Kepler monitoring l_dwarfs_spot

Draft version September 25, 2015
Preprint typeset using LATEX style emulateapj v. 5/2/11
KEPLER MONITORING OF AN L DWARF II. CLOUDS WITH MULTIYEAR LIFETIMES
John E. Gizis1,2
, Kyle G. Dettman1
, Adam J. Burgasser3
, Sara Camnasio4,2
, Munazza Alam4,2
, Joseph C.
Filippazzo5,6,2
, Kelle L. Cruz4,5
, Stanimir Metchev7
, Edo Berger8
, and Peter K. G. Williams8
Draft version September 25, 2015
ABSTRACT
We present Kepler, Spitzer Space Telescope, Gemini-North, MMT, and Kitt Peak observations of
the L1 dwarf WISEP J190648.47+401106.8. We find that the Kepler optical light curve is consistent
in phase and amplitude over the nearly two years of monitoring with a peak-to-peak amplitude of
1.4%. Spitzer Infrared Array Camera 3.6 µm observations are in phase with Kepler with similar light
curve shape and peak-to-peak amplitude 1.1%, but at 4.5 µm, the variability has amplitude < 0.1%.
Chromospheric Hα emission is variable but not synced with the stable Kepler light curve. A single
dark spot can reproduce the light curve but is not a unique solution. An inhomogeneous cloud deck,
specifically a region of thick cloud cover, can explain the multi-wavelength data of this ultracool dwarf
and need not be coupled with the asynchronous magnetic emission variations. The long life of the
cloud is in contrast with weather changes seen in cooler brown dwarfs on the timescale of hours and
days.
Subject headings: brown dwarfs — stars: activity — stars: atmospheres — stars: spots — stars:
individual: WISEP J190648.47+401106.8
1. INTRODUCTION
The condensation of minerals at temperatures below
2500K shapes the properties of very-low-mass stars and
brown dwarfs (see the reviews of Allard et al. 1997,
Burrows et al. 2001, Marley et al. 2013). Condensa-
tion depletes the gas phase of molecules, but the grains
can collect into clouds, removing some sources of opac-
ity and adding others. The clouds not only change the
temperature-pressure profile of the atmosphere, but by
changing the boundary conditions of the fully-convective
interior, lower the effective temperature and mass of the
hydrogen-burning limit into the early-L spectral type.
The observationally-defined spectral type sequence from
M8 and M9 dwarfs to L dwarfs to T dwarfs is understood
as a temperature sequence, with clouds near the photo-
sphere for L dwarfs and below it for T dwarfs (see the
review of Kirkpatrick 2005).
Clouds immediately suggest the possibility of inho-
mogeneous coverage and rotational modulation, and
1 Department of Physics and Astronomy, University of
Delaware, Newark, DE 19716, USA
2 Visiting astronomer, Kitt Peak National Observatory, Na-
tional Optical Astronomy Observatory, which is operated by the
Association of Universities for Research in Astronomy (AURA)
under a cooperative agreement with the National Science Foun-
dation.
3 Center for Astrophysics and Space Science, University of Cal-
ifornia San Diego, La Jolla, CA 92093, USA
4 Department of Physics and Astronomy, Hunter College, City
University of New York, 695 Park Avenue, New York, NY 10065,
USA
5 Department of Astrophysics, American Museum of Natural
History, Central Park West at 79th Street, New York, NY 10034,
USA
6 Department of Engineering Science and Physics, College of
Staten Island, 2800 Victory Boulevard, Staten Island, NY 10301,
USA
7 The University of Western Ontario, Department of Physics
and Astronomy, 1151 Richmond Avenue, London, ON N6A 3K7,
Canada
8 Harvard-Smithsonian Center for Astrophysics, 60 Garden
Street, Cambridge, MA 02138, USA
searches for variability (Tinney & Tolley 1999; Bailer-
Jones & Mundt 1999) began even as the L dwarf spec-
tral type system was being defined. Optical searches
(Bailer-Jones & Mundt 2001; Clarke et al. 2002a,b, 2003;
Gelino et al. 2002; Koen 2003, 2004, 2005a,b, 2006, 2013;
Maiti et al. 2005; Maiti 2007; Lane et al. 2007) have of-
ten found evidence of variability in early L dwarfs. Re-
cently, the “Weather on Other Worlds” survey (Metchev
et al. 2015) using the Spitzer Space Telescope found that
spots are ubiquitous in L and T dwarfs, with a detailed
study of the L3 dwarf DENIS-P J1058.7-1548 demon-
strating the need for inhomogeneous clouds to explain
the observations (Heinze et al. 2013). Near-infrared stud-
ies have also detected variability in L and T spectral
types (Khandrika et al. 2013; Wilson et al. 2014; Buenzli
et al. 2014; Radigan et al. 2014). Remarkably, a num-
ber of very high-amplitude early-T dwarf variables have
patchy clouds that change on the timescale of hours and
days (Artigau et al. 2009; Radigan et al. 2012; Gillon
et al. 2013; Burgasser et al. 2014). Apai et al. (2013)
use multi-wavelength near-infrared observations to show
that early T dwarfs are consistent with distinct regions of
thin and thick clouds. Buenzli et al. (2012) used simulta-
neous Spitzer and Hubble observations of a variable T6.5
dwarf to show pressure-dependent phase shifts, taken to
be evidence of both vertical and horizontal structure in
the clouds. The long-term evolution of clouds, however,
is poorly understood because it is usually impossible to
observe more than a few rotation periods. The Kepler
Mission (Koch et al. 2010) was designed to measure pho-
tometry for long, continuous time series. The L1 dwarf
WISEP J190648.47+401106.8 (Gizis et al. 2011), here-
after W1906+40, happens to lie in the Kepler field of
view, and we observed it in Director’s Discretionary Time
(GO30101) and Guest Observer (GO 40004) programs.
In Gizis et al. (2013) (hereafter Paper I), we reported
initial Kepler results on W1906+40, which has the spec-
trum of a typical L1 dwarf, probably on the stellar side
of the hydrogen-burning limit and a trigonometric par-
arXiv:1509.07186v1[astro-ph.SR]24Sep2015

2
Table 1
Kepler Identifiers for WISEP J190648.47+401106.8
Quarter KIC PRF Flux (e−/s)
10 100003560 295
11 100003605 343
12 100003905 357
13 100004035 256
14 100004076 302
15 100004142 343
16 100004180 360
17 100004298 255
allax distance of 16.35+0.36
−0.34 pc. Over the first 15 months
of Kepler observations, it was variable at a 1.4% level
with a period of 8.9 hours and a stable light curve. The
Kepler filter is very broad, from 430 nm to 900 nm, but
because W1906+40 is very red, the effective wavelength
is 800nm. W1906+40 was also found to be magnetically
active, with quiescent radio and Hα emission and tran-
sient white light flares (Paper I) . Because Kepler has
only one filter, we had no information on the spectral
characteristics of the spot. In this paper, we analyze
the complete Kepler dataset and use supporting ground-
based and Spitzer observations to characterize the nature
of W1906+40’s variability.
2. DATA AND OBSERVATIONS
2.1. Kepler Photometry
W1906+40 was observed during Kepler Quarters 10-
17 in long-cadence mode (Jenkins et al. 2010), providing
photometric measurements every 30 minutes for nearly
two years until the end of the original mission. Here
we re-analyze the Quarters 10-14 data reported in Paper
I, and add the data collected in Quarters 15-17. A new
Kepler Input Catalog (KIC) identification for W1906+40
was generated each quarter (Table 1). Because the space-
craft was rotated by 90 degrees quarterly, each position
was observed twice (i.e., W1906+40 is on the same CCD
pixels during Quarters 10 and 14). We use the Kepler
pixel-response function (Bryson et al. 2010) fitting (PRF)
routines in the PyKE package (Still & Barclay 2012) to
measure photometry. This weights the pixels more op-
timally than simple aperture photometry and allows us
to include a model for potential contamination from the
background star KIC 4996079, though it turns out to be
negligible. The median count rates are given in Table 1;
the variation by quarter is instrumental. Each quar-
ter’s photometry is normalized so that the median Kepler
count rate is 1.0; in these units the uncertainty of each
measurement is 0.005. We remove instrumental long-
term trends with low-order polynomials; this removes the
known instrumental variations on the timescales of weeks
to months (see the discussion in Stumpe et al. 2012) but
does not affect shorter timescales. The 8.9 hour peri-
odic variability is persistent throughout the observations.
We examined all the data by eye and find no convincing
episodes where the variability disappeared.
The Quarters 13 and 17 data show systematic differ-
ences from the other quarters; the period and phase is the
same, but average count rate is lower and the percentage
amplitude of the variability is higher. As noted in Paper
I, two of the pixels yield negative counts and must be
excluded from the aperture photometry. We obtain sim-
ilar light curves for either aperture or PRF photometry.
Since the different light curve is correlated with the de-
tector used, we attribute it to an instrumental effect; a
possible explanation is that the pipeline sky subtraction
is incorrect. Quarter 10 begins at Kepler mission day
906.87, Quarter 16 ends at Kepler mission day 1558.0,
and Quarter 17 ends at day 1591.0.9
We exclude Quar-
ters 13 and 17 from further analysis. On the basis of
the single spot model fitting described later, we adopt
a period of 0.370177 days with phase zero defined to be
Kepler Mission time 1180.0, near the midpoint of our ob-
servations. (This is a different time for phase zero than
in Paper I). In Figure 2, we show the two-dimensional
histogram of the Quarters 10-12 and 14-16 data. We
compute binned Kepler average light curves shown in
Figure 3. Small differences between the first year and
second year observations are evident. The uncertainty of
each measurement is a third of the peak-to-peak ampli-
tude, so we can only detect such subtle changes in the
light curve by combining data over long time periods.
2.2. Spitzer Photometry
W1906+40 was observed (Program ID 90152) with the
Spitzer Space Telescope (Werner et al. 2004) using the In-
frared Array Camera (IRAC, Fazio et al. 2004) for twenty
hours on UT Dates 17-18 October 2013, corresponding
to Kepler Mission day 1750. This is after the end of
the Kepler monitoring on day 1591. The target was lo-
cated at pixel positions X=23.5, Y=231, near the “sweet
spot” recommended by the Spitzer Science Center, with
no dithering in order to minimize the pixel-phase correc-
tion (Ingalls et al. 2012). The observations consist of 130
12-second exposures in IRAC Channel 1 (hereafter [3.6])
while the telescope pointing settled, 2910 12-second ex-
posures in [3.6] used for science, and then 1164 30-second
exposures in IRAC Channel 2 (hereafter [4.5]). For rel-
ative photometry, we use 3-pixel aperture photometry
with a 12-20 pixel sky annulus. For comparison to other
L dwarfs, we apply the Vega zero-points, aperture correc-
tions and array-location dependent corrections provided
by the Spitzer Science Center to obtain median magni-
tudes of 11.24 and 11.23 at [3.6] and [4.5] respectively.
The color is consistent with other early L dwarfs mea-
sured by Patten et al. (2006): L dwarfs have near-zero
[3.6]-[4.5] colors like A0 stars despite their lower tem-
peratures because of the strong CO absorption in the
[4.5] band. Our observations show a slow drift in po-
sition over the entire observation plus an instrumental
periodic (∼ 51 minute) pattern; the total change in po-
sition over 0.2 pixels in X and 0.3 pixels in Y during the
[3.6] observations and 0.1 in X and Y each during the
[4.5] observations. We include a linear correction in our
modeling (discussed in Section 3) and find that slopes
−0.03 in X and −0.06 in Y remove the Channel 1 phase
effect. The Channel 2 phase effect is smaller and we fit
it with slopes -0.05 in X and 0.01 in Y. Figure 3 shows
the Spitzer photometry after pixel phase correction. The
noise estimate from Poisson statistics is 0.45% for [3.6]
and 0.33% for [4.5] for a single observation; we estimate
9 Kepler mission days are barycentric julian dates (BJD) minus
2454833.0.

3
Phase
RelativeBrightness
0.96
0.97
0.98
0.99
1.00
1.01
1.02
Q10 Q14
0.96
0.97
0.98
0.99
1.00
1.01
1.02
Q11 Q15
0.96
0.97
0.98
0.99
1.00
1.01
1.02
Q12 Q16
0.0 0.2 0.4 0.6 0.8 1.0
0.96
0.97
0.98
0.99
1.00
1.01
1.02
Q13
0.0 0.2 0.4 0.6 0.8 1.0
Q17
Figure 1. Observed Kepler data for each quarter. A sine curve with period of 0.3710177 days and peak-to-peak amplitude 1.4% is also
plotted. Note the consistent phase for all quarters. See text for discussion of the systematic error in Quarters 13 and 17.

4
Phase (8.9 hours)
RelativeBrightness
0.0 0.2 0.4 0.6 0.8 1.0
0.97
0.98
0.99
1.00
1.01
1.02
1.03
Kepler Average (all years)
Kepler Average (Year 1)
0.0 0.2 0.4 0.6 0.8 1.0
IRAC [3.6]
0.0 0.2 0.4 0.6 0.8 1.0
IRAC [4.5]
Figure 2. Two-dimensional histogram of Kepler brightnesses for
W1906+40 in Quarters 10-12 and 14-16 phased to the common
period of 0.3710177 days.
that the noise in the binned data shown in Figure 3 is
0.10% at [3.6] and 0.08% at [4.5].
2.3. Ground-based Photometry
We observed W1906+40 using the Kitt Peak National
Observatory (KPNO) 2.1-meter CCD direct imaging
camera (Program 2013B-0340) on UT Dates 01 Septem-
ber 2013 and 03 September 2013, corresponding to Ke-
pler mission dates 1703 and 1705; the other scheduled
nights were too cloudy to observe. We used the g
(KP1584), r (KP1585), i (KP1586), and z (KP1587)
filters with exposure times of 300, 300, 150 and 100 s
respectively. The W1906+40 aperture photometry was
calibrated by comparison to background stars with Sloan
Digital Sky Survey Data Release 9 measurements (Ahn
et al. 2012). As an L1 dwarf, W1906+40 is much red-
der than the comparison stars, which has two conse-
quences. First, there is differential extinction which we
remove with a linear fit to airmass. Second, although
our W1906+40 g and z magnitudes as calibrated by ref-
erence stars match the SDSS magnitudes, our r and i
measurements are 0.4 and 0.2 magnitudes brighter. This
is explained by the KPNO filters being wider in wave-
length than the SDSS filters. The KPNO measurements
are shown in Figure 4 along with the predicted light curve
based on extrapolating the Kepler average light curve.
The i and z observations are consistent with the expected
Kepler light curve. The g and r curves are too noisy to
detect the amplitude of the Kepler signal.
W1906+40 was observed in the near-infrared (J band
only) with the KPNO 2.1-meter on UT dates 24-28 Octo-
ber 2012 (Program 2012B-0233). Because time-varying
structures in the sky were evident, we chopped between
two positions, taking five 60-second exposures at each
position. We used the alternate position to sky subtract
and flat fielded with dome flats (Joyce 1992). We find,
however, that the observed noise for W1906+40 and com-
parison stars is 2% and we therefore did not detect the
variations seen in the simultaneous Kepler data; the am-
plitude at J-band must be < 5%. We make no further
use of the J-band data.
2.4. Ground-based Spectroscopy
Optical (far-red) long-slit spectra were obtained with
the MMT and Gemini-North telescopes to investigate
whether chromospheric Hα emission might track the Ke-
pler optical variability. The MMT observations were on
UT Date 26 and 27 August 2012 with the Red Channel
spectrograph using grating 270, using 600 second expo-
sures. Conditions were non-photometric. This time was
allocated by NOAO as part of program 2012B-0233. The
wavelength coverage was 6170 - 9810˚A with a resolu-
tion of ∼ 12˚A, but we make no use of the spectrum red-
der than 9250˚A due to strong telluric water absorption.
The Gemini-North observations (Gemini program GN-
2012B-Q-105) were on UT Date 24 July 2012, 29 July
2012, and 04 August 2012 with the GMOS spectrograph
(Hook et al. 2004) using grating R831 and 600 second ex-
posures. We thus have spectroscopy on Kepler mission
dates 1299, 1304, 1314, 1332, and 1333. We processed
the spectra with standard IRAF routines and measured
the equivalent width using the task splot. T
The phased Hα data are shown in Figure 5. The 24
July data begin with four observations taken near phase
0.6 with very weak Hα (Equivalent width 0.5˚A) in emis-
sion. Our observations were then interrupted for a Target
of Opportunity, but resumed with twelve observations
covering phase 0.9 to 1.1, during which the Hα emission
increased from 3.5 to 8˚A. The other Gemini nights had
limited phase coverage. The 29 July 2012 had four ob-
servations at phase 0.2-0.3 before becoming dominated
by the white light flares discussed in Paper 1. The 04
August 2012 observations consist of four exposures near
phase 0.1. The MMT 26 August observations began at
phase 0.33 and continued until phase 0.10. The 27 Au-
gust observations were cut short by clouds and cover only
phases 0.3 to 0.4. he random uncertainty in the Hα
equivalent widths is 0.2 ˚A, but the MMT observations
were taken at lower spectral resolution which results in a
higher pseudo-continuum and systematically lower equiv-
alent widths. It is apparent from Figure 5 that the Hα
emission does not follow the Kepler light curve. The 24
July 2012 data could be consistent with an active re-
gion rotating into view, but shifted by ∼ 1/8 of a period
from the Kepler phasing; however, observations on other
nights are not consistent with this phasing either. The
26 August data follows neither the Kepler nor the 24
July light curves; we include a light curve shifted by 3/8
period to illustrate this.
In Paper I, we described infrared spectroscopy of
W1906+40 using the Keck II NIRSPEC near-infrared
echelle spectrograph (McLean et al. 2000). The 11 Au-
gust 2011 observations reported there had a radial veloc-
ity of −22.5 ± 0.5. We report that a second observation,
analyzed in the same way, on 10 Sep 2011 was −24.3±1.3,
consistent with no significant variation.
3. SPOT CHARACTERISTICS
The Spitzer [3.6] and KPNO i/z observations are con-
sistent with the phasing of the Kepler data. We there-
fore begin our discussion by making the fundamental as-
sumptions that we can treat W1906+40 as stable over
the entire time period to compare observations made at
different times, and that the optical and mid-infrared
variability is due to the same source, which for conve-
nience we will term the “spot” regardless of the physical
cause and whether it is actually many features.
The long-term stability of the spot suggests to us that a
simple geometric model is appropriate. In principle, any
observed light curve can be matched by a sufficient num-
ber of spots, so we could fit the light curve with brighter

5
Phase (8.9 hours)
RelativeBrightness
0.0 0.2 0.4 0.6 0.8 1.0
0.97
0.98
0.99
1.00
1.01
1.02
1.03
Kepler Average (all years)
0.0 0.2 0.4 0.6 0.8 1.0
IRAC [3.6]
0.0 0.2 0.4 0.6 0.8 1.0
IRAC [4.5]
Figure 3. Phased light curves for a period of 0.370177 days. The average Kepler light curve is in cyan in all panels. Left: Kepler light curve
for first year [Quarters 10-12, days 907-1182] (dotted) and second year [Quarters 14-16, days 1274-1558] (dashed). Middle: Spitzer IRAC
[3.6] measurements (points) and averaged values (blue histogram) on Kepler Mission day 1750. Right: Spitzer IRAC [4.5] measurements
(points) and averaged values (red histogram). We estimate that the peak-to-peak amplitude of variabilitiy is 1.4% at Kepler, 1.1% at [3.6],
and 0.04% at [4.5] (See Section 3).
Kepler Mission Time
15.60
15.59
15.58
15.57
15.56
z
Kepler light curve
17.12
17.11
17.10
17.09
17.08
17.07
i
19.81
19.80
19.79
19.78
19.77
19.76
19.75
3000K spot
r
1703.5 1704.0 1704.5 1705.0 1705.5 1706.0
22.6
22.5
22.4
22.3
22.2
8000K spot
g
Figure 4. Measured CCD photometry (in AB magnitudes) at
g,r,i,z compared to the average Kepler light curve extrapolated to
the time of the Kitt Peak observations. Also shown is the predicted
light curve at r band if the Kepler light curve is due to a 3000K
spot, and the predicted light curve at g band if the Kepler light
curve is due to an 8000K spot.
(warmer) or darker (cooler) spots. We observe that the
average Kepler light curve and the Spitzer [3.6] curve
both appear asymmetric in the sense that the brightest
portion (phases 0.2 to 0.4 in Figures 2 and 3) is flatter
than the darkest portion (phases 0.6-1.0).10
We begin
by fitting dark spot models and later argue why bright
spots are unlikely.
We therefore fit the Kepler and Spitzer datasets us-
ing a single spot that is dark in both the Kepler and
[3.6] bands. As in Paper I, we model the light curve us-
ing the single circular spot equations of Dorren (1987)
which we implemented in Python. We presented results
for completely dark spots in Paper I. In this case, we use
a spot with a single geometry (spot radius in radians,
latitude, initial longitude, stellar inclination, period) but
allow the unspotted photosphere brightness and spot-to-
star flux ratio to vary for the three bands. A list of all
model parameters is given in Table 1. Here we define
the spot-to-star ratio as the flux per unit area of the
spot divided by the flux per unit area of the unspotted
photosphere; this ratio is less than one for dark spots
and greater than one for bright spots. We furthermore
include X and Y linear pixel-phase corrections for the
two IRAC bands. We adopt linear limb darkening pa-
rameters from Claret et al. (2012). For the photosphere,
we use the 2300K model corresponding to an L1 dwarf:
0.84 for Kepler, 0.48 for [3.6], and 0.31 for [4.5]. For
the spot, we adopt the 1900K limb darkening values,
0.84 for Kepler, 0.44 for [3.6] and 0.34 for [4.5]. We ex-
10 In Paper I, we argued the Kepler light curve had no flat por-
tion, but the new analysis, the second year of Kepler photometry,
and the Spitzer photometry show that the brighter phases are flat-
ter than the darker phases.

6
Phase (8.9 hours)
HalphaEquivalentWidth
0.0 0.5 1.0 1.5 2.0
0
2
4
6
8
10
24 July 2012
29 July 2012
08 August 2012
Kepler Light Curve (rescaled)
Kepler shifted by 1/8 Period
0.0 0.5 1.0 1.5 2.0
26 August 2012
27 August 2012
Kepler Light Curve (rescaled)
Kepler shifted by 3/8 Period
Figure 5. Observed equivalent width of Hα emission (in Angstroms) as a function of phase. The uncertainty for Gemini is ±0.2˚A and
for MMT is ±0.3˚A; the size of these error bars is shown in the upper right of each panel. The systematically smaller MMT widths may be
mainly due to the different instrumental resolutions (see text). The Kepler light curve, arbitrarily scaled, is shown to guide the eye, along
with versions shifted in phase. All data are plotted twice. The Hα emission is not in sync with the broad-band optical variability.
plore parameter space using an affine-invariant ensemble
Markov chain Monte Carlo (MCMC) sampler (Goodman
& Weare 2010) as implemented in the Python code emcee
(Foreman-Mackey et al. 2013) for maximum likelihood
estimation. We use 200 walkers in the 11-dimensional pa-
rameter space to model the 23967 data points, and keep
1.41 million samples after discarding an initial burn-in
sample. The likelihood model is simply based on the χ2
statistic, i.e., ln p = −1
2 n
(fn−mn)2
s2
n
where for each
of the n data points, fn is the observed brightness, sn
is the uncertainty, and mn is the model brightness given
the trial parameters. The mean acceptance fraction was
0.16 and the mess auto-correlation length was 87. The
period is 0.3701770 ± 0.0000006 days and the spot lati-
tude is 1.21±0.06 radians (69.3±3.4 degrees). The [4.5]
star-to-spot flux ratio is 0.974 ± 0.026. The median spot
size is 0.18 radians, but the spot size, other flux ratios
and stellar inclination are highly correlated as we show
in Figure 6 with darker spots being smaller. Median val-
ues and standard deviations for the fitted parameters are
given in Table 1, but we caution that for the parameters
shown in Figure 6 the likelihood function is not a normal
distribution.
We show the light curve predicted by two of the mod-
els from the chain in Figure 7. Model A is typical of the
solutions with a brighter spot: It has spot radius 0.190
radians, inclination 1.01 radians, spot latitude 1.27 ra-
dians, Kepler flux ratio 0.45, and IRAC [3.6] flux ratio
0.48. Model B is typical of the solutions with a darker
spot; it has radius 0.16 radians, inclination 0.99, spot lat-
itude 1.30 radians, Kepler flux ratio 0.20 and IRAC [3.6]
flux ratio 0.20. In Paper I, we used the observed period,
v sin i, luminosity and effective temperature to show that
high inclinations are preferred, with sin i > 0.59. Al-
though we did not include this prior constraint in the
MCMC simulations, all of the inclinations in Figure 6
are acceptable, adding to our confidence in the single
spot model. The most important implication of the sim-
ulations is that a wide range of flux ratios are acceptable,
from completely dark flux ratios of 0 to flux ratios ∼ 0.6
in the Kepler and [3.6] bands. The Kepler-to-[3.6] flux
ratios are similar (0.91 ± 0.12). We caution, however,
that the MCMC statistics should be viewed as illustra-
tive rather than definitive; changes in the assumed limb
darkening, for example, could affect any of the quoted pa-
rameters. These models also give us our best estimates
of the relative peak-to-peak amplitude of the variability:
1.4% for Kepler, 1.1% at [3.6], and only 0.04% at [4.5].
Although these circular dark spot models explain the
main features of the light curve, it would be possible to
fit the data with a spot (or set of spots) brighter than
the photosphere in the Kepler and [3.6] filter. However, a
number of possibilities can be ruled out from the multi-
wavelength data. First, the variability cannot be due
to a hot spot (Teff ≥ 3000K) with continuum emission
because of the g and r photometry. The unspotted pho-
tosphere has an L1 spectral type, confirmed by both the
spectra and the SDSS/KPNO griz photometry. The to-
tal number of additional counts from the spot through
the full Kepler filter down to 430 nm can only be 1.4% of
the total. Putting these counts at the bluer parts of the
Kepler filter, where the L dwarf photosphere is intrinsi-
cally faint, would require greater variability amplitudes
( 1.4%) in the g and r filters. As an example, if these
additional counts were distributed like an 8000K black-
body, the amplitude of variability at g would be 0.3 mag-
nitudes and at r would be 0.08 magnitude. These values

7
0.75
0.90
1.05
1.20
inclination(rad)
0.00
0.15
0.30
0.45
0.60
Keplerfluxratio
0.16
0.20
0.24
spot radius (rad)
0.15
0.30
0.45
0.60
[3.6]fluxratio
0.75
0.90
1.05
1.20
inclination (rad)
0.00
0.15
0.30
0.45
0.60
Kepler flux ratio
0.15
0.30
0.45
0.60
[3.6] flux ratio
Figure 6. Triangle plot of the projection of the multidimensional
likelihood function for the key single spot model parameters spot
radius (radians), inclination (radians), Kepler flux ratio and Spitzer
IRAC [3.6] flux ratio. These parameters are strongly correlated
with each other. Other model parameters (Table 1) are not shown.
are ruled out by the data shown in Figure 4. Even a
3000K blackbody would require an amplitude of 0.047
magnitudes at r which is inconsistent with the optical
data. Second, a hot spot with emission lines is ruled
out because the Hα Balmer line is not strong enough,
and no other red emission lines are observed. Extremely
strong blue emission lines are ruled out by the g and r
photometry in the same way as a hot continuum. Fur-
thermore, the Hα variability (Figure 5) that is observed is
not synched with the Kepler light curve. Third, as Heinze
et al. (2013) argued for their Spitzer observations of an L3
dwarf, the spot cannot emit like a blackbody or a normal
M or L dwarf, whether warmer or cooler than the unspot-
ted photosphere, in the mid-infrared. This is because
such emission, like the unspotted photosphere, would
have near-zero colors in [3.6]−[4.5] and therefore [4.5]
would also have to be variable. A cold (Teff < 1300K) T
dwarf-like spectrum is also ruled out. While a T dwarf-
like spot would indeed be brighter at [4.5] than the Kepler
or [3.6] filters, relative to the unspotted photosphere, the
spot would still be very dark at [4.5] and therefore the
light curve would end up being similar to [3.6].
Despite the success of the single circular dark spot
modeling, the small mismatches between the Kepler av-
erage light curve, the Spitzer [3.6] light curve, and the
model light curves indicate a break-down in the assump-
tion of a single, uniform, unchanging circular spot. The
minimum in the average Kepler light curve around phase
0.9 is not present in the [3.6] curve and is not reproduced
in our models. We note, however, that this feature is not
present in the first year (Figure 3) Kepler light curve,
only the second year, so one simple explanation is that
the spot changed again between the end of the Kepler
observations and the Spitzer. We conclude that small
changes are occurring in the geometry of the spot on the
timescale of months to years, but most of the light curve
can be explain with a large, mainly unchanging feature.
To be sure, the circular spot is an approximation, and we
cannot rule out the possibility of multiple circular spots,
asymmetric bands or other geometric shapes.
4. DISCUSSION
Clouds provide a natural interpretation of our data,
particularly the lack of variability at [4.5]. The pressure
of line formation depth (τ = 2/3) is shown in Figure 8 for
a 2200K, log g = 5.0 “E Cloud” model (Burrows et al.
2001, 2006). The “E cloud” provide the best descrip-
tion of L dwarfs in this model family, and describes a
cloud deck which fully extends from 2300K (the base of
the cloud, where calcium aluminates condense) up to the
condensation point of forsterite (1700-1900K), with ex-
ponential drop offs below and above these points. At
[4.5], we only probe the outermost layers (lowest pres-
sures and temperatures) of the atmosphere because of
CO opacity, above the cloud tops (see Figure 9 of Bur-
rows et al. 2006). The [3.6] and Kepler bands, in contrast,
match spectral windows where we probe deeper into the
atmosphere, around the base of the cloud. Thus, as dis-
cussed by Gelino et al. (2002), a clearing in the cloud
deck will cause brightening in the spectral windows; con-
versely, a thickening of the cloud deck will cause darken-
ing. The dark spot implied by the single spot modeling
would therefore correspond to a stable region of thicker
cloud.
Two solar system planetary analogs are of interest. For
Jupiter, holes in the clouds produce bright spots in 5
µm images (Westphal et al. 1974). Gelino & Marley
(2000) analyzed 5 µm data and showed that when an-
alyzed as a point source, these complex, banded inhomo-
geneities produce a periodic rotational signal dominated
by the Great Red Spot, which is darker at 5 µm due
to its thicker clouds. Mark Marley (priv. comm, 2014)
points to the example of Venus: In the near-infrared spec-
tral windows such as 1.7 and 2.3 µm where the thermal
emission originates deep in the atmosphere, images of
Venus’s night side reveal cloud structures (Allen & Craw-
ford 1984); at other wavelengths, the night side of Venus
appears uniform. Long-term monitoring shows that the
clouds responsible for these structures, especially an
equatorial band of variable thick clouds, change night-to-
night, month-to-month, and year-to-year, with thicker-
than-average clouds appearing darker and thinner-than-
average clouds brighter (Tavenner et al. 2008). Viewed as
a point source, these varying clouds would produce pho-
tometric variability, but only at the wavelengths match-
ing spectral windows. Our observations are consistent
with an analogous system; if we could spatially resolve
W1906+40, the star would look uniform at [4.5] but
cloud structures would be revealed in the optical and
[3.6]. These clouds are non-uniform enough to produce
the 1.4% variability as the viewing angle changes due to
the 8.9 hour rotation period. Like the Great Red Spot
but unlike Venus’s clouds, W1906+40’s cloud structure
would be stable over several years.
For brown dwarfs, many groups (including Rocken-
feller et al. 2006, Littlefair et al. 2006, Radigan et al.
2012, Heinze et al. 2013) have used one-dimensional

8
Table 2
Parameters in Circular Spot Fitting
Parameter Median Standard Deviation Comment
Period (days) 0.3701770 0.0000006
Latitude (degrees) 69.3 3.4
Inclination (degrees) 74.8 2.8 See Figure 6 for correlations
Spot Radius (degrees) 10.5 2.1 See Figure 6 for correlations
Spot-to-Star Ratio, Kepler 0.37 0.14 See Figure 6 for correlations
Spot-to-Star Ratio, [3.6] 0.41 0.15 See Figure 6 for correlations
Spot-to-Star Ratio, [4.5] 0.974 0.026
X Linear Phase Correction, [3.6] -0.03 0.002
Y Linear Phase Correction, [3.6] -0.06 0.001
X Linear Phase Correction, [4.5] -0.05 0.005
Y Linear Phase Correction, [4.5] 0.01 0.005
Longitude (degrees) 58.4 0.4 At Mission Time 1180.0 days
Unspotted flux, Kepler 1.0100 0.0007 Median of all data set to one
Unspotted flux, [3.6] 1.0104 0.0008 Median of all data set to one
Unspotted flux, [4.5] 1.0009 0.0004 Median of all data set to one
Star Linear Limb Darkening, Kepler 0.84 · · · Not Fit, Adopted from Claret et al. (2012)
Spot Linear Limb Darkening, Kepler 0.84 · · · Not Fit, Adopted from Claret et al. (2012)
Star Linear Limb Darkening, [3.6] 0.48 · · · Not Fit, Adopted from Claret et al. (2012)
Spot Linear Limb Darkening, [3.6] 0.44 · · · Not Fit, Adopted from Claret et al. (2012)
Star Linear Limb Darkening, [4.5] 0.31 · · · Not Fit, Adopted from Claret et al. (2012)
Spot Linear Limb Darkening, [4.5] 0.34 · · · Not Fit, Adopted from Claret et al. (2012)
Phase (8.9 hours)
RelativeBrightness
0.0 0.2 0.4 0.6 0.8 1.0
0.990
0.995
1.000
1.005
Kepler Light Curve
Model A
Model B
0.0 0.2 0.4 0.6 0.8 1.0
IRAC [3.6] Light Curve
Model A
Model B
Figure 7. Two sample single spot models shown with the Kepler and Spitzer [3.6] light curves. Model A has spot radius 10.9◦, inclination
57.9◦, spot latitude 72.8◦, Kepler flux ratio 0.45, and IRAC [3.6] flux ratio 0.48. Model B has radius 9.2◦, inclination 56.7◦, spot latitude
74.5◦, Kepler flux ratio 0.20 and IRAC [3.6] flux ratio 0.20. We tested the goodness of fit with a k-sample Anderson-Darling test (included
in the Python scipy package), and found that the null hypothesis that the models and averaged data are drawn from the same distribution
cannot be rejected at even the 25% significance level.

9
1 2 3 4 5
Wavelength (microns)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
PressureofLineFormation(bars)
KEPLER IRAC [3.6] IRAC [4.5]
E CLOUD 2200K
Figure 8. Pressure of line formation (τ = 2/3) in a 2200K “E Cloud” model (Burrows et al. 2001, 2006) compared to the positions of the
Kepler and IRAC ﬁlters. The cloud layer is shown as shaded light grey. Due to the strong CO molecular opacity, IRAC [4.5] photometry
probes low pressure (high altitude) while the Kepler and [3.6] photometry probe deeper layers.

10
model atmospheres to model patchy brown dwarfs, with
the unspotted and spotted regions modeled with differ-
ent effective temperature and cloud properties. In the
Ackerman & Marley (2001) approach, the fsed param-
eter controls the thickness of the clouds. Heinze et al.
(2013) found that an L3 dwarf had [3.6] variability but
none at [4.5]. They use the Saumon & Marley (2008)
family of models with this color constraint to find that
either warmer, thinner or cooler, thicker clouds can pro-
duce this spectral signature. The same applies to the
warmer W1906+40. Our preference for a darker spot
because of the light curve suggests thicker clouds.
Because the strongest evidence for clouds is the relative
[3.6] and [4.5] photometry, we briefly discuss alternative
models. One possibility is emission lines in the [3.6] band
not present in the [4.5] band. An aurora model for vari-
able [3.6] emission is discussed in detail by Heinze et al.
(2013), who ultimately disfavor it for their L3 dwarf.
This concept, discussed by Harding et al. (2011) for op-
tical emission in late-M dwarfs with periodic radio emis-
sion, incorporates a stable magnetic field with a beam of
electrons and ions that excite the atmosphere, creating a
bright spot. Bhardwaj & Gladstone (2000) and Badman
et al. (2014) review aurorae emission mechanisms in the
Solar System giant planets. The electrons ionize molecu-
lar hydrogen, leading to emission of photons from H+
3 at
3-4µm. This would be responsible for the [3.6] emission;
[4.5] would be constant due to the lack of molecular emis-
sion lines there. Visible emission at Kepler wavelengths is
also expected. Through dissociative emission, the heat-
ing causes Balmer emission; other atomic and molecular
emission (James et al. 1998) are also expected. We dis-
favor this model for a number of reasons. First, a dark
spot gives a better match to the light curve. Second, the
Hα data on different nights are not in phase with each
other or with the Kepler light curve (Figure 5): The Hα
emission on 26 August 2012 is bright when the Kepler
light-curve is dim, yet on 24 July 2012 the Hα is very
weak when a Kepler bright spot would still be partially
visible (phase 0.6) but then begins increasing (phase 0.9)
before the bright spot rotates into view. Third, as dis-
cussed previously, continuum emission much bluer than
the L dwarf photosphere would be inconsistent with the
optical photometry. Finally, we have no evidence of pe-
riodic radio emission (see Paper I), although the data do
not include a full rotation cycle. Another emission model
would be a magnetically heated chromospheric active re-
gion. This is a likely explanation of the Hα emission
we do observe, and given the presence of strong white
light flares, it is plausible that microflares or other pro-
cesses heat regions of the chromosphere, but it cannot
be responsible for the stable periodic Kepler light curve.
Finally, we note that Robinson & Marley (2014) discuss
thermal perturbations in brown dwarf atmospheres that
might produce photometric variability on the timescale of
hours or days as an alternative to changing cloud weather
models. Along these lines, we might imagine a region of
cooler gas at depths where P ≈ 0.5 − 0.7 bar, producing
the dark feature at Kepler and [3.6], without affecting
the high altitude region measured by [4.5]. Unlike the
thermal perturbations consider by Robinson & Marley
(2014), this cold gas would have to be stable for years,
which would require an unknown mechanism to main-
tain.
The most important qualitative difference from obser-
vations of cooler L, T, and Y dwarfs, especially the L/T
transition, is the stability of the W1906+40 spot. There
is strong evidence of night-to-night variations in many
brown dwarfs suggesting rapid cloud evolution (Gillon
et al. 2013). In contrast, The W1906+40 light curve is
stable over 843 days (over 2200 rotations); indeed, the
standard deviation of the period in the MCMC simula-
tions is just 50 milliseconds. Evidently the W1906+40
spot is very long-lived compared to the “weather” fea-
tures in cooler L and T dwarfs. Why would the clouds
in W1906+40 be stable? Showman & Kaspi (2013) and
Zhang & Showman (2014) have presented exploratory
models of the atmospheric circulation of brown dwarfs.
W1906+40’s photosphere, however, is considerably hot-
ter and is outside the range of these simulations. Future
models may reveal whether the W1906+40 spot could
be an analog to the Great Red Spot. As Harding et al.
(2013) argue for the M9 dwarf TVLM 513-46546, whose
optical variability is stable for 5 years, magnetic fields
may play a role. Perhaps a stable magnetic field sup-
presses convection to create a cool spot, which in turn
develops thicker clouds. This mechanism would not func-
tion at later type L dwarfs, as shown by Gelino et al.
(2002). Finally, we note that orbits have highly stable
period. However, we have no evidence for a companion
that could be affecting the W1906+40 photosphere.
Our results demonstrate the importance of clouds even
for the warmest L dwarfs. While ground-based studies of
∼ 9 hour period ultracool dwarfs will remain challenging,
the Kepler K2 mission (Howell et al. 2014) is monitoring
many more late-M and L dwarfs in campaigns of ∼ 75
days. This will allow clouds and weather to be measured
through the M/L transition and determine whether the
stability of W1906+40’s clouds is typical or unusual.
We thank Adam Burrows and Mark Marley for discus-
sion of their cloud models. We are very grateful for the
efforts of the Kepler, Spitzer, Kitt Peak National Obser-
vatory, Gemini and MMT teams who made these obser-
vations possible and responded so promptly and helpfully
to questions.
This paper includes data collected by the Kepler mis-
sion. Funding for the Kepler mission is provided by
the NASA Science Mission directorate. The material is
based upon work supported by NASA under award No.
NNX13AC18G. This work is based in part on observa-
tions made with the Spitzer Space Telescope, which is
operated by the Jet Propulsion Laboratory, California
Institute of Technology under a contract with NASA.
Support for this work was provided by NASA through
an award issued by JPL/Caltech. Some of the obser-
vations reported here were obtained at the MMT Ob-
servatory, a joint facility of the Smithsonian Institution
and the University of Arizona. MMT telescope time was
granted by NOAO, through the Telescope System In-
strumentation Program (TSIP). TSIP is funded by NSF.
This work is based in part on observations obtained at
the Gemini Observatory, which is operated by the Associ-
ation of Universities for Research in Astronomy (AURA)
under a cooperative agreement with the NSF on be-
half of the Gemini partnership: the National Science
Foundation (United States), the Science and Technology

11
Facilities Council (United Kingdom), the National Re-
search Council (Canada), CONICYT (Chile), the Aus-
tralian Research Council (Australia), CNPq (Brazil) and
CONICET (Argentina). This research has made use
of NASA’s Astrophysics Data System, the VizieR cat-
alogue access tool, CDS, Strasbourg, France, and the
NASA/ IPAC Infrared Science Archive, which is oper-
ated by the Jet Propulsion Laboratory, California In-
stitute of Technology, under contract with NASA. This
work made use of PyKE (Still & Barclay 2012), a soft-
ware package for the reduction and analysis of Kepler
data. This open source software project is developed
and distributed by the NASA Kepler Guest Observer
Office. This research has made use of IRAF, Astropy, a
community-developed core Python package for Astron-
omy (Astropy Collaboration et al. 2013), and the trian-
gle plotting code (Foreman-Mackey et al. 2014). IRAF is
distributed by the National Optical Astronomy Observa-
tory, which is operated by the Association of Universities
for Research in Astronomy (AURA) under cooperative
agreement with the National Science Foundation.
REFERENCES
Ackerman, A. S., & Marley, M. S. 2001, ApJ, 556, 872
Ahn, C. P., Alexandroff, R., Allende Prieto, C., et al. 2012, ApJS,
203, 21
Allard, F., Hauschildt, P. H., Alexander, D. R., & Starrfield, S.
1997, ARA&A, 35, 137
Allen, D. A., & Crawford, J. W. 1984, Nature, 307, 222
Apai, D., Radigan, J., Buenzli, E., et al. 2013, ApJ, 768, 121
Artigau, É., Bouchard, S., Doyon, R., & Lafrenière, D. 2009, ApJ,
701, 1534
Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al.
2013, A&A, 558, A33
Badman, S. V., Branduardi-Raymont, G., Galand, M., et al.
2014, Space Sci. Rev.
Bailer-Jones, C. A. L., & Mundt, R. 1999, A&A, 348, 800
—. 2001, A&A, 367, 218
Bhardwaj, A., & Gladstone, G. R. 2000, Reviews of Geophysics,
38, 295
Bryson, S. T., Tenenbaum, P., Jenkins, J. M., et al. 2010, ApJ,
713, L97
Buenzli, E., Apai, D., Radigan, J., Reid, I. N., & Flateau, D.
2014, ApJ, 782, 77
Buenzli, E., Apai, D., Morley, C. V., et al. 2012, ApJ, 760, L31
Burgasser, A. J., Gillon, M., Faherty, J. K., et al. 2014, ApJ, 785,
48
Burrows, A., Hubbard, W. B., Lunine, J. I., & Liebert, J. 2001,
Reviews of Modern Physics, 73, 719
Burrows, A., Sudarsky, D., & Hubeny, I. 2006, ApJ, 640, 1063
Claret, A., Hauschildt, P. H., & Witte, S. 2012, A&A, 546, A14
Clarke, F. J., Oppenheimer, B. R., & Tinney, C. G. 2002a,
MNRAS, 335, 1158
Clarke, F. J., Tinney, C. G., & Covey, K. R. 2002b, MNRAS,
332, 361
Clarke, F. J., Tinney, C. G., & Hodgkin, S. T. 2003, MNRAS,
341, 239
Dorren, J. D. 1987, ApJ, 320, 756
Fazio, G. G., Hora, J. L., Allen, L. E., et al. 2004, ApJS, 154, 10
Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J.
2013, PASP, 125, 306
Foreman-Mackey, D., Price-Whelan, A., Ryan, G., et al. 2014,
Zenodo
Gelino, C., & Marley, M. 2000, in Astronomical Society of the
Pacific Conference Series, Vol. 212, From Giant Planets to Cool
Stars, ed. C. A. Griffith & M. S. Marley, 322
Gelino, C. R., Marley, M. S., Holtzman, J. A., Ackerman, A. S.,
& Lodders, K. 2002, ApJ, 577, 433
Gillon, M., Triaud, A. H. M. J., Jehin, E., et al. 2013, A&A, 555,
L5
Gizis, J. E., Burgasser, A. J., Berger, E., et al. 2013, ApJ, 779,
172
Gizis, J. E., Troup, N. W., & Burgasser, A. J. 2011, ApJ, 736, L34
Goodman, J., & Weare, J. 2010, Commun. Appl. Math. Comput.
Sci.,, 5, 65
Harding, L. K., Hallinan, G., Boyle, R. P., et al. 2011, in
Astronomical Society of the Pacific Conference Series, Vol. 448,
16th Cambridge Workshop on Cool Stars, Stellar Systems, and
the Sun, ed. C. Johns-Krull, M. K. Browning, & A. A. West,
219
Harding, L. K., Hallinan, G., Boyle, R. P., et al. 2013, ApJ, 779,
101
Heinze, A. N., Metchev, S., Apai, D., et al. 2013, ApJ, 767, 173
Hook, I. M., Jørgensen, I., Allington-Smith, J. R., et al. 2004,
PASP, 116, 425
Howell, S. B., Sobeck, C., Haas, M., et al. 2014, PASP, 126, 398
Ingalls, J. G., Krick, J. E., Carey, S. J., et al. 2012, in Society of
Photo-Optical Instrumentation Engineers (SPIE) Conference
Series, Vol. 8442, Society of Photo-Optical Instrumentation
Engineers (SPIE) Conference Series
James, G. K., Ajello, J. M., & Pryor, W. R. 1998,
J. Geophys. Res., 103, 20113
Jenkins, J. M., Caldwell, D. A., Chandrasekaran, H., et al. 2010,
ApJ, 713, L120
Joyce, R. R. 1992, in Astronomical Society of the Pacific
Conference Series, Vol. 23, Astronomical CCD Observing and
Reduction Techniques, ed. S. B. Howell, 258
Khandrika, H., Burgasser, A. J., Melis, C., et al. 2013, AJ, 145, 71
Kirkpatrick, J. D. 2005, ARA&A, 43, 195
Koch, D. G., Borucki, W. J., Basri, G., et al. 2010, ApJ, 713, L79
Koen, C. 2003, MNRAS, 346, 473
—. 2004, MNRAS, 354, 378
—. 2005a, MNRAS, 360, 1132
—. 2005b, MNRAS, 357, 1151
—. 2006, MNRAS, 367, 1735
—. 2013, MNRAS, 428, 2824
Lane, C., Hallinan, G., Zavala, R. T., et al. 2007, ApJ, 668, L163
Littlefair, S. P., Dhillon, V. S., Marsh, T. R., Shahbaz, T., &
Mart´ın, E. L. 2006, MNRAS, 370, 1208
Maiti, M. 2007, AJ, 133, 1633
Maiti, M., Sengupta, S., Parihar, P. S., & Anupama, G. C. 2005,
ApJ, 619, L183
Marley, M. S., Ackerman, A. S., Cuzzi, J. N., & Kitzmann, D.
2013, Clouds and Hazes in Exoplanet Atmospheres (The
University of Arizona Press), 367
McLean, I. S., Graham, J. R., Becklin, E. E., et al. 2000, in
Society of Photo-Optical Instrumentation Engineers (SPIE)
Conference Series, Vol. 4008, Society of Photo-Optical
Instrumentation Engineers (SPIE) Conference Series, ed.
M. Iye & A. F. Moorwood, 1048
Metchev, S. A., Heinze, A., Apai, D., et al. 2015, ApJ, 799, 154
Patten, B. M., Stauffer, J. R., Burrows, A., et al. 2006, ApJ, 651,
502
Radigan, J., Jayawardhana, R., Lafrenière, D., et al. 2012, ApJ,
750, 105
Radigan, J., Lafrenière, D., Jayawardhana, R., & Artigau, E.
2014, ApJ, 793, 75
Robinson, T. D., & Marley, M. S. 2014, ApJ, 785, 158
Rockenfeller, B., Bailer-Jones, C. A. L., & Mundt, R. 2006, A&A,
448, 1111
Saumon, D., & Marley, M. S. 2008, ApJ, 689, 1327
Showman, A. P., & Kaspi, Y. 2013, ApJ, 776, 85
Still, M., & Barclay, T. 2012, PyKE: Reduction and analysis of
Kepler Simple Aperture Photometry data, ascl:1208.004,
astrophysics Source Code Library
Stumpe, M. C., Smith, J. C., Van Cleve, J. E., et al. 2012, PASP,
124, 985
Tavenner, T., Young, E. F., Bullock, M. A., Murphy, J., &
Coyote, S. 2008, Planet. Space Sci., 56, 1435
Tinney, C. G., & Tolley, A. J. 1999, MNRAS, 304, 119
Werner, M. W., Roellig, T. L., Low, F. J., et al. 2004, ApJS, 154,
1
Westphal, J. A., Matthews, K., & Terrile, R. J. 1974, ApJ, 188,
L111
Wilson, P. A., Rajan, A., & Patience, J. 2014, A&A, 566, A111
Zhang, X., & Showman, A. P. 2014, ApJ, 788, L6

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