Weather on Other Worlds. V. The Three Most Rapidly Rotating Ultra-cool Dwarfs

We observed the three objects in staring mode with Spitzer's Infrared Array Camera's (IRAC; Werner et al. 2004; Fazio et al. 2004) channels 1 (3.6 μm, [3.6]) and 2 (4.5 μm, [4.5]). The dates of the observations are given in Table 1. The observing sequence was a 10 hr staring observation in channel 1, followed immediately by a 10 hr staring observation in channel 2. All exposures were 12 s long, taken in full-array readout mode. At the beginning of each staring sequence an additional 0.5 hr were used for pointing calibration with the Pointing Calibration and Reference Sensor (PCRS). The PCRS peak-up procedure is intended to correct telescope pointing over long staring observations. We used nearby bright stars for peak-up, as none of our targets were sufficiently bright to perform the peak-up on-target.

The Spitzer IRAC detector is subject to intrapixel sensitivity variations, known as the "pixel phase effect" (Reach et al. 2005). Precise photometry requires correcting for an object's positioning to sub-pixel precision. The pixel phase effect is well characterized in a 0.5 × 0.5 pixel (06 × 06) "sweet spot" (Mighell et al. 2008) near a corner of the IRAC array, and flux correction routines are available at the Spitzer Science Centre IRAC High Precision Photometry website. ¹³

We sought to acquire our targets as closely as possible to the center of the IRAC sweet spot. We used observation epoch-dependent positional corrections for proper and parallactic motions derived from a 2MASS–AllWISE cross-correlation. However, we were not entirely successful. The average centroid position for each of our three targets was up to a pixel away from the center of the sweet spot: i.e., twice its half-width. We therefore used our own custom pixel phase correction code (Heinze et al. 2013) developed for the Spitzer Cycle 8 "Weather on Other Worlds" program (Metchev et al. 2015) and summarized in Section 2.2. Experiments with archival Spitzer GO 13067 data on TRAPPIST-1, which were acquired on the sweet spot, confirmed that for point sources at least as bright as TRAPPIST-1 (WISE W1 = 10.07 mag), our pixel phase correction approach is at least as accurate as the set of sweet spot pixel phase corrections on the IRAC High Precision Photometry website.

We conducted a two-stage photometric and variability assessment, using the Spitzer Basic Calibrated Data images. We first performed approximate [3.6]- and [4.5]-band photometry in 1.5 pixel-radius apertures with the IDL Astronomy User's Library task aper. We applied the corresponding aperture correction from the IRAC Instrument Handbook, and a custom pixel phase correction derived as a two-dimensional quadratic function of the centroid position on the detector. ¹⁴

We identified variable targets by Lomb–Scargle periodogram analysis (Scargle 1982), sampling periods between 0.1 hr and the full 20 hr duration of our Spitzer observations. We use the p-value, a measure of the likelihood that any variations are caused by random noise, to determine the significance of the periodogram peaks. The p-value is ${{Me}}^{-P}$, where P is the periodogram power of the highest peak, and M is the number of independent periods considered (Scargle 1982; Press et al. 1992). Relative to other non-variable field stars, a sinusoidal signal yields the lowest p-value at a given amplitude, making it ideal for detecting rotation-induced photometric variations. We determined a threshold to identify variables by calculating the p-value from pixel phase-corrected light curves of 469 field stars in the IRAC field of view for our full Spitzer sample, with obvious variables (e.g., eclipsing binaries) rejected by visual inspection. We split the field stars into two equal-sized groups based on their magnitudes. From the full Spitzer sample, we selected as candidate variables those L and T dwarfs for which the p-value was below that of 95% of field star p-values. The p-values of the current three L and T dwarfs and of the field stars are shown in Figure 1. The relevant thresholds are shown as dashed horizontal lines.

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The most significant periodogram peaks above the p-value threshold for our three targets are in the 1.1–1.2 hr range (Figure 2). In all three cases, significant periodicity is detected in only one of the two Spitzer IRAC channels: at [3.6] for the L dwarfs 2MASS J0407+1546 and 2MASS J1219+3128 and at [4.5] for the T dwarf 2MASS J0348–6022.

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At this stage of our analysis, the applied pixel phase correction is not in the final form presented in Section 2.3. The preliminary periodicities are potentially affected by Spitzer's known pointing "wobble." The telescope's boresight follows a small sawtooth quasi-periodic oscillation with a mostly sub-hour timescale: the result of heater cycling to maintain adequate battery temperature (Grillmair et al. 2012, 2014). The amplitude of the pointing oscillation, up to 0.4 pix, can be sufficiently high to impact photometric measurements because of the pixel phase effect. During 2015, when our observations were taken, the mean pointing oscillation period was 49 minutes, with an inner quartile range of 43 minutes to 54 minutes (Krick et al. 2018). However, a small fraction of year 2015 observations in the Spitzer archive have pointing oscillation periods up to 80 minutes, similar to the 1.1–1.2 hr long periods identified in our periodograms (Figure 2).

We do not believe that Spitzer's pointing wobble is responsible for the detected 1.1–1.2 hr periodicities for three reasons. First, we expect roughly similar pixel phase-induced behavior of all point sources in our target fields. Therefore, by setting a global 95% p-value threshold in our preliminary analysis, we select for variability beyond what may be incurred by the pointing wobble. Second, in Section 2.3 we describe a more sophisticated photometric analysis that includes an astrophysical variability and a pointing oscillation model, and we clearly identify the wobble separately from the astrophysical periods. Finally, in Section 4 we confirm that the rapid rotations implied by such short periods are expressed as wide Doppler line broadening in moderate-dispersion spectra of our three science targets.

Having identified candidate variables among the science targets with approximate photometry, we iterated our variability assessment with higher-precision photometry. We determined the optimal aperture for each object by seeking the lowest root-mean-square scatter in the measured fluxes. The optimal apertures in the [3.5]- and [4.5]-band data respectively were 1.4 and 2.1 pixels for 2MASS J0348–6022, 1.4 and 2.0 pixels for 2MASS J1219+3128, and 1.5 and 2.1 pixels for 2MASS J0407+1546. We binned the photometry in groups of 10 consecutive measurements to lower the random noise. Our binning interval of 120 s still ensures fast enough sampling to retain sensitivity to the hour-long timescales of interest. We incorporated the initial period estimates from Section 2.2 in an iterative least-squares method to simultaneously fit an astrophysical model (a truncated Fourier series) and a correction for the pixel phase effect in both channels (Heinze et al. 2013). We show the raw and corrected Spitzer light curves for our three targets in the left panel of Figure 3.

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The raw photometry in Figure 3 shows the sawtooth pointing oscillation of Spitzer in the light curves of two of the three science targets. The effect is present mostly throughout the [3.6]- and [4.5]-band staring observation of 2MASS J1219+3128 (middle-left panel of Figure 3), with a sawtooth-like pattern that repeats 10 times over 10 hr at [3.6]. The corresponding 60 minute timescale of the sawtooth pattern is distinct from the 68 minute astrophysical period seen in the corrected [3.6]-band light curve. The latter half of the [3.6]-band observation of 2MASS J0348–6022 also shows sawtooth variations on a 60 minute timescale. However, no astrophysical variability is detected in 2MASS J0348–6022 at [3.6]. This T7 dwarf is variable only at [4.5], where no effect of the sawtooth pattern is seen.

We further verified that there is no residual periodicity effect from the pointing wobble by confirming that there is no correlation between the flux and centroid position on the detector after correcting our photometry for pixel phase (Figure 4). We computed Pearson correlation coefficients of $| r| \leqslant 0.04$ between flux and centroid position for each object and Spitzer channel. We conclude that Spitzer's pointing oscillation is not the cause of the variability we observe.

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We adopt the results from the simultaneous astrophysical and pixel phase model as the true periods and peak-to-trough amplitudes of our variables, rather than the preliminary results from the periodogram fitting shown in Figure 2. In all three cases the final and the preliminary periods agree to within 1%, and the periodogram power of the significant peaks increased for the final, corrected data. From our best-fit astrophysical model, the two L dwarfs require only a single Fourier term for an adequate light-curve fit. The T7 dwarf 2MASS J0348–6022 requires a two-term Fourier fit, and so both significant peaks seen in the [4.5]-periodogram (Figure 2) are astrophysical in nature. However, the higher-frequency oscillation is less significant, and is a harmonic at half the period: 0.54 hr versus 1.08 hr. It may indicate a two-spot configuration on opposite hemispheres of the T dwarf.

We use a Markov chain Monte Carlo (MCMC) analysis, as described in Section 3.4 of Heinze et al. (2013), to determine the uncertainties on the periods and the amplitudes. We fit the [3.6] and [4.5] photometry simultaneously, by requiring the same period but different amplitudes for the two channels. Since in all cases only one of the channels shows significant variability, we set 2σ upper limits on the amplitude ratios of the "non-variable" channels to the variable channels.

The periods of the T7, L3.5, and L8 dwarfs range between 1.08 hr and 1.23 hr: faster than any measured before (see Section 5). We show the phase-folded light curves in the variable channel for each target in the right panel of Figure 3. The object names, spectral types, magnitudes, variable channels, photometric periods, peak-to-trough amplitudes, and amplitude ratios are listed in Table 1.

Two of our three targets have been previously reported as potential variables. For 2MASS J1219+3128 (L8), Buenzli et al. (2014) find a lower limit of 2% on the variability amplitude in a 1.12–1.20 μm subset of their 1.1–1.7 μm HST/WFC3 spectra, over a 36 minute sequence of nine spectroscopic exposures. However, the variability is not significant over any other part of their 1.1–1.7 μm spectra, and they classify the detection as tentative. For 2MASS J0348−6022 (T7), Wilson et al. (2014) report a J-band amplitude of 2.4% ± 0.5% in a three hour long observation. However, a re-analysis of their NTT/SofI observations by Radigan (2014) shows that the reported variability is likely spurious, and related to residual detector and sky-background systematics. Radigan (2014) revised the J-band variability in the Wilson et al. (2014) observations to a <1.1% ± 0.4% upper limit. Similarly, a 1% upper limit for 2MASS J0348−6022 is deduced from a prior six hour J-band monitoring observation by Clarke et al. (2008), also with NTT/SofI. No variability has been previously reported for 2MASS J0407+1546 (L3.5).

The small periodogram p-values and large periodogram powers (Figures 1 and 2) of our Spitzer observations confidently establish that all three L and T dwarfs exhibit periodic variability. Each of our three targets varies in only one of the two IRAC channels within the photometric precision limits. The two L dwarfs vary only at [3.6], whereas the T7 dwarf varies only at [4.5]. Such behavior is consistent with prior observations of infrared variability trends with spectral type. Metchev et al. (2015) found that five of their 19 variable L3–T8 dwarfs varied only at [3.6] (two L3s, two L4s, and a T2), and one (T7) dwarf varied only at [4.5]. Single-band [3.6] variations in an L dwarf have also been reported by Gizis et al. (2015), while [4.5]-only variations are seen in Y dwarfs (Cushing et al. 2016; Leggett et al. 2016).

Wavelength-dependent amplitude differences are explained by the dominant gas absorption species in the atmosphere. In wavelength regions of strong molecular gas opacity, clouds reside below the photosphere and so cloud heterogeneities are obscured. Cloud structures are detectable only in relatively transparent spectral regions, away from dominant molecular bands (e.g., Ackerman & Marley 2001). With CO being a dominant source of upper-atmosphere gas opacity in L dwarfs, cloud condensate-induced variability will be suppressed around the 4.5 μm fundamental CO band (i.e., in IRAC channel 2). Conversely, variability around the 3.3 μm CH₄ fundamental band (within IRAC channel 1) will be suppressed in T dwarfs.

Alternative variability mechanisms that do not require clouds have also been proposed. Such scenarios do not imply that clouds may not exist at all in the atmospheres of brown dwarfs, just that they are not responsible, or not entirely responsible, for the observed variability. For example, some variable brown dwarfs show radio emission that may be best explained as auroral in nature (e.g., Antonova et al. 2008; Hallinan et al. 2015; Kao et al. 2018). Richey-Yowell et al. (2020) correlate such auroral signatures with the presence of Hα emission. One of our three variables, the L3.5 dwarf 2MASS J0407+1546, is a strong Hα emitter (equivalent width of 60 Å; Reid et al. 2008). While Miles-Páez et al. (2017a) find no correlation between Hα emission and large-amplitude (≳1%) variations (a result also confirmed by Richey-Yowell et al. 2020), the more subdued 0.36% variation in 2MASS J0407+1546 could well be magnetic in origin.

Robinson & Marley (2014) propose atmospheric temperature fluctuations as a potential cause of photometric variability. They show that thermal perturbations occuring deep in the atmosphere can cause surface brightness fluctuations at infrared wavelengths. Tremblin et al. (2015, 2020) show that fingering convection in a cloudless atmosphere can also result in variability. Ultimately, the observations that we present are not decisive of the variability mechanism, and our focus is instead on the short rotation periods.

The periodic regularity seen in the light curves of our three targets (Figure 3) argues for one (2MASS J0407+1546, 2MASS J1219+3128) or two (2MASS J0348−6022) dominant photospheric spots. An alternative interpretation of these data is that we are seeing a repeating spot pattern extended along a band on a more slowly rotating object, e.g., as in the case for Jupiter (de Pater et al. 2016). Additionally, Apai et al. (2017) show that the variability of infrared brightness in T dwarfs can be dominated by planetary-scale waves. They find that the combined variability effect of multiple sets of planetary waves or spots may place the periodogram peak at half the true period, or that double peaks may occur near the true rotation period due to differential rotation.

To the sensitivity of our data, none of our objects show the kind of complex light modulations seen in the Apai et al. (2017) T dwarfs. However, Jupiter-like repeated spot patterns remain a possibility. In Sections 3 and 4 we use near-infrared spectroscopy to measure the projected rotation velocities v sin i of our targets and confirm that all three rotate rapidly.

For our FIRE observations we used the cross-dispersed echelle mode with the 06 (3.3 pixel) slit aligned to the parallactic angle to obtain R ≈ 6000 spectra over 0.91–2.41 μm. We observed 2MASS J0348−6022 on 2012 January 3 (UT) under clear skies with 07 J-band seeing and airmass of 1.25–1.27. We obtained two 909 s exposures, dithered along the slit. We observed the A0 V star HD 28667 (V = 6.87 mag) in four 1 s dithered exposures following the 2MASS J0348−6022 observations at a similar airmass (1.28). We observed 2MASS J1219+3128 on 2017 February 16 (UT) under clear skies with 12–14 J-band seeing and airmass of 2.12–2.31. We obtained four 400 s exposures dithered pair-wise along the slit. We observed the A0 V star HD 96781 (V = 10.2 mag) in six 1 s dithered exposures at a similar airmass (1.96–2.05). For both sets of observations we obtained ThAr emission lamp spectra after each target. We obtained dome and sky flat-field observations at the beginning of each night for pixel response and slit illumination calibration.

The FIRE data were reduced using the Interactive Data Language (IDL) pipeline FIREHOSE v2 (Gagné et al. 2015a), which is based on the MASE (Bochanski et al. 2009) and SpeXTool (Vacca et al. 2003; Cushing et al. 2004) packages. Details for standard reduction of point-source data with FIREHOSE are described in Bochanski et al. (2011). The ThAr lamp images were used to trace the spectral orders and derive pixel response and illumination corrections which were applied to the science frames. A combination of OH telluric lines in the science frames and ThAr emission lamp lines were used to determine the wavelength solution along the center of each order and the order tilt along the spatial direction, so as to construct a two-dimensional vacuum wavelength map. The typical uncertainty of the wavelength solution was 0.20 pixels, corresponding to a precision of 3.0 km s⁻¹. The sky background in each frame was fit with a two-dimensional sky model constructed using basis splines (Kelson 2003), which was then subtracted from the frame. One-dimensional spectra were optimally extracted (Horne 1986) in each order onto a heliocentric wavelength frame. Correction for telluric absorption and overall flux calibration was determined from the A0 V star spectra using a modified version of xtellcor from SpeXtool (Vacca et al. 2003; Cushing et al. 2004). Spectra from the individual frames of the FIRE data were combined for each target after relative flux normalization, and the individual orders were merged into one-dimensional spectra. The resulting reduced spectra are shown in Figure 5 for 2MASS J0348−6022 and in Figure 6 for 2MASS J1219+3128, along with comparison spectra, where data at similar resolution of other objects of the same spectral types were available from the literature. ¹⁵

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Our GNIRS observations of the L3.5 dwarf 2MASS J0407+1546 took place on 2017 October 10 (UT). We followed the same procedure and instrument settings as used by Allers et al. (2016) for radial and rotation velocity measurements of an L dwarf. We used the 111 lines mm^–1 grating with the 015 (3.0 pixels) slit aligned to the parallactic angle to obtain R ≈ 12,000 2.27–2.33 μm spectra at an airmass of 1.07–1.28. We obtained eight 600 s exposures, dithered between two positions on the slit. We observed the A0 V star HD 17971 (V = 8.78 mag) for telluric absorption correction in eight 60 s dithered exposures at a similar airmass (1.03) using the same instrument setup. ThAr emission lamp observations were obtained immediately after the 2MASS J0407+1546 observations. The 2MASS J0407+1546 data were reduced using a combination of general and Gemini-specific IRAF routines. Data were prepared, sky-subtracted, and flat-fielded using the Gemini tasks nsprepare, nsreduce, and nsflat. Individual spectra were extracted using apall. The XeAr lamp spectrum was extracted once for each of the science spectra, using the science extraction traces as references, and identify and dispcor were used to identify calibration lines and generate a wavelength solution for each science spectrum. A Legendre polynomial was used with identify, typically of second order. The typical uncertainty in the wavelength calibration was 0.25 pixels, which corresponds to a precision of 2.0 km s⁻¹. The individual wavelength-calibrated spectra were median-combined, and the standard deviation was adopted as the uncertainty. The same reduction steps were repeated for the standard star, and the science spectrum was divided by the standard spectrum to remove telluric lines, and multiplied by a T_eff = 9600 K blackbody. The resulting spectrum is shown in Figure 7, along with a comparison spectrum of another L3.5 dwarf. ¹⁶

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Based on its T7 spectral type, 2MASS J0348−6022 is expected to have an effective temperature T_eff ≲ 1000 K (e.g., Stephens et al. 2009; Filippazzo et al. 2015). Its photosphere should be governed by gas opacity, with a cloud layer buried deeply (f_sed ≥ 3; Ackerman & Marley 2001; Marley et al. 2002) within the atmosphere. Thus we expect the atmosphere of this object to be relatively clear and cloudless. So, the cloud-free Sonora models are appropriate for fitting this object's spectra. A cloudless atmosphere does not imply a completely homogeneous surface, and it is possible that one of the alternative mechanisms presented in Section 2.4 (e.g., temperature variations; Robinson & Marley 2014) is responsible for the observed variability. We also compared this target to the BT-Settl and Morley models. The effective temperature grid of the available SM08 models does not extend to the low temperatures expected for a T7 spectral type.

We selected a grid of parameters ranging from T_eff = 700 to 1000 K, log g = 4.0 to 5.5 dex in steps of 0.5 dex (0.25 for the Sonora models), and, for the Morley models, condensate sedimentation efficiencies from f_sed = 2 to 5 in unit steps. We selected our log g grid based on the range in surface gravities predicted by the SM08 evolutionary models for brown dwarfs. We selected the RV and v sin i grids by first testing a wide, coarse grid to determine approximate RV and v sin i values. We then narrowed it down to between −5 km s⁻¹ and −30 km s⁻¹ for RV and between 75 km s⁻¹ and 115 km s⁻¹ for v sin i, both in steps of 0.1 km s⁻¹.

We find that a wide range in parameters fit the z band equally well, and it is therefore not diagnostic for our study. We exclude the z band from our analysis, and only consider the J-, H-, and K-band spectra for this target. To reliably determine log g, RV, and v sin i, we selected narrow regions dominated by molecular lines within each band: the 1.26–1.30 μm J-band region dominated by H₂O and CH₄ (Figure 8, top left), the 1.520–1.562 μm H-band region dominated by H₂O (Figure 8, top right), and the 2.11-2.19 μm K-band region containing primarily CH₄ lines (Figure 8, bottom). The best-fit photospheric models for the narrow wavelength regions are shown in Figure 8 and for the full bands in Figure 9. The high f_sed values of the Morley et al. (2012) models in all of the full band fits indicate an optically thin, relatively cloudless atmosphere, as expected for a late-T type brown dwarf.

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We adopt the weighted average and unbiased weighted sample standard deviation (Section 4) of the values in Table 3 as our estimates for log g, v sin i, and RV. For v sin i in particular, we find a very high degree of rotational broadening: v sin i = 103.5 ± 7.4 km s⁻¹. This is consistent with the short rotational period (Section 2.4), and will be discussed further in Section 5. The adopted parameters from the spectroscopic fitting are shown in Table 5.

Based on its L8 spectral type, we expect 2MASS J1219+3128 to have an effective temperature of T_eff ∼ 1400 K (e.g., Stephens et al. 2009; Filippazzo et al. 2015). The Morley models are not suitable for this target, as that model grid extends to a maximum of T_eff = 1300 K. The Sonora models are also not appropriate, as they are cloud-free, while late-L dwarfs are very dusty and are expected to have thick, patchy clouds. Therefore, we instead adopt only the SM08 and BT-Settl models as they cover sufficiently high temperatures for this spectral type and include treatments of dust. We selected a grid of parameters ranging from T_eff = 1100 K to 1700 K, log g = 4.0 to 5.5 dex, and for the SM08 models, condensate sedimentation efficiencies from f_sed = 1 to 4 in unit steps. We selected the RV and v sin i grids using the same method as before (Section 4.1): by first testing a large, coarse grid to determine the approximate RV and v sin i values. The final grid was between −5 km s⁻¹ and −30 km s⁻¹ for RV and between 70 km s⁻¹ and 110 km s⁻¹ for v sin i, both in steps of 0.1 km s⁻¹.

As for 2MASS J0348–6022 (Section 4.1), we find that a wide range in parameters fit the z band equally well. It is not diagnostic for our study, and we exclude the z band from our analysis. The J-band data had fairly low signal-to-noise ratio and had no regions with clearly defined lines from which we could measure v sin i. We instead selected two narrow regions in the H band, along with a narrow region in the K band. In the H band we selected 1.50–1.55 μm and 1.72–1.78 μm, where the first region is dominated by H₂O, and the second is dominated by FeH, H₂O, and potentially some CH₄. The best lines in our data set for measuring v sin i in the K band are H₂O lines between 1.970 μm and 2.055 μm, located on either side of a major telluric feature where our data have very low quality. We opted to mask out this region (2.00–2.02 μm) before fitting the models. We show the narrow-band fits in Figure 10, and the full-band fits in Figure 11.

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We also find a high degree of rotational broadening for 2MASS J1219+3128, with v sin i = 79.0 ± 3.4 km s⁻¹ (Table 3). This is consistent with the short photometric period for this object. The adopted parameters from the spectroscopic fitting are shown in Table 5.

Based on its L3.5 spectral type, 2MASS J0407+1546 is expected to have an effective temperature of ∼1800 K (e.g., Stephens et al. 2009; Filippazzo et al. 2015), with a fairly cloudy atmosphere. We therefore select the SM08 and BT-Settl models. We do not include the Sonora models as they are cloudless, or the Morley models as they are for temperatures below 1300 K. We selected the following parameter grid for fitting: T_eff = 1500 K to 2100 K in steps of 100 K, log g = 4.0 dex to 5.5 dex in steps of 0.5 dex, and condensate sedimentation efficiency f_sed = 1 to 4 in unit steps. We selected 30 km s⁻¹ to 60 km s⁻¹ for RV and 75 km s⁻¹ to 100 km s⁻¹ for v sin i, both in steps of 0.1 km s⁻¹. Our GNIRS observations cover the narrow region from 2.275 μm to 2.332 μm, which contains primarily H₂O and CO lines. We show the best-fitting models in Figure 12.

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The narrower-wavelength coverage of our GNIRS data means we have limited effective temperature and sedimentation efficiency information compared to the full-band spectra of the two other objects. Although we cannot place a high confidence on the results for these two parameters, we find that the effective temperature is consistent with expectations for an L3.5 dwarf, with T_eff = 1840 ± 210 K. We find a high degree of rotational broadening, at v sin i = 82.6 ± 0.2 km s⁻¹, consistent with the short rotational period. Table 5 lists all of the physical parameters detemined from the spectroscopic fits.

The ${1.080}_{-0.005}^{+0.004}$ hr, ${1.14}_{-0.01}^{+0.03}$ hr, and ${1.23}_{-0.01}^{+0.01}$ hr photometric periods of our three L and T dwarfs are shorter than any others yet observed (Figure 13; Table A1). The previously reported shortest photometric period for an ultra-cool dwarf was 1.41 ± 0.01 hr for the T6 2MASS J22282889−4310262 (Clarke et al. 2008; Buenzli et al. 2012; Metchev et al. 2015). Route & Wolszczan (2016) have reported an even shorter possible period, 0.288 hr for the T6 dwarf WISEPC J112254.73+255021.5, based on radio flare observations from the Arecibo Observatory radio telescope. However, they indicate that the 0.288 hr period may be a harmonic of a longer period, or that the flares may in fact not have been periodic. They base their period on five flaring events with the first and last separated by ∼240 days. When analyzing the data with the flares removed, they do not find any indication of variability. A later study by Williams et al. (2017) using the Very Large Array confirmed the same object to have variable polarized emission, but with a longer period of 1.93 hr. They also observed the target photometrically in the z band using Gemini/GMOS-N, and did not find any indication of variability. We therefore do not consider WISEPC J112254.73+255021.5 as an ultra-fast rotator, leaving the three objects reported here as the fastest known L or T dwarf rotators.

We find a high degree of rotational line broadening for all three targets, consistent with the short photometric periods. At projected rotation velocities of 103.5 km s⁻¹ for 2MASS J0348−6022 (T7), 79.0 km s⁻¹ for 2MASS J1219+3128 (L8) and 82.6 km s⁻¹ for 2MASS J0407+1546 (L3.5), these are among the most rapidly spinning ultra-cool dwarfs known to date. In the comprehensive compilation of ultra-cool dwarf rotation measurements by Crossfield (2014), he lists only two other ultra-cool dwarfs with v sin i > 80 km s⁻¹: HD 130948C (86 km s⁻¹, L4) and LP 349–45B (83 km s⁻¹, M9), both from Konopacky et al. (2012).

The rapid projected rotational velocities of our targets confirm that the ∼1 hr periodicities of their light curves correspond to their true rotation periods, and that they are not more slowly rotating brown dwarfs with multiple spots at semi-regular longitudinal intervals, as seen on Jupiter (de Pater et al. 2016), or beat patterns arising from planetary-scale waves (Apai et al. 2017).

The v sin i measurements give lower limits on the true rotational velocities and may so be used to constrain the spin-axis inclinations of our targets. We assume that these brown dwarfs rotate as rigid spheres so that the equatorial rotation velocity is $v=2\pi R/P$, where P is the photometric rotation period, and R is the radius. We estimate the radii, masses, and ages by comparing our findings for surface gravities and effective temperatures to the log g–T_eff grid in the evolutionary models of SM08. Oblateness due to the rapid rotation (see Section 5.2; notes in Table 5) and the corresponding increase in equatorial radius produce a second-order effect, which we have ignored in these calculations. Combining the radii (R), the photometric periods (P_rot), and the spectroscopically determined projected rotational velocities (v sin i), we calculate the inclinations (i) and the equatorial rotation velocities (v_eq) of our targets (Table 5). All three L and T dwarfs have equatorial velocities ≳100 km s⁻¹, and 2MASS J0348–6022 (T7) is seen near equator-on.

All three objects are also likely substellar. At a spectral type of L3.5, 2MASS J0407+1546 is the warmest and potentially most massive among our three L and T dwarfs. Its evolutionary model-dependent mass estimate is 0.037–0.073 M_⊙ (Table 5). Optical spectroscopy from Reid et al. (2008) does not reveal lithium absorption, so it must be >0.060 M_⊙ (e.g., Burrows et al. 1997). This still leaves the estimated 0.060–0.073 M_⊙ mass of 2MASS J0407+1546 mostly in the substellar (<0.072 M_⊙) domain.

The L3.5 dwarf 2MASS J0407+1546 is also known to be chromospherically active based on the strong (60 Å equivalent width) Hα emission reported by Reid et al. (2008). Its rapid rotation and Hα emission may well indicate the presence of an aurora. Based on radio detections of three L and T dwarfs with short (1.5 hr–2.2 hr) rotation periods, Kao et al. (2018) conclude that rapid rotation is key to powering auroral emissions via the electron cyclotron maser instability (Hallinan et al. 2007, 2015). Kao et al. (2016), Pineda et al. (2017), and Richey-Yowell et al. (2020) further demonstrate that brown dwarf Hα and radio luminosities and radio aurorae are correlated. It is possible that all three of our rapidly rotating brown dwarfs have strong dipole fields that power auroral emission (Kao et al. 2018). In particular, the near equator-on view of the T7 dwarf 2MASS J0348–6022 makes it an excellent candidate for seeking pulses of circularly polarized electron cyclotron maser emission. This is already known from other rapidly rotating ultra-cool dwarfs seen at their equators (Berger et al. 2001; Hallinan et al. 2007).

An upper limit on the spin rate of brown dwarfs exists from simple arguments of rotational stability. Konopacky et al. (2012) estimate that their two most rapidly rotating ultra-cool dwarfs, HD 130948C (v sin i = 86 km s⁻¹) and LP 349–45B (v sin i = 83 km s⁻¹) rotate at approximately 30% of break-up speed. The break-up periods for typical >1 Gyr-aged field brown dwarfs are in the tens of minutes. For example, a massive 0.07 M_⊙, 0.09 R_⊙ brown dwarf has ${P}_{\mathrm{breakup}}\,=2\pi {({R}^{3}/{GM})}^{1/2}=17\,\min$, while a low-mass 0.02 M_⊙, 0.12 R_⊙ brown dwarf has P_breakup = 49 min. These are approximately consistent with extrapolations from the shortest known (5 hr) brown dwarf rotation period at 5 Myr (Scholz et al. 2015), assuming that the fastest rotators at  5 Myr remain the fastest when they contract and age. Using the evolutionary models of (non-accreting) brown dwarfs from Baraffe et al. (2015), by 3 Gyr conservation of angular momentum, dictates periods in the 10–70 min range (e.g., Schneider et al. 2018).

The 65–74 min periods of our three fast rotators are at the long end of this range. They would be near break-up only if they all had very low masses and large radii, i.e., were young brown dwarfs with low surface gravities. This is highly unlikely, given the wide range in spectral types (L3.5–T7) of our three rapid rotators, and the fact that their moderate-to-high surface gravities (log g ≳ 5.0; Table 5) point to >0.1 Gyr ages. Using our measured RVs and precise proper motions and parallaxes determined from the Hawaii Infrared Parallax Program (Liu et al. 2016; Best et al. 2020) or from Spitzer (Kirkpatrick et al. 2019), the BANYAN Σ young moving group tool (Gagné et al. 2018) reports that the space motions of all three L and T dwarfs are ≥99% consistent with field-dwarf kinematics. Only for 2MASS J0407+1546 (L3.5) is there a 1% chance of membership in the 40–50 Myr Argus association (Zuckerman 2019), and Gagné et al. (2015b) independently discuss that this object may either be ∼200 Myr old or have peculiar metallicity, based on weaker FeH and slightly weaker alkali line widths. Thus, 2MASS J0407+1546 may indeed be moderately young, even if it is not a member of any of the known young stellar moving groups.

To assess the proximity to break-up spin-velocity, we consider the effect of the centrifugal acceleration on surface gravity. Rapid rotation decreases the surface gravity near the equator, and may make the object appear younger. We can determine the surface gravity decrement due to the centrifugal acceleration using the inferred radii and equatorial velocities (Table 5). For our potentially fastest and largest rotator, the L8 dwarf 2MASS J1219+3128, the centrifugal acceleration is ${a}_{c}={v}^{2}/R=1.6\times {10}^{4}\,\mathrm{cm}$ s⁻² ($\mathrm{log}{a}_{c}=4.2$), where v_eq = 107 km s⁻¹ and R = 0.100 R_⊙. The centrifugal acceleration thus reduces the surface gravity at the equator by about 13%, when compared to the log g = 5.1 ± 0.5 surface gravity inferred from the photospheric model fitting (Table 5). While this does indicate that the rotation speed amounts to a significant fraction (35%) of the break-up speed, we note that it has a minor effect on our ability to assess the surface gravity spectroscopically.

The rotational stability limit for brown dwarfs may not necessarily be set by the centrifugal levitation argument above. The stability limit for the oblateness f (fractional difference between polar and equatorial radii) of axisymmetric rotating polytropes for brown dwarf-like structures (n ∼ 1 to 1.5) is about 0.4 (James 1964). The Darwin–Radau relationship (e.g., Barnes & Fortney 2003) connects the oblateness, mass, radius, rotation, and moment of inertia for objects with smoothly varying interiors. Using the central values from Table 5, we compute oblateness factors of 0.08, 0.08, and 0.05 for the most (2MASS J0348–6022, 2MASS J1219+3128) and least (2MASS J0407+1546) oblate objects. This places the spin rates of both 2MASS J0348–6022 and 2MASS J1219+3128 at about 45% of their rotational stability limits: closer to instability than indicated by the rigid-body rotation break-up velocity estimates. For comparison, Saturn, the most oblate planet in the solar system, has an oblateness of 0.1. The brown dwarfs have surface gravities about 100 times greater than Saturn but rotation rates 10 times faster. Since oblateness scales as Ω²/g (where Ω is the rotation rate), it is not surprising the oblateness of these objects is comparable to that of Saturn.

Finally, the preceding discussion ignores the effect of any magnetic dynamo from the metallic hydrogen interior, which may be an important contributor to the energy balance in such rapid rotators, and may further limit the maximum spin velocity. So these three objects may be even closer to instability than indicated by estimates that ignore magnetic fields.

From an observational standpoint, the three rapid rotators delineate a clear lower boundary to the envelope of all 78 L-, T-, and Y-dwarf rotation periods measured to date (Figure 13). This limit holds over a broad range of spectral types, for objects that presumably have different ages. Hence, ∼1 hr may be close to a physical lower limit to the spin period of field-aged Jupiter-sized brown dwarfs.

Because of their significant oblateness, the three rapid rotators are potentially good targets for searches for polarized thermal emission (e.g., Marley & Sengupta 2011; de Kok et al. 2011; Stolker et al. 2017). Several surveys have been successful in detecting polarized thermal emission from brown dwarfs (e.g., Ménard et al. 2002; Zapatero Osorio et al. 2005; Miles-Páez et al. 2013, 2017c; Millar-Blanchaer et al. 2020), which could be attributed to inhomogeneous cloud cover or oblateness. Intriguingly, Miles-Páez et al. (2013) find that ultra-cool dwarfs with the fastest rotation (v sin i ≥ 60 km s⁻¹) are more likely to exhibit linear polarization and at a larger degree than slower rotators.

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