An irradiated brown-dwarf companion to an accreting white dwarf
Brown dwarfs and giant planets orbiting close to a host star are subjected to significant irradiation that can modify the properties of their atmospheres. In order to test the atmospheric models that are used to describe these systems, it is necessary to obtain accurate observational estimates of their physical properties (masses, radii, temperatures, albedos). Interacting compact binary systems provide a natural laboratory for studying strongly irradiated sub-stellar objects. As the mass-losing secondary in these systems makes a critical, but poorly understood transition from the stellar to the sub-stellar regime, it is also strongly irradiated by the compact accretor. In fact, the internal and external energy fluxes are both expected to be comparable in these objects, providing access to an unexplored irradiation regime. However, the atmospheric properties of such donors have so far remained largely unknown. Here, we report the direct spectroscopic detection and characterisation of an irradiated sub-stellar donor in an accreting white dwarf binary system. Our near-infrared observations allow us to determine a model-independent mass estimate for the donor of and an average spectral type of , supporting both theoretical predictions and model-dependent observational constraints. Our time-resolved data also allow us to estimate the average irradiation-induced temperature difference between the day and night sides on the sub-stellar donor, K, and the maximum difference between the hottest and coolest parts of its surface, of K. The observations are well described by a simple geometric reprocessing model with a bolometric (Bond) albedo of at the 2- confidence level, consistent with high reprocessing efficiency, but poor lateral heat redistribution in the donor’s atmosphere[4, 5].
Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK
Department of Physics and Astronomy, University of Sheffield, S3 7RH, UK
The School of Physics and Astronomy, The University of Manchester, Manchester, UK
Instituto de Astrofísica de Canarias, E-38205 La Laguna, Santa Cruz de Tenerife, Spain
Department of Physics, University of Warwick, Coventry CV4 7AL, UK
Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, OX1 3RH, Oxford, UK
Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK
Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
Only a single brown dwarf donor to an accreting white dwarf has been detected spectroscopically to date, and no empirical information at all is available regarding the effect of irradiation on the donor’s atmosphere. We have therefore carried out simultaneous optical and near-infrared time-resolved spectroscopy of one such system with the X-Shooter instrument at the Very Large Telescope (ESO). Our target, SDSS J143317.78+101123.3 (J1433 hereafter), is an eclipsing system with a short orbital period ( min) and a likely donor mass well below the hydrogen-burning limit, as estimated from eclipse modelling ([8, 9]). The exceptionally wide wavelength coverage provided by our data set (0.35 m - 2.5 m) allows us to confidently dissect the overall spectral energy distribution. This is illustrated in Fig. 1. Disk-formed, double-peaked hydrogen emission lines can be seen across the entire spectral range. The presence of broad Balmer absorption lines between 0.3 m and 0.5 m shows that the white dwarf is the strongest emitter in this wave band. However, the donor star spectrum is clearly visible in the near-infrared and dominates between 1.0 m and 2.5 m.
The clear donor signature in the near-infrared allows us to isolate the donor’s spectrum and determine its properties. We decomposed the average spectrum by fitting the optical region with a white dwarf atmosphere model and an accretion disc (modelled as a simple power law). Both of these contributions were then extrapolated to the near-infrared and subtracted in order to retrieve a pure donor spectrum. This donor spectrum was then compared to an empirical brown dwarf spectral sequence. The best-matching spectral type was found to be SpT=L11, which agrees remarkably well with semi-empirical evolutionary predictions[1, 2] and with previous narrow J-band estimates.
These results imply that the donor in J1433 has successfully undergone the transition from the stellar to the sub-stellar regime. The alternative – that the secondary was born as a brown dwarf – is extremely unlikely. First, extreme mass-ratio binary systems containing very low mass objects ( M) are intrinsically rare . Second, the mass of the accreting white dwarf in J1433, M M, is exactly in line with the mean white dwarf mass of known accreting white dwarf systems going through the standard evolution channel, but significantly higher than the average mass of isolated white dwarfs ( M M) and that of any known primary in a white dwarf-brown dwarf binary system. Third, the orbital period of J1433 lies squarely within the “period minimum spike” that coincides with the stellar to sub-stellar transition of the donor star in systems born with main-sequence companions. By contrast, systems born with sub-stellar donors would be expected to populate a wide range of orbital periods below this spike. However, no such systems have ever been found. Indeed, the only accreting white dwarf with a sub-stellar donor and an orbital period well below has been shown to be a low-metallicity object in the Galactic halo, rather than a system born with a brown dwarf secondary.
Models of irradiated planets suggest that irradiation can increase photospheric temperatures by an order of magnitude compared to an isolated object, with significant effects on the planet’s radius and atmospheric structure. Furthermore, a long-standing mismatch between the predicted and observed minimum period for accreting white dwarf binary systems can be traced to a % offset between the donor radii inferred from observations and those predicted by theoretical model atmospheres. However, such large effects are only possible if the irradiating flux is efficiently absorbed in the atmosphere and redistributed across the terminator, i.e. from the day-side to the night-side[2, 20]. This is necessary since it is the blocking effect of the incoming radiation on the outward heat flux from the secondary’s interior that drives the irradiation-induced swelling of the donor.
Globally, the bolometric flux emitted by the irradiated donor must always balance the sum of its intrinsic flux and the irradiation flux it has absorbed. However, in the absence of redistribution, this balance must be maintained locally in the atmosphere. This should produce pronounced temperature differences between the day- and night-sides on the tidally-locked donor. Since the system is seen close to edge-on, such differences should manifest as changes in the apparent spectral type of the donor as a function of orbital phase. We have tested for this by measuring the HO 1.3 m band index. Water vapour is the most sensitive absorber in irradiated hot Jupiters, and water band strength has been shown to correlate well with spectral type and effective temperature. As shown in Fig. 2b, we detect a spectroscopic change of SpT (i.e. M9-L0), with a maximum at phase 0.5, precisely where the day-side of the donor is exposed.
On its own, this spectroscopic signal would be only marginally significant, as a model without irradiation can be ruled out at only a 2 confidence level. However, an independent irradiation signature is provided by the observed broad-band flux variations around the orbit, which are shown in Fig. 2c. This figure reveals a double modulation over one orbit, which is produced by the combination of two effects: the distorted shape of the tidally-locked, Roche-lobe-filling donor star (ellipsoidal variations) and the temperature difference between its day- and night-side (irradiation effect). In order to quantify the irradiation effect, we used the binary light curve synthesis code icarus to fit both the water-band and broad-band modulations under the assumption of no heat redistribution between hemispheres. As shown in Fig. 2, the resulting fit is acceptable and provides a plausible representation of the temperature distribution across the surface of the donor. The average temperature of the day-side is K, and a night-side temperature of K. These numbers are consistent with the mean donor temperature obtained from the template-calibrated spectral type measurements.
The observed difference between the day-side and night-side fluxes is statistically significant and allows us to estimate the reprocessing efficiency of the donor. This efficiency is usually parametrised via the bolometric (Bond) albedo, , which is the fraction of the incident irradiation flux that is not reprocessed, but reflected back into space. The irradiating source in the system is the hot white dwarf. We therefore obtained an improved measurement of its temperature, K, by making use of ultraviolet observations obtained by the GALEX satellite. With this, we find at 2- confidence, as shown in Extended Figure 1. This low value implies a high reprocessing efficiency in the atmosphere of the donor. We can also use the observed difference between day-side and night-side fluxes to estimate the efficiency with which radiation absorbed locally is redistributed across the donor, (see Methods). We find a limit for the redistribution efficiency of at 2- confidence. Efficient reprocessing, coupled with poor heat redistribution, has also been found in hot Jupiters in this atmospheric temperature regime  and suggested for low-mass stars in accreting white dwarfs. If irradiation is the main cause of the larger-than-predicted donor radii, efficient heat redistribution is required. Our finding that day-side to night-side heat transfer must be modest therefore suggests that irradiation is unlikely to be responsible for inflating the donors. Instead, the dominant effect of irradiation is simply an increase in the local temperature.
In most hot Jupiters, the external irradiation overwhelms any internal heat flux. The relatively milder irradiation experienced by the donor in J1433, coupled with the unique prospect of obtaining detailed phase-resolved spectra and line profiles, will permit quantitative tests of irradiated model atmospheres in a regime where these observables are expected to be quite sensitive to irradiation. The system also provides an independent new benchmark for theoretical models that predict the albedo and heat redistribution efficiency in irradiated planetary atmospheres . Finally, the donor in J1433 is a rapid rotator ( km s), which could have interesting and significant effects on its atmospheric dynamics.
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Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 085.D-0489. J.V.H.S acknowledges support via studentships from CONACyT (Mexico) and the University of Southampton, as well as research support by the Royal Astronomical Society. R.P.B. has received funding from the European Union eleventh Framework Programme under grant agreement PIIF-GA-2012-332393. BTG was supported by ERC Grant Agreement n. 320964.
C.K., S.P.L., V.S.D, B.T.G, T.R.M, M.L.P. and J.S proposed and planned the observations. All data analysis was done by J.V.H.S with significant feedback from C.K., R.P.B. and S.P.L. All authors discussed the results and commented on the manuscript.
Correspondence and requests for materials should be addressed to J.V.H.S.
The authors declare that they have no competing financial interests.
.1 Code Availability.
The code used to generate the model, as well as the atmosphere templates, icarus, is available at https://github.com/bretonr/Icarus.
.2 Mass Determination
We performed a radial velocity analysis on the the 1.243 m and 1.252 m Ki absorption lines formed in the atmosphere of the donor. The trailed spectrum of these features is shown as the inset in Fig. 1. We performed a simultaneous fit to both lines and found the best values for the semi-amplitude km s, the systemic velocity km s and the rotational broadening km s. When combined with the observed value for the radial velocity semi-amplitude of the WD, km s , this allows us to derive a purely dynamical estimate of the mass ratio of the system, . For this mass ratio, the occurrence of WD eclipses alone sets a firm lower limit on the inclination of . We can then use the mass function of the secondary, , where is the gravitational constant, to set a purely dynamical 2 upper limit on the mass of the donor star, . We can also use the mass function to obtain a model-independent estimate of the donor mass. In any semi-detached compact binary system, there is a unique, single-valued family of pairs that produce a compact object eclipse with a given width. In the case of J1433, the WD eclipse width can be measured directly from published optical light curves. We can then combine the resulting constraint with our spectroscopic mass ratio and the mass function to obtain a robust donor mass estimate that depends only on Kepler’s third law and the well-understood geometry of Roche-lobe-filling objects. We find M M, well below the hydrogen-burning limit.
.3 Water-band ratios and broad-band fluxes.
In order to provide the cleanest measurements of the donor at any given phase, we subtracted both white dwarf and accretion disc contributions. The flux observed from the white dwarf was assumed to be constant in phase, except for phase bins affected by an eclipse. In these, we reduced the flux by the fraction of the bin width during which the white dwarf was occulted. The accretion disc contribution was modelled by fitting a power-law to the optical (3200–5400 Å) waveband (while masking the emission lines) and extrapolating to the NIR. Due to the low S/N of the individual spectra, the telluric removal created artefacts in some regions of the spectra. We identified these regions and masked them before shifting each spectrum to the donor’s rest frame. We binned the data into eight orbital phase bins and measured a slightly modified water-band index, defined as , where the fluxes are averages over a 5 Å window. This index was then calibrated against brown dwarf spectral type templates. Errors were estimated via 500 bootstrap copies of the median flux inside every orbital bin for all the spectra. The broad-band flux modulation was estimated by integrating the donor flux over the -band (after masking all emission lines) and converting to AB magnitudes.
.4 Day- and night-side temperatures, albedo and intrinsic luminosity.
In order to model the orbital-phase-dependent water band ratios and broad-band flux, we constructed a grid of irradiated donor models with icarus. Each of these models is characterized by two parameters: the irradiating luminosity absorbed by the donor, and the intrinsic luminosity it would produce in the absence of irradiation. For each parameter pair, we use icarus to calculate the resulting temperature distribution across the donor and to predict the observed spectrum at each orbital phase. These calculations assume that all of the irradiating flux absorbed at a given point on the donor’s surface is re-emitted locally and neglect any effect of the donor’s fast rotation on the temperature distribution (which could affect the atmospheric dynamics). However, the distorted shape of the Roche-lobe-filling donor, as well as limb- and gravity-darkening, are fully taken into account in these calculations. The absorbed irradiating and intrinsic luminosities are not directly observable, but they respectively determine the day-side and night-side temperatures, which are. We therefore present our results in terms of these temperatures, which we calculate by summing over all day-side surface elements in the model,
and all night-side elements,
Here, is the intrinsic flux and is given by
where is the area of the surface element, and is the Stefan-Boltzmann constant. As a consequence of the distorted shape of the donor, – the temperature of each surface element in the absence of irradiation – is not constant. Similarly, the total flux that heats each surface element on the day-side, , is given
where is the bolometric (Bond) albedo of the donor. is the irradiating flux seen by this element, given by
Here is the distance of every surface element to the white dwarf, is the white dwarf temperature and is the projected surface intercepting the irradiating flux. Since we have good estimates of the white dwarf temperature and binary parameters, is well-constrained observationally. Thus the absorbed irradiating flux and the day-side temperature can equivalently be thought of as measures of the albedo. We determine optimal values of , , and by fitting the observed phase-dependent water-band and broad-band fluxes using a Markov-Chain Monte Carlo procedure. The results are shown in the Extended Data Figure 1. We find K and K, where the errors represent the 1 confidence levels. The corresponding constraints on the albedo and intrinsic donor luminosity are (at 2-) and . In all of these models, we adopt a white dwarf temperature of K, based on our own analysis of ultraviolet data obtained by GALEX, for the inclination, pc for the distance, and min for the orbital periods, based on previous eclipse modelling estimates. We also adopt a fixed gravity-darkening coefficient of . z
.5 Heat Redistribution Across the Terminator.
Our geometric reprocessing model assumes that none of the irradiating flux is redistributed from the day-side to the night-side. This model fits the data acceptably, suggesting that redistribution is inefficient in the atmosphere of the donor. In order to estimate this efficiency quantitatively, we need to adopt a specific model for redistribution. Here, we assume that a constant fraction of the irradiating flux that is absorbed at any point on the day-side of the donor is redistributed evenly across the entire surface. Similar models are commonly used in studies of irradiated exo-planets . In the context of this simple model, the difference between the fluxes emerging from the day-side and the night-side is given by
where is the flux difference of the equivalent model without any redistribution. The modelling described in the previous section provides us with a set of set of self-consistent flux differences for models with . We can therefore transform these to the flux differences predicted for otherwise equivalent models with . Since our earlier modelling also provides us with estimates of the observed day-side and night-side temperatures, we can estimate by comparing the observationally inferred flux difference to that predicted by our transformed models with . The results are shown in Extended Figure 2. We find that the efficiency of redistribution is indeed low, , with higher values corresponding to lower albedos. The 2 upper limit on the redistribution efficiency (for ) is .
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