key projects identified for the SKA is the usage of pulsars for strong-field tests of gravity and gravitational wave detection (Kramer et al and references therein). Such tests can provide answers to one of the questions posed in Connecting Quarks with the Cosmos: Eleven Science Questions for the New Century 1 : Was Einstein right about gravity? To do so requires timing of pulsars like the extraordinary 1 National Academies Press, 2003, ISBN

4 double-pulsar binary J (Lyne et al. 2004), which comprises a recycled pulsar with 23ms spin period and a canonical pulsar with 2.8s period in a 2.4-hr orbit. Additional such binaries remain to be discovered, some with even smaller orbital periods, allowing correspondingly stronger tests of gravity. A Galactic Census of Pulsars, including Magnetars: We envision a Galactic census of radio pulsars that aims to detect at least half of the active radio pulsars that are beamed at us. Taking beaming and the radio lifetimes of pulsars into account, the fiducial neutron star (NS) birth rate of 10 2 yr 1 implies detectable pulsars in the Galaxy. The recent discovery of rotating radio transients (RRATs) by McLaughlin et al. (2006) through a reanalysis of the Parkes Multibeam pulsar survey suggests that the Galactic RRAT population is comparable in size to that of ordinary pulsars. The relationship between the two populations is not clearly known, but the RRATs, though found through detection of single pulses, have been found, through re-observation, to be periodic sources with periods not unlike those of canonical pulsars. Their discovery, however, illustrates the gain to be had in using algorithms that are less restrictive on signal type. Recently, two magnetars have been detected at radio wavelengths, with remarkably flat spectra extending to at least 100 GHz. Radio emission is episodic and bright, raising the possibility that the Galactic magnetar population may be better sampled through radio rather than X-ray surveys. Furthermore, extragalactic magnetars are detectable out to the Virgo cluster with the SKA. The first reason for proposing a complete Galactic census is obvious: the larger the number of pulsar detections, the more likely it is to find rare objects that provide the greatest opportunities for use as physical laboratories. These include binary pulsars as described above and also those with black hole companions; MSPs that can be used as detectors of cosmological gravitational waves; MSPs spinning faster than 1.5 ms, possibly as fast as 0.5 ms, that probe the equation-of-state under extreme conditions; hypervelocity pulsars with translational speeds in excess of 10 3 km s 1, which constrain both core-collapse physics and the gravitational potential of the Milky Way; and objects with unusual spin properties, such as those showing discontinuities ( glitches ) and apparent precessional motions, including free precession in isolated pulsars and binary pulsars showing geodetic precession. Free precession in neutron stars (which appears to occur in a few objects with long-precession periods) has eluded understanding because superfluid effects should rapidly damp precessional motion. Additional cases that occur under a range of conditions may help us understand the inner workings of NS. The second reason for a full Galactic census is that the large number of pulsars can be used to delineate the advanced stages of stellar evolution that lead to supernovae and compact objects. In particular, with a large sample we can determine the branching ratios for the formation of canonical pulsars and magnetars. We can also estimate the effective birth rates for MSPs and for those binary pulsars that are likely to coalesce on time scales short enough to be of interest as sources of periodic, chirped gravitational waves (e.g. Burgay et al. 2003). The third reason is that a maximal pulsar sample can be used to probe and map the interstellar medium (ISM) at an unprecedented level of detail. Measurable propagation effects include dispersion, scattering, Faraday rotation, and HI absorption that provide, respectively, line-of-sight integrals of the free-electron density n e, of the fluctuating electron density, δn e, of the product B n e, where B is the LOS component of the interstellar magnetic field, and of the neutral hydrogen density. The resulting dispersion measures (DM), scattering measures (SM), rotation measures (RM) and atomic hydrogen column densities (N HI ) obtained for a large number of directions will enable us to construct a much more detailed map of the Galaxy s gaseous and magnetic components, including their fluctuations. Radio data can be combined with multi-wavelength data (e.g. Hα and NaI absorption measurements) for modeling the ISM. Why search for ETI? Detection of a signal from another civilization in the Galaxy arguably would comprise the greatest scientific discovery ever made. Many of the discovery issues are discussed in Tarter (2004) and references therein. A recent paper (Loeb & Zaldariagga 2007) points out that low-frequency arrays now being built or planned (LOFAR, MWA/LFD, the low-frequency part of the SKA) will have sufficient sensitivity to detect Earth-equivalent leakage radiation to tens and hundreds of parsecs. 3. assumptions about the ska We assume in this document that the SKA includes a core array that will allow wide-field surveys, consistent with current nominal specifications. Antennas on long baselines from the core array are less easy to use but may play a role in anti-coincidence spatial filters to filter out radio-frequency interference (RFI) and instrumental interference. Some of our calculations will be based on an architecture based on a large number of small-diameter dish antennas (LNSD) for specificity but our conclusions on surveys are not altered for sky looking, phased-array approaches (aperture arrays).

5 4. search domains Comprehensive censuses are needed to find the rare objects that we know exist within the known source classes (e.g. pulsars in relativistic binaries) and that we suspect will be rare if they exist at all (e.g. radioemitting ETI). A qualitative shift in how a survey is conducted takes place if one recognizes that there may be only one target object in the entire sky. For large numbers, any subvolume of the sky is as good as any other and it is generally true that covering more solid angle is better than integrating longer to fainter levels on a particular sky position. But with a singular, one-in-the-sky type object one must either choose target directions carefully or achieve high sensitivity on all sky positions. Deep censuses for the three source classes suggest that the following regions on the sky need to be searched with high sensitivity and efficiency. Pulsars: 1. Galactic plane: for young pulsars associated with supernova remnants, possible magnetar-like objects; 2. Intermediate latitudes: for millisecond pulsars and relativistic binaries (pulsars with other neutron star and black-hole [BH] companions); 3. Galactic center: pulsars in the star cluster orbiting the M black hole, which are difficult to detect because radio wave scattering from material in the GC region broadens the pulses at standard pulsar search frequencies; 4. Globular clusters; 5. Nearby galaxies ( < 1 Mpc) 6. Galaxies out to 5 Mpc in searches for giant pulses like those typically seen from the Crab pulsar in 1 hour to the Virgo cluster for plausible amplitudes of giant pulses. Transient Sources: 1. Spatial domains similar to those for pulsars, with overlap for giant pulses from pulsars and RRATs; 2. Local regions in the Galaxy (nearby planets and stars) require sampling of an approximately isotropic distribution of sources; 3. Low frequencies for coherent sources; 4. Fast transients: all sky 5. Slow transients: all sky SETI: 1. Targeted searches of nearby stars, especially those with suitable planetary systems; 2. Blind surveys of the Galactic plane and other regions. 5. types of analysis Signal detection inevitably boils down to matched filtering or an approximation thereof, as discussed in Appendix B. For the three broad source classes we consider, signal analysis necessarily considers the structure of the signal in the frequency-time plane and processes that influence the detectability of the signal. Intrinsically, signals include the extremes of narrowband (spectral line) and narrow-time (pulselike) signals. Activities in the source may cause the signal s frequency to drift in time or its emission time to be frequency dependent. Extrinsic effects along the propagation path can also induce drifts of otherwise constant-frequency or narrowtime signals, such as source/observer acceleration or dispersive propagation through intervening plasma. Multipath propagation through the ISM also induce frequency-time structure via constructive and destructive inteference. Faraday rotation produces quasi-periodic structure in the Stokes parameters Q and U. Radio frequency interference (RFI) is strongly episodic and frequency dependent. Finally, scattering of radiation from telescope structure themselves can induce frequency-time structure. Backend processing is specialized for the three broad source classes, though there is some overlap in the kinds of operations that are needed for detection and analysis of the sources. Pulsars: 5

6 1. Dedispersion with trial values of dispersion measure (DM); 2. Matched filtering detection of single pulses of unknown width and shape; 3. Fourier analysis (including harmonic summing); and 4. Statistical tests and confirmation observations of candidate signals. Transient Sources: 1. Fast transients: analyses similar to those for single-pulse searches for pulsars, with perhaps a generalized matched filtering procedure operating in the frequency-time plane. 2. Slow transients: Processing of images obtained at requisite intervals, perhaps with spectral resolution to identify fine structure. SETI: 1. Generalized frequency-time analysis similar to that needed for dispersed, broadband pulses from pulsars but with much smaller channel bandwidths and frequency drift rates ( ν) consistent with anticipated Doppler accelerations. 6. the role of multipath propagation: scintillations, refraction and broadening in angle, time, and frequency The ionized ISM causes angle-of-arrival variations and multipath propagation of radio waves that influence surveys in several ways, all of which are highly frequency dependent. These include slow, broadband, refractive scintillations (RISS) and fast, narrowband diffractive scintillations (DISS) that can render undetectable strong sources and conversely make weak sources occasionally detectable. Pulses are broadened in time by multipath by amounts that are severe at low frequencies and for long paths through the Galactic plane. Short period pulsars are strongly selected against in these directions. Narrowband signals, such as those sometimes targeted in SETI, can be broadened by up to a few Hz at a frequency of 1 GHz on the longest paths. Broadening effects (in time or frequency) usually will conserve flux density, though special geometries can induce violation of flux conservation. DISS produces 100% modulations (1σ) at frequencies below the transition frequency between strong and weak scintillation (typically 5 GHz for 1 kpc distances and up to 100 GHz for the Galactic center) while RISS shows 20% modulations. Propagation effects strongly influence the choice of frequency and methodology in conducting surveys of various kinds. At radio wavelengths, multipath propagation is caused by density fluctuations in intervening plasmas, including the ionosphere, the interplanetary medium, the interstellar medium and, though not yet revealed in any measurements, the intergalactic medium (IGM). Galactic components other than the ISM per se, such as supernova remnants, HII regions, the Galactic center, and the ionospheres and interplanetary media of other stars and their planetary systems will also contribute to propagation phenomena. Observable effects from multipath propagation include: 1. Intensity variations on time scales t d of seconds to years and frequency scales ν d ν (diffractive scintillation) and ν r ν (refractive scintillation). Intensity variations from propagation effects in intervening ionized media (supernova remnants, Galactic center, interstellar medium, intergalactic medium, interplanetary media, ionospheres) occur on a variety of time and frequency scales. These will apply to all sources of fast transients because the sources necessarily must be compact in nature. Slower transients will show fewer such effects because they are likely to be larger in size, thus quenching diffractive interstellar scintillations (DISS). DISS can play a key role in the design of surveys for compact sources. Under general conditions, the intrinsic intensity of a point source is modulated by a gain g that has a one-sided exponential probability distribution, f g (g) = e g U(g), where U(g) is the unit-step function. Multiple trial strategies can exploit the fact that g sometimes boosts the signal strength above a predetermined threshold even though most of the time g < 1 (Cordes & Lazio 1991; Cordes, Lazio & Sagan 1997). The dynamic spectrum in Figure 1 shows strong DISS from a nearby pulsar. Figure 2 shows how the characteristic DISS time scales with dispersion measure over a set of pulsars. 2. Angular broadening ( seeing ) of point sources on angular scales ranging from sub-mas to arcseconds or more.

7 Fig. 1. Left: Dynamic spectrum of pulsar B at 0.43 GHz, showing diffractive ISS with 100% modulations (i.e. rms / mean) of the pulsed flux. The characteristic time and frequency scales are very strong functions of frequency and of the particular scattering along the line of sight to the pulsar. Fig. 2. Right: The characteristic DISS timescale at 1 GHz plotted against DM for a sample of pulsars. For objects with multiple observations, the vertical bars designate the ±1σ variation of the mean value. The solid and dashed lines show predicted DISS timescales for transverse source velocities of 10, 100 and 10 3 km s 1 using results discussed in Cordes & McLaughlin (2004). The DISS timescale varies with frequency as t d ν 1.2 if the scintillation bandwidth has the Kolmogorov scaling, ν d ν 4.4, as appears consistent for some objects. For extragalactic sources, the DISS time scale will differ because the geometry of the scattering medium consists of a foreground region from the Galaxy and another region corresponding to material in the host galaxy (if any). Nonetheless, the order of magnitiude value of the time scale can be estimated using the value of DM expected from just the foreground material in the Galaxy. The points are from Bhat et al. (1999); Bogdanov et al. (2002); Camilo & Nice (1995); Cordes (1986); Dewey et al. (1988); Foster et al. (1991); Fruchter et al. (1988); Gothoskar & Gupta (2000); Johnston et al. (1998); NiCastro et al. (2001); and Phillips & Clegg (1992). 3. Temporal (pulse) broadening caused by multipath propagation. An example is shown in Figure 3. The characteristic time scale τ d has been measured to from sub-ms to 1 sec. This time scale is proportional to the inverse of the diffractive bandwidth, τ d ν d 1. Figure 4 shows the pulse broadening time vs. dispersion measure (DM) for a large sample of pulsars. 4. Spectral broadening of narrow spectral lines caused by temporal changes in geometrical path length; this effect is relevant only to SETI surveys (Cordes & Lazio 1991) because the amplitude is of order ν sb ( t d ) 1 < 1 Hz except for very heavily scattered lines of sight. DISS has characteristic time and frequency scales that scale roughly as ν 4 and ν, respectively, below the transition frequency and are of order MHz and minutes for a typical pulsar at 1 kpc distance. Pulse broadening and spectral broadening are reciprocals of the characteristic DISS bandwidth and timescale, respectively, and thus scale as ν 4 and ν 1. DISS and RISS are both well known in pulsar observations, while only RISS has been convincingly detected from AGNs, owing to the quenching effects of finite source sizes for DISS. Pulsars are sufficiently compact to show DISS and plausible scenarios for ETI transmission suggests that they too will show DISS, unless they are too close to the Earth ( < 100 pc at 1 GHz) for the strong scintillation regime to apply. 7. pulsars and magnetars Detection of pulses from pulsars can exploit the periodicity of their emission but must contend with a number of effects that attenuate Fourier amplitudes: 1. Instrumental response times longer than a pulse width; the narrowest pulse width 40 µs. 2. Differential arrival times caused by plasma dispersion; these can be removed, though there will be residual smearing in post-detection dedispersion techniques or from dedispersing with an approximate value of DM; these effects scales ν Temporal broadening caused by multipath propagation in the interstellar medium; this effect scales strongly with frequency ( ν 4 ). 7

8 1.23 GHz 1.52 GHz 2.40 GHz Fig. 3. Pulse profile vs. frequency for a pulsar with moderate value of dispersion measure (DM; Bhat et al. 2004). The spread of differential arrival times from multipath propagation which causes the asymmetric tail on the pulses is much stronger at lower frequencies owing to the frequency dependence of the index of refraction of the warm ionized interstellar medium. Fig. 4. Right: Pulse broadening time τ d and scintillation bandwidth ν d plotted against DM (see Cordes & Lazio 2002 for references). The open circles represent measurements of τ d while filled circles designate measurements of ν d. Arrows indicate upper limits. The two quantities are related by 2πτ d ν d = C 1 with C 1 = All measurements have been scaled to 1 GHz from the original frequencies assuming τ d ν 4.4. The solid curve is a least squares fit and the dashed lines represent ±1.5σ deviations from the fit. Surveys for pulsars that involve a Fourier search for periodicities or matched-filtering for dispersed, single pulses are strongly affected by pulse broadening, which conserves the pulse area, and thus reduces the pulse amplitude and reduces the number of detectable harmonics in the power spectrum. Continuum (imaging) surveys are, of course, less affected by the angular broadening that accompanies (indeed causes) pulse broadening, because it does not broaden sources significiantly compared to telescope resolutions except on lines of sight through the Galactic center region and lines of sight through the Galactic plane at low frequencies. Nearby, low-dm pulsars are unaffected by pulse broadening, but do show intensity scintillations when the scintillation bandwidth, ν d, is comparable to the receiver bandwidth. 4. Orbital motion is important even for data spans much smaller than the orbital period. 5. Intrinsic variations, such as pulse nulling or other strong modulations, including giant-pulse emission (see below). 6. RRAT sources. 7. Eclipses of binary pulsars. 8. Interstellar scintillations, which modulate the received pulsar flux density on a variety of time and frequency scales. Galactic pulsars are distributed according to their birth from an extreme Population I distribution of stars and modified by the wide pulsar velocity distribution. The luminosity function of pulsars is a broad power law because it is determined by beaming combined with intrinsic variation that depends on spin rate and magnetic field. For pulsars we can factor S min as (See Appendix C): S min = S min 1, (1) h Σ ms sys S min1 =, (2) 1/2 (N pol B T) where S min1 is the minimum detectable flux density for a single harmonic in the power spectrum, m is the threshold in units of sigma (rms flux density), S sys is the system-equivalent flux density (for the entire array in the case of the SKA) and h Σ is the harmonic sum commonly used in pulsar surveys. We define the harmonic sum as a dimensionless quantity, N h h P (N h ) = N 1/2 h f j ; (3) j=1

9 h P is equal to unity if the signal is an undistorted sinusoid but can be much larger than unity when many harmonics (N h ) are significant. For heavily pulse-broadened pulsars, h P is maximized with N h = 1 (the fundamental frequency component) and the amplitude will be exponentially suppressed. For a gaussian pulse with width W (FWHM), the harmonic sum is maximized for N h,max P/2W harmonics (for small duty cycles, W/P 1) and is approximately h Σmax 1 2 (P/W)1/2. Using nominal parameters for Arecibo and the SKA 2 (S sys = 3.0 and 0.14 Jy, respectively, B = 400 MHz, and T = 300 s), we find that 61 µjy AO ( m g θ 10) S min1 = 2.8 µjy g θ f c SKA, where we have included a factor g θ 1 that accounts for off-axis gain and for the SKA a factor f c equal to the fraction comprising the fraction of the collecting area in a core array that is usable for blind searching. We have used a threshold of 10σ (m = 10). The maximum detectable distance is D max = (L p /S min ) 1/2 where L p is the pseudo-luminosity (flux density times the square of the distance, as often used in the pulsar community): ( ( ) m 1/2 1/2 L 4.0 kpc (g θ h Σmax ) p D max = 10) 1/2 AO 1 kpc 2 (5) mjy 18.9 kpc (f c g θ h Σmax ) 1/2 SKA. To evaluate D max, we consider particular directions through the Galaxy and use an electron density model (NE2001, Cordes & Lazio 2002, 2003) to evaluate pulse broadening and its effects on the harmonic structure of the Fourier analysis used to search for periodicities. Figure 6 shows D max calculated for Arecibo and the SKA using this approach. We also include curves for the Green Bank Telescope (GBT) and the Parkes radio telescope using the 1.4 GHz multibeam system. The figure demonstrates that for a wide range of values for periods and L p, the SKA can probe to the anticipated boundaries of the pulsar distribution, even after taking into account the high velocities of some objects. The SKA will provide a great leap in surveying the neutron-star population of the Galaxy. Also, for objects with L p > 10 3 mjy kpc 2 (of which there are a few examples in the known Galactic population), the SKA can reach in standard periodicity searches D max 1 Mpc that includes the nearby galaxies M31 and M33 in standard periodicity searches. (4) An analysis of radio pulsar detection indicates that: General Pulsar and Magnetar Surveys With an Arecibo-size antenna, 400 MHz bandwidth at L band, and 300-s dwell times, some pulsars can be detected out to the far edge of the Galaxy on the opposite side of the Galactic center. However, many objects cannot be detected either because of 1/r 2 effects (luminosity limited) or because the pulses are severely broadening by scattering (scattering limited). Greater sensitivity than Arecibo allows detection of pulsars that are luminosity limited with Arecibo. Surveys at frequencies higher than 1.4 GHz enable detection of objects that are scattering limited at L band because the pulse-broadening time τ d ν 4. Migration of surveys to higher frequencies must be traded against the generally lower flux densities (pulsar flux densities S ν α with typical spectral indices 0.1 < α < 3 at L band) and smaller FOV and array beam sizes. For Arecibo these numbers are for the Arecibo L-band Feed Array (ALFA) system, with approximately 30 K system temperature and 10 K Jy 1 system gain. For the SKA, the value for S sys follows from the nominal requirement of A e/t sys = m 2 K 1. Recent work (2007) suggests that A e/t sys will be reduced from this nominal value by a factor of 2 to 3 for the SKA. 9

10 Fig. 5. D max vs. single-harmonic threshold for 7 pulse periods. At large values of S min1, the slope is -1/2 because D max is luminosity limited. For smaller values of S min1 and especially for short period pulsars, the curve is less steep because D max is scattering limited owing to pulse broadening in the interstellar medium Fig. 6. D max vs. spin period for pulsar detection for two directions through the Galaxy: (left): l, b = 30,0. (right): l, b = 50,5. In each case, the four frames correspond to different values of the pseudo-luminosity L p, which is the periodaveraged flux density D 2 (for a known pulsar, say). The distribution of L p for pulsars is broad, covering several orders of magnitude, because the emission is beamed. The colored, shaded regions shown from top to bottom in each frame are for Arecibo, the GBT, Parkes, and the SKA. Top boundary of each shaded region: full sensitivity. Lower boundary of each shaded region: partial sensitivities. For the SKA the partial sensitivity represents f cg θ = 0.25 (e.g. 25% of the collecting area in the core array at full on-axis gain (g θ = 1, or larger fraction combined with an off-axis gain factor g θ < 1. For Arecibo, the lower boundary is given by g θ = 0.5, i.e. sensitivity at the half-power point. Other survey parameters include ν = 1.4 GHz, B = 400 MHz, time resolution = 64 µs, integration time = 300 s, and a 10σ threshold. An intrinsic pulse duty cycle of 0.05 is assumed. Propagation effects, which smear the pulse, are calculated using the electron density model NE2001. For distances > 5 kpc in directions through the Galactic plane (b = 0), D max is strongly influenced by pulse broadening from scattering. The decrease in D max for smaller P occurs because pulse smearing has a greater effect on the assumed narrower pulses of short-period pulsars.

11 Magnetar radio emission has a remarkably flat spectrum extending to > 100 GHz (Camilo et al. 2006). Though episodic, when on the emission has fairly steady pulse amplitudes that are very bright. From Figure 6 (bottom left panel), pulsars with L p 10 mjy kpc 2 are detectable to 0.1 Mpc. Magnetars as bright as the two currently known radio emitters are therefore detectable across the Galaxy. Radio surveys for magnetars are probably the most efficient method for a full magnetar census of the Galaxy. These facts suggest that pulsar surveys with the SKA can be undertaken in a number of configuration modes: 1. Full FOV surveys with full SKA/core sensitivity; 2. Full FOV surveys with partial SKA/core sensitivity (as a subarray); 3. Multiple FOV surveys with partial SKA/core sensitivity using multiple subarrays; each subarray would survey one FOV s worth of sky. Strawman survey parameters: Assume an L band survey with 300-s dwell time covering the full FOV. We consider the FOV specification of 1 deg 2 for the SKA that matches the actual FWHM of the 12-m dishes of the LNSD concept. If all Galactic longitudes and latitudes b 10 are surveyed 3, the 7200 deg 2 would require 25 days to complete. Higher-latitude surveys are also of interest to find millisecond pulsars, relativistic binary pulsars, and high-space-velocity pulsars. Surveying the entire sky (41,253 deg 2 ) would require 143 days Galactic Center Survey Pulsars in the Galactic center (GC) provide especially important opportunities for probing the magnetoionic medium, the gravitational potential in the GC region, and the central black hole (Sgr A*) (e.g. Cordes & Lazio 1997; Pfahl & Loeb 2004). The GC in this context refers to the region 200 pc in diameter centered on Sgr A* with approximately a 1 deg 2 solid angle. Scattering is especially severe for pulsars in this region, as summarized in Appendix E. Table 1 Sensitivity Calculations for Galactic Center Pulsar Periodicity Searches Note: all calculations assume a 6 hour integration Telescope Frequency BW SEFD S min1 S min1 Dgc 2 S min1 Dgc GHz (GHz) (GHz) (Jy) (µjy) (mjy kpc 2 ) (mjy kpc 2 ) GBT EVLA m South SKA Figure 7 shows D max vs P at two frequencies. At 0.4 GHz, scattering in the inner Galaxy and especially from the scattering screen in the GC itself causes D max to saturate at about 8.4 kpc because pulses 3 This would imply that there are both Northern and Southern hemisphere core arrays! 11

12 Fig. 7. D max vs. spin period for pulsar detection looking toward the Galactic center (l, b = 0,0 ) at two frequencies (left): 0.4 GHz; (right): 9 GHz. The plot format is the same as in Figure 6. originating from beyond the GC scattering screen at this distance are temporally broadened by hundreds of seconds or more. Because such broadening ν 4, the situation at 9 GHz (right panel of Figure 7) is much different. Low-luminosity pulsars (e.g. L p < 1 mjy kpc 2 ) still cannot be seen into the GC region but more luminous pulsars break through the barrier distance, as indicated for the L p = 10 mjy kpc 2 case. Figure 8 summarizes the situation for the known population of pulsars. The points are P and L p = S 1400 D 2 for known pulsars from the latest ATNF pulsar catalog 4, where we use the period-averaged flux density at 1.4 GHz. The plotted curves show detectability of pulsars in periodicity searches at 9 GHz for pulsars at the location of Sgr A* for the GBT and SKA along with a curve for the SKA at 15 GHz. Pulsars need to be above the curves to be detected. The curves are calculated at the indicated frequencies and then referred back to 1.4 GHz assuming a ν 2 spectrum. From the plot, we make the following notes: Only a small fraction of known pulsars is detectable using the GBT at 9 GHz, whereas most of the non-recycled pulsars are detectable with the SKA at 9 GHz. Searches at 15 GHz do not increase the fraction of detectable long-period pulsars but do allow detection of MSPs. Pulsars displaced from Sgr A* along the LOS are easier to detect if they are closer to the Sun, while those further away will be harder to detect owing to the scaling of pulse broadening with offset of the pulsar from the scattering screen (Eq. E1). Overall, our calculations suggest that the SKA can be a powerful probe of the pulsar population in the GC if it can be used to conduct surveys at 9 GHz or higher Globular Cluster Surveys Globular clusters (GCs) are prolific factories for recycled pulsars (e.g. Ransom et al. 2005) and may provide the best opportunities apart from the Galactic center (another GC ) for finding pulsars orbiting a black hole. GCs require high sensitivity but do not place any demands on FoV. Current programs with the GBT and Arecibo reach many GCs, but total radio flux density measurements from imaging observations and pulsar counts suggest that many more faint pulsars remain to be discovered. The more distant GCs also require high sensitivity capabilities, particularly in the Southern hemisphere. 4

13 Fig. 8. Detectability of pulsars in the Galactic center is shown in this plot of pseudo luminosity L p = S 1400 D 2 vs. spin period, where S 1400 is the period-averaged flux density at 1.4 GHz. Duty cycles for pulsars range from 0.01 to 0.7, so the peak flux density can be a large multiple [i.e. 1 / (duty cycle)] of the period-averaged flux density. Plotted curves assume a 6-hr integration time with a threshold of 10σ for bandwidths specified in Table 1. The long dashed curves are for 9 GHz. Solid curves are for 15 GHz and the short dashed curve for the SKA is for 20 GHz. Plotted points use periods and values of L p from the ATNF/Jodrell pulsar catalog. Scattering is assumed to be in a filled region centered on Sgr A* with 1/e cylindrical radius of 0.15 kpc, as included in the NE2001 model (Cordes & Lazio 2002). For pulsars at the location of Sgr A*, the dispersion and scattering measures are DM GC = 1577 pc cm 3 and SM GC = 10 7 kpc m 20/3. The curves are based on harmonic sums of the Fourier power spectra of dedispersed time series. They correspond to surveys at these frequencies but have all been scaled to the equivalent sensitivity at 1.4 GHz assuming that the pulsar flux densities scale as ν 2. Less-steep spectra will move the curves downward. Incoherent summing of power spectra obtained from multiple 6-hr data sets will also move the curves downward. The SKA curves assume that the full, nominal sensitivity of the SKA is available (S sys = 0.14 Jy Extragalactic Pulsars and Magnetars Extragalactic pulsars and magnetars are reachable with the SKA. Figure 6 (bottom-right panel) shows that pulsars with fairly modest L p can be detected to 100 kpc. Milky Way pulsars extend to L p as large as 10 4 Jy kpc 2 at 1.4 GHz, implying D max 10 Mpc for most spin periods > 10 ms. Pulse broadening from scattering within the host galaxies will inhibit detection of short period pulsars in some cases. Sporadic magnetar emission (see below under transients) has very flat spectra in two cases (e.g. Camilo et al. 2006) with L p mjy kpc 2 implying detectability to about 1.7 Mpc in a 300 s observation. D max values plotted in Figure 6 are shown as a band with full-ska, on-axis gain at the top of the band, and for 25% of the full gain the band bottom, either because observations are off axis or because only a subset of the SKA is useable for blind surveys. The numbers quoted above are for approximately the midpoint of the band and of course there are other uncertainties to be considered. 8. transients We know little about the transient radio sky. Giant pulses from radio pulsars are prototypes for fast transients along with solar bursts and flare stars, while sources such as microquasars and gamma-ray burst (GRB) afterglows exemplify longer-duration transients. We may use these sources as initial guides for specifying blind-survey parameters. However, simple observational phase space arguments suggest that instantaneous coverage of a large fraction of the sky with appropriate sampling of the frequency-time plane will yield a rich variety of transient sources, including new classes of objects. Figure 9 shows the phase space of pulse width W against flux density. Lines of constant brightness temperature are calculated assuming that W is the light-travel time across the source, T b = S ( ) 2 ( ) 2 D = Dkpc K S mjy (6) 2k νw ν GHz W ms 13

14 where S mjy is the peak flux density (mjy) at frequency ν (GHz) and D is the distance (kpc). For some sources W can be much smaller than the light travel time owing to relativistic compression and of course other sources can vary much more slowly. ISS IDV ISS GRB ISS IDV ISS GRB B B Type II Type II Type III Type III Jup DAM BD LP Jup DAM BD LP Fig. 9. Time-luminosity phase space for radio transients. Left panel: frame showing already-known radio transients. Right panel: frame that shows hypothetical transients, including maximal giant-pulse emission from pulsars, prompt radio emission from GRBs, and radar signals used to track potentially impacting asteroids and comets (see text). Each frame shows a log-log plot of the product of peak flux S pk in Jy and the square of the distance D in kpc vs. the product of frequency ν in GHz and pulse width W in s. The uncertainty limit on the left indicates that νw > 1 as follows from the uncertainty principle. Lines of constant brightness temperature T = SD 2 /2k(νW) 2 are shown, where k is Boltzmann s constant. Points are shown for the nano-giant pulses detected from the Crab (Hankins & Eilek 2007), giant pulses detected from the Crab pulsar and a few millisecond pulsars, and single pulses from other pulsars. Points are shown for Jovian and solar bursts, flares from stars, a brown dwarf, OH masers, and AGNs. The regions labeled coherent and incoherent are separated by the canonical K limit from the inverse Compton effect that is relevant to incoherent synchrotron sources. Arrows pointing to the right for the GRB and intra-day variable (IDV) points indicate that interstellar scintillation (ISS) implies smaller brightness temperatures than if characteristic variation times are used to estimate the brightness temperature. The growing number of recent discoveries of transients illustrates the fact that empty regions of the νw S pk D 2 plane may be populated with sources not yet discovered, such as those shown in the right panel. These recent discoveries include the rotating radio transients (RRATs; McLaughlin et al. 2006), the Galactic center transient source, GCRT J (Hyman et al. 2006), the bright, bursting magnetar XTE J (Camilo et al. 2006), and recently discovered transients (labelled RT ) associated with distant galaxies (Bower et al. 2007). The rightward-directed triangles used to mark the two RT sources indicate that the transient durations are only known to be longer than 20 min. A lone pulse from the source J (Lorimer et al. 2007) has a DM that is too large (for the source direction) to be accounted for by the Milky Way or by the Small Magellanic Cloud, a few degrees away. In the figure the nominal distance of 500 Mpc advocated by Lorimer et al. is used, with an upward directed arrow signifying that it could be further. Equally arguable, however, is that the source is or is seen through a relatively nearby galaxy or that it is in a binary system in the Milky Way s halo, with the large DM contributed by a companion star. Dashed lines indicate the detection threshold for the full SKA for sources at distance of 10 kpc and 3 Gpc. Dotted lines correspond to a 10% SKA, comparable to the Arecibo telescope. At a given νw, a source must have luminosity above the line to be detectable. The curves assume optimal detection (matched filtering). Slow transients are defined as those with time scales longer than the time it takes to image the relevant region of the sky, either in a single pointing or as a mosaic or raster scan. Detection of such objects can be accomplished simply through repeated mapping of the sky and thus does not require special capabilities beyond those needed for imaging applications. GRBs are currently detected at > 100 µjy levels using the VLA at frequencies of 5 and 8 GHz. The full SKA could detect GRB afterglows to at least 100 times fainter levels. Fast transients, by contrast, require the same observing modes and post-processing as for pulsars. The Crab pulsar is the most extreme known case in terms of showing temporal structure down to 0.4 ns scales (Hankins et al. 2007) and giant pulses that exceed 130 times the entire flux density of the Crab Nebula. Figure 10 shows an example of such a pulse, including the dispersion sweep in the frequency-time plane. Pulsars and giant-pulse emission may represent prototypes for coherent radiation from other high-energy

15 objects in which collimated particle flows can drive the necessary plasma instabilities. Examples include prompt radio burst emission from GRB-type sources, perhaps even from gamma-ray quiet objects; flare stars, jovian-burst like radiation from planets, AGNs, and merging NS at cosmological distances (Hansen & Lyutikov 2001). Using GRBs as a guide, it may be noted that the rate of GRB detection with gamma-ray instruments has relied more on instantaneous wide-field sky coverage than on sensitivity. The same statement holds for the detection of prompt optical emission at m v = 9 in at least one case (Akerlof et al. 1999; Bloch et al. 2000). For this reason, we suggest that use of subarray modes to increase the instantaneous sky coverage at less than full sensitivity will be productive in surveying the transient radio sky. The signal-to-noise ratio for a pulse after dedispersion and matched filtering is S N = S(N polbw) 1/2, (7) S sys where S is the peak flux density and W is the pulse width (FWHM). Requiring S/N > m = 10 and using N pol = 2 polarizations using nominal parameters for Arecibo and the SKA (see footnote 2), we get a minimum detectable flux density ( m ) ( ) 1/2 ( ) 1/2 1 ms 1 GHz S min,sp = 10 W B corresponding to a minimum brightness temperature, 21 mjy g θ 0.98 mjy g θ f c ( m ) ( ) 5/2 ( ) 1/2 ( ) 2 1 ms 1 GHz Dkpc T min,sp = 10 W B ν GHz K g θ AO SKA, K SKA. g θ f c A burst of amplitude S pk from a known source at distance D = D kpc kpc can be detected to a maximum distance D max = D ( Spk S min,sp ) 1/2 ( ) 1/2 ( ) 1/2 ( ) 1/4 ( ) 1/4 Spk 10 W B = D kpc 1 Jy m 1 ms 1 GHz 6.9 kpc g 1/2 θ AO 32 kpc (g θ f c ) 1/2 SKA. The SKA can see about 1.5 orders of magnitude fainter than Arecibo. However, the much greater advantage of the SKA over Arecibo will consist of the sky coverage and greater resilience against RFI. With such coverage we can expect the SKA to yield new discoveries over much of the phase space depicted in Figure 9. AO (8) (9) (10) 8.1. Giant Pulse Detection The Crab pulsar s giant pulses (GPs) are currently the brightest known, with examples at 0.4 GHz of S pk 150 kjy occurring at a rate of once per hour. At this frequency, the pulse width W 100 µs, but is intrinsically much narrower because scattering has broadened the pulse. At high frequencies, structure internal to GPs is as short as 0.4 ns (Hankins & Eilek 2007) with amplitudes as high as 2.2 MJy at 9 GHz. With these numbers, Eq. 10 implies that the 0.4 GHz pulses can be detected with a 50 MHz bandwidth to 0.7 Mpc for nominal values of other parameters at Arecibo and to 3.3 Mpc for the full SKA. The 0.4 ns pulse is detectable to 0.3 Mpc for Arecibo and 1.4 Mpc for the full SKA. Undoubtedly, there are larger but less frequent pulses from the Crab pulsar (Lundgren et al. 1995) and there are GP emitters that are brighter than the Crab pulsar (see below in the transients section). It is therefore clear that GPs can be seen to nearby galaxies and, with reasonable extrapolation to brighter sources, the large number of potential GP emitters in the Virgo cluster (D 20 kpc) can be reached. 15