ARECIBO PULSAR SURVEY USING ALFA: PROBING RADIO PULSAR INTERMITTENCY AND TRANSIENTS

The PALFA survey started in 2004, shortly after the installation of the seven-beam ALFA receiver on the Arecibo telescope. The survey searches for pulsars and transients in the inner and outer Galactic plane regions accessible to Arecibo (see below).

The ALFA receiver is well suited for survey observations, allowing simultaneous data collection from seven fields, each ∼35 (FWHM) across. Taking into account the hexagonal arrangement of the beams on the sky and the near sidelobes, the combined power pattern is approximately 24' × 26' (Cordes et al. 2006). We observe a 100 MHz passband centered on 1440 MHz in each of the seven telescope beams. Wideband Arecibo Pulsar Processors (WAPPs; Dowd et al. 2000) used to synthesize 256-channel filter banks spanning these bands at intervals of 64 μs. During observations, full-resolution data are recorded to disk and, in parallel, decimated down to a time resolution of 1 ms and searched for periodic signals and SPs by a quick-look processing pipeline running in real time at the Arecibo Observatory (Cordes et al. 2006). This approach allows for immediate discovery of relatively bright pulsars with periods longer than a few milliseconds. Searching full-resolution data allows detection of millisecond pulsars and narrower SPs and is done offline at participating PALFA institutions as the processing is much more computationally intensive.

Table 1 lists various ALFA system and survey parameters, including the sky area corresponding to processed and inspected data reported on in the present paper and the total sky area observed to date (see Cordes et al. 2006 for a detailed explanation of other parameters). Standard observation times are 268 s for inner Galaxy pointings (30° ≲ l ≲ 78°, |b| ⩽ 5°) and 134 s for outer Galaxy pointings (162° ≲ l ≲ 214°, |b| ⩽ 5°). Some early observations had a duration of 134 s and 67 s for inner and outer Galaxy pointings, respectively. The quoted system temperature of 30 K is measured looking out of the Galactic plane. The initial threshold of 5σ for the SP search is used when selecting events from dedispersed time series based on their signal-to-noise ratios (S/Ns) only, before any filtering is applied. While there are a significant number of events due to random noise above this threshold, identification of an event as a genuine pulse takes into account not only its S/N but also the fact that it is detected at a contiguous range of trial DMs, which is in general not true of spurious events. Thus weak pulses can be correctly identified, while they would be excluded if the threshold was set according to Gaussian noise statistics.

Here we compute the maximum distance at which sources of a given luminosity are be detectable by the PALFA survey, D_max. We then compare the sensitivity of the PALFA survey to previous work done with the Parkes Multibeam system (Manchester et al. 2001; McLaughlin et al. 2006).

The rms noise in a radio transient search, where the effective observation time is equal to the pulse width, is

$$\begin{equation} \sigma _n = \frac{S_{\rm sys}}{\sqrt{N_{\rm pol} \Delta f W}}, \end{equation} \tag{ 1 }$$

where S_sys is the system-equivalent flux density, N_pol = 2 is the number of polarization channels summed, and Δf is the bandwidth. A pulse's observed width W may be broadened compared to its intrinsic width W_i by several effects. After dedispersing the raw data and obtaining a dedispersed time series, there is residual dispersive broadening due to the finite width of a frequency channel and the error of the trial dispersion measure (DM) used compared to the actual pulsar DM. Scatter broadening is not correctable and will have a contribution that depends on observing frequency and varies with direction on the sky. In general,

$$\begin{equation} W \approx \left(W_{\rm i}^2 + \Delta t_{\rm DM,ch}^2 + \Delta t_{\rm DM,err}^2 + \Delta t_{\rm sc}^2\right)^{1/2}, \end{equation} \tag{ 2 }$$

where Δt_DM,ch = 8.3 μs DMΔf_ch/f³ is the dispersive broadening across a frequency channel of width Δf_ch (MHz) for an observing frequency f (GHz), Δt_DM,err is the dispersive broadening due to the difference between the trial and actual DM of the source, and Δt_sc ∝ f⁻⁴ is the scattering broadening. Broadening conserves pulse area, so that the intrinsic and observed peak flux densities are related through S_p,iW_i = S_pW. If S_p,min = mσ_n is the detection threshold, the minimum detectable intrinsic peak flux density is

$$\begin{equation} S_{\rm p,i,min} = \left(\frac{W}{W_i}\right) \frac{m S_{\rm sys}}{\sqrt{N_{\rm pol} \Delta f W}}. \end{equation} \tag{ 3 }$$

For a one steradian pulsar radio beam, a source of intrinsic peak luminosity L_p,i can be detected out to a maximum distance of

$$\begin{equation} D_{\rm max} = \left(\frac{L_{\rm p,i}}{S_{\rm p,i,min}}\right)^{1/2} = L_{\rm p,i}^{1/2} \left(\frac{W_{\rm i}}{W}\right)^{1/2} \frac{(N_{\rm pol} \Delta f W)^{1/4}}{(m S_{\rm sys})^{1/2}}. \end{equation} \tag{ 4 }$$

For a steadily emitting pulsar with period-averaged luminosity L and duty cycle f_dc, we have L_p ≈ L/f_dc.

The amount of pulse broadening depends on system parameters as well as dispersion and scattering, which vary with direction on the sky so that W = W(W_i, l, b, f, Δf, N_ch, S_sys, Δt). We use the NE2001 model of Galactic ionized electron density (Cordes & Lazio 2002) to calculate representative results for D_max in the direction l = 35°, b = 0°, a region of overlap between PALFA and the Parkes Multibeam survey. Figure 1 shows D_max versus L_p,i detection curves using a threshold m = 6 for both surveys. For lower luminosities, sources are not visible to large enough distances for scattering to affect detectability and the inverse square law dominates the detection curve so that D_max ∝ L^1/2_p,i. For larger distances and smaller intrinsic pulse widths, scattering and (residual) dispersion smearing make pulses increasingly harder to detect and D_max increases more slowly with L_p,i.

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Matched filtering detection of broadened pulses relies on the convolution of a pulse template with the dedispersed time series. Ideally, a pulse template would consist of one or several superimposed Gaussian templates, reflecting the diversity of pulsar pulse profiles, some of which exhibit multiple peaks. In addition, multipath propagation due to scattering adds an exponential tail to the pulse profile. We approximate true matched filtering by smoothing the time series by adding up to 2ⁿ neighboring samples, where n = 0–7, and selecting events above a threshold after each smoothing iteration. The smoothing is done in pairs of samples at each n-stage, so that the resulting template is a boxcar of length 2ⁿ samples (Cordes & McLaughlin 2003). The sampling time used in PALFA observations is 64 μs and therefore our matched filtering search is most sensitive to pulse widths of 64 μs to 8.2 ms. This search strategy is not optimal for SPs from heavily scattered pulsars because the templates are symmetric, while the scattered pulse shape with an exponential tail is not, and significantly scattered pulses can be wider than ∼10 ms.

Two issues make a complement to matched filtering necessary. The pulse templates described above have discrete widths of 2ⁿ samples by algorithm design and there is decreased sensitivity to pulses with widths that are significantly different. In addition, the matched filter search output may be dominated by bright, wide pulses from RFI. In that case, a single RFI burst is detected as an overwhelming number of individual events instead of a single event. The cluster algorithm is similar to the friends-of-friends search algorithm used to find galaxies in optical images (Huchra & Geller 1982), and complements matched filtering by not restricting the width of expected pulse detections. The dedispersed time series is processed sequentially. Each event above a threshold which is found is designated as the first of a cluster. A cluster of events is augmented by broadening it to include any adjacent samples above a threshold. Gaps of n_gap samples are allowed within a cluster, and PALFA data are processed with n_gap = 2. The brightest sample of a cluster is recorded as the event amplitude, and the total number of samples in the cluster as its width. This approach is less sensitive to weak, narrow pulses but results in significantly fewer spurious events due to RFI.

A limiting factor for the largest pulse width detectable by both the matched filtering and friends-of-friends search algorithms is the fact that data are analyzed in blocks much shorter than the complete time series length. The mean and standard deviation of a block are used for thresholding events found within the block. This approach minimizes the effect of baseline variations with timescales much longer than typical pulsar pulse widths of a few to a few tens of ms. The disadvantage is that only pulses with W ≪ T_block can be detected. In processing PALFA data, we use blocks of length T_block = 4096 × 64 μs = 0.26 s. According to the NE2001 model of ionized gas in the Galaxy (Cordes & Lazio 2002), a scattering broadening time of that magnitude in the inner-Galaxy part of the PALFA survey corresponds to DM>1000 pc cm⁻³ and a maximum search distance well outside of the Milky Way for most directions we survey. However, lines of sight intersecting H ii regions can result in large DMs and scattering times and are therefore selected against. Any intergalactic scattering that broadens pulses beyond about 0.1 s will also cause events to be selected against.

Figure 2 shows standard SP search output for the discovery observation of PSR J0627+16 (Section 8.1). The main panel shows S/N versus DM and time for events with S/N>5. The panels on top illustrate event statistics for the observation: from left to right, the number of events versus S/N and DM, and DM versus S/N. The pulsar detection is manifested as a peak in the histogram of the number of events versus DM. There is a corresponding peak in the DM versus S/N plot, since the several detected pulses are significantly brighter than background noise in the dedispersed time series.

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Figure 3 shows events in DM-time space for another PALFA SP discovery, PSR J1928+15 (Section 8.5). In this case, three closely spaced bursts were found at t ∼ 100 s, DM ∼ 250 pc cm⁻³. The pulsar is detected at a range of DMs, with the S/N increasing as trial DM values approach the actual pulsar DM and decreasing as trial DMs further on recede from the pulsar DM. In contrast, events due to interference from terrestrial signals at t ∼ 46, 71, 82, 90, 118 s span the entire range of trial DMs and their S/Ns do not show a significant variation with DM.

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If an excess of candidate pulses is identified in the dedispersed time series for a particular trial DM, we use the expected dispersion sweep across the frequency band in order to test if the pulses are from non-terrestrial origin. For a pulse with S/N ≳ 10 in the time series, we extract a chunk of raw data centered on its time of arrival and look for a sweep across frequency that follows the dispersion relation (Figures 4(a) and (b)).

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In the case of multiple weaker pulses detected in the same beam, we extract a raw data chunk centered on the arrival time of each pulse, stack the chunks, and look for a dispersion sweep in the resulting cumulative dynamic spectrum (Figures 4(c) and (d)).

Stacking can induce spurious dispersion sweeps in the time–frequency plane even when the data consist of only Gaussian-distributed noise. SP events identified in dedispersed time series by definition correspond to sums over a given dispersion path that are above average. When these are used to select chunks for summing, the statistical fluctuations will build up to show a dispersed pulse in the time–frequency plane that follows the cold-plasma dispersion law perfectly. We simulated this effect by generating a time–frequency plane of Gaussian noise, dedispersing it, and selecting events above threshold from the resulting time series. We extracted chunks from the fake time–frequency plane centered on each event and stacked them, thus reproducing the procedure used on real data.

Selecting events with signal to noise above a threshold m_d in the dedispersed time series yields a biased set of noise-only samples in the time–frequency plane. On the other hand, when stacking dynamic spectra, points in the stacked dynamic spectrum must have a minimum signal to noise m_c ∼ 2 for a dispersion sweep to be discernible by eye. The rms noise in the dedispersed time series after summing N_ch channels is a factor of $\sqrt{N_{\rm ch}}$ larger than the rms noise in the time–frequency plane. The rms noise in the stacked dynamic spectrum after stacking N_c chunks is a factor of $\sqrt{N_{\rm c}}$ larger than the rms noise in the time–frequency plane. We calculate the average deviation from the mean in the time–frequency plane implied by the two thresholds m_d and m_c, equate them, and obtain

$$\begin{equation} N_{\rm c} \gtrsim \left(m_{\rm c} / m_{\rm d}\right)^{2}N_{\rm ch}. \end{equation} \tag{ 5 }$$

For the PALFA survey and our processing pipeline, N_ch = 256 and m_d = 5. Therefore if N_c ≳ 40 data chunks are added there will be a spurious, dispersed pulse in the resulting stacked dynamic spectrum even if the chunks contain only noise. Since the noise decorrelates over 1–2 samples, the pulse will have a width on the order of 64–128 μs. To avoid the induced spurious-event effect, the width and S/N of stacked dynamic spectra should be compared with those that would result from noise only. All of our detections that use stacking satisfy the criteria W > > 64 μs and N_c < <40. Typically we sum chunks centered on the brightest 2–5 pulses for a SP candidate, which is safely below the N_c limit. In the case of PSR J1909+06 (Figure 4(d)) only two chunks were added and the dispersed swath in the time–frequency plane is 1 ms wide.

The RFI environment at the Arecibo telescope and the 7-beam configuration of the ALFA receiver present both challenges and opportunities for RFI mitigation to facilitate searching for SPs. PALFA survey data are dedispersed with trial DMs of 0–1000 pc cm⁻³. RFI pulse intensity typically peaks at DM = 0 pc cm⁻³, and incidental low-intensity pulses whose S/N peaks at DM = 0 pc cm⁻³ tend to be smeared below the detection threshold for dedispersed time series with trial DM>50–100 pc cm⁻³. A more complex signature is observed for Federal Aviation Administration (San Juan airport) radar pulses, which are unfortunately common in Arecibo observations. The radar rotation period is P_r = 12 s, and each pulse has an envelope that is ∼1 s wide and consists of sub-pulses with variable period on the order of 2–3 ms. Depending on telescope orientation, radar pulses may be detected in all, some, or none of the ALFA beams due to reflections off the telescope structure. Radar pulses are up to two orders of magnitude brighter than pulsar pulses and, without mitigation, can completely dominate SP search results. In addition, the modulation of the radar signal is manifested as detections with DM ≠ 0 pc cm⁻³ so that unlike other non-radar RFI, their S/N versus DM signature cannot be used for excision.

We exploit the known radar characteristics as well as the pattern of pulse detection in the seven ALFA beams to excise both radar and non-radar RFIs. The first part of our excision algorithm targets radar pulses. After a list of SP events is generated for all trial DMs, we bin the events for trial DM = 0–3 pc cm⁻³ in time (by 0.1 s) and record the number of events in each time bin. Then we treat the histogram as a time series and perform a discrete Fourier transform. A peak near the radar rotation frequency indicates a significant number of radar pulses in the data. From the Fourier components we extract the phase and find the arrival time of the earliest radar pulse, t₀. Since the envelope width is ∼1 s, events within 0.5 s of that location are excised, and the procedure is repeated for events near t = t₀ + NP_r, where N is an integer. The more radar pulses are present, the better the performance of this technique because the radar peak in the DFT is more prominent and the pulses' arrival times are determined more precisely. However, if only a couple of strong radar pulses is present within the typical 268 s PALFA integration time, they may be bright enough to dominate event statistics, yet the DFT method does not excise non-periodic incidental RFI. Consequently, after applying the DFT-based method we use an additional RFI filter that handles aperiodic cases.

The second filter uses the number and proximity of beams in which an event is detected in order to determine if it is due to RFI. Again events for trial DM = 0–3 pc cm⁻³ from each beam are binned in time. After detecting peaks indicating an excess of events for the respective time bins, the algorithm cross checks between results for all seven beams, and each event falling within a histogram peak receives a penalty grade based on how many beams' histograms exhibit a peak and how close to each other they are on the sky. Most pulsars detected blindly via a SP search appear in one beam or two adjacent beams, and very bright pulsars may be detected in three or four adjacent beams. We set the excision penalty threshold just below the value corresponding to the latter configurations and excise events accordingly. This method complements the DFT cleaning scheme and effectively excises sparse radar blasts as well as non-periodic RFI detected in multiple beams. The application of the two excision algorithms makes a marked difference in the final SP search output for pointings contaminated with RFI (Figure 5). The figure shows some false positives, for example, a clump of pulsar pulses in beam 4 around t = 80 s are excised due to low-level RFI at low DMs occurring in non-adjacent beams in the same 0.1 s time bins as the pulses. Lowering the threshold according to which an excess of events is defined and time bins are marked for excision reduces false positives but also diminishes the effectiveness of RFI excision. While tens of pulses are detected within 134 s from the bright pulsar B2020+28 (Figure 5), for sources discovered via a SP search the number is an order of magnitude smaller (see Section 7). Therefore, the chance of RFI occurring simultaneously with pulses of intermittent sources and causing them to be excised is much lower.

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We can define a general model for observed signal intensity in terms of the time- and frequency-dependent flux density S_i(t, ν) as

$$\begin{equation} I(t,\nu) = G_{\rm t}(t,\nu) G_{\rm ISS}(t,\nu) S_{\rm i}(t,\nu) + n(t,\nu) + {\rm RFI}(t,\nu), \end{equation} \tag{ 6 }$$

where G_t is the telescope gain, G_ISS is the variation factor due to interstellar scintillation, n(t, ν) is radiometer noise, and RFI(t, ν) is the contribution from terrestrial RFI.

Variations in telescope gain across the beams of the multibeam receiver or within the power pattern of a single beam impact the detectability of a pulsar as either an SP or a periodic source. As shown by the reobservations of PSR J0627+16, PSR J1909+06, PSR J0848 − 43, and PSR J1754 − 30, classifying a source as intermittent may be due to insufficient sensitivity to detect its periodic emission during the discovery observation. The effectiveness of SP versus FFT-based periodic search depends on the pulse amplitude distribution, and the observed pulse amplitude distribution in turn depends on the pulsar location with respect to the telescope beam power pattern. Figure 6 shows the probability density function (PDF) of event amplitude for PSR B1933+16, a strong pulsar detected in two beams of the same PALFA pointing. One beam of the ALFA receiver points directly at the pulsar and the low-intensity tail of the distribution is clearly visible since all pulses are above the detection threshold. The pulsar is also detected in the first sidelobe of an adjacent beam, in which case only the brightest pulses are above the detection threshold and only the high-intensity tail of the distribution is visible. Thus an off-axis detection of a steadily emitting pulsar may misrepresent it as an intermittent source.

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A different set of effects which affect detectability in SP versus periodic search is due to intervening ionized gas. Turbulence in the ionized interstellar gas and the motion of the pulsar with respect to the gas introduce phase modulations in the pulsar emission which cause the observed intensity to change over time and frequency. In general, the scintillation gain factor has contributions from both diffractive (DISS) and refractive (RISS) interstellar scintillations, such that G_ISS(t, ν) = G_DISS(t, ν)G_RISS(t, ν) (Rickett 1990). The detectability of nearby pulsars with low DMs can be significantly affected by DISS, which can have timescales comparable to typical survey pointing times (minutes) and frequency scales Δf_DISS < <f. In terms of the observing frequency f and the pulsar distance D, the DISS timescale Δt_DISS ∝ f^1.2D^−0.6. The scintillation bandwidth Δf_DISS and scattering timescale τ_s are related through 2πΔf_DISSτ_s ≈ 1. An empirical fit from Bhat et al. (2004) for f in GHz and τ_s in ms gives an estimate for τ_s based on DM:

$$\begin{equation} \log \tau _{\rm s} = -6.46 + 0.154 \log \rm DM + 1.07\left(\log \rm DM\right)^2 - 3.86 \log \emph {f}, \end{equation} \tag{ 7 }$$

but there is significant scatter about this relationship. When the scintillation bandwidth and timescale are small, averaging over the observation time and bandwidth can quench DISS.

For refractive scintillation, Δf_RISS ∝ f and Δt_DISS ∝ f^0.57D^1.6. Unlike for DISS, the timescale of RISS increases with distance and therefore it can become very long for distant pulsars with relatively high DMs. Both RISS and DISS can either help or hinder pulsar detection due to the time-variable constructive or destructive interference of wave fronts they cause. For a single-pass survey, this means that some weak pulsars may be detected because they are modulated above the detection threshold, and some pulsars that are otherwise bright enough may be missed because of scintillation modulation. Cordes & Lazio (1991) discuss in detail the detection probability for scintillating pulsars by single-pass and multi-pass surveys. Since PALFA is a single-pass survey, it may have missed pulsars that scintillate on timescales comparable to or longer than the observation time. None of our discoveries in Table 3 appear to be affected by DISS, though RISS over long timescales may affect the objects with higher DMs.

The detectability of a pulsar as a periodic source depends on the integrated pulse flux within the observation, which is determined by the number of periods within the observation time, N_p = T_obs/P, along with the pulse amplitude distribution. For the same integrated flux per pulse, fewer periods within a fixed T_obs mean that long-period pulsars are less likely to be detected than short-period pulsars by any method relying on detecting an integrated flux such as an FFT-based search or a continuum imaging survey. For FFT searches in particular, this effect is compounded by the fact that when N_p is small, the harmonics of interest are in the low-frequency part of the power spectrum, which is often dominated by non-Gaussian red noise and RFI. Hereafter we use the term "small-N_p bias" to refer to the combined influence of these effects on pulsar detectability.

We can compare the detectability of objects by periodicity and SP search and attempt to narrow down different classes of intermittent emitters by calculating the intermittency ratio

$$\begin{equation} r = \left(\mbox{S/N}\right)_{\rm SP}/\left(\mbox{S/N}\right)_{\rm FFT} \end{equation} \tag{ 8 }$$

for each object in our sample of PALFA and Parkes detections. McLaughlin & Cordes (2003) derive

$$\begin{equation} r = \left(\frac{2\eta }{\zeta N_{\rm p}^{1/2}}\right)\frac{S_{\rm max}}{S^{\prime }_{\rm av}}, \end{equation} \tag{ 9 }$$

where ζ ≈ 1.06 and η ∼ 1 for a Gaussian pulse shape, S_max is the maximum expected pulse intensity within N_p = T_obs/P periods, and S'_av is a modified average pulse peak intensity.

The intermittency ratio is a system-independent measure of the efficiency of the two types of search for objects with different degrees of intermittency. In Figure 7, expected values of r versus N_p are shown for an exponential pulse amplitude PDF and power-law distributions with various indices. Lower limits on r are given for intermittent sources which were not detected via periodicity search. In addition, we show r values for pulsars that were detected using both the periodicity and SP search algorithms in the PALFA and Parkes Multibeam surveys. A total of 283 PALFA pulsar detections and 255 Parkes Multibeam detections are shown in the plot, including multiple detections of some objects.

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In Figure 7, long-period pulsars are predominantly found in the upper left (small N_p, large r) and millisecond pulsars in the lower right (large N_p, small r). PSR B0525+21, with r ∼ 7, has P = 3.7 s and DM = 51 pc cm⁻³, which make it susceptible to both the small-N_p bias and diffractive scintillation and therefore it is detected more readily as an SP source. At the other extreme is PSR B1937+21, a millisecond pulsar which emits giant pulses but is nevertheless detected with a much higher S/N in the periodicity search than in the SP search (r < 0.07) because its period is small compared to the PALFA observation time and the normal pulse amplitude is exceptionally steady (Jenet & Gil 2004). This indicates that the effect of N_p on detectability can overshadow individual properties, and in survey mode millisecond pulsars will show up overwhelmingly as periodic sources. In that case, processing the data with an SP search algorithm can reveal the presence of giant pulses in an otherwise steady emitter.

In between PSR B0525+21 and PSR B1937+21, from upper left to lower right is a relatively smooth distribution of pulsars whose intermittency ratios are predominantly determined by the influence of N_p on the detectability of all types of periodic emitters. We look for unusual objects among the outliers from that trend. There are a number of pulsars detected both in periodicity and SP search in the region where r = 1–5, including PSR B0656+14, which occasionally emits bursts much brighter than the average pulse and would arguably be classified as a RRAT if located farther away (Weltevrede et al. 2006). Interspersed among them in the region are most of the PALFA and Parkes intermittent sources. PSR J1909+06, which was not detected in a periodicity search but is visible as a periodic source when folded with its known period, has r = 1.3, and the long-period PALFA intermittent sources PSR J1854+03 and PSR J1946+24 have r = 1.0 and 1.8, respectively. Of the Parkes intermittent sources, seven have r < 3. PSR J1754 − 30 (r = 0.2) and PSR J0848 − 43 (r = 0.7) were detected through their time-averaged emission in low-frequency follow-up observations. In the r > 5 region we find only five objects: PSR B0525+21, the Crab pulsar, Parkes intermittent sources PSR J1317 − 5759 and PSR J1819 − 1458, and PALFA intermittent source PSR J1928+15. The Crab pulsar has a high-intermittency ratio due to its giant pulses but is otherwise a relatively steady emitter as periodic emission is consistently detected even if the giant pulses are ignored. Of the remaining three intermittent sources none are young pulsars like the Crab. The pulse amplitude distributions of PSR J1317 − 5759 and PSR J1819 − 1458 are described by power laws with indices ∼1 (McLaughlin et al. 2006), smaller than the measured giant pulse indices of ∼2–3 (e.g., Kinkhabwala & Thorsett 2000, Cordes et al. 2004).

We conclude from Figure 7 that periodicity and SP searches should be used in combination by pulsar surveys since there are types of sources which are best detected by either method. As more intermittent objects are found, placing them in r − N_p space may help us identify physically distinct populations. In addition, repeated sky coverage can probe intermittency at timescales of days to months.

PSR J0627+16 was discovered when nine SPs were detected at a trial DM = 125 pc cm⁻³ (Figure 2). The period estimated from the pulse arrival times in the discovery observation is P = 2.180 s. What is unusual about this object is its very narrow peak in S/N versus DM space, indicating a narrow pulse (Cordes & McLaughlin 2003). Figure 4(c) shows the cumulative dynamic spectrum after stacking raw data chunks aligned around the five brightest pulses. A fit to the dispersion sweep in the time–frequency plane gives a best DM of 113 pc cm⁻³ and when the raw data chunk around the brightest pulse is dedispersed with this DM, the FWHM pulse width is only 0.3 ms.

Two follow-up observations at 0.33 and 1.4 GHz yielded 17 pulses in 50 minutes and 22 pulses in 72 minutes, respectively. After removing bright SPs from the dedispersed time series and replacing the respective time samples with a running average, periodic emission with P = 2.180 s was detected throughout the 0.33 GHz observation, confirming the period estimate from the discovery observation at 1.4 GHz and the presence of underlying normal emission.

Many of the RRATs detected by McLaughlin et al. (2006) have short duty cycles, calculated as the ratio between the average width of SPs and the period. PSR J0627+16 has the smallest known duty cycle, f_dc = 0.01% by this definition. However, for steady emitters the duty cycle is typically defined as the ratio of the folded pulse profile FWHM and the period. Individual pulses may occur in a phase window wider than any individual pulse and corresponding to the folded profile width. At 1.4 GHz, the individual 0.3 ms pulses of J0627+16 occur in a 8 ms window, while at 0.33 GHz individual pulses have widths of 0.3–2 ms and occur in a 15 ms window. The folded pulse profile at 0.33 GHz has FWHM of 60 ms, suggesting that bright pulses may be confined to a narrower window than pulses comprising the underlying normal emission.

The detection of bright SPs and a weak periodic signal from PSR J0627+16 when data are folded with an accurate period estimate, along with the absence of a periodic detection in search mode weighs in favor of the proposition of Weltevrede et al. (2006) that some RRATs may have periodic emission with highly variable pulse amplitudes.

PSR J0628+09 was discovered by detecting three pulses at DM = 88 pc cm⁻³. The period estimated from the pulse times of arrival was 2.48 s. In follow-up observations the pulsar was also detected in periodicity searches as it emits on average several bursts per minute. The periodicity detections and the larger number of SPs in subsequent observations allowed the actual pulsar period of 1.241 s to be determined (Cordes et al. 2006).

PSR J1854+03 was discovered in 2008 via an SP search performed on full-resolution survey data. Four pulses were detected at DM = 216 pc cm⁻³ during the 268 s observation. The period P = 4.559 s was estimated by taking the smallest difference between times of arrival (TOAs) of two consecutive pulses and verifying that intervals between all four TOAs are integer multiples of it. A confirmation observation with the more sensitive central ALFA beam yielded within 120 s five pulses whose arrival times match the estimated period.

PSR J1909+06 was observed in 2006 but not identified as a candidate until 2007 when the full-resolution data were searched for SPs. Two pulses with a width of ∼1 ms and S/N of 6 and 9 were detected at DM = 35 pc cm⁻³. The stacked dynamic spectrum clearly shows a dispersion sweep (Figure 4(d)). PSR J1909+06 was discovered in data from the off-axis beam 2 of the multibeam ALFA receiver. Since the on-axis gain of the center beam is 10.4 K Jy⁻¹ compared to 8.2 K Jy⁻¹ for the other six beams (Cordes et al. 2006), we aimed the center beam at the discovery coordinates for a confirmation observation. For the same integration time of 268 s, eight pulses with S/N >5 were detected in the confirmation observation. We used the pulse arrival times to determine a period and arrived at a best estimate of P = 0.741 s.

During the 2007 discovery observation of PSR J1919+17, multiple pulses at DM = 148 pc cm⁻³ were detected in beam 4 of the ALFA receiver, with no corresponding periodic detection. A Fast Folding Analysis (Staelin 1968, Kondratiev et al. 2009) was used to narrow down the period to P = 2.081 s, which was confirmed in 2008, when the pulsar was detected as a normal periodic emitter with the more sensitive central ALFA beam. The pulsar has a double-peak profile with the two peaks ∼100 ms apart, which most likely made it difficult to find its period from pulse arrival times alone.

PSR J1928+15 was discovered in 2005 by detection of what looked like a single bright pulse at DM = 245 pc cm⁻³ in a 120 s observation (Figure 3, top). More detailed analysis revealed that the event was in fact composed of three separate pulses occurring at intervals of 0.403 s, with the middle pulse being brighter by an order of magnitude than the other two (Figure 3, bottom). In Figure 4(a), the dispersion of the brightest pulse by ionized interstellar gas is shown in the time–frequency plane, evidence of the non-terrestrial origin of the pulses. A fit to the pulse signal in the time–frequency plane resulted in a refined estimate of DM = 242 pc cm⁻³. Despite multiple follow-up observations, the source has not been detected again.

Given the DM of this source, 242 pc cm⁻³, it is unlikely that the non-detection can be attributed to diffractive scintillation. Since the three pulses are equally spaced, they can be interpreted as a single event seen in successive rotations of a NS. This signature might be accounted for by an object that is dormant or not generally beamed toward the Earth and whose magnetosphere is perturbed sporadically by accretion of material from an asteroid belt (Cordes & Shannon 2008).

PSR J1946+24 has DM = 96 pc cm⁻³ and P = 4.729 s and was discovered by detecting four individual pulses. The intervals between detected pulses in this case were all >20 s. The brightest detected pulse of PSR J1946+24 has S/N = 29 and its dispersion sweep is visible in the time–frequency plane without any stacking (Figure 4(b)).

SP arrival times collected over multiple follow-up observations were used to obtain partial timing solutions for PSR J0628+09, PSR J1909+06, PSR J1919+17, PSR J1854+03, and PSR J1946+24 and verify their estimated periods. The periods of PSR J0627+16 and PSR J1909+06 were verified by manually folding raw data and detecting a periodic signal. Finally, despite the fact that PSR J1928+15 was not detected after the discovery observation, the ∼0.403 s intervals between the three pulses detected from that source differ by only ∼2 ms, which is approximately half the FWHM pulse width and therefore provides a period estimate to that precision. We are currently timing the six sources which were successfully redetected. Obtaining phase-connected timing solutions will enable us to compare them to other NS populations and will yield positions which will facilitate observations at higher wavelengths.

In addition to detecting radio sources on-axis in data streams from each of the seven beams of the ALFA system, it is possible to detect strong events off-axis with low but non-zero sensitivity over almost the entire hemisphere centered on the zenith. Consequently, it is possible to detect a relatively low rate but very bright transients off-axis as well as the much weaker but higher rate SPs that we have detected in the on-axis parts of the beam pattern.

To establish that a given event is celestial in nature, we need to distinguish it from terrestrial interference. For on-axis events, this classification process is aided by the directionality of the seven beams and the expectation that most real events are likely to be seen in three or fewer contiguous beams rather than in all seven beams. Bright events may violate this expectation, however, because near-in sidelobes are fairly large (c.f. Figure 1 of Cordes et al. 2006). Celestial and terrestrial radio signals can also enter the seven beams of the ALFA receiver indirectly—far off the nominal pointing axis—through reflection and scattering off telescope support structures, as with any antenna. Extremely bright signals (celestial or terrestrial) may be detected after scattering into one or more beams, and the effective gain is approximately that of an isotropic radiator with small gain for events incident far off axis from the pointing direction. For the Arecibo telescope, which has an intricate support structure with many possible scattering surfaces, such wide-angle incidence is likely to provide multiple paths for radiation to enter the feed optics. Radiation arriving along multiple paths will constructively and destructively interfere across ALFA's focal plane, so that the event's strength will be nonuniform in the different data streams.

When radiation enters the telescope optics from wide angles, it is difficult to distinguish celestial from terrestrial signals based on the nominal pointing direction of the telescope and on whether they are detected in a single beam, a subset of beams, or all beams. Conceivably, extremely bright events from a single radio source could be emitted at very rare intervals that would be detected when the telescope is pointed nominally at directions separated by tens of degrees (but within the same hemisphere). Such sources and events will be exceedingly difficult to disentangle from terrestrial RFI.

Of course the most powerful confirmation of a particular event is the detection of similar events in reobservations of the same sky position. For most of the events reported in Section 7 and by McLaughlin et al. (2006), redetections have been made in this manner. They have also relied on establishing that their signatures in the frequency–time plane conform to what is expected. The simplest celestial signals are narrow pulses that show differential arrival times in accord with the cold-plasma dispersion law (e.g., Cordes & McLaughlin 2003). Celestial objects may also show the effects of multipath propagation through the interstellar medium (ISM) either in the frequency structure that is produced in the spectra of nearby pulsars or in the asymmetric broadening of the pulses from more distant objects. For cases where spatial information associated with the nominal telescope pointing direction is insufficient to constrain the celestial nature of a particular event, we must rely especially on a detailed study of the event's structure in the time–frequency plane. Indeed the time–frequency structure of the event discussed by Lorimer et al. (2007) was a key part of the argument for its classification as a celestial event.

A given reflector and feed antenna have a net antenna power pattern with a main lobe and near-in sidelobes that is similar to an Airy function with a main-lobe angular width ∼λ/D_a, where D_a is the effective reflector diameter. The wide-angle part of the antenna pattern has far-out sidelobes that are independent of D_a and have average gains G ∼ 1, similar to that of an isotropic antenna. However peaks in the far-out sidelobe pattern can have gains significantly larger than G = 1, corresponding to special directions where scattering from the telescope support structure is especially efficient. For the Arecibo telescope, we expect sidelobes to have the same general properties, with the caveat that support structures will introduce further complexity in the far-out sidelobe pattern that varies as the telescope is used to track a source. Tracking a sky position is done by rotating the azimuth arm and moving the Gregorian dome along the azimuth arm, thus changing the scattering geometry. We therefore expect the sidelobe structure to change significantly with azimuth and elevation of the targeted position on the sky. For the seven-beam ALFA system, the main beams by design sample different parts of the sky, as do the near-in sidelobes. At wider angles, the power pattern of each feed overlaps the others but with considerable variation in gain from feed to feed.

To derive simple constraints on burst amplitudes and rates, we expand the gain for each feed into inner beam and wide-angle terms:

$$\begin{equation} G\left(\theta,\phi \right) = G_{\rm max} P_n\left(\theta,\phi \right) + \left(1 - \eta _B\right), \end{equation} \tag{ 10 }$$

where θ and ϕ are polar and azimuthal angles, respectively; P_n(θ, ϕ) is the power pattern for the main beam and near-in sidelobes; η_B is the main-beam efficiency, and (1 − η_B) is the average level of the far-out sidelobes. The boresight gain is

$$\begin{equation} G_{\rm max} = \frac{4\pi A_e}{\lambda ^2} = \frac{4\pi }{\Omega _A} = \frac{4\pi \eta _B}{\Omega _{\rm MB}}, \end{equation} \tag{ 11 }$$

where A_e is the effective telescope area, and Ω_A and Ω_MB = η_BΩ_A are the solid angles of the antenna power pattern and of the main beam, respectively. The system equivalent flux density is

$$\begin{equation} S_{\rm sys} = \frac{T_{\rm sys}2k}{A_e} = \frac{8\pi k T_{\rm sys}}{\lambda ^2 G_{\rm max}}, \end{equation} \tag{ 12 }$$

where k is the Boltzmann constant and T_sys is the system temperature. The minimum detectable flux density is

$$\begin{equation} S_{\rm min} = \frac{m S_{\rm sys}}{\sqrt{N_{\rm pol} \Delta f W}}, \end{equation} \tag{ 13 }$$

which is a function of the event duration, W, as well as system parameters. It is useful to define S_min,1 as the minimum detectable flux density for unit gain using Equation (12) with G_max = 1. Substituting into Equation (13) yields, for two polarizations and Δf = 100 MHz,

$$\begin{equation} S_{\rm min, 1} = 10^{4.9}\ {\rm Jy} \left(\frac{m}{5} \right) \left(\frac{10\ {\rm ms}}{W} \right)^{1/2} \left(\frac{T_{\rm sys}}{30\ {\rm K}} \right); \end{equation} \tag{ 14 }$$

we note that for some directions, the system temperature can differ from the fiducial 30 K used.

A brief summary of our results is that (a) a small number of events have been detected from sources that are consistent with their membership in the radio pulsar population, but with a much greater deal of modulation in some cases; (b) no very strong pulses have been identified in the far-out sidelobes of the Arecibo telescope and (c) no bursts have been detected that are extragalactic in origin.

Here we compare our results with those of Lorimer et al. (2007), who surveyed high-Galactic-latitude regions that included the Magellanic Clouds and who discovered a single reported pulse, with amplitude 30 Jy. They surveyed ∼9 deg² with a detection threshold ∼300 mJy, about 100 times fainter than the detected pulse amplitude. To compare any two surveys, we initially assume a population of radio sources that is homogeneously distributed in Euclidean space and we ignore propagation effects that might limit the detectability of bursts from distant sources. The number of events detected N ∝ Ω_iTD³_max for a survey of duration T that samples instantaneously a solid angle Ω_i. For multibeam systems with N_pix pixels, Ω_i = N_pixΩ₁, where Ω₁ is the solid angle of a single beam. We assume that events have the same peak luminosity and pulse width W and are detectable to a distance D_max. The ratio of the number of detected events in two surveys with total observation times T_obs,a and T_obs,b, and bandwidths Δf_a and Δf_b is

$$\begin{eqnarray} \frac{N_b}{N_a} &=& \left(\frac{T_{\rm obs,b}}{T_{\rm obs,a}} \right) \left(\frac{N_{\rm pix,b}\Omega _{\rm 1,b}}{N_{\rm pix,a}\Omega _{\rm 1,a}} \right) \left(\frac{D_{\rm max b}}{D_{\rm max a}} \right)^{3} \nonumber \\ &=& \left(\frac{T_{\rm obs,b}}{T_{\rm obs,a}} \right) \left(\frac{N_{\rm b}\Omega _{\rm 1,b}}{N_{\rm pix,a}\Omega _{\rm 1,a}} \right) \left(\frac{m_a S_{\rm sys,a}}{m_b S_{\rm sys,b}}\right)^{3/2} \left(\frac{\Delta f_b}{\Delta f_a}\right)^{3/4}. \end{eqnarray} \tag{ 21 }$$

As pointed out by Lorimer et al. (2007), the same survey that detected the 30 Jy pulse should have yielded many more detections if the assumptions of a volume limited sample apply. Using Equation (21), the lone 30 Jy pulse implies there should have been N_b/N_a ≈ (m_a/m_b)^3/2 = 10³ additional detections above a 100-times fainter threshold. In the 90 hr of follow-up observations, there should have been N_b/N_a ≈ (T_obs,b/T_obs,a)(m_a/m_b)^3/2 ≈ 80 additional detections. Comparing the Parkes and PALFA surveys,²⁰ we estimate that the PALFA survey should have identified ∼600 pulses above threshold.

The PALFA survey's null result on extragalactic events is therefore in accord with Lorimer et al. 's non-detection of events weaker than the single strong event they reported. With the assumptions made, these results suggest that the non-detections of pulses weaker than the 30 Jy pulse are inconsistent with the source population having a distribution that is homogeneous and isotropic.

There are caveats on these results related to the assumptions about the source population and to the possible role of propagation effects in limiting detectability. The minimum detectable flux density for the PALFA survey is 30 mJy for a 5 ms pulse, implying that a pulse of 30 Jy strength emitted at a distance D_event is detectable to a distance D_max given by D_max/D_event ≈ (30Jy/0.03Jy)^1/2 ≈ 32. If the lone event detected by Lorimer et al. is from a source at the attributed distance D_event ∼ 0.5 Gpc (based on assigning about half of the DM to the intergalactic medium), the PALFA survey would detect fewer pulses than estimated above (for constant luminosity) because the universe is not old enough and from redshifting of the spectrum if it is steep in frequency. Nonetheless, a cosmological population of constant-luminosity sources would extend to ∼eight times the attributed distance, implying from the first form of Equation (21) that ∼ seven pulses should have been detected in the PALFA survey, on average, while ∼500 weaker pulses should have been seen in the discovery survey with Parkes. The difference in yield under this alternative scaling results from the fact that the PALFA survey can detect sources well beyond the cosmological population while the Parkes survey is comparatively shallower (by a factor of 10 in flux density, i.e. 300 compared to 30 mJy), but covers a factor of 30 greater solid angle. Consideration of a broad luminosity function does not alter these conclusions qualitatively. However, we would generally expect the pulse amplitude distribution to extend to lower flux densities (from lower luminosities) given that the sole reported event was much larger than the threshold and that, therefore, many more pulses are expected compared to the constant-luminosity assumption.

Pulse broadening from multipath propagation in either the ISM or the intergalactic medium (IGM) can also limit the number of events detected in a survey because the broadening increases with source distance. The maximum detectable distance is therefore diminished, as demonstrated for the ISM in Figure 1. Lorimer et al. argued that the strong frequency dependence of the width of the 30 Jy pulse was consistent with multipath propagation through a turbulent, ionized IGM. If so, sources from a greater distance would be less-easily detectable. In the simplest scattering geometries, scattering conserves the area of the pulse, so matched filtering yields a test statistic with S/N ∝(W/τ_d)^1/2 when the pulse broadening time τ_d is much larger than the intrinsic pulse width (Cordes & McLaughlin 2003). The 30 Jy pulse therefore could have been broadened by an additional factor of 10⁴ and the S/N still would have been above threshold. The much longer pulses (∼10⁴ × 5 ms = 50 s) would have been difficult if not impossible to identify in the time series owing to high-pass filtering used to mitigate baseline fluctuations. The high-pass filtering was explicit in the Parkes Multibeam data acquisition but is part of the post-processing in the PALFA analysis. Such very broadened pulses could be detected by imaging surveys with relatively short integration times like the NRAO VLA Sky Survey (NVSS) and future surveys with the Australian Square Kilometer Array Pathfinder²¹ or the Allen Telescope Array.²²

In between this extreme case of 50 s broadening and the reported pulse width of ∼5 ms is a substantial search volume in which more distant sources could have produced detectable events. Broadening from sources at redshifts greater than 1 is increased by the larger electron density but is lessened by the frequency redshift, so the net scaling of the pulse broadening with redshift depends on how the scattering material is distributed along the line of sight.