Chapter 4Intermittent Pulsars

Andrew G. Lyne

4.1 Introduction

Transient phenomena are usually difficult to find and characterise, particularly ifmuch of the time is spent in a null state. This is true of two recently discovered typesof transient radio source, namely the Rotating Radio Transient sources (RRATs) andthe Intermittent Pulsars. Both spend much of their time invisible in quite differentways, and both have underlying periodicities which are attributable to rotating mag-netic neutron stars. In these circumstances, they also represent the small tips of muchlarger populations which may cause us to revise our views of what “normal” neu-tron star behaviour is. RRATS are objects which emit occasional single pulses ofradio emission, perhaps once every 100–1,000 rotation periods of the neutron star.The phenomenon is described in detail elsewhere in this volume [9]. The intermit-tent pulsars on the other hand behave like normal regular pulsars for intervals oftime measured in days or years, with longer intervals when there is no emission atall. In this paper, we discuss the phenomenon, the search for other instances, theimplications for pulsar magnetospheric physics and the galactic population of suchobjects.

4.2 PSR B1931+24

PSR B1931+24 has been observed for many years in the pulsar timing programmeusing the 76-m Lovell Telescope at Jodrell Bank. It had been considered to be aseemingly ordinary pulsar, with a spin period of 813 ms [14] and a typical rotationalfrequency derivative of ν = −12.2×10−15 Hz s−1 (cf. Table 1 in [5]). It was noted

A.G. LyneUniversity of Manchester, Jodrell Bank Observatory, Macclesfield, SK11 9DL, UKe-mail: andrew.lyne@manchester.ac.uk

W. Becker (ed.), Neutron Stars and Pulsars, Astrophysics and Space Science Library 357, 67c© Springer-Verlag Berlin Heidelberg 2009

68 A.G. Lyne

Obs.

51400 51500 51600 51700 51800 51900Modified Julian Date (day)

ON

0.0 0.1 0.2Frequency (1/day)

0.0

0.2

0.4

0.6

0.8

1.0

Pow

er

0 10 20 30 40Time (day)

0

2

4

6

8N

umbe

r

a

bc

Fig. 4.1 The intermittent nature of the radiation from PSR B1931+24 [7]. (a) The vertical bars inthe upper diagram show the location of good observations of the pulsar during a 600-day period.The lower diagram shows vertical bars for those observations in which the pulsar was detected(ON). (b) The spectrum of the time sequence in (a), obtained from the Fourier transform of itsautocorrelation function. Inset are histograms of the lengths of the “ON” (filled area) and “OFF”(hatched area) intervals

that it exhibits considerable short-term rotational instability, known as timing noiseand which is usually thought to be intrinsic to the pulsar, but shows no evidence forthe presence of any stellar companion. It became clear a few years ago that the pul-sar was not detected in many of the regular observations and that the flux densitydistribution was bimodal, the pulsar being either ON or OFF [7]. Figure 4.1a showsthe best sampled data span which covers a 20-month period between 1999 and 2001and demonstrates the quasi-periodic fashion of the ON–OFF sequences. The pul-sar is typically ON for a week and completely OFF for the following month. Thepower spectrum of the data (Fig. 4.1b) reveals a strong ∼35-d periodicity with twofurther harmonics, which reflect the duty-cycle of the switching pattern. Studying amuch longer time-series from 1998 to 2005, including some intervals of less denselysampled data, we find that the periodicities are persistent but slowly varying withtime in a range from 30 to 40 days. No other known pulsar behaves this way.

Despite the rarity of the switching events, we have been able to observe oneswitch from an ON state to OFF and found that it occurred within 10 s, the timeresolution being limited by the signal-to-noise ratio of the observations.

To investigate the nature of the switching phenomenon, we have examined therotation rate of the pulsar over a 160-day period during which the sampling ofthe data was particularly dense (Fig. 4.1, top). The variation is dominated by a

4 Intermittent Pulsars 69

Fig. 4.2 Top panel: The variation of the rotational frequency ν of PSR B1931+24 over a periodof 160 days [7]. The increase in slope during the “ON” periods compared with the mean slope canbe seen clearly, indicating an increase in slowdown rate. Bottom panel: Timing residuals relativeto a simple slowdown model over the same period. The line shows a fitted model which includesa single extra parameter, an increase in frequency derivative during the “ON” phase, and providesan excellent description of the data

decrease in rotational frequency which is typical for pulsars. However, inspectionof the longer sequences of the available ON data reveals that the rate of decreaseis even more rapid during these phases, indicating greater values of rotational fre-quency first derivative than the average value (cf. Fig. 4.2). This suggests a simplemodel in which the frequency derivative has different values during the OFF and ONphases. Such a model accurately describes the short-term timing variations seen rel-ative to a simple long-term slow-down model (Fig. 4.1, bottom). Over the 160-dayperiod shown, the pulsar was monitored almost daily, so that the switching times arewell defined, and a model could be fitted to the data with good precision. The addi-tion of a single extra parameter (i.e. two values of frequency derivative rather thanone) reduces the timing residuals by a factor of 20 and provides an entirely satis-factory description of the data. A similar fitting procedure has been applied to otherwell-sampled sections of data and produces consistent model parameters, givingvalues for the rotational frequency derivatives of νOFF = −10.8(2)× 10−15 Hz s−1

and νON = −16.3(4)× 10−15 Hz s−1. These values indicate that there is a ∼50%increase in spin-down rate of the neutron star when the pulsar is ON.

70 A.G. Lyne

Fig. 4.3 The variation of the rotational frequency ν of PSR J1832+0029 over about 4 years. Thepulsar was OFF for the gap of ∼600 days between the two ON periods. Note the increased magni-tude of frequency derivative during the “ON” periods

We have searched our databases carefully for other pulsars which may exhibitthis phenomenon. Four other candidates have been identified and are being studiednow. One of these is PSR J1832+0029 which shows the same basic phenomenon onan even longer timescale. Figure 4.3 shows the variation in its rotational frequency,showing the same increased slow-down rate during the ON periods.

4.3 Discussion

The observed quasi-periodicity in PSR B1931+24’s activity and its time-scale havenever seen before as a pulsar emission phenomenon and are accompanied by mas-sive changes in the rotational slow-down rate. This raises a number of questions.Why does the emission switch ON and OFF? Why is the activity quasi-periodic?Why is the pulsar spinning down faster when it is ON?

On the shortest, pulse-to-pulse time scales, intrinsic flux density variations areoften observed in pulsar radio emission. The most extreme case is displayed by asmall group of pulsars, which are known to exhibit nulls in their emission, i.e. therandom onset of a sudden obvious lack of pulsar emission, typically for betweenone and a few dozen pulsar rotation periods [1]. An acceptable explanation for such“nulling”, which appears to be the complete failure of the radiation mechanism, isstill missing. This nulling represented the longest known time scales for an intrinsicdisappearance of pulsar emission. Although the OFF periods in PSR B1931+24

4 Intermittent Pulsars 71

last five orders of magnitude longer than typical nulling and the activity pattern isquasi-periodic, this may well be the same basic phenomenon as nulling.

The approximate 35-day period might be attributed to free precession, althoughwe find no evidence of expected profile changes (e.g. [13]). The sudden change andthe quasi-periodicity point toward a relaxation oscillation of unknown nature withinthe pulsar system, rather than precession.

What can cause the radio emission to cut off so quickly? The energy associatedwith the radio emission from pulsars accounts for only a very small fraction of thepulsar’s slow-down energy which may suggest that the disappearance of radiationis simply due to the failure of the coherence condition in the emission process [10].However, in this case, the long timescales of millions of pulsar rotations are hard tounderstand.

An alternative explanation is that there is a more global failure of charged par-ticle currents in the magnetosphere. Intriguingly, the large changes in slow-downrate that accompany the changes in radio emission can also be explained by thepresence or absence of a plasma whose current flow provides an additional brak-ing torque on the neutron star. In this model, the open field lines above the mag-netic pole become depleted of charged radiating particles during the OFF phasesand the rotational slow-down, νOFF, is caused by a torque dominated by mag-netic dipole radiation [3, 11]. When the pulsar is ON, the decrease in rotationalfrequency, νON, is enhanced by an additional torque provided by the outflowingplasma, T ∼ 2

3c IpcB0R2pc, where B0 is the dipole magnetic field at the neutron star

surface and Ipc ∼ πR2pcρc which is the electric current along the field lines crossing

the polar cap, having radius of by Rpc (e.g. [4]).1 The charge density of the currentcan be estimated from the difference in loss in rotational energy during the ON andOFF phases. When the pulsar is ON, the observed energy loss, EON = 4π2IννON,is the result of the sum of the magnetic dipole braking as seen during the OFFphases, EOFF = 4π2IννOFF, and the energy loss caused by the outflowing current,Ewind = 2πTν , i.e. EON = EOFF + Ewind where I is the moment of inertia of theneutron star. From the difference in spin-down rates between OFF and ON phases,Δν = νOFF − νON, we can therefore calculate the charge density ρ = 3IΔν/R4

pcB0

by computing the magnetic field B0 = 3.2× 1015√

−νOFF/ν3 Tesla and the polarcap radius Rpc =

√2πR3ν/c for a neutron star with radius R = 10 km and a moment

of inertia of I = 1038 kg m2 [8]. We find that the plasma current that is associatedwith radio emission carries a charge density of ρ = 0.034 C m−3. This is remarkablyclose to the charge density ρGJ = B0ν/c in the Goldreich–Julian model of a pulsarmagnetosphere [2], i.e. ρGJ = 0.033 C m−3.

Such current is sufficient to explain the change in the neutron star torque, butit is not clear what determines the long timescales or what could be responsiblefor changing the plasma flow in the magnetosphere. In that respect, understand-ing the cessation of radiation that we see in PSR B1931+24, may ultimately helpus to also understand ordinary nulling. Whatever the cause is, it is conceivable that

1 In order to be consistent with existing literature, such as [4], we quote formulae in cgs-units butrefer to numerical values in SI units.

72 A.G. Lyne

the onset of pulsar emission may be a violent event which may be revealed withhigh-energy observations. While an archival search for X-ray or γ-ray counterpartsfor PSR B1931+24 has not been successful, the relatively large distance of the pul-sar (∼4.6 kpc) and arbitrary viewing epochs may make such a detection unlikely.The relationship between the presence of pulsar emission via radiating particles andthe increased spin-down rate of the neutron star provides strong evidence that a pul-sar wind plays a significant role in the pulsar braking mechanism. While this hasbeen suggested in the past (e.g. [12]), direct observational evidence has hithertobeen missing. We note that, as a consequence of the wind contribution to the pul-sar spin-down, the surface magnetic fields estimated for normal pulsars from theirobserved spin-down are likely to be overestimated.

The discovery of PSR B1931+24’s behaviour suggests that many more suchobjects exist in the Galaxy but have been overlooked so far because they were notactive during either the search or confirmation observations. The periodic transientsource serendipitously found recently in the direction of the Galactic centre [6] mayturn out to be a short-timescale version of PSR B1931+24 and hence to be a radiopulsar. In general, the timescales involved in the observed activity patterns of thesesources pose challenges for observations scheduled with current telescopes. Instead,future telescopes with multi-beaming capabilities, like the Square-Kilometre-Arrayor the Low Frequency Array, which will provide continuous monitoring of suchsources, are needed to probe such timescales which are still almost completely unex-plored in most areas of astronomy.

References

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