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

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