The Frost Line of the Solar System

[TheMan112]

The Frost Line is the distance from the Sun where the radiation from the Sun becomes too dim to make ice sublimate into vapour. See e.g. http://en.wikipedia.org/wiki/Frost_line_%28astrophysics%29" . It is important because it explains why only terrestrial planets exist inside this boundary.

I'm curious as to how the frost line is calculated though. The Wikipedia page gives a value of 2.7 AU and other sources give similar numbers, but I haven't yet seen a detailed calculation.

I imagine the temperature of an icy particle is the result of a blackbody equivalence equation, i.e:

$$\sigma T_{sun}^4 \left( \frac{R_{sun}}{r} \right)^2 = \sigma T_{particle}^4 (1-a)$$

So by solving for r and using the sublimation temperature of water in vacuum (150 K) for T_particle, the temperature could be found. However, the albedo of the icy particle a is unknown.

If I use a = 0 (perfect black-body) I end up at r = 2.92 AU, which is close, but not very realistic. If I use an albedo like that of the icy bodies of the solar system, a = 0.7 (Europa), I end up with a frost line at about 1.5 AU.

So, what's up with that? How is the 2.7 AU value derived?

Regards
TheMan112

Edit: The luminosity the Sun $$\sigma T_{sun}^4$$ is multiplied with a dimming factor of 0.6, as the early Sun was 40% dimmer than it is today. I want the frost line at the formation of the solar system in order to investigate it's relevance to planet formation.

 

[Ophiolite]

The frost line, or snow line as I prefer, is related to the proto-sun during the stage of planetary formation from the accretion disc. You are using conditions prevalent 4.5 billion years later. That likely explains the discrepancy. (I know the proto-sun was duller, which should make the snow line closer to the sun, but the accretionary disc is a turbulent, hot entity that would push the line out further.

 

[TheMan112]

The frost line, or snow line as I prefer, is related to the proto-sun during the stage of planetary formation from the accretion disc. You are using conditions prevalent 4.5 billion years later. That likely explains the discrepancy. (I know the proto-sun was duller, which should make the snow line closer to the sun, but the accretionary disc is a turbulent, hot entity that would push the line out further.

Actually, as I wrote in the edit, I'm taking the less luminous early Sun into consideration by including a dimming factor of 40%.

Are you suggesting that a Kelvin-Helmholtz effect would have pushed the frost-/snowline further away from the Sun? Would you know how to introduce such a heatsource into the equation?

 

[Ophiolite]

My knowledge in this area is qualitative and minor. There are several papers on the subject available through the SAO/NASA Astrophysics Data System. For example this one, by http://iopscience.iop.org/0004-637X/673/1/502/pdf/71905.web.pdf" gives an equation (3) for the effects of heating from viscous drag in the disc. This is rather broader, I think, than just the Kelvin-Helmholtz issue of onset of turbulence.

 

[psholtz]

The Frost Line is the distance from the Sun where the radiation from the Sun becomes too dim to make ice sublimate into vapour. See e.g. http://en.wikipedia.org/wiki/Frost_line_%28astrophysics%29" . It is important because it explains why only terrestrial planets exist inside this boundary.

I haven't been following this line of research terribly closely, but aren't all these planets that astronomers are finding orbiting stars outside our Solar System always (a) Jupiter-sized planets; and (b) always orbiting the parent star in at a radius something like where Mercury is in our Solar System?

In other words, aren't astronomers finding all kinds of solar systems out there, where the gas giants are orbiting right in tight w/ the parent star?

I would almost seem that our Solar system is more the exception than the rule.

If this is the case, I don't know that the "frost line" would explain why you have only terrerestial planets in near the Sun.

 

[Vagn]

I haven't been following this line of research terribly closely, but aren't all these planets that astronomers are finding orbiting stars outside our Solar System always (a) Jupiter-sized planets; and (b) always orbiting the parent star in at a radius something like where Mercury is in our Solar System?

In other words, aren't astronomers finding all kinds of solar systems out there, where the gas giants are orbiting right in tight w/ the parent star?

I would almost seem that our Solar system is more the exception than the rule.

If this is the case, I don't know that the "frost line" would explain why you have only terrerestial planets in near the Sun.

It is thought that the hot Jupiters formed out beyond the frostline and wandered into their current orbit. Our selection methods tend to be biased towards finding large planets orbiting close to their sun anyway, so they probably aren't as common as the data currently suggests.

 

[psholtz]

It is thought that the hot Jupiters formed out beyond the frostline and wandered into their current orbit. Our selection methods tend to be biased towards finding large planets orbiting close to their sun anyway, so they probably aren't as common as the data currently suggests.

Soooo... what exactly has stopped Jupiter or Saturn from "wandering inwards" in our Solar System?

I thought planets weren't supposed to just "wander around" like that.. :-)

 

[Ophiolite]

Jupiter and perhaps Saturn did move inwards, just not by much. There are three mechanisms which can be at work.

Type 1 Migration where angular momentum is transferred from the planet to the viscous accretion disc.

Type 2 Migration where large planets quickly clear a gap in the disc, but a gap which is routinely refilled, generating further inward migration.

Gravitational scattering, in which bolides hurled into the outer reaches of the system impose inward migration by the giant.

We must presume, I believe, that in our system the dust of the disc was cleared by early t-Tauri activity by the proto-sun, thus limiting the amount of inward migration.

 

[psholtz]

Jupiter and perhaps Saturn did move inwards, just not by much.

Is there evidence of this, or are we just guessing?

There are three mechanisms which can be at work.

Type 1 Migration where angular momentum is transferred from the planet to the viscous accretion disc.

Type 2 Migration where large planets quickly clear a gap in the disc, but a gap which is routinely refilled, generating further inward migration.

Gravitational scattering, in which bolides hurled into the outer reaches of the system impose inward migration by the giant.

Again, is there evidence of this anywhere, or is it all just random conjecture?

I'm not talking sides one way or another.. but I'm just commenting on what seems to me to be a very interesting double-standard in "science"..

It would seem that if your name in Immanuel Velikovsky, and you propose a model whereby planets can randomly "wander around" inside a Solar System, then you're laughed at, ridiculed and your entire life and career is destroyed. On the other hand, if a "wandering planet" hypothesis is what you need to make sense of astronomical data where we're finding dozens of "hot Jupiters" orbiting in at the radius of Mercury, then that's what you invent and you get tenure at Harvard for doing so.

I'm not completely clear on what exactly separates these two lines of conjecture, other than money and politics.

I'm not saying that one person is right, and the other is wrong.

Frankly, the three "mechanisms" you've proposed above strike me as being just as inane as anything Velikovsky ever came up w/.. and that doesn't mean they're right or wrong. Between the three models you propose, and tossing in Velikovsky's model as a fourth, it could be that all four are true, or none of them is true, or some combination of them is true.

But I'm just saying you can't laugh off Velikovsky as a "nutball" charlatan, and then turn around and propose exactly the same thing he's proposing and expect people to take you seriously.

We must presume, I believe, that in our system the dust of the disc was cleared by early t-Tauri activity by the proto-sun, thus limiting the amount of inward migration.

Yes, there are lots of "presumptions" and "beliefs" that are made in this business, aren't there? :-)

 

[Vagn]

But I'm just saying you can't laugh off Velikovsky as a "nutball" charlatan, and then turn around and propose exactly the same thing he's proposing and expect people to take you seriously.




Yes, there are lots of "presumptions" and "beliefs" that are made in this business, aren't there? :-)

But we aren't suggesting the same thing, here's a list of Velikovsky's beliefs from his wiki page:

He arrived at a body of radical inter-disciplinary ideas, which might be summarised as:

* Planet Earth has suffered natural catastrophes on a global scale, both before and during humankind's recorded history.
* There is evidence for these catastrophes in the geological record (here Velikovsky was advocating Catastrophist ideas as opposed to the prevailing Uniformitarian notions) and archeological record. The extinction of many species had occurred catastrophically, not by gradual Darwinian means.
* The catastrophes that occurred within the memory of humankind are recorded in the myths, legends and written history of all ancient cultures and civilisations. Velikovsky pointed to alleged concordances in the accounts of many cultures, and proposed that they referred to the same real events. For instance, the memory of a flood is recorded in the Hebrew Bible, in the Greek legend of Deucalion, and in the Manu legend of India. Velikovsky put forward the psychoanalytic idea of "Cultural Amnesia" as a mechanism whereby these literal records came to be regarded as mere myths and legends.
* The causes of these natural catastrophes were close encounters between the Earth and other bodies within the solar system — not least what were now the planets Saturn, Jupiter, Venus, and Mars, these bodies having moved upon different orbits within human memory.
* To explain the celestial mechanics necessary to permit these changes to the configuration of the solar system, Velikovsky thought that electromagnetic forces might somehow play a greater role to counteract gravity and orbital mechanics.

Some of Velikovsky's specific postulated catastrophes included:

* A tentative suggestion that Earth had once been a satellite of a "proto-Saturn" body, before its current solar orbit.
* That the Deluge (Noah's Flood) had been caused by proto-Saturn's entering a nova state, and ejecting much of its mass into space.
* A suggestion that the planet Mercury was involved in the Tower of Babel catastrophe.
* Jupiter had been the culprit for the catastrophe that saw the destruction of the "Cities of the Plain" (Sodom and Gomorrah)
* Periodic close contacts with a cometary Venus (which had been ejected from Jupiter) had caused the Exodus events (c.1500 BCE) and Joshua's subsequent "sun standing still" (Joshua 10:12 & 13) incident.
* Periodic close contacts with Mars had caused havoc in the 8th and 7th centuries BCE.

As noted above, Velikovsky had conceived the broad sweep of this material by the early 1940s. However, within his lifetime, whilst he continued to research, expand and lecture upon the details of his ideas, he released only selected portions of his work to the public in book form:

* Worlds in Collision (1950) discussed the literary and mythical records of the "Venus" and "Mars" catastrophes
* Portions of his Revised Chronology were published as Ages in Chaos (1952), Peoples of the Sea (1977) and Rameses II and His Time (1978) (The related monograph Oedipus and Akhenaten, 1960, posited the thesis that pharaoh Akhenaten was the prototype for the Greek mythic figure Oedipus.)
* Earth in Upheaval (1955) dealt with geological evidence for global natural catastrophes.

Velikovsky's ideas on his earlier Saturn/Mercury/Jupiter events were never published, and the available archived manuscripts are much less developed.

We have plausible ideas as to how these planets wander in. If you can provide a mathematical model by which any of his suggestions can occur, or how the position of the planets could have changed that significantly over the past 10 000 years, then i will cede the point, until such a time, there is no reason to believe him.

 

[psholtz]

But we aren't suggesting the same thing, here's a list of Velikovsky's beliefs from his wiki page:

If I were a judge in a court, I would dismiss this response as being "frivolous and without merit".. (a favorite retort of judges in this country, if you've ever had the distinct pleasure).

The point being, you haven't addressed the issue at hand (which is the legal definition of the word "frivolous").

Instead, you've built up a strawman, and proceeded to destroy the strawman, and now are trying to present that as some sort of "victory" in the discussion.

The pertinent point I'm making:

* Velikovsky claims that planets wander around solar systems.
* You're making the claim that planets wander around solar systems.

Do you admit or deny this?

I don't care about Velikovsky's other beliefs on mythology or whatever other subjects there. We're just narrowly addressing the claim that planets do in fact wander around solar systems. This is a claim that you share in common w/ Velikovsky, correct?

We have plausible ideas as to how these planets wander in.

No, not necessarily.

As I said before, to me your ideas are just as inane as Velikovsky's are. That doesn't mean that your ideas are right or wrong. They may very well be right. But you're just throwing in a few equations in the hopes that this will "bedazzle" and "impress" others into thinking along your lines. You may be right, and Velikovsky may be right, or you may be wrong, or he may be wrong, or some various combination thereof.

But adding a math equation to your arguments doesn't necessarily make it "right"..

$$e^{i\pi} + 1 = 0$$

There.

Now, does that "prove" that I'm right in this discussion?

Does it even have anything to do w/ this discussion?

Or is that equation I posted above "frivolous and without merit", in the context of this discussion?

To me, this is how most "scientific" debate in the world proceeds.

Getting back to the point, three "mechanisms" have been proposed whereby planets can "wander" around in solar systems: spinning accretion disk losing angular momentum, etc, etc.. Whatever it was, that was posted above.

My question is (from my last post): do you actually have any observational evidence from anywhere that this actually happens, and that if it does happen, that it can cause a planet to change its orbit?

Or is this all just an elaborate guess, backed up w/ a lot of "voodoo" mathematics?

I'm not necessarily taking a pro-Velikovsky stance. I don't necessarily agree w/ him.

I'm rather taking an anti-hypocrisy stance.

If you're going to attack Velivoksky for suggesting planets can wander around solar systems, I'm a bit baffled that you would turn around and suggest exactly the same thing when the only difference is that now the money and politics at Harvard University happen to be in your favor.

That's all..