OBSERVED VARIABILITY AT 1 and 4 μm IN THE Y0 BROWN DWARF WISEP J173835.52+273258.9

W1738 was observed as part of the Gemini North program GN-2013A-Q-21. The brown dwarf was imaged in the Y and J filters using NIRI. The NIRI Y filter differs slightly from the MKO standard, where Y_NIRI − Y_MKO = 0.17 ± 0.03 mag for late-type T and early-type Y dwarfs (Liu et al. 2012).

Long-duration observations were obtained on UT 2013 July 17 and August 23 in photometric conditions with typical seeing 08. Integration times for both filters were 60 s, and offsets of about 12'' were used in dither patterns that were moved slightly on the detector through the observation, to minimize the impact of bad pixels and reduce any flat-fielding artifacts. The filters were alternated so that a five-position dither in Y was executed, followed by a nine-position dither in J, followed by another five-position dither in Y, etc.

On 2013 July 17 the observation ran from UT 07:22:57 to 12:18:09, for a duration of 4.92 hr. Seventeen five-position dithers in Y and 16 nine-position dithers in J were obtained, for an on-source time of 1.4 hr in Y and 2.4 hr in J. On 2013 August 23 the observation ran from UT 5:41:48 to 10:19:56, for a duration of 4.64 hr. Sixteen five-position dithers in Y and 15 nine-position dithers in J were obtained, for an on-source time of 1.3 hr in Y and 2.3 hr in J. Photometric standard FS 27 was observed before the W1738 observation, and FS 35 was observed after, on both nights. The data were reduced in the standard way, using dark and flat-field images, obtained with the on-telescope calibration unit, and Gemini IRAF routines.

The NIRI detector suffers from first-frame pattern noise, which occurs in the first frame following any filter change. Because of this, we discarded all of the first frames in each set and used sets of four Y images and sets of eight J images to first generate sky frames and then co-added images. Aperture photomery with annular skies and an aperture diameter of 24 was performed.

Six stars (or point-like objects) with Y and J magnitudes between 17 and 18 provided the photometric baseline reference. We used five point sources with Y and J magnitudes between 18.9 and 20.7 to further explore the precision of the photometry, in order to determine whether or not the similarly bright W1738 is variable in these filters. The 11 sources were selected for brightness and for being present in every co-added image with a clean annular sky region. The uncertainty in the photometry obtained from the 4-minute Y and 8-minute J co-added images was 1%–2% for the brighter reference stars in both filters and ∼5% in Y and ∼3% in J for W1738 and the five fainter point sources. Figure 1 shows examples of a co-added 4-minute Y and 8-minute J image, with W1738 and the 11 other sources identified. Table 2 gives the nightly average of the photometry for W1738 and the other sources. The last two co-added images for each filter on the night of 2013 August 23 suffered from poor seeing, and while the data were used for relative photometry, the absolute values in Table 2 exclude these two data points.

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We compared the photometry of W1738 and the five fainter sources to the six brighter reference stars, and we also compared each bright reference star to the other five reference stars as a check on data quality. Figures 2 and 3 show the resulting light curves for each night. These are discussed in Section 3.

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W1738 was observed in both the [3.6] and [4.5] filters of the IRAC camera on Spitzer, with the filters observed consecutively. For each filter 12.0 hr long observations were obtained, and the 24.0 hr long observation with the filter pair was repeated 4 months later. The first epoch ran from UT 2013 June 29 19:22:39.36 to 2013 June 30 07:23:48.48 for [3.6], and from 2013 June 30 07:30:00.00 to 19:31:26.40 for [4.5]. The second epoch ran from UT 2013 October 29 18:29:22.56 to 2013 October 30 06:30:31.68 for [3.6], and from 2013 October 30 06:36:25.92 to 18:37:52.32 for [4.5]. The data were obtained as part of program 90015 during campaigns 35100 and 35900. The data were obtained and reduced in the same way as that for W1405, as decribed in Cu16. Briefly, the 100 s images were obtained in "staring" mode for each filter. Photometric analysis starts with the basic calibrated data frames, which are converted from units of MJy sr⁻¹ to electrons. Aperture photometry with a radius of 3 pixels and a background annulus is then obtained using a custom Interactive Data Language (IDL) code. For W1738 the field was more crowded than that of W1405, and extra care had to be taken with placement of the sky annuli. Data points that were extreme outliers, exceeding the median by 50 times the median absolute deviation, were removed. Figure 4 shows the light curves obtained. The apparently bright data points are due to hot pixels, which are caused by cosmic rays.

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The average brightness of the target did not change significantly between 2013 June and October. We derive from the processed mosaics downloaded from the Spitzer archive [3.6] = 16.89 ± 0.08 (where the uncertainty is dominated by the uncertainty in the sky value) and [4.5] = 14.46 ± 0.01.

There are no other published studies of variability at both near-infrared and mid-infrared wavelengths for Y dwarfs at the time of writing. Nine T dwarfs do have such data published, and these results are summarized in Table 5. Variability is found in five of the nine T dwarfs. Generally the periods are found to be the same at both near- and mid-infrared wavelengths, and the near-infrared amplitudes are similar to or larger than the mid-infrared amplitude (although the near- and mid-infrared data are likely to not have been taken at the same time, and amplitudes are likely to vary with time).

The variability measurements presented here for W1738 are in general agreement with results from other brown dwarf studies. Crossfield (2014) presents a multiwavelength collation of variability amplitude and period and projected rotational velocities for late-type M, L, and T dwarfs. The Crossfield sample of L and T dwarfs has variability periods of 1.5–10 hr and peak-to-peak amplitudes of 0.1%–120%, although most have amplitudes of 1%–15%. The Spitzer study of 39 single L3–T8 dwarfs by Metchev et al. (2015) found that 19 varied; peak-to-peak amplitudes were 0.8%–4.6% and periods were 1.6–24 hr. Recently Zhou et al. (2016) have determined a rotation period of about 11 hr for the young planetary-mass L dwarf 2MASSWJ 1207334-393254b, based on near-infrared variability with peak-to-peak amplitudes of ∼2%. In Cu16 we monitored the Y0.5(pec) W1405 with Spitzer and found variability with peak-to-peak amplitude of 7% and a period of 8.5 hr. Cu16 showed that the variability could be reproduced by a single bright spot model, with the light-curve period equal to the rotational period, meaning that W1405 has the longest rotation period measured to date for spectral types later than T3.

Variability seen in the surface features of the solar system gas giants is also a useful reference point for cold Y dwarfs. Gelino & Marley (2000) used observations of Jupiter to show that, were it to be unresolved, 20% variability would be observed at 4.8 μm with a period equal to the planet's rotation period of 9.9 hr. The variability in this case is predominantly due to Jupiter's Great Red Spot. Sromovsky et al. (2012) present observations of episodic bright and dark spots on Uranus. One and then two bright spots were seen on the planet's surface in 2011, drifting at very different rates, and evolving over a period of months. Simon et al. (2016) present a 49-day light curve for Neptune using Kepler. The data are compared to contemporaneous images taken with the Keck telescope at 1.65 μm and to Hubble Space Telescope (HST) visible imaging taken several months later. The authors find that a single large, long-lived storm that is seen in their Keck images dominates the Kepler and HST light curves. The periodicity of the long-term variability is consistent with the planet's rotation and surface wind speed at the latitude of the storm. The short-term variability is interpreted as being due to smaller or fainter clouds.

Three-dimensional simulations of convection in brown dwarf and giant planet interiors by Showman & Kaspi (2013) show that significant circulation is generated at both small and large scales. Large-scale horizontal temperature variations of tens of kelvin are produced, resulting in flux variations of a few percent on rotation timescales. Stratified turbulence can generate vortices and storms, and the circulation can support the formation of patchy clouds. These models produce vertical velocities consistent with the chemical mixing observed in brown dwarf atmospheres, plausible surface wind speeds, and timescales for the evolution of the light curve that are in agreement with observations.

It is likely that both thermal and cloud cover fluctuations are important sources of variability in giant planets and brown dwarfs (e.g., Morley et al. 2014; Robinson & Marley 2014). Although the T_eff ≈ 400 K atmospheres of Y dwarfs are expected to be essentially clear, Morley et al. (2012, their Figure 4) show that flux emitted from the 1 μm region originates deep enough in the atmosphere that it could be impacted by thin layers of KCl and Na₂S clouds. Morley et al. (2014) examine spectral variability that occurs if the clouds are patchy. Figure 1 of Morley et al. (2014) shows the 0.7–10 μm spectrum of a 400 K brown dwarf where one hemisphere has 30% cloud cover and the other 70%, and as a result they also differ by 5 K or >1% of the T_eff. The difference in the resulting spectra, which is the inferred peak-to-peak variability, is calculated to be ∼50% at 1 μm (Y), 40% at 1.2 μm (J), and 2% at 4.5 μm. We ran a similar model with a covering fraction of 45% on the eastern hemisphere and 55% on the western hemisphere, which produced peak-to-peak variability of 7% in Y, 5% in J, 0.5% in [3.6], and 0.8% in [4.5]. Thus, atmospheres with patchy clouds and small variations in surface temperature can reproduce the size of variability we observe at [4.5] and have tentatively observed at Y and J.

Physical constraints on the rotation period of brown dwarfs can be helpful in determining the source of any observed variability. If the variation is caused by multiple surface features such as clouds or several discrete storms, then it can have a period smaller than the rotation period. If it is due to a single feature such as Jupiter's Great Red Spot or the single bright spot model used to reproduce the W1405 variability, then the period will be equal to the rotation period. The lower limit on the rotation period of any stable object can be estimated by assuming solid-body rotation and constraining the surface velocity to be less than the escape velocity. Adopting a radius equal to that of Jupiter's (which is approximately true for most brown dwarfs; see Burrows et al. 1997), we find that the period $P\gt 2.1/\sqrt{M}$ hr, where the mass of the brown dwarf is M Jupiter masses. Marley & Sengupta (2011, their Figure 2) more accurately derive a breakup velocity and show that for brown dwarfs or gas planets older than 0.1 Gyr the lower limit on rotation period is 5 hr or 1.8 hr for a 1 or a 10 M_Jupiter object, respectively. For W1738 with mass ≈5 M_Jupiter and age between 0.15 and 1.0 Gyr (Leggett et al. 2016), the rotational period must be greater than about 3 hr. We have found two dominant periodicities, 3 and 6 hr, in our data sets. The 3 hr component is very close to the breakup speed—which is very unlikely—suggesting that there are multiple features on the surface of the brown dwarf.

Metchev et al. (2015) found substantial power in periods approximately half of the best-fit period for 3 of the 19 variable L and T dwarfs in their sample. Studies of pre-main-sequence stars have also found photometric variability with periods separated by a factor of two (Tackett et al. 2003; Herbst 1989). The pre-main-sequence observations could be reproduced by a model where the rotation period was equal to the longer of the two periods, the star was viewed close to equator-on, and there were two similar spots, one on each hemisphere. The model showed that the shape and amplitude of the light curve evolved as the spots drifted in longitude (Herbst 1989). We attempted to fit a model with two equally bright spots to the W1738 data, where the spots are circular and have their own longitude, latitude, and size. The first epoch, where there is a dominant sinusoid, could be reasonably well reproduced by a two-spot model, but not the second epoch, where there are two sinusoids of different frequency of almost equal amplitude. We did not explore models with more than two spots.

We adopt the rotation period for W1738 to be the longer of the two periods observed, 6.0 ± 0.1 hr, and interpret the double-sinusoid variability as evidence of there being one or more large features present in its atmosphere. The features evolve over a period of months, such that in 2013 June the variability is dominated by a single spot or storm, and by 2013 October smaller features have developed, giving rise to the shorter period variability observed. This configuration of a dominant large system that is long-lived and multiple smaller surface features is similar to what was observed for Neptune by Simon et al. (2016, Section 4.1). We note that for W1738 the amplitude of the variability and the suggested wavelength dependence of the amplitude are well reproduced by models with patchy thin clouds (Section 4.2). The models have one hemisphere slightly more than half covered and the other slightly less than half covered with clouds. A hemisphere half covered in clouds could also be described as a hemisphere with a large spot, depending on the wavelength involved and the height of the clouds.