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The Dynamic Radio Sky

James M. Cordesa ∗ T. Joseph W. Laziob † M. A. McLaughlinc

aAstronomy Department and NAIC, Cornell University, Ithaca, NY, USA; cordes@astro.cornell.edu

bNaval Research Laboratory, Washington, DC, USA; Joseph.Lazio@nrl.navy.mil

cJodrell Bank Observatory, University of Manchester, Macclesfield, Cheshire, SK11 9DL, UK

Transient radio sources are necessarily compact and usually are the locations of explosive or dynamic events,therefore offering unique opportunities for probing fundamental physics and astrophysics. In addition, short-duration transients are powerful probes of intervening media owing to dispersion, scattering and Faraday rotationthat modify the signals. While radio astronomy has an impressive record obtaining high time resolution, usuallyit is achieved in quite narrow fields of view. Consequently, the dynamic radio sky is poorly sampled, in contrast tothe situation in the X-ray and γ-ray bands. The SKA has the potential to change this situation, opening up newparameter space in the search for radio transients. We summarize the wide variety of known and hypothesizedradio transients and demonstrate that the SKA offers considerable power in exploring this parameter space.Requirements on the SKA to search the parameter space include the abilities to (1) Make targeted searches usingbeamforming capability; (2) Conduct blind, all-sky surveys with dense sampling of the frequency-time planein wide fields; (3) Sample the sky with multiple fields of view from spatially well-separated sites in order todiscriminate celestial and terrestrial signals; (4) Utilize as much of the SKA’s aggregate collecting area as possiblein blind surveys, thus requiring a centrally condensed configuration; and (5) Localize repeating transient sourcesto high angular precision, requiring a configuration with long baselines, thus requiring collecting area in both acentrally condensed “core” array and sufficient area on long baselines.

1. Introduction

Transient emission—bursts, flares, and pulseson time scales of order 1 month—marks compactsources or the locations of explosive or dynamicevents. As such, radio transient sources offer in-sight into a variety of fundamental physical andastrophysical questions including

• The mechanisms of efficient particle accel-eration;

• Possible physics beyond the StandardModel;

• The nature of strong field gravity;

∗This work was supported by NSF grants to Cornell Uni-

versity, AST 9819931, AST 0138263, and AST 0206036

and also by the National Astronomy and Ionosphere Cen-

ter, which operates the Arecibo Observatory under a co-

operative agreement with the NSF.†Basic research in radio astronomy at the NRL is sup-

ported by the Office of Naval Research.

• The nuclear equation of state;

• The cosmological star formation history;

• Detecting and probing the interveningmedium(a); and

• The possibility of extraterrestrial civiliza-tions.

A figure of merit for transient detection isAΩ(T/∆t), where A is the collecting area of thetelescope, Ω is the solid angle coverage in thesearch for transients, T is the total duration ofobservation, and ∆t is the time resolution. Effec-tive detection of transients requires

AΩ

(

T

∆t

)

→ “large” (1)

At high energies (X- and γ-rays), detectors withlarge solid angle coverage and high time resolu-tion have had great success in finding classes oftransient objects. At optical wavelengths there

1

2

has been recent progress in constructing wide-field detectors with high time resolution. His-torically, radio telescopes have been able to ob-tain high time resolution (with some modern tele-scopes achieving nanosecond time resolution) orlarge fields of view, but rarely have both high timeresolution and large field of view been obtainedsimultaneously.

Nonetheless, there are a number of indicationsthat the radio sky may be quite dynamic. Radioobservations of sources triggered by high-energyobservations (e.g., radio observations of gamma-ray burst afterglows), monitoring programs ofknown high-energy transients (e.g., radio moni-toring of X-ray binaries), giant pulses from theCrab pulsar, a small number of dedicated radiotransient surveys, and the serendipitous discoveryof transient radio sources (e.g., near the Galacticcenter) suggest that the radio sky is likely to bequite active on short time scales. There also maybe unknown classes of sources.

In this chapter, we discuss radio transientsfrom the standpoint of the available phase spacethat the SKA can probe and how the design ofthe SKA can be optimized to improve its studyof both known and suspected classes of tran-sient radio sources. Several specific classes ofradio transients—including pulsars, supernovaeand gamma-ray bursts, ultra-high energy cos-mic rays, and scintillation-induced variability—are discussed in more depth in additional chap-ters. We summarize the wide variety of bothknown and hypothesized radio transients in §2,the available phase space that the SKA can probein §3, and the operational modes and aspects oftransient detection for the SKA in §4.

2. Known and Potential Classes of Tran-

sient Radio Sources

Searches for radio transients have a long his-tory, and a wide variety of radio transients areknown, ranging from extremely nearby (ultra-high energy cosmic rays impacting the Earth’satmosphere) to cosmological distances (γ-raybursts). There are also a number of classes ofhypothesized classes of transients. In this sec-tion we provide an overview of the wide variety

of radio transients that the SKA could detect andstudy.

Ultra-high energy particles: Intense, short-duration pulses (∼ 1 MJy in ∼ 1 ns) atfrequencies of a few to a few hundred MHzhave been observed from the impact ofultra-high energy particles on the Earth’satmosphere [89,25,41]. High-energy neutri-nos impacting the lunar regolith should alsoproduce radio pulses near 1 GHz, thoughsearches to date have been unsuccessful indetecting any such pulses [34]. Detectionof such particles can place significant con-straints on the efficiency of cosmic accel-erators, and potentially on the existenceof physics beyond the Standard Model ofparticle physics, if particles with energiesbeyond the Greisen-Zatsepin-Kuzmin limit(1019.7 eV) are detected.

The Sun: Type II and III solar bursts are de-tected regularly at radio frequencies of tensof MHz [62,73] while solar flares can be de-tected at tens of GHz [90]. It is not yet clearthat the SKA capabilities will extend to fre-quencies that will optimize studies of theSun, but, if so, the Sun offers a nearby siteto study particle acceleration in detail, par-ticularly when observations are combinedwith optical, ultraviolet, and X-ray obser-vations.

Planets: Jupiter has long been known to emitradio flares at decameter wavelengths [3,58],and all of the planets with strong magneticfields (Earth, Jupiter, Saturn, Uranus, andNeptune) produce radio radiation, thoughnot always above the Earth’s ionosphericcutoff. At least one of the known extra-solar planets3 also appears to have a strongmagnetic field [79]. By analogy to the solarsystem planets, Farrell et al. [26], Zarka etal. [93], and Lazio et al. [56] suggest that ex-trasolar planets would produce bursty emis-

3It is worth noting that the first extrasolar planets

were discovered using radio observations of the pulsar

PSR B1257+12, though any radio emission from these

planets is not likely to be detectable.

3

sion as well. Characteristic frequencies,based on scaling laws from the solar system,suggest that the known extrasolar planetswould radiate primarily in the range 10–1000 MHz with flux densities of 10–100 µJy.Detection of radio emission from extrasolarplanets would constitute direct detection, incontrast to the largely indirect detectionsof the known extrasolar planets achieved todate from the reflex motions of their hostsstars.

Brown dwarfs: Radio flares have been detectedfrom BD LP944−20 [7], and a survey oflate-type stars and brown dwarfs founda number of other objects also exhibitingflares [6]. Typical flare strengths are oforder 100 µJy at frequencies between 5and 8 GHz. The flares are thought to orig-inate in magnetic activity on the surfacesof the brown dwarfs, though some objectshave radio emission that deviates from theexpected radio–X-ray correlation observedfor stars.

Flare stars: Radio flares from various activestars and star systems are observed at fre-quencies of order 1 GHz with flux densitylevels that can reach of order 1 Jy [45,75,29]These systems can show strong polariza-tion, including strong circular polarization.These flares are attributed to particle accel-eration from magnetic field activity.

Pulsar giant pulses: While all pulsars showpulse-to-pulse intensity variations [39],some pulsars have been found to emit so-called “giant” pulses, pulses with strengths100 or even 1000 times the mean pulse in-tensity. The Crab (PSR B0531+21) wasthe first pulsar found to exhibit this phe-nomenon. In one hour of observation, thelargest measured peak pulse flux of theCrab is roughly ∼ 105 Jy at 430 MHz fora duration of roughly 100 µs [36], corre-sponding to an implied brightness temper-ature of 1031 K. Recently, pulses with flux∼ 103 Jy at 5 GHz for a duration of only2 ns have been detected from the Crab [33].

These “nano-giant” pulses imply brightnesstemperatures of 1038 K, by far the mostluminous emission from any astronomicalobject. For many years, this phenomenonwas thought to be uniquely characteristic ofthe Crab. However, giant pulses have sincebeen detected from the millisecond pulsarsPSR B1821−24 [76] and PSR B1937+21[10] and PSR B0540−69, the Crab-like pul-sar in the Large Magellanic Cloud [46].

Transient pulsars: Nice [70] searched for radiopulses along 68 deg2 of the Galactic planeat 430 MHz. This search resulted in the de-tection of individual pulses from 5 knownpulsars and the discovery of one new pul-sar which was previously missed in a stan-dard periodicity search [69]. This pulsar(J1918+08) does not emit giant pulses4 butis a normal, slow pulsar which fortuitouslyemitted one strong pulse during the searchobservations. More recently, Kramer etal. [53] have recognized a class of pulsarsthat produce pulses only a small fraction ofthe time. When “on,” they appear indis-tinguishable from normal pulsars. For in-stance, the 813-ms pulsar PSR B1931+24 isnot detectable more than 90% of the time[53], and the 1.8-s pulsar PSR B0826−34is in a “weak” mode, thought for manyyears to be a complete null, roughly 70%of the time [24]. Single-pulse searches ofthe Parkes Multibeam Pulsar Survey dataalso have resulted in the discovery of severalpulsars whose emission is so sporadic thatthey are not detectable in standard Fourierdomain searches [64].

X-ray binaries: Large radio flares, with peakflux densities during an outbursts beingfactors of 10–100 larger than quiescence,have long been known from X-binaries suchas Cygnus X-3 [87,27]. Search for short-duration, single pulses from the X-ray bi-

4We define giant pulses as those comprising a long tail on

the overall pulse amplitude distribution; for the Crab pul-

sar and the millisecond pulsars B1937+21 and B1821−24,

these tails are power-law in form.

4

naries Scorpius X-1 and Cygnus X-1 havebeen unsuccessful, though [82].

Soft γ-ray repeaters: Vaughan & Large [86]conducted an unsuccessful search for ra-dio pulses from the soft γ-ray repeaterSGR 0526−66.

Maser flares: The emission from OH maserscan vary on timescales of hundreds of sec-onds and be detected as long-duration radiobursts [11,92].

Active galactic nuclei: Active galactic nuclei(AGN) outbursts, likely due to propagationof shocks in relativistic jets, are observedat millimeter and centimeter wavelengths[1,54].

Intraday variability: Intraday variability(IDV), resulting from interstellar scintil-lation of extremely compact components(∼ 10 µas) in extragalactic sources, occursat frequencies near 5 GHz. The typicalmodulation amplitude is a few percent andis both frequency and direction dependent,but occasional rare sources are seen to dis-play much larger amplitude modulationswith timescales of hours to days [50,60].Intraday variability could be an importantissue for calibration and imaging of theSKA as existing surveys suggest that it be-comes more prevalent at lower flux densities(< 100 mJy).

Radio supernovae: With the goal of detect-ing the single, large, broadband radio pulse(< 1 s) expected to be emitted at the timeof a supernova explosion [12], Huguenin &Moore [43] and Kardashev et al. [48] per-formed radio searches for single pulses, butfound no convincing signals of extraterres-trial origin aside from solar flares.

γ-ray bursts: In searches for radio pulses as-sociated with γ-ray bursts, Cortiglioni etal. [18], Inzani et al. [44], and Amy etal. [2] detected some dispersed radio pulses,but found no convincing associations withgamma-ray burst sources. Balsano [5]

found a dispersed radio pulse apparentlycoincident with GRB980329; however, itwas narrowband, which has led to it be-ing interpreted as due to terrestrial inter-ference. Various searches for radio pulsesassociated with gamma-ray bursts (includ-ing precursor pulses) have been conductedat 151 MHz [51,52,?]. Typical upper lim-its have been approximately 100 Jy. The-oretically, Usov & Katz [85] and Sagiv &Waxman [77] have predicted that gamma-ray bursts should have associated promptemission, most likely below 100 MHz.

Gravitational wave sources: In a search forradio counterparts to the gravitationalpulses reported by Weber [88], both Hughes& Retallack [42] and Edwards et al. [23] de-tected excesses of radio pulses from the di-rection of the Galactic center, but did notbelieve them to be correlated with the grav-itational pulses. More recently Hansen &Lyutikov [38] have predicted that inspiral-ing neutron star-neutron star binaries couldproduce radio precursors to the expectedgravitational wave signature.

Annihilating black holes: O’Sullivan etal. [71] and Phinney & Taylor [72] con-ducted searches for radio bursts at frequen-cies near 1 GHz possibly associated withannihilating black holes, as suggested byRees [74], but likewise found no convincingsignals.

Extraterrestrial transmitters: While no suchexamples are known of this class, manysearches for extraterrestrial intelligence(SETI) find non-repeating signals that areotherwise consistent with the expected sig-nal from an extraterrestrial transmitter.Cordes et al. [16] discuss how extraterres-trial transmitters could appear to be tran-sient, even if intrinsically steady.

3. Exploring Phase Space

For definiteness, we consider transients as thoseobjects or emission phenomena that show sub-

5

stantial flux density changes on time scales of onemonth or less. Although our upper limit on rel-evant time scales is arbitary, the lower limit isset by the physics in the source. For instance,the pulsar with the shortest known pulse periodis PSR B1937+21 for which P = 1.56 ms, whilesome giant pulses from the Crab pulsar have sub-structure at 5 GHz as short as approximately 2 ns[33]. Extensive air showers have been hypothe-sized to have time scales as short as 1 ns.

In the Rayleigh-Jeans approximation, a sourcewith brightness temperature T varies (intrinsi-cally) on a time scale or pulse width W givenby

W 2 =1

2πk

SD2

T

1

ν2, (2)

where the observed flux density is S, the source’sdistance is D, the emission frequency is ν, andk is Boltzmann’s constant. Figure 1 shows thephase space of the pseudo-luminosity SD2 vs.νW . There are two notable aspects of this figure.First, the transient radio sources observed span alarge range in this phase space. The range of νWcovers at least 13 orders of magnitude while therange of SD2 covers at least 20 orders of magni-tude. Second, large portions of this phase spaceare empty.

One of two conclusions can be drawn from Fig-ure 1. One could conclude no physical mecha-nisms or sources exist that would populate theempty regions in the phase space of Figure 1. Al-ternately, we regard Figure 1 as an illustration ofthe incompleteness of our knowledge of the tran-sient radio sky and of the potential for the SKA.

In order for the SKA to explore the dynamic ra-dio sky, “equation (1)” must be satisfied; it mustobtain large solid angle coverage, high time res-olution, and high sensitivity simultaneously. Wediscuss the time resolution requirements in moredetail below. Figure 2 illustrates that, histori-cally, radio telescopes have been capable of ob-taining either large solid angle coverage (e.g., theSTARE survey at 610 MHz by Katz et al. [49]with a FWHM beam of 4000′) or high sensi-tivity (e.g., the Arecibo telescope with a gainof 11 K Jy−1 at 430 MHz) but not the two si-multaneously. If the SKA satisfies its design re-

Type II

Type III

Jup DAMBD LP944-20

ADLeo

UVCeti

IDV ISS

GRBISS

Figure 1. The phase space for radio tran-sients. The abscissa is the product of the emis-sion frequency ν and transient duration or pulsewidth W . The ordinate is the product of theobserved flux density S and square of the dis-tance D2. In the Rayleigh-Jeans approximation,these quantities are directly proportional and re-lated to the brightness temperature T (eqn. 2).The sloping lines are labelled by constant bright-ness temperature. A brightness temperatureof 1012 K is taken to divide coherent from incoher-ent sources. Examples of transient emission fromvarious classes of sources are indicated. In thecase of gamma-ray burst afterglows (GRB) andintraday variability (IDV) of active galactic nuclei(AGN), the apparently high brightness tempera-tures are not thought to be intrinsic but relatedto interstellar scintillation (ISS). For these twoclasses of sources we show how the absence of ISSwould affect their locations in this phase space.

6

quirements, it will produce at least an order ofmagntiude sensitivity improvement, over a largefrequency range, with a solid angle coverage thatis comparable to or exceeds that of all but a smallnumber of low-sensitivity telescopes.

4. SKA Operational Modes and Experi-

ments

The SKA is most likely to open up new areas ofparameter space or discover new classes of sourcesby conducting dedicated transient searches. Fora fixed collecting area A and fixed total telescopetime, the transient figure of merit (equation 1)can be optimized either by covering as much solidangle as possible (“tiling”) or by observing asdeeply as possible (“staring”). Various optimiza-tions are possible, depending upon the class oftransient being sought, what is known about thetypical duration and sky distribution of the class,and the importance of interstellar scintillations[17,68,14]. We consider a spectrum of possibletransient searches, ranging from a “pure” star-ing search (extrasolar planets) to a “pure” tilingsearch (an all-sky survey). Our examples are byno means the only classes of potential transientsthat are amenable to these methods of searching,but they represent classes for which the sensitiv-ity of the SKA is either essential or produces qual-itatively larger numbers of such transients to bedetected.

In addition, we envision that a host of tradi-tional radio transient studies will be possible withthe SKA. Much like current interferometers, theSKA will be able to respond to triggers from otherwavelengths. Current examples of this capabilityinclude responding to γ-ray bursts, supernovae,and X-ray transients. With its high sensitivityand high angular resolution, the SKA will bothcontinue and improve on existing studies.

The SKA should also be capable of conductingmonitoring experiments, possibly used to triggerobservations at other wavelengths. In many cur-rent concepts, the SKA is envisioned as havinga “core” and “outlying stations.” (Indeed, be-low we discuss why such a configuration is nec-essary for the SKA for transient searching.) Notall observations will be able to make use of the

Figure 2. A representation of the combined fre-quency coverage, solid angle coverage, and sensi-tivity of a variety of historical and existing radiotelescopes. The solid angle coverage is shown asthe FWHM dimension of the beam (or equiva-lent) in arcminutes. The sensitivity is shown asthe gain in units of K Jy−1. All scales are log-

arithmic. For reference, the largest angle cover-age is provided by the 610 MHz STARE surveywith a FWHM beam equivalent of 4100′ whilethe most sensitive telescope other than the SKAis the Arecibo telescope with a 430 MHz gainof 11 K Jy−1. The SKA is shown assuming thatit has a 60′ field of view at 1 GHz, which scalesas ν−1, and that it has an effective collecting areain the “core” of 500 000 m2, which is constant be-tween 1 and 10 GHz. Not shown is the EVLAwhich will have a similar frequency coverage butan angle coverage of 4 times smaller and a sensi-tivity of 75 times less.

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entire SKA, e.g., use of the outlying stations pro-duces too low of a surface brightness sensitivityfor some kinds of H i observations. Thus, a smallnumber of outlying stations could be used to forma subarray and tasked to measure the flux den-sity of a variety of objects, such as to search forchanges resulting from flares from X-ray binariesor extreme scattering events (ESEs) toward ac-tive galactic nuclei.

4.1. Staring at Extrasolar Planets

The past few years have been an exciting timeas extrasolar planets have been demonstrated tobe widespread and multiple planetary systemshave been found. The current census now num-bers more than 100 extrasolar planets, in over 90planetary systems [78,63].

The vast majority of these extrasolar plan-ets have been detected via the reflex motion ofthe host star. As the existing census shows,this method has proven to be wildly successful.Nonetheless, the reflex motion of the star is ameasure of the planet’s gravitational influenceand is necessarily an indirect detection of theplanet. As a consequence, the only property ofthe planet that one can infer is its mass, and be-cause of the mass function’s dependence on theinclination angle (sin i), one can infer only a min-imum mass.

Direct detection of reflected, absorbed, or emit-ted radiation from a planet allows for the possi-bility of complementary information, and likelya more complete characterization of the planet.The prototype of such a direct detection is thedetection of sodium absorption lines in the at-mosphere of the planet orbiting HD 209458 [9].Unfortunately, the incidence of transiting planetswill always remain low relative to the total num-ber of planets known.

The Earth and gas giants of our solar sys-tem are “magnetic planets” in which internal dy-namo currents generate a planetary-scale mag-netic field. The radio emission from these plan-ets arises from coherent cyclotron emission dueto energetic (keV) electrons propagating alongmagnetic field lines into active auroral regions[32,91]. The source of the electron accelerationto high energies is ultimately a coupling between

the incident solar wind and the planet’s mag-netic field, presumably due to magnetic field re-connection in which the magnetic field embed-ded in the solar wind and the planetary magneticfield cancel at their interface, thereby energizingthe plasma. Energetic electrons in the energizedplasma form a current flow planet-ward along theplanet’s magnetic field lines, with the lines actingeffectively like low resistance wires. The energyin these magnetic field-aligned electric currents isdeposited in the upper polar atmosphere and isresponsible for the visible aurora. Besides auro-ral emissions at visible wavelengths (e.g., north-ern lights), about 10−5–10−6 of the solar windinput power is converted to escaping cyclotron ra-dio emission [32]. The auroral radio power fromJupiter is of order 1010.5 W.

At least one of the known extrasolar planetsis also a magnetic planet. Shkolnik, Walker, &Bohlender [79] have detected a modulation in theCa ii H and K lines of HD 179949 with a period-icity which is that of the planetary orbit. Theyinterpret this as a magnetic interaction betweenthe star and planet, though there is no constraintas yet on the magnetic field strength of the planet.

The SKA offers the possibility of detecting ra-dio emission from extrasolar planets. Detection ofradio emission from an extrasolar planet wouldconstitute a direct detection and can yield fun-damental information about the planet. First, ameasurement of the radio emission is directly in-dicative of the polar magnetic field strength at theplanet. For example, the high-frequency cutoff ofJovian decametric bursts (≃ 40 MHz) is inter-preted as being due to the Jovian polar magneticfield strength, which allowed an estimate for thestrength of the Jovian magnetic field nearly 20 yrprior to the first in situ magnetic field observa-tions. In turn, the presence of a magnetic fieldprovides a rough measure of the composition ofthe planet, insofar as it requires the planet’s in-terior to have a conducting fluid. Combined withan estimate of the planet’s mass, one could de-duce the composition of the fluid by analogy tothe solar system planets (liquid iron vs. metallichydrogen vs. salty ocean).

Second, the periodic nature of the radio emis-sion has been used to define precisely the plane-

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tary rotation periods of all of the gas giant planetsin the solar system, because the magnetic field ispresumed to be tied to the interior of the planet.

Finally, testing the extent to which solar-system models of magnetic fields can be appliedto extrasolar planets may have important impli-cations for assessing the long-term “habitability”of terrestrial planets found in the future. The im-portance of a magnetic field is that it deflects inci-dent cosmic rays. If these particles reach the sur-face of an otherwise habitable planet, they maycause severe cellular damage and disruption of ge-netic material to any life on its surface or mayprevent life from arising at all. A secondary im-portance of a magnetic field is that it can preventthe planet’s atmosphere from being eroded by thestellar wind [67]; this process is thought to be acontributing factor to the relative thinness of theMartian atmosphere. (This is of course unlikelyto be an issue for extrasolar giant planets.)

Farrell et al. [26], Zarka et al. [93], and Lazio etal. [56], building on empirical relations derived forsolar system planets and calibrated by spacecraftfly-bys, have made specific predictions for the ra-dio emission from the known extrasolar planets.Their predictions have made use of two empiri-cal relations, Blackett’s Law and the Radiometric

Bode’s Law.Blackett’s law relates a planet’s magnetic mo-

ment (its surface field times its radius cubed,BR3) to its rotation rate and mass. The Radio-metric Bode’s law relates the incident stellar windpower and the planet’s magnetic field strength toits median emitted radio power.

The predicted radio power for a magneticplanet immersed in its host’s star stellar wind is

Prad ∼ 4 × 1011 W( ω

10 hr

)0.79(

M

MJ

)1.33 (

d

5 AU

)−1.6

,

(3)

where ω is the planet’s rotation rate, M is itsmass, and d is the distance between the planetand host star. All quantities have been nor-malized to those of Jupiter. Farrell et al. [26]discussed slight differences to this radiometricBode’s law derived by various authors; the dif-

ferences result from the statistical spread in thevarious (solar system) planets’ magnetic momentsand amount to slightly different exponents and/ora different coefficient.

We stress various aspects of this radiometricBode’s law. First, it is grounded in in situ mea-surements from spacecraft fly-bys of the gas gi-ants as well as measurements of the Earth’s radioemission.

Second is the importance of the planet-star dis-tance. As Zarka et al. [93] show, the radio powerfrom Earth is larger than that from Uranus orNeptune even though both of those planets havemagnetic moments approximately 50 times largerthan that of the Earth.

Third, the radiometric Bode’s Law of equa-tion (3) describes the median emitted power fromthe magnetospheres of the Earth and all of thesolar gas giants, including the non-Io driven Jo-vian decametric radio emission [93]. Planetarymagnetospheres tend to act as “amplifiers” of theincident solar wind, so that an increase in thesolar wind velocity (and therefore incident pres-sure) leads to geometrically higher emission lev-els. This effect is observed at all of the magne-tized planets. Based on the range of solar windvelocities and emitted radio powers observed atthe Earth [?, Figure 5]e.g.,]gd81, the radio powerlevels from a planet can exceed that predicted byequation (3) by factors of 100 and possibly more.

The required quantities for applying equa-tion (3) are the planet’s mass, distance from itsprimary, and rotation rate. The radial velocitymethod determines a lower limit to the planet’smass (i.e., M sin i) and the semi-major axis ofits orbit. We have no information on the rotationrates of these planets. We have therefore assumedthat those planets with semi-major axes largerthan 0.1 AU have rotation rates equal to that ofJupiter (10 hr), while those with semi-major axesless than 0.1 AU are tidally-locked with rotationrates equal to their orbital periods [30,83]. Fig-ure 3 presents the expected median flux densitiesvs. the emission frequency in a graphical form.

The trend in Figure 3 of increasing emissionfrequency and decreasing flux density is real andreflects two effects. First, the lower envelope re-flects a selection effect. A low flux density and

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Figure 3. The median predicted flux densities for106 known extrasolar planets vs. the character-istic emission frequency based on the radiomet-ric Bode’s Law and Blackett’s Law. The hori-zontal bars indicate the assumed ranges for theemission frequencies, allowing the statistical vari-ations from Blackett’s Law in the estimated plan-etary magnetic moments. The vertical dashedline indicates the cutoff frequency for Jupiter’sradio emission. The dot-dashed line shows thesensitivity of the SKA, assuming an integrationtime of 15 min. and a bandwidth of 4 MHz. Forthe SKA, a nominal sensitivity of Aeff/Tsys =5000 m2 K−1 has been assumed at 100 MHz, im-proving to 20 000 m2 K−1 at 1000 MHz.

small emission frequency results from a low-massplanet in a large orbit. These planets cannotbe detected with the current detection methodol-ogy. Second, the upper envelope reflects the well-known deficit of planets with both large massesand small semi-major axes. Even if high-massplanets with close orbits did exist, however, theyprobably would be tidally locked (as we have as-sumed here). The rotation rate also determinesthe strength of the magnetic field, so tidally-locked planets probably do not radiate at highemission frequencies. However, [94] have sug-gested that such “hot Jupiters” may radiate bythe conversion of stellar magnetic pressure (whichis large in close to the star) into electromotiveforces, currents, and radio emission.

In designing an experiment to detect extrasolarplanets, staring is clearly the preferred method asthe locations of the planets are known and cover-ing large solid angles would not increase the oddsof detection. However, the potential for burstsmust be taken into account. The sensitivity ofa radio telescope improves with increasing inte-gration time as t−1/2. Longer integration timesimprove the sensitivity but at the cost of “dilut-ing” any bursts. For a burst of flux density Sb

and duration ∆tb, its average flux density in anintegration time t is Sb(∆tb/t), i.e., the burst isdiluted with time as t−1. To the extent that ex-trasolar planet radio emission is “bursty” (as isobserved for the solar system planets), multipleshort observations are a better strategy than asingle long integration.

Current design goals for the SKA specifyits sensitivity to be Aeff/Tsys = 5000 m2 K−1

at 100 MHz, improving to 20 000 m2 K−1

at 1000 MHz. In a 15 min. integration, itsflux density sensitivity would be in the range 1–10 µJy, more than sufficient to detect the radioemissions from the most massive extrasolar plan-ets, without relying upon bursts to enhance theemission levels. If bursts are considered, the SKAshould detect a substantial fraction of the currentcensus, if the bursts are comparable in magnitudeto what is seen in the solar system (factors of 10–100).

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4.2. Giant Pulses from Extragalactic Pul-

sars

As discussed above, the Crab pulsar and asmall number of other pulsars are known to emitgiant pulses, pulses that comprise a long tail onthe overall pulse amplitude distribution. Theseprobably arise from coherent emission within theturbulent plasma in the pulsar magnetosphere[33]. Some of these pulses are so strong that,were the Crab pulsar located in a nearby exter-nal galaxy, it could be detected with existing tele-scopes. Exploiting both the SKA’s sheer sensitiv-ity and flexibility, giant pulses from pulsars in ex-ternal galaxies should be detectable well beyondthe Local Group and potentially to the distanceof the Virgo Cluster.

The fraction of its lifetime over which a pulsarmight exhibit the giant pulse phenomenon is notknown. If we take the Crab as an exemplar ofyoung, giant-pulse emitting pulsars, we might ex-pect a birth rate of order 1 pulsar per 100 yr andthat the giant pulse phenomenon lasts for of order1000 yr. With careful accounting for selection ef-fects (e.g., pulsar beaming fraction), giant-pulseemitting pulsars in external galaxies can probethe recent massive star formation in those galax-ies.

Moreover, by their dispersion measures (DM)and rotation measures (RM), extragalactic pul-sars have the potential to probe the baryon den-sity and magnetic field in the Local Group andpotentially beyond. Current models for large-scale structure formation predict that matter inthe current epoch forms a “cosmic web” [8,19,20].Most of the baryons in the Universe reside inlarge-scale filaments that form the “strands” ofthe web, with groups and clusters of galaxies lo-cated at the intersections of filaments. At thecurrent epoch, hydrogen gas continues to accreteonto and stream along these filaments, undergo-ing multiple shocks as it falls into the gravita-tional potential wells located at the intersectionsof the filaments. In this model, the filamentsof hydrogen form a warm-hot ionized medium(WHIM), with a temperature of 105–107 K.

Recent observations of highly ionized species ofoxygen and neon by both the FUSE and Chandra

observatories are considered to be validations of

these predictions. Absorption observations alongvarious lines of sight suggest a diffuse mediumwith a temperature of order 106 K with a densityof order 5×10−5 cm−3. While striking, these ob-servations still suffer from the difficulty of probingonly trace elements. The ionized hydrogen in theWHIM has not been detected directly, but, overmegaparsec path lengths, the implied DMs are oforder 50 pc cm−3, comparable to or larger thanthat for nearby pulsars.

For the Crab pulsar, the most well-studiedgiant-pulse emitting pulsar, the giant pulse ampli-tude distribution is power-law in form at high am-plitudes [61,13]. On average, the strongest pulseobserved from the Crab pulsar at 0.43 GHz in onehour has a signal-to-noise ratio of S/Nmax ≈ 104,even with the system noise dominated by theCrab Nebula. For objects in other galaxies, thesystem noise is essentially unaffected by any po-tential nebular contribution. If the Crab pulsarwere not embedded in its nebula, the S/N of sucha pulse would be larger by the ratio of the systemnoise equivalent flux density when observing theCrab Nebula to the nominal system noise equiva-lent flux density or SCN/Ssys0 ≈ 300 times larger,or 3.3 × 106. Thus, on average, in an hour’s ob-servation, one should be able to detect a Crab-like pulsar to a maximum distance at a specifiedsignal-to-noise ratio, (S/N)det,

Dmax

= DCN

[

(S/N)max

(S/N)det

(

1 +SCN

Ssys0

)

− SCN

Ssys0

]1/2

≈ 1.6 Mpc

[

(S/N)det

5

]−1/2 (

fcASKA

AAO

)1/2

,

(4)

where fcASKA is the SKA’s collecting area thatcan be used for a giant pulse survey and AAO isArecibo’s effective area at 0.43 GHz. The usablearea for the SKA in a blind survey will be limitedby what fraction fc of the antennas are directlyconnected to a central correlator/beamformer.For fc = 1, ASKA/AAO ≈ 20 so the standardone-hour pulse seen at Arecibo could be detectedto 7.3 Mpc. Figure 4 shows that even for moremodest values of fc, e.g., fc ≈ 0.3, the SKA coulddetect giant-pulse emitting pulsars well beyond

11

Figure 4. The distance to which a Crab giantpulse can be detected. The three circles show(in order of increasing size) the distance to whichthe strongest pulse detected in 1 hr using Arecibo(5% of the SKA, assuming that it could see theentire sky), 30% of the SKA, and the full SKA.The distribution of local galaxies is shown in theSupergalactic x and y planes (from [47]), and cer-tain galaxies or groups of galaxies are labelled.

the Local Group.No upper amplitude cutoff has been observed

yet for the Crab pulsar’s giant pulse amplitudedistribution [61]. Observing for longer than 1 hrresults in even stronger pulses being detected. As-suming that the Crab pulsar is not atypical, amodest extrapolation of the giant pulse amplitudedistribution implies that the SKA could detectgiant-pulse emitting pulsars in the Virgo cluster(D ≈ 20 Mpc).

An additional efficiency is obtained toward theVirgo cluster as many galaxies will be containedwithin the SKA’s field of view. Although it isnot yet clear what frequency would be optimalfor a giant-pulse search toward the Virgo cluster,it almost certainly will be not much higher than1 GHz. Thus, the field of view will be at least1 deg.2 and could be potentially nearly 10 timeslarger, e.g., for observations at 0.33 GHz.

The baryon density along the line of sight to

an extragalactic giant-pulse emitting pulsar canbe inferred from the pulsar’s DM. The disper-sion measure is simply the line-of-sight integralof the electron density, DM =

∫

ne dl. As isthe case for more traditional pulsar searches, gi-ant pulse searches require dedispersion, which isaccomplished by searching through a number oftrial DMs [65]. As a line-of-sight integral, theDM for an extragalactic pulsar contains contribu-tions from the Galaxy, the intergalactic medium,and the host galaxy(ies). The Galactic contri-bution to the DM can be predicted from mod-els for the Galactic free electron distribution [15],and in the SKA era even more detailed modelswill be available. However, the contribution fromthe host galaxy will be able to be estimated onlycrudely (e.g., from its inclination and assuming aplane-parallel electron density distribution). Weanticipate that the uncertainty in separating thehost galaxy and intergalactic contributions to theDMs of extragalactic pulsars will scale roughlyas

√N for N extragalactic pulsars. Thus, it is

not sufficient merely to detect one or a few extra-galactic pulsars, as might be accomplished withexisting telescopes (like the 100-m Efflesberg tele-scope, the Green Bank Telescope, or Arecibo).

Similar considerations apply to the measure-ment of the intergalactic magnetic field via therotation measure, RM =

∫

neB · dl. Measure-ment of the RM for extragalactic pulsars wouldprove a unique probe of the magnetic field in theLocal Supercluster, but this requires the detec-tion of many extragalactic pulsars to separate theGalactic, host galaxy, and intergalactic contribu-tions.

Searching for giant pulses from extragalacticpulsars requires time-domain searches, i.e., it isa non-imaging application of the SKA. In or-der to conduct these searches, there are threekey requirements for the SKA. The first is thatit have the capability to provide, in a routinemanner, fast-sampled data. Given that part ofthe motivation for transient searching is to openup new parameter space, an arbitarily fast sam-pling may appear necessary. There are, however,certain physically-motivated limits that can bespecified. First, in order to accomplish the KeyScience Driver of “Strong Field Tests of Grav-

12

ity Using Pulsars and Black Holes” a minimumtime sampling of 10 µs is required in order toconduct pulsar timing observations. Lazio &Cordes [57] summarized various interstellar prop-agation effects that suggest that a time sam-pling faster than a few microseconds is not jus-tified, at least for sources at interstellar or in-tergalactic distances at frequencies near 1 GHz.These effects are strongly frequency dependent,though, so nanosecond time sampling can be tol-erated at frequencies above 5 GHz, as evidencedby the Crab pulsar’s nano-giant pulses. Finally,the coherent pulses from ultra-high energy cos-mic ray impacts on the Earth’s atmosphere havetime scales of order 1 ns. Thus, a useful targetrange for the SKA would be sampling times be-tween 1 ns and 10 µs.

The second requirement for the SKA is on itsconfiguration. Backer [4] has shown that thesignal-to-noise ratio achieved in a search scaleswith the array filling factor f as

√f . Thus, the

SKA should have a reasonably compact “core”where the filling factor is not too small. A use-ful goal might be a core containing a significantfraction of the SKA collecting area (∼ 50%) witha filling factor of a few percent to 10%.

A third requirement is on effective suppres-sion of radio frequency interference (RFI). Thisrequirement is not unique to searches for tran-sients, of course, but it is perhaps more strin-gent for transient searching than for other oper-ational modes. One wishes to ensure that cos-mic transient signals are not confused with ter-restrial RFI and thereby eliminated. A varietyof techniques may end up being applied with theSKA, but two key techniques for extragalactic gi-ant pulses and other fast transients are utilizingthe spatial extent of the SKA and the expecteddispersion smearing of the signals. Cordes &McLaughlin [14] illustrate how dispersion smear-ing can be used advantageously. Briefly, any pulsefrom a source outside the solar system will suf-fer dispersion smearing while most terrestrial RFIwill not. Similarly, terrestrial RFI should not af-fect all SKA antennas equally whereas a celestialpulse should, taking into account the time de-lay between the antennas. The spatial extent ofthe SKA (or of its core) can be used as an anti-

coicidence filter to identify RFI.Finally, targeted transient searches could be

conducted in a “piggyback” synthesis mode. Therelatively large field of view of the SKA impliesthat most continuum synthesis observations willbe conducted in a pseudo-continuum mode, so asto be able to image the entire field of view with-out significant bandwidth smearing. The posi-tions and flux densities of most of the “strong”sources (> 10 mJy) in any given field of viewshould be known reasonably accurately (from sur-veys like the NVSS) and could be subtracted fromthe visibility data. The residual visibility datacould then be imaged on different time scales tosearch for weak point sources that vary. Sucha piggyback mode would be particularly effectiveat finding moderate duration transients in nearbygalaxies and clusters of galaxies.

4.3. Tiling the Sky: An All-Sky Survey

An all-sky survey would be designed to searchfor transients of unknown or poorly known du-ration and distribution. As a strawman for sucha survey, we take the goal of surveying an en-tire hemisphere within 24 hr. If the SKA meetsits current specification of a 1 deg2 field of view,then each pointing can be 1 s in duration (as-suming Nyquist sampling of the sky). Allowingfor 50% efficiency, assuming a bandwidth of only1 MHz, and only half of the collecting area of theSKA (in its core), such a blind, all-sky surveywould still obtain a typical noise level of approx-imately 0.5 mJy. Larger bandwidths or a largerfraction of the SKA collecting area in the core orboth would improve upon this noise level, thoughlarger bandwidths could also imply a heavier com-putational load in order to cope with increasedDM searching. Similarly, the sky could be cov-ered more quickly at lower sensitivity by dividingthe SKA into sub-arrays, each having the same1 deg.2 field of view but reduced sensitivity.

One manner in which an all-sky search wouldnot be challenging would be the slew rate. Theimplied slew rate is comparable to what currentinstruments provide, e.g., for the VLA the slewrate is approximately 0.5 deg. s−1.

A less ambitious “blind” survey would be a sur-vey along the Galactic plane. Existing Galactic

13

plane surveys [55] have provided intriguing hintsof transients to be detected. Such a survey mightalso be possible in the early years of the SKA,before the full computational infrastructure is inplace or as an initial effort before searching theentire sky. As a strawman survey we consider a12-hr survey covering 90 of Galactic longitudeand 10 in Galactic latitude (|b| < 5). Cover-ing 900 deg2, again with a 1 deg2 field of viewat 1 GHz, would allow for approximately 10 s perpointing and produce an rms noise of approxi-mately 0.1 mJy. Alternately, a higher frequencycould be used (to reduce the impact of dispersionsmearing or any possible pulse broadening) at thecost of less time per pointing, a slightly highernoise level, and a loss of sensitivity to steep spec-trum sources. For instance, at 3 GHz, the timeper pointing would be 1 s.

A key aspect of transient searches will be suffi-cient computational power. A full analysis willnot be possible until the SKA concept is cho-sen (as that will affect issues such as the fieldof view). For a strawman analysis, though, con-sider an imaging-based search in which a cor-relator produces an image which is then exam-ined for transients. Preliminary considerationsimply that imaging the full FOV is more effi-ciently done through correlation than through di-rect beam forming.

At each integration time the number of corre-lations to be computed is

Nc =1

2na(na − 1)NpolNν , (5)

where na is the number of antennas, Npol is thenumber of polarization channels (Npol = 4 forfull Stokes), and Nν is the number of frequencychannels. The number of pixels in the FOV for amaximum baseline, bc, in the core array and anaperture diameter D is

Npix ≈ 0.85

(

bc

D

)2

≈ 104 pixels (bc,km/D10)2. (6)

For fast transients (e.g. durations <∼1 sec), suffi-cient channels are needed to allow dedispersion,a requirement that also satisfies the need for the

Table 1SKA Requirements for Transient Surveys

Parameter Requirement

Field of View (at 1 GHz) 1 deg.2

Time Sampling ∼ 1 ns to 10 µsFrequency Coverage ∼ 0.1–10 GHzConfiguration “large” core filling factor

long baselines

“delay-beam” to be large enough for full FOVmapping. Dedispersion in blind surveys requiressumming over frequency with trial values of DM,whose number is approximately the same as thenumber of channels. Additional processing wouldinclude matched filtering to identify individualtransients and Fourier analysis to find periodicsources. For SETI and other spectral-domainsearches, each pixel would be Fourier analyzed(before detection) to identify candidate spectrallines.

5. Conclusions

Transient radio sources offer insight into dy-namic or explosive events as well as being pow-erful probes of intervening media. Historically,the radio sky also has been searched only poorlyfor radio transients, meaning that the SKA hasthe potential to explore previously-unexploredparameter space at radio wavelengths.

In order to be effective at searching for tran-sient radio sources, the SKA must achive a“large” value for the figure of merit AΩ(T/∆t),equation (1). By its very nature, A is anticipatedto be large for the SKA. Table 1 summarizesthe other requirements on the SKA. These re-quirements flow either from the desire to achievea large figure of merit or are based on experiencefrom known radio transients.

In order to conduct successfully the Key Sci-ence Project, “Strong Field Tests of Gravity Us-ing Pulsars and Black Holes,” the SKA is requiredto obtain high time resolution. The challenge forthe SKA, and historically the difficulty with radiotelescopes, is that they have not provided a largefield of view simultaneously with high sensitivity.

14

A related requirement is on the configuration ofthe array, as the filling factor of the array affectsthe signal-to-noise ratio in a search as

√f . Thus,

the SKA requires a core, containing a significantfraction of the collecting area with a reasonablelyhigh filling factor, as well as long baselines, forlocalizing sources and imaging searches such asfor γ-ray bursts and extrasolar planets.

From known classes of sources alone, thissearch promises to be fruitful—one can exploreparticle acceleration by observing radio pulsesfrom ultra-high energy particles impacting theEarth’s atmosphere as well as from flares fromthe Sun, brown dwarfs, flare stars and X-ray bi-naries while using afterglows from γ-ray burstsone can explore the cosmological star formationhistory. Likely, though not yet detected, classesof sources include giant pulses from extragalacticpulsars, which would allow a direct probe of thelocal intergalactic medium, and extrasolar plan-ets, which would be a direct detection of theseobjects.

Most exciting would be the discovery of new

classes of sources.

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