Timing Solution and Single-pulse Properties for Eight Rotating Radio Transients
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TIMING SOLUTIONS AND SINGLE-PULSE PROPERTIES FOR EIGHT ROTATING RADIO TRANSIENTS
B.-Y. Cui Department of Physics and AstronomyWest Virginia UniversityMorgantown, WV 26506, USA
J. Boyles
Department of Physics and AstronomyWest Kentucky UniversityBowling Green, KY 42101, USA
M.A. McLaughlin Department of Physics and AstronomyWest Virginia UniversityMorgantown, WV 26506, USA
N.Palliyaguru
Physics and Astronomy DepartmentTexas Tech UniversityLubbock, TX 79409-1051 Center for Gravitational Waves and Cosmology, West Virginia University, Morgantown, WV 26505
ABSTRACTRotating radio transients (RRATs), loosely defined as objects that are discovered through only theirsingle pulses, are sporadic pulsars that have a wide range of emission properties. For many of them,we must measure their periods and determine timing solutions relying on the timing of their individualpulses, while some of the less sporadic RRATs can be timed by using folding techniques as we do forother pulsars. Here, based on Parkes and Green Bank Telescope (GBT) observations, we introduce ourresults on eight RRATs including their timing-derived rotation parameters, positions, and dispersionmeasures (DMs), along with a comparison of the spin-down properties of RRATs and normal pulsars.Using data for 24 RRATs, we find that their period derivatives are generally larger than those of normalpulsars, independent of any intrinsic correlation with period, indicating that RRATs’ highly sporadicemission may be associated with intrinsically larger magnetic fields. We carry out Lomb − Scargletests to search for periodicities in RRATs’ pulse detection times with long timescales. Periodicitiesare detected for all targets, with significant candidates of roughly 3.4 hr for PSR J1623 − − Keywords: pulsars: individual INTRODUCTIONRotating Radio Transients (RRATs) can generally be defined as pulsars that were originally detectable only throughtheir single pulses and not through standard Fourier techniques (Keane & McLaughlin 2011). They were first discovered a r X i v : . [ a s t r o - ph . H E ] A ug through single-pulse search reprocessing of the Parkes Multibeam Pulsar Survey data (McLaughlin et al. 2006; Keithet al. 2009; Keane & McLaughlin 2011). Currently ∼
100 of these sporadic pulsars are known. Long-term monitoringobservations show that there is a wide range of spin-down and emission properties for objects originally termed RRATs,with some appearing as normal or nulling pulsars in higher sensitivity or lower frequency follow-up observations, orlater observations with the same sensitivity. It has been suggested that some RRATs would be detected in standardFFT approach if they are closer and had higher signal-to-noise (S/N) observations (Weltevrede et al. 2006). However,for many RRATs, it is necessary to measure times-of-arrival and determine timing solutions by using single pulsesinstead of the commonly used folded profiles.Since their initial discovery, many theories have been put forward to explain why RRATs show different emissionbehavior from other pulsars. These include radio emission being disrupted by fallback of supernova material (Li 2006),trapped plasma being released from radiation belts (Luo & Melrose 2007), and circumstellar material affecting thecharge density in the magnetosphere (Cordes & Shannon 2008). Alternatively, RRATs may be just one part of theneutron star intermittency spectrum, which sits as the extension of nulling pulsars with extremely high nulling fractions(Burke-Spolaor 2013). In order to better understand their relation to other pulsars and the nature of the emission, werequire the discovery of additional RRATs and, most importantly, long-term monitoring and timing observations.In this paper, we introduce our observations and data analysis methods for eight RRATs, followed by their timingsolutions and the results from other studies probing other emission parameters. We also conduct a study of the RRATpopulation based on these and other timing solutions in order to find the similarities and differences in the spin-downproperties of RRATs and normal pulsars. DISCOVERY AND OBSERVATIONS
PSR Name Telescope Data Machine Frequency Bandwidth Sample Time Time Span Number Number Burst Rate Mean Flux Density(MHz) (MHz) ( µs ) (Years) of Observations of TOAs (hr − ) for Single Pulses (mJy)J0735 − − − − − − − − Table 1 . Observing parameters for eight RRATs; Here we list information of observations for the eight RRATs. The sampletimes used in GBT data for PSRs J1623 − − − − − Two of the RRATs discussed in this paper, PSRs J0735 − − − − − − − − ANALYSES AND RESULTSWe performed several analyses varying from preparing the raw observation data to the analysis of pulse properties,to measuring phase-connected timing parameters. Here we describe those steps in detail.3.1.
Single-pulse Search
The first step in our timing analysis at each observation epoch is to identify which pulses are from the RRAT. Dueto their sporadic nature, for many RRATs, we cannot use classical search algorithms based on Fourier techniques See http://astro.phys.wvu.edu/rratalog or folding. Therefore, we use the single-pulse search method to search for individual pulses with S/N above somethreshold (in the case of our analysis, 5 σ ) in a number of trial-DM time series. Here DM (dispersion measure) is theintegrated column density of electrons along the line of sight. We do this by searching for pulses that are brighterat the DM of the RRAT than at zero DM using the ‘seek’ command of the SIGPROC package. Figure 1 shows anexample of the single-pulse search output for a portion of a nearly one-hour observation of PSR J1048 − − , indicating theyare astrophysical. The majority of signals that are due to local radio frequency interference (RFI) peak at DM of 0pc cm − . The pulsar only turns ‘on’ for six minutes of this observation. The total numbers of detected pulses andrates of pulse detection for all our target RRATs are listed in Table 1. For follow-up timing observations, we simplifythis process by using only two trial-DM time series at the target RRAT DM and at zero DM, and check the pulsesdiscovered to ensure that they are in phase with the pulse period. Figure 1 . Single-pulse search plot for PSR J1048 − Spin Period and Time-of-arrival Calculation
Prior to getting a timing solution, we must first calculate the spin period. We do this by measuring the differencesbetween pulse arrival times and calculating the greatest common denominator of these differences. With a smallnumber of detected pulses in an observation, there is a probability that this will be an integer multiple of the actualspin period. In order to find the probability of measuring the true period given some number of randomly distributedpulses, we created a large number of simulated RRAT-like timeseries with given sample time, period and pulse number,and calculate the greatest common denominator of the differences. The result shows that the number of pulses largelydetermines the probability of calculating an incorrect period (which is an integer multiple of the true period). Therelationship between this probability and the number of pulses detected is shown in Figure 2 (also see McLaughlinet al. 2006). If eight or more pulses are detected, the probability of this method determining the correct period isgreater than 99%. Note that this calculation assumes that all of the pulses used for the calculation are actually from See http://sigproc.sourceforge.net the source; if RFI pulses are mistakenly included in the calculation, the period will most likely be incorrect regardlessof the number of pulses. Fortunately, the accuracy of the period can be later confirmed through the timing process.
Figure 2 . Probability of calculating an incorrect period from the greatest common denominator method vs. number of pulsesdetected (in logarithmic scale). This simulation is for a 8-minute observation with 100 µ s sample time. However, furthertesting shows that neither spin period, sample time nor observation time significantly affect this probability. The probability ofcalculating an incorrect period from three pulses in a 12 hr observation is 37.40%, comparing with 37.01% in 30 minutes. Once a period is known, we bin the data into single pulses with 256 or 512 bins (depending on the pulse width)to generate profiles for these single pulses, and double check whether the detected pulses are real through visualinspection. If the period is known, the single-pulse profiles should all peak at roughly the same spin phase (i.e. withinthe span of the full profile, which varies from source to source). For the pulsars that we are only able to time throughsingle pulses, we measure times-of-arrival (TOAs) as the arrival times of each single-pulse peak instead of throughcross-correlation with a pulse template because the shapes of individual pulses can vary dramatically. For some RRATsthat are more ‘pulsar-like’ and less sporadic, we measure integrated TOAs by folding the ‘on’-phase data (typicallyon timescales of minutes) or even folding all the data for each observation, and use a template profile based on a highS/N observation for cross-correlation. 3.3.
Dispersion Measure Fitting
A broadband signal will exhibit a frequency-dependent time delay caused by dispersion due to traveling through theinterstellar medium (ISM). The time delay t DM ∝ DM /ν , where ν is the frequency of observation. The DM can beused to estimate the distance to a pulsar (Cordes & Lazio 2002). To calculate a precise DM, we measure TOAs inmultiple frequency bands and fit for the delay using TEMPO2 (Hobbs et al. 2006).We were able to fit DM for three RRATs. For PSRs J1623 − − − TIMINGWe calculate a timing model and fit for timing residuals using the pulsar timing software TEMPO2 (Hobbs et al.2006). The full solutions are listed in Table 2, and some remarks about the timing parameters of eight RRATsare provided here. Most of the RRATs we timed have been observed for the time span of one to three years, butPSR J1048 − PSR Name R.A. Decl. P ˙ P RMS DM Epoch Width B ˙E τ (J2000) (J2000) (s) (10 − s s − ) (ms) (pc cm − ) (MJD) (ms) (10 G) (10 erg s − ) (Myr)J0735 − − − − − − − − − − − − − − − − Table 2 . Timing solutions and derived parameters for all eight RRATs: Right Ascension, Declination, spin period, periodderivative, root-mean-square of residuals, DM, epoch of period measurement, width of composite profile, magnetic field, spin-down energy loss rate and characteristic age are listed. Here the width is calculated at 50% of the peak intensity (W50), themagnetic field is at the pulsar surface and assumes alignment between spin and magnetic axis ( B = 3 . × (cid:112) P ˙ P ). Thepulsar spin-down luminosity is calculated by ˙ E = − × ˙ P /P . Figure 3 . Left: all timing residuals from the four-year observation of PSR J1048 − Position
Most of the RRATs have timing-derived positions within the original discovery beam, such as the 3 (cid:48) difference forPSR J1048 − (cid:48) in size. However, for PSRJ1623 − (cid:48) away from the discovery position (outside the GBT’s 820 MHzbeam) as an offset in position during an observation acts like a decrease in gain of the telescope, thus lowering thesensitivity. A timing solution was only attainable with the increased sensitivity of GUPPI (with twice the bandwidthof the original SPIGOT backend used for the discovery observation) and a dense set of observations to obtain a phasecoherent timing solution at 350 MHz. 4.2. Period
When PSR J1739 − ∼ − − . In Keane et al. (2011) it was reported to have a period of 1.32 s and a DM of 293(19) pc cm − . Here wereport the same period as in Keane et al. and a DM of 99.38(10) pc cm − . The difference between our period andMcLaughlin et al. (2006) is due to the misidentification of a terrestrial radio pulse as an astrophysical pulse (Keaneet al. 2011). The difference between our DM and Keane et al. (2011) is due to a formatting error in their paper,resulting in PSR J1754 − − − − . Here it is reported with a period of 0.933 s and a DM of 293.2(6) pc cm − . The difference in DM maybe due to the coarse frequency resolution of the PMPS and is less than a 2 σ difference from the discovery DM. Thedifference between the discovery period and the period reported here is much larger than what would be producedby the measured ˙ P . It was only seen in one of 10 observations reported in McLaughlin et al. (2006) and has neverbeen detected in 38 observations with the Parkes telescope since its discovery. It is possible that the low S/N of thediscovery pulses is responsible for the significant differences between the calculated periods.4.3. Pulse Profiles
Many RRATs cannot be detected by summing all the rotations over an observation. Therefore, to create integratedpulse profiles, the most straightforward way is adding all detectable single pulses after phase corrections from thetiming model. This provides us with relatively stable pulse profiles. For some RRATs that are less “transient-like”,we can create integrated pulse profiles by folding the ‘on’-phase data for each observation, or even folding the entireobservation as for other pulsars.Profiles of the eight RRATs are presented in Figure 4 in the upper panels. Most of them are narrow (with duty cyclesof less than 5%), except for the double-peaked profiles of PSR J1739 − − − − − ∼ minute-long time periods when the RRATs are ‘on’. The profiles of PSRs J0735 − − − − − − − − − − − − J0735-63024863 ms1.4 GHz CompositeWeak J1048-58381231 ms1.4 GHz CompositeWeak J1226-32236193 ms1.4 GHz CompositeWeak J1623-0841503 ms820 MHz CompositeWeakJ1739-25211818 ms820 MHz CompositeWeak J1754-30141320 ms820 MHz CompositeWeak J1839-0141933 ms820 MHz CompositeWeak J1848-1243414 ms820 MHz CompositeWeak
Figure 4 . Composite pulse profiles (upper) and weak pulse profiles (lower) of eight RRATs based on the observations describedin Table 1. The spin periods and frequencies are listed. The profiles of PSRs J0735 − − − − − − − − min for J1848 − ANALYSISIn this section, we explore the pulse amplitude distributions and weak pulse emission for the RRATs.5.1.
Pulse Amplitude Distribution
One of the most important features of the single pulses is their amplitude distribution, since this is a direct probeof the internal emission mechanism of RRATs and provides a comparison with other pulsars. We take the peak S/Nof each single pulse and calculate its flux density based on the radiometer noise calculation using the equation S sys = T sys G (cid:112) t obs n p ∆ f (1)where S sys is the system equivalent flux density, T sys is the system noise temperature, G is the gain of the telescopes(2 K/Jy for GBT and 0.6 K/Jy for Parkes), t obs is the observation sample time, ∆ f is the observed bandwidth, and n p is the number of polarizations (2 for all our observations).The peak S/N is calculated from the single-pulse profile SN R peak = A peak σ off (2)where A peak is the peak amplitude of the profile, and σ off is the standard deviation of the profile amplitude in theoff-pulse region.Then the peak pulse flux density can be calculated by S pulse = SN R peak × S sys (3)The results are shown in Figure 5, where we fit these binned histograms to three different functions: log-normaldistribution, power-law distribution, and the combination of the two. We choose these distributions because mostpulsars show log-normal distributions and giant pulses show a power-law distribution (Mickaliger et al. 2012). Theresults indicate that a log-normal distribution overall provides the most accurate fit, but PSRs J1226 − − − − Figure 5 . Pulse amplitude distribution of eight RRATs. All peak flux densities are calculated based on the pulse S/N andradiometer noise. To reduce the influence from non-detected weak pulses, we fit only the distribution with flux densities above thedistribution peak (dashed line) with three base functions (in different colors) : log-normal distribution, power-law distributionand the combination of the two, with the χ results listed. From these results, we can see that the log-normal distribution fitsall the eight RRATs very well and mostly dominates the combined function. Weak Pulse Analysis
Inspecting the pulse amplitude distributions shown in Figure 7, it is true that there are a fair number of weak pulseswith S/Ns lower than the threshold that are not detectable by the single-pulse search pipeline. In order to confirmthis, we constructed ‘weak pulse’ profiles by subtracting all detected single-pulse profiles from the composite profilecreated through folding all data in each observation using the timing model. The profiles here are scaled with numbers
Figure 6 . Fraction of pulses missed vs. S/Ns in our detectability simulations. The period in the simulated timeseries is 1 s.For S/Ns larger than four, the missed fraction is small, which means most of the pulses should be detected despite other factorssuch as human error in the process. Note that this is not the S/N returned by the single-pulse search code (discussed in section5.1), and the simulation parameters such as period, sample time, and pulse width must be specified for different RRATs. of the pulses per observation so that each observation has the same weight. The results are shown in the lower panelsof Figure 4 for all of the RRATs. The weak pulse profiles of PSR J1048 − − − − − − − − Periodicities in the Emission Timescales
As shows in Figure 8, some RRATs turn “on” and “off” seemingly regularly, so there is a possibility that someperiodicities exist in their on/off timescales. We have applied Lomb − Scargle analysis (Scargle 1982) to the unevenlysampled pulse arrival times for this task. These time series data include all detected pulse arrival times and the timesof rotations without a detected pulse within the time span of all radio observations. This L − S analysis can then revealpossible periodicities with significances proportional by the power spectral density. Given the same numbers of pulsesbut randomly varying their position in time series by shuffling their flags of “on” and “off” for every arrival time.Keeping the same windows of observation and gaps between the observations, we also performed the same analysis inorder to check whether the observed pulse time sequences are consistent with a random distribution. Details of thistechnique can be found in Palliyaguru et al. (2011). Figure 9 shows the spectra for the actual data and an exampleof one randomized time series. All spectra have peaks of over 2.5 σ (99%) significance. In order to test whether thisresult is reasonable, we created 1000 random realizations by randomly placing each detected pulse for each RRATwith the observation windows. No peak was detected at the same or higher significance level detected within severalbins at the discovered peak frequencies, or in the overall frequencies, in any of these realizations. This is consistentwith the derived more than 99% significance of these periodicities. Periodicities that are longer than half of the overallobservation time span are ignored. Examining these frequencies with significant power, we can say with confidencethat emission periodicity exists at different timescales for all eight RRATs checked. The periodicities with the largestsignificance are listed in Table 3 in order of their significance level.For PSR J1623 − Figure 7 . The detectability correction to the pulse S/N distribution for eight RRATs. The dotted lines are the expected “real”S/N distributions after correction for all pulses from the RRATs above detection threshold, and the solid lines are the originalS/N distributions before correction for pulses detected. From this figure we can see that many weak pulses are missed in thesingle-pulse detection algorithm for PSRs J0735 − − − of each other, leading to a fundamental period of 3.39 hr. This period is consistent with our detection of only oneon period for this RRAT in any observation. One possible cause of this periodicity that a single asteroid orbits thepulsar, producing emission, which is variable on the orbital timescale. This would also cause a perturbation in theTOAs for this RRAT. Assuming a circular orbit and a neutron star mass of 1.4 solar masses, we can calculate thatthe orbital radius of the asteroid would be roughly 4 × km, and using Equation 6 in Cordes & Shannon (2008),1 J0735 − − − − − − − − σ ) 1.9166(1)(12.5 σ ) 1.2713(7)(4.5 σ ) 28.58(7)(34.8 σ ) 0.3637(1)(12.5 σ ) 41.8(9)(20.5 σ ) 0.68317(2)(33.3 σ ) 6.892(4)(6.3 σ )18.88(7)(63.5 σ ) 0.88912(2)(11.75 σ ) 2.550(3)(4.25 σ ) 14.57(2)(34.5 σ ) 0.3583(1)(12.3 σ ) 3.235(1)(18.8 σ ) 0.70325(2)(31.8 σ ) 8.624(4)(6.0 σ )21.12(9)(55.0 σ ) 0.99261(2)(11.5 σ ) 4.433(8)(3.8 σ ) 3.390(1)(33.8 σ ) 0.4429(1)(11.5 σ ) 16.38(1)(18.5 σ ) 0.67232(2)(30.0 σ ) 65.4(3)(6.0 σ )7.16(1)(53.8 σ ) 3.9436(5)(11.3 σ ) 2.496(3)(3.8 σ ) 3.258(1)(32.8 σ ) 0.4512(1)(11.5 σ ) 3.470(1)(18.3 σ ) 0.59866(2)(29.3 σ ) 3.814(1)(6.0 σ ) Table 3 . Results of Lomb − Scargle tests on all eight RRATs. This table provides four periodicities (hours) for each RRATs in thepulse arrival time that are ranked in the order of peak significance. The errors of periodicities are in the first parentheses, and thesignificance in the second parentheses to compare with the 2.5 σ (roughly 99% confidence) level. The error is calculated as randomstatistical error with 1 σ Figure 8 . Pulsar folding plot shows “on” and “off” phases for PSR J1839 − assuming an edge-on orbit, the upper limit of the asteroid mass would be 2 × M (cid:76) ( ∼ − M (cid:76) ( ∼ DISCUSSIONAt this time, 25 of roughly 100 RRATs have timing solutions with period and period derivative, shown on the P − ˙ P diagram in Figure 10. We apply the Kolmogorov − Smirnov (KS) test to the RRAT and normal (non-recycled) pulsarpopulations to see how their spin-down properties compare. The result gives the probability P that two distributionsare identical, and the largest differences between the two groups are found in the distributions of period (with P = 1.1 × − ) and magnetic field (with P = 1.9 × − ). While selection effects may be responsible for some of theperiod dependence, as longer period pulsars are more likely to be detected with higher S/Ns in single-pulse searches(see McLaughlin & Cordes (2003) equation 2), the difference in period derivative (of P =2.5 × − ), which along withthe period is used to calculate the surface inferred magnetic field, hints that there is a fundamental difference in thesepopulations. However, because young pulsars generally have higher period derivatives, period derivative is correlatedwith period, and it is therefore possible that the difference in period derivative distributions is due to a selection effect.We tested this by comparing the period derivatives of RRATs with pulsars with similar spin periods (see Figure 11).It is clear that the RRATs’ period derivatives are higher than those of normal pulsars overall despite any selectioneffects.We have provided timing solutions for eight RRATs, and also analyzed their pulse and emission properties. In theseanalyses, we find out that the amplitude distributions of RRATs generally follow a log-normal distribution, and someof the RRATs show periodicities in their emission timescales with a scenario of orbiting asteroids around these pulsarsshown to be reasonable (other scenarios are still possible). We also explored how many pulses are missed in standardsingle-pulse searches and found that for some RRATs, this is a significant number. This analysis, as well as plots ofthe RRATs’ weak pulse emission shows that some RRATs, like PSR J1048 − Figure 9 . Lomb − Scargle test results for all eight RRATs. Here the power spectral densities (PSDs) are plotted versus log-scaledperiods of emission in units of days. The peaks in the PSD curves show the most significant candidates, while the dashed lineprovides a 2.5 σ (99%) significance threshold. The plots in the left column show tests on the original RRATs pulse arrival times,and in the right are the tests upon randomized time series with same spin period and observation time as on the left. The2.5 σ dashed line is not visible because it lies above all of the randomized data points. Note the difference in scales of PSD axisbetween the real data and randomized data. We can see that, for all our RRATs, we detect PSD peaks that exceed the thresholdand are far higher than the random test, indicating that all of these RRATs show true periodic behavior in their emission times. However, to better understand their mechanism and evolution, we still need to extend our database of timingsolutions and emission test results for more RRATs, in both quantity and quality. Further surveys for new RRATs,accompanied by sensitive timing observations and the development of new techniques, will help us achieve our goals.3
Figure 10 . P − ˙ P diagram of RRATs and pulsars with timing solutions (Manchester et al. 2005). The RRATs with new timingsolutions are shown as red stars and previously timed RRATs as blue stars. The black squares are magnetars with timingsolutions (Camilo et al. 2007), and black diamonds indicate X-ray isolated neutron stars with timing solutions (Kaplan & vanKerkwijk 2009). Lines of constant magnetic field (dashed) and characteristic age (dotted-dashed) are shown. The KS test givesprobabilities of 1.1 × − , 2.5 × − , 1.9 × − , 0.16, and 0.04 that the period, period derivative, magnetic field, characteristicage, and spin-down energy-loss rate, respectively, were derived from the same distribution as those for other non-recycled pulsars. Figure 11 . Comparison of period derivative between normal pulsars and RRATs. Each data point is the average value of P and˙ P of the population within a small period range. The Y-axis is the difference in logarithm values (log( ˙ P RRAT ) - log( ˙ P pulsar )).We can see that for most period, the ˙ P values of the RRATs are larger than those of normal pulsars, so that the differences areabove zero overall. All P and ˙ P data used are from the ATNF Pulsar Catalog (Manchester et al. 2005) and RRATalog website b . a see http://astro.phys.wvu.edu/rratalog b see http://astro.phys.wvu.edu/rratalog Facility:
Green Bank Telescope,
Facility: