[math-fun] possible explanation for KIC 8462852
To T.Boyajian & J. Wright 15 Oct 2015 I have a possibly stupid and possibly correct explanation for KIC 8462852. (If the former, you likely can rapidly recognize that.) See, it would be handy to explain it, if there were big dense clouds of asteroids, sometimes occluding the star. But it seems a priori nutty for a suitable cloud to be able to exist, and stably enough that it still is here. But actually: two such clouds, called the TROJAN ASTEROIDS, do exist in our solar system, 60 degrees ahead and 60 degrees behind, Jupiter. And they are stable enough to still be here over 4 billion years later. And our trojan "clouds" are physically very large in diameter, I think easily larger than the sun. No problem about that. But our trojans produce only a tiny occlusion effect on our sun as viewed by some suitable extrasolar observer. KIC's would have to be a much more severe occulder. So postulate KIC 8462852 contains 1 (or perhaps more) jupiter-analogues orbiting it -- which might be massive planets, perhaps more compact than jupiter and more massive. Whatever parameters are needed to make it work. Or perhaps they might even be a cold neutron star or white dwarf, not a "planet." The question of whether those jupiter-analogues exist could be addressed by more observation including doppler wobble observations, incidentally. Have any been done? The jupiter(s) (my hypothesis would guess) are herding clouds of trojans, with much more surface area than our solar system's trojan clouds, hence capable of much more occluding. But having enough random motions and/or low enough mass so these clouds stay clouds, not condensing into new planets. (There are stability demands, known since Routh, about systems of this type which force the clouds of trojans each to have much less mass than the star and the jupiter, anything below 1% should suffice.) So, that's about it. Oh, of course, if this turns out to be a good candidate, it has to be named the "trojan horse." -- Warren D. Smith (PhD) http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
Hi, Please see section 4 of this paper http://arxiv.org/pdf/1509.03622.pdf <http://arxiv.org/pdf/1509.03622.pdf> Thanks for your interest, Tabetha
On Oct 16, 2015, at 1:40 AM, Warren D Smith <warren.wds@gmail.com> wrote:
To T.Boyajian & J. Wright 15 Oct 2015
I have a possibly stupid and possibly correct explanation for KIC 8462852. (If the former, you likely can rapidly recognize that.)
See, it would be handy to explain it, if there were big dense clouds of asteroids, sometimes occluding the star. But it seems a priori nutty for a suitable cloud to be able to exist, and stably enough that it still is here.
But actually: two such clouds, called the TROJAN ASTEROIDS, do exist in our solar system, 60 degrees ahead and 60 degrees behind, Jupiter. And they are stable enough to still be here over 4 billion years later. And our trojan "clouds" are physically very large in diameter, I think easily larger than the sun. No problem about that. But our trojans produce only a tiny occlusion effect on our sun as viewed by some suitable extrasolar observer. KIC's would have to be a much more severe occulder.
So postulate KIC 8462852 contains 1 (or perhaps more) jupiter-analogues orbiting it -- which might be massive planets, perhaps more compact than jupiter and more massive. Whatever parameters are needed to make it work. Or perhaps they might even be a cold neutron star or white dwarf, not a "planet." The question of whether those jupiter-analogues exist could be addressed by more observation including doppler wobble observations, incidentally. Have any been done?
The jupiter(s) (my hypothesis would guess) are herding clouds of trojans, with much more surface area than our solar system's trojan clouds, hence capable of much more occluding. But having enough random motions and/or low enough mass so these clouds stay clouds, not condensing into new planets. (There are stability demands, known since Routh, about systems of this type which force the clouds of trojans each to have much less mass than the star and the jupiter, anything below 1% should suffice.)
So, that's about it. Oh, of course, if this turns out to be a good candidate, it has to be named the "trojan horse."
-- Warren D. Smith (PhD) https://urldefense.proofpoint.com/v2/url?u=http-3A__RangeVoting.org&d=AwIBaQ... <-- add your endorsement (by clicking "endorse" as 1st step)
On 10/16/15, Tabetha Boyajian <tabetha.boyajian@yale.edu> wrote:
Hi,
Please see section 4 of this paper http://arxiv.org/pdf/1509.03622.pdf <http://arxiv.org/pdf/1509.03622.pdf>
Thanks for your interest,
Tabetha
--if you are trying to imply that sec 4 of that paper already examined my hypothesis, the answer is "no, it didn't." The word "trojan" occurs nowhere in that paper. That right there proves my hypothesis is new to you. Sec 4.4 does consider dust clouds (then the lack of infrared excess is claimed to argue against that explanation). But clouds not of "dust" but rather of "asteroids" (or "comets" -- the two are for my purposes the same; perhaps also "pebbles") are what I am proposing, thereby bypassing the IR objection. Why should there BE a cloud of asteroids? Sec 4 has no good reason such a cloud should exist and persist, but does mutter about temporary "aftermaths" in 4.4.2 and 4.4.3, which would seem inherently temporary and unstable and therefore unlikely, as well as argued against due to the IR excess lack, as well as unsupported by any discovery ever of any occurrence of this (far as I saw cited, anyhow?). Meanwhile my hypothesis does provide a reason why such a cloud of asteroids should be, and it is supported by experimental evidence in the sense that in our solar system, the trojans really are a localized cloud of over 6000 asteroids, they really did form, and they really did persist for gigayears, they really still are here. Our solar system's trojans seem capable of doing everything needed to explain KIC 8462852, except that (1) we need greater occlusion, so have to propose the same idea but bigger (2) perhaps your data (e.g. occlusion timings) can be used to see the trojan idea is wrong. Well, to do some actual arithmetic, let's say our solar system's trojans in total mass equalled Mars, but split into 6000 equal pieces. Their surface area would then be that of Mars times cuberoot(6000)=18. This is clearly inadequate to produce the occlusion levels you observed, but it is not peanuts -- this is approximately equal to the surface area of the planet jupiter. So our solar's trojans if they lay in a ball of the same size as our sun would produce about the same occlusion jupiter produces, i.e. 1% dimming of the sun. It does not seem impossible that in some other solar system, there could be an factor 20 more Trojans measured by surface area, thus being entirely capable of causing 20% dim of their sun. The question is: (a) is this really possible, and (b) with those trojans in a pretty small-diameter cloud (about the size of their star in diameter... or more but then with still more surface required). That is not obvious. Little is known about how our solar systems trojans formed, or about how they could form in general, so I doubt this is understood, which means you cannot refute me without considerable effort. Re (2) you'd have to actually look at the data. You can't just refute me in 1 sentence without doing so. Note there are TWO not 1 cloud of trojans in our solar system, and if we had more than 1 jupiter analogue then still more could be possible, so some fairly complex timing behavior would be possible under my hypothesis... but certainly most timing behaviors would be incompatible with the hypothesis, so it should be quite falsifiable, at least if enough observational data were got and enough computing done. But, if so, that falsification might not be a trivial matter. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
Correction to the arithmetic I just did: (the following is a rewrite of old paragraph that contained wrong arithmetic, sorry) Well, to do some actual arithmetic, let's say our solar system's trojans in total mass equalled Mars, but split into 6000 equal pieces. Their surface area would then be that of Mars times cuberoot(6000)=18. This is clearly inadequate to produce the occlusion levels you observed, but it is not peanuts -- this is approximately equal to the 1/20 of the surface area of the planet jupiter. So our solar's trojans if they lay in a ball of the same size as our sun would produce about 1/20 the occultation jupiter produces. Jupiter produces 1% dimming of the sun. It does not seem impossible that in some other solar system, there could be an factor 400 more Trojans measured by surface area, for example from 20 times the total mass, and the splitting is into pieces with 20 times smaller radius, and 20*20=400. The result would be entirely capable of causing 20% dim of their sun, but without any dust needed. [Numbers I used: radius mars = 3386 radius jupiter = 69173 radius sun = 695500 km.] -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
You can learn more about trojans from https://en.wikipedia.org/wiki/Jupiter_trojan It says there are over 6000 named, BUT it also says that the total number of jupiter trojans over 1 km in diameter is believed to be "over 1 million." Also, trojan clouds exist not only for Jupiter, but also for Neptune (13 named examples) and Mars (7) -- so just in case you were doubting that multiple Jupiters could coexist all herding their own trojan clouds and all staying stably around for gigayears... don't.
I'm aware of trojans, and I have certainly discussed this possibility with colleagues. I apologize, I thought we had included the Trojans hypothesis in the paper, but you are right, we did not mention it. If all of the Trojans you mentioned were somehow in a swarm tight enough to produce one of the dips in the curve, they would have low mutual velocity, and tend to self-gravitate into planet. It's possible that the 1:1 resonance with the larger body would preclude this, but the swarm would still experience collisions over the life of the star and grind itself up into dust. So given the age of the star, this is an unlikely solution, but it's a good idea to keep thinking about. Jason On Fri, Oct 16, 2015 at 10:44 AM Warren D Smith <warren.wds@gmail.com> wrote:
You can learn more about trojans from https://en.wikipedia.org/wiki/Jupiter_trojan It says there are over 6000 named, BUT it also says that the total number of jupiter trojans over 1 km in diameter is believed to be "over 1 million."
Also, trojan clouds exist not only for Jupiter, but also for Neptune (13 named examples) and Mars (7) -- so just in case you were doubting that multiple Jupiters could coexist all herding their own trojan clouds and all staying stably around for gigayears... don't.
On 10/16/15, Jason Wright <jtw13@psu.edu> wrote:
I'm aware of trojans, and I have certainly discussed this possibility with colleagues.
I apologize, I thought we had included the Trojans hypothesis in the paper, but you are right, we did not mention it.
If all of the Trojans you mentioned were somehow in a swarm tight enough to produce one of the dips in the curve, they would have low mutual velocity, and tend to self-gravitate into planet.
--well, maybe. You are not dong a calculation here, just intuiting. It may be mathematically possible for said swarm of pebbles never to collide and just stay with the same "low mutual velocities" forever. I don't see how this can be disproven as a matter of mathematics.
It's possible that the 1:1 resonance with the larger body would preclude this, but the swarm would still experience collisions over the life of the star and grind itself up into dust.
--again, calculation seems needed. The trojans in our solar system have neither ground themselves up into dust, nor gravitated into a planet, after 4 gigayears. Nobody understands how they got there, suggesting making confident assertions might be infeasible. If dust were produced, perhaps it would soon be ejected by the solar wind. If collisions occurred they might produce more small bodies, counteracting the "gravitating into a big body" trend. The fact the mutual velocities "low" might mean collisions do not have enough oomph to "grind into dust" and do not occur frequently. Etc. The calculations might not be trivial. There seems to be a pretty large parameter space to search and finding out which parts of it are ruled out by such thoughts as these, and by observations, and whether any part of said space survives, is not something you can do by waving your hands.
So given the age of the star, this is an unlikely solution, but it's a good idea to keep thinking about. Jason
--I'm sympathetic to your objections, and they might be right, but it requires calculation. Also, the papers I saw did not attempt to make numerical estimates of HOW unlikely various candidates were, which if you are comparing unlikely #1 versus unlikely #2, seems essential... For example I saw you quoted saying alien megastructures had to be regarded as the most unlikely candidate, but saw zero calculation of any likeliness number for that or main rival hypotheses. Personally, I thought the alien megastructures looked pretty likely compared to the candidates I saw listed, which is one reason I invented the trojan idea. I mean, you yourself had observation-based objections to every one of your own listed rival ideas, but the alien megastructure idea has zero objections to it (no?) which would seem to make it the MOST not least likely? I mean if we are going to base it on evidence not on prejudices...
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Warren D Smith