This announcement briefly discusses the method used to measure a recently discovered planet, 55 Cancri e. It’s all pretty fantastic, but the idea of an entire planet denser than lead triggered my “What the fu . . .” reflex. In fact, I ended up spending quite a while reconstructing the method in my mind, and on paper.
It got me to wondering if there isn’t a fairly simple source of error that would cause the results to be skewed at least somewhat toward a larger planet, with a lower density. This is my logic.
The luminosity variations of the parent star are recorded over a long period, multiple transits, and it’s occultation measured as a percentage of the total change in luminosity. This value gives you a proportional radius for the planet, compared to the star. However, given the optical geometry of the observed phenomenon, it seems to me that gravitational lensing from the planet would affect the light from the entire disk of the star, and given its very close orbit, optically reduce the effective amount of occultation by a significant factor. If that is the case, then the actual diameter of the planet is greater than the estimate which does not include that effect.
I have no where near the skill set needed to estimate how much greater the diameter would be. But, since it’s mass is calculated by an unrelated method, the difference in density would be inversely proportional to the cube of the difference in radius. It only takes a small difference in radius to bring that density down by quite a bit.
So, if I am missing the obvious, or did the imaginary math totally wrong, I would appreciate someone who does this sort of thing for a living fighting my ignorance.
Off the top of my non-expert head I don’t think gravitational lensing is strong enough to make a difference in this case… I think you need the gravity of large galaxies to see clear examples of bending light. The gravity of a star or planet might only just barely cause measurable but mostly insignificant lensing.
There’s a much simpler bias towards discovering massive planets with a close orbit. Until very recently extrasolar planets were primarily discovered by measuring the wobble in their parent stars – massive planets have a larger amplitude of wobble, and close orbits give a greater frequency. Thus our sample of known extrasolar planets is entirely composed of the heaviest extreme of all possible planets to be discovered. I’m not surprised that one of these previously discovered massive planets also happens to have extremely high densities – though having the density of lead is definitely unusual. I presume that if it’s true, it must be formed from the densest remnants of a supernova.
But those remnants have to end up somewhere, right? And with our biased searches, we’re almost guaranteed to find any massive lumps of superheavy supernova debris that orbit nearby stars.
It’s just that we have light junk on top of the core that makes the average density lower.
So why is it so hard to believe that a planet so close to a star might have the volatile light mantel boiled or scoured off, leaving only the denser core behind?
And your link says almost as dense as lead, not denser.
Not at all. One of the first tests of the General Theory of Relativity was the bending of starlight by the sun as measured during the eclipse of 1919. I’m sure we could do much better now almost 100 years later. But I suspect you’re right that there isn’t enough lensing in this case to measure.
Lensing of stars by planets can occur, leading to observable changes in brightness, but the geometry needs to be just right (which, among other issues, will only happen for extremely close objects). Eclipsing (what Kepler looks for) is much, much more common.
The scenario to form such a planet is probably over our heads. (Yes, pun intended).
One explanation for the moon’s origin is that a planetoid struck the Earth at an early stage of formation. The planetoid essentially blasted the crust off the Earth and into orbit, where much of it coalesced into the moon, explaining why the moon is so light and dry (among other things). The iron/heavier components of the planetoid merged with the Earth and sunk to the core.
If you fine-tune the variables, this model could go a long way toward increasing a planet’s density.
Of course, surface temperatures of 2700 C would also help, since you’d be melting or vaporizing so many things that we think of as solids here on Earth. Amazing collisions might be redundant.
OK, but would it be if it did not have all the other stuff pressing down on it. It is thought to be made mostly of iron and nickel, right? Surely, at surface-level pressures that mixture would not be denser than lead, and, by the same token, a more-or-less Earth-mass planet made entirely of earth’s-core stuff would not be denser than lead (although its core might be).
Unless this ‘planet’ is really something like a burned out white dwarf, consisting of neutronium or some other, similar exotic matter (in which case it would be a lot denser than lead), this seems hard to believe.
As for potential measurement errors: if the researchers did their job well, they will have assessed the sources of error and calculated the effects on the answer. Looking at the journal article itself (which, of course, doesn’t make any comparisons to lead – that’s the pop-sci writing), it seems that the planet’s mean density is found to be 10.9 +/- 3.1 g/cm[sup]3[/sup]. Since there is quite a large uncertainty on the number, making specific material comparisons (like “vs. lead”) a little silly. (Also: the paper also only reports a mean density, naturally, since only radius and mass are directly measured.)
The planet also has stuff pressing down on its core. The planet. A planet that is 60% larger than the earth and eight times as massive. Why wouldn’t an ordinary iron core become dense under those conditions?
I don’t understand why people are complicating this. A planet is formed when the gas clouds around a star coalesce. Over time the heavier elements sink to the core. The pressure of gravity increases the density. The lighter materials rise to the top. But they are vulnerable to the heat and solar wind and the other forces that exist very near a sun’s surface and are lost over time. The surface is 2700 C, which means that most light elements would be over their boiling points. This leaves only the denser metallic elements that are too far down the gravity well.
Why do you need to posit exotic materials or anything other than the same processes that formed the earth?
I really am sorry to have said “denser than”, rather than the slightly less imprecise “almost as dense as.” I would like to point out that the unquantified difference was never particularly relevant to much of anything, but it was an error, and I do freely admit making it. <Rips off his buttons, and breaks his pencil>
It is is obvious to me the planet must be denser than Earth, and it seems equally obvious that all of it’s volatile materials would be evaporated by heat, driven off by solar wind, and light pressure. I am not well enough versed to know what qualifies as volatile at 2700 degrees, but I am certain it would include a lot of the type of stuff you find in Earth’s mantle. I am relatively confident that the planet has to have a mean density far higher than Earth’s. I doubt that it requires some extreme elemental distribution to achieve that density, just plain old nickle iron would be enough, if you had a solid nickle iron sphere with eight times the mass of the Earth. That is a whole lot of interior pressure. (Not to mention a lot less rigidity in it’s surface at that temperature.)
None of that had any particular significance with respect to my initial question. I will try to explain the specific question I have, not about the research cited directly, but rather about the theoretical optics upon which it rests.
Take two sphere, one stellar sized and luminous, and one opaque, and planetary sized. Place them close enough to **simulate the appropriate distance for an eighteen hour orbital period **and observe them from forty light years away. The planetary sized spheres is not a planet, but an opaque magical ball, with a magically constant radius, with a variable mass machine at it’s center. This magical machine cycles from 0 mass to a mass equivalent to ten times the mass of earth. The observer waits forty years, and then he watches. He accurately measures the total luminosity of the stellar object, over two thousand cycles of the mass generator. Does this change the observed luminosity? If so, is the correlation of luminosity of the star direct, or inverse with the mass of the planet? And, for bonus points, what fundamental constants do I need to do the math to figure it out. (Wild ass guesses are not fundamental constants.)
It’s actually four times larger, since a 60% larger diameter gives four times the volume. With that much more physical matter, it makes sense that it would also be more dense.
I am not saying that the core would not be as dense or denser than the Earth’s core. I am just saying that even if a whole planet were made of iron and nickel, as our core is supposed to be, the planet as a whole would not be as dense as the Earth’s core, only its core would be.
Furthermore, it seems to me (I admit that I have not done the math) that, given what we know about the relative abundances of elements in the universe, and how elements are formed, a whole planet made of normal matter that is denser than lead, or even almost as dense as lead is extremely unlikely to form. (We are talking about stuff like osmium, gold, uranium, and, of course lead itself - all pretty rare elements compared to lighter stuff like the oxygen, silicon, aluminum, and even iron, that largely comprise the Earth. Out there in space, neutronium from a burned out white dwarf seems much more likely to turn up.)
ETA: OK, I had not realized we were talking about 60% larger than Earth. I thought we were talking Earth sized, more-or-less. I guess at that size I can believe that the pressure of the outer layers of an iron-nickel planet might squash the deeper layers enough to make the planet as a whole dense enough. I still think neutronium (or measurement error) is a better bet, though.
I agree that it’s unlikely that a super-dense planet would form in a proto-planetary disc. However, there are a couple of mechanisms proposed in this thread which can result in the outer layers and much of the mantle of a planet being stripped away, which results in a dense core being left behind.
Measurement error is a possibility, the original article reported an error margin of about 25%. “Neutronium” isn’t a possibility. It is only present in neutron stars, not white dwarfs. There is no possibility of mistaking a white dwarf or neutron star for a planet. A white dwarf has a density of approximately one ton/cm3, rather than a few grams for a planet. A neutron star is even more dense. This is due to gravitational compression. It also isn’t possible for materiel from a neutron star to be introduced into a planetary body. It only remains in that state and density due to the stars gravity, if it was possible to remove some it would rapidly expand.
Small-angle gravitational lensing gives a ray of light a bend angle of (4GM)/(Rc[sup]2[/sup]). Using Earth’s numbers, a ray passing just past the edge of the planet would deflect by 3x10[sup]-9[/sup] radians.
From this information, you can calculate the lensing properties of whatever star/planet/observer arrangement you are interested in, as long as you stay in the small-angle regime. You will typically be interested in point-to-parallel focusing, which for the Sun/Earth system (i.e., a 1-AU lever arm) leads to a “from-behind-the-Earth” viewing reach of about 450 m, or a 1-part-in-14000 reduction in effective Earth radius, or a 1-part-in-7000 reduction is area.
For a point-mass, there would be no net flux change, since you de-focus as much as you focus, but I think for an opaque central region, you will in fact get a net flux gain – although I haven’t bothered to actually sketch out the rays to make sure that makes sense. In any case, this effect would be very tiny for the parameters in question.