Samstag, 26. November 2016

Timing of next big Dip

When will the next Dip appear at Boyajians Star ?

In the last posts (d792, d1519), I described a model of the different large dips. This model is based on a beam that lifts matter from the star surface into an orbit. Due to the geometric situation, it should be possible to calculate the rotation speed of the beam. Actual the rotation speed is part of the parameter set in the shape calculation of the beam.
In this post, I will suggest a possible period.

The parameter rotation speed

The timing in the beam calculation is based on the equation

α(t) = ((BJD-2454833) – t) ω

BJD-2454833 is the time for all the Kepler datas [1], based on the BJD time,
t0 describes the dip at day 792 and has the exact value 792.7216d
ω is the rotation speed and has to be fitted to the data.
If we know the exact value, we caught the rotation period of the beam and can calculate the reappearance of more dips.

In the first paper, I suggest ω has the value of 1.00E-02[1/d]. This correlates to a period of circulation of 628 days (2pi*100). The loosely guess of the 100 was done with no special precision.
In a review of the situation, I changed the value from 100 to 115,67 (Distance from d792 to 1519) and checked the effect to the shape of the calculated dips, with a special concentration on the lower part of the absorption. As shown in figure 1.


Figure 1: Dip 792 optimized right part
This fits very nicely in the in the area where the error was considered, shown as red error bars. A calculation when I change the period by one day results already in a higher error in this region.
The other part of the plot is not that perfect, but other factors are not optimal implemented in the model, like the beam cross section.
To remember, in the right part under investigation, only the beam generates a shadow, the shape of the beam is not as influential as in the area of the deep dip.

Dips in the context

If we use the flux calculation for the whole Kepler period, we can see the repetition of the calculated flux as shown in figure 2:


Figure 2: Flux over the whole period (Right scale "Calculated Flux" lowered for good readability)

We see of course the tick at d792, which is the base of calculation. But we see also a dip at day 429, and day 1156, both are in some way an artefact, because the equation works with the absolute sin and contains in this sense a beam that would be on the other side of the star.
But there is a interesting detail, very near to this dips, we see in each case a small dip in the measure of Kepler. Let's have a look into the detail of dip d429 in figure 3:


Figure 3: Timing of d426 and the timing of the dip artefact.

It might be, that the technology behind star lifting generates some small beam at the opposite site of the star, this might be due to a magnetic field. But this can also be a pure coincidence. Due to the fact, that at day 1150 another similar dip is visible, should focus some resources to understand this coincidence.

The second appearance

At day 1519, we see the second appearance of our dip d792. The shape has changed but an interesting detail is still there, look into figure 4:



Figure 4: The dips around day 1519

In this plot, the shape of the d792 reappears due to the period of 726.78 days. Other elements add to that dip as discussed in the post 1519, but there is one amazing element, at day 1518, the flux recovers just to the level of the remaining effect of d792, but not more. This might be interpreted in a way, that this is in fact the separate structure of dip 792 appearing together with other elements of beams which reduce the flux at other times in the interval.

When will the next Dip apear

The most interesting question is, when will the next Dip apear?
I make the prediction as following in a table:


Time of dips in UTC time, Kepler starts at t = 0 (BJD-2454833) : 2009-Jan-1 11:29:59, I used the converter from Ohio State University

  dip      BJD              UTC
   -   2454833      2009-Jan-1  11:29:59 (Start of Kepler time)
  792  2455625.722  2011-Mar-5   4:49:40
 1519  2456352.500  2013-Mar-1   0:35:59
 2246  2457079.278  2015-Feb-25 18: 4:19
 2973  2457806.057  2017-Feb-21 13:58: 4
 3700  2458532.835  2019-Feb-18  7:26:24
 4427  2459259.614  2021-Feb-14  3:20: 9 


(I am not completely sure about the time conversion, if someone is here an expert, he may check the Kepler start time) I have now revisited the timing conversion, using Eastman, Jason tool [2] and U.S. Naval Observatory Astronomical Applications Department the result is slightly different but very well within the error margin. Tuesday, A.D. 2017 Feb 21, 13:18:25.1 (JD 2457806.054457)

On February 21st should see a dip!
 I am very curious to see if the result matches the prediction. 

I am very curios to see the result.

Reference:
[1] http://archive.stsci.edu/kepler/
[2] Eastman, JasonSiverd, RobertGaudi, B. Scott, 
Achieving Better Than 1 Minute Accuracy in the Heliocentric and Barycentric Julian Dates
DOI 10.1086/655938

Freitag, 11. November 2016

Dip Day 1519 in Detail

Solving the puzzle of Dip 1519

This post continues the analysis of different dips seen by the Kepler telescope at Boyajian's star (KIC 8462852). To understand the discussion, I recommend to read the analysis of Dip 792, because I use the same basic model.

Again a Starlift model

The very useful starlift model of the last post is reused to understand the very complex signature of the dips around day 1519, as presented in fig 1.

Fig 1: Komplex deep Dip 1519
The dip includes a very deep double dip, with 22% absorption, and a asymmetric basic structure, similar to dip 792.
My idea was, to use the simulated shape of a starlift with "smoke" as described in detail in Dip 792, to understand the shape 1519. Therefore the shape was positioned three times in the time frame with different position in time and different absolute absorption.
The result is shown in fig 2.


Fig 2: A first attempt to reproduce dip 1519

The simulated black line does not reproduce the blue measured values, but some very significant elements are well done. First of all, the double asymmetric main dip fits just perfect. And this was done by simple adding the model of Dip 792 with the same intensity, the factor is in both cases exact 1.0 (one)!
The first deep dip is deeper than the second, the reason is, that the "smoke" of the second dip deepens the first. The numerical distance in time was set to 5h. The length of the starlift beam is 1.50 higher as in dip 792. This also means, that the orbit of the smoke in this simulation is by a factor 1.50 further away as in dip 792. 

To complete the picture, a third starlift beam was introduced 12.5h before the main dip.  
The factor for this dip is 0.36789. Ever seen this number? It is 1/e, but it seems so, that value is by accident similar.
e is the very well known Euler number 2.7182.... the number of natural growth and the mathematical basis for the success of any civilisation. (More about e at wikipedia)

Some Problems

But the simple model does not reproduce the measured line in all parts. In the area A, B and and C, the signal is brighter than it should be. There are two possible explanations:
  1. The starlift beam had some interruptions and so the smoke has some breaks.
  2. The material of the smoke was used for construction and is no longer at this place in the orbit.
If we like solution 2, then it is not to hard to understand bumper D in fig 2. It might be some material in the orbit, it could even be a mirror to power the starlift itself. But this is pure speculation. 
A better solution is given as hard puzzle to the reader.

Thank you for reading and please give me feedback. 
Hopefully a paper, concerning this research is soon completed.

Sonntag, 6. November 2016

Dip Day 792 in Detail

Calculation of Dip 792d with Star lifting

This post is the second part of the calculations to understand the shape of the dip at day 792 of Boyajian's star (KIC 8462852). For part one visit post: "Do we see Star lifting".

The Beam is Bent

The Dip day 792 is not symmetrical, therefore we have to introduce a beam, that is not perfect on a straight line from the center of the star. it is not difficult, to find reasons why the beam of matter is bent in a direction. A simple reason my be kepler dynamics during departure from the surface. 
As long as we don't understand the process in detail, I will again start with a simple model and try to fit the model with the data.
Figure 1 describes the new model of the beam. The beam starts at a the surface of the star, and with height H it starts to have a optical density due to reduced temperature and therefore is no longer ionized.  

Fig 1: Properties of the physical model.

The beam is now modeled with small fractions of the length ds which are distorted against the direction angle depending on the distance l. At the end of the beam, the "smoke" comes to a rest and is distributed in this orbit by an exponential law, the density is maximal at the beam end and decays with distance in the bending direction, .
For the simulation, the beam contains 105 elements. Each represents a beam length of 5 star radii, The first 5 star radii (first element in the simulation) are transparent due to high temperature near the star surface.
Each simulated beam element has a transparency of 0,9984722. Each element is a little bit bent by
ap = -0,3971 day.
If a element is within the line of sight between Kepler and KIC 8462852, the resulting transparency is calculated by the multiplication of the transparency of every element.
At the end of the beam, the material enters an orbit, for some reason, and is accumulated. The optical density of the accumulated material decays by an exponential function d = d0 exp(a*w) thereby d0 = 0,001588, w = 3,30025 [1/day]. (The unit hour is used and could be converted in an angle if the distance and rotation period would be known). The value of the simulation was always averaged over 2.5h to adapt a little bit the shape of the unknown optical elements.
The result of this simple physical simulation is shown in fig 2:


Fig 2: Measured and simulated flux using the model
The model, containing only simple and plausible parameters fits within the limits of the Kepler data precision. The value of the free parameters, namely bending, optical density and the exponential function, were optimized manually.

I did not expect a result with such a low error.

There are some aspects not included in the simulation: exact cross section of the beam, surface flux of the star (it was assumed to be constant).

Other posts related to Tabbys Star

Dips part two
A simple model of Dip 792


Dienstag, 1. November 2016

Do we see Star lifting

The Try of an Explanation of the Dip at day 792

In the last time there has been the suggestion, that the very strange dip around day 792 might be the signature of star lifting. A reasonable explanation of star lifting can be found at wikipedia.

Fig 1: The dip at day 792 has a very interesting homogenous shape.

The basic Idea is, that a super civilisation is able to harvest matter from the local star by magnetic or other means. This is quite difficult, due to the high temperature at the surface of the star. Therefore a beam of matter, similar to a natural solar solar flare has to be produced. I don't go into the technical details how or if this is possible, but I try to simulate the visible lightcurve of such an activity. 

Fig 2: Natural solar flare at our Sun.

The most simple model

(A more complex model is described here "Dip 792 in Detail")
To generate the situation, we start with a very simple model. A long beam from the star points radially away from the center of the star. by accident, we are in the line of sight and see the beam crossing the star.
Fig 3: Simple model, a beam of matter, pointing away from the star.

To describe this model, we assume, that the beam is rotating around the star and a fraction of the beam absorbs the starlight on our line of sight.
The amount of dimming is then a function depending on geometric factors and the rotation angle as shown in the fig 4 viewing the situation from the rotation axis of the system. 

Fig 4: Geometric situation, Kepler looks from the right side to the star with center C.

The star has a radius of r and the center is marked by C, a beam with a optical density d, at the surface of the star starts at point A and ends at point D. The dimming is proportional to the length, of the distance |AB|, because only this part of the beam covers our line of sight. We can calculate the distance CB, depending on the angle a, it is

|CB| = r/sine(a)

len(AB) = r/sine(a) - r  (1)

The angle a is depending on the time t, and the angular velocity w, by which the beam rotates around the star like a hand at a clock. 
It is convenient to set the time t to zero, when a = 0. To suppress the infinite length of AB at a = 0, we have to take into account, that the beam is not infinite, but has the length AD. The equation (1) holds therefore only as long as the beam does not cross the sightline BE. This happens at the angle 

ac = arcsine( r / |CD| )

ac = arcsine( r / ( |AD| + r ))  (2)

The measured flux f(t) is then calculated, assuming f0 is the brightness of the star, by

f(t) = f0 - d ( r / sine( w t ) - r)   in the case {||wt|| > ac}

f(t) = f0 - d |AD|   in the case  {||wt|| < ac}   (3)

Let's have a look at our dip at day 792:

Fig 5: Very simple model of star lifting. (Sorry, for some reason this image is flipped in time)
Although we have used the most simple model, the left part of the graph is astonishingly similar to the measured dip. The parameters used for equation (3) are d = 0.16, f0 = 1, r = 1, w = 0,14 [1/30min].

An inhomogen absorbing beam

A further approximation to the real situation can start with the optical density of the beam. At the surface of the star, the beam has the same temperature as the sun surface and will not absorb any light. By leaving the surface the beam cools down and the atoms might absorb light by ionisation. Again, I try a very simple model, the temperature is then depending from the visible surface of the sun, depending on the height. 
My geometric model is plotted in fig 6.
Fig 6: Temperature of the beam as a function of height |AB|

At the point B the beam has a height above the star of |AB|=h. The visible angle a is therefore given by the geometric relation in the rectangular triangle BCD.

|AB| + r = |BC| 
and
sin(a)=r/|BC|

sin(a)=r/(|AB| + r)

a = arcsine(r/(h + r))   (4)

The visible cone P is therefore relative to the 2 pi surface situation

P = 2 pi sin(a) /2 pi

P = (r/(h+r))   (5)

A plot of this function is shown in fig 7.

Fig 7: Showing the surface of the star, a beam sees at a distance from the star

To keep things simple, we define a height, where the reionization happens. The function in fig 7 drops fast and the black body radiation is depending on the fourth power, so I guess with a height of two star radii, the beam is re ionized. 

To include this in our model, we replot a modified figure 4 in fig 8.

Fig 8: Modified beam with optical density starting at H
In the new model, the beam starts to have a optical density, starting at the point H and going up to D. Using this, we can replot the simple calculation from fig 5 again, only presenting the falling edge for better visibility:

Fig 9: The model matches the measured flux better in the first part.

Although the model is still very simple, the match between measured flux and model is now also in the first part good. Be aware, that the ionisation doesn't happen instantan and has to be modeled by a more sophisticated model the basic effect of a certain threshold seems to exist. 
The steep side of the dip is not perfect, this may be due to the inhomogen radiation density of the star, another point that a better model should include.

In the next post, I will try to model the very steep rising edge by bending the beam. 

If anyone wants to support me with efficient computer models, he is invited please drop an email heindl(a)gmail.com

Other posts related to Tabbys Star

Dips part two
A more complex model of Dip 792

Montag, 17. Oktober 2016

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/



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 what 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 PhD 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

Lets 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 happend.

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 an new thread of conspiracy, but it should be mentioned, that the moment of failure of the reaction wheel#2 in July 2014 [1] happend short after the most exiting 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.

Lets 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 then 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 manuell 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 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 manuell 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 manuell 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 dip 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 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 manuell 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 wich 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 interprete 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 manuell drawing of the shapes, Black line present linear elements, green lines are splines to fit mor 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 a interesting fingerprint. In some aspects it has a similar shape as one of the last strong dips.
Fig 11: Dip 10 d694, this is a multidip 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 manual 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 is beyond anything we have ever seen. It starts with a continuous declining line, which can be described by a very steep function like Tangens. 
Fig 13: Dip 8 at day 792 is by far the most mysterious dip
I tried hard to find a relative simple and plausibel 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 astonishing 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 a 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 a first conclusion about KIC8462852 in the next part.
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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