A low-mass planet around a white dwarf
Numerous exoplanets have been detected around Sun-like stars. These stars end their lives as white dwarfs, which should inherit any surviving planetary systems. Manser et al. found periodic shifts in emission lines from a disc of gas orbiting around a white dwarf (see the Perspective by Fossati). They used numerical simulations to show that the most likely explanation for the spectral shifts is a low-mass planet orbiting within the disc. The planet must be unusually small and dense to avoid being ripped apart by tidal forces. The authors speculate that it may be the leftover core of a planet whose outer layers have been removed.
Abstract
Many white dwarf stars show signs of having accreted smaller bodies, implying that they may host planetary systems. A small number of these systems contain gaseous debris discs, visible through emission lines. We report a stable 123.4-minute periodic variation in the strength and shape of the Ca ii emission line profiles originating from the debris disc around the white dwarf SDSS J122859.93+104032.9. We interpret this short-period signal as the signature of a solid-body planetesimal held together by its internal strength.
More than 3000 planet-hosting stars are known (1), the vast majority of which will end their lives as white dwarfs. Theoretical models indicate that planetary systems, including the Solar System, can survive the evolution of their host star largely intact (2–4). Remnants of planetary systems have been indirectly detected in white dwarf systems via (i) the contaminated atmospheres of 25 to 50% of white dwarfs, arising from the accretion of planetary material (5, 6); (ii) compact dust discs (7, 8), formed from the rubble of tidally disrupted planetesimals (9, 10); and (iii) atomic emission lines from gaseous discs colocated with the circumstellar dust (11, 12). The most-direct evidence for remnant planetary systems around white dwarfs is provided by transit features in the light-curve of WD 1145+017, which are thought to be produced by dust clouds released from solid planetesimals orbiting the white dwarf with a period of
The gaseous components of debris discs identified around a small number of white dwarfs enable us to probe the underlying physical properties of the discs. Double-peaked emission profiles are observed in a number of ionic transitions, such as the Ca ii 850- to 866-nm triplet, indicating Keplerian rotation in a flat disc (19). Previous repeat observations of the gaseous debris disc at the white dwarf SDSS J122859.93+104032.9 (hereafter SDSS J1228+1040) have revealed long-term variability—on a time scale of decades—in the shape of the emission lines (20), indicating ongoing dynamical activity in the system.
We performed short-cadence spectroscopy (a cadence of 100 to 140 s) targeting the Ca ii triplet in SDSS J1228+1040 on 20 and 21 April 2017 and again on 19 March, 10 April, and 2 May 2018. Our observations were conducted with the 10.4-m Gran Telescopio Canarias [(GTC) on La Palma, Canary Islands], with the goal of searching for additional variability on the Keplerian orbital time scales within the disc, which are on the order of hours (21). We detected coherent low-amplitude
Five hundred nineteen spectra of SDSS J1228+1040 were taken over two nights in 2017 [(A) to (C)] and three nights in 2018 [(D) to (F)]; see table S1 for a log of observations. (A and D) Averaged, normalized spectrum of the Ca ii triplet. (B and E) Phase-folded trailed spectrograms using a 123.4-min period (one cycle is repeated for display). The color map represents the normalized flux. Subtracting the coadded spectrum from the phase-folded trailed spectrogram (done separately for each year) illustrates the variability in both flux and wavelength on the 123.4-min period in all three components of the Ca ii triplet (C and F). The dashed black curve is not fitted to the data but simply illustrates the typical S-wave trail for a point source on a circular orbit with a semimajor axis of
The equivalent widths [(EWs), a measure of the strength of the lines relative to the continuum] of the Ca ii triplet profiles are shown in Fig. 2 along with the ratios of blueshifted to redshifted flux throughout the 123.4-min period. This illustrates the variation in the overall brightness of the emission lines and the strong asymmetry of the velocity of the additional flux. The variable emission shown in Fig. 1, C and F, alternates (moves) from redshifted to blueshifted wavelengths as a function of phase. Assuming that the additional, variable emission is generated by gas in orbit around the white dwarf, this indicates that we observe emission only when the additional gas is on the far side of its orbit around the white dwarf, with respect to our line of sight. This additional emitting region is obscured, either by the disc or the region itself, when the material is traveling in front of the star, where we would otherwise observe the blueshifted-to-redshifted transition. We fitted sinusoids to both the EW and blue-to-red ratio data, finding them to be offset in phase by 0.14 ± 0.01 cycles and 0.09 ± 0.01 cycles in 2017 and 2018, respectively. These phase shifts imply that the maximum EW is observed when the region emitting the additional flux is at its maximum visibility and thus furthest from us in its orbit around the white dwarf, whereas the maximum blueshifted emission occurs up to 0.25 cycles afterward, once the region has orbited into the visible blueshifted quadrant of the disc. The smoothness of the EW and blue-to-red ratio variations, along with the extent in orbital phase
Equivalent width (EW) (A and C) and blue-to-red ratio (B and D), which is the ratio of blueshifted to redshifted flux centered on the air wavelengths of the Ca ii triplet in the rest frame of the white dwarf at +19 km s−1, with the mean set to 1.0. The data are phase-folded on a 123.4-min period [one cycle repeated for clarity (21)] for the 2017 [(A) and (B)] and 2018 [(C) and (D)] datasets. The EWs and blue-to-red ratios for the 8498-, 8542-, and 8662-Å components of the Ca ii triplet are colored (marked) in black (circles), magenta (squares), and orange (triangles), respectively. The data are averaged over the three profiles and fitted with a sinusoid (green curves). The EW and the blue-to-red ratio curves are offset in phase by 0.14 ± 0.01 cycles (49° ± 4°) and 0.09 ± 0.01 cycles (31° ± 5°) for the 2017 and 2018 profiles, respectively. Phase zero for both the 2017 and 2018 datasets has been shifted such that the fit to the 2017 EW data passes through zero at zero phase, and the vertical dashed lines denote the phases 0.5, 1.0, and 1.5. Error bars indicate the standard error of the data.
Several scenarios could plausibly explain the short-term emission detected from SDSS J1228+1040 (see supplementary text): (i) A low-mass companion could be found, with Ca ii emission originating from the inner hemisphere irradiated by the white dwarf. This would naturally match the observed phase dependence (22). However, radial velocity measurements rule out the presence of any companion with mass greater than 7.3 MJ (where 1 MJ, the mass of Jupiter, is 1.90 × 1027 kg) (21), and the nondetection of hydrogen in the accretion disc excludes brown dwarfs and Jupiter-mass planets. (ii) Vortices have been invoked to explain nonaxisymmetric structures detected in submillimeter observations of protoplanetary discs (23). The presence of a weak magnetic field is expected to destroy any vortex that forms within a few orbital cycles. Although our observations place only an upper limit on the magnetic field of the white dwarf B < 10 to 15 kG (21), the field strength required within the disc at SDSS J1228+1040 to render vortices unstable is 10 μG to 50 mG. This field strength can be reached rapidly, owing to the exponential growth rate of the magnetic field in the disc (21), and we therefore rule out the presence of long-lived vortices in the disc. (iii) The photoelectric instability (24) can possibly produce arc-shaped structures within a disc. However, these structures vary in both radial location and shape within the disc on the time scale of months, so we reject this scenario. (iv) A planetesimal orbiting in the disc and interacting with the dust could generate the detected gas (Fig. 3). We exclude (i) to (iii) as possible scenarios, and thus argue that (iv) is the most plausible explanation for the coherent short-term variation detected in the Ca ii triplet lines at SDSS J1228+1040.
(A) Top-down view of the disc around SDSS J1228+1040 with a planetesimal orbiting within the disc, assuming circular orbits. Both the disc and the planetesimal orbit clockwise, as indicated by the curved arrow. Lines of sight for specific phases from Fig. 1 are denoted by the straight arrows. The solid red region of the disc indicates the location of the observed Ca ii triplet emission, and the gray curved line trailing the planetesimal shows the azimuthal extent
The short period of the orbit around SDSS J1228+1040 requires any planetesimal to have a high density or sufficient internal strength to avoid being tidally disrupted by the gravity of the white dwarf. By contrast, the debris fragments orbiting WD 1145+017 are detected on orbits consistent with the tidal disruption radius of a rocky asteroid (13). Assuming that the body in orbit around SDSS J1228+1040 has no internal strength and that its spin period is tidally locked to its orbital period, we calculate the minimum density needed to resist tidal disruption on a 123.4-min period as 39 g cm−3 for a fluid body deformed by the tidal forces (21). If the body has enough internal strength to remain spherical, then the minimum density required is reduced to 7.7 g cm−3, which is approximately the density of iron at 8 g cm−3 (however, the internal strength could be greater and the density lower). We therefore conclude that the body in orbit around SDSS J1228+1040 needs some internal strength to avoid tidal disruption, and we calculate bounds on the planetesimal size, s, as 4 km < s < 600 km, with an uncertainty of 10% (21).
What is the origin of the planetesimal? This object may be the differentiated iron core of a larger body that has been stripped of its crust and mantle by the tidal forces of the white dwarf. The outer layers of such a body would be less dense and would disrupt at greater semimajor axes and longer periods than those required for core disruption (25). This disrupted material would then form a disc of dusty debris around SDSS J1228+1040, leaving a stripped corelike planetesimal orbiting within it.
Whether the variable emission originates from interactions with the dusty disc or from irradiation of the surface of the planetesimal remains unclear. Small bodies are known to interact with discs and induce variability in spatially resolved discs; one such object is the moon Daphnis, which produces the Keeler gap in the rings around Saturn (26, 27). Some debris discs around main-sequence stars show evidence of gas generated after the main phase of planet formation (28). The origin of this nonprimordial gas is uncertain, but it could be generated by collisional vaporization of dust (29) or collisions between comets (30). If the body is not interacting with the disc to generate the additional gas, then the planetesimal must be producing the gas. The semimajor axis of the planetesimal,
We hypothesize that gaseous components detected in a small number of other white dwarf debris discs (11, 31) may also be generated by closely orbiting planetesimals. Although sublimation of the inner edges of debris discs (32) and the breakdown of 1- to 100-km rocky bodies (33) have been proposed to explain gaseous debris discs at white dwarfs, not all metal-polluted white dwarfs with high accretion rates and/or large infrared excesses host a gaseous component. The Ca ii triplet emission profiles from the gaseous debris disc around SDSS J1228+1040 have shown variability over 15 years of observations [(20), see also Fig. 1, A and D]. This emission can be modeled as an intensity pattern, fixed in the white dwarf rest frame, that precesses with a period of
The gaseous disc has been present at SDSS J1228+1040 for at least 15 years (20), implying that the planetesimal has survived in its current orbit for at least that long. A planetesimal on an eccentric orbit that precesses owing to general relativity could explain the observed precession of a fixed intensity pattern. In this scenario, the planetesimal would need an eccentricity
Supplementary Materials
www.sciencemag.org/content/364/6435/66/suppl/DC1
Materials and Methods
Supplementary Text
Figs. S1 to S8
Tables S1 to S3
This is an article distributed under the terms of the Science Journals Default License.
