A&A 493, 1161-1170 (2009)
R. Smits1 - M. Kramer1 - B. Stappers1 - D. R. Lorimer2,3 - J. Cordes4 - A. Faulkner1
1 - Jodrell Bank Centre for Astrophysics, University of Manchester, UK
2 - Department of Physics, 210 Hodges Hall, West Virginia University, Morgantown, WV 26506, USA
3 - National Radio Astronomy Observatory, Green Bank, USA
4 - Astronomy Department, Cornell University, Ithaca, NY, USA
Received 13 June 2008 / Accepted 31 October 2008
The square kilometre array (SKA) is a planned multi purpose radio telescope with a collecting area approaching 1 million square metres. One of the key science objectives of the SKA is to provide exquisite strong-field tests of gravitational physics by finding and timing pulsars in extreme binary systems such as a pulsar-black hole binary. To find out how three preliminary SKA configurations will affect a pulsar survey, we have simulated SKA pulsar surveys for each configuration. We estimate that the total number of pulsars the SKA will detect, is around 14 000 normal pulsars and 6000 millisecond pulsars, using only the 1-km core and 30-mn integration time. We describe a simple strategy for follow-up timing observations and find that, depending on the configuration, it would take 1-6 days to obtain a single timing point for 14 000 pulsars. Obtaining one timing point for the high-precision timing projects of the SKA, will take less than 14 h, 2 days, or 3 days, depending on the configuration. The presence of aperture arrays will be of great benefit here. We also study the computational requirements for beam forming and data analysis for a pulsar survey. Beam forming of the full field of view of the single-pixel feed 15-m dishes using the 1-km core of the SKA requires about operations per second. The corresponding data rate from such a pulsar survey is about bytes per second. The required computational power for a deep real time analysis is estimated to be operations per second. For an aperture array or dishes equipped with phased array feeds, the survey can be performed faster, but the computational requirements and data rates will go up.
Key words: stars: neutron - stars: pulsars: general - telescopes
To harvest the copious amount of information and science accessible with pulsars, two different types of observations are required. Firstly, suitable pulsars need to be discovered via radio surveys that sample the sky with high time and frequency resolution. Depending on the particular region of sky to be covered (e.g. along the Galactic plane vs. higher Galactic latitudes), different technical requirements may be needed. Secondly, after the discovery, a much larger amount of observing is required to extract most of the science using pulsar timing observations, i.e. the regular high-precision monitoring of the pulse times-of-arrival and the pulse properties. Again, depending on the type of sources to be monitored (e.g. young pulsars in supernova remnants vs. millisecond pulsars in Globular clusters) the requirements are different.
In the past 40 years, astronomers have impressively demonstrated the potential of pulsar search and timing observations (e.g. Hulse & Taylor 1975). However, the next 10-15 years promise to revolutionise pulsar astrophysics in a way that is without parallel in the history of pulsars or radio astronomy in general. This revolution will be provided by the next generation radio telescope known as the ``Square Kilometre Array'' (e.g. Terzian & Lazio 2006). The SKA will be the largest telescope ever built, with a maximum baseline of 3000+ km and about a factor of 10-100 more powerful (both in sensitivity and survey speed) than any other radio telescope. The SKA will be particularly useful for pulsars and their applications in astrophysics and fundamental physics. Due to the large sensitivity of the SKA, not only a Galactic census of pulsars can be performed, but the discovered pulsars can also be timed more precisely than before. As a result, the pulsar science enabled by the SKA and described by Cordes et al. (2004) and Kramer et al. (2004) includes:
We will express different sensitivities as a fraction of one ``SKA unit'' defined as m2 K-1. Following the preliminary specifications given by Schilizzi et al. (2007), we assume the SKA to consist of a sparse aperture array of tiled dipoles in the frequency range of 70 to 500 MHz and above 500 MHz it consists of one of the following three implementations:
One of the main science goals for the SKA is to find the majority of the pulsar population in the Galaxy. These should include binary and millisecond pulsars, as well as transient and intermittent sources. A pulsar survey consists of two parts. The first part is using the telescope to observe parts of the sky with a certain dwell time. The total amount of telescope time depends on the FoV of the telescope, the chosen dwell time of the observation and the amount of sky that is searched. The second part is the analysis of the observations, which can be performed either real time, or off-line. Depending on the amount of data that needs to be analysed and especially if acceleration searches are employed to search for binary pulsars (see e.g. Lorimer & Kramer 2005), this can be a very computationally expensive task. Real time processing has been done in the past, but any major pulsar survey has always had an off line processing component (see e.g. Lorimer et al. 2006).
The FoV of a survey has a maximum that depends on the characteristics of the elements used. In the case of circular dishes with a one pixel receiver, the FoV can be approximated as steradians, where is the wavelength at which the survey is undertaken and is the dish diameter. However, by placing a phased array feed at the focal point of the dish (see e.g. Ivashina et al. 2004), the FoV can be extended by a factor which we denote . The total FoV then no longer depends on . In the case of the AA, the FoV of the elements is about half the sky. The actual size of the FoV that can be obtained will be limited by the available computational resources. This is because the signals from the elements will be combined coherently, resulting in ``pencil beams'', the size of which scales with , where is the distance between the furthest elements that are used in an observation. To obtain a large synthesised FoV it is therefore necessary to restrict the beam forming to using only the elements in the core of the telescope (so that ), which will, however, reduce the sensitivity.
To find out how the SKA pulsar survey performance depends on different SKA configurations, we simulated SKA pulsar surveys for different collecting areas and different centre frequencies.
The simulations were performed following Lorimer et al. (2006) and using their Monte Carlo simulation package. In their study, Lorimer et al. (2006) used the results from recent surveys with the Parkes Multibeam system to derive an underlying population of 30 000 normal pulsars with an optimal set of probability density functions (PDFs) for pulsar period (P), 1400-MHz radio luminosity (L), Galactocentric radius (R) and height above the Galactic plane (z). We make use of these results in our simulations described below which adopt the PDFs of model C' in Lorimer et al. (2006).
Our simulation procedure begins, following the findings of Lorimer et al. (2006), by generating 30 000 normal pulsars which beam towards the Earth. Each pulsar is assigned a value of P, L, Rand z based on the assumed PDFs. Their initial positions in the plane of the Galaxy follow the spiral-arm modeling procedure described by Faucher-Giguère & Kaspi (2006). The intrinsic pulse width of each pulsar follows the power law relationship with spin period given in Eq. (5) of Lorimer et al. (2006) (see also their Fig. 3). To compute the expected DM and scatter broadening effects on each pulse, we use the NE2001 electron density model (Cordes & Lazio 2002). Note that, since we are primarily concerned with the distant population of highly dispersed pulsars in these simulations, we do not attempt to account for interstellar scintillation. Finally, to allow us to extrapolate the 1400-MHz luminosities to other survey frequencies in the next step, we make the reasonable assumption that pulsar spectra can be approximated as a power law (Lorimer et al. 1995) and assign each pulsar a spectral index drawn from a normal distribution with mean of -1.6 and standard deviation 0.35. The same procedure was used to obtain a millisecond pulsar population, but with pulsar period and pulsar luminosity distributions from Cordes & Chernoff (1997) and assuming 30 000 potentially detectable millisecond pulsars in the Galaxy (Lyne et al. 1998).
Given the above model for the underlying population, which is consistent with the results of current-day surveys, we proceed to apply it to different configurations of the SKA. For each configuration, we compute the observed flux density of each pulsar and compare it with the limiting flux threshold, which depends on the sky temperature ( ) and the observed width of the pulsar profile. For the AA we reduced the sensitivity by the cosine of the zenith angle of the source, as the AA is sensitive only to the component of the radiation projected onto the plane of the AA. In addition, because the core of the SKA will be located near a declination of -30, the sky visible to the SKA was limited to a maximum declination of 50.
As discussed by Lorimer et al. (2006), we make the important distinction between the observed (i.e. post-detection) pulse width which is related to the pulsar's intrinsic pulse width by the quadrature sum of contributions from sampling, dispersion smearing and scattering (see Eq. (4) of Lorimer et al. 2006). To scale the scatter-broadening time to arbitrary SKA survey frequencies, we adopt a frequency power law index of -4 (Cordes & Lazio 2002). We consider a pulsar to be detected by a given configuration if its flux density exceeds the threshold value, and its observed pulse width is less than the spin period.
Initially, we determined the optimal centre frequencies for a survey
in the Galactic plane (defined as |l
and an all-sky survey excluding the Galactic
plane. This was done by comparing the detected number of normal
pulsars by simulating surveys with sensitivities in the range 0.1 to
0.5 SKA units (in steps of 0.1 SKA units) and with centre frequencies
in the range 0.4 to 2 GHz (in steps of 0.25 GHz). For each
sensitivity and for both survey types, the frequency that provided the
largest number of pulsars was chosen as the optimal frequency. To find
the frequency that provided the largest number of pulsars, a cubic
polynomial function was fitted through the points. The optimal centre
frequencies for a pulsar survey inside and outside the Galactic plane
are shown in Fig. 1. It can be seen that the
optimal survey frequency decreases with lower sensitivity. The reason
for this is that for lower sensitivity, the average distance to the
detected pulsar is smaller. Thus, frequency dependent propagation
effects are smaller, allowing lower frequencies to be used. It is
surprising that the optimal centre frequencies for normal and
millisecond pulsars are similar, since scattering effects on the
pulsar profile have a larger impact on the detection of millisecond
pulsars than on the detection of normal pulsars. Thus it can be
expected that in the Galactic plane, higher observation frequencies
would favour the detection of millisecond pulsars. However,
millisecond pulsars have a steep luminosity distribution (e.g. Cordes & Chernoff 1997), leading to many low-luminosity millisecond pulsars which are not detected at high
observation frequencies. It should be noted that with 500 MHz
bandwidth, the lowest centre frequency is 750 MHz for the 500-MHz
dishes and 1.05 GHz for the 800-MHz dishes. Once the optimal centre
frequencies were determined, these restrictions were included in the
|Figure 1: Optimal frequency to survey the Galactic plane ( , |l ) or outside the Galactic plane ( , |l ) as a function of sensitivity. The dotted horizontal lines show the lowest available centre frequency of the 500-MHz ( bottom line) and 800-MHz ( top line) dishes. Surveys with the AA were performed at a centre frequency of 650 MHz.|
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A Galactic centre survey with the SKA will allow for testing the conditions near a black hole. Simulating such a survey requires a detailed modelling of the scattering in the Galactic centre. Previous work (e.g. Bhat et al. 2004; Cordes et al. 2004; Lazio & Cordes 1998) shows that frequencies above 10 GHz are required to penetrate the scattering screen surrounding the Galactic centre. These results can be used for a detailed study of a Galactic centre survey with the SKA. However, such a study is beyond the scope of this paper. Further results on this issue will be presented in Deneva et al. (in prep.)
Figure 2 shows the fraction of normal and millisecond pulsars that were detected in the simulation of 4 different surveys as a function of sensitivity. Only 1.5% of the pulsars could not be detected due to the declination of the SKA of -30. As will be shown in Sect. 5, we expect that initially only the 1-km core of the SKA can be used for the pulsar survey. This leads to a sensitivity of 0.1 SKA units, which is similar to having a fully steerable Arecibo-class telescope in the southern hemisphere. Performing an all-sky survey with only the 1-km core of the SKA, will detect about 14 000 normal pulsars out of a possible 30 000 and about 6000 millisecond pulsars out of a possible 30 000, regardless of the SKA implementation. The total observation time of the survey, however, does depend on the implementation. Using single-pixel feed dishes to perform an all-sky survey or a survey of just the Galactic plane will take 600 days and 30 days, respectively. With phased array feed dishes or an AA the total survey time can be much less, depending on the available computation power (see Sect. 6). Because of the large natural FoV of the SKA and it's location in the southern hemisphere, the 1-km core of the SKA complements and extends work done by both Arecibo and the Five hundred meter Aperture Spherical Telescope (FAST), which is expected to be completed around 2014.
|Figure 2: Fraction of normal ( top) and millisecond ( bottom) pulsars detected from different pulsar survey simulations as a function of sensitivity of the SKA. For both the 500-MHz and 800-MHz dishes, the surveys were performed at the optimal centre frequency, taking the frequency limits into account (see Fig. 1). The frequency range of the AA was 500 to 800 MHz.|
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All pulsars that will be found by the SKA need to become part of a regular timing programme to find the interesting pulsars. Ideally, they need to be timed once every two weeks for about 6 months to a signal-to-noise ratio of about 9 (which is only a nominal target to characterise the new pulsars and to identify those sources which are interesting for high precision timing). The minimum timing duration is also restricted by the pulsar stabilisation time, which is the time it takes to obtain a stable integrated profile. Assuming that they will be timed using dishes, the total duration of timing all newly discovered pulsars just once depends on how the observations are performed, i.e. at which points on the sky the telescope is pointed. To estimate the total duration of this timing process, we therefore suggest the following scheme that minimises the average observation time per pointing, by grouping dim pulsars together in one FoV. Let be the angle of the FoV.
|Figure 3: Hammer projection of the Galaxy with 14 000 detected pulsars from an SKA pulsar survey simulation. The horizontal axis corresponds to longitude and the vertical axis corresponds to latitude. The Galactic centre is located in the middle of the plot. The dashed lines running from top to bottom correspond to steps of 60 in longitude, whereas the dashed lines running from left to right correspond to steps of 30 in latitude. The circles indicate all pointings (700) that result from the timing optimisation method, assuming a FoV of 20 deg2.|
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To perform strong field tests of General Relativity and gravitational wave detection, as defined in the key science project, it is essential to time a large number of specific pulsars to signal-to-noise ratios of up to 100 on a regular basis. To estimate how much observation time is required for such high-precision timing, we have to distinguish between timing millisecond pulsars (for the Pulsar Timing Array) and timing pulsars in a binary with a neutron star or a black hole companion. We calculated the observation time for timing the 250 millisecond pulsars with the best signal-to-noise ratio's for the three configurations. We assumed that for timing purposes, the nearly full collecting area (out to several hundreds of kilometres from the core) of the SKA can be used. As a conservative estimate (subject to current studies), we timed every pulsar for at least 5 mn to ensure a stable pulsar profile to minimise the error in the time of arrival. With the single-pixel feed 15-m dishes this takes about 20 h, the 15-m dishes with phased array feeds take about 15 h and the AA only takes about 6 h. However, this assumes that the polarisation purity after calibration of the AA is similar to that of the dishes, which might not be the case. To estimate the maximum required observation time for timing pulsars in a binary with a neutron star or black hole, we will assume a (somewhat optimistic) number of 200 such binaries that are potentially detectable in the Galaxy. We further assume that the characteristics of the pulsars in these binaries are similar to isolated pulsars. This leads to a detection of 90 compact binary pulsars. With the single-pixel feed 15-m dishes it takes about 2 days to time these binary pulsars, the 15-m dishes with phased array feeds take about 1.5 days and the AA only takes about 8 h (once again, assuming similar polarisation purity as the dishes). However, timing only the brightest 80% of the binary pulsars, would take about half the observation time. It should be noted that these are only initial estimates to give an indication of the maximum required observation time for high-precision timing and to compare the performance of the different configurations. A paper containing a more detailed study on high-precision timing is in preparation (Smits et al. in prep.).
A pulsar survey requires the coherent addition of the signals from the elements in the core of the SKA and to form sufficient pencil beams to create the required FoV. These pencil beams will produce a large amount of data which will need to be analysed. We estimate the required computation power and data rates for 3000 15-m dishes with a bandwidth of 500 MHz and 2 polarisations and for the AA with a frequency range from 500 to 800 MHz and 2 polarisations.
Following Cordes (2007), we estimate the number of operations per
to fill the entire FoV of a dish with pencil
As an alternative to beam forming by coherently adding the signals from the dishes up to a certain core size, it is also possible to perform the beam forming by incoherently adding the signals from sub-arrays. This process is similar to beam forming in two stages as mentioned above, except that in the second stage the beams that were formed in the first stage are added incoherently. This leads to a much larger beam size, which reduces the required computation power for beam forming significantly. It also reduces the total data rate and the required computation power for the data analysis. The drawback is that it reduces the sensitivity of the telescope by a factor of , where is the number of sub-arrays, which will be several hundred. However, this can be partially compensated as this method allows utilising all elements that are placed in sub-arrays of the same size, which can possibly be as much as 5 times the collecting area of the core of the SKA.
|Figure 4: The number of operations per second required to perform the beam forming for the 15-m dishes and the AA. It is assumed that there are 2400 15-m dishes and the bandwidth is 500 MHz. The FoV of 0.64 deg2 corresponds to filling the natural FoV of the dishes () at a frequency of 1.4 GHz. For the AA we assume a FoV of 3 deg2 and a total collecting area of 500 000 m2. The frequency range is 0.5 to 0.8 GHz. In all cases the number of polarisations is 2. The thick black line corresponds to the beam forming of the 15-m dishes in one stage. The thin black line corresponds to the beam forming of the 15-m dishes in two stages. The striped/dotted line corresponds to the beam forming of the AA.|
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There are two factors which impact the total data volume to be analysed. Firstly, the FoV will be split up in many pencil beams, each of which will need to be searched for pulsar signals. Secondly, the SKA will be able to see the majority of the sky, all of which we want to search for pulsars and pulsar binaries. There are two ways to achieve this. The first option is to analyse the data as it is received, immediately discarding the raw data after analysis. This requires the analysis to take place in real time. The second option is to store all the data from part of the survey and analyse them at any pace that we see fit before continuing with the next part of the survey. Both approaches pose serious technical challenges, which we will discuss here.
First we consider the dishes for which we estimate the data rate of one pencil beam as
|Figure 5: Data rate from pulsar surveys using the 15-m dishes or the AA, as a function of core diameter.|
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|Figure 6: Operations per second required to perform a real time analysis of pulsar surveys using the 15-m dishes or the AA, as a function of core diameter.|
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Alternatively, we can consider storing the data from a part of the survey and analyse it at a much slower rate (see further discussion in Sect. 6.2). From Eq. (5) we can estimate the total amount of data from a survey. Figure 7 shows the total amount of data from an all-sky survey and a survey of the Galactic plane as a function of core diameter, assuming a frequency range of 1 to 1.5 GHz, s, DM cm-3 pc, , an observation time of 1800 s and 2 bits digitisation. Assuming a storage capacity of 1 exa-byte, an all sky survey would have to be split up in about 40 parts. The total time of the survey would then depend on the speed at which the analysis takes place.
|Figure 7: Total amount of data from an all-sky survey (35 000 deg2) and a survey of the Galactic plane (900 deg2) as a function of core diameter, assuming a frequency range of 1 to 1.5 GHz. A 1-km core would correspond to 20% of the collecting area of the SKA.|
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To express the trade-off between the SKA design and survey speed, we define the figure of merit for dishes as (see appendix for derivation)
|Figure 8: The frequency dependence of the figure of merit. This function expresses the speed of the survey for a fixed sensitivity of the telescope.|
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Figure 8 shows the strong dependence of the figure of merit on the observation frequency. The slope at high frequencies is due to the spectral index of pulsars and the decrease of the FoV. At low frequency the figure of merit becomes flat as the sky temperature begins to dominate the system temperature. In practise, pulsars become harder to detect at low frequencies where scattering effects broaden the pulsar profile. Since the scattering depends on the location on the sky, it was not included in the merit function. Thus, at low frequencies the figure of merit is overestimated. However, scattering effects are only significant for pulsars located in the Galactic plane. For non-millisecond pulsars, low frequencies are very favourable (see van Leeuwen & Stappers 2008).
The total observation time of a survey is given by:
An estimate of the computational power by 2015 is given by Cornwell (2005) to be 10 Pflop for $100 M. To estimate what the SKA can achieve for pulsar searches and timing, we will assume that several 1016 ops are available for beam forming and data analysis when this survey will be performed, which will be after 2020.
We consider three scenarios, two with full coherent beam forming, where the analysis takes place either in real time or off-line and one scenario where part of the beam forming takes place incoherently.
First we assume that the analysis takes place real time. The immediate benefits are that no time is lost for the data analysis and that only reduced data needs to be stored. One drawback, however, is that the data can only be processed once. Experience with current pulsar surveys show that it is extremely advantageous to have multiple passes at pulsar survey data analysis (see e.g. Faulkner et al. 2005).
As calculated in Sect. 5.1.1, for a 1-km core the data rate from the dishes with a single-pixel feed is bytes/s. The required computational power for real time analysis is ops. Both values scale linearly with FoV. Only with SKA implementation B, where the dishes have phased array feeds, can the FoV of the dishes be increased beyond 0.64 deg2. Using the 1-km core of the AA and using a FoV of 3 deg2 leads to a data rate of bytes/s and requires a computation power of ops to analyse the data in real time.
SKA implementation A suggests the all-sky survey to be performed with single-pixel 15-m dishes. At low frequencies the FoV of the dishes is about 1 deg2. The entire survey will then take about 600 days. (This value assumes 100% telescope time. In practice this survey might take up to 5 years to perform). In implementation B a larger FoV can be used. The survey time of 600 days then scales inversely with the FoV, however the data rates and required computation power go up linearly with the FoV. Implementation C has the benefit of the AA for which an all-sky survey takes only about 200 days and the survey of the Galactic plane with single-pixel 15-m dishes takes about 30 days. The data rates and required computation power for the AA are larger than for the dishes. When we take this into account the total survey time for all implementations become similar, except that implementations B and C allow for a faster survey and the AA in implementation C might be used for other observations simultaneously (see Cordes 2007, for using the SKA as a synoptic survey telescope).
The off-line analysis requires the full data from an observation to be stored. Thus, the data rates from Fig. 5 become the rates at which data is written to a storage device. When the maximum data storage has been reached, the observation can be stopped and the data analysis can be performed at any pace suitable. After the data analysis has been completed, the next observation can be run. This allows a trade-off between computation cost and survey speed. A drawback is that, depending on available future storage solutions, the total survey time may easily become more than a decade for any SKA implementation.
For real time analysis, restrictions on the computational power and data rate will likely limit the FoV to about 3 deg2. The survey time will then become at least 200 days. Off-line analysis requires the huge data rates to be written to a storage device and will increase the survey time by a significant factor. We therefore consider the possibility of incoherent addition of the sub arrays, as described in Sect. 5.1.
We will assume that all the elements in the SKA are placed such that their signals can be combined to form sub-arrays (or stations in the case of the AA) of 60 m in diameter (similar to van Leeuwen & Stappers 2008, for LOFAR). The pencil beams that are formed by coherently adding the signals from the sub-array elements are about 17 times larger than the pencil beams from coherently beam forming the 1-km core. Thus the number of pencil beams required to fill the FoV becomes about 280 times smaller. The computational requirements for beam forming, data analysis as well as the data rates go down linearly by this factor. This method of beam forming utilises the full collecting area of the SKA, which increases the sensitivity by a factor of 5. However, because the sub-arrays are added incoherently, the sensitivity decreases by the square root of the number of sub-arrays. For the AA there will be about 180 stations. Thus the sensitivity goes down by a factor of . Assuming that the dishes are placed in sub-arrays with a 20% filling factor, the number of sub-arrays will be between 600 and 900, depending on the SKA implementation. For incoherent beam forming the sensitivity will then go down by a factor between 5 and 6. Applying this to an all-sky survey leads to a detection of about 20% of all the detectable pulsars.
We have investigated the pulsar yields for different SKA configurations by simulating SKA pulsar surveys for different collecting areas and centre frequencies. For the Galactic plane, the optimal centre frequency lies just above 1 GHz. Outside the Galactic plane the optimal centre frequency lies between 600 and 900 MHz, depending on the collecting area. Combining the dishes and the AA to perform a survey inside the Galactic plane and outside the Galactic plane, respectively, would result in detection of roughly 14 000 normal pulsars and 6000 millisecond pulsars. As Fig. 2 shows, increasing the collecting area within the 1-km core would improve the detected number of pulsars significantly. The number of detected pulsars scales roughly as , where is the fraction of collecting area in the core.
We also describe a simple strategy for follow-up timing observations and find that, depending on the configuration, it would take 1-6 days to obtain a single timing point for 14 000 normal pulsars. Configuration C, containing the AA, will be of great benefit here. Obtaining a single timing point for the high-precision timing projects of the SKA, will take less than 14 h, 2 days, or 3 days, depending on the configuration. Once again, the presence of the AA allows for the fastest timing. In the case of high-precision timing, however, this assumes that the polarisation purity of the AA is similar to that of the dishes.
Performing a pulsar survey with the SKA requires the coherent addition of the signals of the individual elements, forming sufficient pencil beams as to fill the entire FoV of a single dish. Because of the extreme computational requirements that arise due to large baselines, it is not possible to combine the signals of all of the elements in the SKA. Rather, only the core of the SKA can be used for a pulsar survey. We have derived the computational requirements to perform such beam forming as a function of core-diameter for the 15-m dishes and the AA. For a 1-km core the requirements are and ops for the 15-m dishes and the AA, respectively. When the dishes are placed such that they can form sub-arrays, the computational requirement for beam forming goes down significantly. We have also calculated the data rates and the computational requirements for applying a search-algorithm to the data to find binary pulsars. Both limit the usage of the SKA for pulsar searches to a core of about 1 km.
The authors would like to thank Simon Johnston and Andrew Lyne for their useful suggestions and the referee, Scott Ransom, for his useful suggestions and comments. This effort/activity is supported by the European Community Framework Programme 6, Square Kilometre Array Design Studies (SKADS), contract no 011938. DRL is supported by a Research Challenge Grant from West Virginia EPSCoR. Research at Cornell University was supported by NSF Grant AST0507747.
Cordes (2007) estimated the number of operations to perform the beam forming
for a pulsar survey as one operation (corresponding to the phase shift of one
element) for each dish and each polarisation at the Nyquist frequency. This
needs to be performed for each of the pencil beams that fill the total
FoV. This leads to the total number of operations per second
The following list summarises the meaning of the most important parameters in this paper.