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Is a cosmic string playing with Tabby's star?

Aliens, you're fired: that's how Trump supporters do Tabby's science

It's almost midnight but I could have problems to sleep because of this idea that I have to record somewhere. The blog seems like a better place than my scribbling notebook now – despite the fact that the idea could be embarrassingly wrong.

Thousands of young people are excited about a cosmic superstring in the constellation Cygnus.

Let me start with this nice music called "Superstring" by "Cygnus X". I've known it for some 15 years – around 2001, I found it as one composition among several others that appeared when I inserted superstring-like keywords to music searches. ;-) If these words were a hint, what would it tell you? Yes, Cygnus is a constellation so if you look for an experimental proof of superstrings, you should look in the constellation Cygnus (swan).

OK, if you were gazing in that direction for years, you would finally find a seemingly ordinary star, Tabby's star or KIC 8462852, which is some 1480 light years away from the Earth. Its radius and mass are about 50% higher than the Sun's. This star became famous because of its strangely behaving flux. Hundreds of news outlets argue that these adjustments of the flux were caused by extraterrestrial aliens, more specifically by a Dyson swarm they built to extract the energy from their Sun.

Let me offer you a potentially equally groundbreaking but arguably less unnatural solution: a cosmic string. This very blog contains several posts about a possible discovery of a cosmic string through two nearby images of a galaxy that have seemed identical for a few years.

The two nearby images could have been identical and the doubling could have been caused by the gravitational lensing through a cosmic string.

Because of the cosmic string in between – which "attracts" the light rays thanks to its deficit angle \(\delta = GT\) or so – a part of the image is doubled, the optimistic story said. Cosmic strings are the only objects that are capable of creating identical undistorted images via gravitational lensing. The space around a cosmic string is flat almost everywhere – except at the location of the cosmic string. The spacetime looks like a cone and the deficit angle describes how much it differs from a flat plane. It was exciting for some 3 years before sharper images from the Hubble showed in 2006 that there were two similar but distinct galaxies. The cosmic string explanation of CSL-1 was dead.

But now, Tabby's star is another baffling object. Montet and Simon published a preprint about the bizarre time dependence of the flux coming from Tabby's star just a few days ago. In 3 years when it was observed by Kepler, the flux was dropping approximately linearly, by 0.9% in total. However, in half a year afterwards, the drop accelerated to 2% per 7 months. And then the fast drop stopped although some linear decrease may be continuing now.

The cloud models basically suck and one of the reasons might be that they think that the high intensity is the "normal" value – and the low intensity is obtained by some partial shielding. Well, the truth may be the other way around. The low value of the flux may be the normal one and something – the cosmic string lensing – may have been temporarily enhancing the flux simply because the cosmic string made the star temporarily wider.

This image of CSL-1 shows that the cosmic string – cutting the picture along a line so that the two red disks are on the opposite sides – could have doubled the image and therefore the flux. If the tension and the deficit angle were smaller, it could have just increased the width of the star.

Now, the radius of the star is some 3 light seconds. We need to increase its flux – and therefore width – by a few percent, so the distance by which the cosmic string shifts parts of the image should be some 0.1 light seconds. On the other hand, the distance of Tabby's star is 1480 light years which is \(5\times 10^{10}\) light seconds. The ratio is roughly \(10^{11}\) so we need a cosmic string with a deficit angle comparable to \(\delta \sim GT\sim 10^{-11}\). That's a much lower tension and deficit angle than generally expected for popular cosmic strings, \(\delta \sim 10^{-6}\), but I will look at the problems it causes tomorrow. (I do think that this lower string tension could be compatible with the unification ideas in Witten's strongly coupled heterotic strings, for example.) The location of the cosmic string that is very far from the middle of the Earth-Tabby_star segment (i.e. close to the Earth or to Tabby's star) could change the numbers.

How should the intensity be affected? The cosmic string basically adds a "strip" of the stellar disk. As the cosmic string is moving across the star, the added area basically behaves as the thickness of the disk \(y(x)\) at a given \(x\) of the star, so the graph of the flux as a function of time \(P(t)\) should basically be a positive semicircle.

On the left side and the right side from the blue semicircle, the blue semicircle should be extended by the constant horizontal axis. The cosmic string may hypothetically vibrate and add lots of complexity but I think that this simple graph should be the "zeroth approximation" of the graph for the flux from Tabby's star as a function of time – assuming that a straight cosmic string is moving uniformly and simply crossing the star. Clearly, we need Kepler's observation to start near the center of the picture – the maximum of the flux when Tabby's star was maximally widened.

The August 2016 paper contains Figure 3:

You see that they tried to describe the observations of the flux in terms of some piecewise linear function or something of the sort. Can you try to fit the observations with my semicircle graph instead? Is a semicircle (well, a semiellipse because the stretching and units are different for the two axes) continuing with the constant function afterwards a good enough fit? It's after the midnight now and I want to sleep. But I hope that when I wake up, a TRF commenter will clarify all the missing details of this stupidity and the Nobel committee won't wake me up before 7 am.

Thank you very much and good night.

Update, Wednesday, 8 am

Mathematica is efficient so within minutes, I created this best fit using the semicircle function (the Mathematica source has less than 20 commands):

It looks very good to me assuming that the datapoints (in my picture ellipses) are 1-sigma intervals.

BTW when I was sleeping, I realized that the gravitational lensing by a less exotic object than a cosmic string could possibly do a similarly good job. Well, I don't know the functions for the total flux from an object deformed by a localized gravitational lensing source so the cosmic string is the easiest case for me to calculate.

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