---
title: 'PSR B1931+24: Long-Term Intermittent Pulsar'
url: https://www.emergentmind.com/topics/psr-b1931-24
type: topic
---

# PSR B1931+24: Long-Term Intermittent Pulsar

PSR B1931+24 is the prototypical long-term intermittent pulsar, exhibiting strikingly regulated switching between radio-emitting and quiescent phases that is tightly coupled to its rotational dynamics. A 13-year timing and monitoring campaign established that it alternates between two discrete emission states and two discrete spin-down states on an average timescale of approximately \(38 \pm 5\) days, while later FAST observations showed that the radio-off state is not fully silent but contains continuous weak emission and occasional dwarf pulses [1212.0327] [2507.04816].

## 1. Observational basis and basic parameters

The long-baseline characterization of PSR B1931+24 is based on approximately 13 years of observations from 29 April 1998 to 19 May 2011, largely with the 76-m Lovell Telescope and the 28\(\times\)25-m Mark II at Jodrell Bank, with additional observations from the 94-m Nançay Radio Telescope to bridge maintenance gaps. Two backends were employed at Lovell: the Analogue Filter Bank to May 2010 and the Digital Filter Bank from January 2009. Typical center frequencies and bandwidths were 1402 MHz/32 MHz, 1520 MHz/384 MHz, 1396 MHz/32 MHz, and 1368 MHz/64 MHz, with intensified twice-daily monitoring starting in 2006 to sharpen transition constraints. The analysis used a one-bit “activity” time series for activity duty cycle estimation with bootstrap resampling (\(10^{6}\) resamples), a weighted wavelet Z-statistic with tuning constant \(c=0.001\), and timing residual fits that explicitly allow two spin-down rates, augmented by Monte Carlo propagation of transition-time uncertainties (\(10^{5}\) trials per interval). A stride-fitting approach was used in both emission and rotational analyses to enhance temporal resolution [1212.0327].

The pulsar period is \(P \approx 0.814\) s, corresponding to a spin frequency \(\nu = 1/P \approx 1.228965 \pm 0.000001\) Hz as measured in the timing fits. The long-term study adopted a distance \(d \approx 4.6\) kpc to convert fluxes to pseudo-luminosities. Where needed, period and frequency derivatives are related via
\[
\nu = \frac{1}{P}, \qquad \dot{\nu} = -\frac{\dot{P}}{P^{2}}.
\]

A concise parameter summary is given below.

| Quantity | Value |
|---|---|
| Spin period \(P\) | \(\approx 0.814\) s |
| Spin frequency \(\nu\) | \(1.228965 \pm 0.000001\) Hz |
| Mean radio-on duration | \(8 \pm 4\) d |
| Mean radio-off duration | \(22 \pm 7\) d |
| Mean cycle timescale | \(38 \pm 5\) d |
| Radio-emitting duty cycle | \(26 \pm 6\%\) |
| \(\dot{\nu}_{\rm on}\) | \(-16 \pm 1 \times 10^{-15}\,\mathrm{s}^{-2}\) |
| \(\dot{\nu}_{\rm off}\) | \(-10.8 \pm 0.4 \times 10^{-15}\,\mathrm{s}^{-2}\) |
| Torque ratio \(R\) | \(1.48 \pm 0.11\) |

Later FAST observations used the catalog value \(DM = 106.03\,\mathrm{pc\,cm^{-3}}\), and the faint off-state pulses line up at the same DM as the on state, confirming astrophysical origin and rejecting radio-frequency interference as the cause [2507.04816].

## 2. Intermittency cycle and state-duration phenomenology

The radio-on and radio-off durations span broad ranges. In high-cadence subsets, radio-on durations are typically 1–19 days, with average \(8 \pm 4\) days, while radio-off durations are typically 4–39 days, with average \(22 \pm 7\) days. There is no evidence for emission cessations shorter than a day in the long-term monitoring data. Across the full data set, PSR B1931+24 cycles between phases on an average timescale of about \(38 \pm 5\) days [1212.0327].

The weighted wavelet Z-statistic shows short-term modulation between \(\sim 20\)–50 days but a remarkably stable long-term average periodicity. The integrated WWZ power peaks near \(\sim 0.028\,\mathrm{d^{-1}}\) (\(\sim 36\) days), with peak frequencies generally in \(\sim 0.024\)–\(0.032\,\mathrm{d^{-1}}\) (\(\sim 31\)–42 days). Data-windowing WWZ segments repeatedly recover significant (\(\geq 5\sigma\)) power at periods \(\sim 28\)–47 days, and the overall variance around the 38-day mean is \(\approx 5\) days. On average, the neutron star is radio emitting for \(26 \pm 6\%\) of the time, consistent with \(26 \pm 7\%\) from stride-fitting with \(T=100\) d windows offset by 25 d [1212.0327].

Statistical tests indicate no significant temporal evolution in the activity duty cycle, no correlation between the lengths of consecutive radio-on and radio-off intervals across nine high-cadence subsets, and no systematic intrinsic pulse-intensity variation during the radio-emitting phases. This combination of broad duration ranges, quasi-periodic cycling, and long-term stability is central to the classification of PSR B1931+24 as a long-term intermittent pulsar rather than a conventional short-nulling source [1212.0327].

A distinct statistical interpretation was proposed in which the source is described by a two-state Markov model with periodically modulated transition rates. In that framework, the non-monotonic duration histograms and the quasi-period \(T \approx 38 \pm 5\) days suggest stochastic resonance in an asymmetric bistable magnetospheric system, rather than the purely exponential residence-time distributions expected from a time-homogeneous two-state chain [1304.5803].

## 3. State-dependent rotational dynamics

The defining dynamical property of PSR B1931+24 is the stability of its two spin-down rates over the full observing baseline:
\[
\dot{\nu}_{\rm on} = -16 \pm 1 \times 10^{-15}\,\mathrm{s}^{-2}, \qquad
\dot{\nu}_{\rm off} = -10.8 \pm 0.4 \times 10^{-15}\,\mathrm{s}^{-2}.
\]
These values were determined via least-squares fits to timing residuals that explicitly model dual spin-down rates across radio-on and radio-off segments. The residual model is
\[
t_{\rm res} = \Delta\phi\,P + \frac{\Delta P}{P}\,(t - t_i) + \frac{\Delta \dot{P}_i}{2P}\,(t - t_i)^2,
\]
with \(\Delta\phi\), \(\Delta P\), and \(\Delta \dot{P}\) fitted per emission phase, and with transition-time uncertainties propagated by Monte Carlo sampling [1212.0327].

A complementary stride-fit of \(\Delta \nu\) versus radio-on duration \(t_{\rm on}\) across many three-burst windows yields a strong linear relation,
\[
\Delta \nu = \Delta \dot{\nu}\, t_{\rm on},
\]
with \(\Delta \dot{\nu} \approx -(5.2 \pm 0.2)\times 10^{-15}\,\mathrm{s}^{-2}\), reinforcing the stability of the on-state torque. From \(P=0.814\) s, the corresponding period derivatives are
\[
\dot{P}_{\rm on} \approx 1.06 \times 10^{-14}\,\mathrm{s\,s^{-1}}, \qquad
\dot{P}_{\rm off} \approx 7.15 \times 10^{-15}\,\mathrm{s\,s^{-1}}.
\]

The torque ratio between the two states is
\[
R \equiv \frac{|\dot{\nu}_{\rm on}|}{|\dot{\nu}_{\rm off}|} = \frac{16}{10.8} \approx 1.48 \pm 0.11.
\]
Assuming a canonical moment of inertia \(I = 10^{45}\,\mathrm{g\,cm^{2}}\), the spin-down powers are
\[
\dot{E}_{\rm on} \approx 7.8 \times 10^{32}\,\mathrm{erg\,s^{-1}}, \qquad
\dot{E}_{\rm off} \approx 5.2 \times 10^{32}\,\mathrm{erg\,s^{-1}},
\]
reflecting the \(\sim 50\%\) torque enhancement in the radio-on state [1212.0327].

Higher-order derivatives are not constrained: fits to \(\ddot{\nu}_{\rm off}\) do not yield significant values because of anti-correlated errors between \(\dot{\nu}_{\rm on}\) and \(\dot{\nu}_{\rm off}\) arising from finite transition-time uncertainties. Within a pulsar-wind formulation, the off state is treated as magnetic dipole braking with negligible wind contribution, while the on state adds a particle-wind torque; the measured spin-down ratio \(r \approx 1.5\) then yields model-dependent inclination angles and on-state braking indices in the range \(1.7\)–\(2.4\), depending on the accelerator prescription [1312.1016].

## 4. Radio emission in the on and off states

In the 13-year study, 12-minute averaged profiles showed \(S_{\rm on} = 40 \pm 8\,\mu\mathrm{Jy}\) and \(S_{\rm off} \lesssim 2.0 \pm 0.4\,\mu\mathrm{Jy}\) in the \(\sim 1520\) MHz Digital Filter Bank setup, implying that the radio-off phases were consistent with emission cessation. Scaled to 1400 MHz, the corresponding pseudo-luminosities are \(L_{1400,\rm on} \approx 0.84\,\mathrm{mJy\,kpc^{2}}\) and \(L_{1400,\rm off} \lesssim 0.04\,\mathrm{mJy\,kpc^{2}}\). Pulse-shape stability during on phases was supported by a first/second peak ratio of \(0.69 \pm 0.09\), with Anderson-Darling and reduced-\(\chi^{2}\) tests finding no significant deviations from normal noise behavior [1212.0327].

FAST observations revised the observational picture of the off state. Contrary to two decades of null detections, PSR B1931+24 does not fully turn off. Even after removing all obvious “bursting dwarfs,” the residual off-state integrated profile shows a significant detection with peak S/N \(\approx 5\)–10 and flux density \(\approx 1\)–2 mJy. Sporadic, narrow dwarf pulses were detected in every off-state epoch, with single-pulse S/N from 5 to 30 and flux densities \(\approx 1\)–6 mJy; the occurrence rate is typically around \(1\%\) per epoch, with 63 dwarfs out of 4055 pulses at MJD 58790 [2507.04816].

The FAST campaign also found a substantial contraction in the integrated pulse width in the off state. The on-state integrated width is \(W_{50}=10.11^{\circ}\) in the transition dataset and the catalog value is \(W_{50,\rm on}=11.46^{\circ}\), whereas the off-state value is \(W_{50}=7.57^{\circ}\). The \(W_{50}\) shrinkage is therefore \(25\%\) using FAST-on versus FAST-off, or \(34\%\) using catalog-on versus FAST-off. The mean flux density per individual pulse in the on state is \(S_{\rm mean}=120.78 \pm 15\) mJy, while off-state dwarfs have \(S_{\rm mean,off}=5.70 \pm 0.8\) mJy, giving \(S_{\rm mean,on}/S_{\rm mean,off}\approx 21\) [2507.04816].

Single-pulse statistics further show continuity rather than disjunction between the states. The single-pulse flux distributions for on-state and off-state dwarf pulses are both lognormal and overlap at their margins. Off-state dwarfs populate the full on-pulse longitude window but concentrate around the leading component A. The off-state integrated profile retains the same three-component structure, A, B, and C, at reduced intensity and contracted width. FAST also captured an off-to-on switch within one rotation: after 13 consecutive null pulses, the 14th pulse appeared abruptly with S/N \(\approx 13\), flux \(\approx 2.6\) mJy, and \(W_{50}=1.80^{\circ}\), after which the profile and intensity gradually recovered [2507.04816].

## 5. Magnetospheric interpretations

The persistent, state-dependent \(\dot{\nu}\) values and the stable \(\sim 38\)-day switching strongly indicate two global magnetospheric states: a lower-conductivity, more vacuum-like configuration in the radio-off phase with smaller torque, and a higher-conductivity, plasma-loaded, pair-producing state in the radio-on phase with larger torque. In torque terms, the standard comparison is between an approximate vacuum dipole,
\[
N_{\rm vac} \sim \frac{2}{3}\frac{\mu^{2}\Omega^{3}}{c^{3}} \sin^{2}\alpha,
\]
and a force-free magnetosphere,
\[
N_{\rm ff} \sim \frac{\mu^{2}\Omega^{3}}{c^{3}}(1+\sin^{2}\alpha),
\]
with \(\Omega=2\pi\nu\). The measured ratio \(R \approx 1.48 \pm 0.11\) sits well below the force-free/vacuum extreme, suggesting that the on-state is more conductive than the off-state but not fully force-free [1212.0327].

The long-term study argued that the year-to-year stability of both the switching timescale and the two spin-down values implies a high degree of magnetospheric memory, in spite of comparatively rapid \(\sim\)ms dynamical plasma timescales. This suggests hysteresis-like behavior in which the magnetosphere remains in a quasi-stable configuration until a slow trigger initiates a global reconfiguration. In the same framework, the additional on-state torque corresponds to an estimated plasma charge density \(\rho_{\rm plasma} \sim (1.7\text{–}5.4)\times 10^{-2}\,\mathrm{C\,m^{-3}}\), comparable to the Goldreich–Julian co-rotational value \(\rho_{\rm GJ} \approx 0.033\,\mathrm{C\,m^{-3}}\), indicating that the on-state magnetosphere achieves a substantial fraction of the nominal co-rotation density [1212.0327].

The FAST results refine, rather than overturn, this magnetospheric picture. The off state is not a vacuum state; both on and off states are better described as largely force-free, with localized acceleration and pair-cascade regions turning up or down. The narrower off-state beam, lower pair supply, and dyssynchronous component behavior support a picture of spatially inhomogeneous pair cascades in a resistive magnetosphere, with magnetic reconnection near the Y-point intermittently returning charges via the separatrix to the cap, thereby producing dwarf pulses and sustaining the faint continuous off-state emission [2507.04816].

A related torque prescription is the pulsar-wind model, in which the on-state spin-down is written as the sum of dipole and particle-wind terms. In that approach the timing-derived wind duty cycle for PSR B1931+24 is \(D_{\rm p}\approx 26\%\), matching the independently measured radio on-state duty cycle of \(26\pm 6\%\). The model also predicts \(n_{\rm off}=3\) and model-dependent \(n_{\rm on}\) values below 3, while ruling out the inverse Compton scattering induced space charge limited flow with field saturation for intermittent pulsars because it implies unrealistic parameters [1312.1016].

## 6. Alternative models, comparative context, and open questions

PSR B1931+24 inaugurated the class of long-term intermittent pulsars, with similar behavior reported for PSR J1832+0029 and PSR J1841−0500. Compared to conventional short-nulling pulsars, whose nulls are typically \(\lesssim 100\) rotations, its week-to-month emission cycles and stable torque bistability point to a more global magnetospheric phenomenon [1212.0327].

Several alternative explanations have been proposed. One is the Markov-plus-stochastic-resonance interpretation, in which the pulsar occupies two metastable states with periodically or quasi-periodically modulated transition rates. In that picture, the binary radio-emission and torque states, wide and non-monotonic duration distributions, and the \(38 \pm 5\) day quasi-period are quantitatively consistent with stochastic resonance in an asymmetric bistable magnetospheric system, possibly driven by feedback from the outer magnetosphere or return currents from an equatorial disk [1304.5803].

A distinct class of proposals invokes orbital dynamics. One paper examined whether a companion orbiting with a period of 35 or 70 days could account for the intermittent behavior and concluded that none of the large-orbit companion configurations explains the whole set of peculiar properties, especially the measured spin-down change, the lack of a measurable period change between on and off, and the absence of timing residuals expected from a massive companion [1305.6724]. A companion paper instead proposed that PSR B1931+24 may be surrounded by a stream of small bodies of kilometric or sub-kilometric sizes orbiting at close distance to the star, with the recurrence period of 70 days interpreted as the period of precession of the periastron; in that scenario, Alfvén wings from fragments near the light cylinder perturb the magnetospheric current system [1305.6726].

Another orbital interpretation treats the pulsar as a hidden ultra-compact binary. In that model, geodetic precession of the pulsar’s spin axis alters the azimuth and latitude at which the line of sight crosses the emission beam, so that timing-noise quasi-periodicity and intermittency arise from the same precessional geometry. For PSR B1931+24, the fitted residuals show rapid oscillations with period \(\approx 7\) days and slower modulation \(\approx 45\) days, and the best-fit ultra-compact orbit is \(P_b^{\ast}=0.016\) hr \(\approx 0.96\) min, although the authors explicitly note parameter degeneracies and limited data [1302.6299].

The current observational situation favors magnetospheric-state switching as the governing mechanism, while leaving the trigger mechanism illusive. Higher-cadence, broadband, and multi-messenger observations remain decisive. LOFAR, MeerKAT, and the SKA were identified as facilities that can track transitions at hourly cadence, probe spectra and polarization through transitions, collect single-pulse statistics, and coordinate high-energy coverage. FAST has already shown that sensitive observations can recover off-state emission that was previously inaccessible, suggesting that other intermittent pulsars and even nulling pulsars with detected off-state dwarfs may reveal similarly faint continuous emission when observed with sufficient sensitivity and integration [1212.0327] [2507.04816].

Source: https://www.emergentmind.com/topics/psr-b1931-24