UPPER LIMITS ON PULSED RADIO EMISSION FROM THE 6.85 s X-RAY PULSAR XTE J0103−728 IN THE SMALL MAGELLANIC CLOUD

In the first analysis, the data were split into sixteen 16 MHz subbands, and each subband was dedispersed at an assumed dispersion measure (DM) of 100 pc cm⁻³. This is within the range of expected DMs for pulsars in the SMC (Manchester et al. 2006). A range of DMs was tried by shifting the subbands with respect to each other in phase, then summing the subbands in each case. DMs from 0 to 5000 pc cm⁻³ were searched in this way. A barycentric folding period was determined using the measured periods from the two previous X-ray detections of XTE J0103−728. Using the reported periods and their associated uncertainties from the 2003 May (Corbet et al. 2003) and 2006 October (Haberl & Pietsch 2008) observations, we extrapolated the period to the 2008 February epoch and determined the barycentric folding period to be 6.8563(3) s. Since the spin period of XTE J0103−728 is so large, a dedispersion error would not significantly degrade the sensitivity of our search. A dedispersion error of 100 pc cm⁻³, for instance, would lead to only a 5 ms smear in the pulse across each subband, less than 0.1% of the pulse period. Even for the extreme case of a dispersion error of 5000 pc cm⁻³, pulsations would probably still be detectable since the corresponding pulse smear would only be 3.6% of the pulse period.

Periods ±40 ms from the nominal period were searched, which easily encompassed the estimated 0.3 ms uncertainty in the pulse period. In a separate analysis, the data were split into 10 segments, with each segment starting at intervals of 10% of the data length and consisting of 20% of the data length. Each segment was separately searched for variable strength pulsations (owing to scintillation, for example) in the manner described above. No candidate signals were detected in any of these analyses.

We also conducted a more detailed separate search in which we dedispersed and folded the data into pulse profiles at a range of DMs and folding periods around the nominal period. Periods spanning ±1.5 ms from the nominal 6856.3 ms pulse period (i.e., a range of ±5σ) were searched in steps of 1 μs. Each of these folding trials was conducted for DMs between 0 and 800 pc cm⁻³ in steps of 5 pc cm⁻³. For each DM trial, the full 256 MHz of bandwidth was dedispersed. A total of 480,000 period and DM combinations were tried (3000 folds per DM trial, and 160 DM trials), and for each trial the χ² significance of the folded profile was recorded. For this number of random trials, we would expect a ∼25% likelihood of producing at least one signal at the 5σ significance level or higher from noise alone. We therefore chose 5σ as a reasonable threshold to apply, and we found no folded profiles at the 5σ significance level or higher in the search.

This second search was more sensitive to pulsations having very small duty cycles, and we estimate the effects on the pulse width that either folding the raw data at a period that is offset from the true period or dedispersing the data at a DM that is offset from the true DM would have. We compare this amount of pulse smearing to the smearing already present in the finite frequency channels. Significant smearing of the pulse would greatly reduce the sensitivity of the search, so it is therefore important to ensure that the search parameters do not allow this. For the chosen period step size of 10⁻⁶ s in the search, the maximum folding period offset is 5 × 10⁻⁷ s from the true period. Folding the raw data at this offset period would cause a pulse smear across the folded profile of 1.7 ms (2.5 × 10⁻⁴ cycles) over the length of the observation. This is an order of magnitude larger than the intrachannel dispersive smearing of 0.16 ms (2.3 × 10⁻⁵ cycles) for an assumed DM ∼100 pc cm⁻³, but it is still negligible for any reasonable duty cycle expected for the pulsar. The DM step size of 5 pc cm⁻³ produces a maximum DM offset from the true DM of 2.5 pc cm⁻³, which for 256 MHz of bandwidth at our observing frequency yields a maximum dispersive smearing of 2.0 ms (2.9 × 10⁻⁴ cycles). Thus, any duty cycle ≳10⁻³ should not be significantly affected by any of these smearing effects. The grid spacing of the period and DM search ensured that no pulsations with very small duty cycles (narrow pulses) would have been missed in the search.

We also conducted a periodicity search of the data, which included a fast folding algorithm (FFA) search in addition to the more common Fourier search. A Fourier search is particularly important if the estimated spin period at the epoch of observation was not correct (e.g., if there were irregularities in the spin-down behavior or significant accelerations from binary motion that are not accounted for in the predicted folding period). For the Fourier search, two different packages were used: SIGPROC⁷ (e.g., Lorimer et al. 2000) and PRESTO⁸ (Ransom 2001; Ransom et al. 2002). A total of 828 DM trials ranging from 0 to 800 pc cm⁻³ were used in the search. The DM trials were spaced so that there would be no significant pulse smearing introduced beyond the smearing already present in the 0.5 MHz frequency channels. Each dedispersed time series was filtered, and a 2²⁵ point fast Fourier transform was performed.⁹ Each resulting spectrum was harmonically summed using 16 harmonics and searched for candidate periodicities. For the PRESTO search, an acceleration search spanning ±100 Fourier bins was also performed on each dedispersed time series. This maintained full sensitivity to accelerations of up to 24 m s⁻² for the 6.856 s fundamental and 16 of its harmonics. No acceleration search was performed in the SIGPROC analysis. Candidates recorded in the frequency spectrum were further checked by dedispersing and folding the raw data at DMs and periods near the candidate values in the manner described in the folding search above. No promising candidates were detected in this search.

During the Fourier search, each dedispersed time series was also searched for significant periodicities using the FFA (Staelin 1969). We used publicly available FFA search code,¹⁰ described in detail by Kondratiev et al. (2009), which has been previously used to search for pulsed radio emission from XDINs. No signals were detected in the FFA periodograms above a signal-to-noise threshold of 5 for periods between 2 and 12 s.

The recent discovery of bursting radio sources subsequently identified as rotating neutron stars (RRATs; McLaughlin et al. 2006) suggests that looking for dispersed single pulses is a powerful method by which to detect rotating neutron stars that would otherwise not be detectable in a periodic search. Besides RRATs, other classes of persistent and transient radio sources are sometimes detectable through their single pulses. For example, the AXP XTE J1810−197 exhibited very bright single pulses at the time of its radio detection (Camilo et al. 2006), and single pulse searches have been used to detect radio emission from a number of pulsars, including the Crab pulsar (Staelin & Reifenstein 1968). Dispersed, extremely luminous radio bursts from cosmological sources may also be present in the data and would only be detectable through this kind of search (Lorimer et al. 2007).

We searched for dispersed single pulses in the data using the same set of DMs used for the Fourier search described above (828 DMs of variable spacing from 0 to 800 pc cm⁻³). The single pulse analysis procedure is outlined by Cordes & McLaughlin (2003) and uses a matched filtering approach to detect impulses of different widths in each dedispersed time series. A range of boxcar filter widths is used to maximize sensitivity on different timescales. Pulse widths between 0.5 and 1024 ms were searched by increasing factors of 2 for the boxcar filter width, and the detection threshold was determined for each filtering window by the level of RFI present. For pulse widths ≳1 s, the high-pass filter present in the observing system would significantly attenuate the impulse amplitude (see discussion below), so windows greater than ∼1 s were not searched. Owing to the increased RFI presence as the window size increased, the signal-to-noise (S/N) detection threshold changed from 8 to 20 for boxcar windows greater than or equal to 4 ms. No significant dispersed single pulses were detected in this search.

We used the modified radiometer equation (Dewey et al. 1985) to estimate the flux density limit on periodic emission in the folding search. For a detection S/N threshold of 5, 1-bit sampling, a gain of 0.735 K Jy⁻¹ for the center beam of the multibeam receiver (Manchester et al. 2001), an assumed duty cycle of 5%, and the observing parameters outlined above, we estimate the 1400 MHz flux density limit on pulsed emission from XTE J0103−728 to be ∼13 μJy. This estimate does not include the effect of RFI, which can quite significantly degrade the sensitivity, especially at long periods. The corresponding 1400 MHz luminosity limit can be calculated using L = Sd², where S is the 1400 MHz flux density limit and d is the distance. In this definition, no geometrical factor for the beaming is included which would change the calculated luminosity limit. Using a distance of 60 kpc to the SMC (Hilditch et al. 2005), we estimate the 1400 MHz luminosity limit to be ∼45 mJy kpc² (see Table 1). The sensitivity limit from the FFA search is comparable to the radiometer limit for the periodic emission.

For the single pulse search, no pulses were detected down to the flux density limit of 0.60–0.03 Jy (depending on the S/N threshold and window size used in the filtering; see the discussion above). These limits correspond to 1400 MHz luminosity limits of 2150–120 Jy kpc² (Table 1) using a distance of 60 kpc to the SMC and the same luminosity definition.

The limits obtained by the modified radiometer equation are accurate representations of the sensitivity of the folding search (see Dewey et al. 1985; Lorimer et al. 2006). However, for the sample of pulsars that were detected in the Parkes Multibeam Survey (Manchester et al. 2001), the S/N values of the Fourier detections from the blind Fourier search are lower than the corresponding folded profile S/N values by about a factor of 2 (on average) near the detection threshold (F. Crawford et al. 2009, in preparation). This difference would apply here also since the same observing system and a similar analysis procedure were used. We therefore estimate the baseline sensitivity limit for the Fourier search to be ∼25 μJy, roughly twice the modified radiometer equation limit. Since we had a good estimate of the folding period for this search, we elect to keep the radiometer limit as an accurate estimate of the sensitivity to periodic emission for our discussion.

Another factor which must be considered in the estimate of the sensitivity to pulsed emission (either impulsive or periodic) is the presence of a high-pass filter in the observing system which severely limits the sensitivity to long-period pulsars having large duty cycles. This high-pass filter is modeled as a two-pole filter with a time constant of 0.9 s (Manchester et al. 2001), and the effect of this filter on long-period signals depends on the duty cycle of the pulse as it is received at the telescope (i.e., after interstellar dispersive and scattering effects have already affected the pulse width and shape). In order to quantify this filtering effect on the sensitivity, we created synthetic pulse trains in software with various periods and duty cycles and passed these signals through a two-pole high-pass filter (in software) in order to gauge the amount of signal attenuation and hence reduction in the detected S/N. We found that for duty cycles greater than ∼20%–30%, the attenuation is significant for a ∼6 s pulsar (there is a reduction of ≳10% in the pulse amplitude). For duty cycles less than ∼10%, the effect is negligible; this is due to the presence of a larger number of high-frequency harmonics of the fundamental in the signal that are not as significantly affected by the high-pass filtering. These results are consistent with the simple expectation that pulse widths greater than the 0.9 s filtering time constant would be significantly attenuated. This filtering effect also has relevance for the flux density upper limits recently reported for several radio search observations of AXPs conducted with Parkes. Both Burgay et al. (2006b) and Crawford et al. (2007) searched four AXPs with periods of 6 and 11 s with the multibeam observing system. For small assumed duty cycles (less than 10%), the attenuation is negligible for these periods. For our single pulse search of XTE J0103−728, impulsive signals having widths ≳1 s are attenuated by the filter, which is why our single pulse search window range did not extend beyond 1024 ms.

There are three binary radio pulsars known to have nondegenerate orbital companions: PSRs J0045−7319 (Kaspi et al. 1994), J1740−3052 (Stairs et al. 2001), and B1259−63 (Johnston et al. 1992). Of these three, only PSR B1259−63 orbits a Be star. There are also many Be/X-ray HMXBs that are known, including more than 60 in the SMC (Haberl & Pietsch 2008), but apart from PSR B1259−63, none of these has yet been observed as a radio pulsar. For this reason, PSR B1259−63 is a natural system with which to compare our results for XTE J0103−728.

PSR B1259−63 is in a highly eccentric and wide orbit, with an eccentricity of 0.87 and an orbital period of 3.4 years (Johnston et al. 1994). The pulsar passes quite close to its Be star companion at periastron, coming within 24 stellar radii of the star (Johnston et al. 2005). This distance is comparable to the estimated radius of the circumstellar disk of the Be star, which is thought to be at least 20 stellar radii in size (Johnston et al. 1994). Near periastron, the radio pulses from PSR B1259−63 are eclipsed for ∼40 days by the circumstellar disk. Enhanced X-ray emission is also detected near periastron, since the pulsar interacts with the stellar wind (Kaspi et al. 1995). However, pulsed X-rays have not been detected from PSR B1259−63, unlike XTE J0103−728. Melatos et al. (1995) modeled the B1259−63 system near periastron and investigated two models which could explain the observed eclipsing behavior. They found that a model employing a cool, dense equatorial disk around the Be star successfully predicted the observed eclipse duration at ∼1.5 GHz, if free–free absorption were the primary eclipsing mechanism. They also found that scattering in the disk may be contributing to the radio eclipse. In any case, it seems reasonable that free–free absorption and scattering could also be preventing the detection of radio pulses from XTE J0103−728 if it is in a similarly eccentric orbit and was near periastron at the time of our observation.

The 1400 MHz flux density of pulsed emission from PSR B1259−63 has been measured and published in a variety of papers using data collected over the course of several orbits (Hobbs et al. 2004; Johnston et al. 1992, 1994, 1996, 2005; Connors et al. 2002). The measured values vary considerably, but consideration of all the measurements suggests an average flux density of ∼5 mJy around 1400 MHz. We use this estimate for the comparison with our observation of XTE J0103−728. Near periastron, when PSR B1259−63 is eclipsed, there is no detectable radio emission at this frequency. We adopt ∼1 mJy as a conservative upper limit on the flux density during eclipse by considering the uncertainties in the 1400 MHz flux reported both before and after the eclipse during the 2000 and 2004 periastron passages (Connors et al. 2002; Johnston et al. 2005). The best estimate for the distance to PSR B1259−63 is 1.5 kpc, based on optical observations of the Be star companion (Johnston et al. 1994). From this, the resulting 1400 MHz luminosities are calculated to be ∼11 mJy kpc² away from periastron and ≲2 mJy kpc² during eclipse near periastron. In either case, the luminosity is below the limit of ∼45 mJy kpc² that we have established for pulsed emission from XTE J0103−728 at the epoch of our observation. We therefore cannot rule out radio emission from XTE J0103−728 that is comparable in luminosity to the emission seen from PSR B1259−63.

In this section, we compare the luminosity upper limit for XTE J0103−728 to the radio luminosities (or luminosity upper limits in some cases) of neutron stars which have long spin periods like XTE J0103−728.

In the ATNF pulsar catalog (Manchester et al. 2005), there are five radio pulsars with periods greater than 6 s that have measured 1400 MHz flux densities and corresponding estimated luminosities. The radio luminosities of these pulsars range from 0.03 to 23 mJy kpc², which is below our upper limit of ∼45 mJy kpc² for periodic emission from XTE J0103−728. The sample of six long-period XDINs for which new, sensitive radio limits have recently been obtained using the Green Bank Telescope (Kondratiev et al. 2009) has 1400 MHz luminosity limits that are several orders of magnitude below our limit. These XDINs have periods ranging from 7 to 11 s. There are five AXPs with periods longer than 6 s which have been searched at 1400 MHz for radio emission and for which luminosity upper limits have been established (Burgay et al. 2006b; Crawford et al. 2007; Burgay et al. 2006a). Although these AXPs are believed to have much stronger magnetic fields than the neutron stars in these other classes, they may have similar beaming and detectability selection effects in the radio owing to their similarly long spin periods (see discussion below). The luminosity limits established for these AXPs are all around 1 mJy kpc², which is more than an order of magnitude below our limit for XTE J0103−728. A radio search was also previously conducted on SGR 0526−66 in the Large Magellanic Cloud, which, like the AXPs, is also believed to be a magnetar. No radio emission was detected from SGR 0526−66 down to an upper limit of ∼350 mJy kpc² at 1400 MHz (Crawford et al. 2002).

By looking at these values, one can see that it is entirely possible that XTE J0103−728 could have radio emission comparable in strength to these long-period radio pulsars, XDINs, and AXPs (if these latter two classes are in fact radio emitters), and that we are simply not detecting radio pulsations due to a lack of sensitivity. Unfortunately, the large distance to XTE J0103−728 makes the limit impossible to significantly improve upon until next-generation instruments, such as the Australia Square Kilometer Array Pathfinder (ASKAP; Johnston et al. 2007, 2008), can be developed and used. Even if XTE J0103−728 were a strong radio emitter, its radio beam might not be aligned with its X-ray beam and could miss our line of sight. If this were the case, XTE J0103−728 might remain undetectable to us in the radio owing to its emission geometry.

Narrow pulse widths are also generally observed for long-period radio pulsars. For instance, the two cataloged radio pulsars with the longest spin periods, PSRs J2144−3933 and J1001−5939, have full width at half-maximum radio pulse widths of 0.2% and 0.5% of the pulse period, respectively (Young et al. 1999; Lorimer et al. 2006). These duty cycles are among the smallest measured for the radio pulsar population and indicate the severity of the selection effects that might be preventing the detection of many long-period radio pulsars, of which XTE J0103−728 might be one. Note that the small duty cycle associated with the narrow pulses would partially compensate for the sensitivity selection effect on long-period pulsars from the high-pass filtering (described above), since there would be many high-frequency harmonics in the signal.