Dienstag, 23. Mai 2017

A deep dive into Dip 792 part II

Calculating the residual Signal

In my last post, I started to analyze Dip d792 in detail. But my work was suspended due to a very exciting new dip that has been observed in May 2017.
The first part is here A deep dive into Dip 792 part I.

Mathematical description

The remaining signal might be the result of a fog cloud, that is in an orbit around the star.

The intensity of this cloud could be calculated, if we subtract from the measured signal from Kepler the basic dip. If we choose the timing of the symmetric axis a little bit shifted, to take into account the cloud in the area of the peak of the dip, we find two very smooth exponential decays, as shown in the next graph:

The remaining signal shows two exponential growth factors.
(missing data points are marked with black dashed circle lines)

Let's look into the details of the plot:
All data are relative to the central peak in a convenient time scale t = t_k-792.740 d (Zero is at the peak of dip 792)


  • The raw dip data from Kepler are marked as black vertical x marks.
  • The assumed basic dip is presented as a black line and is the mirror of the right half of the dip, not shown in this plot, both data rows use the left linear scaling.
  • The remaining density is shown in a logarithmic scaling as shown at the right axis. The first part with very noisy data is presented as grey dots and not further processed. 
  • The middle part is presented by violett squares and can be approximated by an exponential function with a starting value of 0.022 and a growth factor of tau1 = 0.5298 per day.


This part changes obviously the direction at t = -0.633 d to a steeper growth with a growth factor of tau2 = 1.6655 per day, presented as green x marks.

Both approximations have a very high coefficient of determination, R² = 0.9809 for the first part, which has more noise and R² = 0.9953 for the second steep part.

Here comes a high zoomed plot of the second steep part:
The measured signal x marks and the calculated function as circles match in the time range -0.6d to 0.2 day within  0.1% as shown as vertical x marks in the center.
The second plot is focused to the steep function (green in the first plot) in the second part, the deviation is below 0.1% over 0.5 days.

It should be mentioned, that the ratio between the growth factors is 3.143... for whatever reason. (I think it is by pure chance, because any intelligent species would use 2 * PI = 6.28... to signal their math level).

But beside this strange coincidence, the exponential decay could have some physical reason. It might be, that dust particles stick together, brightening the "dust" in the orbit.

The two different growth factors my result from two different processes with different efficiency.

Has anyone seen something like this in a comet tail?

Thank you for your attention and give me feedback if you have any comments on this.

Montag, 22. Mai 2017

Dip in May brings Ideas away

What changed due to 2017 May Dip?


The most exciting thing of the May Dip is, that we now know for sure, the dips at KIC 8462852 are not a Kepler measurement artifact, the Dips are real.
This helps a lot, because there is nothing as frustrating as a stupid measurement. I remember the neutrino experiment in Italy, where the speed of light as defined in Einstein's theory was in doubt, only to learn a few weeks later, that a cable was not connected as proposed.

Time and timing

The next big thing is, that the timing of the dip was not unexpected. The main dips of Kepler happened at day 792 (2011/03/05) and in a time window between day 1518 and 1570, with a strange symmetric peak at day 1539. If the time between this events is in some sense the same, and I try hard not to be to specific, than we can propose a period somewhere in the range of 750 to 770 days. Assuming, that we missed a dipping event in 2015 due to the late detection of the strange star by citizen scientists, the next events should take place in the first half year of 2017

Dips during the second big dip period between d 1518 and d1570 [1]

But the new dip seems not to be a deep dip beyond 10% flux reduction. The measurement suggests only a <3% dip. 
The dip has about 98% at peak dipping. (Source: Jason Wright, Twitter)
It should be noted, there have been many dips during the four year period of the Kepler mission with dips of less than 1%, at Tabby's Star, for details see "Meditation over Tabby's Star".

The second interesting thing is the length of the new dip, it seems to last about seven days, when we assume the soft start at 16 May 2017 and the sharp end at 19 May 2017 as shown in the graph above. This timing matches the mysterious  dip of day 792 [2] very well, a dip that lasted also seven days! It is hard not to believe that this is not a coincidence.

Superposition of dip d792 and the May 2017 dip. Be aware of the scaling and sorry for the poor design.
As long as we don't register a stronger peak we can hardly say anything about the internal shape. It may be, that the combination of all available results from multiple sources reduce the error bars significant. 

The spectrometric results are not public in the moment, the only information I could gather is, that there is no significant absorption line and infrared might show a lower absorption as visible light.


Which Hypothesis get stronger, which one loose?

There is a very long list of hypothesis [2] what is going on at KIC 08462852. Let me give my judgement, what has changed at the state of our knowledge today (22 May 2017):

  • A object in our local solar system: This seems not to be the case, given the periodicity of 2 years and the knowledge of our solar system. Hypothesis gone!
  • A cloud in the interstellar medium (ISM) in between us and the star. Due to repeated measurement of the signal very low possibility.  Hypothesis not worth to mention any more!
  • Black hole, Hypothesis gone!
  • Comets: This is a tricky one, there are no new supports to a comet, but an other observation should here be mentioned: Beside the new dip event, it seems, that the star is still under a global dimming regime as observed by large telescopes. This could hardly be explained by comets. Hypothesis very low chance!
  • Planet collision: The big question is, where is the infrared signal! Hypothesis very low chance!
  • Star is changing its behavior: We have no model, how a star of that size and age could do that, in addition, the new dip does not support this hypothesis. Hypothesis gone!
Remaining: 
  • Something we have not thought about
  • Very special thin dust cloud (ring structure) interacting with a magnetic field
  • Large scale Dyson structure of unknown shape (not very good matching the data)
  • Star lifting by natural or artificial cause (My favorite)
Star Lifting: Eduard Heindl, A physically inspired model of Dip d792 and d1519 of the Kepler light curve seen at KIC8462852, 2016, https://arxiv.org/abs/1611.08368

Comments?

I am very happy, if you comment on my ideas.

References
[1] Gary D. Sacco, https://www.reddit.com/r/KIC8462852/comments/56kdfw/95_day_abnormal_equilibrium_of_periodicity_and/
[2] Jason T. Wright, Families of Plausible Solutions to the Puzzle of Boyajian's Star
    https://arxiv.org/abs/1609.03505
[3] Eduard Heindl, Blogpost 2017, Dip 792 http://some-science.blogspot.de/2017/05/dip-792-at-boyajian-star-kic-8462852.html


Freitag, 19. Mai 2017

Dip 792 at Boyajian Star KIC 8462852 revisited

A deep dive into Dip 792 (part I)

The dip 792 of the most mysterious star in the galaxy has a very regular shape and is different from all other signals seen in the Kepler mission. (If new, find an introduction at Dips in Tabby's Star)
The famous Dip of Day 792 at Boyajian Star (Data-Source: NASA Kepler Mission)

What makes the Dip so unique?

The first thing is, this dip is very deep, about 15% of the light of the star is invisible to the telescope during the peak of the dip. This is a very high number, when we compare that to a transit of a Jupiter like planet, which would absorb about 1% of the starlight and when we remember, that Jupiter is near to the maximum size of a planet.

The second thing is the shape, it is definitely not the shape of a planet, as has been shown by Ksanfomality [2], The asymmetric structure does not match with a high eccentric planet due to timing and absorption. The same is true for comets, the density of a comet and the homogeneity of the dip is not something we expect to see by well known comets analysed in our solar system.

The third mystery is the obvious smoothness of the dip, this is only possible, if a relatively simple shape or process is the cause of the dip. we should be very happy to have this dip 792 near the other much more complex and hard to understand dips later in the Kepler mission survey. If we understand D792, we might be able to take the hints to comprehend the other dips.

The fourth mystery is the total time of the dip, that is about 8 days. No massive object, even another star, would occlude this star for so long.

Analysing the shape

In this post, I do not try to give a possible explanation of the shape as done before [3][4], but I look into the characteristics of the shape.

End and Start of the Dip

The first tricky thing is, to determine the length of the event. The end of the event seems to be easy to determine using a graphical extrapolation. If we look in a high resolution plot of the data we find, that the dip ends at day 794.85. The uncertainty is within an hour or a few measurement points (0.5h).
Dip 792 end at day 794,85 within a well defined uncertainty of a few measurement points.

The begin of the dip is much harder to define, due to the very smooth beginning of the dropping light intensity. It seems so, that the density of the absorbing object is fading away with no sharp border as seen in the high resolution image, be aware of the slightly wider time scale.
Dip 792 starts with a very smooth slope of the signal at day 787.

We might get a better understanding of this shape when we assume an exponential decay as shown later in this post.

Missing Datapoints

A look into the measured brightness at the recovering brightness at Day 792 shows a lot of missing data points. This is more an instrumental issue, but it should be mentioned. For further calculations, the missing data points were substituted by calculated values, using a linear interpolation of the value of the points before and after the gap.
Missing data points were calculated by linear interpolation using the two data points at the border of the gap.
The steepness of the curve at the most dramatic part is 0.5%, that compares to a Jupiter sized object, that is leaving the solar disc within one hour. 


Symmetric Dip?

The shape of the dip is not symmetric, but what, if we assume, there are two parts, one symmetric event (basic dip) and another part (fading part) which is adding to the symmetric part and resulting in the visible dip? 

This calculation can be done, if we assume, that the first part of the basic dip has the same shape as the second part. The second part is well known and the only thing is, to generate a mirror picture with a meaningful axis. To generate an easy to read mirror image, the missing data points during the measurement of Kepler were substituted by a linear interpolation of the available border points of the gap, in most cases, only one point was missing, resulting in a minor error.

The result is visible in the next plot, where both plots are visible. Blue is the original time series, red is the same graph, mirrored at the axis at the time point 792.73d. 

The symmetric assumption of the dip 792.

We can now syntesis the basic dip and the fading part. First look at the basic dip:
The basic dip is a artificial constructed dip using symmetric assumptions.
The basic dip has now a defined start and end, using the point of symmetry, 792.73d, and the value found for the end of the dip at 794.85d. We define with this information:
Start of basic dip: t1 = 790.61d
Maximum: ts = 792.73d
End of basic dip: t2 = 794.85d
Duration: T =  4,24d

Further analysis of this shape might be interesting, but is not part of this post, may be I will discuss this in another post.

The remaining Signal

Very interesting is now the question, what happens to the remaining signal. The remaining signal, calculated by subtracting the basic dip from the measured value, is shown in the next plot:

The remaining fading part, if we subtract the artificial basic dip from the measured data. 
The fading part seems to have an exponential character. This should be analysed further.
The best way to see the exponential character is, to plot the data in a logarithmic scaling in the absorption axis. 


To optimize the result, the data before day 791 are reduced in noise, by not subtracting the symmetric signal but  by using a constant baseline with the value one. Otherwise, meaningless noise and fluctuations from the baseline beyond the basic dip would appear.


Log-plot of the absorption in the remaining signal after subtraction of basic dip.
Different colors mark different slopes.
The log-plot shows at least four different areas. At the left part, there is a lot of noise and a relative steep slope. The blue squares mark an area with constant slope, the exponential factor is 0.46 1/day. Around day 92 the slope increases significant to a higher value of 1.32 1/day. The last points at day 792.55 and following, don't show any pattern and may result from a remaining error concerning the unknown exact shape of the basic dip.

Here comes the second part.


2017 May 19: We have a new dip, I publish this, and wait for new results.

Live: https://youtu.be/eYpIGZS8nJc