Freitag, 7. Oktober 2016

Meditation over the Dips in Tabbys Star

Some aspects of  KIC 8462852

We still don't know what the strange light curves at WTF Star could mean, is it something that happens in nature very rarely or is it an artificial structure?

To dig into the data, I will try to find some clues and describe the details. My background is, I have a Ph.D. in Physics and did some research in pattern recognition. Don't overestimate my knowledge, I want to discuss the ideas and not give a final answer.

The Data

Let's start with the data. Kepler measured the intensity of the light of KIC 8462852, some call it Boyajian's Star, over a period of four years. during that period depending on the counting, 16 significant dimming events have happened.

The first strange thing is, the longer the observation lasted, the weird the shape of the dips were. It is very sad to know, that Kepler stopped observation when things got most interesting! I don't want to start a new thread of conspiracy, but it should be mentioned, that the moment of failure of the reaction wheel#2 in July 2014 [1] happened shortly after the most exciting dips. It should be mentioned, that at that time, as far as we know, nobody was aware of the strange behavior of Tabby's star.

Let's start to look into the details of every Dip. I present every dip in a window with a width of 10 days. This makes it easy to compare the shape of the dips. All dips are downloaded from the stsci Archive [1]. The number of the dips are the numbers in the archive.

Dip 1

 This is the first significant Dip (Fig 1) that the Kepler Mission recognized.

Fig 1.: Dip 1 d140 with a triangular shape [2]
Although this dip looks more or less simple, it is by far not a standard dimming of a planet transit. The dip (Fig 2) begins with a slow dimming till day 139, changes them into a continuous steeper dimming, reaching the floor at day 140,2 and after six hours the intensity gets in a similar slope back til end of day 141 and then with another lower slope back to normal within ten days after the first change in brightness appeared.
Fig 2: Dip 1 d140 including some manually drawn trend lines

Imagine, if this would be the only dip we ever have seen from KIC 8462, we would not have any simple natural explanation. A simple solution (figure 3) is something in the orbit with a long triangular shape, entering the line of sight, causing the continuous first dimming. Then another, wider diamond shape enters the theater, till the maximum of the dip. After six hours, the end of the wide diamond shape starts to leave the line of sight, at day 142 a slim triangular object also starts to leave the line of sight.
Fig. 3: Shape of an object that could result in the dip 1. The painting is only qualitative, precise calculations, including the surface brightness of a star, could result in exact shape size. An exercise is given to the reader.

Dip 2

The second dip at day 216 is very noisy, due to the small intensity change of 0.15%, this is still a Uranus size object.  
Fig 4: Dip 2 d216 [1]
When I try to give a manual approximation of the shape (Fig 5), it seems a little bit similar to dip 1, but without the first slope.
Fig 5: Dip 2 with manual approximation of the dip shape

Dip 4b

Dip 3 has not sufficient data, so I continue with the dips under number 4 in the archive. Dip 4b is later then dipped 4a, but 4b is more similar to the preceding dips than dip 4a. Dip 4b (Fig 6) is different to the preceding dips, it shows no floor, instead of that (Fig 7) only a continuous descending ramp and then a steeper ascending ramp.
Fig 6: Dip 4b d426 [1]
It should be noted, that the descending ramp shows also a continuous lower noise with a lower intensity of the observed light, this might be an artifact, but other dips show also unusual noise fluctuations nearby the dip.

Fig 7: Dip 4b with a manual approximation of the dip shape, there seems to be no floor.

Dip 4a

Dip 4a is the first complex dip in the series of dips which appear with very deep dimming at the end of the observation period. 
Fig 8: Dip 4a d359, shows a very complex internal structure [2]
It is hard to interpret the exact shape of dip 4a, but at least it seems a combination of three different dips. The first part between day 356 and 357 seems to be linear, similar to the first observed dips (1,2,4b), then follows a u-shape dip, but this could also be a combination of ramps as seen in dip 1. The second and deepest dip in 4a is 0.24% below the baseline, a structure similar to the shading effect of a Saturn size planet. But the shape is not a typical shape of a planet occlusion in front of a star. After a flat observed intensity around day 360, a third wide dip appears and seem to end this episode around day 364. At the end, there might be one or two more dips, but this can also be "special" noise as seen in other dips.
Fig 8: Dip 4a with a manual drawing of the shapes, Blackline present linear elements, green lines are splines to fit more or less parabolic looking elements
It is interesting, that this set of dips has a similar duration of eight days, as seen in the other dips. 

Dip 5

This dip has a similar shape and size as dip 4b, a slow slope and a steep regeneration from the dip.
Fig 9: Dip 5, very noisy dip and some artifact from the telescope at the end of the period.
A parabolic type of dip could also fit the data of the lower part of dip 5.
Fig 10: Dip 5, a simple linear dimming defined by black lines
and a possible parabolic type of dimming shown by a green line
We skip dip 6 because this seems to be an artifact of the instrument.

Dip 7

Dip 7 is a week dip but with an interesting fingerprint. In some aspect, it has a similar shape as one of the last strong dips.
Fig 11: Dip 10 d694, this is a multi-dip event.
If we zoom into a five day period, some aspects are similar to the shape of the dip at day 1519.
Fig 12: Dip 7 with manually drawn lines to stress the structure
It seems that dip 7 consists at least of four elements. three dips with increasing depth and a last small dip. The shape of the different elements is hard to evaluate due to the high noise level.

Dip 8

The shape and depth of dip 8 are beyond anything we have ever seen. It starts with a continuous declining line, which can be described by a very steep function like Tangent. 
Fig 13: Dip 8 at day 792 is by far the most mysterious dip
I tried hard to find a relatively simple and plausible model for the dip function. I estimated a star disk with constant flux and a width relative to the orbit time of 0.21 days. In front of this disc appears an object (Fig 15) with different width. 
Fig 14: Dip 8 (red) and a fit (black) for the flux, the green line shows the error of the fit.
The construction of the object results from the value size as calculated by

size = scale*tan((t-t0)*f1)*exp((t-t0)*growth)    (1)
used values:
scale = 0.002
t0 = 909.46 (timescale in plot)
f1 = 0.19247596
growth = 0.18389495

The equation was used to produce the shape in Fig 15, the left part has little different values for the parameters f1 and growth. The right part has a negative sign for the time to result in a similar shape as the left part. 
The central, red marked area is a manually generated fit with values reducing the error.

Fig 15: A object of this shape can produce dip 8, the blue part is following equation 1, only the red points were entered manually.

The resulting calculated dip line (black) in Fig 14 looks astonishingly similar to the measured flux (red). The error is given as the difference between flux and fit line.
I have no simple explanation for the equation, but an exponential growth combined with a geometric function could result from a construction with constant growth and a special shape.

You find the discussion of further dips and the first conclusion about KIC8462852 in the next part.
Please give feedback.

Watch out for my other blogs, like the 


[1] NASA Kepler Mission Manager, 31 July 2014
[2] Source of plots,

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