Draft version November 28, 2016 A Preprint typeset using LTEX style emulateapj v. 03/07/07

LONG-TERM, MULTIWAVELENGTH LIGHT CURVES OF ULTRA-COOL DWARFS: II. THE EVOLVING LIGHT CURVES OF THE T2.5 SIMP 0136 & THE UNCORRELATED LIGHT CURVES OF THE M9 TVLM 513 Bryce Croll1, Philip S. Muirhead1 2, Jack Lichtman3, Eunkyu Han2, Paul A. Dalba2, Jacqueline Radigan4 Draft version November 28, 2016

ABSTRACT We present 17 nights of ground-based, near-infrared photometry of the variable L/T transition brown dwarf SIMP J013656.5+093347 and an additional 3 nights of ground-based photometry of the radio-active late M-dwarf TVLM 513-46546. Our TVLM 513-46546 photometry includes 2 nights of simultaneous, multiwavelength, ground-based photometry, in which we detect obvious J-band vari- ability, but do not detect I-band variability of similar amplitude, confirming that the variability of TVLM 513-46546 most likely arises from clouds or aurorae, rather than starspots. Our photometry of SIMP J013656.5+093347 includes 15 nights of J-band photometry that allow us to observe how the variable light curve of this L/T transition brown dwarf evolves from rotation period to rotation period, night-to-night and week-to-week. We estimate the rotation period of SIMP J013656.5+093347 as 2.406 ± 0.012 hours, and do not find evidence for obvious differential rotation. The peak-to-peak amplitude displayed by SIMP J013656.5+093347 in our light curves evolves from greater than 6% to less than 1% in a matter of days, and the typical timescale for significant evolution of the SIMP J013656.5+093347 light curve appears to be approximately <1 to 10 rotation periods. This suggests that those performing spectrophotometric observations of brown dwarfs should be cautious in their interpretations comparing the spectra between a variable brown dwarf’s maximum flux and minimum flux from observations lasting only approximately a rotation period, as these comparisons may depict the spectral characteristics of a single, ephemeral snapshot, rather than the full range of characteristics. Subject headings: brown dwarfs – techniques: photometric – stars: rotation – stars: individual: SIMP J013656.5+093347 – stars: individual: TVLM 513-46546

1. INTRODUCTION free regions, or caused by varying haze layers (Yang et Over the last number of years simultaneous, multi- al. 2015). wavelength photometric and spectrophotometric obser- However, a number of these detailed studies only ob- vations of variable brown dwarfs at the L/T transition served these variable brown dwarfs for tens of minutes have enabled a number of detailed investigations at- (e.g. Buenzli et al. 2014), to hours at a time (e.g. tempting to elucidate the cause of the observed variabil- Apai et al. 2013; Buenzli et al. 2015a; Yang et al. ity (e.g. Artigau et al. 2009; Radigan et al. 2012; Buen- 2015). This is in spite of the fact that, since the first zli et al. 2012; Apai et al. 2013; Buenzli et al. 2014, detections of large amplitude variability in L/T transi- 2015a; Yang et al. 2015, 2016). The result of these in- tion brown dwarfs, the photometric light curves of some vestigations has been increased understanding of the role of these objects have been shown to display significant that fluctuations in cloud condensate opacity play in the evolution in their light curves (e.g. Artigau et al. 2009; observed variability. Upon the first detections of signif- Radigan et al. 2012; Gillon et al. 2013). Thus, the conclu- icant variability at the L/T transition (e.g. Artigau et sions these detailed, spectrophotometric studies reach are al. 2009; Radigan et al. 2012) the belief was that the ob- based inherently on an ephemeral snapshot, that might served fluctuations were caused by gaps or holes in thick not be indicative of the usual behaviour of the L/T dwarf, clouds exposing hotter regions underneath, rotating in or might not cover the extreme range of variability be- and out of view (Ackerman & Marley 2001; Burgasser haviour displayed by the ultra-cool dwarf. et al. 2002; Artigau et al. 2009). More recent simultane- To determine whether these detailed, spectrophoto- ous multiwavelength photometry, or spectrophotometry metric observations capture the range of characteristics – especially driven by the impressive, spectrophotomet- of ultra-cool dwarfs, longer-term light curves of these ric capabilities of the WFC3 instrument (MacKenty et variable ultra-cool dwarfs are required. To date, a hand- al. 2010) on the Hubble Space Telescope (HST) – have ful of nights of photometry have captured the evolu- revealed the possibility that these variations were more tion of the light curves of the L/T transition brown specifically caused by thick or thin clouds (Radigan et al. dwarf SIMP J013656.5+093347 (e.g. Artigau et al. 2009; 2012; Buenzli et al. 2015a), rather than outright cloud- Metchev et al. 2013; Radigan et al. 2014), and the sig- nificant night-to-night evolving variability of the L/T 1 Institute for Astrophysical Research, Boston University, transition Luhman-16 binary system (Gillon et al. 2013). 725 Commonwealth Ave. Room 506, Boston, MA 02215; Kepler has now returned photometry of two early L [email protected] dwarfs allowing the evolution, or lack thereof, of their 2 Department of Astronomy, Boston University, 725 Common- wealth Ave., Boston, MA 02215, USA optical light curves to be tracked for two years for an 3 Department of Physics, University of Connecticut, 2152 Hill- L0 dwarf (WISEP J190648.47+401106.8; Gizis et al. side Road, Unit 3046 Storrs, CT 06269-3046 ∼ 4 2013, 2015) and 36 days for an L8 dwarf (WISEP Utah Valley University, Orem, UT 84058, USA J060738.65+242953.4; Gizis et al. 2016). Relatively con- 2 Croll et al. stant variability was detected for the L0 dwarf WISEP occasional aurorae (Hallinan et al. 2015). Longer term J190648.47+401106.8 (Gizis et al. 2013, 2015), while for light curves of ultra-cool dwarfs can also inform our un- the L8 dwarf WISEP J060738.65+242953.4 a lack of vari- derstanding of whether one or more of these physical ability was detected, arguably due to a pole-on inclina- mechanisms play a role in the observed variability on a tion of the ultra-cool dwarf (Gizis et al. 2016). What is single ultra-cool dwarf. needed to advance this science is many more long term To illuminate these various questions here we attempt light curves of ultra-cool dwarfs that accurately track to observe how the variability of two well known variable the evolution, or lack thereof, of the light curves of these ultra-cool dwarfs evolves from rotation period to rotation objects from rotation period to rotation period, night-to- period, night-to-night and week-to-week. In Section 2 we night, week-to-week, season-to-season and even year-to- provide an overview of our two targets: the variable T2.5 year. brown dwarf SIMP J013656.5+093347, and the variable In addition to L/T transition objects, the cause of vari- M9 dwarf TVLM 513-46546. In Section 3 we present 17 ability of M/L transition objects has also attracted grow- nights of photometry of SIMP J013656.5+093347, and ing interest recently (e.g. Gelino et al. 2002; Littlefair et 3 nights of photometry of TVLM 513-46546, including al. 2008; Harding et al. 2013; Metchev et al. 2015; Halli- 2 nights of simultaneous multiwavelength photometry of nan et al. 2015). Starspots are the usual explanation for TVLM 513-46546. In Section 4 we analyze the rapidly variability of ultra-cool dwarfs on the stellar side of the evolving light curves of SIMP J013656.5+093347; for hydrogen-fusing limit. M-dwarfs are notoriously active – SIMP J013656.5+093347 the peak-to-peak amplitude of nearly all very late M-dwarfs are active, with detections variability evolves from a minimum of less than 1% to a of Hα, a common activity marker, rising throughout the maximum of greater than 6% in just a handful of nights. M-spectral class (West et al. 2004; Schmidt 2015). Ro- This suggests that those performing detailed compar- tation periods for M-dwarfs, revealed by Doppler imaging isons of the spectra of L/T transition brown dwarfs be- techniques (Barnes & Collier Cameron 2001 ; Barnes et tween the maximum flux and minimum flux displayed al. 2004), and by photometry (Rockenfeller et al. 2006; in a observation lasting only a single rotation period, Irwin et al. 2011), have indicated that starspots are per- should be aware that this comparison may reveal very vasive on M-dwarfs. different conclusions if the variability amplitude is small Recently, clouds have been found to play a role not only (less than ∼1% peak-to-peak amplitudes), compared to on L/T transition objects, but possibly throughout the when the variability is considerably greater. We find no whole L spectral class (Metchev et al. 2015). Therefore, evidence for obvious differential rotation in our it is possible that clouds may even lead to some of the SIMP J013656.5+093347 light curves. In Section observed variability for very late M-dwarfs (e.g. Jones 5 we show that the fact we detect near-infrared variabil- & Tsuji 1997). The detection of anti-correlated light ity without detectable accompanying optical variability curves on the M9 dwarf TVLM 513-46546 was at first from our multiwavelength photometry confirms that the inferred to be due to the presence of clouds even on this variability of TVLM 513-46546 most likely arises from late M-dwarf (Littlefair et al. 2008). clouds or aurorae. More recently, in addition to clouds, aurorae – similar 2. OUR ULTRA-COOL DWARF TARGETS to the planetary aurorae in our solar system (e.g. Clarke 2.1. et al. 1980) – have been suggested to be another pos- The T2.5 dwarf SIMP 0136 sibility to explain the observed variability of ultra-cool The T2.5 dwarf SIMP J013656.5+093347 (hereafter dwarfs. Such auroral activity has been observed on an SIMP 0136; Artigau et al. 2006) is one of the best stud- M8.5 dwarf at the end of the main sequence (Hallinan et ied variable brown dwarfs at the L/T transition. It is al. 2015). Multiwavelength photometry of this dwarf dis- arguably the archetype for L/T transition brown dwarfs plays light curves that are anti-correlated in phase, and displaying significant variability, as it was the first brown Hallinan et al. (2015) speculate that the aforementioned dwarf discovered that exhibited large amplitude variabil- anti-correlated light curves of TVLM 513-46546 (Little- ity; Artigau et al. (2009) first announced that SIMP fair et al. 2008), and possibly other late M-dwarfs, may 0136 displayed prominent ∼5% variability from a num- result from auroral activity. In addition, auroral activity ber of nights of J-band monitoring of this dwarf using may not simply be constrained to the M/L transition, the 1.6-m Observatoire du Mont Megantic. The Artigau as recent radio detections of polarized, pulsed emissions et al. (2009) SIMP 0136 light curves displayed obvious from a T2.5 dwarf (Kao et al. 2016) and a T6.5 dwarf evolution from night-to-night, as some nights of J-band (Route & Wolszczan 2012; Williams and Berger 2015) monitoring displayed quasi-sinusoidal variability, while indicate this phenomenon may extend even to the L/T others displayed double-peaked behavior indicative of at transition. Therefore, an additional possibility is that least two spot/cloud groups separated in longitude on the variability at the L/T transition is caused in part the brown dwarf. In spite of the obvious evolution from or wholly by auroral activity, rather than the commonly night-to-night of the SIMP 0136 light curves, Artigau et accepted fluctuations in cloud condensate opacity. al. (2009) estimated the rotation period of SIMP 0136 Furthermore, it is also possible, or arguably likely, that to be 2.3895 ± 0.0005 hours from fitting two sinusoids the variability of a single ultra-cool dwarf may be driven to their two nights of double-peaked, ground-based light by more than a single one of the previously mentioned as- curves. trophysical variability mechanisms. Magnetically driven Despite the obvious, large amplitude variability dis- cool or hot starspots may be periodically obscured by played by SIMP 0136, the number of nights of photomet- time evolving clouds (Lane et al. 2007; Heinze et al. 2013; ric follow-up to observe how the light curve of SIMP 0136 Metchev et al. 2015), or the variability of predominantly evolves from rotation period to rotation period, night-to- cloudy brown dwarfs may be affected by the presence of night, and season to season has been limited. Metchev Multiwavelength Photometry of Ultra-Cool Dwarfs 3 et al. (2013) presented an additional 6 nights of J-band of I and i’-band monitoring of TVLM 513 with peak-to- monitoring of SIMP 0136 from the 1.6-m Observatoire peak variability amplitudes that varied between ∼0.6 - du Mont Megantic. Apai et al. (2013) obtained six HST 1.2% from their photometry; Harding et al. (2013) used orbits of SIMP 0136 utilizing HST/WFC; they found the these light curves to infer a rotation period of 1.95958 ± spectra were best-fit by a combination of thick, dimmer, 0.00005 hr, while Wolszczan & Route (2014) in- low-temperature clouds and thin, brighter, warm clouds. ferred a rotation period of 1.959574 ± 0.000002 Radigan et al. (2014) observed SIMP 0136 in J-band for hr from a combination of optical and radio moni- ∼2.3 hours and detected 2.9% peak-to-peak variability. toring of TVLM 513. Perhaps most intriguingly, Lit- Yang et al. (2016) performed simultaneous HST/J-band tlefair et al. (2008) performed 2.7 hours of simultaneous and Spitzer/IRAC 3.6 µm, and some 4.5 µm, photom- optical monitoring of TVLM 513 in the g’ and i’-bands etry of SIMP 0136 for a few hours and detected a ∼30 and detected anti-correlated 3-4% sinusoidal variability degree phase shift between their J-band and 3.6 µm pho- with a period of approximately 2 hours. Littlefair et tometry; Yang et al. (2016) confirmed that SIMP 0136 al. (2008) initially interpreted this anti-correlated light variability was driven by clouds, with different layers of curve to likely be the result of inhomogeneous cloud cov- clouds at different pressure levels, and therefore depths in erage on TVLM 513; however, more recently, with the the atmosphere, causing the observed phase shifts. Most detection of auroral emission on another similar late M- recently, Kao et al. (2016) detected SIMP 0136 at radio dwarf (the M8.5 dwarf LSR J1835+3259; Hallinan et al. wavelengths, although they were not able to determine 2015), auroral emission is now another plausible expla- a radio period from 4 hours of Very Large Array nation for the observed anti-correlated variability. More observations. recently, Miles-Paez et al. (2015) performed optical linear Here we attempt to probe the evolution of the light polarimetry of TVLM 513 and detected ∼2 hour period- curve of SIMP 0136 by presenting 15 nights of J-band icity in their data. photometric monitoring of SIMP 0136 spread out over Here we present 3 nights of photometry of TVLM 90 days using the 1.8-m Perkins Telescope at Lowell Ob- 513, including 2 nights of simultaneous optical and servatory. Our many nights of J-band observations allow near-infrared photometric monitoring of this ultra-cool us to observe how the variability of SIMP 0136 evolves dwarf. Our simultaneous, multiwavelength photometry from rotation period to rotation period, night-to-night of TVLM 513 displays prominent J-band variability with and week-to-week. Specifically, we demonstrate that the a ∼2.0 hour period, similar to the previous radio detec- peak-to-peak amplitude of variability evolves from less tions of this object. As we are unable to detect prominent than 1% to greater than 6% for a rotation period in ap- I-band variability from our simultaneous optical photom- proximately a week. etry for this object, the most likely explanation for the variability of TVLM 513 is either clouds or aurora, rather 2.2. The M9 dwarf TVLM 513-46546 than starspots. The rapidly-rotating, radio active M9 dwarf TVLM 3. 513-46546 (hereafter TVLM 513) has undergone consid- OBSERVATIONS erable monitoring at radio wavelengths and occasional We observed the ultra-cool dwarfs SIMP 0136 and monitoring at optical wavelengths. Although TVLM 513 TVLM 513 using a variety of telescopes at the Lowell was originally assigned a spectral type of M8.5 (Kirk- Observatory. SIMP 0136 was observed for 17 nights patrick et al. 1995), more recently Reid et al. (2008) spread out over 122 days, while TVLM 513 was ob- and West et al. (2011) assign a spectral type of M9 to served for 3 nights over 46 days. The observations TVLM 513, and Dahn et al. (2002) report an effective of these dwarfs were conducted using the Perkins 1.8- temperature of ∼2300 K. TVLM 513 is most likely a star m telescope, and the Hall 1.1-m telescope. Our pho- at the very bottom of the main sequence (Tinney et al. tometry from the Perkins telescope was obtained us- 1993); a lack of lithium absorption from TVLM 513 sug- ing either the PRISM imager (Janes et al. 2004; ′ ′ gests a mass in excess of ∼0.06 M⊙, and an age greater which has a 13.65 ×13.65 field-of-view), in the op- than ∼100 Myr (Martin et al. 1994; Reid et al. 2002). tical and very near-infrared, or the Mimir instrument TVLM 513 has been a frequent target for monitoring (Clemens et al. 2007; which has a 10′×10′ field- at radio wavelengths (e.g. Berger 2002; Hallinan et al. of-view) in the near-infrared. On the Hall telescope we 2007; Berger et al. 2008). Hallinan et al. (2007) de- used the NASA42 imager (which has a 22′×22′ field- tected prominent radio bursts from TVLM 513 with a pe- of-view). The filters used on the various tele- riod of ∼1.96 hours that they inferred to be the rotation scopes were: the Perkins/PRISM observations period of this ultra-cool dwarf. Emission from TVLM employed a Sloan-z’ filter, the Hall/NASA42 ob- 513 has also been detected at millimeter wavelengths servations employed either a Sloan-z’ or a John- (Williams et al. 2016) with the Atacama Large Mil- son I-band filter, and the Perkins/Mimir observa- limeter/submillimeter Array (ALMA), a detection that tions employed Mauna Kea Observatories (MKO) is inferred to be due to the synchrotron process. Hα emis- J or Ks-band filters. sion has also been detected from TVLM 513 (Martin et Our optical and near-infrared photometry was reduced al. 1994; Basri 2001; Berger et al. 2008). and analyzed using the techniques described fully in Croll TVLM 513 has also undergone significant optical pho- et al. (2016). Unlike the data presented in Croll et tometric monitoring of its variability. Lane et al. (2007) al. (2016) we do not attempt to employ fringe frames detected I-band variability at the ∼10 mmag level from to remove the obvious fringes in any of our I-band or 12 hours of optical monitoring, and suggested this vari- z’-band data on the Hall or Perkins telescope. For ability was driven by magnetic starspots on this ultra- our Perkins/Mimir data we employ the Clemens et al. cool dwarf. Harding et al. (2013) presented 10 nights (2007) non-linearity correction; we have also repeated 4 Croll et al.

TABLE 1 SIMP 0136 Observing Log

a c e Date Telescope Filter Duration Exposure Airmass Conditions Aperture # of σF b d (UTC) &Instrument (hours) Time (sec) (pixels) Stars (%)

2015/08/18 Perkins/MIMIR J 3.23 30;3 1.34 → 1.11 → 1.13 Clear 5,15,25 5 0.5 2015/08/21 Perkins/MIMIR J 3.21 30;3 1.29 → 1.11 → 1.14 Clear 6,15,25 5 0.6 2015/09/27 Perkins/PRISM z’ 7.75 150;18 1.83 → 1.11 → 2.01 Clear 6,15,27 7 2.7 2015/10/09 Perkins/MIMIR J 2.87 30;8 1.17 → 2.14 Clear 6,15,25 3 0.5 2015/11/10 Perkins/MIMIR J 8.82 30;3 2.61 → 1.11 → 2.18 Clearandwindy 6,15,25 3 0.8 2015/11/12 Perkins/MIMIR J 9.47 30;3 2.62 → 1.11 → 3.00 Clear 6,15,25 5 1.0 2015/11/13 Perkins/MIMIR J 8.82 30;3 2.34 → 1.11 → 2.40 Thincirrus 6,15,25 5 1.2 2015/11/18 Perkins/MIMIR J 8.71 30;3 2.12 → 1.11 → 2.56 Occasionalclouds 6,15,25 5 2.3 2015/11/19 Perkins/MIMIR J 7.96 30;3 1.99 → 1.11 → 2.00 Occasionalclouds 6,15,25 5 1.5 f 2015/11/20 Perkins/MIMIR J,Ks 8.56 30,15;3,3 2.01 → 1.11 → 2.57 Clear 6[7] ,15,25 5,5 0.8,1.6 2015/11/21 Perkins/MIMIR J 8.74 30;3 2.01 → 1.11 → 2.78 Occasionalclouds 6,15,25 4 1.2 2015/11/22 Perkins/MIMIR J 8.61 30;3 2.05 → 1.11 → 2.54 Clear 6,15,25 5 0.6 2015/11/25 Perkins/MIMIR J 5.41 30;3 1.76 → 1.11 → 1.23 Occasionalclouds 6,15,25 5 1.4 2015/11/27 Perkins/MIMIR J 8.78 30;3 1.86 → 1.11 → 3.26 Clear 6,15,25 5 1.0 2015/11/29 Perkins/MIMIR J 8.10 30,25;3 1.78 → 1.11 → 2.42 Clear 6,15,25 5 1.7 2015/11/29 Hall/NASA42 z’ 7.92 180;9 1.76 → 1.11 → 2.27 Clear 4,14,26 19 0.5 2015/11/30 Perkins/MIMIR J 8.46 30;3 1.78 → 1.11 → 2.90 Clear 6,15,25 5 0.9 2015/12/17 Perkins/MIMIR Ks 6.42 15;3 1.26 → 1.11 → 2.38 Clear 6,15,25 5 1.2 a The duration indicates the time between the first and last observation of the evening, and does not take into account gaps in the data due to clouds, humidity or poor weather. b The time before the semi-colon is the exposure time, while the time after the semi-colon is the overhead. The overhead includes time for read-out, and any other applicable overheads. c We give the radius of the aperture, the radius of the inner annulus and the radius of the outer annulus that we use for sky subtraction in pixels. d The “# of Stars” column denotes the number of comparison stars used in our differential photometry to correct our target star photometry. e σF is our estimate of the photometric error of an individual exposure. f 6 is the radius of the aperture for our J-band analysis, while 7 is the aperture radius for our Ks-band analysis from this night.

TABLE 2 TVLM 513 Observing Log

a c e Date Telescope Filter Duration Exposure Airmass Conditions Aperture # of σF b d (UTC) &Instrument (hours) Time (sec) (pixels) Stars (%)

2016/03/31 Perkins/PRISM z’ 2.77 40;18 1.02 → 1.26 Clear 10,17,29 10 0.6 2016/05/15 Perkins/MIMIR J 7.28 10;3 1.27 → 1.02 → 1.96 Initiallightclouds 6,15,25 3 2.3 2016/05/15 Hall/NASA42 I 8.16 180;9 1.54 → 1.02 → 1.93 Initiallightclouds 7,14,26 3 0.8 2016/05/16 Perkins/MIMIR J 8.69 10;3 1.59 → 1.02 → 2.27 Clear 6,15,25 3 1.3 2016/05/16 Hall/NASA42 I 8.04 180;9 1.49 → 1.02 → 1.95 Clear 4.5,14,26 5 0.3

a The duration indicates the time between the first and last observation of the evening, and does not take into account gaps in the data due to clouds, humidity or poor weather. b The time before the semi-colon is the exposure time, while the time after the semi-colon is the overhead. The overhead includes time for read-out, and any other applicable overheads. c We give the radius of the aperture, the radius of the inner annulus and the radius of the outer annulus that we use for sky subtraction in pixels. d The “# of Stars” column denotes the number of comparison stars used in our differential photometry to correct our target star photometry. e σF is our estimate of the photometric error of an individual exposure. the forthcoming analysis not using a non-linearity cor- while our TVLM light curves are displayed in Figure 3. rection for our Perkins/Mimir data and note that the 4. SIMP 0136 major conclusions of the paper are basically unchanged. We summarize our SIMP 0136 observations in Table 1 4.1. The Rotation Period of SIMP 0136 and our TVLM 513 observations in Table 2. All dates Here we attempt to determine the rotation period of given in this paper are UT dates. In these tables we SIMP 0136 from our photometric light curves. The give the aperture sizes, and annuli sizes, we used for our quasi-sinusoidal variability displayed in our SIMP 0136 aperture photometry, as well as the number of com- light curves suggest that Lomb-Scargle periodograms parison stars used in our differential photometry (Lomb 1976; Scargle 1982) may be a suitable method to for each of our data-sets. In Table we also quote determine the rotation period of SIMP 0136. We present our estimate of the photometric uncertainty for Lomb Scargle periodograms of all our unbinned J-band each individual exposure, σF ; due to the intrinsic photometry of SIMP 0136 in Figure 4. We utilize the variability of our target stars we calculate σF us- technique discussed in Croll et al. (2016) to estimate ing nearby non-variable reference stars using the the associated errors on the peak periodogram value, and technique discussed in Croll et al. (2015b). Our infer a photometric period of 2.48 ± 0.10 hours. Simi- SIMP 0136 light curves are displayed in Figure 1 and 2, larly, we present a Lomb-Scargle periodogram of the Multiwavelength Photometry of Ultra-Cool Dwarfs 5

Hours from Epoch Hours from Epoch -8 -6 -4 -2 0 2 64 66 68 70 72 74

1.04 J-band 72'' 1.04 J-band 72'' 1.02 1.02 1 1 Flux Flux 0.98 0.98 0.96 2015/08/18 0.96 2015/08/21

252.6 252.7 252.8 252.9 253 255.6 255.7 255.8 255.9 256 BJD - 2457000 BJD - 2457000 Hours from Epoch Hours from Epoch 952 954 956 958 960 962 1240 1242 1244 1246 1248 1250

1.04 z'-band 72'' 1.04 J-band 72'' 1.02 1.02 1 1 Flux Flux 0.98 0.98 0.96 2015/09/27 0.96 2015/10/09

292.6 292.7 292.8 292.9 293 304.6 304.7 304.8 304.9 305 BJD - 2457000 BJD - 2457000 Hours from Epoch Hours from Epoch 2008 2010 2012 2014 2016 2018 2056 2058 2060 2062 2064 2066

1.04 J-band 72'' 1.04 J-band 72'' 1.02 1.02 1 1 Flux Flux 0.98 0.98 0.96 2015/11/10 0.96 2015/11/12

336.6 336.7 336.8 336.9 337 338.6 338.7 338.8 338.9 339 BJD - 2457000 BJD - 2457000 Hours from Epoch Hours from Epoch 2080 2082 2084 2086 2088 2090 2200 2202 2204 2206 2208 2210

1.04 J-band 72'' 1.04 J-band 72'' 1.02 1.02 1 1 Flux Flux 0.98 0.98 0.96 2015/11/13 0.96 2015/11/18

339.6 339.7 339.8 339.9 340 344.6 344.7 344.8 344.9 345 BJD - 2457000 BJD - 2457000 Fig. 1.— Photometry of SIMP 0136 on the dates given in the lower-right of each panel (UT) with the Perkins 1.8-m (72”) telescope, at various wavelengths as indicated in the panels. The vertical dashed lines indicate cycles of the apparent ∼2.406 hour rotation period of SIMP 0136, compared to the apparent flux maximum in our J-band photometry at a barycentric julian date (BJD) of: BJD-2457000 ∼252.899. For clarity we plot our photometry binned every ∼4 minutes (∼0.003 d). unbinned data of our highest quality Ks-band light 13) this date, appear to flip, suggesting that the longi- curve of SIMP 0136 (Figure 4); the peak periodogram tude of the cloud gaps5 leading to the observed variability value from our 2015 December 17 Ks-band photometry have significantly changed. This large change in longi- of SIMP 0136 is 2.55 ± 0.12 hours. Both these values are tude of the apparent cloud gaps may have been caused slightly longer than a previous estimate of the rotation by the cloud gaps completely disappearing and reappear- period of SIMP 0136; Artigau et al. (2009) estimated the ing, or a gradual evolution in the longitude of these cloud rotation period of SIMP 0136 as 2.3895 ± 0.0005 hours gaps (due to spot evolution or differential rotation, for in- from fitting two sinusoids to their two nights of double- stance). If the longitudes of these gaps in clouds are con- peaked quasi-sinusoidal J-band photometry. stantly evolving from night-to-night then a Lomb-Scargle We note that the periodic repetition of features, such periodogram of a long-term data-set may not give the as maxima or minima, in the light curve of SIMP 0136 best estimate of the rotation period of this brown dwarf. may not provide an accurate estimate of the rotation pe- Another method that has been used previously to esti- riod of this ultra-cool dwarf. The first reason this might mate the rotation period of SIMP 0136 from photometric be the case, is due to evolution of the SIMP 0136 light light curves (Artigau et al. 2009) has been to fit a short curve. Our SIMP 0136 light curves show occasion sig- segment of data that appears to display obvious period- nificant evolution in the apparent longitude of minima icity and limited light curve evolution. As long as the & maxima, compared to the nominal rotation period of longitude of cloud gaps on SIMP 0136 are stable for a this L/T transition brown dwarf. On the night of 2015 5 November 12 the variability of SIMP 0136 nearly com- For the following discussion we assume that the SIMP 0136 variability is driven by thinner gaps in thick clouds (Artigau et pletely disappears, with peak-to-peak amplitudes of less al. 2009; Apai et al. 2013), but our conclusions are essentially un- than ∼0.5%. The phase of the maxima from two days changed if the variability is driven by spots, aurorae, different cloud prior (2015 November 10) to a day after (2015 November behaviour, or another mechanism. 6 Croll et al.

Hours from Epoch Hours from Epoch 2224 2226 2228 2230 2232 2234 2248 2250 2252 2254 2256 2258

1.04 J-band 72'' 1.04 J-band 72'' Ks-band 72'' 1.02 1.02 1 1 Flux Flux 0.98 0.98 0.96 2015/11/19 0.96 2015/11/20

345.6 345.7 345.8 345.9 346 346.6 346.7 346.8 346.9 347 BJD - 2457000 BJD - 2457000 Hours from Epoch Hours from Epoch 2272 2274 2276 2278 2280 2282 2296 2298 2300 2302 2304 2306

1.04 J-band 72'' 1.04 J-band 72'' 1.02 1.02 1 1 Flux Flux 0.98 0.98 0.96 2015/11/21 0.96 2015/11/22

347.6 347.7 347.8 347.9 348 348.6 348.7 348.8 348.9 349 BJD - 2457000 BJD - 2457000 Hours from Epoch Hours from Epoch 2368 2370 2372 2374 2376 2378 2416 2418 2420 2422 2424 2426

1.04 J-band 72'' 1.04 J-band 72'' 1.02 1.02 1 1 Flux Flux 0.98 0.98 0.96 2015/11/25 0.96 2015/11/27

351.6 351.7 351.8 351.9 352 353.6 353.7 353.8 353.9 354 BJD - 2457000 BJD - 2457000 Hours from Epoch Hours from Epoch 2464 2466 2468 2470 2472 2474 2488 2490 2492 2494 2496 2498

1.04 J-band 72'' 1.04 J-band 72'' z'-band 42'' 1.02 1.02 1 1 Flux Flux 0.98 0.98 0.96 2015/11/29 0.96 2015/11/30

355.6 355.7 355.8 355.9 356 356.6 356.7 356.8 356.9 357 BJD - 2457000 BJD - 2457000 Hours from Epoch 2896 2898 2900 2902 2904 2906

1.04 Ks-band 72'' 1.02 1 Flux 0.98 0.96 2015/12/17

373.6 373.7 373.8 373.9 374 BJD - 2457000 Fig. 2.— Photometry of SIMP 0136 on the dates given in the lower-right of each panel (UT) with the Perkins 1.8-m (72”) and Hall 1.1-m (42”) telescopes, at various wavelengths as indicated in the panels. For clarity we plot our photometry binned every ∼4 minutes (∼0.003 d) for panels featuring single wavelength photometry, and binned every ∼6 minutes (0.004 d) for panels featuring multiwavelength photometry. The figure format is otherwise identical to Figure 1. few rotation periods at a time then this method should 2007). Although photometric starspot models are noto- give a precise estimate of the photometric period. Our riously non-unique (e.g. Croll 2006; Walker et al. 2007; highest precision light curves that display the most ob- Aigrain et al. 2015), in general they are well-suited to re- vious periodicity with little evolution during the night cover the period of variability (Aigrain et al. 2015). We are the following light curves: our J-band light curves on therefore fit each of our light curves with a two starspot 2015 November 10, 2015 November 13, 2015 November model utilizing the Markov Chain Monte Carlo function- 19, 2015 November 21, 2015 November 22, 2015 Novem- ality we discuss in Croll (2006); these starspot model fits ber 27, & 2015 November 30. To determine the pho- are not intended to be unique, but only to return an ac- tometric period from these nights of photometry we fit curate estimate of the period. For the following nights the light curves with circular spots employing a Bud- we remove linear trends from the light curves (see Sec- ding (1977) model utilizing the methodology discussed tion 4.3) to ensure the light curve maxima display rela- in StarSpotz (Croll et al. 2006; Croll 2006; Walker et al. tively constant flux: 2015 November 21, 2015 November Multiwavelength Photometry of Ultra-Cool Dwarfs 7

Hours from Epoch ensure the reduced χ2 of the resulting StarSpotz fits are -1106 -1104 -1102 -1100 -1098 -1096 approximately one. We inspect each one of the result- 1.04 z'-band 72'' 1.03 ing fits from the individual nights to ensure the resulting 1.02 spot model period accurately tracks both the minima 1.01 and maxima in the light curves. All our light curves ap-

Flux 1 0.99 pear to be well fit by a single period, except our 2015 0.98 2016/03/31 0.97 November 30 light curve. A single photometric period 478.7 478.8 478.9 479 479.1 does not appear to track all the minima and maxima of BJD - 2457000 our 2015 November 30 light curve, and therefore we ar- Hours from Epoch tificially scale up the errors on the period determination -26 -24 -22 -20 -18 -16 from that night by a factor of 2. We display the pho- 1.04 J-band 72'' tometric period estimates from the individual nights in 1.03 I-band 42'' Figure 5. The weighted mean and error of these estimates 1.02 of the photometric period are 2.406 ± 0.004 hours. 1.01 Flux 1 Given the obvious evolution in variability that we ob- 0.99 serve, we suggest that the combination of the indepen- 2016/05/15 0.98 dent estimates of the photometric period of SIMP 0136, 523.7 523.8 523.9 524 524.1 from our best nights of photometry (those with the most BJD - 2457000 obvious periodicity, and displaying little light curve evo- Hours from Epoch lution), provides our most suitable estimate of its pho- -2 0 2 4 6 8 tometric period. As we occasionally observe light curve 1.04 J-band 72'' evolution even within a single night of observations, but 1.03 I-band 42'' 1.02 our spot model assumes constant spots for each night of 1.01 observations, we artificially scale up the uncertainty on Flux 1 our period estimate to take this evolution into account; 0.99 0.98 2016/05/16 we choose to scale up the error by a factor of 3 to be con- 524.7 524.8 524.9 525 525.1 servative and to take into account this systematic 7 BJD - 2457000 uncertainty . Therefore, we quote the photometric pe- riod, and therefore the likely rotation period, of the L/T Fig. 3.— Photometry of TVLM 513 on the dates given in the ± lower-right of each panel (UT) in various bands as indicated in transition dwarf SIMP 0136 as 2.406 0.012 hours. the panels. The vertical dashed lines indicate cycles of the ap- These independent estimates of the photometric pe- parent ∼2.0 hour rotation period of TVLM 513-46546 (Hallinan riod of SIMP 0136 from night-to-night, can also be used et al. 2007; Harding et al. 2013), compared to the apparent flux ∼ to search for variations in the photometric period, such as maximum in our J-band photometry at BJD-2457000 524.75. could be caused by differential rotation with latitude, or different wind speeds at different epochs, or at different 500 depths in the atmosphere. Jupiter experiences differen- 400 SIMP 0136 J-band tial rotation, as clouds near Jupiter’s pole rotate 5 min- 300 utes slower than the equator (Newburn & Gulkis 1973). 200 SIMP 0136 may display similar behaviour. To determine Power 100 if the photometric period of our SIMP 0136 light curves 0 evolves from night-to-night we utilize the same high pre- 1 2 3 4 5 6 cision light curves without significant light curve evolu- Period (hours) tion, and the associated StarSpotz fits (Figure 5). The reduced χ2 of these estimates of the cloud rotation pe- 30 riod on different nights compared to this weighted mean 25 Ks-band 2015/12/17 is ∼1.8. Given that we argued that it was justified above 20 15 to scale up the errors on our period estimates (to take

Power 10 into account that in some cases we observe light curve 5 evolution within a single night of observations, but our 0 spot model assumes constant spots), if we do likewise 1 2 3 4 5 6 here then the reduced χ2 would be close to one. There- Period (hours) fore, we believe there is no strong evidence for variabil- Fig. 4.— Lomb-Scargle Periodogram of our SIMP 0136 photom- ity in the photometric period from night-to-night that etry in J-band (top), and in Ks-band on 2015/12/17 (bottom; note might result from differential rotation or a similar mech- the different vertical scales on the y-axis). The peak periodogram value in our J-band photometry is 2.48 ± 0.10 hours, while for our are as follows: on 2015/11/27 the errors were scaled Ks-band photometry on 2015/12/17 the peak periodogram value by a factor of 3 for BJDs before 2457353.598, and after is 2.55 ± 0.12 hours. 2457353.886, due to the impact of twilight; on 2015/11/30 22, & 2015 November 30. We increase our photomet- the errors were scaled by a factor of 6 for BJDs before ric error bars during intervals that we believe the data 2457356.58, and after 2457356.894, due to the impact of twilight, and between 2457356.763 and 2457356.803 due might be affected by systematic errors (such as due to to a passing cloud. 6 passing clouds, or just before/after civil twilight) ; we 7 We admit that our choice to scale up the error by a subsequently also scale our photometric uncertainties to factor of 3 is subjective, but we feel it accurately repre- sents the systematic uncertainty in our rotation period 6 The epochs that we scale our errors on these nights estimate. 8 Croll et al.

2.44 2.42 2.4 2.38 2.36 Period (hours) 2.34 SIMP 0136

335 340 345 350 355 BJD - 2457000 Fig. 5.— Photometric starspot model estimates of the photometric period of SIMP 0136 from our highest precision, J-band light curves with the least light curve evolution (2015 November 10, 2015 November 13, 2015 November 19, 2015 November 21, 2015 November 22, 2015 November 27, & 2015 November 30.) The dashed horizontal line represents the weighted mean of these various estimates of the rotation period, while the dotted horizontal lines represent the 1σ upper and lower limits on this weighted mean after scaling up our weighted error by a factor of 3 (as discussed in Section 4.1). There is no strong evidence for variations in the estimates of the cloud rotation periods from night-to-night, and therefore we do not present evidence in favour of differential rotation, or similar phenomena. If differential rotation dominated periodicity exists during an entire night of our observations, it must cause variations in the photometric period of less than ∼2%. anism. We note that within a single night of photometry, we find no obvious evidence for two different spot/cloud 12 groups rotating with different periods and therefore dif- ferentially, as has been previously obviously observed for 10 SIMP 0136 solar analogues (e.g. Rucinski et al. 2004; Walker et al. 2007). If differential rotation is occurring during our six 8 nights of precise photometry with little light curve evo- lution, and this differential rotation results in a different 6 Number photometric period for a complete night of our observa- 4 tions, then the range in periods must be less than ∼2% (as calculated by comparing the period of the most dis- 2 crepant night to our weighted mean). We also perform a StarSpotz fit to our Ks-band light 0 curve on 2015 December 17 that similarly displays little 0 1 2 3 4 5 6 7 8 9 light curve evolution8. The resulting period is 2.55 ± 0.07 ε -- Amplitude (%) hours. As our Ks-band photometric period from our 2015 Fig. 6.— Histogram of the peak-to-peak amplitudes per complete December 17 light curve is not sufficiently different from rotation period of our J-band photometry of SIMP 0136. SIMP our estimate of the J-band photometric period, we find 0136 displays significant evolution in the peak-to-peak amplitudes no evidence for different rotation periods at the arguably of the light curve from rotation period to rotation period. different depths in the atmosphere probed by our Ks- dwarf. In conclusion, our photometric period estimate band observations. Our z’-band light curves, and our of 2.406 ± 0.012 hours is probably best described as the other Ks-band light curve, are not sufficiently accurate rotation period of clouds, or cloud gaps, enveloping this to enable a similar comparison. L/T transition brown dwarf. Lastly, it should be noted that even if we are able to ac- curately estimate the timescale of the periodic repetition 4.2. The amplitude evolution of SIMP 0136 of features in the light curves of SIMP 0136, this may not provide an accurate estimate of the rotation period of the We also measure the evolution of the SIMP 0136 J- ultra-cool dwarf. For Jupiter the rotation period of the band light curves with time. Specifically we investigate planet’s magnetosphere, as measured via radio observa- the change in variability amplitude of the SIMP 0136 tions, is different than the rotation period of clouds near light curves from rotation period to rotation period, and the equator (Newburn & Gulkis 1973). Although SIMP night-to-night. We use the technique detailed in Croll 0136 has been detected at radio wavelengths (Kao et al. et al. (2016) that we summarize here. For each com- 2016), a radio period has yet to be determined for this plete rotation period of SIMP 0136 we determine the peak-to-peak amplitude, ǫ, of the observed variability of 8 We scale the errors before BJD 2457373.586 by a factor that rotation period. To approximate ǫ we first exclude of 3, and after 2457373.7835 by a factor of 6, due to the significant outliers (we cut out all data greater than 4 impact of twilight. standard deviations from the mean); then we time-bin Multiwavelength Photometry of Ultra-Cool Dwarfs 9

7 wavelength photometry of SIMP 0136 and other highly 6 variable L/T transition brown dwarfs to continue to ob- 5 serve the evolution, or lack thereof, in their variability. 4 Those performing spectrophotometric studies of the variability of L/T transition brown dwarfs should be 3 aware that significant evolution in the light curves may 2

-- Amplitude (%) occur that might drastically change the conclusions one ε 1 draws on the physical causes of the observed variability, 335 340 345 350 355 360 or the exact ratio of spectral features from the minima BJD-2457000 to maxima of the observed variability. For instance, the Apai et al. (2013) HST/WFC3 spectrophotometric study Fig. 7.— The peak-to-peak amplitude of variability (ǫ) per com- plete rotation period for a subset of our J-band photometry of of SIMP 0136 occurred when SIMP 0136 seemed to dis- SIMP 0136 (from 2015 November, during which we have the most play ∼5% J-band variability, and examined the resulting complete nights of data). changes in the near-infrared spectra of SIMP 0136 be- tween the maximum and minimum flux levels observed. the data, by taking a running average of the photometry It seems likely that the changes in HST/WFC3 spectra, every 0.008 days (or ∼11.5 minutes). We then define ǫ or other spectra, of SIMP 0136 may be drastically dif- as the difference between the maximum and minimum ferent when the peak-to-peak amplitudes of variability points of the time-binned data observed over each rota- are less than 1% compared to when they are in excess of tion period. We calculate ǫ for each complete rotation 6%. Therefore, one should be aware that the conclusions period that we have observed; a complete rotation pe- reached by Apai et al. (2013), when they observed ∼5% riod is defined when we have observed 2.406 hours of peak-to-peak J-band variability, resulted from an epoch photometry without noticeable gaps (such as due when SIMP 0136 displayed larger amplitude variability to clouds, or instrumental effects); for our calcu- than on average (Figure 6; assuming that our photomet- lation of ǫ we exclude ∼4 minutes of photometry ric monitoring constitutes an accurate representation of at the start and end of each night of observations the long-term variability of SIMP 0136). to avoid possibly, systematically biased photom- We also note that the amplitudes of variability from etry9. one rotation period to the next are not random for SIMP We display a histogram of the peak-to-peak amplitude 0136, but appear to be highly correlated with the vari- values, ǫ, for each complete rotation period for our J- ability amplitude of the previous rotation period. In Fig- band photometry in Figure 6. Our J-band photometry ure 7 we present the peak-to-peak amplitudes per com- features significant evolution in the light curve from ro- plete rotation period in November 2015 when we col- tation period to rotation period. The maximum peak-to- lected most of our SIMP 0136 data. Several distinct peak amplitude we observe in our J-band photometry is clumps are apparent on most of the nights of observa- in excess of ∼6% (displayed for a few rotation periods in tions compared to the other nights, and therefore it ap- a row on 2015 November 19), while the minimum is less pears that for most rotation periods the amplitude of than ∼1% (displayed for a handful of rotation periods on variability is highly correlated with the variability ampli- 2015 November 12). tude from the previous rotation period. Although some Therefore, our 15 nights of J-band photom- evolution is readily apparent from one rotation period to etry of SIMP 0136 spread over ∼3.5 months the next (in Figures 1 & 2), in general the amplitude of display peak-to-peak variability amplitudes that variability is closely correlated with the amplitude from vary from in excess of ∼6% to less than ∼1%, with the previous rotation period. On the other hand we fre- this range in variability occurring on a timescale quently observe significantly different variability ampli- of approximately a week. We can compare this tudes, or the profile of variability, from one night’s ob- to previous detections of the J-band variability servations to the next; for instance the small amplitude amplitudes for SIMP 0136: Artigau et al. (2009) variability, reaching a minimum of less than 1%, on 2015 presented ∼4 - 6% peak-to-peak amplitude vari- November 12 is followed by consistent peak-to-peak vari- ability from 4 nights of photometry spread over ability of ∼3% the next night (2015 November 13). We a week, while Metchev et al. (2013) presented an note that the variability at the start of the night on 2015 additional six nights of J-band monitoring spread November 12, might signal the possibility of significant over ∼3.5 years that suggests ∼1 - 6% peak-to- evolution on a timescale of less than a rotation period, peak amplitude variability. Other snapshots of as ∼2% variations appear to abruptly disappear. There- SIMP 0136 J-band peak-to-peak amplitudes in- fore the timescale for significant evolution of the gaps in clude: ∼5% from 9.6 hours of HST/WFC3 spec- clouds that are believed to be driving the variability on trophotometry (Apai et al. 2013), and ∼2.9% SIMP 0136 appear to be from as short as <1 rotation pe- from 2.3 hours of photometry (Radigan et al. riod, and typically not longer than ∼10 rotation periods; 2014). The significant evolution that we and oth- the variability of this L/T transition brown dwarf seems ers have observed in our J-band photometry under- to frequently evolve on timescales longer than a rotation scores how important it is to continue performing multi- period, but less than a day.

9 4.2.1. For each night of observations we start our calculation of the Comparison to other Brown Dwarfs number of complete rotation periods at the start of each night’s photometry, and therefore complete rotation periods on different Our estimate that the timescale for significant nights will not necessarily be separated by integer multiples of 2.406 evolution of the SIMP 0136 light curve appears to hours. be as short as a rotation period, and as long as ap- 10 Croll et al. proximately a day is arguably the first time that of observations; the 2015 November 21 and 2015 Novem- this timescale of evolution has been robustly mea- ber 30 observations are prime examples. We do not know sured for an L/T transition brown dwarf. With the source of these decreasing trends, and whether they the possible exception of Luhman-16, for other are astrophysical, systematic or instrumental. On 2015 highly variable L/T transition brown dwarfs there November 31 when differential photometry is performed have yet to be published a sufficient number on our reference stars in the exact same manner as is per- of multi-night light curves in a single observing formed on our target star, several of the reference stars band for the timescale of evolution to be robustly show decreasing or increasing trends. However, this is measured (e.g. Radigan et al. 2012 for 2MASS not the case for reference stars on 2015 November 21. J21392676+0220226). As for Luhman-16, Gillon If these trends are not astrophysical, and therefore do et al. (2013) published observations suggesting not represent a decrease in flux of SIMP 0136 over the strong night-to-night variations, but it is less course of a night, then the likely cause of these trends clear if the binary exhibits significant rotation pe- are systematic or instrumental. Systematic possibilities riod to rotation period variations. Nonetheless, include that the trends represent imperfect sky subtrac- determining a precise timescale for the light curve tion, or are related to colour effects with airmass of the evolution of a single member of the Luhman-16 redder target star, compared to the bluer reference stars binary brown dwarf system is challenging due to (as we likely observed for Ks-band near-infrared photom- the fact that both L/T transition binary mem- etry of the M-dwarf GJ 1214; Croll et al. 2011b). We bers are variable (Biller et al. 2013; Buenzli et note that such nightly trends are not obviously present in al. 2015b). However, several studies have in- our J-band Perkins/Mimir photometry of the L3.5 dwarf dicated that the majority of the variability from 2MASSW J0036159+182110 (Croll et al. 2016), which is the Luhman 16 system originates from Luhman even redder than SIMP 0136 (J − K=1.41 for 2MASSW 16B (Gillon et al. 2013; Burgasser et al. 2014; J0036159+182110, compared to J − K=0.89 for SIMP Buenzli et al. 2015a); if this is the case, then 0136, for which both have typically bluer reference stars). the significant correlation that we observe of the Also, we frequently observed linear or quadratic trends peak-to-peak amplitudes from one rotation to the in the out-of-eclipse light curves for our previous ob- next for SIMP 0136 suggests that the timescale servations of the near-infrared thermal emission of hot for significant evolution of the light curve might Jupiters, and the transit of a super-Earth (Croll et al. be longer for SIMP 0136 than for Luhman-16B. 2010a,b, 2011a,b, 2015), however these trends were of much smaller magnitude than we observe here. There- 4.2.2. Comparison to Theoretical Predictions fore, it is possible that these trends are astro- physical (such as may be the case on the night Our estimate of the timescale of significant ∼ of 2015 November 21), and represent a decrease light curve evolution of <1 to 10 rotation pe- in the flux of SIMP 0136 caused by, for instance, riods for SIMP 0136 can be compared to nu- the gradual, global thickening of clouds on SIMP merical predictions from brown dwarf circula- 0136 over the course of the night. However, tion models. Showman & Kaspi (2013) utilize we note that we cannot rule out the possibility three-dimensional, numerical circulation models that these trends are systematic or instrumental of brown dwarfs to suggest that brown dwarf light in origin (as seems likely for the night of 2015 curve evolution should typically be evident on November 30). timescales of ∼10 - 100 rotation periods. They calculate this by comparing their estimate of the 5 6 advective timescale, τadv ∼ 10 - 10 s, to that of 4.4. Transiting Planets & Flares a typical brown dwarf rotation period, P ∼ 104 rot We further note that our long-term light curves of s, so that qualitative changes in the light curve SIMP 0136 should also allow us to rule out transiting shape should occur approximately τ /P ∼ 10 adv rot Earth or super-Earth sized and larger sized planets in - 100 brown dwarf rotation periods. The advec- the so-called habitable zone of this ultra-cool dwarf. We tive timescale is typically estimated as τ ∼ L/U, adv do not perform injection and recovery of transiting planet where L is a characteristic length scale and U is for our SIMP 0136 light curves, as we do for the ultra-cool the characteristic wind speed; Showman & Kaspi dwarf 2MASSW J0036159+182110 (Croll et al. 2016); (2013) estimate L∼107 m and U∼10 - 100 m/s. however, we note that we recover no obvious signs of Our indication of much more rapid light curve a transiting planet during our 17 nights of photometry evolution for SIMP 0136 on timescales of ∼1 - of SIMP 0136. In general, super-Earth sized transiting 10 rotation periods, therefore suggests smaller planets should be readily apparent in our photometry. characteristic length scales (L∼106 m for U∼10 - Our near-infrared and optical photometry of SIMP 100 m/s), or faster winds (U∼100 - 1000 m/s for 0136 also allows us to place a limit on the occurrence rate L∼107 m), on this L/T transition brown dwarf – of flares exhibited by this L/T transition brown dwarf. if this τ /P timescale is an accurate estimate adv rot Inspection of the unbinned light curves suggest that we of what is leading to the evolution of variability can rule out flaring events lasting thirty minutes or more on this ultra-cool dwarf. that increase the flux of SIMP 0136 by 10% or more ∼ 4.3. for all 124 non-overlapping hours of photometry that Variability over the Night of SIMP 0136 we present here. More detailed inspection of the light We note that several of our SIMP 0136 J-band light curves could likely present considerably more stringent curves appear to feature decreasing trends over the night limits on the occurrence of flares. Multiwavelength Photometry of Ultra-Cool Dwarfs 11

Hours from Epoch 160 -1106 -1104 -1102 -1100 -1098 -1096 140 120 TVLM 513 J-band 1.03 z-band 72'' 100 1.02 80 1.01

Power 60 40 Flux 1 20 0.99 0 0.98 2016/03/31 1.5 2 2.5 3 3.5 4 478.7 478.8 478.9 479 479.1 Period (hours) BJD - 2457000 Hours from Epoch 8 -26 -24 -22 -20 -18 -16 7 6 TVLM 513 z'-band 1.03 J-band 72'' 5 1.02 I-band 42'' 4 1.01 Power

3 Flux 1 2 0.99 1 0.98 2016/05/15 1.5 2 2.5 3 3.5 4 523.7 523.8 523.9 524 524.1 Period (hours) BJD - 2457000 Hours from Epoch 14 -2 0 2 4 6 8 12 TVLM 513 I-band 1.03 10 J-band 72'' I-band 42'' 8 1.02 6 1.01 Power 4 Flux 1 2 0.99 0 0.98 2016/05/16 1.5 2 2.5 3 3.5 4 524.7 524.8 524.9 525 525.1 Period (hours) BJD - 2457000 Fig. 8.— Lomb-Scargle Periodogram of our photometry of TVLM Fig. 9.— Sinusoid fits (dotted lines) to the simultaneous, mul- 513 in various bands as indicated in the panels (note the different tiwavelength Perkins, & Hall DCT photometry of TVLM 513 in vertical scales on the y-axis). Only our J-band photometry displays the J and I-bands. The colour of the dot-dashed lines corresponds periodicity that is statistically significant; our J-band photometry to the wavelength of observations as denoted by the colours of the has a peak periodogram value of 1.99 ± 0.04 hours. data-points as indicated in the legend. The figure format is other- wise identical to Figures 3. For plotting clarity we remove linear trends from our J-band data-sets. TABLE 3 plitude, A, phase, φ, and a vertical offset, y. φ is defined Sinusoid Fits to Individual Photometric Light Curves of TVLM 513 from 0 - 1 and φ = 0 denotes the flux maximum of the sinusoid. The results are given in Table 3, and presented Date Telescope Band Peak-to-Peak Phase (UTC) Amplitude A (%) (φ) in Figure 9. To enhance plotting clarity we subtract out linear trends from our J-band data-sets in Figure 9. Sim- 2016/03/31 Perkins z’ 0.37 ± 0.20 0.056 ± 1.056 ilarly as for SIMP 0136 (see Section 3 and 4.3), it is 2016/05/15 Perkins J 0.72 ± 0.11 0.088 ± 0.026 unclear whether these linear trends are astrophysical or 2016/05/15 Hall I 0.27 ± 0.20 0.262 ± 1.068 systematic/instrumental in nature. 2016/05/16 Perkins J 0.95 ± 0.06 0.058 ± 0.009 2016/05/16 Hall I 0.16 ± 0.11 0.352 ± 0.818 Our sinusoidal fits to the individual nights of TVLM photometry (Table 3) make clear that both nights of J-band photometry display statis- ∼ 5. tically significant variability with a 1.99 hour period, TVLM 513 while the simultaneous I-band photometry on either Our simultaneous J and I-band TVLM 513 light curves night does not display statistically significant variability display prominent J-band variability. We present Lomb- with this period. Similarly, our z-band photometry on Scargle periodograms of our unbinned TVLM 513 light 2016 March 31 does not display statistically significant curves in Figure 8. For our J-band photometry the peak variability with a ∼1.99 hour period. We also fit our I periodogram value is 1.99 ± 0.04 hours. For our I and and z’-band light curves with the peak periodogram val- z’-band photometry the peak periodicity is small enough ues from our Lomb-Scargle analysis in Figure 8 – we con- that we do not believe it to be statistically significant firm that the variability in our I and z’-band light curves (as we indicate below). The J-band peak periodogram at these periods are not significant at the 3σ level. value of 1.99 ± 0.04 hours is very similar to the previ- The fact that we detect prominent ∼0.7 - 0.9% J-band ously claimed rotation period of this dwarf: Hallinan et variability while the I-band variability is significantly less al. (2007), Lane et al. (2007), Littlefair et al. (2008) & during our simultaneous, multiwavelength photometry Harding et al. (2013) detected ∼2 hour radio and optical of TVLM 513 suggests that clouds or aurorae are re- variability from TVLM 513 and inferred that this was sponsible for the variability displayed by this M9 dwarf. the rotation period of this M-dwarf. Stronger near-infrared variability than optical variabil- For our TVLM 513 light curves to determine the am- ity is inconsistent with starspot driven variability for plitude of the J-band variability, and to place limits on starspots that are either hotter or cooler than the TVLM the I and z’-band variability, we fit the individual light 513 photosphere. curves with sinusoidal fits utilizing a period of 1.99 hours. We also note that our lack of detection of I-band vari- For each individual band we fit for the peak-to-peak am- ability, with a 3σ upper limit on sinusoidal variability on 12 Croll et al. our two nights of multiwavelength photometry of ∼0.90% of the variability that we observe from rotation period on 2016/05/15 and ∼0.67% 2016/05/15, is inconsistent to rotation period is due to the size of thinner-cloud (or with previous detections of obvious variability for TVLM cloud-free) regions growing or shrinking, or that the char- 513. Our limits on I-band variability are less than the acteristics of the clouds (e.g. the thickness, height, or ∼10 mmag variability detection of Lane et al. (2007) from type of clouds) in thinner-cloud regions of approximately ∼12 hours of monitoring, less than the ∼4-5 mmag constant size are changing. Although spectrophotomeric variability detection of Miles-Paez et al. (2015) studies to date have suggested that that the variability from ∼8 hours of monitoring, and inconsistent with observed in L/T transition brown dwarfs over approxi- most of the nights of I and i’-band monitoring from Hard- mately a single rotation period are well modeled by only ing et al. (2013) with peak-to-peak amplitudes of ∼0.6 two surfaces consisting of thick clouds, and warmer, thin- - 1.2%. Although the wavelength regions do not com- ner clouds (Apai et al. 2013; Buenzli et al. 2015a), our pletely overlap, we also note that our variability ampli- observations indicate that this comparison may only be tudes are considerably less than the 3-4% variability de- representative of the spectral characteristics at a single tection of Littlefair et al. (2008) from a few hours of ephemeral snapshot in time, and may not represent the g’ and i’-band monitoring. Therefore, it appears clear full continuum of spectral characteristics. that the amplitude of optical variability from TVLM 513 The timescale for significant evolution of the SIMP varies considerably from epoch to epoch. 0136 light curve appears to be as short as a rotation period, and as long as approximately a day. This is ar- 6. DISCUSSION & CONCLUSIONS guably the first time that the timescale for the evolution We have returned long-term, ground-based photome- of the light curve of a L/T transition brown dwarf has try of two ultra-cool dwarfs: the T2.5 L/T transition been robustly measured. brown dwarf SIMP 0136 and the M9 radio-active, ultra- For the radio-active, ultra-cool dwarf TVLM 513, our cool dwarf TVLM 513. 2 nights of simultaneous, ground-based photometry dis- Our 17 nights of ground-based, near-infrared photom- play obvious J-band variability, without accompanying etry of SIMP 0136, including 15 nights of J-band photo- obvious I-band variability of similar amplitude. This con- metric monitoring spread out over 90 days, allow us to firms that the variability of TVLM 513 likely arises from observe how the variability of SIMP 0136 evolves from ro- clouds or aurorae, rather than starspots. tation period to rotation period, night-to-night, & week We encourage further monitoring of these two intrigu- to week. We estimate the rotation period of SIMP 0136 ing ultra-cool dwarfs, and other ultra-cool dwarfs, to bet- as 2.406 ± 0.012 hours. We do not detect any signifi- ter constrain the long-term evolution, or lack thereof, of cant deviations in the photometric period from night-to- their variability. night, and therefore constrain the frequency and magni- tude of obvious differential rotation; if differential rota- tion is present on SIMP 0136 and drives the variability We thank the referee for a careful review. with a different period for an entire night during our We thank Peter Williams for a careful reading of observations, then the period must deviate by less than this manuscript and comments that improved this ∼2% from our estimate of the rotation period of SIMP manuscript. We also thank Saul Rappaport & Adam 0136. Burgasser for helpful discussions that improved this The peak-to-peak amplitude displayed by SIMP 0136 manuscript. in our J-band light curves evolves from greater than 6% Some of this effort was supported by the NASA to less than 1% in the space of just a few days. Longer- Exoplanet Research Program (XRP) under Grant No. term spectrophotomeric studies, and/or Doppler imag- NNX15AG08G issued through the Science Mission Di- ing studies, of individual L/T transition brown dwarfs rectorate, and by the National Science Foundation under are crucial in determining whether the rapid evolution Grant No. 1359205.

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