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A measurement of the wind speed on a brown dwarf

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Science  10 Apr 2020:
Vol. 368, Issue 6487, pp. 169-172
DOI: 10.1126/science.aaz2856

High winds in an extrasolar atmosphere

Brown dwarfs are objects intermediate in mass between large planets and small stars, and their atmospheres share many characteristics with gas giant planets. Wind speeds in Solar System gas giant atmospheres can be derived by comparing the planet's rotational periods in the infrared (tracing the upper atmosphere) and radio (tied to the interior). Allers et al. observed a nearby brown dwarf, 2MASS J10475385+2124234, and determined its infrared and radio periods. They derived an average wind speed of ∼650 meters per second in a west-to-east direction. This technique should also work for exoplanets.

Science, this issue p. 169

Abstract

Zonal (latitudinal) winds dominate the bulk flow of planetary atmospheres. For gas giant planets such as Jupiter, the motion of clouds can be compared with radio emissions from the magnetosphere, which is connected to the planet’s interior, to determine the wind speed. In principle, this technique can be applied to brown dwarfs and/or directly imaged exoplanets if periods can be determined for both the infrared and radio emissions. We apply this method to measure the wind speeds on the brown dwarf 2MASS J10475385+2124234. The difference between the radio period of 1.751 to 1.765 hours and infrared period of 1.741 ± 0.007 hours implies a strong wind (+650 ± 310 meters per second) proceeding eastward. This could be due to atmospheric jet streams and/or low frictional drag at the bottom of the atmosphere.

Gas giant exoplanets and brown dwarfs (objects with masses of 13 to 72 times that of Jupiter) rotate on time scales of hours to days (14). If there are any inhomogeneous features at the top of their atmospheres, such as clouds, the rotational modulation causes quasi-periodic variability in their brightness. Photometric searches for periodic brightness modulations can therefore probe the rotational properties of these objects. Quasi-periodic near- and mid-infrared (IR) variability is common in isolated brown dwarfs of spectral types L and T (2, 5).

Within the Solar System, it is possible to observe the effects of rapid rotation on the atmospheric physics of the giant planets. Zonal winds—latitudinal flows resulting from rapid rotation and convection—dominate the bulk atmospheric flow of Jupiter (6). Models of the atmospheric dynamics of brown dwarfs and exoplanets incorporate the effects of rotation and zonal winds (79). These studies have shown that wind speeds and flow patterns are determined by the efficiency with which the atmosphere can radiatively cool and the coupling between the atmosphere and interior of the planet, among other atmospheric conditions.

Wind speeds have been measured for some hot, gas giant exoplanets using Doppler shifts in transit spectroscopy (10). This technique requires a tidally locked planet (for which the rotation period and orbital period are equal) as well as high-speed winds (several kilometers per second) driven by heat redistribution from the highly irradiated day side to the night side of the planet (10). These conditions are not typical for planetary-mass objects, particularly those with wide separations from their parent star or free-floating objects that are not gravitationally bound to a star.

Photometric variability studies of brown dwarfs and free-floating, planetary-mass objects have inferred the presence of zonal winds (11, 12). Changes in the rotational brightness modulation of a highly variable brown dwarf over several months could be due to wind speeds of 45 m s−1 (11). Quasi-periodic variability data for two brown dwarfs have been modeled as originating from beating, planetary-scale, atmospheric wave pairs with differential wind velocities of several hundred meters per second (12).

We describe an alternative technique for measuring wind speeds (vwind) on exoplanets and brown dwarfs. Observations of Jupiter are typically interpreted using a coordinate system determined from Jupiter’s radio emission, known as System III, whose rotation period is 9 hours 55 min 30 s (13). This radio periodicity corresponds to the rotation rate of Jupiter’s magnetosphere. Because the Jovian magnetic field originates >7000 km below its visible surface (14), the radio period is determined by the rotation of the interior of the planet, which is expected to rotate as a rigid body (15). An alternative coordinate system derived for Jupiter’s surface is known as System I, which has a period of 9 hours 50 min 30 s, measured from the rotation of its atmospheric features in optical and infrared light from 10°N to 10°S. The 5-min difference between the radio System III period (Tinterior) and optical–infrared (IR) System I period (Tatmosphere) corresponds to a velocity difference at the radius of Jupiter’s visible surface (R = 71,492 km) ofvwind=2πR(1Tatmosphere1Tinterior)=+106 m s-1(1)which agrees with the measured wind speed observed in Jupiter’s equatorial region (16).

Radio observations of brown dwarfs have been used to measure the rotational modulation of their magnetic field (17), in some cases with period uncertainties as low as 0.11 min. Radio emission from brown dwarfs originates from the same mechanism (electron-cyclotron maser instability, ECMI) as Jupiter’s radio emission, as shown by observations (18) and models (19). For brown dwarfs of spectral types L and T, the magnetic field is expected to originate well below the visible surface (20). Therefore, we expect the radio period of brown dwarfs and exoplanets to represent their interior period of rotation, as it does for Jupiter.

If global maps of Jupiter were degraded to unresolved photometric measurements (akin to those available for brown dwarfs), they would have variability amplitudes as large as 20% (21), which is similar to those seen in the most highly variable brown dwarfs (3). Optical–IR photometric monitoring of brown dwarfs can determine rotational periods with precisions <1 min from the ground (22) or from space (2). Wind speed measurements of brown dwarfs and planetary-mass objects should therefore be possible by measuring radio and IR periods using current facilities.

We applied this method to observations of two brown dwarfs: 2MASS J10475385+2124234 (hereafter 2MASS J1047+21) and WISE J112254.73+255021.5 (hereafter WISE J1122+25). No infrared period was detected for WISE J1122+25 (23), so we focus our discussion on 2MASS J1047+21.

2MASS J1047+21 is a brown dwarf of spectral type T6.5 which is 10.6 pc away (24). On the basis of its luminosity and evolutionary models for typical brown dwarf ages of 0.5 to 10 billion years, 2MASS J1047+21 has an estimated mass of 16 to 68 times that of Jupiter and an estimated temperature of 880 ± 76 K (24), which is cooler than other brown dwarfs with detected radio emission. Circularly polarized bursts of radio emission have been detected from 2MASS J1047+21, consistent with ECMI and indicating a rotation period of 1.77 ± 0.04 hours (25) and a magnetic field strength of 5.6 kG (26).

We used the Infrared Array Camera on the Spitzer Space Telescope to search for photometric variability of 2MASS J1047+21 at 4.5 μm (23). Observations were conducted on 7 April 2017 for 7 hours and on 15 April 2018 for 14 hours. We detect sinusoidal variability in both epochs with an amplitude of 0.5% (Fig. 1), indicating that a single, long-lived atmospheric feature is likely responsible for the variability. We used two approaches to determine the IR period: a sinusoidal model fitted using a Markov Chain Monte Carlo (MCMC) algorithm (Fig. 1), and an analysis of the Lomb-Scargle periodogram (Fig. 2A) using bootstrap and Monte Carlo techniques for uncertainty determination (Fig. 2, B and C). The resulting periods and uncertainties agree with each other (23). We adopt an IR period of 1.741 ± 0.007 hours.

Fig. 1 Spitzer infrared photometry of 2MASS J1047+21 on 15 April 2018 and our MCMC analysis.

(A) Photometry in 5.5-min bins of 2MASS J1047+21 at 4.5 μm (points) and the fitted sinusoidal model (black curve). (B) The residuals between the model and observations. The residuals are consistent with Gaussian-distributed noise. (C) Posterior probability distributions for the model parameters. “Amp” refers to the semi-amplitude of the sinusoidal model. The mean refers to the average relative flux of our target. Vertical dashed lines show the median and 1σ uncertainties on the best-fitting model parameters, which are defined by the 16% and 84% quantiles of each distribution. Contours show the 0.5, 1.0, 1.5, and 2.0σ uncertainties of the posterior probabilities in each two-dimensional parameter space.

Fig. 2 Lomb-Scargle periodogram analysis of infrared photometry on 15 April 2018.

(A) Periodogram showing an estimate of the Fourier power as a function of rotation period. The highest-power period is 1.740 hours. (B) Distribution of retrieved highest-power periods from boot-strapping and (C) Monte Carlo methods. The solid vertical lines show the median of the distribution, and the dotted vertical lines show the 1σ uncertainties. Both methods indicate an uncertainty of 0.007 hours.

We also observed 2MASS J1047+21 at 4–8 GHz with the Karl G. Jansky Very Large Array (VLA) on the nights of 12 to 14 October 2018 (23). Our radio observations (Fig. 3) show periodic, highly circularly polarized bursts of ECMI emission, consistent with previous observations (25). We determined the radio period using a time-of-arrival (TOA) analysis and an analysis of the Lomb-Scargle periodogram, which give consistent radio periods of 1.758 hours. The uncertainties calculated by bootstrap and Monte Carlo approaches are both very low, 0.0012 hours, which we interpret as an underestimate of the true uncertainty, because the pulse profiles are highly variable. Taking a more conservative approach, we computed a range of plausible periods from the TOA of the first and last pulses and their pulse widths. This approach yields a period range of 1.751 to 1.765 hours. Folding the radio data by different periods (Fig. 4) shows that pulses align in phase for periods in the range 1.751 to 1.765 hours but are not well aligned for periods outside that range.

Fig. 3 Radio light curve of 2MASS J1047+21 from VLA observations.

(A to C) Left-circularly polarized radio flux in microjanskys (points) on three consecutive nights of observations, each lasting about 10 hours. 1σ uncertainties are plotted as vertical lines for each data point. Radio pulses of varying intensity are evident. Thin vertical dashed lines indicate pulse TOAs (23). Thick vertical solid lines indicate TOAs from the best-fitting period derived from these data, labeled with the number of rotations since the start of the observation. The data cover about 18 rotations out of 34 that occurred in this period.

Fig. 4 Alignment of pulses for possible periods of the radio data.

(A to E) The data (points) from Fig. 3 are folded by periods that differ by 0.007 hours for comparison of the phase (fraction of a rotation period) of radio pulses. Each color (arbitrarily) indicates the data from a separate rotation. 1σ uncertainties are plotted as vertical lines for each data point. (C) The radio pulses folded at the period preferred by our analysis (23). At this period, the pulses from all of our observed rotations are aligned at a phase of around 0.5. The pulses are aligned at a phase of around 0.5 for periods of 1.751 to 1.765 hours (B to D), whereas the phases of the pulses are not aligned for periods outside of this range (A and E).

For an IR period of Tatmosphere = 1.741 ± 0.007 hours, a uniformly distributed radio period of Tinterior = 1.751 to 1.765 hours, and a radius of 67,200 km (24), Eq. 1 gives a wind speed for 2MASS J1047+21 of 650 ± 310 m s−1. This assumes that the IR variability originates in the equatorial region, but Eq. 1 can be adapted to other latitudes by scaling by the cosine of the latitude. The inclination of 2MASS J1047+21’s rotation is unknown, but all other radio-bursting brown dwarfs with known inclinations are viewed nearly equator-on (18). Photometric variability most commonly originates at equatorial to mid-latitudes of less than 35° (21, 27). Thus, latitudinal or viewing-angle effects would likely change the result by less than the uncertainty. The measured wind speed is that of the (unknown) atmospheric inhomogeneity that dominates the photometric variability. If this atmospheric feature occurs between bands of zonal wind having alternating wind direction, our measured wind speed would underestimate the true zonal wind speeds. Some of Jupiter’s atmospheric features are transported by processes other than wind (28), but the effect of these processes would fall within the uncertainties of our wind speed measurement for 2MASS J1047+21.

We detect a positive (eastward) wind speed at >98% confidence (2.1σ). As with Jupiter, the IR period of 2MASS J1047+21 is shorter than its radio period, indicating an atmosphere that is rotating faster than the interior. The wind speed on 2MASS J1047+21 is higher than on the gas giant planets in the Solar System (16, 29). Analytic theory predicts that larger atmospheric heat fluxes lead to higher wind speeds (7). Three-dimensional numerical simulations show that zonal winds of hundreds of meters per second can occur when strong convective forcing and/or weak damping (either radiative or frictional) promote the formation of atmospheric jet streams (9).

Our method for determining the wind speed can in principle also be applied to exoplanets, which have rotation rates and periodic variability similar to those of brown dwarfs (1, 4). Exoplanets with masses similar to Jupiter’s have magnetic field strengths of around 100 G (30), which is weaker than the kilogauss fields of brown dwarfs (26). Because the frequency at which ECMI emission is detected is proportional to the magnetic field strength, we expect exoplanets to emit at lower radio frequencies.

Supplementary Materials

science.sciencemag.org/content/368/6487/169/suppl/DC1

Materials and Methods

Supplementary Text

Tables S1 to S3

Figs. S1 to S6

References (3258)

References and Notes

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Acknowledgments: This study was based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This work benefited from the Exoplanet Summer Program in the Other Worlds Laboratory (OWL) at the University of California, Santa Cruz, funded by the Heising-Simons Foundation. We acknowledge S. Beiler, E. Berger, M. Kao, L. Lanwermeyer, M. Marley, S. Metchev, B. Pantoja, D. Powell, E. Shkolnik, A. Showman, X. Tan, J. Tolman, and X. Zhang for useful conversations. We also thank the anonymous reviewers, whose thoughtful comments improved this manuscript. Funding: Support for Program numbers 14188 and 14686 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS 5-26555. J.M.V. acknowledges funding support from the National Science Foundation under award AST-1614527 and Spitzer Cycle 14 Caltech/JPL Research Support Agreement 1627378. Author contributions: K.N.A. planned and proposed the Spitzer Space Telescope observations, conducted an independent check of the data reduction, calculated the wind speeds, and wrote the manuscript. J.M.V. led the reduction and analysis of the Spitzer data, including the MCMC modeling, production of Figs. 1 and figs. S1 to S5, and associated text. B.A.B. performed the Lomb-Scargle analysis, produced Fig. 2 and fig. S6, and wrote part of the manuscript. P.K.G.W. planned, proposed, and reduced the VLA data, conducted the radio pulse time-of-arrival (TOA) analysis, produced Figs. 3 and 4, and wrote the corresponding text. Competing interests: We declare no competing interests. Data and materials availability: The VLA data are available via the NRAO Science Data Archive http://archive-new.nrao.edu/ under Project Code 18A-427. The Spitzer data are available via the Spitzer Heritage Archive http://sha.ipac.caltech.edu using Program IDs 13031 and 13231. The light curve data and code used for analysis and figure production are available at https://github.com/johannavos/BDwindspeeds/ and archived at https://doi.org/10.5281/zenodo.3700897. The VLA dynamic spectrum (an intermediate data product) is archived at Zenodo (31).

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