Memo 135 Very High Angular Resolution Science with the SKA

L. Godfrey

H. Bignall

S. Tingay

International Centre for Radio Astronomy Research,

Curtin University, Bentley, WA, Australia

May 2011

www.skatelescope.org/publications

Very High Angular Resolution Science with the SKA

Leith Godfrey, Hayley Bignall & Steven TingayInternational Centre for Radio Astronomy Research, Curtin University, Bentley, WA, Australia

Contact: L.Godfrey@curtin.edu.au

Contents

1 Summary 3

2 Introduction 4

3 High Angular Resolution Science Case 53.1 Key Science Project: Strong Field Tests of Gravity . . . . . . . . . . . . . . . . . . . . . . . . 5

3.1.1 Enabling strong field tests of gravity with precise parallax distancemeasurements to compact, relativistic pulsar binaries . . . . . . . . . . . . . . . . . . . 5

3.2 Key Science Project: Cosmic Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2.1 Enabling tomographic modelling of the Galactic magnetic field with pulsar parallax

distance measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 Key Science Project: The Cradle of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.3.1 Imaging proto-planetary disks at centimetre wavelengths . . . . . . . . . . . . . . . . . 93.4 Key Science Project: Galaxy Evolution, Cosmology, and Dark Energy . . . . . . . . . . . . . 10

3.4.1 Resolving AGN and Star Formation in Galaxies . . . . . . . . . . . . . . . . . . . . . . 103.4.2 Hi absorption against AGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.5 Key Science Project: Probing the Dark Ages and the Epoch of Reionization . . . . . . . . . . 103.5.1 Finding the first generation of AGN jets, and radio/CO studies . . . . . . . . . . . . . 10

3.6 Exploration of the Unknown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.6.1 Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.7 Binary Supermassive Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.8 X-ray binary systems and relativistic jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.9 Small-scale structure and evolution in AGN Jets . . . . . . . . . . . . . . . . . . . . . . . . . 153.10 Strong gravitational lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.11 Absolute Astrometry and Geodesy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.12 Relative Astrometry: Parallax and Proper Motions . . . . . . . . . . . . . . . . . . . . . . . . 183.13 Galactic Masers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.14 Mapping high mass star formation in nearby galaxies . . . . . . . . . . . . . . . . . . . . . . . 203.15 Stellar winds/outflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.16 Stellar Atmospheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.16.1 Imaging stellar atmospheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.16.2 Resolving stellar radio flares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.17 Spatial and temporal changes in the fundamental constants . . . . . . . . . . . . . . . . . . . 213.18 Ultra High Energy Particle Astronomy at & 2 degree angular resolution via the Lunar

Cerenkov technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.19 Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.19.1 Probing the Intergalactic Medium via Angular Broadening . . . . . . . . . . . . . . . 233.19.2 Resolving AU-scale structure in the ISM via diffractive scintillation . . . . . . . . . . . 233.19.3 Extreme scattering events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.20 Spacecraft tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

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4 Calibrators and Phase Referencing 244.1 Global Fringe Fit Sensitivity σglbl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.2 Estimating Calibrator Source Counts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3 Consequences for Phase Referencing Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

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Abstract

The science goals and corresponding technical requirements for the high angular resolution componentof the SKA are significantly different to those of the SKA core. Consequently, the requirements forremote stations must be considered separately. The aim of this memo is to bring together in one placea discussion of the broad range of science goals being proposed for the high angular resolution SKA, asa first step towards defining the science and technical requirements for the remote stations. For much ofthe proposed science, general statements and order of magnitude estimates demonstrate the in-principlefeasibility, however more detailed work is required to determine the minimum technical specifications thatwill enable specific science outcomes. We conclude the memo with a requirements matrix for a subset ofexperiments, illustrating that a number of important science goals can be achieved with feasible technicalspecifications.

1 Summary

High angular resolution requiring baselines greater than 1000 km features in two areas of “headlinescience”1 for SKA Phase 2 (strong field tests of gravity and protoplanetary disks, see §3.1.1 and §3.3.1),and provides a rich science case with projects from many other areas of astrophysics, including importantcontributions to a number of the Key Science Projects2. Much of the high angular resolution science canbe achieved at frequencies within the SKA-mid range (0.5 — 10 GHz) or can be recast for this frequencyrange. The science goals for the long baseline component of the SKA are many, and include the following:

• Precise parallax distance and proper motion measurements for a large fraction of the radio pulsarpopulation detected in the SKA Galactic pulsar census, to enable a range of scientific goals, including:

– Strong field tests of gravity in a broad range of relativistic binary systems,

– Tomographic modelling of the large scale Galactic magnetic field,

– Mapping the ionized interstellar plasma in the Galaxy,

– Core-collapse physics and the physics of neutron stars,

– Tying the inertial quasar reference frame to the solar system dynamic frame using pulsar timingand trigonometric parallax measurements in order to remove a potential source of systematicerror in pulsar timing array data that could mimic gravitational waves.

• Imaging protoplanetary disks at cm-wavelengths to inform planet formation theory by by addressingimportant questions such as: where do cm- to decimetre-sized grains grow within protoplanetarydisks, and in what environments do these large grains occur?

• High resolution imaging of a large sample of extragalactic radio sources to distinguish between, andstudy the effects of star formation and AGN on galaxy formation and evolution.

• High resolution “movies” of jet formation and propagation in black hole, neutron star and whitedwarf X-ray binaries to determine the relationship between jet formation and system parameters(eg. stellar surface vs. event horizon, depth of the potential well, black hole spin, stellar magneticfields etc.).

• Mapping high mass star formation in nearby, face-on spirals as traced by the Hii region populationsto address the question of what triggers massive star formation and discriminate between densitywave and self-propagating models of spiral structure.

The high angular resolution SKA will make many more important contributions to fundamental questionsof physics and astrophysics, as outlined in the following sections. In addition to the specific science goals,some more general arguments in favour of high angular resolution have been made. Simulations of theextragalactic radio source population indicate that in high sensitivity SKA images, individual radio sourceswill appear blended. Angular resolution of at least 50 mas at 1.4 GHz (i.e. > 1000 km baselines) will benecessary to separate individual sources in deep SKA images (Jackson, 2004). Higher resolution still isrequired to distinguish emission from star formation and AGN activity (DRM v1.0, 2010, chapter 2), andto resolve the majority of radio sources in the sky (Garrett, 1999). Furthermore, high angular resolutionis required for synergies with future instruments. For example the Giant Magellan Telescope, due to beginoperation in 2018, will be capable of 15 - 30 mas resolution in the near-infrared. Similarly, the GAIA3

mission, due for launch in 2013, will provide astrometric precision in the order of tens of µas or better atoptical wavelengths.

1Headline science for the SKA is defined in Schilizzi (2007)2Key Science Projects for the SKA can be viewed at http://www.skatelescope.org/the-science/ska-key-science-projects/3See ESA-RSSD Gaia homepage: http://www.rssd.esa.int/GAIA

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The extremely high imaging dynamic range required for short SKA baselines should be relaxed sub-stantially for the long baselines. For the short baselines and wide fields of view, dynamic range of 106 isrequired in order to detect weak sources while very strong sources are simultaneously in the field of view.For the long baselines, with narrower fields of view and generally weaker sources at higher angular reso-lution, much lower dynamic ranges are required. Further, a substantial amount of long baseline science istargeted at objects that have relatively simple source structures and do not require high dynamic range.Dynamic range of order 10,000 may be adequate for the great majority of long baseline science (cf. DRMv1.0, 2010, chapter 2).

Station beam-forming is preferred from a cost point of view (McCool, 2010), but this will not impactthe science return, due to the absence of wide field of view requirements. Moreover, combining theindividual antennas into stations improves the phase-referencing capabilities of the array, with the globalfringe fit sensitivity improving roughly in proportion to the square root of the number of antennas perstation.

Many of the high resolution experiments require accurate phase referencing calibration. Multi-viewin-beam phase calibration with several in-beam calibrators will be possible over much of the SKA-midband. However, at frequencies nearing 10GHz, multi-view in-beam calibration using multiple calibratorsmay not be possible due to the lack of available calibrators within the primary beam (§4). Alternativetechniques, such as cluster-cluster style calibration using station sub-arrays may be required to enablecontinuous monitoring of multiple phase calibrators at the upper frequencies of SKA-mid.

We compile a requirements matrix for a subset of science cases at the end of this document. It shouldbe noted that for many proposed experiments, while general statements have been made, and oftenorder of magnitude estimates indicate the science goals are feasible, further modelling and/or simulationsbeyond the scope of this memo are required to elucidate the relevant technical requirements that willenable specific outcomes. We hope that this memo may promote such work. Despite this fact, we notethat a number of important science goals will be achieved with the high angular resolution component ofthe SKA given feasible technical specifications.

2 Introduction

Preliminary SKA specifications indicate that the Phase 2 SKA will have 25% of the total collecting areaoutside a 180 km radius, with maximum baselines at least 3000 km from the array core (Schilizzi, 2007).Such an array will provide angular resolution of θ . 20 / FGHz mas and will be capable of detectingbrightness temperatures in the order of several hundred Kelvin.

This memo addresses the merits of long baselines as part of the SKA, which have been questioned inprevious submissions (Faulkner et al., 2010). In §3 we compile a list of science drivers for the long baselinecomponent of the SKA, as a first step towards the goal of identifying the requirements, particularly forthe major cost drivers, for remote stations of the SKA. The high angular resolution science cases areextracted largely from the book “Science with the Square Kilometre Array” (Carilli, 2004), and theDesign Reference Mission for SKA-mid and SKA-lo (DRM v1.0, 2010), but we do include additionalscience cases and more recent advances. The technical requirements for a subset of these experiments arepresented in a requirements matrix at the end of this document. In §4 we discuss issues relating to phasereferencing observations for the high angular resolution component of the SKA.

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3 High Angular Resolution Science Case

3.1 Key Science Project: Strong Field Tests of Gravity

3.1.1 Enabling strong field tests of gravity with precise parallax distancemeasurements to compact, relativistic pulsar binaries

The goal of the “Strong Field Tests of Gravity” Key Science Project is to test relativistic theories of gravityin the strong field regime via precision timing of pulsars. This will be achieved by (1) timing relativisticbinary systems — eg. pulsar-neutron star and pulsar-black hole binaries; and (2) monitoring an arrayof millisecond pulsars (a pulsar timing array) to detect gravitational waves with nano-Herz frequencies(Kramer et al., 2004; Cordes et al., 2004). This key science project is discussed in DRM v1.0 (2010)chapters 16 and 17. However, the importance of high angular resolution for maximising the science returnhas so far been neglected in that document.

Approximately 100 compact relativistic binaries are expected in the SKA Galactic pulsar census (Smitset al., 2009), of which some fraction (& 5 − 25) are expected to be in pulsar-black hole binary systems(Lipunov et al., 2005). The likelihood of dynamic interactions in globular clusters means that the chancesof finding exotic binaries such as millisecond pulsar-BH systems is enhanced in these environments (eg.Sigurdsson, 2003). However, the most common BH-pulsar binary system may be normal rather thanrecycled (millisecond) pulsars (see Pfahl et al., 2005; Lipunov et al., 2005).

Accurate distances are essential

Precise measurements of the proper motion and distance to each of the relativistic binaries detected inthe pulsar census is essential for these systems to be used as laboratories for testing theories of gravity.Accurate distance and proper motion measurements are required in order to correct for the accelerationterms that affect orbital parameters such as the spin and orbital period derivatives. The latter parameteris of particular relevance for testing alternative theories of gravity (Cordes et al., 2004; Stairs, 2010;Kramer, 2010) and potentially detecting, or at least constraining, extra spatial dimensions (Simonetti etal., 2010). Let Pb be the binary period, Pb the corresponding time derivative, c the speed of light, dthe distance and µ the proper motion of the system. The so-called Shklovskii-effect (Shklovskii, 1970)contributes to the observed period derivative as:

PbPb

=µ2d

c(1)

This effect, if not precisely accounted for, limits the precision with which theories of gravity may be testedin relativistic binary pulsars. In some cases, the magnitude of the Shklovskii-effect can be comparable to,or greater than the intrinsic orbital period derivative due to gravitational radiation (see eg. Bell & Bailes,1996). A similar effect arises due to the differential acceleration of the solar system and the pulsar inthe gravitational potential of the Galaxy (Damour & Taylor, 1991). The determination of this Galacticacceleration term requires precise knowledge of the pulsar’s spatial position, as well as the Galactic radius(R0) and speed of the solar system (v0). To underline the importance of precise distance measurements,it is worth noting that the tests of relativistic gravity in the Hulse-Taylor binary system B1913+16, whichcurrently provides the most precise constraints of this kind, are limited by the uncertainty in the distance,which has been determined using the pulsar’s dispersion measure to a precision of ∼ 30% (Weisberg etal., 2008).

As noted above, the Galactic constants R0 and v0 are of fundamental importance in correcting forthe acceleration terms that impact the observed binary period derivative. Deller et al. (2009) note thatto attain the 10−5 fractional uncertainty in orbital period derivative that is necessary to measure theneutron star moment of inertia in the binary system PSR J0737-3039A/B, the constants R0 and v0 mustbe measured to a precision approaching 1%. The high angular resolution component of the SKA couldprovide a measurement of R0 with 1% precision (Fomalont & Reid, 2004).

Trigonometric parallax measurements are required to maximise the science return

Pulsar distances, in some cases, may be determined by timing measurements alone via the method oftiming parallax. A pulsar at a finite distance produces a curved wavefront at Earth and the curvatureof the wavefront is related to the pulsar distance. The orbital motion of the Earth causes a 6 monthlyvariation in the pulse arrival times due to the curvature of the wavefront, and consequent periodic changein the path length from the pulsar to Earth. The amplitude of this timing parallax signature is very small:

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Figure 1 : Motion of PSR J0737-3039A/B plotted against time (from Deller et al., 2009). Trigonometricparallax measurements for this relativistic binary pulsar system revealed that the distance was more thana factor of 2 greater than previous distance estimates based on dispersion measure and timing parallaxmeasurements. The precise interferometric distance and proper motion measurements combined with adecade of additional timing data will enable tests of GR at the 0.01% level using the orbital period derivativeof this system (Deller et al., 2009).

∆tπ ≈ 1.2µs× cosβ d−1kpc, where β is the ecliptic latitude, and dkpc is the pulsar distance in kpc (Ryba &

Taylor, 1991). Therefore, accurate timing parallax measurements are limited to a subset of pulsars withvery high timing precision; that is, millisecond pulsars with stable timing characteristics (Smits et al.,2011). In contrast, trigonometric (imaging) parallax depends only on the flux density of the source andis therefore applicable to a much wider range of systems.

It may be the case that some of the most interesting relativistic binary systems do not provide sufficienttiming precision to allow accurate timing parallax distance determination, but could still provide excellenttests for relativistic theories of gravity. This is possible because, despite the limited timing precision,accurate measurement of long term secular trends such as the orbital period derivative, Pb, can still beachieved, given a long enough time. For example, the measured uncertainty in Pb decreases approximatelyas T−2.5, where T is the total time span of data for the system (Damour & Taylor, 1992).

A good example of this is the pulsar-white dwarf relativistic binary system, J1141-6545. Owing tothe asymmetry in self-gravitation between the pulsar and white dwarf companion, this system provides aunique laboratory for testing alternative theories of gravity (Bhat et al., 2008). However, the young pulsarin this system exhibits significant “timing noise” which limits the timing precision (Bailes, 2005). Despitethe timing noise, J1141-6545 is likely to provide the most stringent tests of alternative theories of gravityto date: already four post-keplarian parameters have been measured, and the orbital period derivative forthis system is expected to be determined to better than 2% by 2012, at which point uncertainty in thekinematic Doppler term, or Shklovskii-effect (the term involving the pulsar distance and proper motion)will dominate the errors (Bhat et al., 2008). With this example in mind, it should be noted that many ofthe pulsar-black hole binaries are likely to be normal pulsars (and probably young pulsars like J1141-6545,due to evolution of the systems), rather than recycled (millisecond) pulsars (see Pfahl et al., 2005; Lipunovet al., 2005). This suggests that trigonometric (imaging) parallax measurements may be required for alarge fraction of pulsar-black hole binaries.

Smits et al. (2011) simulated and compared the accuracy of trigonometric parallax measurements withvarious methods of timing parallax distance determination, and concluded that both timing parallax andtrigonometric parallax capabilities are required for the key science project “Strong Field Tests of Gravity”.The results of the simulations suggest that the SKA can potentially measure the trigonometric parallaxdistances for ∼9000 pulsars up to a distance of 13 kpc with an error of 20% or better, and timing parallaxdistances for only about 3600 millisecond pulsars out to 9 kpc, with an error of 20% or better. It is clearthat a high angular resolution component of the SKA, capable of precision astrometry, is required in orderto maximise the scientific return of the “strong field tests of gravity” key science project.

Why is the SKA required?

The high sensitivity of the long baseline SKA is required not only to detect weak and distant pulsars,but also to provide a high density of calibrator sources surrounding the target that will enable multi-viewin-beam calibration, and therefore high precision astrometry (Rioja et al., 2009; Fomalont & Reid, 2004).Owing to its high sensitivity, the long baseline component of the SKA will be able to perform multi-viewin-beam calibration using several compact, closely spaced calibrator sources, the closest of which will be

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Figure 2 : From Smits et al. (2011). Comparison between imaging and timing parallax histograms forthe quantity π/∆π, where π is the parallax and ∆π is the estimated error in the parallax for a simulatedpulsar population detected in a simulated SKA galactic pulsar census. The vertical dotted lines mark theπ/∆π = 5 cutoff (20% error). (Left) Histogram of π/∆π for trigonometric parallax measurements withthe high angular resolution component of the SKA. The SKA can potentially measure the trigonometric(imaging) parallaxes for ∼9, 000 pulsars with an error of 20% or better. This includes pulsars up to adistance of 13kpc. (Right) Histogram of π/∆π for the timing parallax measurements of 6000 millisecondpulsars detected in the simulated SKA galactic pulsar census. Timing parallax measurements are limitedto millisecond pulsars with very high timing precision, and therefore will not be possible for many pulsarsdetected in the Galactic pulsar census. The SKA can potentially measure timing parallax distances forabout 3600 millisecond pulsars out to 9 kpc, with an error of 20% or better.

in the order of several arcminutes from the target (see §4). This technique will provide extremely accuratephase calibration at the position of the target, and provide astrometric precision of order 15µas at 1.4GHz (Fomalont & Reid, 2004). Observations at frequencies below ∼ 5 GHz are affected by ionosphericrefraction, but the ionospheric effects may be calibrated out using a wide bandwidth (Brisken et al., 2000).Only with the substantial improvement in sensitivity provided by the SKA will high precision astrometryon weak pulsars be possible.

Benefits of high angular resolution to the pulsar timing array

High angular resolution will also be important in setting up the pulsar timing array. Accurate positionalinformation from imaging decreases the amount of observing time required to obtain a coherent timingsolution by breaking the degeneracies between position uncertainty and pulsar spin-down (Smits et al.,2011). In the absence of accurate positional information, this can take 12 months or more. Therefore,the high angular resolution component of the SKA will be highly beneficial in selecting stable millisecondpulsars to be included in the pulsar timing array.

Further to this, the high angular resolution component of the SKA will compile a significant sample ofSMBH binaries (see §3.7). The identification of a large sample of SMBH binaries would enable statisticalstudies of the inspiral rates in various phases of the binary evolution. The inspiral rates, and the possibleexistence of a “stalling radius” are important factors in the interpretation of the gravitational wavebackground that will be observed by the pulsar timing array (Jaffe & Backer, 2003).

Reference frame ties with pulsars — benefits for gravity wave detection.

A slight offset between the quasar and solar system reference frames can cause a signal in the pulsar timingresiduals that mimics that of a gravity wave passing through the solar system (Fomalont & Reid, 2004).Therefore, tying the inertial quasar frame and the dynamical solar system frame together is importantfor the detection of gravity waves with the pulsar timing array.

By combining timing and interferometric information from strong millisecond pulsars, it will be possibleto tie the quasar and planetary reference frames with great precision, since timing information is basedon the dynamic solar system frame, while interferometric information is based on the inertial quasarreference frame. We note that it will also be possible to tie the optical frame to these frames with greatprecision. GAIA will provide data on white dwarf companions to millisecond pulsars which can provideboth interferometric and timing information.

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3.2 Key Science Project: Cosmic Magnetism

3.2.1 Enabling tomographic modelling of the Galactic magnetic field with pulsarparallax distance measurements

Precise parallax distance measurements are not only a key ingredient for strong field tests of gravity, theyare also of fundamental importance in mapping the magnetic field of the Milky Way. Wavelet tomographyusing a grid of thousands of pulsars with known rotation measures (RMs), dispersion measures (DMs) anddistances will provide the best possible map of the Galactic magnetic field and electron density on large(& 100 pc) scales (Stepanov et al., 2002; Noutsos, 2009; Gaensler et al., 2004; Beck & Gaensler, 2004;Gaensler, 2006). Pulsars have negligible internal Faraday rotation and dispersion so that the measuredRMs and DMs sample only the ISM. Currently, distance estimates to pulsars are most commonly obtainedvia the pulsar’s dispersion measure combined with the galactic electron density model. Distance estimatesbased on pulsar dispersion measures are typically uncertain by ∼ 30% and can be in error by a factor of2. Precise pulsar distances will require either parallax distance measurements, or an improved electrondensity model, which itself will require parallax distance measurements to a large sample of pulsars (Cordeset al., 2004). Precision astrometry capabilities are a requirement for the SKA to enable the best possiblemodel of the large scale Galactic magnetic field. Mapping the magnetic field of the Milky Way providesan excellent opportunity to address the issues surrounding the generation and preservation of galacticmagnetic fields. The importance of understanding the large scale Galactic magnetic field configuration inthe context of fundamental questions of astrophysics is discussed at length in eg. Gaensler et al. (2004);Beck & Gaensler (2004, and refs. therein).

Time commitment

Typically ∼6 × 12 hour VLBI observations, spread over a period of 2 years, are required to measure theparallax and proper motion of a single pulsar. Thus, a total observing time of approximately 72 hoursper pulsar is required. In the Galactic plane, there can be up to 25 pulsars in the FoV when using a singlepixel receiver. Smits et al. (2011) calculate that if all the pulsars in the FoV can be imaged at once, it willtake 215 days to measure the parallaxes of all the pulsars (9000) in the Galactic plane and 450 days tomeasure the parallaxes of all the detectable pulsars to a parallax error of 20%. The number of tied-arraybeams per FoV will be limited by the maximum available data rate per station, so it may not be possibleto simultaneously image 25 pulsars in a single FoV. However, switching tied-array beams between targetswithin the FoV at high cadence may enable multiple pulsars to be imaged within a single FoV at lowerdata rates.

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3.3 Key Science Project: The Cradle of Life

3.3.1 Imaging proto-planetary disks at centimetre wavelengths

The scientific motivation for obtaining high angular resolution radio observations of protoplanetary disksis two-fold. Firstly, it will enable direct imaging and monitoring the proper motion of various structuresin the disk such as density waves and radial gaps in the disk that are formed due to the interaction of thedisk with a planetesimal. Secondly, it will enable studies of the spatial dependence of spectral signaturesrelating to different grain properties. Such information will be of great benefit in modelling protoplanetarydisks and understanding the process of planet formation (Wilner, 2004; Wilner et al., 2005; Greaves, 2009;Natta et al., 2007). The reader is referred to Greaves (2009) for a detailed discussion of the science casefor imaging protoplanetary disks at cm-wavelengths.

More recently, Kamp et al. (2007) have indicated that mapping the Hi line in nearby systems willbe an important tool for studying circumstellar disks with the high angular resolution component of theSKA. In addition to these primary scientific motivations, high angular resolution would be potentiallyuseful to pin-point the location of any ETI signals detected from planets orbiting relatively nearby stars(Morganti et al., 2006), by direct imaging and measuring the orbit of the planet.

Imaging protoplanetary disks with the SKA was initially proposed for frequencies in the range 20GHz— 35 GHz (Wilner, 2004). However, studies of protoplanetary disks can, and should, be partly carried outin the SKA-mid frequency range . 10 GHz (Hoare, 2009; Greaves, 2010, 2009). It is expected that SKA-mid will be able to image in detail the distribution of large dust particles in the disks around hundredsof nearby young stars (Wilner et al., 2005).

Figure 3 : Image of surface density structure in a protoplanetary disk from a smooth particle hydrodynamicssimulation (from Greaves et al., 2008). This image shows the surface density structure of a 0.3 M� diskaround a 0.5 M� star. A single dense clump has formed in the disk (upper right), at a radius of 75 AU andwith a mass of ∼ 8 MJupiter.

Grains grow from sub-micron sizes up to mm sizes in protoplanetary disks by sticking together inlow-velocity collisions. However, larger grains tend to shatter in collisions rather than sticking together.How, and under what conditions, do the mm-sized grains overcome this barrier to become pebble sizedgrains? This question is the subject of much debate, and is a question that may be addressed with thehigh angular resolution component of the SKA. Dust particles emit inefficiently at wavelengths larger thantheir size, and therefore centimetre flux provides evidence for pebble sized grains, which in turn providesevidence for significant progress towards planet formation. Important questions that may be addressedwith the high angular resolution component of SKA-mid include: where does the growth of decimetre-sized grains occur within the disk? Are the grains clumping into protoplanets? In what environments dothese large grains occur (stellar age, spectral type, etc.)? The results will inform planet formation theory,and allow comparison with extrasolar planetary systems. The e-MERLIN Legacy Project “PEBBLES” isaimed at studying the centimetre emission from pebble sized dust grains to show where and when planet-core growth is proceeding, and to identify accreting protoplanets. The initial results of the PEBBLESe-MERLIN survey will help to inform the scientific and technical requirements for this project withSKA-mid. Initial estimates of the technical requirements to enable ∼ 5 - 10 GHz observations of Earth

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analogues forming in southern star clusters (the beta Pic, TW Hya, AB Dor, Tuc/Hor groups) at ∼ 20- 60 pc indicate the need for very high sensitivity (∼ 100 nJy/beam) on long (∼ 1000 km) baselines(Greaves, 2010).

As already mentioned, in addition to dust emission, the Hi line will be an important tool for studyingcircumstellar disks with the SKA (Kamp et al., 2007). Hi traces the surface layers of circumstellar disks.The Hi line could be used to constrain both the photochemistry in the disk surface and the strength ofthe dissociating radiation field. The Hi line could also be an important tool in tracing disk dispersal andin particular photoevaporation processes (Kamp et al., 2007).

3.4 Key Science Project: Galaxy Evolution, Cosmology, and Dark Energy

3.4.1 Resolving AGN and Star Formation in Galaxies

The following is a summary of DRM v1.0 (2010, chapter 2). The reader is referred to that document formore detailed discussion of the science goals, motivation, and proposed observations.

The stated goal of this project is to distinguish between and track the contribution of star formationand AGN to the evolution of galaxies. This science goal will be achieved by compiling a statisticallysignificant sample of galaxies with which to explore the contribution and role of AGN vs. star formation.The survey field will be coordinated with multi-wavelength surveys to maximise the scientific return. Anadditional benefit will be in studying the cosmic evolution of AGN activity, which will address importantquestions relating to radio AGN, such as the lifetimes, duty-cycles, fuelling and triggering mechanisms.

The brightness temperature of a galaxy can provide a clear indication as to whether its radio emissionis dominated by AGN processes or star formation. A measured brightness temperature of Tb > 107Kclearly distinguishes between AGN activity and emission produced due to the birth and death of massivestars. Baselines longer than 3000 km are required to unambiguously distinguish AGN and star-formationin sources up to redshift z = 7 with flux densities down to at least 30 µJy. The required image sensitivityis therefore 5− 6µJy. Discriminating between AGN and starburst galaxies may also be possible using themorphological information provided by high angular resolution images (eg. a single, compact radio sourcerelated to AGN activity vs. a distribution of multiple supernova remnants. See eg. Garrett, 1999).

3.4.2 Hi absorption against AGN

This project is discussed in detail in DRM v1.0 (2010, chapter 15). The reader is referred to that documentfor more detailed discussion of the science goals, motivation, and observations.

Measuring the spatially resolved velocity field of Hi absorption line systems against AGN would allowthe complex morphological and kinematical properties of the gas to be studied, important for under-standing the accretion disk structure (advective vs. optically thick accretion), the characteristics of thecircumnuclear tori, as well as outflows of neutral gas and their effect on the environment of the centralAGN (eg. Morganti et al., 2006; DRM v1.0, 2010, chapter 15). Massive, jet-driven outflows of neutralgas in radio-loud AGN may be a major source of feedback in radio loud AGN (Morganti et al., 2005). Ofparticular importance is how these Hi structures relate to other observables.

3.5 Key Science Project: Probing the Dark Ages and the Epoch of Reion-ization

3.5.1 Finding the first generation of AGN jets, and radio/CO studies

Observations of powerful distant quasars indicate that super massive black holes > 109M� exist at z & 6.This suggests that the first supermassive black holes formed before, or during, the epoch of reionization.Indeed, it has been suggested that AGN jets may play a key role in the formation of some of the first starsand galaxies in the universe, through jet-induced star formation (Elbaz et al., 2009; Elbaz, 2010; Klameret al., 2004).

Klamer et al. (2004) reviewed molecular gas observations for a sample of z > 3 galaxies, and foundthat the gas and dust are often aligned with the radio emission. Based on these results, they proposed ascenario in which CO is formed at the sites of star formation that are triggered by relativistic jets. High

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sensitivity, high angular resolution imaging of high redshift radio galaxies will be required to complementhigh redshift CO imaging with ALMA, in order to study the relationship between radio jets and earlystar formation. Resolution of order tens of mas will likely be required at low frequency (. 1.4 GHz) tomap the radio structures in detail.

Falcke et al. (2004a) suggest that the first generation of AGN jets produced by accreting supermassiveblack holes will be frustrated in their dense environment and appear as distant Gigahertz Peak Spectrum(“GPS-like”) sources — that is, faint, compact sources with unusually low turn-over frequencies. Theturn-over frequency, νpeak and linear size, L, of GPS/CSS sources are found to follow an expression of theform

νpeak = 10−0.21−0.65×log(L/kpc) (2)

which reflects some basic properties of synchrotron theory (Falcke et al., 2004a). Since the source size andturn-over frequency of GPS sources are correlated but angular size and frequency scale differently withredshift, the first AGN jets should stand out from their low redshift counterparts in the parameter spacedefined by the angular size, turn-over frequency, and flux density (see Figure 4).

Figure 4 : From Falcke et al. (2004a). Plot of a combination of the turn-over frequency and angular sizeversus the peak flux density for a sample of GPS sources. Size, turn-over frequency, and flux densityroughly form a fundamental plane for GPS radio galaxies. Standard GPS sources found at z ∼ 1 occupy theupper right of the plot. High redshift “GPS-like” sources are expected to stand out from their low redshiftcounterparts, and occupy the lower left portion of the plot. See Falcke et al. (2004a) for details.

Falcke et al. (2004a) suggest the following strategy for finding the first generation of AGN jets in theuniverse:

• a shallow all-sky multi-frequency survey in the range 100 – 600 MHz down to 0.1 mJy at arcsecondresolution,

• identification of compact, highly peaked spectrum sources in that frequency range,

• identification of empty fields in the optical,

• re-observation to exclude variable sources,

• observation with long baselines and resolutions of ∼10 mas to determine sizes and to pick out theultra-compact low-frequency peaked (ULP) sources,

• spectroscopic confirmation of remaining candidates with Hi observations or by other means.

The stated goal of 10 mas resolution, at a frequency of 1.4 GHz, would require baseline lengths up to ∼4000 km.

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3.6 Exploration of the Unknown

Whilst not being an official key science project, “Exploration of the Unknown” has been identified asan important guiding principle for the design of the SKA. This is in essence a recognition of the dis-covery potential provided by instruments that are capable of probing unexplored regions of parameterspace. While high angular resolution has been achieved previously, it has not been explored at SKAsensitivity. The combination of high sensitivity and high angular resolution with the SKA will increasethe observational phase space being searched, by opening up a large, unexplored region of the brightnesstemperature–angular size plane. Observations at mas-scale resolution will, for the first time, be possi-ble for thermal and non-thermal emission regions with brightness temperatures possibly as low as a fewhundred Kelvin. Current VLBI arrays are, in general, limited to non-thermal sources with brightnesstemperatures & 106 K. The combination of high sensitivity with a broad range of angular resolution upto mas-scales will provide greater discovery potential for the SKA. Furthermore, high angular resolutionfollow-up of transient radio sources will maximise the science return of transient searches, as discussedbelow.

3.6.1 Transients

High angular resolution will play an important role in localising, identifying and understanding transientradio sources. Arcsecond resolution may be sufficient to identify the host galaxy of fast transients, andfollow-up spectroscopy of the host galaxy would provide the redshift. However, mas-scale resolution couldpotentially localise transient sources on a much finer scale. No doubt, high angular resolution follow-up observations of newly discovered classes of radio source could be of great benefit. Slow transients,for example, are likely to be compact with rapidly evolving structures. Moreover, long baselines are anexcellent discriminant between RFI and genuine astronomical events.

A triggered buffer such as that described in Macquart et al. (2010b) would allow for off-line analysisof the transient sources. Data from antennas on long baselines could be stored for a couple of minutesin a rolling buffer. A transient source detected within the long baseline field-of-view (effectively the 15mantenna primary beam) would trigger the download for this buffer for post-processing. The station beamscould be formed in the direction of the transient source whose location would be determined by the SKAcore to within a few arcseconds. A pilot survey (V-FASTR) for VLBI detection of fast transients usinga triggered buffer is currently being implemented on the VLBA. The results of the V-FASTR survey willinform the technical requirements for this experiment with the SKA.

3.7 Binary Supermassive Black Holes

Binary supermassive black holes play an important role in a number of areas of astrophysics, includingthe formation and evolution of galaxies, galactic dynamics, and gravitational wave science. Hierarchicalstructure formation models predict that a significant fraction of supermassive black holes reside in binarysystems (Volonteri et al., 2003), and these systems will have a strong impact on the central galacticenvironment (eg. Merritt, 2006). Simulations of binary black hole evolution in a galactic environmentsuggest that the inspiral efficiency may decrease at an orbital radius of 0.001 pc . r . 10 pc (Yu, 2002),potentially leaving a fraction of SMBH binaries “stalled” for extended periods of time at these orbitalradii.

The identification of a large sample of SMBH binaries would enable statistical studies of the inspiralrates in various phases of the binary evolution. This will be an important step in understanding thedynamical processes responsible for removing angular momentum from these systems, and delivering themto the gravitational wave dominated phase of evolution. The inspiral rates, and the possible existence ofa “stalling radius” are important factors in the interpretation of the gravitational wave background thatwill be observed by the pulsar timing array (Jaffe & Backer, 2003). Statistical studies would also allowmeasurements of the influence of accretion versus mergers in SMBH growth, and lead to a more preciseestimate of binary merger rates (Burke-Spolaor, 2011).

Nearby binary systems that are sufficiently massive may generate gravitational radiation strong enoughto enable the object to be resolved above the stochastic background (eg. Sesana et al., 2009). Whilstit may not carry a high probability (Burke-Spolaor, 2011; Sesana et al., 2009), the detection of bothelectromagnetic and gravitational wave emission from a nearby SMBH binary system would have a greatscientific impact. Identification of the sky position and rough orbital solution for a nearby binary wouldnot only raise the sensitivity of the pulsar timing array to the object manyfold (Jenet et al., 2004), butallow a study of the impact of the binary system on the host galaxy dynamics.

High angular resolution imaging is an effective method of searching for SMBH binaries over a widerange of orbital radii, at both high and low redshift. Binary BH candidates may be identified by surveying

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a large number of radio-emitting AGN (which could be initially identified in lower resolution surveys) tolook for closely spaced, unresolved, weakly polarised, flat-spectrum radio cores (Burke-Spolaor, 2011).Furthermore, some SMBH binary merger models predict ejected AGN, which could be revealed by astro-metric measurements of AGN showing an offset from the optical host’s kinetic centre. Source statisticsare rather uncertain, since the binary black hole inspiral time-scale, and the probability that both blackholes in the binary system will be radio loud, are unknown factors. At present, only one supermassiveblack hole binary has been identified via VLBI imaging (0402+379; Rodriguez et al., 2006). In a search ofarchival VLBA data aimed at SMBH binary detection, this was the only binary detected from a sampleof more than 3000 radio loud AGN (Burke-Spolaor, 2011). The results indicate that this project cannotbe done efficiently with the VLBA. However, the excellent u-v coverage, high sensitivity and dynamicrange provided by the SKA means that a snapshot survey will be an effective means to identify SMBHbinaries. The great improvement in sensitivity and dynamic range will increase the detection efficiencyby allowing weaker binary companions to be identified, and weaker AGN to be searched. Improved sam-ple selection may also significantly improve the binary detection efficiency. The archival VLBA sampleof Burke-Spolaor (2011) was largely composed of geodetic sources and VLBA calibrator survey targets.Such a sample is likely to have been biased against the most probable systems — wide separation binaries.Regardless, it is likely that tens of thousands of AGN must be surveyed in order to compile a significantsample of SMBH binaries, and the sensitivity of the SKA will be crucial in this regard, reducing therequired integration time per source, and enabling a much larger sample of objects to be searched. Sucha survey could be done in combination with a strong gravitational lense survey and Hi absorption againstAGN survey. Angular resolution of ∼ 1 mas could resolve projected separations of 8.5 pc at all redshifts,and sub-pc separations for the nearest galaxies. This survey could feasibly be carried out at the upperend of SKA mid band.

In addition to high angular resolution imaging, Hi absorption profiles may allow the identification ofbinary supermassive black holes in the centre of active galaxies (see Morganti et al., 2009; Rodriguez etal., 2009).

Figure 5 : From Rodriguez et al. (2006). VLBA images of the binary black hole system 0402+379 at 8 and15 GHz. The pair of unresolved, flat spectrum radio cores are easily identified in this sequence of images.The projected separation between the two black holes is 7.3 pc.

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3.8 X-ray binary systems and relativistic jets

Jet Formation and Evolution

Understanding the connection between accretion and jet production is a fundamental problem in astro-physics that has implications for the understanding of AGN and γ-ray bursts as well as X-ray binaries.X-ray binary systems (XRBs) provide a unique tool to study the coupling between jet production andaccretion flow, due to the rapid evolution of the systems through a wide range of characteristic accretionstates (on the time-scale of weeks to months), and the associated rapid changes in jet characteristics(Fender, 2004).

The high angular resolution component of SKA-mid could be used for tracing the evolution of jets inGalactic X-ray binary systems. Monitoring of bright radio jets in X-ray binaries will result in “movies”that capture the jet formation and propagation in great detail. These movies can be compared with X-rayand optical light curves to determine the nature of the coupling between jet formation and accretion flow(see Fender, 2004).

Relativistic ejections in X-ray binary systems can exhibit significant amplitude and structural changesover the course of a typical VLBI imaging run of several hours. Thus, high sensitivity, high angularresolution radio observations with good snapshot (u, v)-coverage are required to enable high time reso-lution “movies” of these relativistic outflows and avoid the problems that arise from rapid evolution ofthe jet morphology and brightness within a single observation, on a time-scale of hours (Tingay et al.,1995; Mioduszewski et al., 2001). Such observations are crucial in order to tie jet ejection events to X-raytiming and spectral changes in the accretion flow. The high angular resolution component of the SKA willbe of fundamental importance in this regard, particularly in the case of neutron star XRBs. Radio jetsfrom neutron star XRBs are inherently fainter than their black hole XRB counterparts at the same X-rayluminosity (Migliari & Fender, 2006). Due to sensitivity limitations, the jets of neutron star XRBs havenot been imaged directly. The high sensitivity of the long baseline component of the SKA will enable thejets of neutron star XRBs to be imaged in detail. By comparing the jets produced by accreting black hole,neutron star and white dwarf systems, the relationship between jet formation and system parameters (eg.depth of the potential well, stellar surface, stellar magnetic field, black hole spin etc.) can be determined.Understanding the similarities and differences between disk-jet coupling in black hole, neutron star andwhite dwarf systems is a crucial step in understanding the jet production mechanisms and the role playedby various physical parameters.

The SKA will also have the sensitivity to track the jets to large distances from the source, far enoughto observe the interaction between the jet and the ISM and the jet deceleration — something that is notusually possible with existing radio instruments (Fender, 2004). High angular resolution is required notonly for the direct imaging of jets, but also to resolve X-ray binary systems in nearby galaxies from thebackground emission.

The formation of stellar mass black holes

Compiling the full 3-dimensional space velocities for a large sample of X-ray binaries will provide con-straints on theoretical models of stellar mass black hole formation. It is generally accepted that neutronstars receive a “kick” during their formation, due to intrinsic asymmetries in the supernova explosion orthe recoil due to the associated mass ejection (see eg. Nordhaus et al., 2010, and refs therein). Super-nova kicks are invoked to explain the anomalously high space velocities that are common among pulsars.It is currently not known whether stellar mass black holes receive kicks during formation. Theoreticalmodels predict that the highest mass black holes are formed via direct collapse of the progenitor star,with little mass ejection. These systems are not expected to show anomalously high space velocities. Theless massive systems are thought to form in two stages: initially a neutron star is created in a supernovaexplosion, followed by fallback of ejected material which pushes the compact object over the stable masslimit, resulting in the formation of a stellar mass black hole (Fryer, 1999; Fryer & Kalogera, 2001). Theselower mass systems are expected to exhibit high velocities, similar to neutron stars.

Do the most massive black holes form via direct collapse, rather than a two stage process involvingan initial supernova explosion? What is the mass threshold between these two black hole formationmechanisms? How does binarity and compact object mass affect the supernova explosion? Accuratedistances and proper motions for a large sample of accreting black holes, when combined with data inother wavebands, can address these important questions (Miller-Jones et al., 2009a).

Very few X-ray binaries have accurate proper motion measurements (eg. Mirabel et al., 2001; Dhawanet al., 2007). Astrometry on X-ray binaries is only possible during the so-called “low-hard” or quiescentstates. During these states in which X-ray binaries spend the majority of their time, there exists a faint,steady, unresolved radio jet, and there is no contribution from the bright mas-scale jet that exists during

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the flaring states. With its great increase in sensitivity and excellent astrometric precision, the SKA willbe capable of compiling accurate distance and proper motion data for a large sample of X-ray binariesout to distances of up to several kpc. Optical spectroscopy will provide line-of-sight velocities so that thefull 3-dimensional space velocities can be recovered (Miller-Jones et al., 2009a).

Precise distances and luminosities

At present, X-ray binary distances, and therefore luminosities, have substantial uncertainties. Distancesare typically only known to within a factor of two (Jonker & Nelemans, 2004). Due to the limitedsensitivity of existing VLBI arrays only two X-ray binary parallax distances have been measured to date(Miller-Jones et al., 2009b; Bradshaw et al., 1999). The high sensitivity and astrometric precision of theSKA will enable precise parallax distances to be measured for a large number of X-ray binary systems.Accurate distances and luminosities will enable a number of fundamental questions to be addressed, forexample, by what factor can Galactic X-ray binary systems exceed their Eddington luminosities? Thisissue is relevant to the interpretation of ultra-luminous X-ray sources (ULXs), from which the existence ofintermediate-mass black holes has been inferred. Furthermore, it is claimed that a discrepancy between thequiescent luminosities of black hole and neutron star X-ray binaries provides evidence for the existenceof event horizons in black holes (Garcia et al., 2001). Accurate luminosities are required to test thisclaim. Accurate distances will also enable more precise estimates of the basic physical parameters suchas component masses, orbital orientation, and black hole spins (eg. McClintock et al., 2006).

3.9 Small-scale structure and evolution in AGN Jets

AGN jets are an extraordinary phenomenon, worth studying in their own right, but they also play asignificant role in the formation and evolution of galaxies, and may be the sites of ultra-high energycosmic ray acceleration. Fundamental questions relating to the composition, formation, acceleration andcollimation of AGN jets remain to be answered. Understanding the physical parameters and dynamics ofextragalactic jets are key ingredients in understanding the role of radio sources in structure formation andcosmic ray acceleration. The combination of very high angular resolution, sensitivity and dynamic range ofthe SKA will provide high fidelity images of the complex and evolving structures associated with AGN jetsover a wide range of frequency and spatial scales, as a means to address these fundamental astrophysicalquestions. Importantly, the SKA will enable deep images of jets resolved in the transverse direction.Complex structures in parsec scale jets may contain the signatures of complex magnetic field structure,hydrodynamic and magnetic instabilities, shocks and other phenomena (Bicknell et al., 2004). With theSKA, the structure of parsec scale jets may be traced with high fidelity out to hundreds of milliarcsecondsfrom the core, providing an excellent source of data for comparison with numerical simulations and modelsof jets from parsec to kpc-scales. The high sensitivity of the SKA may provide the ability to detect thefaint, self-absorbed radio emission from the inner jet regions associated with high energy X- and γ-rayemission - a region where the jet flow may be established (Bicknell et al., 2004). The high sensitivity ofthe SKA will also extend the study of jets to include those in low luminosity “radio quiet” AGN, as wellas counter-jets in a large number of objects.

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3.10 Strong gravitational lensing

The high angular resolution component of the SKA will play an important role in the study of stronggravitational lenses (Koopmans et al., 2004). High resolution, high fidelity images of Einstein ringsand arcs can provide constraints on the dark matter substructure in galaxies (Koopmans, 2005; Vegetti& Koopmans, 2009). Complementary to this, measurements of flux anomalies (Metcalf & Zhao, 2002;McKean et al., 2007) and astrometric perturbations (Chen et al., 2007) will further probe the dark mattersubstructure of galaxies.

Sensitive high angular resolution observations of gravitationally lensed radio sources will also providethe opportunity to detect and measure the masses of supermassive black holes in ordinary galaxies atintermediate redshifts. Models predict that, under certain circumstances, the central supermassive blackhole of a gravitational lensing galaxy will result in two faint, closely spaced lensed images near the centreof the gravitational lense (Mao et al., 2001). The properties of the pair of central images probe the inner10 - 100 pc of the lensing galaxy, and allow a measurement of the mass of the supermassive black hole,and possibly the identification of binary SMBHs (Bowman et al., 2004; Rusin et al., 2005).

Figure 6 : Taken from Koopmans et al. (2004). Simulated images of a simulated strong gravitationallens system. The upper (lower) panels show an early-type lens with an Einstein radius of RE = 1.2(0.4)arcseconds. From left, middle to right, the FWHM resolution decreases from 0.7 arcsec, 0.1 arcsec to 0.02arcsec (e.g. expected for LSST, WFIRST, SKA, respectively). The two right panels show the radio system,as observed with SKA, without the lens galaxies. Note that in the optical the lens-galaxy significantlycontaminates the emission from the lensed source, making it harder to identify these systems as lenses,whereas in the radio even small separation systems are relatively easier to identify.

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3.11 Absolute Astrometry and Geodesy

At present, the main limitation to the accuracy of absolute astrometry and geodesy is in the calibration ofthe troposphere. If the SKA design allowed for several (∼ 10) independent sub-arrays on long baselines,the temporal and angular properties of the tropospheric/ionospheric phase screen could be accuratelycalibrated, and the main limitation to astrometric accuracy would then be due to source structural effectsresulting in the apparent variability of calibrator positions (Fomalont & Reid, 2004). Another key limitingfactor in today’s VLBI geodesy is a deficit in the number of southern hemisphere baselines. The long-baseline component of the SKA will solve this problem. Fomalont & Reid (2004) estimate that with itshigh sensitivity and multiple independent sub-arrays, the SKA could potentially improve the absoluteastrometric accuracy, and fundamental geodetic experiments by at least an order of magnitude. Withsuch an improvement, the fundamental quasar reference frame could be defined with < 10µas precision,and tied to the solar system dynamic frame with similar accuracy.

There are various combinations and permutations that could provide the requisite number of sub-arrays with adequate (u, v)-coverage for the purposes of absolute astrometry/geodesy, albeit with a smallnumber of dishes (. 5) per sub-array element. This of course hinges on the ability of the remote stationsto operate as a set of multiple independent sub-stations.

Precise position measurements of pulsars will allow the optical, solar system and quasar referenceframes to be tied with great precision. Timing positions are based on the dynamic solar system frame,while interferometric positions are based on the inertial quasar reference frame. By combining timingand interferometric information from strong millisecond pulsars, it will be possible to tie the quasar andplanetary reference frames with ∼ 10µas precision. Further to this, GAIA will provide data on whitedwarf companions to millisecond pulsars. SKA observations of the millisecond pulsars in such systemswill provide interferometric and timing positions, thereby allowing the three reference frames to be tiedtogether with similar precision.

The International Celestial Reference Frame (ICRF) is the basis of the International Terrestrial Ref-erence Frame (ITRF), which in turn is the basis of the World Geodetic Coordinate System and of alllocal/national coordinate systems. Whilst GAIA may revolutionise the defining ICRF, high precisionradio astrometry will be required for geodesy and to tie the radio and optical frames together with highprecision.

VLBI geodesy uniquely defines the Earth orientation parameters (EOP): precession, nutation, radiusof the Earth, polar motion and length of day. EOP time series contain a wide variety of geophysical andclimate information, and can be of great benefit when combined with other techniques in the analysis ofEarth sciences (Solomon et al., 2002).

Astrometry and Cosmology

High-precision radio astrometry, applied to quasar proper motions, has applications in three keenly de-bated fundamental problems: (1) gravitational wave detection (Pyne et al., 1996; Gwinn et al., 1997; Jaffe,2004; Book & Flanagan, 2011), (2) anisotropy of the Hubble constant (McClure & Dyer, 2007; Schwarz& Weinhorst, 2007), and (3) measurement of the constant of the secular aberration drift (acceleration ofthe solar system barycentre) (Sovers et al., 1998; Klioner, 2005).

Studies of quasar proper motions using the IVS database (>2000 quasars, 25 years of observations)suggests the presence of both dipole and quadrupole characteristic patterns in the observed distribution ofquasar proper motions on the sky (Titov, 2008; Titov et al., 2010). The dipole pattern can be interpretedin the framework of the secular aberration drift (Kopeikin & Makarov, 2006) caused by the Galactocen-tric acceleration of the solar systems barycentre. A characteristic quadrupole pattern in quasar propermotions can be interpreted either in the framework of angular anisotropy of the Hubble constant, or asa manifestation of very low frequency gravitational waves (Titov, 2008), arising naturally in inflationarycosmologies (Rubakov et al., 1982; Fabbri & Pollock, 1983).

Historically, the more frequently observed northern quasars have higher positional accuracy (. 10µas)than southern quasars (Feissel-Vernier, 2003; Ma et al., 1998). Positional inaccuracy and noticeable short-age of data for the Southern Celestial Hemisphere could be responsible for all the observed systematics(Titov, 2004). The long-baseline portion of the SKA will allow more high-precision, high-quality obser-vations of the southern quasars, and determine the true cause of the patterns in quasar proper motions.

Jaffe (2004) considered an experiment to place a limit on the gravitational radiation background bysearching for proper motions of distant galaxies that results from time-dependent “gravitational lensing”.With > 10 sub-arrays, approximately 106 pointlike AGN could be observed over a month, in two epochsseparated by at least a year. The sensitivity of such an experiment to gravitational radiation would becompetitive with other methods such as pulsar timing (Jaffe, 2004; Book & Flanagan, 2011).

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3.12 Relative Astrometry: Parallax and Proper Motions

The high angular resolution component of the SKA may be capable of relative astrometry with ∼10µas or better precision on faint sources (Fomalont & Reid, 2004). With such high astrometric precision,it is possible to measure the parallax of virtually any detected galactic object and proper motions ofsome extragalactic objects. We have discussed the importance of parallax distance and proper motionmeasurements for pulsars (§3.1.1 and §3.2.1), X-ray binaries (§3.8) and Galactic masers (§3.13). Furtherapplications of high precision radio astrometry on faint sources include: improved calibration of theuniversal distance scale, proper motions of all radio stars with flux densities greater than 0.5 mJy, dynamicsof clusters, orbital motions of binary stars, detection of jupiter sized planets around stars up to about1 kpc via reflex motions of the star, measuring the distance and proper motions of local group galaxiesand so on (see Fomalont & Reid, 2004, for more details). Moreover, high precision radio astrometry ofquasars will complement optical astrometry from space telescopes, such as GAIA.

Studying the ISM and the physics of core-collapse supernova with pulsars

In addition to enabling strong field tests of gravity (§3.1.1) and mapping the Galactic magnetic field(§3.2.1), parallax distance and proper motion measurements for thousands of normal pulsars will enablea variety of ISM studies (Cordes et al., 2004; Lazio et al., 2004). In addition, proper motions for alarge sample of radio pulsars will provide insight into the physics of core-collapse supernovae (Cordes etal., 2004). It is generally accepted that neutron stars receive a “kick” during their formation, due tointrinsic asymmetries in the supernova explosion or the recoil due to the associated mass ejection (see eg.Nordhaus et al., 2010, and refs therein). Supernova kicks are invoked to explain the anomalously highspace velocities that are common among pulsars. A well sampled velocity distribution is a crucial stepin understanding the physics of core-collapse supernovae particularly in regards to neutron star kicks.Full 3-D velocities may be obtained for a sample of pulsars detected in the Galactic pulsar census usingastrometric and timing measurements (Cordes et al., 2004).

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3.13 Galactic Masers

Methanol masers arising at 6.7-GHz are a unique tracer of the sites of ongoing massive star formation,which in turn trace the spiral arms of the Milky Way. The GAIA astrometric mission will map the MilkyWay on Galactic scales, but will suffer from dust extinction in the Galactic plane and towards the Galacticcentre. Astrometry of 6.7 GHz methanol masers with the SKA will provide an important complementto GAIA by mapping out the spiral structure and rotation of the Milky Way without the limitations ofdust extinction (Rygl et al., 2010; Reid et al., 2009; Brunthaler et al., 2011). The strength, long lifetimesand small internal motions of 6.7 GHz masers make them excellent targets for this purpose (Rygl et al.,2010). Mapping the spiral structure of the Milky Way will be important for example in comparison withmaps of the Galactic magnetic field.

As well as locating the positions of on-going massive star formation, the polarization of maser spec-tral lines can be used to study interstellar magnetic fields. Methanol masers exhibit a small degree oflinear polarization but this is hard to measure as the methanol molecule has a weak dipole. In manycases methanol masers co-exist with OH masers and the OH molecule is paramagnetic, which makes itsusceptible to Zeeman splitting of maser lines in the presence of interstellar magnetic fields. An on-goingsurvey (MAGMO, Green et al.) using the Australia Telescope Compact Array aims to characterise thelarge-scale magnetic field structure of our Galaxy, using measurements of OH masers that arise fromregions of massive star-formation. In many regions of our Galaxy, masers comprise of many small-scalespots of emission, often separated in velocity and with different polarization properties. VLBI studiesof OH masers have shown that linear polarization angles of maser spots can vary over angular scales of100s of milliarcseconds (Fish & Reid, 2006). Unless observations are carried out with a sufficient angularresolution, the differing linear polarization angle of overlapping adjacent maser spots will yield misleadingresults.

OH and methanol masers can provide useful information in the analysis of accretion and outflows inthe formation of high mass stars. Further opportunities for OH and methanol maser studies with theSKA have been discussed by eg. Norris (2000) and Green & Baan (2007).

Figure 7 : Taken from Reid et al. (2009). Artist conception of the Milky Way (R. Hurt:NASA/JPL-Caltech/SSC) with the positions of the high mass star forming regions for which trigonometric parallaxeshave been measured. Symbols indicate parallaxes from 12 GHz methanol masers (dark blue); H2O and SiOmasers or continuum emission (Orion) (light green); the Galactic center (red asterisk) and the Sun (red Sunsymbol). Labels refer to the spiral arms. Astrometric measurements of methanol masers with the SKA willtrace the spiral structure throughout the Galaxy.

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3.14 Mapping high mass star formation in nearby galaxies

The combined sensitivity and high angular resolution of the SKA will permit detailed studies of extra-galactic Hii regions for the first time. Global aspects of massive star formation, as traced by the Hiiregion population, are best studied in nearby, face-on spirals such as M33 (Hoare, 2004). Figure 8 showsthe location of some Hii regions in M33 discovered with the VLA overlaid on an Hα image of the spiralgalaxy. Only the top end of the initial mass function is accessible with the VLA due to the limited sensi-tivity. The increased sensitivity of the SKA will be of fundamental importance in this regard. The highangular resolution component of the SKA will be able to distinguish ultra-compact Hii regions, which areyoung and therefore most relevant to identifying conditions at the star’s birth-place. UCHii regions aretypically deeply embedded in their parent molecular cloud and so cannot be studied at optical or near-IRwavelengths. The SKA will be capable of detecting individual UCHii regions out to a distance of nearly50 Mpc, and will be able to resolve UCHii regions from their surrounding environment out to the distanceof 1 Mpc (Johnson, 2004). Questions such as “what triggers massive star formation?” are much easier toanswer in nearby spirals than in the Milky Way because a wider range of conditions can be investigatedand there are no line-of-sight issues with everything lying in the Galactic plane (Hoare, 2004; Johnson,2004).

The SKA will determine the exact location of massive star formation relative to other protostars,density enhancements in the molecular gas, shock fronts and other features of the ISM, and will enablean investigation into the relationship between properties of star formation and environmental parameterssuch as metallicity, pressure, turbulence, stellar density, triggering scenarios, and how star formationdiffers in “burst” and quiescent modes (Johnson, 2004; Hoare, 2004).

Figure 8 : Taken from Hoare (2004). Crosses mark the locations of young, dense Hii regions found in a 5GHz VLA A configuration observation overlaid on an Hα image of the nearest relatively face-on spiral M33. Due to limited sensitivity, the VLA only samples the top of the initial mass function — the SKA willdistinguish UCHii regions and probe more completely the Hii region population.

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3.15 Stellar winds/outflows

Stellar winds and outflows from young stellar objects likely play an important role in angular momentumloss and setting the final mass of a star. Winds and outflows can interact with the larger scale cloud, andin the case of more massive stars, can trigger further star formation or disperse the cloud (Hoare, 2004,and refs. therein).

The SKA will make a significant contribution to the study of stellar winds and outflows. A widevariety of potential science applications involving high angular resolution are discussed in Hoare (2004),White (2004) and Johnson (2004). Below we summarise a selection of the science case presented by theaforementioned authors.

RRLs

The unique capability of the SKA in studies of stellar winds and outflows will be in studying the out-flow dynamics with radio recombination lines at very high spatial resolution. Detailed modelling of thestrengths and profiles of radio recombination lines needs to be done for stellar outflows to better under-stand the potential capabilities of the SKA, particularly given the SKA-mid upper frequency limit of 10GHz and the fact that RRL strengths are weaker and pressure broadening is more pronounced below 10GHz than at higher frequencies. In high mass stars, RRL mapping of equatorial outflows will determinewhether disk ablation is important in setting the final mass and hence the upper end of the initial massfunction. SKA recombination line studies will complement ALMA observations of molecular disks to allowa comprehensive theory of accretion, outflow and angular momentum transport in low mass stars to berealised (Johnson, 2004).

21cm Observations

A key aim of SKA studies will be to detect Hi emission from highly collimated jets of young stellar objects.The surface atomic layer of accretion disks may also be mapped. High angular resolution is required inorder to resolve out the confusing Hi emission along the line of sight from the star forming clouds and theGalaxy.

3.16 Stellar Atmospheres

3.16.1 Imaging stellar atmospheres

Cool main sequence stars have non-thermal corona with particles up to MeV energies that produce strongand steady non-thermal radio emission. This is in addition to their thermal corona with temperatures of106 - 107K. The nature of these non-thermal coronae and their relationship to the thermal stellar atmo-sphere is poorly understood. Spatially resolved SKA images will add important additional information tothe modelling of this phenomenon. Only a few nearby stellar atmospheres are currently accessible withexisting radio telescopes. The SKA will provide a much larger sample of stars for which their non-thermalcorona can be imaged, and studied in detail (White, 2004).

3.16.2 Resolving stellar radio flares

VLBI observations show that the size of stellar radio bursts can grow with time and reach sizes muchlarger than the star. The improved sensitivity of the SKA is likely to enable the identification of radioflare phenomena presently unknown, across a wide range of stellar types. Resolving stellar radio flaresmay aid in understanding the nature of energy releases in the atmospheres of stars of different massesand ages (White, 2004).

3.17 Spatial and temporal changes in the fundamental constants

High resolution mapping of redshifted radio absorption lines may be used for measuring changes in thefundamental constants with time (Curran et al., 2004). Many of the modern Grand Unification Theoriespredict spatio-temporal variation of physical constants. Indeed, recent studies of redshifted optical absorp-tion line systems suggest there is variation of the fine structure constant with space and redshift (Webbet al., 2010). By comparing the redshift of an object as determined from the Hi 21cm and OH absorptionlines, as well as mm rotational lines and the optical fine structure lines, it is possible to constrain various

21

combinations of the physical constants α = e2/~c (fine structure constant), gp (proton g-factor) and theratio of proton to electron mass me/mp.The SKA will provide a statistically large sample of 21cm and OHabsorption line systems, which will enable studies of the cosmological evolution of various fundamentalconstants, and could provide a means of experimentally testing current Grand Unified Theories.

Mapping of Hi and OH absorption lines in quasar emission on milliarcsecond scales would ensurecomparisons between different absorption lines are made for similar lines of sight. High angular resolutionwill also allow measurement of absorption spectra along lines of sight towards different source componentsto provide many independent measurements of changes in the fundamental constants (Curran et al., 2004).

3.18 Ultra High Energy Particle Astronomy at & 2 degree angular resolutionvia the Lunar Cerenkov technique

The origin of ultra high energy (UHE) cosmic rays with energies & 1018 eV remains a mystery. Under-standing where and how UHE cosmic rays are accelerated is seen as one of the great scientific challengesof this century (Committee On The Physics Of The Universe et al., 2003). The deflection of lower energycosmic rays by cosmic magnetic fields makes the flux appear isotropic, regardless of the angular distri-bution of their sources. However, the flux of UHE cosmic rays with E & 6 × 1019 eV is known to beanisotropic (The Pierre AUGER Collaboration et al., 2010) and the deflection of these UHE cosmic raysdue to galactic and extragalactic magnetic fields in the nearby universe are expected to be relatively small(. a few degrees) if the composition is mostly protons or light nuclei (Dolag et al., 2004; Nagar & Mat-ulich, 2010). The angular distribution of UHE cosmic rays is therefore expected to contain informationabout the source of UHE cosmic rays and/or very large scale magnetic field structures.

Theoretically, UHE neutrinos are closely related to UHE cosmic rays. UHE neutrinos may be producedin association with UHE cosmic ray acceleration, and they will also be produced due to the interaction ofUHE cosmic rays with the CMB along their trajectory from the source to the Earth. In either case, theneutrinos are not deflected by magnetic fields, and hence the arrival directions will point directly to thesource of UHE cosmic rays. Therefore, measuring the angular distribution of the highest energy cosmicrays and neutrinos will address the question of where and how UHE particles are accelerated.

Coherent, nanosecond-scale bursts of Cherenkov radiation are predicted to arise from the lunar surfacedue to ultra-high energy cosmic rays and neutrinos interacting with the outer layers of the Moon (seeeg. James & Protheroe, 2009). The idea of indirectly observing UHE particles via the detection ofcharacteristic radio pulses from the surface of the Moon is known as the Lunar Cherenkov technique.The predicted event rate for UHE (E > 5.6× 1019 eV) cosmic ray detections using the lunar Cherenkovtechnique and the SKA low frequency aperture array (. 200 MHz) is about 0.1 − 0.4/hour (James &Protheroe, 2009; Ter Veen et al., 2010). This is at least an order of magnitude greater than the detectionrate of such particles at the Pierre Auger Observatory (James & Protheroe, 2009). At higher frequencies,the Lunar Cherenkov detection rate may decrease, but it is currently unknown by how much. In the caseof UHE neutrinos, the flux is unknown, and the predicted detection rates using the SKA range from lessthan 10−4/hour up to around 1/hour (James & Protheroe, 2009).

The lunar Cherenkov technique cannot determine the composition of UHE cosmic rays, nor can itdetermine the energy of the individual cosmic rays with any great precision. The major contributionto cosmic ray astronomy provided by the lunar Cherenkov technique with the SKA is the potential togather a large sample of arrival directions for the highest energy cosmic rays and neutrinos, enabling moreaccurate statistics in identifying the source(s) of UHE cosmic rays.

Detection of the characteristic nanosecond-scale bursts of radio emission from the Moon due to UHEparticles does not require long baselines. In fact, moderate length (∼ 100 km) baselines, when combinedwith polarisation information, could provide approximately 10 degree resolution for the arrival directionof UHE particles (James et al., 2008). However, post-event analysis of lunar Cherenkov bursts usingbaselines of several thousand km at an observing frequency of 1.4GHz can localise the origin of the burstto a region as small as 200m on the lunar surface. Event reconstruction using detailed maps of the lunarsurface and polarisation information could then provide angular resolution of up to 2 degrees (Falckeet al., 2004b; James et al., 2008). Baseline lengths & 1000 km will also provide the ability to rule outother sources of nano-second scale pulses, such as atmospheric events or low-earth orbit and geostationarysatellites.

22

3.19 Scattering

3.19.1 Probing the Intergalactic Medium via Angular Broadening

The potential to detect scatter broadening by a clumpy IGM represents a unique and powerful probeof this component of the universe. Assuming that most of the IGM is in the form of electron density“cloudlets”, Lazio et al. (2004) predict that a resolution of better than 4 mas is required to detect angularbroadening due to the IGM at 1.4 GHz, while at 330MHz a resolution of only 80 mas or better is required.The latter requirement is within the capabilities of current VLBI facilities, however, a large improvementin sensitivity is required to increase the sample of objects for which angular broadening can be searched,and to achieve high enough source density to sample the cluster angular size scale. This will also toenable statistical analyses to identify trends such as redshift dependence. Angular broadening studies ofthe IGM would require at least 5 – 10% of the SKA collecting area distributed on long baselines, witha maximum baseline of & 5000 km for frequencies ∼ 0.5 GHz, or a maximum baseline of & 1000 km forfrequencies of ∼ 0.2 GHz (Lazio et al., 2004).

3.19.2 Resolving AU-scale structure in the ISM via diffractive scintillation

Small-scale (∼ 0.1 − 10 AU) structures in the ISM may be probed through high sensitivity long base-line observations of scintillating pulsars (Brisken et al., 2010). This requires observations in the strongscattering regime, generally at frequencies below 1 GHz.

3.19.3 Extreme scattering events

Extreme scattering events (ESEs) are large, time-symmetric excursions in the measured flux density of acompact source, lasting typically between 10 days and a few months. They have been shown to be causedby refractive lensing due to small, AU-scale structure in the foreground ionized interstellar medium ofthe Galaxy (Fiedler et al., 1987a). ESEs are relatively rare, with an estimated event rate of 0.013 percompact source per year (Fiedler et al., 1987b), and studies to date have been hampered by the lackof a monitoring programme that could find sufficient numbers of them and identify the events as theyoccur. Very little is known about the lensing structures responsible, and models advanced to explain themare either problematic or contraversial (Walker & Wardle, 1998). Sensitive long baseline observations ofsources undergoing extreme scattering events can potentially yield a determination of the electron column-density profile, distances and transverse velocities of the Galactic ”lenses” responsible for the ESEs, whichare expected to cause multiple imaging (see eg. Lazio et al., 2000a). To date most ESEs have been foundin historical light curves, with only one bright quasar ESE having been “caught in the act” and observedat high angular resolution by (Lazio et al., 2000a), who detected a slight increase in the source diameter at13cm, from near 0.6 mas outside the ESE to near 1 mas during the ESE. With its multi-beam, wide fieldcapabilities, the SKA could monitor the flux densities of a large number (>> 100) sources on a regular (∼daily) basis to detect transient scattering events (Lazio, 2000b). The high angular resolution capabilitieswill be important for imaging the sources during these events, to monitor changes in apparent sourcesize, position, and to detect multiple images. The required angular resolution is not yet well determined,but would be milliarcsecond scale or smaller (Johnston et al., 2008). ESEs would ideally be observed atseveral frequencies between 1-10 GHz.

3.20 Spacecraft tracking

Long baselines of greater than 1000 km could provide real-time plane-of-sky spacecraft position measure-ments of order 0.1 mas by combining in-beam phase referencing techniques with phase-delay astrometricposition measurements using a strong spacecraft signal. This corresponds to a linear distance of lessthan 1km at the distance of Saturn (Jones, 2004). The accuracy and speed with which the SKA will beable to provide spacecraft position measurements could be extremely valuable during critical stages of amission, for example if aerocapture or atmospheric entry to distant celestial bodies is attempted (Jones,2004). While the need for SKA support of science spacecraft will likely be infrequent, precision spacecrafttracking enabled by the SKA in these rare cases will be extremely valuable. Jones et al. (2010) haverecently demonstrated VLBI astrometric measurements of the Cassini spacecraft orbiting Saturn.

23

4 Calibrators and Phase Referencing

Many of the high angular resolution science projects require accurate phase referencing to achieve veryhigh astrometric precision and/or high image sensitivity and dynamic range. Accurate phase calibrationis most important for astrometry and the astrometric precision can be approximated by the angularresolution of the array divided by the dynamic range (eg. Marti-Vidal et al., 2009). A dynamic range oforder 1000:1 may be possible using multi-view in-beam calibration (Fomalont & Reid, 2004), in whichcase the astrometric precision of the SKA may be 15µas or better at 1.4 GHz, and of order 3 µas at8 GHz, provided there are several suitable calibrator sources within the primary beam of the individualantennas.

In this section we present an analysis of the expected number of calibrators per primary beam area atfrequencies between 1 and 10 GHz for a given fringe fit sensitivity, as a means to determine: (a) what isthe minimum global fringe fit sensitivity that is required to enable very high precision astrometry usingmulti-view in-beam calibration. (b) at what frequencies will multi-view in-beam calibration be viable,and (c) how many tied array beams are likely to be required at each frequency.

Multi-view in-beam calibration requires at least 3 calibrator sources surrounding the target within theprimary beam of the individual antennas. A 2D phase plane (or higher order function if several calibratorscan be used) is fitted to the measured phases, and this allows continuous interpolation of the phases atthe position of the target source. This calibration technique results in a significant improvement in thedynamic range and astrometric precision (Fomalont & Reid, 2004; Jimenez-Monferrer et al., 2010).

Let us assume that the calibrator population is Poisson distributed on the sky, and the surface densityof calibrators is Σc. Let

R = AΣc (3)

be the average number of calibrator sources within an area of sky of solid angle A. For in-beam calculationswe use the area of the primary beam to the FWHM as the region of interest. For simplicity, we do notaccount for the drop in sensitivity with increasing distance from the primary beam centre, which wouldintroduce a correction of order tens of percent. For a 15m diameter dish, A ≈ 1 deg2 at 1 GHz, so that

R ≈ Σcν−2GHz (4)

To obtain nc in-beam calibrators at an observing frequency νGHz over about 60% of the sky, the requiredcalibrator surface density is

Σc ≈ ncν2GHz (5)

Multi-view in-beam calibration at 1.4 GHz requires Σc & 6 deg−2, and at 10GHz requires Σc & 300 deg−2.The potential for multi-view in-beam calibration will depend on the global fringe fit sensitivity of eachstation.

4.1 Global Fringe Fit Sensitivity σglbl

Global fringe fitting requires that the calibrator source be detected with high signal to noise on thecombined baselines to each station. The relevant sensitivity for station j is therefore

σglbl, j =

Nstns∑i=1,i6=j

1

σ2i,j

−1/2

(6)

where σi,j is the baseline sensitivity between stations i and j, and Nstns is the number of stations in thearray. Let us first consider the case of the remote station only array, in which each remote station containsNants/stn identical antennas. The baseline sensitivity is

σi,j =SEFD√2∆ν∆t

1

Nants/stn(7)

Then

σglbl,j =SEFD√2∆ν∆t

1√N2

ants/stn (Nstns − 1)(8)

For a fixed total number of antennas Nants, such that Nants = Nants/stn ×Nstns

σglbl,j =SEFD√2∆ν∆t

1√Nants Nants/stn

(1− Nants/stn

Nants

) (9)

24

In a large array with Nants >> Nants/stn, the relevant sensitivity for global fringe fitting improves approx-

imately with the square root of the number of antennas per station: σglbl ∝ N−1/2ants/stn.

Incorporating the SKA core with Ncore ants antennas

σglbl,j =SEFD√2∆ν∆t

1√N2

ants/stn (Nstns − 1) +Nants/stn Ncore ants

(10)

Let us consider a nominal high resolution SKA comprised of 25 stations with 24 antennas per station,and a core station with 1200 antennas in a single tied array. All antennas are identical 15m dishes withTsys = 30K and 70% efficiency, so that the single antenna SEFD = 670 Jy. Then

Without Core σglbl,j ≈16√(

∆νGHz

∆tmins

) µJy (11)

With Core σglbl,j ≈9√(

∆νGHz

∆tmins

) µJy (12)

4.2 Estimating Calibrator Source Counts

Flux density [Jy] Flux density [Jy] Flux density [Jy]

Num

ber o

f Sou

rces

Num

ber o

f Sou

rces

Num

ber o

f Sou

rces

1.4 GHz 4.86 GHz 10 GHz

Figure 9 : The predicted source counts per primary beam area as a function of flux limit for a 15m dishat various frequencies. Source counts for each frequency are compiled from the S-Cubed SEX simulation ofextragalactic radio sources (Wilman et al., 2008). The output of this simulation has been shown to be ingood agreement with measured source counts (see Wilman et al., 2008). For the purposes of the currentanalysis, we do not consider the uncertainties on measured source counts. These are the low resolutionsource counts. In estimating source counts at milliarcsecond resolution, we must account for the fraction ofresolved flux (see text).

The mas-scale calibrator surface density can be estimated from the low resolution surface density asfollows. Let us assume that a calibrator requires an nσ detection and, on average, the fraction of totalsource flux remaining on >1000km baselines is denoted by fmas−scale. The VLBI calibrator surface densityΣc is related to the low resolution surface density, Σ, by

Σc = Σ

(Fν >

n σglbl,j

fmas−scale

)(13)

The fraction fmas−scale will be a function of frequency and source population.We use the output of the S-Cubed simulation to estimate the likely surface density of calibrator sources

as a function of sensitivity. The S-Cubed simulation identifies four source populations: (1) quiescent starforming galaxies (2) starburst galaxies (3) radio loud AGN and (4) radio quiet AGN. Discrete supernovaremnants account for a small fraction of the radio emission of normal star forming galaxies (Condon,1992). We therefore do not consider quiescent star forming galaxies as potential calibrator sources for the

25

high angular resolution component of the SKA. Starburst galaxies will exhibit emission on long baselines(see eg. Garrett, 1999). Only a small fraction of the total emission will remain at mas-scales, and thesesources are likely to be non-ideal calibrators, but we include starburst galaxies here for completeness.

Several recent studies have addressed VLBI scale detection statistics in the faint radio source popula-tion (Porcas et al., 2004; Garrett et al., 2005; Wrobel et al., 2005, 2004). With some extrapolation, thesestudies suggest that around 10 sources per square degree are detectable at VLBI scale resolutions abovea detection threshold of 1 mJy at 1.4 GHz. The work of Porcas et al. (2004) indicates that up to ∼30sources per square degree may be detectable above a detection threshold of 1 mJy at 1.4 GHz. In order tomake a first order estimate of calibrator density for the high angular resolution SKA, we therefore assumefmas−scale ∼ 0.1 for both radio loud and radio quiet AGN. The predicted surface density of mas-scalecalibrators having Fν > 10σglbl,j is then

Σc ≈ ΣRL−AGN(Fν > 100σglbl,j) + ΣRQ−AGN(Fν > 100σglbl,j) (14)

In Figure 9 we plot the surface density of radio sources as a function of flux density threshold, aspredicted by the S-Cubed simulation.

4.3 Consequences for Phase Referencing Projects

The above calculations suggest that multi-view in-beam calibration may become difficult at the upper endof the SKA-mid band, particularly if only the best calibrators are to be used. Assuming ∆ν = 2.5 GHzand ∆t = 2 minutes at an observing frequency of 10GHz, σglbl,j ≈ 7µJy for the remote-station-onlyarray. Reading from Figure 9 and applying equation 14, the predicted calibrator density is less than 1per beam at 10 GHz. Provisions for cluster-cluster style phase referencing, i.e. splitting the stations into4 sub-arrays, may be required to achieve high precision phase calibration and astrometry at the upperend of the SKA-mid band. This should be quantified further in future analysis. In contrast, in-beammultli-view calibration with as many calibrators as desired will be possible at frequencies . a few GHz.

26

Projec

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KSP

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and

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> 3

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ld

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27

Acknowledgements

We would like to thank the following people for helpful discussions and/or input to various sections of thismemo: Lisa Harvey-Smith, Sarah Burke-Spolaor, James Miller-Jones, Clancy James, Michael Kramer,Jane Greaves, Sergei Gulyaev, Melanie Johnston-Hollitt, Richard Dodson, Maria Rioja, Ron Ekers andTim Colegate. We would also like to thank the referee, Joe Lazio, for his thorough reading of the memoand helpful suggestions for it’s improvement.

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