In a prior posting, we “put some bounds” on the Nemisis thesis (that there is a small dark ‘companion star’ to the sun). In this posting, we will be looking at bounding the question of “does precession of the equinoxes mean we orbit Nemisis?”. So first we looked at “how complicated is this problem and what else is going on?”. Now we’re looking at “Ignoring all that, if there WERE a Nemisis, how big and how far?”. Then “Is that reasonable to be unfound?”
One part of the “Dark Passenger” idea is that the object is dark. It needs to be dark so that we don’t have an obvious large bright star just a tiny bit of a light year away. Kind of hard to not see that…
So looking at the Brown Dwarf wiki, we find they are bounded by 80 Jupiter Masses ( Mj) at the upper end, and an ill defined lower bound, but somewhat near 10 Mj. As the “orbital calculator” I found online uses Solar Masses (Ms) we need to convert those. Mj is about 0.0009546 Ms, so those become LB: 0.009546 Ms and UB: 0.076368 Ms.
At this orbital calculator:
I made the simplifying assumption that if we are ‘swinging’ in an orbit with the object, that both will have the same period. (Something of a tautology for a 2 body system, but in fact, as we have an N-body neighborhood, it’s really a bit more complicated. But I think most of that ‘ends up in the noise’ of 4th to 20th digits of precision and can be ignored for a ‘first cut’). Realistically, we ought to be using a 2 body mutually orbiting formula. Then again, at 1/100ths place relative mass, it isnt’ really all THAT wrong to assume the sun in the center).
OK, plug in the Ms numbers, make the AU distance some random thing, then look at the orbital period and “fiddle with” the AU distance until you get about 24,000 to 25,000 year period. That’s about how far away an object can be and still be causing us to orbit with it, with that period, and be small enough to not be bright in our field of view while still being big enough for us to notice a bit of a tug.
Lower Bound: 24,717 year orbit. 180 Astronomical Units. 0.009546 Solar Masses
Upper Bound: 24,204 year orbit. 355 Astronomical Units. 0.076368 Solar Masses
Just for fun, I put in a 1/10 solar mass. Yes, it ought to be glowing. But say someone didn’t measure EVERY star and just thought it was further away? Where would it have to be?
1/10 Solar: 25,298 year orbit. 400 AU. 0.1 Solar Masses
Not surprisingly, not that far off from a 1/10 x 3/4 upper bound to a Brown Dwarf. Surprisingly, very close.
OK, so it doesn’t move much further out as you bump the mass. How about a 1/4 solar mass?
1/4 Solar: 25,797 year orbit. 550 AU. 0.25 Solar Masses
At that point we’ve pretty much bounded it.
A 1/4 Solar Mass object is going to be glowing fairly strongly. “We’d notice”. Even a 1/10 Solar Mass object we would most likely have seen by now. (It’s kind of hard to not notice a star, even a dim one, at 400 AU).
How Far Is That?
The Kuiper Belt runs out to about 55 AU (Neptune is at 30 AU). So about 3 to 10 times the Kuiper Belt. Since we are finding planet sized things in the Kuiper Belt, and they are pretty dark, that implies we could see a “dark star” too, though with difficulty and most likely only in infrared.
The Oort Cloud picks up somewhere beyond that and runs out to about 50,000 AU (or nearly a light year, per the wiki). As we saw in the prior posting, the Hill Sphere of the sun is what matters for who orbits whom, and it runs out to about a light year for small objects.
So this places any such “dark star” as clearly INSIDE the Oort Cloud. And at about 1% of the distance to the outer edge (or 99% of the way IN from the outer edge). This ought to do a heck of a lot of perturbation of both the Kuiper Belt and the Oort cloud. Again, “I think we’d notice”. For this to work, we need a pretty good sized “gap” between Kuiper Belt Objects and the inner edge of the Oort Cloud. Then again, per the wiki, the Oort Cloud is: “is a hypothesized spherical cloud of comets”. So there really isn’t any problem hypothesizing it to be whatever we need it to be.
Or just outside all of this stuff in the Kuiper Belt (about 3 x or near the far edge of the calendar on my screen):
The green bits are KBOs.
Now, one bit of “finesse”. As you get to about the size of Brown Dwarfs, mass rises but radius holds more or less constant. We reach a realm where added “stuff” gets crushed by gravity enough to not add much radius but rather to increase density. So a “just smaller than brown dwarf” object, that did NOT glow in the Infrared, might well be “out there” and not visible easily. After all, something the size of Jupiter but several times more massive could still be pretty small in the visual field and it would be dark, even in the infrared (assuming it didn’t generate it’s own heat as Jupiter does…)
So how small and far a dark object can we see in the night sky “out there”?
2000 CR105 and Sedna
(148209) 2000 CR105,[…]is currently about the seventh most distant known object in the solar system. Considered a detached object, it circles the sun in a highly eccentric orbit every 3240 years at an average distance of 219 astronomical units (AU).
2000 CR105 has a diameter of around 253 km. This small size will probably prevent it from ever qualifying as a dwarf planet.
2000 CR105 and Sedna differ from other scattered disc objects in that at their perihelion distances, they are not within the gravitational influence of the planet Neptune. It is something of a mystery how these objects came to be in their current far-flung orbits. Several hypotheses have been put forward:
They were pulled from their original positions by a passing star.
They were pulled from their original positions by a very distant and as-yet-undiscovered (albeit unlikely) giant planet.
They were pulled from their original positions by an as-yet-undiscovered companion star orbiting the Sun. (See: Nemesis (star).)
They were captured from another planetary system during a close encounter early in the Sun’s history. According to Kenyon and Bromley, there is a 15% probability that a star like the Sun had an early close encounter, and a 1% probability that outer planetary exchanges would have happened. 2000 CR105 is 2–3 times more likely to be a captured planetary object than Sedna.
So here we have an object that is vastly smaller than Jupiter (at 71,492 km radius) and much further away, yet we can see it. The orbit ranges from 44 AU to 394 AU, so it’s “in the neighborhood” of any “Dark Passenger” that would be in the inner 1% of the Oort Cloud. It would need to be in some sort of “resonance” orbit to avoid being tossed out of the system (or into the inner parts). Dividing 25,787 (one of the estimates of the precession interval) by the orbital period of 3240.91 gives 7.949927644 which looks to me to be inside the error band of an 8:1 orbital resonance. OK, that argues for a “possible”.
Puts Sedna at 76 AU closest and 960 AU furthest orbit distances. With an 11,809 year orbital period (which, at 2.1818 is close to a 2:1 resonance so it could still “work”, but things are getting more complicated). At about 1500 km in diameter, it’s pretty small compared to a “Brown Dwarf”, yet we found it. So we are able to find things of about the aparent magnetude of our “Dark Passenger” (assuming that something of similar brightness, but 100 times greater diameter, and 100 times further away, would have about the same brightness; which ignores the inverse square light loss, but we’re ignoring so much already ;-)
OK, at this point it’s looking to me like any Brown Dwarf would have been spotted as they are certainly large enough and glow enough in the infra red that we ought to have noticed them at the inner edge of the Oort Cloud location. At the same time, an object just smaller than a Brown Dwarf might go un-noticed as we’ve not scanned the whole sky in fine enough detail and, frankly, once you are at “Jupiter diameter” but 1000 AU away, it will be very hard to see as it’s pretty dark out there. You are looking for a planet illuminated by “starlight” as the sun is just another star (albeit a bright one) in the sky at that distance. Darned Hard.
But I’d not call such an object a “Dark Star”, more of a “Big Cold Planet”.
In the Sedna wiki it also states:
It has been suggested that Sedna’s orbit is the result of influence by a large binary companion to the Sun, thousands of AU distant. One such hypothetical companion is Nemesis, a dim companion to the Sun which has been proposed to be responsible for the supposed periodicity of mass extinctions on Earth from cometary impacts, the lunar impact record, and the common orbital elements of a number of long period comets. However, to date, no direct evidence of Nemesis has been found. John J. Matese and Daniel P. Whitmire, longtime proponents of the possibility of a wide binary companion to the Sun, have suggested that an object of five times the mass of Jupiter lying at roughly 7850 AU from the Sun could produce a body in Sedna’s orbit
But as we’ve seen, for Nemesis to also account for the Precession, it would need to be so close we’d likely have seen it as “it glows”. So we’ve ended up at the “Dark Passenger” planet as the only thing likely. And that is the same thing suggested at the end of that wiki article. A 5 Mj giant planet at 7850 AU. But does that “work” in our orbital calculator?
5 Mj is 0.004773 Ms. Plugging that in with 7850 AU gives an orbital period of 10,067,232 years. Ooops. Not going to work… Put it at 150 AU and you get 26591 as the orbital period.
So we seem to be at a conundrum. If you make the proposed object big enough to account for the “action” while far away, it’s rather large and ought to be visible (a Brown Dwarf or other object glowing in the visible or infrared). As you move it further away, it must get larger and even more self luminous. As you bring it closer (so smaller and not self luminous) you must be inside a range that has much smaller objects already discovered (it must be an object larger than those we have already found by a couple of orders of magnetude). To be both dark, and accounting for the orbit of Sedna, it must be way too far away to account for precession.
At this point, we’re back into the N-body problem. It’s always possible that the object has a very eccentric orbit, so only sometimes does it come close enough to cause precession effects and / or disturb KBOs or eccentrics like Sedna.
But for that to hold, we can’t have much “stuff” left in the Oort Cloud. Such an eccentric orbit would have a very large (multiple Jupiters) sized object scouring the Oort Cloud turf with a hill Sphere of giant proportions. It would have captured or disrupted anything out there some long time ago. Even then, for our present precession to be accounted for by it, it would presently have to be at about the calculated distances. We’re back in the “size / visibility” conundrum again, but only for “now” as “later” it could be “far far away” at 50,000 AU.
In the end, it all comes down to: What are the odds that an object roughly the diameter of Jupiter, but not glowing in the IR band much or at all, and with about 5 Jupiter Masses, could be on a very elipitical orbit (so Sedna could have it’s orbit work out as a resonance) and yet be near enough at the moment to account for our precession (or about 150 AU) and remain unobserved?
I’d make that “very low”, but clearly non-zero. At 2 x the Sedna distance but 100 times the Sedna diameter, it ought to be visible. But we might just not have looked in the right place, at the right time, with the right spectrum to have noticed it.
To go beyond this point will take more compute facilities and more time looking at more “odd cases” than I can manage to do. It requires solving an N-body problem for at least 2 large objects “in the area” with the proposed “Dark Passenger” along with the central solar system as a body and D.P. itself. That’s at least a 4 body problem even with simplifications like lumping everything inside the Kuiper Belt into one object. But my sense of it is that it’s highly unlikely to “work out”.
Though if we find one it would be “way cool” as it implies the Oort Cloud has been given a good scouring over the last few billion years. Perhaps that is where the 4+ Billion year ago “cometary bombardment” came from…
IMHO, much more likely would be some collection of other explanations. Some collection of objects in the inner Oort Cloud orbital area accounting for Sedna’s orbit. The combined gravitational vectors of all the OTHER Brown Dwarfs et. al. inside a 5 light year area of Sol creating a “local stars barycenter” about which the solar system orbits on a 25,000 year period (but with instabilities as various stars leave our local group). Then you can have your mass, but keep it dark enough and far enough away to be effectively invisible. Could we really see 10 Brown Dwarfs that were at the lower bound (so about 700 C) and a light year or so away? It would be very hard.
So far we’ve found only a couple, and they tend to be orbiting other things (that would make finding them easier) or somewhat brighter:
The rare object is only 12.7 light years from Earth, circling a primary star that itself was discovered only recently in the southern hemisphere constellation Pavo (the Peacock).
Only one other brown dwarf system has been found closer to Earth, and it’s only marginally closer.
The primary star is only one-tenth the mass of our sun. This is the first time astronomers have found a cool brown dwarf companion to such a low-mass star. Until now, none has been found orbiting stars less than half the mass of our sun.
The brown dwarf is 4.5 AU from the star, or four and one-half times farther from its star than Earth is from our sun. Astronomers estimate that the brown dwarf is between nine and 65 times as massive as Jupiter.
Brown dwarfs are neither planets nor stars. They are dozens of times more massive than our solar system’s largest planet, Jupiter, but too small to be self-powered by hydrogen fusion like stars.
Only about 30 similarly cool brown dwarfs have been found anywhere in the sky, and only about 10 have been discovered orbiting stars.
“Besides being extremely close to Earth and in orbit around a very low-mass star, this object is a ‘T dwarf ‘ – a very cool brown dwarf with a temperature of about 750 degrees Celsius (1,382 degrees Fahrenheit),” said Beth Biller, a graduate student at The University of Arizona.
“It is also likely the brightest known object of its temperature because it is so close,” Biller said. “And it’s a rare example of a brown dwarf companion within 10 astronomical units of its primary star.”
“What’s really exciting about this is that we found the brown dwarf around one of the 25 stellar systems nearest to the sun,” Close said. “Most of these nearby stars have been known for decades, and only just recently a handful of new objects have been found in our local neighborhood.”
Close helped develop the special adaptive optics camera, the NACO Simultaneous Differential Imager(SDI), that the team used to image the brown dwarf. The camera is used on ESO’s Very Large Telescope (VLT) in Chile. Another SDI camera is used at the 6.5-meter MMT Observatory on Mount Hopkins, Ariz.
The discovery of this brown dwarf suggests there may be more cool brown dwarfs in binary systems than single brown dwarfs floating free in the solar neighborhood, Close said. A “binary system” is where a brown dwarf revolves around a star or another brown dwarf.
Astronomers now have found five cool brown dwarfs in binary systems but only two single, isolated cool brown dwarfs within 20 light years of the sun, Close noted. They can expect to find more T dwarf companions in some newly found stellar systems within 33 light years of our solar system, he added.
The NACO Simultaneous Differential Imager(SDI) uses adaptive optics to remove the blurring effects of Earth’s atmosphere to produce extremely sharp images. The camera enhances the ability of the VLT to detect faint companions that would otherwise be lost in the glare of their primary stars.
So if we’re seeing these guys at 12 light years away, with stars or alone, it seems very unlikely that we’d miss one at under 1 light year. Possible, yes, as it’s easier to spot one thing where you are looking than to have looked everywhere. Since these are relatively new tools, the odds that we’ve done a full scan of the night sky is pretty slim. It will all come down to “how many wide scan instruments of this sort are in use and how much of the sky have they looked at?”. That is specialized information I don’t have.
Given all that, my conclusion has to remain:
It’s not highly likely, but it’s a distinct possible. We don’t know, and we can’t know until a long inventory of the sky is completed. Whatever it might be, it would need to be small diameter and dark, and that limits the placement in the sky to ‘fairly close’, and that reduces the odds that we’ve “missed it” and increases the odds that “it just isn’t there”. It would need to be at the inner edge of the Oort cloud and that implies a fairly empty Oort cloud.