M. Huynh R. Smits L. Harvey-Smith A. Bouchard R. Beck D. Obreschkow I. Stairs A. Popping L. Staveley-Smith J. Lazio R. Norris

Transcription

1 Memo 142 Is There an Optimum Frequency Range for Phased Array Feeds? Question 2 of the Magnificent Memoranda II M. Huynh R. Smits L. Harvey-Smith A. Bouchard R. Beck D. Obreschkow I. Stairs A. Popping L. Staveley-Smith J. Lazio R. Norris (on behalf of the SKA Science Working Group) August

2 2 1. Background Phased array feeds (PAFs) are being explored under an advanced instrumentation programme (AIP) as a means for increasing dramatically the survey speed of the SKA Phase 1, and ultimately Phase 2 (Garrett et al. 2010). Current implementations obtain a frequency dynamic range of about 2.5:1. Following discussions within the SKA Program Development Office and with various engineering teams, the goal of this memo is to address the following question: Within the Phase 2 frequency range for parabolic dishes (0.45 GHz 10 GHz), what is the optimum center frequency for an initial implementation of PAFs that will maximize the science return? 2. High Survey Speed Science with PAFs In this section we briefly describe high survey-speed science areas addressed by PAFs and propose an optimum frequency range for each based on current theoretical and observational knowledge. This Memo is also not intended to be a re-write of the science case or the design reference mission, so it is not complete in its references and cites only relevant recent literature Cosmic Magnetism Faraday Grids The main goal of the SKA Magnetism Key Science Project is to obtain an all-sky, dense grid of Faraday rotation measures (RM) towards polarized background sources. This will allow us to investigate the properties of the magnetic fields in intervening objects,

3 3 like the Milky Way and embedded objects, galaxies, galaxy clusters and the intergalactic medium. PAFs are crucial for high survey speed. A pilot survey with PAFs installed on the SKA1 dishes will yield a density of the RM grid of about 800/deg 2 with 1h integration per pointing, about 30x better than with ASKAP (project POSSUM). In addition to high sensitivity and high survey speed, the RM survey also requires high RM precision. Galactic halos and intergalactic filaments are expected to have RM of 1-10 rad/m 2 (Arshakian & Beck 2011). The frequency range of polarization observations defines the response in Faraday depth (FD) space, the RM Spread Function (RMSF), which is the shape of a point source in Faraday space, a Faraday screen. In case of a polarized background source, Faraday rotation in the foreground can be described by a Faraday screen, so that FD=RM. The half-power width of the RMSF is (Brentjens & de Bruyn 2005): σ FD 2 3 / Δλ 2 3(λ 2 0 (Δν/ν 0 )) 1. For PAFs in the frequency range MHz σ FD 17 rad/m 2 and σ FD 46 rad/m 2 for MHz. For comparison, the ASKAP-POSSUM project ( MHz) has σ FD 120 rad/m 2 The location of the peak of a Gaussian distribution can be determined to much better than the HPW if the signal-to-noise ratio S is high. Similarly, the precision of an FD measurement is proportional to the inverse of twice the signal-to-noise S p of the polarization signal integrated over the total bandwidth, hence: ΔFD 3/(S p Δλ 2 ) The larger the total coverage in λ 2 space, the smaller is ΔFD, allowing higher precision of FD measurements. This calls for low frequency and wide bandwidth. Measurement of a

4 4 source with S p =10 allows measurement of FD with a precision of ΔFD 0.8 rad/m 2 in the range MHz. The FD precision is ΔFD 2.3 rad/m 2 in the range MHz. To reach the same precision as in the lower band, about 3 higher S p (about 9 longer integration time) is needed. Hence the lower frequency range is favoured. A slightly smaller frequency range of MHz still gives an excellent value of ΔFD 1.0 rad/m 2. Note that a high FD precision is also needed to separate unresolved components in the Faraday spectrum (Faraday screens) from extended components (i.e. regions with mixed emission and Faraday rotation located on the line-of-sight). With the high precision enabled by PAFs, details in the Faraday spectrum can be distinguished with unprecedented detail. On the other hand, polarization observations at low frequencies suffer from various Faraday depolarization effects which increase with decreasing frequency (see below). If the polarized background sources have small angular diameters, depolarization in the Milky Way foreground is small, and the remaining effect is depolarization within the sources themselves. This reduces the number of useful sources and hence the density of the RM grid. Little is known about the density of polarized sources at 600 MHz, but surveys with the GMRT and LOFAR are underway. The hope is that the decrease in S p at low frequencies due to depolarization is much less than the gain due to the larger λ 2. In summary 800 to 2000 MHz is probably the optimal frequency for the RM grid experiment. However, we note that other, related, studies of Faraday depth and internal depolarisation effects need higher FD precision and hence are best carried out at lower frequencies, 600 to1500 MHz. Results from GMRT, ASKAP and LOFAR will inform whether RM grid experiments will also benefit from higher FD precision (i.e. 600 to 1500 MHz).

5 Diffuse Polarized Emission Another goal of the SKA Magnetism KSP is to map diffuse polarized emission from nearby galaxies and galaxy clusters with high resolution and high sensitivity. The optimum frequency range to detect diffuse polarized emission is governed by Faraday depolarization. Assuming a simple one-component Faraday spectrum (one region with emission and rotation on the line-of-sight), Arshakian & Beck (2011) computed the frequency spectra of polarized intensity as a function of RM, or RM dispersion, and gave a table of the optimum frequency under various conditions. Most astrophysical objects can best be observed at around 2 GHz, except regions with strong magnetic fields like spiral arms and cluster cores which need higher frequencies. In summary, diffuse polarized emission is best observed PAFs at higher frequencies (e.g MHz) Pulsars Tests of relativistic gravity with pulsars and black holes form one of the SKA Key Science Projects. Accomplishing these tests requires several capabilities: 1. Ability to find large numbers of pulsars, including millisecond pulsars, throughout the Galaxy. 2. Ability to time multiple millisecond pulsars to sub-100-ns precision. 3. Ability to time pulsars in orbit around stellar-mass black holes (if the previous goal is met, this one will be). 4. Ability to find and time pulsars orbiting SgrA*.

6 6 Here we ignore the last capability as realistically it will require the SKA-High, although some experiments will likely be made at the high-frequency end of SKA-mid Searches Searching for new pulsars requires recording timestreams with fast sampling (100 μsec or faster) and narrow frequency channels (of order 50 khz or smaller). Wide-field searching with an interferometer will require recording correlations to disk at the sample rate and processing after the observations, or immense computing power to process the data in real time; see Smits et al. (2009) for estimates. Although we are assuming here that there will be adequate computing power to address wide fields, we nevertheless abide by the anticipated restriction on such searches of using only the central 1-km diameter core of the SKA; with large baselines the number of pixels/pencil beams to be searched becomes entirely unwieldy. With this in mind, we have investigated the predicted discoveries Aeff/Tsys of 500, 1000 and 2000 m 2 /K. Two different population synthesis and survey detection codes were used, based on Faucher-Giguère & Kaspi (2006) and Smits et al. (2009). Several different frequency ranges were tested, and 3 survey regions (Galactic Plane, mid-latitude and high-latitude) were considered. Results from the Smits et al. (2009) code are shown in Tables 1 to 3. Results from both codes for Aeff/Tsys of 1000 m 2 /K are plotted in Figure 1. Despite some differences in modeling the mid- and high-latitude populations, where the existing data sets are comparatively small, both codes clearly point to the 600 MHz to 1500 MHz frequency range as optimal, with the 450 MHz to 1125 MHz frequency range a viable second choice. The range 1000 MHz to 2500 MHz would also be acceptable. At higher frequencies, the number of detected pulsars tends to drop off. Increasing the sensitivity results in more

7 7 Fig. 1. Left: Simulated pulsar detections for Aeff/Tsys of 1000 m 2 /K based on the Faucher- Giguère & Kaspi (2006) population synthesis. Black curves indicate the Galactic Plane, blue the mid-latitudes and green the high latitudes. Right: Simulated pulsar detections for the same sensitivity, based on the Smits et al. (2009) code. In this case, red curves indicate the Galactic Plane, green the mid-latitudes and blue the high latitudes. In both plots, solid lines indicate normal pulsars and dashed lines millisecond pulsars. pulsars overall, but no large change in the relative numbers of pulsars of either type. We note that the sole advantage gained by using the PAF for searches is the decreased amount of total observing time needed to cover the same area of sky. The sensitivity, total data storage and processing requirements remain the same as when using single-pixel feeds with the same Aeff/Tsys; one difference is that we would need much more storage and/or processing power at any one time in order to cope with the amount of data.

8 8 Frequency range b < 5 5 < b < < b MHz 6130, , , MHz 6550, , , MHz 5950, , , MHz 4050, , , 350 Table 1: Survey detection predictions (including previously known pulsars) for Aeff/Tsys of 500 m 2 /K. In each entry, the first number represents normal pulsars and the second millisecond pulsars. Frequency range b < 5 5 < b < < b MHz 9010, , , MHz 9850, , , MHz 9380, , , MHz 6480, , , 530 Table 2: Survey detection predictions (including previously known pulsars) for Aeff/Tsys of 1000 m 2 /K. In each entry, the first number represents normal pulsars and the second millisecond pulsars Timing For timing individual systems of great interest, such as a pulsar black-hole binary, the PAF provides no advantage over single-pixel feeds and may in fact provide less sensitivity if the Tsys is worse. For routine monitoring of millisecond pulsars, which will be needed in order to directly detect and study gravitational waves, PAFs may provide an advantage if there are several cases where multiple target MSPs can be observed within one FOV. Again the Tsys/observing-time tradeoff would have to be evaluated against the number of such

9 9 Frequency range b < 5 5 < b < < b MHz 12340, , , MHz 13810, , , MHz 13800, , , MHz 10110, , , 710 Table 3: Survey detection predictions (including previously known pulsars) for Aeff/Tsys of 2000 m 2 /K. In each entry, the first number represents normal pulsars and the second millisecond pulsars. multiples. The polarization characteristics of the PAFs will also be important for this endeavour. In terms of observing frequency, the 600 MHz to 1500 MHz range may no longer be optimal, as interstellar medium variability will have a much stronger effect on lower-frequency observations. The range 1000 MHz to 2500 MHz may be more desirable, based on current observations at existing telescopes. However, there is currently much activity directed at quantifying and mitigating the effects of the ISM (e.g., Demorest 2011), so it may be that the slightly lower frequency range will be viable after all. The range 450 MHz to 1125 MHz would most likely not be suitable for this work Continuum Surveys Science Drivers Broadly, the key science goals for a PAF continuum survey observation with SKA are: To trace the evolution of star-forming galaxies from z = 7 to the present day. Radio data are unaffected by dust, enabling us to use radio flux as a sensitive and accurate measure of star formation rate.

10 10 To trace the evolution of massive black holes throughout the history of the Universe, and understand their relationship to star formation. Those AGN buried beneath many magnitudes of extinction, which are invisible at optical/ir wavelengths are particularly interesting, because they are in the process of rapid star formation which the AGN has not yet quenched. To use the distribution of radio sources to explore the large-scale structure and cosmological parameters of the Universe, and to test fundamental physics. For example, by using brute-force statistics to measure the effect of weak gravitational lensing and the Integrated Sachs-Wolfe effect, Raccanelli et al. (2011) have shown that PAF surveys such as EMU will make the best measurement yet of dark energy and modified gravity, and a PAF-equipped SKA will have an even greater impact. To determine how radio sources populate dark matter halos, as a step towards understanding the underlying astrophysics of clusters and halos. For example, we expect to detect thousands, and possibly hundreds of thousands, of clusters by using wide-angle-tail galaxies as cluster probes (e.g. Mao et al. 2010). Most of these science goals are best satisfied by a survey that is able to detect, and resolve, galaxies at high redshift. The quality of the science increases with the redshift at which a galaxy may be imaged Frequency-dependent factors First we consider the factors that might influence the optimum frequency for a continuum survey using an SKA equipped with a PAF. It should be noted that all source statistics quoted below (e.g. confusion) are based on an extrapolation of source counts measured by Kellermann (2000) and Huynh et al. (2005) and use the formalism of Condon

11 11 (2011), and may be significantly in error at low flux densities, as we have no way of estimating the source counts at these low flux densities. Primary beamwidth For single-pixel feeds, the primary beam decreases with frequency, and so the survey speed (the survey area covered per hour of integration time) decreases with frequency. For a PAF feed, the primary beam of each antenna is determined by the geometry of the PAF, and is (to first order) frequency-independent, and so is not a determining factor for frequency. Spectral Index Radio surveys at high flux densities are dominated by radio-loud AGN which typically have steep-spectrum lobes and a compact flat-spectrum core. Whether the integrated source flux density is steep or flat depends on the beaming and orientation of the central source, but most are steep spectrum. At lower flux densities, radio surveys are increasingly dominated by star-forming galaxies and low-luminosity AGN, which have a spectral index of -0.7, and below 150 μjy/beam(seymour et al. 2008) are dominated by star-forming galaxies. SKA Phase 1 will reach an rms of 0.3 μjy/beam in a 12-hr observation, which is sufficient to detect a Milky Way at z 1, but not beyond. As the measurement of star formation rates is one of the key science drivers, this argues for a lowering of frequency, which will increase the number of detectable objects. The full SKA will reach an rms of 0.03 μjy/beam in a 12-hr observation, which is sufficient to detect a Milky Way at z 2, but not beyond. Thus all phases of SKA will be sensitivity limited for studies of high-redshift star formation, which argues for a lowering of the observing frequency.

12 12 Resolution For most continuum survey projects, the science is dominated by compact objects such as high-redshift AGN and star-forming galaxies. For a given baseline length, the spatial resolution θ ν 1. For example, SKA Phase 1 (assumed to have a max baseline of 200km) has a resolution of 0.3 arcsec at 1.4 GHz, corresponding to 2kpc at z > 1, which is fairly well-matched to imaging high-redshift galaxies, but it would be advantageous to have higher resolution. For the final SKA, the corresponding resolution is 0.1 kpc, which is ample for most experiments. While high resolution is desirable for imaging of astrophysical objects, the sensitivity to low surface brightness objects decreases as resolution increases. However, it is difficult to quantify this without knowing the array configuration. Confusion Confusion is a strong function of frequency because (a) the resolution increases with frequency, and (b) the flux density of most sources decreases with frequency. Consequently, confusion for a fixed baseline length varies roughly as ν 2. Deep continuum surveys with current arrays are often confusion-limited. As the rms flux density of the survey decreases, the number of detected sources increases, and so the number per synthesised beam increases. For example, a 1.4 GHz survey with a resolution of 10 arcsec and a rms of 10 μjy/beam will detect about 1 source every 80 beams, so that about 1% of sources will be confused with another radio source, which is manageable. At a theoretical rms of 1 μjy/beam, however, there is about 1 source every synthesised beam, and in fact the rms of the image will be about 6 μjy/beam because of the fluctuations from the sea of confused sources. Thus a 1.4 GHz survey with a 10-arcsec beam can never

13 13 produce an image with an rms lower than 6 μjy/beam. SKA phase 1 will have 200km baselines, resulting in a resolution of 0.2 arcsec at 1.4 GHz, and a confusion noise of 0.01 μjy/beam, so that a survey with rms = 0.01 μjy/beam would be the most sensitive survey that could be conducted with this array. Assuming A eff /T sys = 1000 m 2 /K, this will be achieved in hours of integration. Assuming a 30 sq. deg. beam, it will take many years to survey the entire hemisphere to this confusion limit. With the 3000 km baselines of SKA phase 2, the resolution is arcsec, confusion noise is 0.3 njy/bm. Making the same assumptions as for phase 1, the confusion limit will be reached in a single pointing only after many years of integration. Thus SKA phase 2 will never be confusion-limited. In summary, it is unlikely that confusion will be a limiting factor for SKA continuum surveys. It is noted in passing that these limits ignore the intrinsic confusion caused by detectable galaxies overlapping in the sky. Simple extrapolations from the modern Universe are unrealistic, and so careful modelling is needed to estimate the impact (if any) of intrinsic confusion Conclusion Confusion will not be an issue for any foreseeable project on SKA in any phase. The trade-off is therefore between resolution, which increases with frequency, and sensitivity which effectively decreases with frequency because of the spectral index of most sources of interest.

14 14 For SKA phase 1, both sensitivity and resolution at 1.4 GHz are adequate for a star-forming galaxy at z 1. A frequency a factor of 2 lower would significantly degrade the resolution, while a frequency a factor of 2 higher would significantly degrade the sensitivity. It is considered that 1.4 GHz is roughly optimum for Phase 1. For the final SKA, resolution is no longer an issue, and so the trade-off is driven by sensitivity, so a lower frequency (e.g. 700 MHz) would be optimum HI Surveys Galaxy evolution and Cosmology form one of the Key Science projects of the SKA (Carilli & Rawlings 2004). The ability to detect neutral gas in galaxies at high redshift has been one of the first motivations for building the SKA. Neutral atomic Hydrogen is the most abundant element in the Universe and the main fuel for star formation. With the large collecting area of the SKA we can study the distribution of neutral gas in the Local Universe at high resolution and with better sensitivity than ever before HI science Galaxy evolution By observing the 21 cm hydrogen line line we are able to study the evolution of neutral gas from our own galaxy out to high redshifts. Although the final values are currently not exactly known, the sensitivity of the SKA will be about an 1-2 orders of magnitude better compared to precursors such as ASKAP (DeBoer et al. 2009) and MeerKAT (Jonas 2009). Observing around the HI rest frequency ( 1420 MHz) will give an unprecedented view of the Local Volume at very high sensitivity. High sensitivity and good resolution

15 15 are also crucial to study the extended environment of galaxies and the Cosmic Web. Very high brightness sensitivity is required at a reasonable resolution to allow resolving diffuse structures. Dark Energy Probing the nature of dark energy is one of the key questions of Cosmology. A way of measuring this is to measure the acoustic oscillations in the galaxy power spectrum. The redshift range z<0 < 1.5 is key for these sort of experiments and it is important to reach a redshift of z 1.5 to cover a sufficiently huge cosmic volume (Rawlings et al. 2004). Intensity mapping The three-dimensional intensity field of neutral hydrogen can be used to map the cosmic web without detecting individual galaxies and to measure the 21-cm brightness and neutral gas density at high redshift (Chang et al. 2010). Optical redshift surveys are used as galaxy position guides to locate likely spots of the 21-cm glow. The intensity mapping techniques are expected to provide results around redshift z Frequency range The frequency range in which HI studies can be performed using a Phased array feed (PAF) is quite limited by nature and even more by the capabilities of the current PAF designs. The rest frequency of the 21 cm hydrogen line is at MHz. The lowest frequency at which PAFs should be considered for HI observations is set by the current upper frequency cutoff of Aperture Arrays, which is 450 MHz, corresponding to a redshift of z 2.1. The highest frequency at which HI can be observed is around 1425 MHz, which

16 16 corresponds to blue-shifted galactic gas at a radial velocity of approximately km s 1. Given the assumed frequency dynamic range of the current PAF design of 2.5:1 and the lower limit of 450 MHz, there is not very much space for variation. Telescope Characteristics We cannot decide on the optimum frequency range for the PAFs, without looking at the performance of the Single pixel feed (SPF) operating at the high frequencies and the Aperture Array (AA), operating at low frequencies. We look at the survey speed of each of the three receivers in Fig. 2; the survey speed (SS) of a telescope is defined as Frequency [MHz] Survey speed [deg 2 m 4 K 2 ] PAF SPF AA Redshift z Fig. 2. Survey speed of HI observations with the SKA as function of redshift and frequency using a Phased array feed, a single pixel feed and an Aperture Array.

17 17 SS FB ( A T ) 2 (1) where F is the field of view in square degrees, B is the bandwidth, A is the effective collecting area and T is the system temperature. The assumed telescope characteristics are a synthesis of those published by Dewdney et al. (2010); Garrett et al. (2010); Schilizzi et al. (2007) and summarized in Obreschkow et al. (2011). SPF: Dish diameter D =15m. FOV=(λ/D) 2. A eff /T sys =10 4 m 2 K 1. PAF: Dish diameter D =15m. FOV=30deg 2. A eff /T sys = m 2 K 1. This makes the simple assumption that PAFs will have twice the T sys of SPFs. AA-low: Station diameter D = 180 m. FOV = 10 4 (λ/d) 2, assuming 10 4 instantaneous beams. A = 250 (180 m/2) 2 π, assuming 250 stations. T sys = T rec + T sky with T rec = 150 K and T sky =60 (λ/m) 2.55 K (Bregman 2000). Efficiency ɛ =0.8 (ν 0 /ν) 2, where 0.8 is the long-wavelength maximum efficiency and ν 0 = 115 MHz is the Nyquist sampling frequency of the individual station arrays. At all frequencies the survey speed of the PAF is superior to the single pixel feed due to the much larger field of view. At lower frequencies this effect however decreases as the field of view of the PAF remains approximately constant, while the field of view of the single pixel feed increases significantly. On top of this the system temperature of the single pixel feed is lower, although this becomes of less importance at low frequencies. The Aperture Array performs better again compared to the PAFs, although we have to emphasise here that AAs will only operate at low frequencies up to 450 MHz, or slightly above.

18 HI number counts We here study the number of HI sources and the cosmic volume probed by comparable surveys with three different telescope scenarios. Those scenarios, called RED, GREEN, and BLUE, are depicted in Fig. 3 (top) and have the following structure. Scenario RED: An array of PAF dishes covers local HI at redshift z = 0 to distant HI at z =1.5, starting at 1425 MHz to include blueshifted nearby HI. An array of aperture array stations (AA-low) covers the frequency range below 450 MHz, i.e. at z The remaining gap between 450 MHz and 570 MHz is covered by an array of SPF dishes. Scenario GREEN: The PAFs are the same as in scenario RED, but the whole frequency range from 570 MHz downwards is covered by AA-low. Scenario BLUE: The PAFs lower frequency limit is set equal to the conventional upper limit of the AA-low at 450 MHz, which imposes an upper limit of 1125 MHz for the PAFs. The remainder from 1125 MHz to 1425 MHz is then covered by an array of SPF dishes. Survey assumptions The survey assumptions are as follows: The survey time is 10 7 s (roughly 10 2 days) excluding telescope maintenance and off-times where the sky-field is invisible. This time is on the order of the maximal time of a single pointing for the aperture arrays. In other words, a longer survey of N 10 7 s will find more HI sources using N different sky fields. Therefore all results

19 19 Frequency [MHz] PAF SPF AAS PAF AAS SPF PAF AAS 10 8 PAF better than SPF AAS better than PAF/SPF dn/dz SPF better than PAF Field of view Redshift Fig. 3. HI number counts and field of view for different PAF scenarios. The dotted lines show results for AA-low with 10 4 instantaneous beams, while solid lines show the results for AA-low with a more optimistic 10 5 instantaneous beams.

20 20 (number counts and cosmic volume) scale proportionally to the survey time if the latter exceeds 10 7 s. The AAs image a single sky field during Δt =10 7 s, whereas the dishes (SPFs and PAFs)lookat10 2 distinct sky fields with Δt =10 5 s( 1 day) exposure time each. A source is considered detected if the peak flux density of its HI line profile exceeds 3-times the RMS channel noise σ for a channel width of 75 km s 1 and co-added polarizations, σ = 2 ktsys Aɛ ΔtΔν, 75 km s 1 where Δν = ν (2) c Simulation of HI galaxies Our analysis uses the virtual sky of the S 3 -SAX simulation described in detail in Obreschkow et al. (2009a,b). This simulation predicts a negligible evolution of the HI mass function from z =0toz = 2. Hence the analysis presented here is similar to that obtained with a no-evolution assumption. The simulation is complete for HI masses above 10 8 M. This limit only affects the value of dn/dz in the lowest redshift range (z 0.1) Other emission lines - Hydroxyl Megamasers Extragalactic hydroxyl megamaser emission has been detected in luminous and ultra-luminous infrared galaxies (see e.g. Baan 1985; Darling & Giovanelli 2002; Klöckner 2004). The main hydroxyl lines are at 1667 MHz and 1665 MHz, and only very few studies exist of the satellite-lines at 1720 MHz, 1612 MHz, and the higher excitation hydroxyl lines at 4 GHz and beyond. The anticipated frequency range of ν<1425 MHz to maximise HI science allows the investigation of hydroxyl in emission and absorption at z>0.17, higher than the range that has been or will be thoroughly probed by pre-ska

21 21 facilities. The hydroxyl studies will allow (i) determination of the merger rate versus redshift using the hydroxyl number density, (ii) constraints on the physical properties of the maser environment in active nuclei by combining the hydroxyl main-line and satellite-line properties (e.g. van Langevelde et al. 1995), (iii) constraints on the variation of the fundamental constant G at cosmological distances (Kanekar et al. 2004), and (iv) the identification of contaminants of blind SKA hydrogen surveys (Briggs 1998) Results and conclusion The lowest frequency that can be observed with the PAF is 450 MHz, which corresponds toaredshiftofz 2.1, however most if not all of the HI science can be done within a redshift limit of z 1.5. Only dark energy surveys might benefit from the redshift coverage between z =1.5 and 2 to provide extra cosmic volume. The highest frequency that needs to be observed to be able to do galactic science is at 1425 MHz. Taking these conditions into account, there are two logical options to define the PAF frequency range. The first option is to favour dark energy surveys which is new scientific territory, and place the frequency range between 450 and 1125 MHz, covering the redshift range z=0.26 to 2.1. This option would exclude all galactic studies and studies of the Local Volume. The second option is to favour all local studies and to cover the frequency range from 1425 MHz to as low as possible, which is 570 MHz. This frequency range covers all redshifts from z=0 to 1.49 and does not rule out any HI science. The best scientific output with SKA can therefore be achieved by placing the Phased array feed at the frequency range covering 570 MHz to 1425 MHz. This range is supported by the results presented in Fig. 2 & 3 which favour PAFs in this frequency range. The figures further reveal that aperture arrays are still efficient in the frequency range from 450 MHz to 570 MHz, despite their low Nyquist frequency of 115 MHz and hence very low efficiency (< 10%) at frequencies above 400 MHz.

22 22 3. Conclusions & Recommendations The optimum frequency for the different science areas is summarised in Table 4. Science Frequency Range Central Frequency Magnetism MHz (RM grid) MHz (Diffuse Polarised Emission) - Pulsars MHz (Searches) MHz (Timing) - Continuum Surveys MHz (Phase 1) MHz (Phase 2) HI Surveys MHz - Table 4: Summary of the optimum frequency range, or central frequency, for the various science cases, assuming a PAF frequency dynamic range of 1:2.5. We find that a low frequency PAF, covering the frequency range 600 to 1500 MHz, would be ideal for pulsar searches. This overlaps well with the optimum frequency range for HI surveys, 570 to 1425 MHz. Continuum surveys would benefit from a slightly higher central frequency (1400 MHz) in Phase 1, and a rotation measure grid experiment is probably optimised with a frequency range of 800 to 2000 MHz. For these two science cases 600 to 1500 MHz would still be close to optimum. The majority of the high survey-speed science is therefore optimised by the 600 to 1500 MHz range, and we consider this the frequency range which will maximise the science return of PAFs. Diffuse polarised emission and pulsar timing require higher frequencies (greater than 1000 MHz), but the 600 to 1500 MHz range would still be useful for pulsar timing if ISM effects can be mitigated.

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