Extinction and the Dimming of KIC 8462852
Huan Y. A. Meng George Rieke Franky Dubois Grant Kennedy Massimo Marengo Michael Siegel Kate Su Nicolas Trueba Mark Wyatt Tabetha Boyajian C. M. Lisse Ludwig Logie Steve Rau Sigfried Vanaverbeke








1Steward Observatory, Department of Astronomy, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721

2Astrolab IRIS, Verbrandemolenstraat, Ypres, Belgium and Vereniging voor Sterrenkunde, Werkgroep Veranderlijke Sterren, Belgium

3Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK

4Department of Physics and Astronomy, Iowa State University, A313E Zaffarano, Ames, IA 50010

5Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Lab, University Park, PA 16802

6Department of Physics and Astronomy, Louisiana State University, 261-A Nicholson Hall, Tower Dr, Baton Rouge, LA 70803

7Applied Physics Laboratory, Johns Hopkins University, 11100 Johns Hopkins Road, Laurel, MD 20723

8Center for Mathematical Plasma Astrophysics, University of Leuven, Belgium




hyameng@lpl.arizona.edu





To test alternative hypotheses for the behavior of KIC 8462852, we obtained measurements of the star over a wide wavelength range from the UV to the mid-infrared from October 2015 through December 2016, using Swift, Spitzer and at AstroLAB IRIS. The star faded in a manner similar to the long-term fading seen in Kepler data about 1400 days previously. The  dimming rate for the entire period reported is 22.1 ± 9.7 milli-mag yr^-1 in the Swift wavebands, with amounts of 21.0 ± 4.5 mmag in the groundbased B measurements, 14.0 ± 4.5 mmag in V, and 13.0 ± 4.5 in R, and a rate of 5.0 ± 1.2 mmag yr^-1 averaged over the two warm Spitzer bands. Although the dimming is small, it is seen at ≳ 3 σ by three different observatories operating from the UV to the IR.  The presence of long-term secular dimming means that previous SED models of the star based on photometric measurements taken years apart may not be accurate. We find that stellar models with T_eff = 7000 - 7100 K and A_V ∼ 0.73 best fit the Swift data from UV to optical. These models also show no excess in the near-simultaneous Spitzer photometry at 3.6 and 4.5 μm, although a longer wavelength excess from a substantial debris disk is still possible (e.g., as around Fomalhaut). The wavelength dependence of the fading favors a relatively neutral color (i.e., R_V ≳ 5, but not flat across all the bands) compared with the extinction law for the general ISM (R_V = 3.1), suggesting that the dimming arises from circumstellar material.









§ INTRODUCTION


KIC 8462852, also known as Boyajian's Star, is an enigmatic object discovered by citizen scientists of the Planet Hunters project studying data from the Kepler mission <cit.>. The main-sequence F1/2 V star <cit.> at ∼400 pc <cit.> has undergone irregularly shaped dips in flux up to ∼ 20% with durations of one to a few days <cit.>. A new episode of dips has started in May- June, 2017 <cit.>. The star also faded throughout the  Kepler mission <cit.>, initially in a slow decline, and 
then a more rapid fading by ∼ 2% over about 300 days <cit.>.  Such behavior is virtually unique among normal main-sequence stars <cit.>. Archival data have also been used to suggest a  decline in stellar brightness over the past century with an average rate of -0.151 ± 0.012% yr^-1 <cit.>, though the existence and significance
 of the century-long trend are disputed <cit.>. In addition, adaptive 
optics-corrected images in the JHK bands reveal a nearby source 2 from the primary star, with 
brightness and color consistent with a M2 V companion at a projected distance of ∼800 AU <cit.>.

Peculiar light curves and slow trends are common among young stellar objects (YSOs) <cit.>, and may result from the obscuration by dust generated by disintegrating planets <cit.> or planetesimal/planet collisions <cit.> if viewed edge-on <cit.>. However, KIC 8462852 does not appear to fit into either scenario.
The optical to mid-IR spectrum of the star confirms that it is a mature main-sequence dwarf; spectral energy distribution (SED) modeling finds no significant IR excess in the 3-5  region that could arise from a warm debris disk <cit.>; no excess is seen in the WISE photometry <cit.>; and  millimeter and sub-millimeter continuum observations also find no significant excess emission towards the star <cit.>. 

To characterize the effects of apparent astrometric motions that are driven by variability of field stars, the Kepler data have been studied using a principal component technique to remove correlated trends that are not relevant to the phenomena under investigation <cit.>.  It was found that some variations seen in the Kepler light curve are likely from other sources close to the line of sight of KIC 8462852. In particular, the study suggests that the 0.88-day period, presumed to be the rotational modulation of KIC 8462852 <cit.>, is likely from a contaminating source. While the major dips in Q8 and Q16/17 (and the long-term secular dimming) are confirmed to be from KIC 8462852, the origin of the smaller dips is less certain.

A viable explanation for the bizarre dips in the light curve of KIC 8462852 is the apparition of a large family of comets <cit.>, possibly the onset of a period like the Late Heavy Bombardment <cit.>. <cit.> show that the hypothesis is plausible by successfully modeling the last episode of dimming events in Kepler Quarters 16 and 17. Similar simulations by <cit.> also reproduce the primary features of the dips with one dust-enshrouded planetary object for each dip. However, this latter type of model would require additional comets or dust-enshrouded planets to explain any additional dips, essentially adding a large number of new free parameters. 

A number of other possibilities have been proposed.  A possible explanation is that one or more planetary bodies have spiraled into the star. It is speculated that the return of the star to thermal equilibrium may explain the slow dimming, while the deep dips may arise from transits of planetary debris <cit.>. <cit.> model the events as being due to a  Trojan-like asteroid system orbiting the star. In contrast, <cit.> suggest that the dimming might be caused by foreground dust in the ISM, with dense clumps in an intervening dark cloud responsible for the deep dips. Extinction by clumpy material in the outer Solar System has also been suggested <cit.>. In addition, instabilities in the star itself have been proposed <cit.>.

To investigate this mystery, we are conducting ongoing monitoring of KIC 8462852 and its surrounding field with two space telescopes in seven wavebands, Swift/UVOT in uvw2 (effective wavelength 2030 Å), uvm2 (2231 Å), uvw1 (2634 Å), u (3501 Å), and v (5402 Å) bands <cit.>, and Spitzer/IRAC at 3.6 and 4.5  <cit.>. In this paper, we report the results from the monitoring from October 2015 through December 2016 (we include a few measurements past this cutoff but have not made use of them in the analysis). We also use the automated and homogeneous observations from the AAVSO database obtained through December 2016 in optical BVR bands with the Keller F4.1 Newtonian New Multi-Purpose Telescope (NMPT) of the public observatory AstroLAB IRIS, Zillebeke, Belgium.



§ OBSERVATIONS


In this section, we describe the basic observations obtained with Swift/UVOT, AstroLAB IRIS, and Spitzer. Each of these sets of data indicates a subtle dimming of the star. However, gaining confidence in this result requires a detailed analysis of calibration issues, which is reserved for Section 3. 



 §.§ Swift/UVOT


The Ultraviolet/Optical Telescope (UVOT) is one of three instruments aboard the Swift mission. It is a modified Ritchey-Chrétien 30 cm telescope with a wide (17× 17) field of view and a microchannel plate intensified CCD detector operating in photon-counting mode <cit.>. UVOT provides images at 2.3 resolution and includes a clear white filter, u, b, and v optical filters, uvw1, uvm2, and uvw2 UV filters, a magnifier, two grisms, and a blocking filter. The uvw2 and uvw1 filters have substantial red leaks, which have been characterized to high precision by <cit.> and are included in the current UVOT filter curves. Calibration of the UVOT is discussed in depth by <cit.> and <cit.>.

In full-frame mode, the CCD is read every 11 ms, which creates a problem of coincidence loss (similar to pile-up in the X-ray) for stars with count rates greater than 10 cts s^-1 (∼15 mag, depending on filter).  The camera can be used in a windowed mode, in which a subset of the pixels is read. Given the brightness of KIC 8462852, to reduce the coincidence corrections we observed in a 5× 5 window (70 × 70 pixels), resulting in a 3.6 ms readout time. The observations were generally 1 ks in duration, utilizing a mode that acquired data in five filters (v, u, uvw1, uvm2 and uvw2, from 5900 to 1600 Å). To improve the precision of the photometric measurements and ensure that the target star and comparison stars all landed in the readout window, observations were performed with a “slew in place,” in which Swift observed the field briefly in the “filter of the day" – one of the four UV filters – before slewing a second time for more precise positioning. The slew-in-place images were used for additional data points in the UV. KIC 8462852 was first observed on October 22, 2015 and then approximately every three days from December 4, 2015 to March 27, 2016. It was later observed in coordination with the Spitzer campaign starting August, 2016.

X-ray data were obtained simultaneously with the Swift/XRT <cit.>. 
No X-ray emission within the passband from 0.2 to 10 keV is seen from KIC 8462852 in 52 ks of exposure time down to a limit of 5 × 10^-15 erg s^-1 cm^-2 using the online analysis tools of <cit.>.



 §.§ AstroLAB IRIS


Optical observations in B, V, and R bands were taken with the 684 mm aperture Keller F4.1 Newtonian New Multi-Purpose Telescope (NMPT) of the public observatory AstroLAB IRIS, Zillebeke, Belgium. The CCD detector assembly is a Santa Barbara Instrument Group (SBIG) STL 6303E operating at -20C. A 4-inch Wynne corrector feeds the CCD at a final focal ratio of 4.39, providing a nominal field of view of 20× 30. The 9  physical pixels project to 0.62 and are read out binned to 3 × 3 pixels, i.e., 1.86 per combined pixel. The B, V, and R filters are from Astrodon Photometrics, and have been shown to reproduce the Johnson/Cousins system closely <cit.>. The earliest observation was made on September 29, 2015. There is a gap in time coverage from January 8 to June 8, 2016. We report the observations through December 2016.



 §.§ Spitzer


Spitzer observations are made with the Infrared Array Camera (IRAC) with a uniform exposure design, which uses a cycling dither at 10 positions on the full array with 12 s frame time. Using multiple dither positions tends to even out the intra- and inter-pixel response variations of the detector; repeating the same dither pattern at every epoch puts KIC 8462852 roughly on the same pixels of the detector, further reducing potential instrumental bias on the photometry[<http://ssc.spitzer.caltech.edu/warmmission/news/>
<18jul2013memo.pdf>]. 
Our first Spitzer observation was executed on January 16, 2016. There is a gap in the time baseline of the monitoring in the period from April to July 2016 (from MJD 57475 to 57605) when KIC 8462852 was out of the visibility window of Spitzer[Note that the time coverage gap in the Swift and Spitzer data is only partially overlapped with the gap in the ground-based data.]. The Swift-Spitzer coordinated monitoring is still underway at the time this paper was written. 

cccccccc

UVOT Photometry of KIC 8462852


Waveband    MJDa     raw     σ     corrected      σ     relative comparisonb     σ  

         magnitude     magnitude     magnitude      magnitude     magnitude     magnitude  

uvw2	   	57317.518	   	14.820	   	0.050	   	14.776	   	0.089	   	0.045	   	0.074	

uvw2	   	57317.521	   	14.800	   	0.030	   	14.793	   	0.055	   	0.007	   	0.046	

uvw2	   	57317.552	   	14.790	   	0.030	   	14.787	   	0.047	   	0.003	   	0.036	

uvw2	   	57317.554	   	14.810	   	0.030	   	14.784	   	0.043	   	0.026	   	0.030	

uvw2	   	57317.584	   	14.780	   	0.030	   	14.755	   	0.058	   	0.025	   	0.050	

uvw2	   	57317.587	   	14.820	   	0.030	   	14.735	   	0.061	   	0.085	   	0.053	

aModified Julian date
bAverage brightening of the comparison star measurements
This table is available in its entirety in a machine-readable form in the online journal and as an appendix to this posting. A portion is shown here for guidance regarding its form and content.






§ DATA PROCESSING AND ANALYSIS 


Our three data sources provide multiple accurate measurements of KIC 8462852 over a year. They were all interrupted when the viewing angle to KIC 8462852 passed too close to the sun. Because of differing viewing constraints, exactly when this gap in the data occurs differs among the observatories. Because of the differences in time coverage, 
we analyze long-term trends in the data sets in two ways. First, within a given data set, we fit a linear trend and use the slope and its error as an indication of any change.  The Swift measurements are mostly prior to the gap, so we fitted both before the gap and for the whole set of measurements.  For the sake of comparison, we treat the groundbased data the same way. The Spitzer observations began at the end of the first groundbased sequence, so we only fit the whole set. 

Although these fits make use of all the data in each band, they may give misleading information on the color behavior because the data do not have identical time coverage. In discussing color trends we focus just on the UVOT and groundbased data obtained in overlapping time sequences. For the Spitzer data, we calculate the difference from the first measurement to the later ones, and compare with a similar calculation for the groundbased point closest in time to the first Spitzer point, relative to the post-gap results from the ground. Details of these procedures are given below.  



 §.§ Swift  Data


Swift/UVOT data were obtained directly from the HEASARC archive[<http://heasarc.gsfc.nasa.gov/cgi-bin/W3Browse/swift.pl/>. The same processed UVOT data are also available through the MAST archive at STScI, <http://archive.stsci.edu>.]. We then used the HEASARC FTOOLS software[<http://heasarc.gsfc.nasa.gov/docs/software/lheasoft/>]
program UVOTSOURCE on the transformed sky images to generate point source photometry. 

The Swift/UVOT photometry includes a filter-dependent correction that accounts for the decline in instrument sensitivity <cit.>.  However, the potential fading of KIC 8462852 pushes the boundaries of the UVOT calibration, which is specified to within 1%.  To check for any residual sensitivity changes, we made photometric measurements for four additional field stars in the UVOT field. The reference stars selected are KIC 8462934, KIC 8462763, KIC 8462843, and KIC 8462736, which all lie 14 to 20 from KIC 8462852. Since these reference stars are all fainter than KIC 8462852 by 2 - 5 magnitude in the UV and have larger photometric errors individually, we took their weighted average as our photometric reference to minimize the noise. Their linear fits indicate that the average reference star appears to get brighter in the UVOT data over the full range of our time coverage, especially when the post-gap data are considered (-22.2 ± 5.2 mmag yr^-1). We examined the reference stars individually and found that all four of them follow similar and consistent brightening rates, eliminating the possibility of "bad" star contamination. This suggests a small residual instrumental trend in the UVOT data, which could reflect a small overestimate of the sensitivity loss or a small residual in the coincidence loss correction. 

To remove the instrumental trend of Swift/UVOT, we subtract the normalized magnitude of the average reference star from the absolutely calibrated magnitude of KIC 8462852. This inevitably propagates the photometric uncertainties of the average reference star into the KIC 8462852 light curve.  In all following discussions, we only use the corrected calibration data of Swift/UVOT. All the Swift photometry is given in Table <ref> and is displayed in Figure <ref>.
 For a first search for trends in the brightness of the star, we performed a linear fit to the photometry. As shown in Table 2,  
with the corrected calibration the fading of KIC 8462852 is seen at a 3 σ significance level in the pre-gap data and by > 2 σ in the full data set.

ccccccccccc

Trends of the brightness of KIC 8462852


         4cPre-Gap         4cFull Data 

3-6 8-11
Waveband     λ_eff     dm/dt     σ(dm/dt)     χ_red^2     siga         dm/dt     σ(dm/dt)     χ_red^2     siga 

     ()     (mmag yr^-1)     (mmag yr^-1)                 (mmag yr^-1)     (mmag yr^-1)         

uvw2     0.2030     83.7     66.6     0.81             71.8     31.5     0.92 

uvm2     0.2231     210.5     203.9      1.03             -60.3     86.5     1.07 

uvw1     0.2634     108.5     61.5     0.96             17.4     24.5     1.04 

u     0.3501     69.0     44.0     0.29             42.7     17.8     0.30 

v     0.5402     54.9     32.7     0.27             1.9     14.5     0.34 

2cSwift Averageb     71.0     22.6         Y         22.1     9.7         

B     0.435     20.2     11.4                 26.3     1.5         Y 

V     0.548     16.2     8.1                   21.6     1.5d        Y

R     0.635     1.6     6.7                 13.1     1.0         Y 



[3.6]c     3.550                        5.1     1.5     1.99     Y 

[4.5]c     4.493                        4.8     2.0     1.84     

2cSpitzer Averageb                         5.0     1.2         Y 


aSignificance flag. “Y” means that the magnitude changing rate is significantly different from zero at the  3σ level or higher. Otherwise this is left blank.
bAveraging the data ignoring the wavelength information implicitly assumes a grey color of the fading.
cWe only have 2 epochs of Spitzer observations before the gap, and the gap is offset relative to the groundbased data, so we do not quote values pre-gap.
d Computed omitting the first night, which is systematically high and had a large number of measurements that drive the slope inappropriately.








 §.§ Ground-based Data


The Swift data suggest that the star faded during our observations, and such behavior would be consistent with the long-term secular fading of KIC 8462852 observed previously <cit.>. To probe this behavior further, we turn to the ground-based  BVR photometry obtained at AstroLAB IRIS and available from AAVSO. We did not detect any major dips in the flux from the monitoring up to December 2016, but our measurements do indicate a slight long-term secular dimming. 

We used differential photometry relative to four stars in the field, selected to be similar in brightness and color to KIC 8462852  (see  Table <ref>). These observations were obtained simultaneously with those of KIC 8462852, typically in a series in V followed by B and then R. The reductions utilized the LesvePhotometry reduction package <cit.>, which is optimized for time-series observations of variable stars. It automates reduction of the data in a series of observations, providing a homogeneous database of photometry for KIC 8462852.  Errors from photon noise on the source, scintillation noise and background noise are determined for each observation, using the methodology in <cit.>. We eliminated data from a single night when the source was at large (> 2) airmass. We also eliminated data from nights with larger than normal estimated errors (> 0.025 magnitudes rms) for KIC 8462852, as identified either by the reduction package or by large rms errors for the data obtained within that night. The remaining photometry in B, V, and R bands is displayed in Figure <ref>. The scatter is somewhat larger than implied by the internal error estimates; therefore, we will base our error estimates on the scatter. Linear fits show a dimming in all three colors over the full data set, and probable dimming but not at signficant levels pre-gap (see Table 2). No significant dimming is seen post-gap.  In estimating the uncertainties of these slopes, we found that the reduced χ^2 using the reported internal errors was large (2 to 4 depending on the band), consistent with our finding that the rms scatter of the measurements is larger than the reported errors. We brought the reduced χ^2 of the fit to ∼ 1 by adding an additional error of 0.01 mag in quadrature to each measurement. 

cccccccccc

Comparison stars for BVR photometry


ID    RA  (2000)      DEC (2000)     V     B-V      V-R 

KIC 8462852     20 06 15.46     +44 27 24.6      11.86     0.54     0.40 

Star 1     20 07 09.07     +44 20 17.1     11.59     0.54     0.40 

Star 2     20 06 01.24     +44 29 32.4     12.42     0.79     0.51  

Star 3     20 06 21.21     +44 30 52.2     12.81     0.51     0.40  

Star 4     20 06 48.09     +44 22 48.1     11.26     0.47     0.35  



There are two issues with the linear fits. The first is that, given that there is no evidence for fading in the data after the interruption due to solar viewing constraints (see  Figure <ref>), the fits tend to be high toward the beginning and low toward the end of the post-gap sequence. This is particularly prominent in the v and V fits as shown in  Figure <ref>. The linear fits are meant as the simplest way to quantify the dimming that would include all the data in each band, but they appear not to be exactly the correct dependence.

The second issue is that, for the groundbased data, our discussion above does not include the possibility of systematic errors affecting the comparison pre- and post-gap, effects that are not included in the  LesvePhotometry package. (We have already eliminated such errors for the Swift/UVOT data and, as discussed below, they should be negligible for the Spitzer measurements.) To test for such effects, we turned to the photometry of the four reference stars to estimate night-to-night and longer-term  errors and to select the nights with the most consistent observations to see if the dimming was apparent just using this subset of best measurements. 
Since these further steps made no reference to the photometry of KIC 8462852, they should introduce no bias in its measurements. 

We first computed the standard deviations of running sets of 45 measurements for each of these four stars. When this value exceeded an average of 0.015 per star, we investigated the photometry involved and eliminated nights contributing disproportionately to the value. Following this step, we examined the consistency of the remaining measurements of the reference stars. Since we do not know the “true” magnitudes of the stars, we instead tested for the consistency of the measurements of each star across the gap in time coverage. To establish a baseline, we identified two long consecutive sets of measurements for each star and each color, one on each side of the gap, that agreed well. We then tested each of the additional nights of data to see if they were consistent with this baseline, and added in the data for the nights that did not degrade the agreement across the gap. We carried out this procedure individually for each of the three colors, but found that the same nights were identified as having the highest quality photometry in each case. The final typical mis-match in photometry across the gap was 0.0032 magnitudes, showing that this vetting was effective in identifying nights with consistent results for the four reference stars. The photometry of KIC 8462852 on these nights is listed in Table <ref> and plotted in Figure  <ref>. 

The photometry selected to be of highest internal consistency is generally consistent with the rest of the measurements. The final averages for KIC 8462852 just based on these nights before and after the gap in the time series are shown in  Table <ref>. Each band shows a small but statistically significant dimming from pre-gap to post-gap, both in the initial photometry (Table 2) and in that selected to be of highest quality.   

There is a hint of fading in the pre-gap data, but averaged over the three bands the net change is 0.010 ± 0.005 magnitudes, i.e. small and potentially insigificant. The post-gap data indicate no significant long-term secular changes beyond the errors of ∼ 0.003 magnitudes in any of the bands. These results suggest that most of the change in brightness occurred while the star was in the gap for the groundbased photometry. This behavior would be consistent with that observed for long-term dimming using Kepler data, where most of the change is a drop in brightness by ∼ 2% over a period of 300 days <cit.>. The gap in our data is intriguingly about 1400 days (∼ twice the interval between the two large dips in the light curve) past the time of the similar dimming seen in the Kepler data. The amplitude in the V and R bands (which together approximate the Kepler spectral response) is about 1.4 ± 0.3% (Table 5), and the duration of the gap in our highest quality BVR data is ∼ 150 days, values that are also reminiscent of the Kepler observations.

ccccccc

Selected High-Quality BVR photometry


JD     B (mag)     erra     V (mag)     erra      R(mag)     erra 

2457328.25	     12.379    	0.009     11.846     0.009     11.455     0.009  

2457365.29	     12.373      0.009     11.841     0.009     11.453     0.009  

2457366.23	      12.363     0.009     11.837     0.009     11.448     0.009  
 
2457380.25	       12.380     0.009     11.844     0.009     11.453     0.009  

2457386.26	      12.372     0.009     11.850     0.009     11.453     0.009  

2457395.26	      12.372     0.010     11.850     0.010     11.451     0.010  

2457396.25	      12.378     0.009     11.849     0.009     11.462     0.009  

2457631.38	      12.396     0.003     11.860     0.003     11.467     0.003  

2457640.31	      12.381     0.013	    11.851     0.013     11.460     0.013  

2457652.3	      12.372     0.013     11.848     0.013     11.459     0.013  

2457658.29	      12.396     0.013     11.860     0.013     11.461     0.013  

2457660.37	      12.392     0.011     11.856     0.011     11.460     0.011  

2457664.36	      12.394     0.013     11.850     0.013     11.458     0.013  



aCombined rms errors of the mean, i.e. rms scatter divided by the square root of (n-1) where n is the number of measurements.



ccccccc

Summary of ground-based monitoring of KIC 8462852


MJD Range    ⟨ B⟩a     err(B)b     ⟨ V⟩a     err(V)b      ⟨ R⟩a     err(R)b

57322 - 57396     12.374     0.0032     11.845     0.0032     11.453     0.0032 

57549 - 57693     12.395     0.0032     11.859     0.0032     11.466     0.0032 

Differences     0.021     0.0045     0.014     0.0045     0.013     0.0045 

aAverage magnitude.
bCombined rms errors of the mean, i.e. rms scatter divided by the square root of (n-1) where n is the number of measurements.






 §.§ Spitzer  Data


For the purpose of probing for a long-term secular trend, we do not consider the earlier Spitzer photometry <cit.>. That observation was made under the SpiKeS program (Program ID 10067, PI M. Werner) in January 2015, too far from the epochs of our new data. In addition, the SpiKeS observation was executed with an AOR design different from ours for the dedicated monitoring of KIC 8462852, which may lead to different instrumental systematics in the photometry.

The photometry we did use is from AORs 58782208, 58781696, 58781184, 58780928, 58780672, 58780416, and 58780160 (PID 11093, PI K. Y. L. Su) and 58564096 and 58564352 (PID 12124, PI Huan Meng). 
Photometric measurements were made on cBCD (artifact-corrected basic calibrated data) images with an aperture radius of 3 pixels and sky annulus inner and outer radii of 3 and 7 pixels, with the pixel phase effect and array location dependent response functions corrected. Aperture correction factors are 0.12856 and 0.12556 magnitudes at 3.6 and 4.5 , respectively <cit.>. Individual measurements were averaged for each epoch. The photometry is summarized in Table <ref>. 
During the period when the KIC 8462852 data were obtained, the photometric performance of IRAC is expected to have varied by 
less than 0.1% per year (i.e., < 1 mmag yr^-1)  <cit.>.  There is a suggestion of a fading at the ∼ 3 σ level of significance in the 3.6 μm band; there is also a fading in the 4.5 μm band at lower significance. 


ccccc

Spitzer photometry


MJD     [3.6] (mag)     err     [4.5] (mag)     err   

57040.367        10.4627       0.0022      10.4243       0.0029  

57403.587        10.4510       0.0012       10.4334       0.0015  

57453.618        10.4551       0.0012       10.4346       0.0016  

57606.748        10.4537       0.0012       10.4375       0.0016  

57621.036        10.4554       0.0012       10.4392       0.0016  

57635.443        10.4579       0.0012       10.4324       0.0017  

57648.371        10.4543       0.0012       10.4345       0.0016  

57672.538        10.4559       0.0012       10.4382       0.0016  

57676.320        10.4549       0.0012       10.4383       0.0016  

57690.430        10.4580       0.0012       10.4377       0.0016  

57704.534        10.4574       0.0012       10.4363      0.0016  

57719.375        10.4604       0.0012       10.4357      0.0016  

57732.497        10.4514       0.0012       10.4392      0.0016  

57756.319        10.4486       0.0012       10.4344      0.0015  

57813.968        10.4511       0.0012        10.4388      0.0016  
 




 §.§ Color-dependence of the dimming


The three independent sets of observations presented in this paper all show evidence of dimming in KIC 8462852.  Measurements reported by the All-Sky Automated Survey for Supernovae (ASAS-SN) <cit.> do not completely overlap with ours, but a preliminary analysis shows that they show a fading of about 8 mmag at V, comparing their data between MJD of 57200 and 57334 with that between MJD of 57550 and 57740; their measurements may indicate a further small fading after that. The  ASAS-SN photometry has not been tested thoroughly for systematic errors at this small level (K. Stanek, private communication, and see warning at <https://asas-sn.osu.edu/>); nonetheless, the results agree within the mutual errors with ours. The dimming is also corroborated in measurements by <cit.>.

However, we find that the amount of dimming is significantly less 
in the infrared than in the optical and ultraviolet, as shown in  Figure <ref>. We will investigate in 
Section 4 what constraints the wavelength dependence lets us put on this event. To do so, we need to focus on periods when measures are available in all the relevant bands (see  Figure <ref>), since otherwise wavelength-independent and -dependent brightness changes are degenerate. 

The first sequence of Swift measurements extends well beyond the end date for the first sequence of BVR measurements. 
For the purposes of Section 4, we compute the dimming using the average of the measurements through MJD 57396. For the groundbased measurements, we take only the measurements on nights that passed our test for consistency of the comparison star measurements. We average all the data from such nights pre-gap and, separately, post-gap, and base the errors on the rms scatter of the individual measurements. For Spitzer, there is only a single measurement close in time to the first groundbased sequence, namely at JD 2457404.  To analyze these data, we first confirm the errors by computing the scatter in both bands (combined). This calculation indicates an error of 0.002, slightly larger than the quoted errors of 0.0012 - 0.0016. Using our more conservative error estimate, the change from the first point to the average of the post-gap ones at 3.6 μm is 0.0049 ± 0.0021 mag, and at 4.5 μm it is 0.0033 ± 0.0021 mag, or an average of 0.0041 ± 0.0015. We  compare this value with the change between the average of the two sets obtained from the ground closest in time to the first Spitzer one, namely at MJD 57395 and 57396 (both of which passed our tests for high quality data), versus the later (post-gap) groundbased measurements. We averaged the measurements in B and V  together into a single higher-weight point for these two nights and then compared with the similar average of the post-gap measurements. The net change is 0.012 ± 0.0023 magnitudes, i.e., significantly larger than the change in the infrared.

 Table 7 summarizes the measurements we will use to examine the color-dependence of the dimming of KIC 8462852. It emphasizes conservative error estimation (including systematic ones) and homogeneous data across the three observatories, at the cost of nominal signal to noise. The dimming is apparent, at varying levels of statistical significance, in every band. The values in the table also agree with the slopes we computed previously (and noting that the time interval for the differences is about 74% of a year), as shown in the table for the cases with relatively high weight values so comparisons are meaningful.

cccccccccc

Color dependence of the dimming


Band    Wavelength (μm)     Interval     magnitudea     Dimming      Errorb     Telescope

uvw2     0.203     pre-gap     14.809     —     —     Swift 

uvw2     0.203     post-gap     14.826     0.017     0.018     Swift 

uvm2     0.223     pre-gap     14.808     —     —     Swift 

uvm2     0.223     post-gap     14.810     0.002     0.037     Swift 

uvw1     0.263     pre-gap     13.635     —     —     Swift 

uvw1     0.263     post-gap     13.649     0.014     0.011     Swift 

u     0.346     pre-gap     12.575     —     —     Swift 

u     0.346     post-gap     12.595     0.020     0.006     Swift 

u       0.346      —      —      0.0316        0.0132       from slope calculation 

B     0.435     pre-gap     12.374     —     —     AstroLAB-IRIS 

B     0.435     post-gap     12.395     0.021     0.0045     AstroLAB-IRIS 

B     0.435      —         —        0.0195      0.0015       from slope calculation 
 
v     0.547     pre-gap     11.894     —     —     Swift 

v     0.547     post-gap     11.904     0.010     0.006     Swift 

V     0.548     pre-gap     11.845     —     —     AstroLAB-IRIS 

V     0.548     post-gap     11.859     0.014     0.0045     AstroLAB-IRIS 

V     0.548       —         —         0.0160       0.0015        from slope calculation 

R     0.635     pre-gap     11.453     —     —     AstroLAB-IRIS 

R     0.635     post-gap     11.466     0.013     0.0045     AstroLAB-IRIS 

R     0.635      —        —         0.0097       0.001       from slope calculation 

[3.6]     3.6     pre-gap     10.4510     —     —     IRAC 

[3.6]     3.6     post-gap     10.4559     0.0049     0.0021     IRAC 

[4.5]     4.5     pre-gap     10.4334     —     —     IRAC 

[4.5]     4.5     post-gap     10.4367     0.0033     0.0021     IRAC 

aAverage magnitude.
bCombined rms errors of the mean, i.e. rms scatter divided by the square root of (n-1) where n is the number of measurements.





§ DISCUSSION




 §.§ Mass Limit of Circumstellar Dust


Many of the hypotheses to explain the variability of KIC 8462852 depend on the presence of a substantial amount of circumstellar material. Excess emission from circumstellar dust is therefore an interesting diagnostic. Such an excess has not been found at a significant level <cit.>. However, previous searches have used data from 2MASS <cit.>, GALEX <cit.>, warm Spitzer <cit.>, WISE <cit.>, and new optical observations, which were taken more than 10 years apart, to constrain the stellar atmospheric models that are used to look for excess. The variability of the star, particularly if it has been fading for years <cit.>, could undermine the searches for excesses. 

Now we can test if KIC 8462852 has had a significant excess at 3.6 and 4.5  by fitting stellar models with the Swift data taken at specific epochs and compare the model-predicted stellar IR flux with the simultaneous Spitzer measurements. By October 2016, there have been five epochs at which we have Swift and Spitzer observations taken within 24 h: MJD 57403, 57454, 57621, 57635, and 57673. The first two are before March 2016, whereas the last three epochs are observed after the gap. To analyze these results, we adopt the ATLAS9 model <cit.> with the stellar parameters obtained from spectroscopic observations, log (g) = 4.0, and [M/H] = 0.0. We allow T_eff to vary between 6700 and 7300 K with an increment of 100 K. We find that the stellar models with T_eff = 7000 and 7100 K provide the best fits to the Swift photometry at all five epochs, with a minimum reduced χ^2 from 0.08 to 1.5 (see Figure 2). We did not use the Spitzer/IRAC measurements to further constrain the fit, since we did not want to bias any evidence for an infrared excess. Although these temperatures are slightly higher than originally estimated by <cit.>, they are in reasonable agreement with the SED model based on the 2MASS photometry <cit.> and the recent IRTF/SpeX spectrum leading to a classification of F1V - F2V, i.e., ∼ 6970 K  <cit.>.  All of these values can be somewhat degenerate with changes in the assumed  logg and metallicity. For our purposes, however, having a good empirical fit into the ultraviolet allows placing constraints on the extinction. All five best-fit stellar models, one for each epoch, have A_V in the range of 0.68 to 0.78, 2.0 to 2.3 times higher than A_V = 0.341 found by <cit.> with photometric measurements years apart.
In the Spitzer/IRAC wavebands at 3.6 and 4.5 , the observed flux densities match the model-predicted stellar output fairly well at all five epochs. The average excess is -0.39 ± 0.30 mJy at 3.6  and -0.29 ± 0.21 mJy at 4.5 . We conclude that we do not detect any significant excess of KIC 8462852 with near-simultaneous Swift and Spitzer observations.  Our conclusion is consistent with that of <cit.>, showing that it is independent of the uncertainties in fitting the stellar SED.




We have tested these conclusions using the average post-gap B, V, R, [3.6], and [4.5] measurements (Table 7) rather than the UVOT UV ones, standard stellar colors <cit.>, and a standard extinction law <cit.>. The best fit was obtained assuming the star is of F1V spectral type (nominal temperature of 7030 K), with A_V = 0.61. Given the uncertainties in the extinction law, the stellar models, and intrinsic stellar colors (e.g., the effects of metallicity), this agreement is excellent. The assigned extinction level also agrees roughly with the relatively red color of the star relative to a F2V comparison star in infrared spectra (C. M. Lisse, private communication). The conclusion about the absence of any infrared excess is unmodified with this calculation.

Upper limits to the level of circumstellar dust were also determined at 850 μm with JCMT/SCUBA-2 <cit.>, and from WISE at 12 and 22 μm, in all cases where the stellar variations are relatively unimportant. Assuming that the grains emit as blockbodies and are distributed in a narrow, optically thin ring at various radii from the star, we place upper limits of ∼  4 × 10^-4 for the fractional luminosity, L_dust/L_*, for warm rings of radii between 0.1 and 10 AU and an order of magnitude higher for cold rings lying between 40 and 100 AU, which would be a typical cold-ring size for a star of this luminosity (see also <cit.>). These limits are consistent with the presence of a prominent debris disk, since even around young stars these systems usually have L_dust/L_* ≲ 10^-3 <cit.>. 

We carried out a second calculation to place upper limits on the possible dust masses. We again assumed that the dust is distributed in an optically thin ring (0.1 AU wide in the ring plane). We took the optical constants derived for debris disk material <cit.> and used the Debris Disk Radiative Transfer Simulator[<http://www1.astrophysik.uni-kiel.de/dds/>] <cit.>. The minimum grain radius was set to 1 , roughly the blowout size for spherical particles around a F1/2 V star, and the power law index of the particle distribution was taken as 3.65 <cit.>. We take the upper limit at 850  to be 4.76 mJy, or 5.6σ above zero, i.e., 3σ added to the 2.6σ “signal” at the position of the star <cit.>. Similarly, we take a 3σ upper limit of 0.63 mJy at 4.5 . We took the cataloged upper limits for the two WISE bands, which are computed in a similar way but at a 2σ level. Stellar parameters are assumed to be T_eff = 7000 K and L_* = 5 L_ <cit.>.



The resulting limits are shown in Figure <ref>. The upper limit at 100 AU is slightly higher than the mass of 0.017 M_ for a similar range of dust sizes (i.e., up to 2 mm) in the Fomalhaut debris ring <cit.>. Again, a prominent but not extraordinary debris disk is allowed, corresponding for example to 2 - 3 orders of magnitude more dust than orbits the sun. The upper limits also permit sufficient dust mass to yield significant extinction. To demonstrate, we 
assume that the dust is in a ring at radius R with a thickness perpendicular to the orbital plane of 0.1 R; for simplicity we take an ISM-like dust particle size distribution with constant density within this ring. The resulting upper limit on the extinction is A_V ∼ 0.1  <cit.>. This value is independent of the radius assumed for the ring, since as shown in Figure 3, the upper limits for the mass scale roughly as R^2, which is also the scaling of the ring area under our assumptions. Of course, this is only a rough estimate, but it is sufficient to demonstrate that detectable levels of extinction can be consistent with the upper limits on the thermal emission of any material surrounding the star.  That is, current measurements allow enough material to orbit KIC 8462852 to account for a number of the hypotheses for its behavior, such as the inspiralling and disintegration of massive comets. The minimum mass required to account for the long-term secular dimming 
through extinction is also within these mass constraints.  



 §.§ Extinction Curve


We now explore the hypothesis that the long-term secular dimming of KIC 8462852 is due to variable extinction by dust in the line of sight. The absence of excess emission at 3.6 and 4.5  means that the photometry at these wavelengths is a measure of the stellar photospheric emission. Under the assumption that the fading of the star indicated in Table <ref> is due to dust passing in front of the star, the relative amounts of dimming at the different wavelengths can therefore be used to constrain the wavelength dependence of the extinction from the UV to 4.5 μm in the IR. 

Under this hypothesis, the dimming of KIC 8462852 may arise either from the interstellar medium (ISM) or circumstellar material. For convenience, we describe the color of the fading in the terminology of interstellar extinction, although circumstellar material might have different behavior if the color were measured to high accuracy.   The Galactic ISM extinction curve from 0.1 to 3  can be well characterized by only one free parameter, the total-to-selective extinction ratio, defined as R_V = A_V / E(B - V) <cit.>. Longward of 3 , measurements towards diffuse ISM in the Galactic plane <cit.>, towards the Galactic center <cit.>, and towards dense molecular clouds in nearby star-forming regions <cit.> reveal consistent shallow wavelength dependence of the ISM extinction in the Spitzer/IRAC bands. We find that extrapolating the analytical formula in <cit.> (CCM89,hereafter) to the 3.6 and 4.5  bands of IRAC yields A_[3.6]/A_K_s from 0.42 to 0.54 and A_[4.5]/A_K_s from 0.28 to 0.37 for R_V values from 2.5 to 5.0, a range suitable for most sight lines in the Milky Way. Although the  extinction law does not claim to apply to these wavelengths, the 3.6 and 4.5  extrapolations are in good agreement with the IRAC observations <cit.>. Therefore, for simplicity we adopt the  extinction law for all the seven bands monitored.

We have fitted the wavelength-dependent dimming in Table <ref> with extinction curves using the formulation in ,  parameterized by R_V and extended to 4.5 μm. Figure 4 shows the results. Because of the relatively small level of dimming in the ultraviolet, the best-fitting extinction curves are relatively `gray', i.e., have large values of R_V. The vertical dashed lines show confidence levels corresponding to 1, 2, and 3 σ. Values of R_V ∼ 5 are favored; the general value for the ISM, R_V = 3.1 is disfavored at a confidence level > 90%. Extinction even more gray than given by R_V = 5 (or a form differing more fundamentally from the interstellar law) is a definite possibility. However, a completely neutral extinction law is excluded because of the small variations at [3.6] and [4.5].














So far we have conducted simple fits via χ^2 minimization to the fading and extinction curves individually. However, they are interrelated. Therefore, we now fit them simultaneously using the Feldman and Cousins method (F&C, Feldman & Cousins, 1998; Sanchez et al. 2003). The method differs from a regular χ^2 minimization by allowing setting of physical boundaries in the fitting parameters (e.g. 2 < R_V < 6), and by adjusting the χ^2 statistics accordingly, via a Monte Carlo approach. Figure 5 shows the resulting confidence intervals. Those for χ^2 minimization agree excellently with the simple single-parameter results in Figure 4. The F&C formalism suggests a similar conclusion, i.e. R_V > 3.1, but at somewhat higher confidence, > 98%. The derived best fit dimming rate also agrees with the simple χ^2 analysis. We also tried to fit the pre- and post-gap data separately. The result was not successful: the F&C method fails to constrain reasonable values of R_V and dA_V /dt. This suggests that there is no measurable dimming in the pre- and post-gap datasets separately (e.g. the dimming happened during the gap), which is also in agreement with the findings from simple χ^2 minimization.



§ CONCLUSIONS


This paper continues the study of the long-term secular dimming of KIC 8462852, such as that seen during the Kepler mission <cit.>. 
We have observed a second dimming occurence, similar to that seen with Kepler. Our data extend from the UV (0.20 μm) to the mid-infrared (4.5 μm), allowing us to determine the spectral character of this event.  The dimming is less in the infrared than in the visible and UV, showing that the responsible bodies must be small, no more than a few microns in size. We analyze the colors under the assumption that the dimming is due to extinction by intervening dust. We find that the colors are likely to be more neutral than the reddening by typical sight lines in the ISM (confidence level > 90%). That is, the dust responsible for the dimming differs from that along typical sight lines in the ISM, suggesting that the dust is not of normal interstellar origin. 

The discovery of a dimming pattern similar to that seen with Kepler roughly 1400 days previously <cit.>  is challenging to reconcile with the hypothesis that these events result from dust produced during the assimilation of a planet <cit.>. 
The long-term secular dimming could correspond to some dusty structure in the Oort Cloud of the Sun with a column density gradient on ∼1 AU scale. The high ecliptic latitude of KIC 8462852 (β = +62.2) is not necessarily a problem for this hypothsis, as the Oort cloud should be nearly isotropic <cit.>. The primary difficulty with this picture is that the orbital timescale of any Oort cloud dust concentrations is 10^5 to 10^7 yr. Over the 8-year-long time line from the beginning of Kepler to our latest observations, the astrometric movement of such a structure should be dominated by the Earth's parallactic motion, and thus most of the observed light curve features should be recurrent relatively accurately on a yearly basis <cit.>. 

We conclude that  extinction by some form of circumstellar material is the most likely explanation for the long-term secular dimming. 




§ ACKNOWLEDGEMENTS

This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech. GMK is supported by the Royal Society as a Royal Society University Research Fellow.

We acknowledge with thanks the variable star observations from the AAVSO International Database and the infrastructure maintained by AAVSO, which were used in this research. We thank Professor Jason Wright for his contiributions in acquiring the data. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This publication also makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.

AAVSO, Spitzer (IRAC), Swift (UVOT, XRT)



[Ansdell et al.(2016)]ansdell2016 Ansdell, M., Gaidos, E., Rappaport, S. A. 2016, , 816, 69

[Ballering et al.(2016)]ballering2016 Ballering, N. P., Su, K. Y. L., Rieke, G. H. & Gáspár, A. 2016, , 823, 108
[Ballesteros et al. (2017)]ballesteros2017 Ballesteros, F. J., Arnalte-Mus, P., Fernández-Soto, A., & Martínez, V. I. 
2017, arXiv 1705.08427v2
[Bodman & Quillen(2016)]bodman2016 Bodman, E. H. L. & Quillen, A. 2016, , 819, L34
[Boley et al.(2012)]boley2012 Boley, A. C. et al. 2012, , 750, L21
[Borucki et al.(2010)]borucki2010 Borucki, W. J., Koch, D., Basri, G., et al. 2010, Sci, 327, 977
[Boyajian et al.(2016)]boyajian2016 Boyajian, T. S., LaCourse, D. M., Rappaport, S. A. et al. 2016, , 457, 3988
[Boyajian et al. (2017)]boyajian2017 Boyajian, T., Croft, S., Wright, J. et al. 2017, The Astronomer's Telegram, #10406
[Bozhinova et al.(2016)]bozhinova2016 Bozhinova, I., Scholz, A. & Eislöffel, J. 2016, , 458, 3118
[Breeveld et al.(2010)]breeveld2010 Breeveld, A. A., Curran, P. A., Hoversten, E. A. et al. 2010, , 406, 1687
[Breeveld et al.(2011)]breeveld2011 Breeveld, A. A., Landsman, W., Holland, S. T. et al. 2011, in AIP Conf. Ser. 1358, Gamma Ray Bursts 2010, ed. J. E. McEnery, J. L. Racusin, & N. Gehrels (Melville, NY: AIP), 373
[Burrows et al.(2005)]burrows2005 Burrows, D. N., Hill, J. E., Nousek, J. A. et al. 2005, , 120, 165

[Cardelli et al.(1989)]cardelli1989 Cardelli, J. A., Clayton, G. C. & Mathis, J. S. 1989, , 345, 245
[Carey et al.(2012)]carey2012 Carey, S., Ingalls, J., Hora, J. et al. 2012, , 8442, 84421Z
[Castelli & Kurucz(2004)]castelli2004 Castelli, F. & Kurucz, R. L. 2004, arXiv:astro-ph/0405087
[Chapman et al.(2009)]chapman2009 Chapman, N. L., Mundy, L. G., Lai, S.-P. & Evans, N. J., II 2009, , 690, 496
[de Ponthière(2013)]deponthiere2013 de Ponthière, P. 2013, Software Programs for Variable Star Observers, <http://www.dppobservatory.net/astroprograms>
</software4vsobservers.php>

[Dones et al.(2015)]dones2015 Dones, L., Brasser, R., Kaib, N. & Rickman, H. 2015, , 197, 191

[Evans et al.(2009)]evans2009 Evans, P. A., Beardmore, A. P., Page, K. L., et al. 2009, , 397, 1177

[Fazio et al.(2004)]fazio2004 Fazio, G. G., Hora, J. L., Allen, L. E. et al. 2004, , 154, 10
[Feldman & Cousins (1998)]feldman1998 Feldman, G. J., & Cousins, R. D. 1998, Phys. Rev. D, 57, 3873



[Foukal (2017)]foukal2017 Foukal, Peter 2017, , 842, 3
[Fritz et al.(2011)]fritz2011 Fritz, T. K., Gillessen, S., Dodds-Eden, K. et al. 2011, , 737, 73
[Gaia (2017)]gaia2017 <http://gea.esac.esa.int/archive/>
[Gary (2017)]gary2017 Gary, B. L. 2017, <http://www.brucegary.net/KIV846/>
[Gáspár et al.(2012)]gaspar2012 Gáspár, A., Psaltis, D., Rieke, G. H. & Özel, F. 2012, , 754, 74
[Güver & Özel (2009)]guver2009 Güver, Tolga, & Özel, Feryal 2009, MNRAS, 400, 2050


[Henden(2009)]henden2009 Henden, A. 2009, Astrodon Photometrics Test Summary, <http://www.astrodon.com/uploads/3/4/9/0/34905502/>
<astrodonphotometrcshendentestsummary.pdf>


[Hippke et al.(2016a)]hippke2016a Hippke, M., Angerhausen, D., Lund, M. B., Pepper, J. & Stassun, K. G. 2016b, , 825, 73
[Hippke et al.(2017)]hippke2017 Hippke, M., Kroll, P., Matthei, F. et al. 2017, , 837, 85

[IRSA (2015)]irsa2015 IRSA 2015, http://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/
[Indebetouw et al.(2005)]indebetouw2005 Indebetouw, R., Mathis, J. S. & Babler, B. L. 2005, , 619, 931
[Katz (2017)]katz2017 Katz, J. I. 2017, arXiv 1705.08377
[Kenyon & Bromley(2008)]kenyon2008 Kenyon, S. J. & Bromley, B. C. 2008, , 179, 451
[Kochanek et al. (2017)]kochanek2017 Kochanek, C. S., Shappee, B. J., Stanek, K. Z. et al. 2017, asXiv 1706.07060v1



Nuclei, ed. L. C. Ho & J.-W. Wang (San Francisco, CA: ASP), 561
[Lisse et al.(2015)]lisse2015 Lisse, C. M., Sitko, M. L. & Marengo, M. 2015, , 815, L27
[Lund et al.(2016)]lund2016 Lund, M. B., Pepper, J., Stassun, K. G., Hippke, M. & Angerhausen, D. 2016, arXiv:1605.02760
[Makarov & Goldin(2016)]makarov2016 Makarov, V. V. & Goldin, A. 2016, , 833, 78
[Mamajek (2017)]mamajek2017 Mamajek, E. M. 2017,  A Modern Mean Dwarf Stellar Color and Effective Temperature Sequence, < http://www.pas.rochester.edu/ emamajek/>
<EEM_dwarf_UBVIJHK_colors_Teff.txt>
[Marengo et al.(2015)]marengo2015 Marengo, M., Hulsebus, A. & Willis, S. 2015, , 814, L15
[Meng et al.(2014)]meng2014 Meng, H. Y. A., Su, K. Y. L., Rieke, G. H. et al. 2014, Science, 345, 1032
[Meng et al.(2015)]meng2015 Meng, H. Y. A., Su, K. Y. L., Rieke, G. H. et al. 2015, , 805, 77
[Metzger et al.(2017)]metzger2017 Metzger, B. D., Shen, K. J. & Stone, N. C. 2017, arXiv:1612.07332
[Montet & Simon(2016)]montet2016 Montet, B. T. & Simon, J. D. 2016, , 830, L39
[Morrissey et al.(2007)]morrissey2007 Morrissey, P., Conrow, T., Barlow, T. A. et al. 2007, , 173, 682
[Neslušan & Budaj(2017)]neslusan2017 Neslušan, L. & Budaj, J. 2017, å, 600A, 86
[Newberry (1991)]newberry1991  Newberry, M. V. 1991, PASP, 103, 222
[Pecaut & Mamajek(2013)]pecaut2013 Pecaut, M. J. & Mamajek, E. E. 2013, , 208, 9
[Poole et al.(2008)]poole2008 Poole, T. S., Breeveld, A. A., Page, M. J. et al. 2008, , 383, 627

[Rappaport et al.(2012)]rappaport2012 Rappaport, S., Levine, A., Chiang, E. et al. 2012, , 752, 1
[Rappaport et al.(2014)]rappaport2014 Rappaport, S., Barclay, T., DeVore, J. et al. 2014, , 784, 40
[Reach et al. (2010)]reach2010 Reach, W. T., Vaubaillon, J., Lisse, C. M., Holloway, M., & Rho, J. 2010, Icarus, 208, 276
[Rebull et al.(2014)]rebull2014 Rebull, L. M., Cody, A. M., Covey, K. R. et al. 2014, , 148, 92
[Rieke & Lebofsky (1985)]rieke1985 Rieke, G. H., & Lebofsky, M. J. 1985, , 288, 618
[Roming et al.(2000)]roming2000 Roming, P. W., Townsley, L. K., Nousek, J. A., et al. 2000, , 4140, 76
[Roming et al.(2004)]roming2004 Roming, P. W. A., Hunsberger, S. D., Mason, K. O., et al. 2004, , 5165, 262
[Roming et al.(2005)]roming2005 Roming, P. W. A., Kennedy, T. E., Mason, K. O. et al. 2005, , 120, 95
[Sanchez et al.(2003)]2003PhRvD..68k3004S Sanchez, M., Allison, W. W., Alner, G. J., et al. 2003, , 68, 113004
[Sanchis-Ojeda et al.(2015)]sanchis-ojeda2015 Sanchis-Ojeda, R., Rappaport, S., Pallè, E. et al. 2015, , 812, 112
[Schaefer(2016)]schaefer2016 Schaefer, B. E. 2016, , 822, L34
[Shappee et al. (2014)]shappee2014 Shappee, B. J., Prieto, J. L., Grupe, D., et al. 2014, ApJ, 788, 48
[Sheikh et al. (2016)]sheikh2016 Sheikh, M. A., Weaver, R., & Dahmen, K. A. 2016, Phys. Rev. Let., 117, 261101


[Schlecker (2016)]schlecker2016 Schlecker, Martin 2016, MSc thesis, Tech. Univ. Munich 
[Skrutskie et al.(2006)]skrutskie2006 Skrutskie, M.F., Cutri, R. M., Stiening, R. et al. 2006, , 131, 1163
[Stauffer et al.(2015)]stauffer2015 Stauffer, J., Cody, A. M., McGinnis, P. et al. 2015, , 149, 130


[Thompson et al.(2016)]thompson2016 Thompson, M. A., Scicluna, P., Kemper, F. et al. 2016, , 458, L39



[Wolf & Hillenbrand(2005)]wolf2005 Wolf, S. & Hillenbrand, L. A. 2005, CoPhC, 171, 208
[Wright, et al. (2016)]wright2016b Wright, J. T., Cartier, K. M. S., Zao, M.  et al. 2016, , 16, 17
[Wright & Sigurdsson(2016)]wright2016 Wright, J. T. & Sigurdsson, S. 2016, , 829, L3
[Wright et al.(2010)]wright2010 Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K. et al. 2010, , 140, 1868
[Wyatt et al.(2007)]wyatt2007 Wyatt, M. C., Smith, R., Greaves, J. S. et al. 2007, , 658, 569





§ APPENDIX


The following table provides the full set of UVOT photometry:

cccccccc

UVOT Photometry of KIC 8462852


Waveband    MJDa     raw     σ     corrected      σ     relative comparisonb     σ  

         magnitude     magnitude     magnitude      magnitude     magnitude     magnitude  

uvw2	   	57317.518	   	14.820	   	0.050	   	14.776	   	0.089	   	0.045	   	0.074	

uvw2	   	57317.521	   	14.800	   	0.030	   	14.793	   	0.055	   	0.007	   	0.046	

uvw2	   	57317.552	   	14.790	   	0.030	   	14.787	   	0.047	   	0.003	   	0.036	

uvw2	   	57317.554	   	14.810	   	0.030	   	14.784	   	0.043	   	0.026	   	0.030	

uvw2	   	57317.584	   	14.780	   	0.030	   	14.755	   	0.058	   	0.025	   	0.050	

uvw2	   	57317.587	   	14.820	   	0.030	   	14.735	   	0.061	   	0.085	   	0.053	

uvw2	   	57357.014	   	14.790	   	0.030	   	14.772	   	0.049	   	0.018	   	0.039	

uvw2	   	57357.017	   	14.830	   	0.040	   	14.828	   	0.061	   	0.003	   	0.046	

uvw2	   	57360.465	   	14.790	   	0.040	   	14.802	   	0.063	   	-0.012	   	0.049	

uvw2	   	57363.857	   	14.870	   	0.040	   	14.802	   	0.067	   	0.068	   	0.054	

uvw2	   	57366.258	   	14.810	   	0.040	   	14.778	   	0.065	   	0.032	   	0.051	

uvw2	   	57369.981	   	14.770	   	0.040	   	14.791	   	0.061	   	-0.021	   	0.046	

uvw2	   	57369.983	   	14.760	   	0.040	   	14.746	   	0.064	   	0.014	   	0.050	

uvw2	   	57372.245	   	14.780	   	0.040	   	14.790	   	0.066	   	-0.010	   	0.053	

uvw2	   	57375.302	   	14.760	   	0.040	   	14.750	   	0.064	   	0.010	   	0.050	

uvw2	   	57378.828	   	14.810	   	0.040	   	14.799	   	0.063	   	0.011	   	0.049	

uvw2	   	57381.281	   	14.790	   	0.030	   	14.843	   	0.048	   	-0.053	   	0.037	

uvw2	   	57381.284	   	14.880	   	0.040	   	14.865	   	0.063	   	0.015	   	0.049	

uvw2	   	57384.147	   	14.760	   	0.040	   	14.791	   	0.063	   	-0.031	   	0.049	

uvw2	   	57387.934	   	14.870	   	0.040	   	14.951	   	0.060	   	-0.081	   	0.045	

uvw2	   	57390.524	   	14.910	   	0.040	   	14.979	   	0.063	   	-0.069	   	0.049	

uvw2	   	57393.641	   	14.760	   	0.030	   	14.766	   	0.045	   	-0.006	   	0.034	

uvw2	   	57393.645	   	14.810	   	0.040	   	14.870	   	0.064	   	-0.060	   	0.049	

uvw2	   	57396.567	   	14.800	   	0.040	   	14.876	   	0.063	   	-0.076	   	0.049	

uvw2	   	57399.031	   	14.790	   	0.040	   	14.736	   	0.065	   	0.054	   	0.051	

uvw2	   	57402.617	   	14.830	   	0.040	   	14.865	   	0.062	   	-0.035	   	0.047	

uvw2	   	57405.339	   	14.790	   	0.030	   	14.907	   	0.046	   	-0.117	   	0.035	

uvw2	   	57405.342	   	14.840	   	0.040	   	14.796	   	0.064	   	0.044	   	0.050	

uvw2	   	57408.274	   	14.820	   	0.040	   	14.809	   	0.064	   	0.011	   	0.050	

uvw2	   	57411.458	   	14.830	   	0.040	   	14.857	   	0.063	   	-0.027	   	0.049	

uvw2	   	57414.395	   	14.790	   	0.050	   	14.793	   	0.091	   	-0.003	   	0.076	

uvw2	   	57416.976	   	14.820	   	0.040	   	14.856	   	0.065	   	-0.036	   	0.051	

uvw2	   	57420.169	   	14.930	   	0.040	   	14.924	   	0.064	   	0.006	   	0.050	

uvw2	   	57423.164	   	14.870	   	0.040	   	14.797	   	0.066	   	0.073	   	0.052	

uvw2	   	57426.828	   	14.810	   	0.040	   	14.746	   	0.064	   	0.064	   	0.050	

uvw2	   	57429.809	   	14.780	   	0.040	   	14.761	   	0.059	   	0.019	   	0.043	

uvw2	   	57429.811	   	14.750	   	0.040	   	14.761	   	0.062	   	-0.011	   	0.047	

uvw2	   	57432.017	   	14.820	   	0.040	   	14.811	   	0.066	   	0.010	   	0.053	

uvw2	   	57435.009	   	14.780	   	0.040	   	14.783	   	0.064	   	-0.003	   	0.050	

uvw2	   	57438.533	   	14.810	   	0.040	   	14.821	   	0.064	   	-0.011	   	0.050	

uvw2	   	57441.518	   	14.780	   	0.040	   	14.777	   	0.060	   	0.004	   	0.045	

uvw2	   	57441.520	   	14.820	   	0.040	   	14.790	   	0.065	   	0.030	   	0.052	

uvw2	   	57444.565	   	14.870	   	0.040	   	14.819	   	0.066	   	0.051	   	0.053	

uvw2	   	57447.422	   	14.830	   	0.040	   	14.841	   	0.065	   	-0.011	   	0.052	

uvw2	   	57450.279	   	14.800	   	0.040	   	14.741	   	0.064	   	0.060	   	0.050	

uvw2	   	57453.599	   	14.820	   	0.040	   	14.898	   	0.061	   	-0.078	   	0.046	

uvw2	   	57453.601	   	14.800	   	0.040	   	14.767	   	0.064	   	0.033	   	0.050	

uvw2	   	57459.388	   	14.820	   	0.040	   	14.892	   	0.064	   	-0.072	   	0.050	

uvw2	   	57462.313	   	14.840	   	0.040	   	14.844	   	0.063	   	-0.004	   	0.049	

uvw2	   	57465.238	   	14.760	   	0.040	   	14.774	   	0.061	   	-0.014	   	0.046	

uvw2	   	57465.240	   	14.800	   	0.040	   	14.823	   	0.063	   	-0.023	   	0.049	

uvw2	   	57468.099	   	14.780	   	0.040	   	14.802	   	0.064	   	-0.022	   	0.050	

uvw2	   	57471.164	   	14.790	   	0.060	   	14.788	   	0.104	   	0.003	   	0.085	

uvw2	   	57474.015	   	14.820	   	0.040	   	14.802	   	0.064	   	0.018	   	0.050	

uvw2	   	57621.142	   	14.790	   	0.040	   	14.813	   	0.061	   	-0.023	   	0.046	

uvw2	   	57621.144	   	14.870	   	0.040	   	14.972	   	0.061	   	-0.102	   	0.046	

uvw2	   	57635.448	   	14.770	   	0.040	   	14.839	   	0.060	   	-0.069	   	0.045	

uvw2	   	57656.697	   	14.740	   	0.040	   	14.700	   	0.066	   	0.040	   	0.052	

uvw2	   	57672.645	   	14.860	   	0.040	   	14.917	   	0.065	   	-0.057	   	0.051	

uvw2	   	57677.098	   	14.880	   	0.040	   	14.932	   	0.061	   	-0.052	   	0.046	

uvw2	   	57677.101	   	14.720	   	0.040	   	14.830	   	0.061	   	-0.110	   	0.046	

uvw2	   	57708.730	   	14.750	   	0.050	   	14.840	   	0.082	   	-0.090	   	0.065	

uvw2	   	57719.421	   	14.780	   	0.040	   	14.785	   	0.066	   	-0.005	   	0.052	

uvw2	   	57723.277	   	14.780	   	0.040	   	14.810	   	0.061	   	-0.030	   	0.046	

uvw2	   	57730.131	   	14.740	   	0.040	   	14.743	   	0.066	   	-0.003	   	0.053	

uvw2	   	57737.433	   	14.720	   	0.070	   	14.896	   	0.113	   	-0.176	   	0.089	

uvw2	   	57737.450	   	14.790	   	0.040	   	14.867	   	0.061	   	-0.077	   	0.046	

uvw2	   	57742.752	   	14.730	   	0.040	   	14.777	   	0.063	   	-0.047	   	0.049	

uvw2	   	57744.212	   	14.790	   	0.040	   	14.814	   	0.064	   	-0.024	   	0.050	

uvw2	   	57751.851	   	14.780	   	0.040	   	14.774	   	0.066	   	0.006	   	0.052	

uvw2	   	57756.312	   	14.790	   	0.040	   	14.855	   	0.064	   	-0.065	   	0.050	

uvw2	   	57765.268	   	14.750	   	0.040	   	14.796	   	0.063	   	-0.046	   	0.049	

uvw2	   	57765.271	   	14.760	   	0.030	   	14.767	   	0.049	   	-0.007	   	0.038	

uvw2	   	57765.274	   	14.850	   	0.040	   	14.831	   	0.066	   	0.020	   	0.053	

uvw2	   	57772.977	   	14.770	   	0.040	   	14.793	   	0.060	   	-0.023	   	0.045	

uvw2	   	57779.890	   	14.760	   	0.040	   	14.897	   	0.063	   	-0.137	   	0.049	

uvw2	   	57786.140	   	14.780	   	0.040	   	14.829	   	0.064	   	-0.049	   	0.050	

uvw2	   	57789.993	   	14.790	   	0.040	   	14.864	   	0.064	   	-0.074	   	0.050	

uvw2	   	57792.322	   	14.780	   	0.040	   	14.913	   	0.063	   	-0.133	   	0.048	

uvw2	   	57795.382	   	14.800	   	0.040	   	14.903	   	0.063	   	-0.103	   	0.049	

uvw2	   	57798.502	   	14.810	   	0.040	   	14.919	   	0.062	   	-0.109	   	0.047	

uvw2	   	57801.894	   	14.800	   	0.040	   	14.790	   	0.067	   	0.010	   	0.054	

uvw2	   	57804.938	   	14.730	   	0.040	   	14.735	   	0.065	   	-0.005	   	0.052	

uvw2	   	57807.728	   	14.760	   	0.030	   	14.827	   	0.049	   	-0.067	   	0.039	

uvw2	   	57810.385	   	14.830	   	0.040	   	14.848	   	0.066	   	-0.018	   	0.052	

uvw2	   	57853.037	   	14.740	   	0.040	   	14.825	   	0.061	   	-0.085	   	0.046	

uvw2	   	57853.039	   	14.720	   	0.030	   	14.750	   	0.047	   	-0.030	   	0.037	

uvw2	   	57853.043	   	14.760	   	0.040	   	14.798	   	0.063	   	-0.038	   	0.048	

uvm2	   	57317.528	   	14.730	   	0.040	   	14.819	   	0.111	   	-0.089	   	0.104	

uvm2	   	57357.022	   	14.790	   	0.040	   	14.923	   	0.120	   	-0.133	   	0.113	

uvm2	   	57360.470	   	14.660	   	0.040	   	14.678	   	0.141	   	-0.018	   	0.135	

uvm2	   	57363.862	   	14.850	   	0.050	   	15.042	   	0.133	   	-0.192	   	0.124	

uvm2	   	57366.256	   	14.710	   	0.040	   	14.697	   	0.129	   	0.013	   	0.122	

uvm2	   	57372.250	   	14.720	   	0.050	   	14.742	   	0.143	   	-0.022	   	0.134	

uvm2	   	57375.307	   	14.700	   	0.040	   	14.696	   	0.137	   	0.004	   	0.131	

uvm2	   	57378.825	   	14.730	   	0.040	   	14.985	   	0.090	   	-0.255	   	0.081	

uvm2	   	57378.833	   	14.740	   	0.040	   	14.715	   	0.141	   	0.025	   	0.135	

uvm2	   	57381.290	   	14.790	   	0.040	   	14.751	   	0.131	   	0.039	   	0.125	

uvm2	   	57384.152	   	14.770	   	0.050	   	14.916	   	0.128	   	-0.146	   	0.117	

uvm2	   	57387.939	   	14.860	   	0.050	   	14.818	   	0.136	   	0.042	   	0.127	

uvm2	   	57390.521	   	14.690	   	0.030	   	14.788	   	0.086	   	-0.098	   	0.081	

uvm2	   	57390.529	   	14.900	   	0.050	   	15.006	   	0.134	   	-0.106	   	0.124	

uvm2	   	57393.650	   	14.760	   	0.050	   	14.763	   	0.140	   	-0.003	   	0.131	

uvm2	   	57396.572	   	14.670	   	0.040	   	14.802	   	0.133	   	-0.132	   	0.127	

uvm2	   	57399.036	   	14.690	   	0.040	   	14.604	   	0.147	   	0.086	   	0.141	

uvm2	   	57402.614	   	14.740	   	0.040	   	14.765	   	0.101	   	-0.025	   	0.093	

uvm2	   	57402.622	   	14.740	   	0.040	   	14.866	   	0.123	   	-0.126	   	0.117	

uvm2	   	57405.347	   	14.850	   	0.050	   	15.068	   	0.120	   	-0.218	   	0.109	

uvm2	   	57416.981	   	14.770	   	0.050	   	14.785	   	0.140	   	-0.015	   	0.131	

uvm2	   	57426.826	   	14.830	   	0.060	   	14.562	   	0.200	   	0.268	   	0.191	

uvm2	   	57426.833	   	14.800	   	0.050	   	14.932	   	0.132	   	-0.132	   	0.122	

uvm2	   	57444.570	   	14.810	   	0.050	   	14.876	   	0.142	   	-0.066	   	0.133	

uvm2	   	57447.427	   	14.750	   	0.050	   	14.955	   	0.128	   	-0.205	   	0.117	

uvm2	   	57450.276	   	14.880	   	0.040	   	14.953	   	0.095	   	-0.073	   	0.087	

uvm2	   	57450.284	   	14.660	   	0.040	   	14.646	   	0.149	   	0.014	   	0.144	

uvm2	   	57453.606	   	14.700	   	0.050	   	14.925	   	0.134	   	-0.225	   	0.124	

uvm2	   	57459.393	   	14.840	   	0.050	   	15.158	   	0.122	   	-0.318	   	0.111	

uvm2	   	57462.310	   	14.770	   	0.040	   	14.902	   	0.112	   	-0.132	   	0.104	

uvm2	   	57465.246	   	14.790	   	0.050	   	14.835	   	0.134	   	-0.045	   	0.124	

uvm2	   	57474.013	   	14.680	   	0.050	   	14.765	   	0.139	   	-0.085	   	0.130	

uvm2	   	57474.021	   	14.820	   	0.050	   	14.721	   	0.155	   	0.099	   	0.147	

uvm2	   	57621.149	   	14.750	   	0.050	   	14.840	   	0.140	   	-0.090	   	0.131	

uvm2	   	57635.454	   	14.640	   	0.040	   	14.668	   	0.129	   	-0.028	   	0.123	

uvm2	   	57656.702	   	14.820	   	0.050	   	14.911	   	0.138	   	-0.091	   	0.128	

uvm2	   	57672.650	   	14.680	   	0.050	   	14.647	   	0.146	   	0.033	   	0.137	

uvm2	   	57677.106	   	14.720	   	0.040	   	14.785	   	0.131	   	-0.065	   	0.125	

uvm2	   	57708.734	   	14.620	   	0.060	   	14.766	   	0.176	   	-0.146	   	0.166	

uvm2	   	57719.426	   	14.690	   	0.040	   	14.938	   	0.122	   	-0.248	   	0.115	

uvm2	   	57730.124	   	14.760	   	0.040	   	14.933	   	0.102	   	-0.173	   	0.094	

uvm2	   	57730.128	   	14.740	   	0.040	   	14.731	   	0.107	   	0.009	   	0.099	

uvm2	   	57730.136	   	14.750	   	0.050	   	14.931	   	0.129	   	-0.181	   	0.119	

uvm2	   	57742.746	   	14.750	   	0.050	   	14.702	   	0.151	   	0.048	   	0.142	

uvm2	   	57742.749	   	14.710	   	0.040	   	14.844	   	0.100	   	-0.134	   	0.092	

uvm2	   	57742.757	   	14.720	   	0.050	   	14.740	   	0.139	   	-0.020	   	0.130	

uvm2	   	57772.983	   	14.740	   	0.040	   	14.904	   	0.115	   	-0.164	   	0.107	

uvm2	   	57786.137	   	14.740	   	0.040	   	14.878	   	0.097	   	-0.138	   	0.088	

uvm2	   	57789.986	   	14.800	   	0.040	   	14.846	   	0.100	   	-0.046	   	0.091	

uvm2	   	57789.990	   	14.740	   	0.040	   	14.880	   	0.099	   	-0.140	   	0.091	

uvm2	   	57792.315	   	14.750	   	0.040	   	14.782	   	0.102	   	-0.032	   	0.093	

uvm2	   	57792.319	   	14.770	   	0.040	   	14.866	   	0.098	   	-0.096	   	0.089	

uvm2	   	57795.376	   	14.760	   	0.040	   	14.811	   	0.110	   	-0.051	   	0.102	

uvm2	   	57795.379	   	14.800	   	0.040	   	14.908	   	0.097	   	-0.108	   	0.088	

uvm2	   	57798.495	   	14.710	   	0.040	   	14.809	   	0.106	   	-0.099	   	0.098	

uvm2	   	57798.498	   	14.800	   	0.040	   	14.794	   	0.104	   	0.006	   	0.096	

uvm2	   	57804.932	   	14.710	   	0.040	   	14.674	   	0.101	   	0.036	   	0.093	

uvm2	   	57804.935	   	14.720	   	0.040	   	14.874	   	0.099	   	-0.154	   	0.091	

uvm2	   	57810.378	   	14.700	   	0.040	   	14.864	   	0.097	   	-0.164	   	0.088	

uvm2	   	57810.382	   	14.730	   	0.040	   	14.844	   	0.098	   	-0.114	   	0.090	

uvm2	   	57819.013	   	14.680	   	0.040	   	14.886	   	0.093	   	-0.206	   	0.084	

uvm2	   	57819.017	   	14.820	   	0.040	   	14.935	   	0.097	   	-0.115	   	0.088	

uvm2	   	57853.048	   	14.750	   	0.040	   	14.697	   	0.140	   	0.054	   	0.134	

uvw1	   	57317.531	   	13.650	   	0.030	   	13.646	   	0.038	   	0.004	   	0.023	

uvw1	   	57357.025	   	13.630	   	0.030	   	13.635	   	0.038	   	-0.005	   	0.024	

uvw1	   	57360.473	   	13.660	   	0.030	   	13.644	   	0.040	   	0.016	   	0.026	

uvw1	   	57363.855	   	13.650	   	0.030	   	13.549	   	0.049	   	0.101	   	0.038	

uvw1	   	57363.864	   	13.660	   	0.030	   	13.655	   	0.042	   	0.005	   	0.029	

uvw1	   	57369.991	   	13.600	   	0.030	   	13.585	   	0.042	   	0.015	   	0.029	

uvw1	   	57372.253	   	13.650	   	0.030	   	13.695	   	0.040	   	-0.045	   	0.026	

uvw1	   	57375.299	   	13.620	   	0.030	   	13.635	   	0.037	   	-0.015	   	0.022	

uvw1	   	57375.310	   	13.600	   	0.030	   	13.588	   	0.040	   	0.012	   	0.026	

uvw1	   	57378.836	   	13.620	   	0.030	   	13.584	   	0.040	   	0.036	   	0.026	

uvw1	   	57381.292	   	13.660	   	0.030	   	13.629	   	0.040	   	0.031	   	0.026	

uvw1	   	57387.930	   	13.620	   	0.030	   	13.644	   	0.037	   	-0.024	   	0.022	

uvw1	   	57387.942	   	13.660	   	0.030	   	13.610	   	0.040	   	0.050	   	0.026	

uvw1	   	57390.532	   	13.720	   	0.030	   	13.754	   	0.040	   	-0.034	   	0.026	

uvw1	   	57393.652	   	13.610	   	0.030	   	13.631	   	0.040	   	-0.021	   	0.026	

uvw1	   	57396.575	   	13.630	   	0.030	   	13.673	   	0.040	   	-0.043	   	0.026	

uvw1	   	57399.028	   	13.620	   	0.020	   	13.619	   	0.028	   	0.001	   	0.020	

uvw1	   	57399.038	   	13.630	   	0.030	   	13.652	   	0.040	   	-0.022	   	0.026	

uvw1	   	57402.625	   	13.610	   	0.030	   	13.611	   	0.040	   	-0.001	   	0.026	

uvw1	   	57405.350	   	13.660	   	0.030	   	13.621	   	0.040	   	0.040	   	0.026	

uvw1	   	57408.282	   	13.720	   	0.030	   	13.700	   	0.042	   	0.020	   	0.029	

uvw1	   	57411.454	   	13.620	   	0.020	   	13.618	   	0.027	   	0.002	   	0.018	

uvw1	   	57411.465	   	13.700	   	0.030	   	13.684	   	0.042	   	0.016	   	0.029	

uvw1	   	57416.983	   	13.650	   	0.030	   	13.628	   	0.042	   	0.022	   	0.029	

uvw1	   	57420.176	   	13.680	   	0.030	   	13.667	   	0.042	   	0.013	   	0.029	

uvw1	   	57423.161	   	13.630	   	0.020	   	13.634	   	0.028	   	-0.004	   	0.020	

uvw1	   	57423.171	   	13.690	   	0.030	   	13.630	   	0.042	   	0.060	   	0.029	

uvw1	   	57426.836	   	13.680	   	0.030	   	13.716	   	0.040	   	-0.036	   	0.026	

uvw1	   	57429.819	   	13.610	   	0.030	   	13.628	   	0.040	   	-0.018	   	0.026	

uvw1	   	57432.024	   	13.660	   	0.030	   	13.658	   	0.042	   	0.002	   	0.029	

uvw1	   	57435.016	   	13.660	   	0.030	   	13.695	   	0.044	   	-0.035	   	0.032	

uvw1	   	57441.528	   	13.700	   	0.030	   	13.675	   	0.042	   	0.025	   	0.029	

uvw1	   	57444.572	   	13.660	   	0.030	   	13.679	   	0.040	   	-0.019	   	0.026	

uvw1	   	57447.419	   	13.640	   	0.030	   	13.657	   	0.036	   	-0.017	   	0.020	

uvw1	   	57447.430	   	13.620	   	0.030	   	13.580	   	0.042	   	0.040	   	0.029	

uvw1	   	57450.287	   	13.660	   	0.030	   	13.683	   	0.041	   	-0.023	   	0.028	

uvw1	   	57453.608	   	13.630	   	0.030	   	13.677	   	0.041	   	-0.047	   	0.028	

uvw1	   	57459.386	   	13.690	   	0.030	   	13.647	   	0.044	   	0.043	   	0.032	

uvw1	   	57459.395	   	13.670	   	0.030	   	13.722	   	0.040	   	-0.052	   	0.026	

uvw1	   	57462.320	   	13.640	   	0.030	   	13.668	   	0.040	   	-0.028	   	0.026	

uvw1	   	57465.248	   	13.630	   	0.030	   	13.613	   	0.040	   	0.017	   	0.026	

uvw1	   	57468.107	   	13.630	   	0.030	   	13.634	   	0.040	   	-0.004	   	0.026	

uvw1	   	57474.023	   	13.670	   	0.030	   	13.673	   	0.040	   	-0.003	   	0.026	

uvw1	   	57621.151	   	13.640	   	0.030	   	13.687	   	0.040	   	-0.047	   	0.026	

uvw1	   	57635.446	   	13.630	   	0.030	   	13.676	   	0.038	   	-0.046	   	0.024	

uvw1	   	57635.456	   	13.610	   	0.030	   	13.667	   	0.039	   	-0.057	   	0.025	

uvw1	   	57656.705	   	13.590	   	0.030	   	13.659	   	0.040	   	-0.069	   	0.026	

uvw1	   	57672.652	   	13.640	   	0.030	   	13.642	   	0.042	   	-0.002	   	0.029	

uvw1	   	57677.109	   	13.580	   	0.030	   	13.552	   	0.042	   	0.028	   	0.029	

uvw1	   	57708.725	   	13.630	   	0.030	   	13.642	   	0.046	   	-0.012	   	0.035	

uvw1	   	57719.418	   	13.600	   	0.030	   	13.594	   	0.037	   	0.006	   	0.022	

uvw1	   	57719.429	   	13.640	   	0.030	   	13.635	   	0.042	   	0.005	   	0.029	

uvw1	   	57723.274	   	13.590	   	0.030	   	13.613	   	0.038	   	-0.023	   	0.024	

uvw1	   	57723.285	   	13.640	   	0.030	   	13.663	   	0.038	   	-0.023	   	0.024	

uvw1	   	57730.139	   	13.640	   	0.030	   	13.691	   	0.040	   	-0.051	   	0.026	

uvw1	   	57742.760	   	13.620	   	0.030	   	13.627	   	0.040	   	-0.007	   	0.026	

uvw1	   	57744.219	   	13.610	   	0.030	   	13.656	   	0.040	   	-0.046	   	0.026	

uvw1	   	57751.845	   	13.590	   	0.030	   	13.654	   	0.039	   	-0.064	   	0.025	

uvw1	   	57751.848	   	13.660	   	0.030	   	13.672	   	0.037	   	-0.012	   	0.022	

uvw1	   	57751.859	   	13.640	   	0.030	   	13.677	   	0.041	   	-0.037	   	0.028	

uvw1	   	57756.319	   	13.640	   	0.030	   	13.680	   	0.042	   	-0.040	   	0.029	

uvw1	   	57772.986	   	13.620	   	0.030	   	13.651	   	0.039	   	-0.031	   	0.025	

uvw1	   	57779.884	   	13.600	   	0.030	   	13.642	   	0.038	   	-0.042	   	0.024	

uvw1	   	57779.887	   	13.630	   	0.030	   	13.668	   	0.037	   	-0.038	   	0.022	

uvw1	   	57779.898	   	13.600	   	0.030	   	13.635	   	0.042	   	-0.035	   	0.029	

uvw1	   	57786.148	   	13.620	   	0.030	   	13.672	   	0.042	   	-0.052	   	0.029	

uvw1	   	57790.001	   	13.620	   	0.030	   	13.655	   	0.042	   	-0.035	   	0.029	

uvw1	   	57792.329	   	13.640	   	0.030	   	13.693	   	0.042	   	-0.053	   	0.029	

uvw1	   	57795.389	   	13.620	   	0.030	   	13.650	   	0.042	   	-0.030	   	0.029	

uvw1	   	57798.510	   	13.600	   	0.030	   	13.672	   	0.040	   	-0.072	   	0.026	

uvw1	   	57804.946	   	13.620	   	0.030	   	13.636	   	0.042	   	-0.016	   	0.029	

uvw1	   	57807.739	   	13.640	   	0.030	   	13.677	   	0.038	   	-0.037	   	0.023	

uvw1	   	57810.392	   	13.620	   	0.030	   	13.659	   	0.040	   	-0.039	   	0.026	

uvw1	   	57819.027	   	13.580	   	0.030	   	13.645	   	0.041	   	-0.065	   	0.028	

uvw1	   	57853.051	   	13.610	   	0.030	   	13.628	   	0.040	   	-0.018	   	0.026	

U	   	57317.534	   	12.560	   	0.020	   	12.557	   	0.025	   	0.003	   	0.015	

U	   	57357.028	   	12.580	   	0.020	   	12.594	   	0.025	   	-0.014	   	0.015	

U	   	57360.463	   	12.560	   	0.030	   	12.563	   	0.035	   	-0.003	   	0.017	

U	   	57360.475	   	12.560	   	0.030	   	12.574	   	0.034	   	-0.014	   	0.016	

U	   	57363.867	   	12.580	   	0.030	   	12.567	   	0.034	   	0.013	   	0.016	

U	   	57369.993	   	12.560	   	0.030	   	12.559	   	0.034	   	0.001	   	0.015	

U	   	57372.243	   	12.570	   	0.030	   	12.584	   	0.034	   	-0.014	   	0.015	

U	   	57372.255	   	12.570	   	0.030	   	12.579	   	0.034	   	-0.009	   	0.015	

U	   	57375.313	   	12.570	   	0.020	   	12.574	   	0.025	   	-0.004	   	0.015	

U	   	57378.838	   	12.550	   	0.020	   	12.549	   	0.025	   	0.001	   	0.015	

U	   	57381.295	   	12.590	   	0.020	   	12.579	   	0.025	   	0.011	   	0.015	

U	   	57387.944	   	12.590	   	0.020	   	12.589	   	0.025	   	0.001	   	0.015	

U	   	57390.534	   	12.590	   	0.030	   	12.602	   	0.034	   	-0.012	   	0.015	

U	   	57393.654	   	12.580	   	0.030	   	12.564	   	0.034	   	0.016	   	0.015	

U	   	57396.565	   	12.590	   	0.030	   	12.574	   	0.034	   	0.016	   	0.015	

U	   	57396.577	   	12.580	   	0.030	   	12.594	   	0.034	   	-0.014	   	0.015	

U	   	57399.040	   	12.550	   	0.030	   	12.575	   	0.035	   	-0.025	   	0.017	

U	   	57402.627	   	12.570	   	0.020	   	12.589	   	0.025	   	-0.019	   	0.015	

U	   	57408.272	   	12.570	   	0.030	   	12.559	   	0.034	   	0.011	   	0.015	

U	   	57408.284	   	12.600	   	0.030	   	12.596	   	0.035	   	0.004	   	0.017	

U	   	57411.467	   	12.590	   	0.030	   	12.589	   	0.034	   	0.001	   	0.015	

U	   	57416.973	   	12.580	   	0.030	   	12.579	   	0.034	   	0.001	   	0.015	

U	   	57416.986	   	12.600	   	0.030	   	12.589	   	0.035	   	0.011	   	0.017	

U	   	57420.166	   	12.590	   	0.030	   	12.584	   	0.034	   	0.006	   	0.015	

U	   	57420.179	   	12.590	   	0.030	   	12.552	   	0.035	   	0.038	   	0.017	

U	   	57423.174	   	12.600	   	0.030	   	12.580	   	0.035	   	0.020	   	0.017	

U	   	57426.839	   	12.570	   	0.020	   	12.559	   	0.025	   	0.011	   	0.015	

U	   	57429.822	   	12.580	   	0.020	   	12.572	   	0.025	   	0.008	   	0.015	

U	   	57432.014	   	12.570	   	0.030	   	12.574	   	0.034	   	-0.004	   	0.015	

U	   	57432.027	   	12.600	   	0.030	   	12.605	   	0.034	   	-0.005	   	0.016	

U	   	57441.530	   	12.640	   	0.030	   	12.600	   	0.035	   	0.040	   	0.017	

U	   	57444.561	   	12.590	   	0.020	   	12.599	   	0.025	   	-0.009	   	0.015	

U	   	57444.574	   	12.560	   	0.030	   	12.557	   	0.034	   	0.003	   	0.015	

U	   	57447.432	   	12.580	   	0.030	   	12.582	   	0.034	   	-0.002	   	0.015	

U	   	57450.289	   	12.580	   	0.030	   	12.569	   	0.034	   	0.011	   	0.015	

U	   	57453.611	   	12.560	   	0.030	   	12.564	   	0.034	   	-0.004	   	0.015	

U	   	57459.397	   	12.580	   	0.030	   	12.607	   	0.034	   	-0.027	   	0.016	

U	   	57462.322	   	12.590	   	0.030	   	12.599	   	0.034	   	-0.009	   	0.016	

U	   	57465.251	   	12.590	   	0.020	   	12.604	   	0.025	   	-0.014	   	0.015	

U	   	57468.096	   	12.630	   	0.030	   	12.632	   	0.034	   	-0.002	   	0.015	

U	   	57468.109	   	12.580	   	0.020	   	12.572	   	0.025	   	0.008	   	0.015	

U	   	57474.026	   	12.600	   	0.020	   	12.601	   	0.026	   	-0.001	   	0.016	

U	   	57621.154	   	12.580	   	0.030	   	12.587	   	0.034	   	-0.007	   	0.015	

U	   	57635.459	   	12.580	   	0.020	   	12.599	   	0.025	   	-0.019	   	0.015	

U	   	57656.695	   	12.600	   	0.030	   	12.604	   	0.034	   	-0.004	   	0.015	

U	   	57656.707	   	12.590	   	0.030	   	12.597	   	0.034	   	-0.007	   	0.015	

U	   	57672.642	   	12.650	   	0.030	   	12.642	   	0.034	   	0.008	   	0.015	

U	   	57672.654	   	12.580	   	0.030	   	12.587	   	0.034	   	-0.007	   	0.015	

U	   	57677.111	   	12.590	   	0.030	   	12.622	   	0.034	   	-0.032	   	0.015	

U	   	57708.727	   	12.560	   	0.030	   	12.587	   	0.035	   	-0.027	   	0.017	

U	   	57719.431	   	12.570	   	0.020	   	12.557	   	0.025	   	0.013	   	0.015	

U	   	57723.288	   	12.590	   	0.020	   	12.592	   	0.025	   	-0.002	   	0.015	

U	   	57730.141	   	12.590	   	0.030	   	12.582	   	0.034	   	0.008	   	0.015	

U	   	57742.763	   	12.580	   	0.020	   	12.597	   	0.025	   	-0.017	   	0.015	

U	   	57744.209	   	12.600	   	0.020	   	12.604	   	0.025	   	-0.004	   	0.015	

U	   	57744.222	   	12.600	   	0.030	   	12.594	   	0.034	   	0.006	   	0.016	

U	   	57751.861	   	12.580	   	0.020	   	12.574	   	0.025	   	0.006	   	0.015	

U	   	57756.307	   	12.620	   	0.030	   	12.607	   	0.034	   	0.013	   	0.015	

U	   	57756.309	   	12.640	   	0.030	   	12.629	   	0.034	   	0.011	   	0.015	

U	   	57756.322	   	12.590	   	0.030	   	12.564	   	0.034	   	0.026	   	0.015	

U	   	57772.970	   	12.600	   	0.030	   	12.599	   	0.034	   	0.001	   	0.015	

U	   	57772.973	   	12.610	   	0.020	   	12.607	   	0.025	   	0.003	   	0.015	

U	   	57772.989	   	12.590	   	0.020	   	12.589	   	0.025	   	0.001	   	0.015	

U	   	57779.900	   	12.590	   	0.030	   	12.568	   	0.035	   	0.022	   	0.017	

U	   	57786.150	   	12.600	   	0.030	   	12.587	   	0.035	   	0.013	   	0.017	

U	   	57790.003	   	12.600	   	0.030	   	12.566	   	0.034	   	0.034	   	0.016	

U	   	57792.331	   	12.590	   	0.030	   	12.529	   	0.035	   	0.061	   	0.017	

U	   	57795.391	   	12.600	   	0.030	   	12.587	   	0.035	   	0.013	   	0.017	

U	   	57798.512	   	12.600	   	0.020	   	12.602	   	0.025	   	-0.002	   	0.015	

U	   	57804.948	   	12.590	   	0.030	   	12.577	   	0.034	   	0.013	   	0.015	

U	   	57807.743	   	12.590	   	0.020	   	12.587	   	0.025	   	0.003	   	0.015	

U	   	57810.395	   	12.590	   	0.030	   	12.597	   	0.034	   	-0.007	   	0.015	

U	   	57819.029	   	12.580	   	0.030	   	12.577	   	0.034	   	0.003	   	0.016	

U	   	57853.053	   	12.580	   	0.020	   	12.564	   	0.025	   	0.016	   	0.015	

V	   	57317.524	   	11.890	   	0.020	   	11.880	   	0.025	   	0.010	   	0.014	

V	   	57317.557	   	11.900	   	0.020	   	11.899	   	0.023	   	0.001	   	0.012	

V	   	57317.591	   	11.900	   	0.020	   	11.910	   	0.025	   	-0.010	   	0.014	

V	   	57357.020	   	11.890	   	0.020	   	11.878	   	0.023	   	0.012	   	0.012	

V	   	57360.468	   	11.880	   	0.020	   	11.880	   	0.023	   	0.000	   	0.012	

V	   	57363.860	   	11.910	   	0.020	   	11.888	   	0.023	   	0.022	   	0.012	

V	   	57366.260	   	11.880	   	0.030	   	11.850	   	0.035	   	0.031	   	0.019	

V	   	57369.986	   	11.890	   	0.020	   	11.887	   	0.023	   	0.003	   	0.012	

V	   	57372.248	   	11.900	   	0.020	   	11.906	   	0.023	   	-0.006	   	0.012	

V	   	57375.305	   	11.890	   	0.020	   	11.877	   	0.023	   	0.013	   	0.012	

V	   	57378.831	   	11.910	   	0.020	   	11.912	   	0.023	   	-0.002	   	0.012	

V	   	57381.287	   	11.900	   	0.020	   	11.901	   	0.023	   	-0.001	   	0.012	

V	   	57384.149	   	11.890	   	0.020	   	11.908	   	0.023	   	-0.018	   	0.012	

V	   	57387.936	   	11.900	   	0.020	   	11.900	   	0.023	   	0.000	   	0.012	

V	   	57390.527	   	11.920	   	0.020	   	11.916	   	0.023	   	0.004	   	0.012	

V	   	57393.647	   	11.900	   	0.020	   	11.903	   	0.023	   	-0.003	   	0.012	

V	   	57396.570	   	11.900	   	0.020	   	11.900	   	0.023	   	0.000	   	0.012	

V	   	57399.033	   	11.880	   	0.020	   	11.899	   	0.023	   	-0.019	   	0.012	

V	   	57402.619	   	11.890	   	0.020	   	11.887	   	0.023	   	0.003	   	0.012	

V	   	57405.345	   	11.920	   	0.020	   	11.916	   	0.023	   	0.004	   	0.012	

V	   	57408.277	   	11.920	   	0.020	   	11.916	   	0.023	   	0.004	   	0.012	

V	   	57411.460	   	11.920	   	0.020	   	11.913	   	0.023	   	0.008	   	0.012	

V	   	57416.978	   	11.890	   	0.020	   	11.891	   	0.023	   	-0.001	   	0.012	

V	   	57420.171	   	11.920	   	0.020	   	11.900	   	0.023	   	0.020	   	0.012	

V	   	57423.166	   	11.920	   	0.020	   	11.911	   	0.023	   	0.009	   	0.012	

V	   	57426.831	   	11.900	   	0.020	   	11.899	   	0.023	   	0.001	   	0.012	

V	   	57429.814	   	11.890	   	0.020	   	11.883	   	0.023	   	0.007	   	0.012	

V	   	57432.019	   	11.910	   	0.020	   	11.903	   	0.023	   	0.008	   	0.012	

V	   	57435.012	   	11.900	   	0.020	   	11.909	   	0.023	   	-0.009	   	0.012	

V	   	57438.535	   	11.910	   	0.020	   	11.911	   	0.023	   	-0.001	   	0.012	

V	   	57441.523	   	11.930	   	0.020	   	11.907	   	0.023	   	0.023	   	0.012	

V	   	57444.567	   	11.920	   	0.020	   	11.911	   	0.023	   	0.010	   	0.012	

V	   	57447.425	   	11.900	   	0.020	   	11.903	   	0.023	   	-0.003	   	0.012	

V	   	57450.282	   	11.930	   	0.020	   	11.926	   	0.023	   	0.004	   	0.012	

V	   	57453.603	   	11.890	   	0.020	   	11.903	   	0.023	   	-0.013	   	0.012	

V	   	57459.390	   	11.890	   	0.020	   	11.901	   	0.023	   	-0.011	   	0.012	

V	   	57462.315	   	11.900	   	0.020	   	11.911	   	0.023	   	-0.011	   	0.012	

V	   	57465.243	   	11.900	   	0.020	   	11.915	   	0.023	   	-0.015	   	0.012	

V	   	57468.101	   	11.910	   	0.020	   	11.921	   	0.023	   	-0.011	   	0.012	

V	   	57474.018	   	11.900	   	0.020	   	11.902	   	0.023	   	-0.002	   	0.012	

V	   	57621.146	   	11.890	   	0.020	   	11.904	   	0.023	   	-0.014	   	0.012	

V	   	57635.451	   	11.880	   	0.020	   	11.899	   	0.023	   	-0.019	   	0.012	

V	   	57656.700	   	11.890	   	0.020	   	11.898	   	0.023	   	-0.008	   	0.012	

V	   	57672.647	   	11.870	   	0.020	   	11.875	   	0.023	   	-0.005	   	0.012	

V	   	57677.103	   	11.880	   	0.020	   	11.897	   	0.023	   	-0.017	   	0.012	

V	   	57708.732	   	11.940	   	0.030	   	11.928	   	0.034	   	0.012	   	0.016	

V	   	57719.424	   	11.940	   	0.020	   	11.917	   	0.023	   	0.023	   	0.012	

V	   	57723.280	   	11.920	   	0.020	   	11.887	   	0.023	   	0.033	   	0.012	

V	   	57730.133	   	11.930	   	0.020	   	11.910	   	0.023	   	0.020	   	0.012	

V	   	57742.755	   	11.940	   	0.020	   	11.914	   	0.023	   	0.026	   	0.012	

V	   	57744.214	   	11.940	   	0.020	   	11.909	   	0.023	   	0.031	   	0.012	

V	   	57751.853	   	11.930	   	0.020	   	11.909	   	0.023	   	0.021	   	0.012	

V	   	57756.314	   	11.950	   	0.020	   	11.930	   	0.023	   	0.020	   	0.012	

V	   	57765.275	   	11.920	   	0.030	   	11.895	   	0.036	   	0.025	   	0.020	

V	   	57772.980	   	11.930	   	0.020	   	11.903	   	0.023	   	0.027	   	0.012	

V	   	57779.893	   	11.930	   	0.020	   	11.890	   	0.023	   	0.040	   	0.012	

V	   	57786.143	   	11.950	   	0.020	   	11.930	   	0.023	   	0.020	   	0.012	

V	   	57789.996	   	11.930	   	0.020	   	11.885	   	0.023	   	0.045	   	0.012	

V	   	57792.324	   	11.940	   	0.020	   	11.914	   	0.023	   	0.026	   	0.012	

V	   	57795.384	   	11.950	   	0.020	   	11.877	   	0.023	   	0.073	   	0.012	

V	   	57798.504	   	11.930	   	0.020	   	11.897	   	0.023	   	0.033	   	0.012	

V	   	57801.896	   	11.940	   	0.020	   	11.920	   	0.023	   	0.020	   	0.012	

V	   	57804.941	   	11.910	   	0.020	   	11.865	   	0.023	   	0.045	   	0.012	

V	   	57807.732	   	11.930	   	0.020	   	11.899	   	0.023	   	0.031	   	0.012	

V	   	57810.387	   	11.930	   	0.020	   	11.908	   	0.023	   	0.022	   	0.012	

V	   	57819.022	   	11.930	   	0.020	   	11.913	   	0.023	   	0.017	   	0.012	

V	   	57853.045	   	11.920	   	0.020	   	11.885	   	0.023	   	0.035	   	0.012	

aModified Julian date
bAverage brightening of the comparison star measurements




