Magnetosphere and space dust problems

[AotrsCommander]

(I am of two minds about posting this here or in the main satrophytsics forum, but I think it's probably better to go here.)

So, I have a tide-locked planet at approximately 104AU out around a clone of R Coronae Borealis, with has a carefully designed , bright shiny silvery moon (small and close by) which is a relatively recent (few billion years) capture; with a rotational speed of three days on it's own axis and six days around the planet.

I have two, proabbly related problems that have come up, the former due to the latter.

a) Given that these are both well within the (theorised) carbon dust cloud resulting from the star, why are they both not completely black with picked up carbon?

b) Given that for what little I've been able to glean from the subject, R Coronae Borealis will have a stronger stellar wind than Sol (which will presumably not tail off at that distance), albiet one that will fluctuate more, so how does the planet maintain its atmopshere?

It is clear that there needs to be A Field of some description to prevent these problems.

The magnetosphere is the most obvious one, since if it was strong enough, it would both counteract the stellar wind and - I presume, correct me if I'm wrong - be enough to deflect the carbon dust around the planet (in the majority of the time). The problem is... How do you generate a magnetosphere with no significant planetary rotation to speak of?

I had thought about the liquid iorn (et al) cores of the planet and moon interacting and forming some sort of dynamo effect but that has a few problems:

1) I'm not quite sure Magnets Work That Way

2) If it does work that way, it seems to be a magnetic interaction btween a planet and a moon (especially one that's going to be spiralling IN, not out) is more likely to end up pulling the moon smack into the planet.

3) If it does work that way and it doesn't cause the moon to smash into the planet - it still begs the question of how the planet's atmosphere would have formed before the moon was captured.I'm getting the impression - bearing in mind I've only got wiki articles tro work from - that its sort of possible to get a magnetosphere in other ways than just the dynamo effect (or at least without such a significant imput of rotational energy).

I am floundering a bit in how to proceed further here: I would greatly appreciate any suggestions - magnetopshere related or anything else which might do the job (or places on the internet I might be able to at least make a spirited attempt to hazard and answer). I'd have to have to, at this stage, resort to essentially "it's magic, shut up..."

It's obviously a fairly major issue (can't quite understand how it's slipped past until now), which needs resolving before I can go any further: especially because it may well have an influence on the flora and fauna of the planet. (If it has to have has a crazy-strong magnetic field, for example, magnetosense might be a very common sense in most creatures.)

 

[AotrsCommander]

Okay, so I'm guessing it was either a stupid question or (probably more likely, since I'm sure you'd tell me if it was a stupid question!) no-one is sure of the answer...!

So then, does anyone know of somewhere or someone that I might be able to put the question to?

 

[Bandersnatch]

Damn, AC, you're really determined to make your SF diamond-hard.

I'm not sure I can be of much help here. But let's see.

You've probably read a bit more about RC Borealis stars since our last conversation. That bit about solar wind - what are the estimates you've found? How much higher than the Sun's is it? At 100AU the inverse square law should dissipate a lot. Are you sure about the carbon component of the wind? Is it significant enough to worry about in the time frame you've chosen for the lifetime of your system(I don't remember what it was).

Assuming the wind is indeed a problem, remind me what characteristics of the moon have you settled for? I think we ruled out water ice surface(which would conceivably allow for new ice layers to form and solve the problem of any surface contaminants). Was high-tidal activity in play? Maybe strong tide-induced volcanism leads to spewing out of sulfur, or whatever reasonably-reflective elements or compounds you can think of, that then fall onto the surface creating a reflective layer? For comparison, Io's albedo is .6, but maybe you can stretch it a bit if you really need it higher. But that'd require a rather large satellite.

 

[AotrsCommander]

Damn, AC, you're really determined to make your SF diamond-hard.

I'm not sure I can be of much help here. But let's see.

You've probably read a bit more about RC Borealis stars since our last conversation. That bit about solar wind - what are the estimates you've found? How much higher than the Sun's is it?

Thanks! I was really floundering.

Funny how these things work... I've been searching on and off for weeks (though usually while out), and as soon as I tried to find a source to reply to your post, I turned up a paper on "stellar wind: mechanism as and dynamics!" The sort of thing I'd hoped to find when I started looking a few weeks ago. Irony. Or google, one of the two...!

I swear I found an abstract that said something about the stellar wind and how it was much more variable, but all I've turned up here is this abstract which gives the intensity as "(M˙gas≈2.1×10−7M⊙/year)" which "obeys a Reimers law (?)" (That might have been it - though maybe when I'm next at my placement I can steal a few minutes to see if I found anything different in their browser history.)

So, I think, if I'm parsing things correctly, this is about ten million times more mass loss than Sol's (2–3)×10−14 mass per year. I think. Maybe.

(Having NOW found that paper, I can perhaps read through it and have a stab at some calulations, or at least maybe glean some understanding of the numbers I'm looking for... So if nothing else, just this exchange has given me a new avenue to investigate!)

That might be way-crazy too high... But it could be moderated somewhat by assuming whatever makes the star burn "slower" means it has a lower emission rate (and the dust would collate and fall back toards the star more or something.) But before I can bovine excrement, I need to at least have some understanding of the thing I'm bullcrapping about!

At 100AU the inverse square law should dissipate a lot. Are you sure about the carbon component of the wind? Is it significant enough to worry about in the time frame you've chosen for the lifetime of your system(I don't remember what it was).

That answers the first question, whether or not the inverse square law would apply to it! I figured it probably WOULD, but as I say, until literally in replying to this post, I have failed to find anything more concrete in mathmatical terms that wikipedia's anemic entries for stellar wind to say definitively. Yeah, that should vastly reduce potential load.

As for the other parts, I'm fairly sure that at "merely" 105AU, the planet is still well within the dust cloud of the star and I'm not sure on the latter! Stellar wind verses magnetosphere is surprisingly hard to find numbers on, considering...

Assuming the wind is indeed a problem, remind me what characteristics of the moon have you settled for? I think we ruled out water ice surface(which would conceivably allow for new ice layers to form and solve the problem of any surface contaminants). Was high-tidal activity in play? Maybe strong tide-induced volcanism leads to spewing out of sulfur, or whatever reasonably-reflective elements or compounds you can think of, that then fall onto the surface creating a reflective layer? For comparison, Io's albedo is .6, but maybe you can stretch it a bit if you really need it higher. But that'd require a rather large satellite.

The moon is a 609km radius body slightly denser than the moon (3650kg/m³ - for about 98% Luna tidal acceleration, not enough to significant;y un-tide-lock the planet on a civilisation time-scale) that orbits around the planet once every six Earth-days and rotates on it's own axis once every three-Earth days. This means that a visible surface feature, a dark spot the "eye of the moon" is only visible from the day side and appears to be poetically "opening" and "closing." It has an otherwise bright durface beause of the high concentration of surface silver deposits and magnesium oxide residue left from when the moon's water ice photodissociated.

I was considering, in light of the magnetosphere problem, having an iron core (and potentially giving the planet a liquid iron core that rotates due due the magnetic interaction or something like that, if that would actually work. If the moon really needed to be very hot at the core to allow this, I as planning to assume either the impact that caused it to be currently rotatiing and causing the eye of the moon, or some connection to the elemental place of fire or something would serve as sufficient. But I'd prefer to avoid too much exotic explanations if I can.)

 

[AotrsCommander]

Okay, I fianly, ahd time to try and read the stuff I found and have a crack at it.

Unfortunately, despite a good thre or four hours, I'm still fairly lost.

http://www.astronomy.ohio-state.edu/~ryden/ast825/ch11.pdf

(Though there is this http://www.bartol.udel.edu/~owocki/preprints/Oleron-review-Oct03.pdf source as well.)

This was my starter for ten in trying to calculate the solar wind velocity.

On page 7,. there is an approximation for the isothermal Parker wind speed (rough order of magnitude is all I'm looking for really).

"This equation may be integrated, using the boundary restriction u = a₀ at r = r_s, to yield the Bernoulli integral for an isothermal wind:

$\frac{u^2}{a0^2} −ln (\frac{u^2}{a0^2})=4ln \frac{r}{r^s}+ 4\frac{r^s}{r}−3$

This equation gives the wind velocity u as a function of r; a plot of u (r)for different temperatures is shown in Figure 11.3

At large radii, the wind velocity is approximately u ≈ 2a₀ [ln(r/r_s)]^1/2.At small radii, the velocity is u ≈a₀e^3/2exp(−2r^s/r). For the sun, the sonic radius r_s= 2×10¹¹cm is only three times the radius of the base of the corona. At 1 AU, the radius is r=75r_s, and the solar wind velocity predicted by the isothermal Parker model is u ≈ 4.1a0 ≈740kms−1 (T₀/2×10⁶)^1/2."

Where u is the velocity, r is the radius of the distance in question, r_s is the sonic radius and a₀ is the constant sound speed of isothermal ionised hydrogen (I think.)

r_s appears to be:

$\frac{GM}{2a0^2}$

Where G is the gravitational constant and M ius the solar mass. (I believe - it doesn't specifically say.)

The a₀ appears to be dervived from

An isothermal wind of ionized hydrogen has the constant sound speed

$a0 = (\frac{2kT0}{mp})^\frac{1}{2} = 180kms^-1 (\frac{T0}{2 ×10^6 K})^\frac{1}{2}$

(from page 6)

Where To is the tempertaue of the star (I think), k is the Boltzmann constant and m_p is the proton mass.

I think this is the problem point. I am not sure whether in the second equation, the 2 ×10⁶ K is supposed to mean 2 ×10⁶ Kelvins or whether it's something like the electron conductivy coefficient or something... or indeed whether it's an explantion of how the 180km/s or part of the equation... so I am working from the first part.

I can't seem to approach the u ≈ 4.1a0 ≈740kms−1 (T₀/2×10⁶)^1/2 figures (though 740/4.1 is roughly 180).

Plugging the numbers, as far as I can determine, into my spreadsheet in comes out very wrong. I get a u of 946553394m/s for Sol. I can't see where I'm making unit - or other errors, or whether I've just completely misunderstood everything.

For sol

r = 149597870.7km (1AU)

a0 = 2 × 1.38E-23 J/K(Boltzmann constant) × 5778 (T_o in K)/1.67262178 × 10-27kg (m_p (proton mass) =
95343012.93 (units? presumably m/s...?)

rs = 0.00000000006673841 m3 kg-1 s-2 × 1.98855E+30kg/ 2 x a0^2 =7299.693603

I have tried using 1.38E-16 ergs/degree for the Boltzmann constant, which gives me 4.02e+16 m/s... which is the right number ... sorta... but ten orders of magnitude out.

(I did try looking at whether I could ascertain if the planet was actually out of the heliopause... but you need to know the solar wind velocity befoe you can even do that!)

Any help would be appreciated at this point - I'm now well and truly lost!

 

[dbmorpher]

Extrapolating from your responses, I'd say the answer to question b would be that the carbon has formed carbon dioxide and thus become an invisible gas. However due to the fact that your star has a mass of 0.8 suns I would think that a planet would not exist at your radius. Pluto exists at a radius of half of that and is too small to support an atmosphere. Your planet would most likely not form that far out and therefore not exist. If it was closer, say 1 or 2 AU I could see its occurrence.

Note you probably have researched this more than me, I am going off approximation and simple reasoning

 

[AotrsCommander]

In reply to dbmorpher (whose post I received via email notification, but cannot see on the thread for some reason):

The planet has to be at that radius (approx 104AU) because of the stellar flux (as it is, it's a bit on the warm side) to be aqueous (and thus support terrestrial (ish) life), and it has to be aqueous because that's what the majority of the atmosphere data is from to give me at least a starting basis!

The planet being there is the whole start of the premise - a planet where (in the right places) it is eternal twilight (i.e. evening) save for irregular period where it goes dark for extended periods, to the consternation of the local civiisations. (An effect achieved by essentially taking R Coronae Borealis' dimming effect and making it happen over longer periods fo [unknown reason, possibly exotic compounds in the star's make-up]. The star is essentially a carbon (aha) copy of RCB.)

You do raise a point that I hadn't considered (i.e. a planet is unlikely to have formed that far out) - but I can think of a few vaguely plausible suggestions as to how the planet might ended up there - perhaps (as one theory suggets) if RCB variable are formed by the collision of dwarf stars, it actually formed much closer to a star, but some catastrophic event ended up pushing it out until it stabilised in its current orbit (the same event could be one that made its rotational velocity slow enough it became tide-locked. (The planet itself could be much older than Earth before it finally developed life, after all!)
As to the main topic, as I am no clearer, I have tried a different approach. If we take the inverse square law, and Sol's solar wind as one unit, I can approximate the strength of the solar wind, yes? I will perhaps have a look later to see if I can find some more sensible mass-loss figures for another comparison, but for the sake or argument if we take the solar wind velocity as proportional to the luminousity (not completely, unreasonable, yes?) That gives us18800/(104^2), which is about 1.73 Sol solar winds. So we probably need a magnetosphere that's a bit stronger than Earth's... Maybe created from mantle convection because of surface heating the same way the winds are...? (Stretching a bit, I know.)

Alternatively, one other idea that struck me which might possible deal with two anomalies at once: a high-gravity body (like a red or brown dwarf) orbiting quite close to the star (and therefore quite fast), which is essentially pulling the carbon ejecta enough that rather than just all floating out, it (at least roughly in the system's orbital plane) is being dragged into or following the body (and possibily re-desposited back into the RCB star itself). This would allow a handwave to the solar wind a it (since its force would be assumed to be reduced in the orbital plane), as well as perhaps going slightly further to explain why the star is burning "longer" than it would be expected to.

(Note that it doesn't matter if the body's orbit not stable and slowly it is spiralling in, the time scale is probably irrelevant to civilisations.)

Do either of those ideas (or a combination of both) sound even within spitting distance of plausible? I realize I'm reaching a bit here, but with the lack of information or easily comprehensible maths I'll have to do a bit of handwaving - the trick it so keep it down as much as possible.

 

[dbmorpher]

Perhaps if you want eternal twilight you could instead have a system with a binary planet where their revolution is locked to the star so the planet farther away would be in an eternal eclipse?
However I don't think all this work is necessary, while I'm no expert in planetary formation I would be able to believe a system you described if you phrase it well enough and I'm sure most people reading would too.

 

[AotrsCommander]

Okay.

I think I may have maybe got something like maybe somewhere.

Equation for atmosphereic mass loss (since that's what we're looking for, really) found here http://arxiv.org/pdf/1006.0021v1.pdf

$Mdot = (\frac{Rp}{D})^2 \frac{Mwα}{2}$

where Mdot is the atmosphereic mass loss (the paper is discounting magnetic fields), Rp is the radious of the planet, D is the orbital distance, Mw is the stellar mass loss and α is the entrainment efficiency. (Which is estimated at 0.03, but might be 0.01 to 0.3: for my puroses we'll just opt for 0.03 as Earth for the sake of argument and lack of better judgement!)

So, if I plug in the numbers for Earth (Mw = 2 × 10¹⁴), we get 5.44 × 10^-25.

I have manage to find a stellar mass loss for R Coronae Borealis that suggests it is 2.1 × 10^-7, (here) which gives us a comparitive value of 5.47× 10^-23.

Which is 100 times higher. Okay. Well, considering the mass loss is a million times... This is also about as concrete a result as I have managed to figure out, suggestig that the plabet would lose atmosphere at 100 times the rate of Earth (and presumably requiring a very signficant magnetic force to compensate.)On the other hand, I have found several sources which suggest stellar wind speed is about 200m/s (Earth's being 400 or 750m/s (slow and fast solar wind). So... I dunno.So, I think we're back to the quetion of "how do we generate an arbitarily large magnetic force without planetary rotation?"

Progress...?

Perhaps if you want eternal twilight you could instead have a system with a binary planet where their revolution is locked to the star so the planet farther away would be in an eternal eclipse?
However I don't think all this work is necessary, while I'm no expert in planetary formation I would be able to believe a system you described if you phrase it well enough and I'm sure most people reading would too.

No, that doesn't work - it's one of the first things I looked at myself! Orbital mechanics mean that you can't have two bodies orbiting another in synch with each other - the outer one would have to be accelerated to maintain position. (The speed at which a body orbits is basically a fixed value dependant on the distance.)

 

[Bandersnatch]

Hey AC,

I keep telling myself to get around and grok the problem and maybe try to cook up some sort of answer, but I never do. :(

Perhaps if you were to distill a couple of narrow, specific questions and post them in the astronomy section, you'd get better responses. The sad truth is, the SF writing section is not the most frequented alley on PF.

 

[AotrsCommander]

Over Christmas, I spoke to one of my Dad's mates, whose a bit more into physics than me (he does a lot of reading on the internet, as he can't do much else during the winter or when he's having a bad day). He basically said that the answer is pretty much you can't generate a magnetic field without a rotating planet.

So we're basically into fudging it territory. One thing he suggested was to have a supercool, liquid core (or some dense, hitherto extoic material) surrounded by a warmer, molten mantle of iron or something, so that with the properies of said liquid exotic, you'd then get an electrical differential which would generate a magnetic field. So that's my current nominal plan, subject to any better ideas or refinement anyone can suggest and/or I have time to have another solid look at it.

 

[mfb]

An interesting world.

The first problem I see is the timescale. The origin of those stars is a bit unclear, but with their luminosity and mass they cannot be long-living in that state (rough estimate: 10 million years or less). Something happened within the last few million years, if you want intelligent life it has to have some history elsewhere: a planned migration outwards as the luminosity increased, some really weird event kicking the planet outwards (into a circular orbit), or something else.

That also means the current status is a very recent development - the planet might lose its atmosphere now, but the timescale could be short enough to make the losses acceptable.

but for the sake or argument if we take the solar wind velocity as proportional to the luminousity (not completely, unreasonable, yes?)

That is unreasonable. Some power law (with an exponent significantly above 1) would fit better, I guess.

Stellar wind - at least the wind of our sun - is way too fast to fall onto a second star in relevant quantities.

Perhaps if you want eternal twilight you could instead have a system with a binary planet where their revolution is locked to the star so the planet farther away would be in an eternal eclipse?

That would be highly unstable.

 

[AotrsCommander]

An interesting world.

The first problem I see is the timescale. The origin of those stars is a bit unclear, but with their luminosity and mass they cannot be long-living in that state (rough estimate: 10 million years or less). Something happened within the last few million years, if you want intelligent life it has to have some history elsewhere: a planned migration outwards as the luminosity increased, some really weird event kicking the planet outwards (into a circular orbit), or something else.

I made a rather more extensive thread on the planet in the sci-fi writing section (where it is more appropriately suited, so I will be brief here) - this thread was intended primarily to see if I could ascertain the same sort of first/second order calculations I'd been using, pertaining directly to the magnetosphere problem that had arisen (when, on another forum, as I was about to start working on the flora/fauna, some unkind soul asked me about it and I went "um... crap. Gonna have to answer that one first, aren't I?"

Anyway, the longevity of the RCB is something I am taking a few liberties with. The periods of dimming are thus extended to centuries, rather than months, and the star is for some reason (not entirely clear even in-universe) has been in this state significantly longer than would be expected (theories are that there is some form of exotic matter in the star's composition, observations suggest there may be some sort of body orbiting very nearly in the corona of the star, which might be a planet, an artifical structure or even a small dwarf star - in the latter two cases it is suggested that its effect in concert with the much further binary pair in the cluster, are somehow "recycling" the carbon dust back into the star somehow.)

The upshot of this is the star burns "slower" that others of its type, and thus the planet has had plenty of time to develop advanced life naturally.

This bit of.. creativity... I am prepared to live with, but I am trying to keep such instances down as much as possible. (It appears unavoidably, the same sort of thing will have to apply to the magnetic field.)

(I could legitimately use "technology/magic did it" given the rest of the universe, but I again try to avoid that as a general rule for this sort of instance. (And even then, never without some sort of attempt at an explanation as to HOW technology/magic did it! I like to at least start with as much basis in science as possible and go up, using magic/technology/exotic new materials only to slather into the cracks where possible.)

That is unreasonable. Some power law (with an exponent significantly above 1) would fit better, I guess.

Stellar wind - at least the wind of our sun - is way too fast to fall onto a second star in relevant quantities.

I am not sure we're talking the same thing here? Your second paragraph confuses me a bit.

I meant that, I took the solar wind strength on Earth from the sun (so stellar wing at 1 AU = from luminosity of 1 Sol) as one unit, then I would extrapolated a value for stellar wind from the star from the difference of distance and luminosity (in this case 104 AU and 18000 solar luminosity) using the inverse square law. (On the basis stellar flux falls off at that rate.) I was working on ther assumption of solar wind strength, as opposed to just speed, on the basis it would speed + density which would erode an atmosphere and that the former probably wouldn't change at distance, but the latter would.

I have no idea if that's reasonable, as I say. (I'm not sure, for example, was proportion of the strength at Earth the solar wind is in the Sol system at 104 AU.)

 

[mfb]

Anyway, the longevity of the RCB is something I am taking a few liberties with.

You care about details of carbon dust, but ignore energy conservation? Okay...

Converting 100% hydrogen to 100% iron gives at most 9 MeV per proton. A part of this will be lost due to neutrinos and converting everything to iron is unrealistic as well, but it will give a very conservative upper estimate. With one solar mass and 10000 times the solar luminosity, this gives 14 million years as upper estimate on the lifetime of the star with its current luminosity. You can get one million years more if you let the core collapse to a white dwarf (without the surface collapsing, for some reason). Making a neutron star inside could give something like 200 million years, but I don't see how that would happen with a nice, shining star of one solar mass. Even a complete collapse to a black hole would not increase that time significantly. Using 18000 instead of 10000 times the solar luminosity reduces all values correspondingly.

The inverse square law should be fine for stellar wind, but 18000 times the luminosity should give more than 18000 times the stellar wind density.