KIC 8462852 Hereford Arizona Observatory Photometry Observations #6
Bruce Gary, Last updated: 2018.04.23, 03 UT

A brightening appears to have occurred that is ABOVE the U-shaped model. I have no explanation!

I've taken the position that the current fade slope is less steep than previously modeled. This leads to an increase of depths for the March dips by ~ 1 %.

I want to suggest that careful use of AAVSO data can be used to produce good quality light curves, as I illustrate below. Congratulations, certain AAVSO observers!

1) This web page is for the 2018 observing season for KIC 8462852 (e.g., "Tabby's Star"), hereafter KIC846.

2) By now everyone knows about two important papers that appeared at the arXiv preprint web site on Jan 03: the Tabby Team paper (199 authors) summarizing Kickstarter observations & others, and a Deeg et al. paper reporting GTC (10.4-m) observations of dip depth vs. wavelength. Both confirm that dust with a small size component (< 0.5 micron radius) produce the dips. (Long-timescale variations are a completely different thing.) Links to these two papers are given in the References section (below).

3) Rafik Bourne and I have published two articles in AAS Research Notes: 1) "KIC 8462852 Brightness Pattern Repeating Every 1600 Days" at link, and 2) "KIC 8462852: Potential repeat of the Kepler day 1540 dip in August 2017" at link. Preprints are available at arXiv:1711.04205 and arXiv:1711.07472. A full-length (9-page) article, covering both AAS Research Notes topics more fully, has been published by MNRAS. You can see the final version (after 3 revisions) at link or link.

4) Finally, since I have probably observed KIC846 more than anyone, I may have earned the right to comment about the suggestion of "alien mega-structures" as a possible explanation for the unexplained dimming behavior before natural explanations had been exhausted. I'm going to repeat a complaint by the Dutch astronomer Ignas Snellen of Leiden Observatory, but first I want to present a brief justification for my right to complain by describing my pro-SETI credentials: 1) In the 1950s I demonstrated the feasibility of an alien civilization in our interstellar neighborhood to broadcast its location by transmitting a map of how constellations appeared from their location, and 2) when I led the JPL Radio Astronomy Group in 1968 I suggested that SETI should be a group goal with a Deep Space Station radio telescope, which my successor eventually did, using DSS-14, until it was killed by a Nevada senator who complained about this NASA project. (As an aside, I was hired at JPL in 1964 by Frank Drake who was apparently impressed by my Jupiter observations with the radio telescope he used for Project Ozma). OK, here's what Dr. Snellen wrote (from link):
"...there is no place for alien civilizations in a scientific discussion on new astrophysical phenomena, in the same way as there is no place for divine intervention as a possible solution. One may view it as harmless fun, but I see parallels in athletes taking banned substances. It may lead to short-term fame and medals, but in the long run it harms the sport. Same for astronomy: we should be very careful not to be ridiculed. I really hope we can stop mentioning SETI for every unexplained phenomenon. The article (by Elizabeth Howell) ends with a quote from Morris Jones, an Australian space observer: "The media is under pressure to deliver attention-grabbing news, but its hard to expect them to judge fringe SETI as spurious when it comes from reputable institutions and qualified researchers. The best way to reduce these reports is to stop the production of questionable scientific papers in the first place.  Amen!

Links on this web page

    V-mag and g'-mag vs. date   
    Comparison with other observer observations   
    List of observing sessions   
Finder image showing new set of reference stars
    HAO precision explained (580 ppm)  
    My collaboration policy

  Go back to 5th of six web pages  (for dates 2017.11.13 to 2018.01.03)
  Go back to 4th of six web pages  (for dates 2017.09.21 to 2017.11.13)
  Go back to 3rd of six web pages  (for dates 2017.08.29 to 2017.09.18)
  Go back to 2nd of six web pages  (for dates 2017.06.18 to 2017.08.28)
  Go back to 1st of six web pages  (for dates 2014.05.02 to 2017.06.17)

    Reference Star Quality Assessment  (the 10 best stars out of 25 evaluated)  

This is the 6th web pages devoted to my observations of Tabby's Star. When a web page has many images the download times are long, so this is the latest "split."

V-mag and g'-mag vs. date

Figure 1. Note that the "U-Shaped Model" is not well constrained for dates after 2017 Nov. I've arbitrarily adopted a straight line fit that fits data so far taken. 

Figure 2. This 300-day magnitude light curve shows the latest 10 months of data, with magnitude symbols coded for OOT vs. dip. Note the steep slope for 2017 Nov to now, which was "unexpected" and may not be be real. We'll need more observations to sort this out.

Figure 3. 1100-day version of above graph, showing some unfiltered observations converted to g'-band magnitude scale. I wonder if the OOT line for 2018 is less steep than shown here. Just a suspicion. We need more data!

Figure 4. If I adopt the U-shaped model (as shown in the previous graph) any departures can be identified as "dips." The latest measurements reveal a 6th and 7th dips (with a depth greater than 1.0 %) since Kepler.

Figure 5. This is just a date expanded version of the previous graph.

Figure 6. Detail of above graph. I have a 2-day data gap for the first dip ingress, and a one week data gap for the second dip ingress (due to weather in both cases).

Comparison of HAO with AAVSO Observations

David Lane (AAVSO Observer Code LDJ) has reprocessed his 3 year's of KIC846 observations (lot's of work!), and has re-submitted them to the AAVSO database. Rafik Bourne has downloaded them and we have performed an analysis on the V- and B-band measurements. The LDJ V-band data for times of known dips were excluded, and the remaining OOT (out-of-transit) data was averaged in groups of 7 observing sessions. An arbitrary offset was applied to achieve maximum agreement (this is legitimate since every observer has a unique and unknown absolute calibration uncertainty). The purpose for performing these adjustments was to allow for an assessment of the presence of a U-shaped OOT pattern with an approximate 1-year timescale that has been derived using HAO data. The next figure is a light curve showing how the LDJ V-mag measurements compare with HAO data.

Figure 7. Three-year light curve for two observers, LDJ (David Lane) and HAO (Bruce Gary). The LDJ symbols are averages of 7 observing sessions (3 images per session for early data, ranging up to ~ 25 images per session lately) while the HAO symbols are for individual observing sessions (>200 images per session, typically). LDJ data taken during known dip times have not been included in the 7-session averages. The LDJ symbols can therefore be compared with the HAO OOT symbols (solid squares and circles). (Clear filter and V filter observations have been converted to a g'-magnitude scale.)

This figure shows agreement of both LDJ and HAO data with the U-shaped, long timescale variation model. During the first half of 2016 we don't have information about the presence of dips, so some of the low LDJ symbols may be due to dip activity that lowered measured brightness.

I conclude that the U-shaped OOT model has support from both data sets. The depth of the U-shape is ~ 1.0 % and the duration of the U-shape is ~ 1.0 year. So far, the LDJ and HAO data agree in suggesting that since the time of maximum brightness at the end of the U-shape (near JD4 = 8050) a steep fade has been underway. LDJ B-band measurements will be presented here that show a greater U-shape depth than for V-band! This will provide a significant constraint on modeling the physical mechanism for the U-shape (large dust cloud vs. reflection of starlight by the dip clouds).

The next graph is a comparison of downloaded AAVSO data for March and April. Data for 7 observers is shown with offsets chosen to maximize agreement with HAO and each other. 

Figure 8. Comparison of "normalized flux" for 5 AAVSO observers and HAO during March and April, 2018. Uncertainty bars have been established using a neighbor difference method. An arbitrary offset has been applied to each observer data set to achieve agreement with HAO data, where overlap exists, and with each other (i.e., internal consistency). The 6 % dip at JD4 = 8203.4 is fitted well by an "asymmetric hyper-secant" (AHS) function. (The data in this figure was downloaded from the AAVSO web site:

Transit Pattern and Speculation about Model for KIC846 Dust Cloud Geometry (not Physical Mechanism Model)

A thorough description of this matter is given in the 5th web page of this 6-part series of web pages: link.

List of Observations (for all earlier observations, before 2018 Feb 25, go to link)


Daily Observing Session Information (most recent at top)

2018.04.21, g'-band, 4.1 hrs, data  

Excellent observing conditions, good focus all night - so I have no explanation for the unprecedented brightness.

2018.04.18, g'-band, 1.3 hrs, data 

2018.04.10, g'-band, 4.5 hrs data

2018.04.08, g'-band, 3.5 hrs  data 

2018.04.05, g'-band, 4.6 hrs  data 

2018.04.04, g'-band, 4.6 hrs data    

2018.04.02, g'-band, 1.7 hr data 

2018.03.30, g'-band, 4.6 hrs data 

2018.03.28, g'-band, 3.7 hrs, data  

2018.03.27, g'-band, 3.1 hrs, data  

2018.03.21, g'-band, 2.5 hrs, data  

2018.03.20, g'-band, 2.8 hrs, data  

2018.03.19, g'-band, 2.2 hrs, data    

2018.03.16, g'-band,  1.4 hrs, data  

Changed optical configuration: inserted Optec focal reducer. Determined empirical correction to apply to this and subsequent data to be +0.0007 mag.

2018.03.15  g'-band, 2.6 hrs, Data  

"Atmospheric seeing" (PSF's FWHM) was bad, and variable, due to wind.

2018.03.02, g'-band, 2.1 hrs, Data

2018.02.25, g'-band, 1.2 hrs   DataExchangeFile  

Finder Chart

It has taken over a year to figure out which stars are reliably stable. I now use 17 stars for reference, some of which are shown in the next image.

Figure F1. Finder image, FOV = 12.5 x 9.6 'arc, north-east at upper-left, showing the 17 stars that I have determined are stable at about the 1 mmag level, out of 34 that have been evaluated. KIC846 is inside the blue square. 

I have evaluated stability of 34 stars near KIC846, and have accepted 17 for calibration use and have rejected 17. My acceptance criterion is based on RMS of daily averages, and also trend, during several months of data. My use of the 17 accepted stars began with observing date 2017.09.07. Some star behavior is described at link.  I will eventually create a another web page summarizing behavior of all 34 stars. 

HAO Precision Explained  

Some people may have noticed that my HAO measurements of KIC846 exhibit better precision than other observers. In this section I'll explain why. First, let's review the distinction between "accuracy" and "precision."

Accuracy vs. Precision

Precision is related to an observer's measurement-to-measurement RMS. It makes no claims regarding calibration. Accuracy is the orthogonal sum of precision and calibration accuracy. For example, I claim that my KIC846 g'-mag observing session precision and calibration accuracies are 0.0007 and 0.0200 magnitude. Their orthogonal sum (SQRT of the sum of squares) is 0.0201 magnitude. The task of describing a dip's depth and structure depends only on precision, whereas any comparison of HAO r'-mag with Tabby's LCO r'-mag, for example, would be evaluated in terms of our two estimated accuracies.

Measurement Precision
Ground-based measurements of a single image exhibit a noise level (i.e., precision per image) that is influenced by three principal factors: 1) thermal noise (CCD noise per pixel), 2) Poisson noise (fundamental limit set by sampling theory), and 3) atmospheric scintillation (produced mostly at the tropopause). I describe these, and other smaller sources of noise, in my photometry book Exoplanet Observing for Amateurs (Chapter 20). The most important of these noise sources, and probably the least appreciated, is scintillation! 
Scintillation noise can be approximated using the following equation (pg. 132):

where sigma = fractional RMS intensity fluctuation, D is telescope diameter [cm], sec(Z) is atmospheric air mass, h is observatory site altitude above sea level [m], ho = 8000 m, and g = exposure time [seconds]. Substituting D = 35 cm (14-inch), sec(Z) = 1.8, h = 1420 m and g = 30 seconds yields (these are typical HAO values) yields sigma = 0.0025 mag. This fluctuation occurs for all stars in an image, regardless of brightness. Note that this includes reference stars, which will scintillate differently (assuming they're > ~ 10 "arc apart). Use of just one reference star will cause the target star's scintillation noise to be root-2 greater (which is an argument for using many reference stars). Scintillation noise level can vary by a factor of two on hourly timescales; some nights can be significantly different from others (approximately 1/3 of nominal to 3 times nominal).

Poisson noise (for HAO) is typically 0.0024 mag (for KIC846). Thermal noise is typically 0.0015 mag (for KIC846). Scintillation noise, at 0.0025 mag typically, can easily become the most important noise component.

Its my impression that few observers realize that scintillation is often the dominant source of noise per image for bright stars. There are two ways to overcome scintillation noise: 1) use a very large aperture telescope (i.e., > 1 or 2 meters), and 2) average many images to obtain a more precise observing session average. It's possible that scintillation is too often overlooked because it's unimportant for faint stars. For professional astronomers it may be overlooked because it's unimportant when using large telescopes. However, with large telescopes short exposures are needed (to avoid CCD saturation), and this is only feasible when download times are short (to preserve duty cycle). Some professional observatories don't emphasize short download times (e.g., LCO). Every telescope system has an optimum observing strategy for a specific target and observing goal, and it is often the case that for a specific target and observing goal some telescope systems are closer to optimum than others. HAO can observe unbinned with exposure times of 120 seconds and download plus autoguide adjust time of 10 seconds. If the same CCD was on a 1-meter telescope, such as the LCO for example, exposure time would be limited to 15 seconds and download time would be 40 seconds. The improvement in scintillation by using a larger telescope would be lost by having to use a shorter exposure time with a much reduced duty cycle. The HAO may be within that "sweet spot."

Empirical RMS Noise Level: a Dose of Reality

Here's a plot of empirically-measured RMS noise level vs. star brightness for two air mass segments of one observing session.

Figure H1. Empirically-measured RMS noise level vs. star brightness for two air mass portions of one observing session when scintillation was about twice as bad as normal.

The brighter the star the more it departs from a simple SNR model. This is because scintillation is the same for all stars, regardless of brightness, so for brighter stars scintillation becomes the dominant source of noise.
The constant term for airmass = 1.7 is ~ 5.0 mmag, and since the Poisson noise level (for KIC846) is ~ 2.4 mmag and the thermal level (for KIC846) is ~ 2.0 mmag, we can estimate that the scintillation component was ~ 3.9 mmag (SQRT(5.0^2 - 2.4^2 - 2.0^2)). This is greater than the nominal 2.5 mmag (using the above equation).

Figure H2. Empirically-measured RMS noise level vs. star brightness for air mass = 1.6 for an observing session when scintillation was about normal.

This plot of RMS vs. g'-mag is for a date with an apparently lower level of scintillation noise. The constant term is ~ 3.5 mmag, and since the Poisson noise level (for KIC846) is ~ 2.4 mmag and the thermal level (for KIC846) is ~ 1.1 mmag, we can estimate that the scintillation component was ~ 2.3 mmag (SQRT(3.5^2 - 2.4^2 - 1.1^2)). This is slightly lower than the nominal 2.5 mmag (using the above equation).

Implications for KIC846 Observing

What are the implications for all of this when only a few images are made during an observing session? The above figure shows that if I took just one image the KIC846 g'-mag could have a SE uncertainty (precision) of 0.004 magnitude (for air mass = 1.6). That corresponds to a normalized flux SE = 0.37 %. If, for example, 4 images are taken, and their g'-mags were averaged, the expected observing session SE would be 0.002 magnitude (0.19 % normalized flux). I typically obtain > 200 images per observing session, so I can expect a precision that could be as low as 0.00028 mag (0.03 % normalized flux). Other systematics will become important at these high precision levels, so what's actually achievable from a 200-image observing session will be higher than the above estimates (as shown below).

It's possible to estimate actual observing session precision by comparing average magnitude for an observing session of one date with neighbor date values (when KIC846 is thought to be constant, or slowly varying). For example, consider the following light curve segment:

Figure H3. Normalized flux light curve for dates when KIC846 appeared to be either stable or changing slowly (late Sep and Nov).
This light curve was used to determine observing date precision using a "neighbor difference method." (It relies on the fact that a set of values that are the difference of a value from the average of its immediate neighbors, i.e., "neighbor difference" values, will have a STDEV = sqrt(1.5) x STDEV of the original values. The sequence of "neighbor differences" will be unaffected by real variations provided they are slow compared with the interval between values.) The data after mid-December can't be used because all observations at those dates were
short observing sessions (fewer than 100 images per night) at high air mass. There are 34 dates within the two intervals of apparent stability or slow variation, and the precision per measurement for both intervals is ~ 580 ppm, or 0.6 ppt, or 0.06 % of normalized flux. This corresponds to 0.00058 magnitude, which is (unsurprisingly) somewhat greater than the theoretically predicted best possible 0.00035 magnitude. The fact that the measured precision is greater is due to systematic errors that apparently were ~ 460 ppm (0.46 ppt, 0.046 %) for the two date intervals analyzed. I think I know what they are, but it is difficult proving any such speculation, and for present purposes it's not important.

The message of this sub-section is that when an observing session includes ~ 200 or more images, and when care is taken in their photometric processing, it is possible to achieve a precision for KIC846 of ~ 580 ppm.

Miscellaneous Photometry Practices

At the start of each observing session I carefully position the star field at a chosen standard location on the pixel field. This is meant to minimize the effect of flat field imperfections.

The CCD is kept at the same temperature for all observing sessions (until a seasonal temperature change requires, or permits, a change). Ghosting becomes noticeable for temperatures colder than about - 27 C (for my SBIG ST-10XME CCD), so I never observe colder than that. 

My master dark frame is made from a couple dozen dark images with the same exposure times and CCD temperature as all subsequent KIC846 imaging.

I use many reference stars (17) for calibration. The SNR penalty for using just one reference star is root-2. As discussed in the previous section these 17 reference stars have been carefully chosen to be stable over a timescale of many months.

I have adopted a standard photometry aperture size set for all observing sessions (currently 4 pixels for signal aperture radius, 4 pixels for gap annulus width, 12 pixels for sky background annulus width). This minimizes the effect of changing atmospheric "seeing" (causing PSF FWHM to vary). If I allowed the signal circle size to vary with "seeing" (as some observers do) then when seeing degrades (i.e., PSF broadens) the photometry signal circle for the reference stars (or target star) could expand into an area that includes a nearby star, thus affecting the flux reading of that star. 

Each observing session is calibrated with the chosen (17) reference stars using a "star color sensitivity" plot (which is a better practice than using "CCD transformation equations"). Visual inspection of this plot can identify whenever a reference star is "misbehaving" (due to unusually bad "seeing," for example), which allows outlier reference stars to be identified and toggled off for use.

Outlier KIC846 magnitudes are identified on a per image basis and any that exceed nearby median values by 3.3-sigma are rejected. Visual inspection is also employed for outlier identification.

Other quality assurance practices are described in my photometry book Exoplanet Observing for Amateurs.

Conclusion for this Section

The message of this section (for observers using telescopes of aperture smaller than ~ 1 meter) is that:

    To achieve a date-averaged precision of 1 mmag (0.1 % normalized flux), for example, scintillation noise requires that an observing session must consist of at least 50 images!

Observers who take only 4 images per date, for example, can expect their date-averaged precision to be no better than ~ 2 mmag (0.2 % normalized flux).

My Collaboration Policy

At my age of almost 79 I'm entitled to have fun and avoid work. Photometric observing and figuring things out is fun. Writing papers is work. Besides, most people really don't care about what others have done. So, if anyone wants to use any of my observations for a publication, you're welcome to do so. But please don't invite me for co-authorship!

My light curve observations are "in the public domain." This means anyone can and may download of all LC observations, and use or misuse any of that data for whatever purpose. If my data is essential to any publication just mention this in the acknowledgement section.


    Boyajian, Tabetha S. and 198 others, "The First Post-Kepler Brightness Dips of KIC 8462852" arXiv 
    Deeg, H. J., R. Alonso, D. Nespral & Tabetha BOyajian, Non-grey dimming events of KIC 8462852 from GTC spectrophotometry" arXiv 
    Bourne, R., B. L. Gary and A. Plakhov, "Recent Photometric Monitoring of KIC 8462852, the Detection of a Potential Repeat of the Kepler Day 1540 Dip and a Plausible Model," arXiv:1711.10612     
    Bourne, Rafik and Bruce Gary, "KIC 8462852: Potential repeat of the Kepler day 1540 dip in August 2017," submitted to AAS Research Notes, preprint: arXiv:1711.07472
    Xu, S., S. Rappaport, R. van Lieshout & 35 others, "A dearth of small particles in the transiting material around the white dwarf WD 1145+017," approved for publication by MNRAS link, preprint arXiv: 1711.06960 
    Gary, Bruce and Rafik Bourne, 2017, "KIC 8462852 Brightness Pattern Repeating Every 1600 Days," published by Research Notes of the AAS at link; preprint at arXiv:1711.04205
    Gary, B. L., S. Rappaport, T. G. Kaye, R. Alonso, J.-F. Hambsch, 2017, "WD 1145+017 Photometric Observations During Eight Months of High Activity", MNRAS, 2017, 465, 3267-3280; arXiv
    Neslusan, L. and J. & Budaj, 2016, "Mysterious Eclipses in the Light Curve of KIC8462852: a Possible Explanation, arXiv: 1612.06121v2  (a "tour de force"; I highly recommend this publication)
    Neslusan & Budaj web site with animation of their way of explaining Kepler D1540 dip:
    Wyatt, W. C., R. van Lieshout, G. M. Kennedy, T. S. Boyajian, "Modeling the KIC8462852 light curves: compatibility of the dips and secular dimming with an exocomet interpretation," submitted to MNRAS, arXiv  
    Grindlay interview about Schaefer's assertion that KIC846 exhibited a century long fade using DASCH data: link
    Hippke, Michael and Daniel Angerhausen, "The year-long flux variations in Boyajian's star are asymmetric or aperiodic," submitted to ApJL, arXiv 
    Sacco, G., L. Ngo and J. Modolo, "A 1574-day Periodicity of Transits Orbiting KIC 8462852," arXiv
    Rappaport, S., B. L. Gary, A. Vanerdurg, S. Xu, D. Pooley and K. Mukai, "WD 1145+017: Optical Activity During 2016-2017 and Limits on the X-Ray Flux," arXiv, Mon. Not. Royal Astron. Soc.
    Steele, I. A. & 4 others, 2017, "Optical Polarimetry of KIC 8462852 in May-August 2017,"MNRAS (accepted), arXiv.
    Simon, Joshua D., Benjamen J. Shappee and 6 others, "Where is the Flux Going? The Long-Term Photometric Variability of Boyajian's Star," arXiv:1708.07822 
    Meng, Huan Y. A., G. Rieke and 12 others (including Boyajian), "Extinction and the Dimming of KIC 8462852," arXiv: 1708.07556  
    Sucerquita, M., Alvarado-Montes, J.A. and two others, "Anomalous Lightcurves of Young Tilted Exorings," arXiv: 1708.04600   Also: New Scientist link and Universe Today link.
    Rappaport, S., A. Vanderburg and 9 others, "Likely Transiting Exocomets Detected by Kepler," arXiv: 1708.06069 
    Montet, Benjamin T. and Joshua D. Simon, 2016, arXiv 
    Boyajian et al, 2015, MNRAS, "Planet Hunters X. KIC 8462852 - Where's the flux?" link
    Ballesteros, F. J., P. Arnalte-Mur, A. Fernandez-Soto and V. J. Martinez, 2017, "KIC8462852: Will the Trojans Return in 2011?", arXiv
    Washington Post article, 2015.10.15: link
    AAVSO Campaign Notice requesting KIC646 observations
    AAVSO LC Generator (enter KIC 8462852)
    Web page tutorial: Tips for amateurs observating faint asteroids (useful for any photometry observing)
    Book: Exoplanet Observing for Amateurs, Gary (2014): link (useful for any photometry observing) 
    wikipedia description of Tabby's Star  
    My web pages master list, resume

    B L G a r y at u m i c h dot e d u    Hereford Arizona Observatory    resume 
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