Close binary red dwarf system: habitable zones, tidal locking

[splicer]

Okay, a couple of questions regarding a world I'm fleshing out for MTU. I'll probably also go ask these questions over at "Bad Astronomy", but I figured the grognards at CotI might enjoy a crack at 'em first.

1. Habitable zones of close binaries: The HZ for M stars is orbit 0. Assuming this is a tight binary system, would the stars' combined luminosities move this farther out?

I assume it would. Then again, it might still be in orbit 0 around the combined mass. If this info is in a book somewhere, a pointer would be great. I had B6:Scouts years ago, but who knows where it is now. I'm ordering the CT CD-ROM this weekend. I'm not averse to buying DGP products, either, if/when I can find them at a "reasonable" price.

2. Tidal locking: Assuming orbit 0, would the nature of the gravity well around a tight binary prevent full tidal locking?

Even slow rotation would be helpful. This isn't essential to my plans because the atmosphere code is 8, and some scientists speculate that a thick atmosphere might be enough to moderate temps on a planet tidally locked to an M star. Still, I'd love to give this planet a day/night cycle. A slow rotation might even give the planet a day-summer/night-winter cycle, which would be ideal for storytelling purposes. I realize that I can handwave anything I want, but I'd love it if I didn't have to.

 

[splicer]

Hmmm, no takers? Where's my Scouts at?

I managed to answer my first question. T20 wisely suggests that better results for star system modelling can be obtained from either Book 6: Scouts or GT: First In. The CT CD-ROM is on its way, but hasn't arrived yet. Craving some instant gratification, I purchased the PDF of First In. It gives a nice treatment of the subject, although I'm still left with questions which I hope can be answered with a few more readings and exercises.

1. Habitable zones of close binaries: The HZ for M stars is orbit 0. Assuming this is a tight binary system, would the stars' combined luminosities move this farther out?

The answer is "Yes." (Hooray! ) The text refers to "tight binaries" as having Very Close separation. And says:

"As a general rule, if a pair of stars has Very Close separation, simply add their masses together, add their luminosities together, and treat them as a single star with the resulting mass and luminosity...." GT: First In. 53.

"In the case of a pair of stars at Very Close separation...treat the stars as one when placing orbits." GT: First In. 55.

So, I did a little bit of math (and a little fudging to reflect an already existing world). I also fudged the stellar radius because my math gave me a funny answer. I'll try to do it again later. Anyway, these are the tentative results:

M0V/M1V pair with Very Close separation
M0 luminosity 0.063, mass 0.50
M1 luminosity 0.053, mass 0.46
Combined luminosity 0.116, combined mass 0.96

0.192 orbit 1/inner limit; size 3 world
0.32 habitable zone, inner edge
0.43-0.50 orbit 2 (0.467 with 0.08 eccentricity); mainworld C688000-0
0.44 habitable zone, outer edge
0.888 orbit 3; planetoid belt
1.01 100 diameter jump limit
1.488 orbit 4; size 9 world with size 1 moon
1.70 snow line
2.688 orbit 5; size 10 world with 1 30mi and 2 60mi moons

For now, I didn't finish any of the other orbits up to the outer limit of 38.40 AU. The mainworld orbit skips back and forth across the outer edge of the habitable zone. It has a thick atmosphere and has a year of about 84 days (guesstimate for now), so I don't think it will be a problem for temperature. The text allows for up to 30% change in luminosity, so I can always fudge the luminosity upwards if I need to. I already applied a 5% shift in orbit towards the binaries (also allowed). So far, I'm pretty happy with these results (and with First In; reminds me a lot of Scouts -- or, at least, what I remember of it some 20 years later. ).

I didn't find an acceptible answer to the tidal locking problem. First In mentions tidal locking and M stars, and mentions 3/2 resonance possibilities, but it doesn't say anything about binaries and planet locking. Or, maybe it does? There's some math for moon locking. I'm going to print out the relevent pages and look over them a few more times. FWIW, the combined mass is about the same as a G star. On a side note, the math in the Wikipedia article on tidal locking gave me a Jack O'Neill headache. o:

 

[Gadrin]

Make sure you check the GURPS site for software too.

Someone must have done First In on the computer someplace.

http://www.sjgames.com/general/gm-aids.html#gurps
go down to Solar System Constructor. I don't think it's
First In, maybe GURPS Space, but it should be nice if you
have Windows.

the SJG BBS also has a Traveller forum too.
http://forums.sjgames.com/forumdisplay.php?f=16

You can ask if anyone has First In in a computer program.

>

 

[Blue Ghost]

Last I heard habitability was determined more by a planet's magnetic field, than merely its proximity to its sun.

 

[splicer]

...Solar System Constructor. I don't think it's
First In, maybe GURPS Space, but it should be nice if you
have Windows.

Gadrin,

Good tip, thanks! I grabbed Solar System Constructor and a couple of other things. I'm actually running Debian and not Windows -- but, SSC is an Excel spreadsheet, so probably I can get it to work with something. I'll tinker around with it this week and post any positve results.

the SJG BBS also has a Traveller forum too.

Hah! I just browsed around over there for a second and (completely by accident and in the first thread I clicked) stumbled into an off-topic discussion of habitable worlds around M stars -- and the desire to avoid tidal-locking them. I'll poke around over there a little more tomorrow and see what i can learn. (I'd sign up now, but my eyelids are getting heavy; too bad my JTAS login doesn't work there too.. or does it? Maybe I typo'd my way into a failed login :nonono

Cheers

 

[splicer]

Last I heard habitability was determined more by a planet's magnetic field, than merely its proximity to its sun.

I think that has more to do with deflecting solar hazards (flares, etc.) and helping to keep the atmosphere. Having a thick atmosphere helps moderate temperatures, so the field plays a role in keeping that healthy. The problem with M stars/red dwarfs is that they are so dim that in order to be close enough to warm the planet enough for it to be habitable, you get so close that the planet's rotation gets tide-locked to the star; day side gets cooked, night side freezes. (All of this is anthrocentric thinking, of course. )

My goal is to avoid having the planet that close. The .sec data for this world states that it has two stars, both of them bright (as far as it goes) red dwarfs, so I just decided to make them really close together. Anyway, I am giving the planet a molten core and a strong magnetic field to deal with random/light flare activity somewhat. A tide-locked world might not rotate fast enough to generate a good field.

 

[splicer]

...Solar System Constructor[/B]. I don't think it's
First In, maybe GURPS Space, but it should be nice if you
have Windows.

It is GT: First In. I was able to open the .xls using Gnumeric. It seems to work okay. Using it to model a Very Close binary system requires one to manually combine data for the two stars and then enter the figures into some cells which are normally locked (this weakness is acknowledged by the programmer, and it's one I can live with). I did have some trouble unlocking the spread sheet to do this. A little more tinkering should do the trick.

One other thing -- the CT CD-ROM arrived today! So, according to Book 6: Scouts, "Assuming the two companion stars are close, and can be considered a single source of energy....Add the two luminosities together. Select the effective temperature of the more luminous of the stars." Hmmm.. lots more tables here. Not sure I agree with all of these assumtions. Still, every resource helps.

 

[shaunhilburn]

1. Habitable zones of close binaries: The HZ for M stars is orbit 0. Assuming this is a tight binary system, would the stars' combined luminosities move this farther out?

I assume it would.

Yes.

Calculate the HZ based on their combined output. Use L=R^2*T^4. *Don't* use luminosity derived from absolute magnitudes.

Then again, it might still be in orbit 0 around the combined mass. If this info is in a book somewhere, a pointer would be great.

Just place it in the appropriate orbit, and don't worry about the Scouts orbit number.

2. Tidal locking: Assuming orbit 0, would the nature of the gravity well around a tight binary prevent full tidal locking?

No, not a prayer. The gravity gradients and tidal effects in M dwarf HZs are tremendous, even the largest and brightest M dwarf will solidly and firmly synch the rotation of any planetary bodies in its HZ. Doubly so for a double star, although a planet close to tiny dim M dwarfs will experience oscillating tidal effects that may throw it into a spin-orbit resonance.

Even slow rotation would be helpful. This isn't essential to my plans because the atmosphere code is 8, and some scientists speculate that a thick atmosphere might be enough to moderate temps on a planet tidally locked to an M star. Still, I'd love to give this planet a day/night cycle.

Give it an eccentric orbit and resonant spin-orbit coupling like Mercury. Likely orbits:
e = 0.143 R=3:4
e = 0.2 R=2:3
e = 0.33 R=1:2

A slow rotation might even give the planet a day-summer/night-winter cycle, which would be ideal for storytelling purposes. I realize that I can handwave anything I want, but I'd love it if I didn't have to.

Stable circumbinary orbits (P-type) exist beyond the system barycenter, outside of 2× the apastron hill radius of the less massive member (it swings out farther and causes more havoc)

My 'Tatooine' rule says "identical twins with a *maxmimum* separation of six diameters or less always have an exterior habitable zone, never an interior one." Six is a number that works for minimal red dwarfs, therefore across the entire main sequence. It can be as high as 20 diameters for A-type stars.

 

[splicer]

Shaun,

Thanks for the thorough (and very helpful!) response.

...will solidly and firmly synch the rotation of any planetary bodies in its HZ. Doubly so for a double star, although a planet close to tiny dim M dwarfs will experience oscillating tidal effects that may throw it into a spin-orbit resonance.

Oh good, that was kinda what I was getting at. Maybe I didn't phrase it well.

Give it an eccentric orbit and resonant spin-orbit coupling like Mercury. Likely orbits:
e = 0.143 R=3:4
e = 0.2 R=2:3
e = 0.33 R=1:2

Thanks especially for this!

 

[shaunhilburn]

Anyway, I am giving the planet a molten core and a strong magnetic field to deal with random/light flare activity somewhat. A tide-locked world might not rotate fast enough to generate a good field.

The need for rotation and magnetic moment is overrated.

Venus has almost no magnetic shield, yet still has a massive atmosphere despite being subjected to more sputtering effects than Earth. Even so, a young but tide-locked planet still has enough core heat to generate the necessary currents for a rather strong field. Don't forget self-induced magnetic fields arising from the planet's metallic core cutting across the M stars own magnetic flux lines (M dwarfs have powerful magnetic fields)

The main radiation threat to your world is UV flare radiation. An oxygenated atmosphere is completely opaque to extreme doses of X-rays and gamma rays, but the ozone layer will allow a small percentage of the UV flux to reach the surface.

On this world, groundside UV is no problem during the average 'moderate' flare' event, it only becomes an issue during major flares. During an extended (eight-hour) superflare outbreak, ocean surface heating will generate thunderstorms within a few hours that block most of the UV on the dayside (water-laden clouds block up to 80% of incident UV), these storms will take a day or so to subside after the flare event.

 

[splicer]

Don't forget self-induced magnetic fields arising from the planet's metallic core cutting across the M stars own magnetic flux lines...

I completely did. Good point.

During an extended (eight-hour) superflare outbreak, ocean surface heating will generate thunderstorms within a few hours that block most of the UV on the dayside (water-laden clouds block up to 80% of incident UV), these storms will take a day or so to subside after the flare event.

All while the PCs are around, naturally. Nothing like a crazy weather event to liven up a party!

Any thoughts on starspots, or their relationship to magnetic fields, flares, or temperatures on the mainworld?

Also, how much of this applies to K stars? I'm assuming that late Ks are like early Ms. Where is the dividing line, do you think, between dim stars with tide-locked or resonant HZ worlds and "normal" main sequence systems with HZs that don't lock? Mid K? Earlier?

 

[shaunhilburn]

Any thoughts on starspots,

They are patches of inhibited convection, where tangled local magnetic fields puncture the photosphere. Temperature is reduced within the spot because convection from the interior is reduced, a sort of magnetic bottle isolating the plasma from the interior. The spots are about the same size on all main-sequence stars, on M stars their size is significant relative to the star's smaller surface area. Significant spot coverage will reduce the M star's effective temperature, so that its unblemished photosphere may actually be hotter than the published temperature.

or their relationship to magnetic fields

The are a regional magnetic phenomenon, separate from the stars overall dipole field.
The have their own N and S poles, and their flux lines form coronal loops.

flares

Flares occur within the coronal loops between sunspots. The local flux lines become entangled and eventually unravel, releasing colossal kinetic energy. They occur above the surface of the star, but when seen (with filters) away from the edge of the disc, they appear as sinuous surface patches. An ordinary flare on a small M dwarf (say, M6V) easily shines as brightly as the entire visible disc, its *effective* temperature is around 20,000 K, which makes it shine with an bluish-white actinic light (like a welding arc), in stark contrast to the yellowish light of the M dwarf photosphere. They aren't any different from ordinary solar flares, it is the contrast to the feeble star producing them that makes them so conspicuous.

In the habitable zone, the flare's hellish gamma rays, x-rays, and proton storms will kill anyone and anything exposed to the flare above your world's atmosphere that doesn't have a *lot* of shielding. In space, flares cause serious issues with both biological and electrical systems. Underneath the oxygen atmosphere, the surface of your world is completely unaffected, except for the geomagnetic upheaval caused by the proton storms causing the planet's magnetosphere to 'quiver'. Groundside power grids may be impractical. The nightside will see spectacular auroral displays.

or temperatures on the mainworld?

M star flares seldom last long enough to affect surface temperatures on a habitable planet. The atmosphere and oceans have too much thermal inertia, and blur out the temperature swings. Flares typically last 5 - 30 minutes from onset to fadeout, and only a few minutes at peak amplitude. A strong flare could produce brief localized overheating, especially on dark objects like asphalt roads. The real danger is from UV damage like sunburn and snowblindness.

Also, how much of this applies to K stars?

K stars can produce the same flares as M dwarfs and our own sun. They don't seem to be as active as M dwarfs, and their habitable worlds are farther removed from the flares. Flares are less conspicuous on the hotter K stars.

I'm assuming that late Ks are like early Ms.

An M0 star is not much different than a K9 star, no difference at all to human eyes. The orbital period for a habitable world is longer for these stars than for a smaller red dwarf. Planets in a spin-orbit resonance will have a long interval between sunrises. A planet orbiting a pair of minimal red dwarfs with a shorter (4 - 6 day) orbit will have a more reasonable sunrise interval.

Where is the dividing line, do you think, between dim stars with tide-locked or resonant HZ worlds and "normal" main sequence systems with HZs that don't lock? Mid K? Earlier?

There is no dividing line. All planetary bodies eventually become tide-locked, the question is how long does it take? In all red dwarf HZs the timescale is very small.

If you take a 1-earth mass planet with a 6-hour rotation, and transplant it in the earth equivalent orbit of a red dwarf, the spin-down time to synchrony is about 10,000 years for the smallest red dwarfs and about 40,000,000 years for the largest red dwarf. Its difficult to say with precision, tide-locking is a complex subject. M dwarf worlds don't really spindown anyway, since the planet accretes under enormous tidal effects, the nascent planet never spins very fast to begin with and is tide-locked from its very beginning.

Exobiologists prefer 4.5 billion years when discussing the tide-locking radius. This is the cutoff line on those distance-mass HZ graphs. In that context, the 'dividing line' seems to occur around K4V to K5V, at 0.7 solar masses. Given a 4.5 Gyr system age, planetary bodies in any K dwarf HZ will spin very slowly if they're not already tide locked. Even the very youngest, molten planetary bodies in an M dwarf HZ will definitely be tide-locked.

 

[splicer]

Here are the full stats of the world in question:

Allemagne/Trojan Reach 0503: C688000-0, Ba Lo Ni, R020, Na, M1V M0V

IMTU, Allemagne is interdicted by Strend/Trojan Reach 0505 because of a "biological hazard." Strend was once a local power, controlling a cluster of four worlds and an asteroid belt, lately reduced to defending it's own space and maintaining the interdiction on Allemagne.

Groundside power grids may be impractical.

Shaun,

How would this effect groundside power usage in general, local power generation, local TL, and PC's equipment? (1)

If you take a 1-earth mass planet with a 6-hour rotation, and transplant it in the earth equivalent orbit of a red dwarf, the spin-down time to synchrony is about 10,000 years for the smallest red dwarfs and about 40,000,000 years for the largest red dwarf. Its difficult to say with precision, tide-locking is a complex subject. M dwarf worlds don't really spindown anyway, since the planet accretes under enormous tidal effects, the nascent planet never spins very fast to begin with and is tide-locked from its very beginning.

IMTU, the planet was originally in an orbit farther from its stars and was moved to its current position ~300, 000 years ago.

Exobiologists prefer 4.5 billion years when discussing the tide-locking radius. This is the cutoff line on those distance-mass HZ graphs. In that context, the 'dividing line' seems to occur around K4V to K5V, at 0.7 solar masses. Given a 4.5 Gyr system age, planetary bodies in any K dwarf HZ will spin very slowly if they're not already tide locked. Even the very youngest, molten planetary bodies in an M dwarf HZ will definitely be tide-locked.

So mid K then, as a rough guide when glancing at extended UPPs in .sec data. Thanks for giving the big picture too; helps to avoid any misconceptions.

1. Now that I think about it, I think GT:FI has something to say about it. I'll have to read up on it.

 

[shaunhilburn]

How would this effect groundside power usage in general

The Coronal Mass Ejections AKA proton storms associated with flares often collide with the planet's magnetosphere. The pressure causes the magnetosphere to buckle and compress on the sunward side and stretch into an elongated teardrop shape in the opposite direction.

As the planetary magnetic field quivers, the swaying motion of the flux lines across long transmission lines induces large currents that will damage relays, transformers and breakers.

A good example of this is the March 1989 flare that fried equipment in the Quebec power grid. An even better example is the "Carrington Flare" of 1859. This flare rivaled the brightness of the sun itself, and is the benchmark for solar superflares. The induced currents shocked telegraph operators, and when they shut down their equipment and disconnected the batteries, they found they that the lines were still energized by flare currents and that they could still transmit messages.

local power generation, local TL

The setup on an M dwarf planet would probably be a distributed system of dedicated powerplants servicing individual buildings and homes, or perhaps a powerplant serving a small block of structures. A centralized system with long transmission lines must be avoided.

For a tide-locked world, solar power would work best on the dayside. The sun shines around the clock , and since it stays in one spot in the sky, tracking motors aren't necessary, just erect scaffolds and slant the panels in the right direction. The shade from the panels would make decent protection against flare UV rays.

Coal and geothermal steam becomes available ~ TL 4, fission power becomes available at TL 6, solar power at TL 7, and fusion at TL 8.

and PC's equipment?

Compact portable devices will be unaffected. Devices connected to a grid usually have decent power supplies with surge protection, fuses, and breakers built-in. Radio sets with long antennas could be damaged, and the flare upheaval in the ionosphere will affect those frequencies that bounce off it.

The thing to avoid is long conductors, say a few hundred feet or more. Flares won't affect a fiber optic communication network, except where copper lines connect to it.

 

[shaunhilburn]

Here are the full stats of the world in question:
IMTU, the planet was originally in an orbit farther from its stars and was moved to its current position ~300, 000 years ago.

That sounds like a mass-extinction event. 300 Kyrs wouldn't be enough time for the ecologies to recover. The planet would still have some spin left over from its previous orbital position, since it hasn't had enough time to reach synchrony in its new orbit.

 

[splicer]

That sounds like a mass-extinction event. 300 Kyrs wouldn't be enough time for the ecologies to recover. The planet would still have some spin left over from its previous orbital position, since it hasn't had enough time to reach synchrony in its new orbit.

Shaun,

It's not set in stone yet, of course; I'm still working out the particulars. I realize I'm using quite a handwave here (A Wizard Did It), but the planet possibly originated outside of the habitable zone with no natural ecology; in such a case, it was moved by the Ancients as part of a terraforming project. There's OTU precedent for this, whether or not it's actually realistic. I'm hoping that attention payed to realism in most other areas (combined with the Rule of Cool) will help me avoid wrecking the Suspension of Disbelief.

I still haven't fully committed to this particular detail. It would change the planets rotation if I do, but don't think you've wasted any time discussing the topic. This thread is full of useful thoughts for any GM who is faced with the need to detail an M-star system's main world, and who desires a certain level of realism.

In any case, I'm not just using the Ancients as a convenience. They play a sizable role in the campaign backstory IMTU. Their presence had other effects in the local star cluster, including some number of planetoid belts which are the remains of planets destroyed in the Final War. The PCs won't know much of this at the beginning, although some vague info might be available. Saying more might require a spoiler tag.

 

[splicer]

An even better example is the "Carrington Flare" of 1859. This flare rivaled the brightness of the sun itself, and is the benchmark for solar superflares. The induced currents shocked telegraph operators, and when they shut down their equipment and disconnected the batteries, they found they that the lines were still energized by flare currents and that they could still transmit messages.

Shaun,

Thanks for that example. Some brief googling came up with this article on the subject: http://science.nasa.gov/headlines/y2008/06may_carringtonflare.htm

From there, I also learned about the journal Space Weather:
http://www.agu.org/journals/sw/

That last link went straight into my research bookmarks.

 

[shaunhilburn]

Still, I'd love to give this planet a day/night cycle. A slow rotation might even give the planet a day-summer/night-winter cycle, which would be ideal for storytelling purposes.

I mentioned strong tidal effects, but neglected to emphasize the magnitude of ocean tides and their effect on a freely rotating planet.

In the HZ of an M1 star, the ocean tides will be about 50x greater than Earth's solar tides. At the bottom of the main sequence, the HZ ocean tides near an M8 star are abut 6000x greater. The tidal bulge is deepest on the equator directly beneath the star, and at the antipode opposite the star.

This isn't important for a tidelocked world, since the planet and the oceanic tidal bulge revolve at about the same rate, and so the ocean depth remains fairly static relative to the coastlines.

Significant libration from an eccentric tidelocked orbit causes the (solid) planet to rock back and forth WRT the central star while the liquid ocean bulge maintains its lock, and this creates a slosh effect that would inundate and then expose large stretches low-lying coastal areas each orbit.

On such an M-star planet with independent rotation (the desired state), all of its landmasses will be exposed to enhanced tides, and the equatorial landmasses will be flooded most. Twice each day, the sea will literally 'walk the lands' up to the maximum tide level.

For an M1 star the tides would be around 200 - 300 feet, but for an M8 star, they are several thousands of feet.

 

[splicer]

I think you have the makings of a good JTAS article here, Shaun.