Scientists at the University of Warwick have discovered the first white dwarf pulsar we’ve ever seen. The super-dense body is housed in an exotic binary star system 380 light-years away from Earth.
Professors Tom Marsh and Boris Gänsicke of the University’s Astrophysics Group together with Dr David Buckley from the South African Astronomical Observatory, have made astronomical history — they have identified the first white dwarf pulsar humanity has ever seen, in the neighboring system of AR Scorpii (AR Sco). Astronomers have been on the lookout for this class of pulsar for over half a century now.
Small but lively
AR Sco is only 380 light-years away from Earth, in the Scorpius constellation. It has two stars — a very rapidly spinning former star known as a white dwarf pulsar, and an actual star known as a red dwarf — locked together in a 3.6-hour orbit.
The red dwarf isn’t very noticeable in and of itself. It weighs one-third of a Solar mass (the biggest ones reach one-half of a solar mass). It ‘burns’ hydrogen just like our Sun but at a much slower rate. So it’s not particularly hot or very bright at all. Standard red dwarf across the board.
However, its choice of companions creates some spectacular interaction which brought the scientists’ attention to the system in the first place. Its neighboring pulsar isn’t much bigger than Earth, but it’s an estimated 200,000 times denser. Like other pulsars, it’s a very lively celestial body.
What sets it apart is the way it formed. Neutron stars/pulsars are the naked cores of huge stars squashed by supernovae into pure matter — they’re one huge atomic nuclei, without any empty space for electron orbits or personal space or whatnot. It’s the closest a star can get to a black hole without turning to the dark side. The white dwarf pulsar is smaller, less dense, and formed after the outer layers of a Sun-like star breezed away into a planetary nebula.
“White dwarfs and pulsars represent distinct classes of compact objects that are born in the wake of stellar death,” NASA explains.
“A white dwarf forms when a star similar in mass to our sun runs out of nuclear fuel. As the outer layers puff off into space, the core gravitationally contracts into a sphere about the size of Earth, but with roughly the mass of our sun. […] neutron stars are even denser, cramming roughly 1.3 solar masses into a city-sized sphere.”
“Pulsars give off radio and X-ray pulsations in lighthouse-like beams.”
A white dwarf pulsar, like AR Sco, doesn’t cool off into a black dwarf but retains enough energy to accelerate subatomic particles as a pulsar.
“Similar to neutron-star pulsars, the pulsed luminosity of AR Sco is powered by the spin-down of the rapidly rotating white dwarf that is highly magnetized,” the paper reads.
It has an electromagnetic field 100 million times more powerful than our planet’s and makes a full rotation in just under two minutes. Because of this gargantuan magnetic field, AR Sco acts kind of like a natural particle accelerator. We’re talking about monumental levels of energy here. Matter inside it is squashed down to extreme conditions and emits huge levels of radiation and charged particles as focused ‘beams’. These occasionally whip at its neighbor, causing the entire system to spectacularly brighten and fade every two minutes.
“The new data show that AR Sco’s light is highly polarised, showing that the magnetic field controls the emission of the entire system, and a dead ringer for similar behaviour seen from the more traditional neutron star pulsars,” Prof Marsh says.
The beams radiate outwards from the pulsar’s magnetic poles. Think of it like a huge lighthouse in space spinning really fast. Each time the beam hits the atmosphere of the red dwarf, it speeds up electrons there to almost the speed of light. This interaction is what causes the red dwarf’s brightness to flicker. It suggests that the star’s inner workings are dominated by its neighbor’s kinetic energy — an effect which has never been observed before, not even in similar types of binary stars.
“AR Sco is like a gigantic dynamo: a magnet, size of the Earth, with a field that is ~10.000 stronger than any field we can produce in a laboratory, and it is rotating every two minutes. This generates an enormous electric current in the companion star, which then produces the variations in the light we detect,” Professor Boris Gänsicke added.
The distance between the two stars is around 1.4 million kilometers — which is three times the distance between the Moon and the Earth.
The full paper ‘Polarimetric evidence of a white dwarf pulsar in the binary system AR Scorpii’, has been published in the journal Nature Astronomy. Also we are hosting this article below!
The variable star AR Scorpii (AR Sco) was recently discovered to pulse in brightness every 1.97 min from ultraviolet wavelengths into the radio regime. The system is composed of a cool, low-mass star in a tight, 3.55-hour orbit with a more massive white dwarf. Here we report new optical observations of AR Sco that show strong linear polarization (up to 40%) that varies strongly and periodically on both the spin period of the white dwarf and the beat period between the spin and orbital period, as well as low-level (up to a few per cent) circular polarization. These observations support the notion that, similar to neutron-star pulsars, the pulsed luminosity of AR Sco is powered by the spin-down of the rapidly rotating white dwarf that is highly magnetized (up to 500 MG). The morphology of the modulated linear polarization is similar to that seen in the Crab pulsar, albeit with a more complex waveform owing to the presence of two periodic signals of similar frequency. Magnetic interactions between the two component stars, coupled with synchrotron radiation from the white dwarf, power the observed polarized and non-polarized emission. AR Sco is therefore the first example of a white dwarf pulsar.
Radio pulsars, discovered nearly 50 years ago, are fast-rotating magnetized neutron stars with spin-modulated synchrotron radio emission, powered by spin-down energy loss of fast rotating neutron stars 1 . The star AR Sco was recently discovered to be a 3.56-h close binary, containing a fast-spinning (spin period P s = 117.1 s) white dwarf, showing strong brightness variations across most of the electromagnetic spectrum (ultraviolet to radio), most strongly modulated on the P b = 118.2-s beat (synodic) period, and its harmonics 2. The spin-down of the white dwarf ( ) powers non-thermal emission, whose luminosity far exceeds (by a factor of ≥14)2 the combined luminosity of the stellar components and dominates the spectral energy distribution (SED). These observations were explained in terms of beamed synchrotron radiation from the white dwarf, some of which is reprocessed by the companion star 2 . The weak X-ray emission suggests that little accretion power is produced in AR Sco, which either implies that it is currently in a propeller mass ejection phase or there is no mass transfer at all. If the former, then it would be similar to the white dwarf in the cataclysmic variable AE Aquarii 3,
We present and explain the first polarimetric study of AR Sco, which shows strong pulsed linear polarization (up to 40%), highly modulated on the spin and beat periods, and little circular polarization (a few per cent at most). We develop a model that interprets the modulated polarized emission, as well as the earlier observations 2 of the unpolarized emission, in terms of synchrotron radiation produced at two separate sites: the magnetosphere of the magnetic white dwarf, and interaction regions involving the magnetosphere of the M-star. The combined synchrotron emission from these sites produces the pulsed emission seen at both the spin and beat periods, as well as producing a synchrotron-dominated SED.
High-speed all-Stokes optical polarimetry of AR Sco was obtained using the HIPPO polarimeter 7 on the South African Astronomical Observatory (SAAO) 1.9-m telescope on two consecutive nights in March 2016 in two broad spectral bands (see Methods: Data sources). These observations revealed the system to be strongly linearly polarized, reaching levels of 40%. This is demonstrated in Fig. 1, where the flux and polarization variations in the broad red band on the first night are presented. In the Methods section, we also discuss additional observations and variations of the Stokes parameters (I, Q, U, V) on both nights. Obvious features are the strongly modulated total intensity (I) variations, found from a period analysis (discussed below) to be predominantly at the beat period and its harmonics, as previously reported 2 . The degree of linear polarization, p, shows pulse fractions up to 90%, while the position angle is seen to rotate through ∼180° at the frequency of the first harmonic of the spin or beat frequency. In contrast, the level of circular polarization is comparatively low, at a few per cent, with variations in V that are sometimes seen to be correlated with the Q, U variations, when they are most strongly modulated.
The data were subjected to a period analysis (see Methods : Period analysis), and the power spectra for the Stokes Q and U parameters are presented in Fig. 2. We see power at both the spin (ω) and beat (ω − Ω) frequencies (where ω and Ω are the spin and orbital frequencies, respectively). These results show that, as expected for a dipolar white-dwarf magnetic field, the modulation is strongest at the first harmonic of the spin period, namely 58.55 s, implying that polarized emission is seen from both magnetic poles. These results can be explained by the white-dwarf magnetic field producing a magnetically confined bipolar outflow of charged particles emitting strong linearly polarized synchrotron radiation which, together with the magnetic field of the white dwarf, sweeps across our line of sight and across the inner face of the M-star companion, where it leads to unpolarized reprocessed optical emission.
The spin-phase-folded polarimetry is shown in Fig. 3, which clearly shows the double-peaked variations of the polarized intensity, and particularly the strongly modulated (∼90% pulse fraction) linear polarization, together with the large swing in position angle through 180°, a likely consequence of viewing the dipole perpendicular to its axis. The folded data are different on the two nights, with a much higher percentage polarization and a higher pulse fraction seen on the first night. The different nature of the spin modulations on the two nights may be due to the different orbital phases of the two observations, which were at ϕ orb ≈ 0.15 and ϕ orb ≈ 0.64, respectively, although further observations over a number of orbital cycles will be needed to confirm this. Both the spin and beat modulations combine differently on the two nights, resulting in the variability of the waveforms for the phase-folded variations. Extracting the two pure spin and beat signals, as a function of orbital phase, will require more extensive observations, and likewise for discriminating between repeatable orbital modulations and stochastic effects.
In Fig. 4, we plot the average Q and U data pairs over a white-dwarf spin cycle. We draw the trajectories of their motion in the Q−U plane, which follow anticlockwise loops, and demonstrate how they vary as the magnetic orientation changes. On the first night (ϕ orb ≈ 0.15), the main peak maps to the outer circle and the secondary peak maps to the lower half of the small loop inside it. For the observation on the second night (ϕ orb ≈ 0.64), there is an apparent phase change and more complex polarized flux variations, leading to a different trajectory in the Q−U plane, possibly indicative of a variation in the magnetic field orientation over the two nights due to orbital modulation.
These Q and U variations are qualitatively similar to that seen in the optical polarimetry of the Crab pulsar 8 , although the latter’s p and θ variations show rather different morphologies, with more abrupt θ ‘swings’ than we see for AR Sco in our lower-resolution data. Although the polarized flux was not shown for the Crab in this study, the duty cycle of the light curve for the Crab is ∼30% (for a normalized intensity ≥0.1), much less than the minimum duty cycle of ∼60% seen for the polarized and total ultraviolet flux 2 in AR Sco. Also, there are a range of different θ swing morphologies observed in radio pulsars 9 , which have been interpreted in terms of a rotating vector model 10 in which the linear polarization vector (p, θ) represents a projection of the magnetic field in which the polarized radiation is produced on the plane of the sky. In this model the emission is confined to the magnetic poles, where the field lines of the dipole are essentially parallel to each other, with a small opening angle. The morphologies of Q−U ‘loop diagrams’ have been used to model other magnetic systems, for example the oblique rotator model as applied to the polarized Zeeman spectra of magnetic Ap stars 11 .
The polarization behaviour of AR Sco is quite different from the other polarized asynchronous magnetic white-dwarf binaries, namely intermediate polars, which, unlike AR Sco, are systems whose luminosity comes predominantly from accretion, with significant X-ray emission. In the nine intermediate polars for which polarization has been measured, it is typically only at the few percent level 12,13 and is predominantly circularly polarized, as expected from cyclotron emission from an accreting magnetic white dwarf. The high level of linear polarization and lower level of circular polarization are consistent with synchrotron emission, for which a maximum value for the latter of ∼15% is expected 14 .
Constraining the white-dwarf magnetic field
The lack of the usual signatures for accretion, namely flickering and strong, broad and variable Doppler-broadened emission lines, coupled with the relatively low X-ray luminosity 2 (∼5 × 1030 erg s−1), some two orders of magnitude less than a typical accreting magnetic white dwarf, is evidence that the white dwarf in AR Sco is currently not accreting, or has a very low accretion rate. The ratio of X-ray to spin-powered luminosity (α = 3.3 × 10−3; see Methods: Luminosities) indicates that the white dwarf in AR Sco is currently behaving as a rotation-powered pulsar, similar to AE Aqr 4 (see also Supplementary Fig. 8). Most of the luminosity of the system is being driven by rotational kinetic energy losses. The bulk of the spin-down power is expected to be lost by a combination of magnetic dipole radiation (see Methods: Magnetic dipole radiation; see also ref. 4 and references therein), as well as MHD interactions of the fast-rotating white dwarf’s magnetic field with the secondary star. Additional losses may also come from an outflow of relativistic charged particles from the magnetic white dwarf and a wind from the M-star companion.
The upper limit on the magnetic dipole strength can be derived assuming that the bulk of the spin-down power is radiated by dipole radiation (Poynting radiation; see Methods: Magnetic dipole radiation). So if 2 , the upper limit placed on the white-dwarf magnetic field for a maximum dipole tilt angle to the spin axis of χ = 90° is given as(the spin-down power)
where P s and R wd are the spin period and radius of the white dwarf, respectively. This value is in the regime for high-field magnetic white dwarfs, either isolated or in magnetic cataclysmic variables 15 .
Another approach 16 , assuming that a fraction of the spin-down power is dissipated through a magnetic stand-off shock near the secondary, gave an estimate of the magnetic field of ∼100 MG. If rotational energy is also dissipated through MHD pumping of the secondary star, then a constraint can be placed by estimating the MHD power dissipated in the surface layers of the secondary 17 . Dissipation will occur through magnetic reconnection and Ohmic heating, particularly in the part of the secondary star’s photosphere that faces the white dwarf. This could contribute to both the observed line emission and the strong orbital photometric modulation, which is at maximum (after removal of the spin pulsations) at ϕ orb ≈ 0.5 2 when the secondary star is at superior conjunction.
MHD pumping of the secondary allows an independent constraint to be set on the white dwarf’s surface magnetic field strength. If the white-dwarf magnetic field lines sweep periodically across the secondary star, the penetration depth of the magnetic flux into the surface layers is 17 (Methods: Spin-down torque), where η tur and ω b are the turbulent diffusivity and beat (synodic) angular frequency, respectively. For the photospheric conditions of a M-type dwarf, δ ≈ 108 cm, using 17 η tur ≤ 1015 cm2 s−1. The power dissipation of magnetic energy through reconnection and Ohmic heating can be estimated from (see for example ref. 17 and references therein).
For a 500-MG magnetic white dwarf, the field strength at the distance of the secondary (at a distance of a = 8 × 1010 cm; see Methods: Binary parameters) will be 160 G. This implies P MHD = 4 × 1031 erg s−1, which is ∼30% of the average optical luminosity of AR Sco in excess of the combined stellar contributions 2 , namely L + = 1.3 × 1032 erg s−1. The equation for power dissipation through MHD pumping can then be expressed as:
implying a dipole surface magnetic field of
where it was assumed that the secondary star fills, or nearly fills, its Roche lobe, so equals R L,2 (see Methods: Binary parameters). If other processes are also responsible for the line emission and heating of the secondary, for example beamed synchrotron radiation, dipole radiation or charged particles, all from the white dwarf, then this will lower P MHDand hence the estimate of B and B 1,* based on MHD interactions alone.
The white dwarf pulsar
We propose that the highly asynchronous binary system AR Sco contains a strongly magnetic white dwarf, probably having been spun-up to the current short rotation period (P s = 117 s) by accretion torques during a high mass-transfer phase in its history, as has also been proposed 4,
The high level of linear polarization in AR Sco is consistent with synchrotron emission of relativistic electrons in ordered magnetic fields 14 . The periodicities, at both the white-dwarf spin and the beat periods, are also consistent with this emission being produced in the white-dwarf magnetosphere, which is additionally modulated at the binary period.
The SED in AR Sco 2,21 shows a (α 1 ≈ 1.3) self-absorbed power-law spectral distribution for ν ≤ 1012−1013 Hz, that is, at infrared to radio wavelengths. We suggest that these originate from pumped coronal loops of the nearly Roche-lobe-filling secondary star 22,
At higher frequencies, ν ≥ few × 1014 Hz (optical–ultraviolet–X-ray), the SED follows a different 2 , clearly distinguishable from the spectral components of both the M5 secondary and the white dwarf, where α 2 ≈ −0.2 (also see ref. 21 ). This component is produced by non-thermal synchrotron emission from the magnetic white-dwarf dipole and shows a high level of linear polarization.power law
The absence of accretion, and hence conducting plasma, allows the induction of significant electrical potentials 29 of the order of ΔV e ≈ 1012 V in the vicinity of the light cylinder, r lc ≈ 6 × 1011(ω wd/0.054 rad s−1) cm, which is ~7.5 times greater than the orbital separation, where the white dwarf magnetic field is of the order B lc ≈ 0.4 G. This electric field can produce a relativistic wind of electrons (and ions), with energies of the order of γ e ≈ 106, which will emit synchrotron radiation at frequencies up to ν syn ≤ 3 × 1017(B lc/0.4 G)(γ e/106)2 Hz (soft X-rays) in the vicinity of the light cylinder radius. Since the whole binary system is inside the accelerator zone (that is, the light cylinder radius; see Methods: Binary parameters), this emission may be modulated at both the spin and beat periods.
If the white dwarf is an oblique rotator, with the magnetic dipole tilted relative to the spin axis, the rotating magnetosphere is expected to produce a relativistic outflowing MHD wind outside the light cylinder, with alternating regions of opposite polarity — a ‘striped’ wind 30,
The high degree of asynchronism in AR Sco (P s/P orb = 0.009) indicates a previous spin-up phase of the white dwarf, owing to a higher mass-transfer rate, similar to other highly asynchronous intermediate polar magnetic cataclysmic variables, such as AE Aqr, DQ Her, XY Ari and GK Per 33 . These systems are still undergoing mass transfer but are now likely to be in, or close, to spin equilibrium. For AE Aqr, it has been shown 34,35 that during a high mass-transfer phase the secondary star may have shed its outer envelope in a catastrophic run-away mass-transfer process, resulting in the white dwarf being spun-up to a period close to its current value of ∼33 s. There is currently no observational evidence that AR Sco has evolved through such an extreme high mass-transfer phase, and so the evolutionary path that AR Sco took to its current configuration is still an open question.
Given the high magnetic fields that we are estimating, AR Sco presents a problem when it comes to spinning up the white dwarf in the first place, since material will tend to be ejected rather than accreted, except at very high accretion rates. Since the observed white-dwarf spin-down timescale 2 of ∼107 yr is less than the spin–orbit synchronization timescale of ∼2.5 × 108 yr, calculated for MHD torques alone (Methods: Spin-down torque), this implies the bulk of the spin-down power is dissipated through magnetic dipole radiation and other channels. The high value of the magnetic field is therefore the reason for the current large spin-down rate, through the various mechanisms (for example dipole radiation, MHD interactions) we have described here, which rob the white dwarf of its angular momentum.
The strongly pulsed polarized optical emission in AR Sco is analogous to that observed in pulsars, like the Crab. The ratio α = (L x/L sd) ≈ 10−3(where L x and L sd are X-ray and spin-down luminosities) derived for AR Sco implies that most of the luminosity of the system is not produced by accretion of matter, but by spin-down energy loss, implying that the white dwarf behaves like a spin-down powered pulsar (Supplementary Fig. 8). Electric potentials ΔV of the order ∼1012 V can be induced between the white dwarf and the light cylinder (Methods: Magnetic field interactions), accelerating particles to energies of the order of γ e ≈ 106 (Methods: Pulsar-like particle acceleration), resulting in pulsed and strongly polarized synchrotron emission, possibly up to to X-ray frequencies. However, we argue that a striped relativistic MHD wind, outside the light cylinder, may also be present (Methods: Pulsar-like particle acceleration). The pulsed emission below optical frequencies (that is, radio) arises from synchrotron emission in pumped coronal loops of the secondary star, which is consistent with the observed SED2,21 . Future observations, particularly at X-ray and radio wavelengths, will be important in determining the exact nature of the emission mechanisms operating in AR Sco. More extensive time-resolved polarimetry will also help to disentangle the two closely spaced polarized signals, at the spin and beat period, leading to more definitive conclusions regarding geometry.
The data presented in this paper arise from observations taken at the SAAO using the 1.9-m telescope. High-speed photopolarimetry of AR Sco was conducted utilizing the HIPPO photopolarimeter on two consecutive nights, on 14 and 15 March 2016 (see Supplementary Table 1 for observing log). HIPPO is a two-channel all-Stokes photon-counting photopolarimeter 36 which records all observations as intensity measurements every millisecond. Rotating half- and quarter-waveplates modulate the signal at 10 Hz, and the data are accumulated in 100 bins per waveplate rotation. The Stokes parameters are then determined by a Fourier decomposition of the modulated signal — the 4θ and 8θ terms determining Q and U, and the 6θ term determining V (note that θ here should not be confused with the position angle of linear polarization). The total intensity (Stokes I) data were post-processed by summing the millisecond measurements to a time resolution of 1 s. Likewise, the 100-ms polarization arrays were summed to a time resolution of 10 s. Calibration observations of the polarized standard star 37 HD160529 were observed on both nights to determine the zero points for both waveplate angles. In addition, an observation was made of a nearby star, ∼40 arcsec northeast of AR Sco, to estimate the level of background polarization.
Simultaneous observations were undertaken in two broad wavebands defined by the convolution of the intrinsic response of the GaAs photomultipliers with the respective filters used. For both observations we used a clear fused silica filter (essentially no filter) and a Schott OG 570 glass filter, respectively, for the two channels. Channel 1 had a bandpass of 350–900 nm, while channel 2 covered 570–900 nm. All of the data were converted to Barycentric Julian Date using the accurate prescription presented elsewhere 38 . In Supplementary Figs 1 and 2 we show the variation of the Stokes parameters I, Q, U and V for the broadband filter on both nights, while in Supplementary Figs 3 to 6 we show the polarized flux (s), degree of linear polarization (p) and position angle (θ) for both nights and both filters.
The reduced HIPPO photopolarimetry was analysed using a discrete Fourier transform periodogram program. The two consecutive nights of data (14 and 15 March) were combined and power spectra derived for (i) the Stokes Q and U parameters (Fig. 2), (ii) the total and polarized intensity, (iii) the degree of linear polarization (p) and the position angle of the linear polarization: that is, the E-vector (θ). The periodograms suffer from significant aliasing due to the relatively short spin (117.1 s) and beat (118.2 s) periods, which are unresolved on single nights, and because of the ∼24-h data gap, which results in ambiguity in cycle count.
Just as was seen in the original study 2 for the g′ band variability, the total intensity (I) varies predominantly at the beat frequency and its first harmonic (Supplementary Fig. 7, right panels), with the latter being the stronger of the two. In addition, the harmonic of the spin frequency is also clearly seen, but at a lower power than for the beat harmonic. The power spectra of the ultraviolet light curves derived from the Hubble Space Telescope observations 2 , although strongly aliased, clearly show that the power in the first harmonics of the spin and beat frequencies are approximately equal, implying that the white dwarf’s magnetic field is directly (through beaming) or indirectly (through reprocessing) modulating the ultraviolet emission. In the case of the polarized flux (Supplementary Fig. 7, left panels), we see a broad spread of power at the first harmonic, consistent with power at both spin and beat harmonic frequencies. In the case of the third harmonics, the spin component (4θ) dominates, at 29.3 s. The fact that the power of the spin-modulated polarized flux and p is less than for the beat modulation is attributed to the modulation of I occurring at two closely spaced periods (beat and spin), while Q and U vary predominantly at the spin period. Thus any calculation involving Q, U and I (as for p) will introduce some additional power at the beat period.
AR Sco consists of a magnetic white dwarf and an M5 dwarf star orbiting one another with an orbital period of P orb = 3.56 h. The pulsations observed from the ultraviolet to the radio show a double-peaked pulse profile, predominantly at the beat period P b, implying that the secondary star must be a site for spin-modulated reprocessing. Furthermore, narrow line emission is seen which clearly follows the orbital motion of the secondary star and is situated near the L1 point. Based on the limits placed, the white dwarf has a mass of M 1 ≈ 0.8 M☉, while the secondary star has a mass of about M 2 ≈ 0.3 M☉ and therefore a mass ratio of q = (M 2/M 1) = 0.375. Sinusoidal variations in the optical/infrared light suggest that the secondary star is being irradiated, with its hotter/brighter side facing the white dwarf, which is best seen at orbital phase ϕ orb = 0.5 (superior conjunction of the secondary).
Assuming that the secondary is close to filling its Roche lobe, then the standard relationship 39 between the Roche-lobe size of the secondary (R L,2) and binary separation (a), applicable to binaries in the range 0.3 < q < 20 is given by R L,2/a = 0.38 + 0.2 log q. For AR Sco (q = 0.375), the orbital separation . Thus the Roche-lobe radius of the secondary star is estimated to be RL,2 ≈ 0.3a ≈ 2.53 × 1010 cm. The distance, b1, of the L1 region from the white dwarf primary can be estimated from the relation (for 0.1 < q < 10) 40 , resulting in b1 ≈ 0.6a ≈ 5 × 1010 cm. In comparison, the radius of the light cylinder, where the white dwarf’s magnetosphere co-rotates with the speed of light (c = ω wd r lc), is of the order of r lc ≈ 6 × 1011(ω wd/0.054 rad s−1)cm, implying that the binary system is inside the light cylinder of the white dwarf pulsar.
It has been found 2 that the white dwarf in AR Sco is currently spinning down on a timescale of . The spin-down luminosity, assuming a white dwarf, is of the order of (where I is the moment of inertia). The X-ray luminosity is L x = 4.9 × 1030 erg s−1, implying . This is very similar to the ratio found in spin-powered pulsars as well as the white dwarf in the cataclysmic variable system AE Aquarii (Supplementary Fig. 8), which has a ratio α ≈ 10−3, where L x ≈ 5 × 1030 erg s−1 and (see for example refs 4,5,26).
Magnetic dipole radiation
The luminosity coming from magnetic dipole radiation (also known as Poynting flux) in AR Sco is given as:
where B 1,*, ω wd, R wd and χ represent the surface polar field of the white dwarf, the white dwarf’s spin angular velocity and radius, and the angle between the spin and magnetic axes. For our calculations of luminosities we used the Hamada–Salpeter relation to determine that the white dwarf has a radius of.Re-arranging this equation to determine the magnetic field strength gives:
It has been shown 41,
The total magnetic torque exerted on the secondary star, 17 η tur ≤ 1015 cm2 s−1, the magnetic torque exerted on the secondary star is of the order . The resulting timescale for spin-synchronization through MHD torques for a 500-MG white dwarf is therefore t syn ≈ 2.5 × 108 yr. This supports the notion that the magnetic dissipation in the thin surface layers of the secondary star (δ ≈ 0.004R L,2) will contribute to the dissipation of rotational kinetic energy of the white dwarf, together with other mechanisms such as magnetic dipole radiation. This will eventually lead to the synchronization of the two stars during the current low mass accretion phase. When accretion eventually switches on, once the M-star re-attaches to the Roche lobe, then AR Sco will become a synchronized magnetic cataclysmic variable, or polar, consisting of a highly magnetized white dwarf rotating synchronously with its M5 secondary companion., results in a synchronization timescale which is given by t syn = Iω b/TD, where I is the moment of inertia of the white dwarf, which is of the order of I ≈ 1.5 × 1050 g cm2. If we assume a 500-MG dipolar magnetic field for the white dwarf (the upper limit derived from the dipole radiation), the field strength at the distance of the secondary star is B b1 ≈ 160 G. For δ ≈ 108 cm, using
Magnetic field interactions
It has been demonstrated 17 that mass-transferring secondary stars with orbital periods in the range P orb = 3−4 h can have surface polar magnetic fields of the order of B ≈ 3,000 G, which implies that the M5 secondary star of AR Sco will most probably be magnetically active. This is supported by MHD modelling in convective envelopes of dwarf stars22 . This provides a mechanism for explaining the observed SED of AR Sco below ν ≈ 1013 Hz in terms of magnetic energy dissipation in the field of the secondary star.
The field-aligned electric potentials in the M-star magnetic flux tubes are of the order of
where we have assumed that ΔB ⊥ → B b1 ≈ 700 G represents the perturbation induced in the coronal loops, or flux tubes, of the secondary as a result of the white-dwarf field periodically pushing against it. These coronal structures will be periodically perturbed, pushed sideways by the rotating white-dwarf field and generating a ‘fracture zone’ which will induce large field-aligned potentials that can accelerate charged particles 26 .In these interactions, the magnetic pitch can increase γ ϕ = (ΔB ⊥/B) → 10 (see for example refs 44,45) before the fields become unstable to reconnection. It should be mentioned that the magnetic field perturbation is still below the maximum magnetic field near the poles of the secondary, which can be of the order of 3,000 G (see for example ref. 17 ). Electrons with energies of the order of γ e ≤ 400 trapped in pumped coronal fields of the order of 〈B cor〉 ≈ 100 G (at a distance from the secondary surface of ∼2R 2) will radiate synchrotron radiation at frequencies up to , in the infrared to radio regime.
Pulsar-like particle acceleration
For AR Sco, electrical potentials of the order
can be induced between the white dwarf and the light cylinder 29 , where the white-dwarf magnetosphere co-rotates at the speed of light (c = ω wd r lc). For AR Sco, the light cylinder radius is of the order of r l c ≈ 6 × 1011(ω wd/0.054 rad s−1) cm. Since this electric field is several orders of magnitude stronger than gravity, charged particles such as electrons can be pulled from the surface of the white dwarf and accelerated to relativistic energies 46 , of the order of γ e ≈ 106, resulting in synchrotron emission up to frequencies of the order of
with peak emission occurring at ν c ≈ 0.3ν syn ≈ 3 × 1017 Hz, in the X-ray regime.Additionally, outside the light cylinder, the fast-rotating magnetosphere will turn into a relativistic magnetohydrodynamic ‘striped’ wind (see refs 30,
A characteristic of the synchrotron radiation from the striped wind outside the light cylinder radius is the fact that the toroidal magnetic field component oscillates in the same sense as the rotating pulsar, which results in pulsations at both the fundamental and first harmonic of the spin period. The emission is also expected to be polarized, emitting both linear and a small component of circular polarized light 32. Applied to the Crab pulsar, numerical simulations of the expected pulse profiles produced by a striped wind exactly mimic the observed pulse profiles, together with the position angle swings through 180°. The observed polarized pulse profiles of AR Sco (Figs 3 and 4), especially near orbital phase Φo ≈ 0.15, mimic that of the Crab pulsar, perhaps implying that a striped pulsar wind is active in AR Sco. The fact that the striped wind occurs in a binary system may further introduce a beat frequency in the pulsations.
Both these processes, namely synchrotron emission in the vicinity of the light cylinder, or outside in the striped pulsar-like wind, can account for the nature of the polarized pulsed emission seen in optical light curves of AR Sco. Both processes can explain the polarization as a signature of synchrotron radiation, pulsed at both the white-dwarf spin period and the beat (synodic) period.
The data used to produce the plots in this paper and other findings of this study are available from the corresponding author upon reasonable request. All of the reduced HIPPO photopolarimetry is available (in ASCII format) on the SAAO CloudCape website for downloading at: https://cloudcape.saao.ac.za/index.php/s/npMF46F1K56fsPt.
How to cite this article: Buckley, D. A. H. et al. Polarimetric evidence of a white dwarf pulsar in the binary system AR Scorpii. Nat. Astron. 1,0029 (2017).
For D.A.H.B., P.J.M. and S.B.P., this work was supported by the National Research Foundation of South Africa. T.R.M. was supported by the Science and Technology Facilities Council (STFC) under grant ST/L000733. B.T.G. is supported through European Research Council grant 320964. This work is based on observations obtained at the SAAO.