Meditation over the WTF Star Dips, Part II

KIC 8462852 and the really deep dips

This is the second part of my meditation over the strange dips in the light curve of Tabby's Star. You find the first part here: "Some aspects of KIC 8462852".

Dip 9 

The following dip 9 is not very spectacular, the signal is near the noise limit. 

Fig 1: Dip 9 at d848

Be aware, that most of the signal in this plot is due to the rotation of the star, period 0.88 days, and the fluctuation of the brightness is, as far as we understand other stars, a result of sun spots.

Beside this very natural signal change we see a dip, that starts at day 846 goes down to a minimum near day 848 and then the brightness recovers again. The exact shape is not known, due to the noise and influence of the sun spots. The shape in depth and time is not unlike a small planet, similar a transit of the earth in front of our sun. 

Dip 10 and 11

The dip numbers, to be exact the time frame, are automatically generated by the computer. The size of any signals in this period is not useful for any further discussion. May be we find a periodicity then it could be a hint for any object like a planet.

Dip 12

In the case of dip 12a we have no information for the dimming part, due to some measurement errors. 

The recovery of this relative small dip, 0,11% depth, shows a unusual behavior for a planet transit. But it has a very similar shape as dip 8, going back to normal brightness with some type of exponential looking shape.

Fig 2: Dip 12a at d1126

The strange thing with this dip is, why do we see the measurement error at the beginning and then an exponential recovery? We can only understand the quality of the shape, if we understand exactly the reason, why we see a measurement error. If anyone reads this blog with more background on the detector system of Kepler and this glitch, he is welcomed to give me a hint.

The case of dip 12b looks again structured.

Fig 3: Dip 12b at d1143

The dip 12b has a deepth of 0,12% and has a ramp before a very steep dip follows. this is a little bit similar to dip 1, although there is much more signal available. Then follows a floor as already seen in dip 2, and then a similar ramp to recover from the dip. A planet with a accreditation disc might show a similar shape, the problem is the timing. The central dip lasts more than two days, this is hardly possible for a planet orbiting a large star.

Fig 4: Dip 12b with manually interpretation of the shape

Short, within the ramp of dip 12b follows dip 12c, a small dip with a typical shape of a planet transit,

Fig 5: Dip 12c at d1151 lasts about one day

The duration of one day is about 2 times shorter as the central part of dip 12b.

Dip 13

 Dip 13 may be a member of another class of dips, looking very symmetrical. But it could also be interpreted as a case of 3 to 4 consecutive dips, which are by chance similar in size.

Fig 6: Dip 13 at d1205 a very symmetric shape

We could compare this dip with dip 4a, also a set of dips, that starts with a small dip, then a center dip and then another small dip. There has been some discussion about timing and depth within this dip.

Depending on the baseline, there could be a rational 1:2 between the minor dips and the major dip in the center.

Fig 7: Dip at d1205 with a projection of the mirror of the image.

I will look in the interesting symmetric shape of the dip. Therefore I include the mirror image into figure 7. We could see at least four elements, A, B, C, D, ups and downs in the flux, which apperare with perfect timing relative to the central symmetric line. It is hard to believe, that this happens by chance. Some physical reason could be a ring system around a planet. But the shape of the central dip does not support this idea. Very strange is, that dip 16d at day 1536 has a similar shape, but a different size, I will discuss this later.

A Planet?

If we look into some details of the complex dip structure, it should be mentioned, that at d1208,2 a small rectangular dip shows up, similar do other dips like 12c at d1143. A time difference or 137 days.  Adding this, the next expected dip should be at d1417 and the at d1554. At d1417, Kepler has no signal due to technical problems, but at 1554 there seems to be the same dip (depth delta 21 [e-/sec]), may be the same object! There is also a small dip at 1007, nothing at 869, no data at 732, and 321, but a small signal at 185. Planet hunters should look into the details.

Period 14 and 15

Due the time interval from day 1274 till day 1471 no very significant event appears. It should be mentioned, that at d1433 a drop in the flux with the typical duration, often seen before, of 8 days but with a small amplitude 38 (s-/sec) is visible.

Fig 8: Dip at d1433, amplitude in the range of typical fluctuations due to sunspots(?).

Period 16 and 17

Period 16 and 17 contain the most dramatic fluctuations ever seen in a star of this type. The flux is up to 22% dimmed. Very hard to understand by well known astronomic events. The shapes seem to be part of one larger, symmetric event, as pointed by Gary D. Sacco in the reddit thread "95 Day Abnormal Equilibrium of Periodicity and Flux Variation" [1]

Fig 9: a 95 day period with more or less symetric deep dips, source gdsacco [1]

As Gary D. Sacco points out, the distance between the different dips seem to be arranged near a central dip at day 1539. The shape of dip d1539 (depth 670 [e-/sec]) is visual similar to dip 13 at d1205 (deepth 111 [e-/sec]), although 6,03 times deeper.  

The symmetry is by far not perfect and the optical center of the dips is not the center of symmetry. Very strange is the aspect, that the sequence before the first and second large dips are a little bit similar on the time axis. If we look into the structure of d1519 in fig 10, we see a complex structure.

Fig 10: The left large dip at day 1519 seems to be a double dip 

To get the details, I added some lines see fig 11. 

Fig 11: The elements of dip group around d1519.

After two small dips A,B, the flux recovers and starts to drop strong along a line C. Another object D comes into the scene and accelerates the drop. The flux recovers a little before dip E and F come in. For some reasons, after dip F recovers, a linear flux reduction, given by line G appears this might be part of another element that is wider than the object that resulted in E and F. Object H might produce the next dip and another, different thing, shown by line I leads to the final recovered intensity.

Together at least nine different elements of whatever nature result in the strange flux signature.

Now look into the second big dip:

Fig 11: The right dip at day 1568 has a single full dip.

I also try to introduce some helpful lines shown in fig 12:

Fig 12: The elements of the dip group around d1568.

It starts with a slight decay of the flux during period A, and a first dip B five days before the full dip F shows up. But before that after s light lower plateau, again a slight decay C and then the first large dip D, and similar to d1590 dip C, and then a stronger dip E, similar to D in d1590. After a slight recovery the main dip F appears. During return to normal, a small dip G appears, might be in some way similar to dip H in d1590.

The choreography is similar, the values are not similar and they are not simple mirror signals around the symmetric center. This makes the understanding of the reason of the signal much more difficult. For example a disk like Saturns rings could not explain the flux.

It should also be mentioned, that the choreography is by the structure similar to dip 7 d694, although this dip is are much smaller in depth.

Conclusions so far

• The different dips seem not to be from the same family of natural events, of whatever type they are. 
• Interestingly, most of the dips have an internal structure. Only very weak dips don't show a visible structure, but this is a effect of noise, we are not able to see them.
• Most events have a similar choreographic structure, they start with small events and the biggest dip is at the end of the event, a little like in a firework (:-).
• There are at least two events d1205 and d1540 (and d359 a little) that show an astonishing symmetric structure, that is hard to be explained by accident, like comets coming with the right timing. Although there might exist natural explanations like ring systems around a planet, which could lead to such a flux variation.
• The strangest of all dips is d792, it seems not to be the product of a multi event. My best guess is, that something pointing away from the star, like a column of smoke, is the cause. This is implied by the tangent function and the exponential function, that fits very well (see first part). If the "smoke" is a little bend to one side, even the asymmetric structure can be plausible explained. 
• The reason of the smoke column could be a internal event of the star, similar to a solar flare, but millions of miles high and cooling down. The artificial star lifting should be included into the discussion.
• All events seem to happen within a time frame of less than 10 days and last at least five days. This tight time frame is another strange independent element of the KIC 8462852 story.

back to part one of the meditation over WTF Star dips

Next part is the dip of day 792 a sign of star lifting, the post contains some mathematical analysis.

References

[1] Gary D. Sacco, https://www.reddit.com/r/KIC8462852/comments/56kdfw/95_day_abnormal_equilibrium_of_periodicity_and/

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 energy-age.blogspot.de 

Reference

[1] NASA Kepler Mission Manager, 31 July 2014
[2] Source of plots, archive.stsci.edu