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Arcane
2009-Dec-04, 04:24 AM
I was watching a show about the Sun the other day. Seeing all the solar flares mass ejections that the Sun does all the time it got me to wondering.

If the Sun is 5 billion years old and it has been ejecting mass for all those years, surely it was much larger when it first started it's fusion process and ignited.

My questions are,

1) How big/massive was the sun when it first ignited.

2) If it was more massive that would surely have had some affect on how the Solar System developed. Any opinions on how this would affect the development of the planets we now have, along with their satellites?

3) The Sun has around 5 billion years left in it. In that time will it not eject even more mass thereby getting even smaller/less massive? How does this affect the future of the Planets?

Thanks.:)

WayneFrancis
2009-Dec-04, 04:54 AM
about 4.289x109km/s
31,556,926 seconds in a year
4.5x109 years
that is
142,006,167,000,000,000 seconds
or
1.42006167x1017 seconds

that means about 6.09064450263x1026kg in that 4.5 billion years.
sun is about mass is ~1.9891Ũ1030kg

or about 3.06201x10-4 of its mass?

Back of the napkin calculation.
IE in the 4.5 billion years its lost less then .03% of its mass

Can someone check my numbers?

G O R T
2009-Dec-04, 11:14 AM
Not only that but much of the ejected mass never leaves the Heliosphere, it eventually falls back to the sun.

antoniseb
2009-Dec-04, 03:16 PM
Looking at the title and not the OP, I was going to answer about 80 Jupiter masses. It started having some fusion going on while it was still accreting material.

Arcane
2009-Dec-05, 01:40 AM
about 4.289x109km/s
31,556,926 seconds in a year
4.5x109 years
that is
142,006,167,000,000,000 seconds
or
1.42006167x1017 seconds

that means about 6.09064450263x1026kg in that 4.5 billion years.
sun is about mass is ~1.9891Ũ1030kg

or about 3.06201x10-4 of its mass?

Back of the napkin calculation.
IE in the 4.5 billion years its lost less then .03% of its mass

Can someone check my numbers?

5billion years is a long time heh. I would have thought it would be a lot more than that. I mean, not even a half of a half a percent?

Thanks for the answers everyone.

neilzero
2009-Dec-05, 05:44 AM
Can someone give details on the 4.289 billion kilograms per second? Is that the calculated amount of mass converted to energy in the Sun's core? Does it include the average mass of alpha, beta etc in the solar wind? Is the mass which falls into the sun ignored or subtracted to get a net loss of mass?
My guess is significant numbers of photons are absorbed in the the sun's plasma even beyond the photosphere in the corona = energy converted back to matter and significant fission also occurs outside the core of the Sun; does this affect the 4.289 ?
Why do we think the fusion of hydrogen to helium occurs mostly on the outer surface of the core, instead of distributed throughout the core? Neil

korjik
2009-Dec-05, 07:49 AM
Can someone give details on the 4.289 billion kilograms per second? Is that the calculated amount of mass converted to energy in the Sun's core? Does it include the average mass of alpha, beta etc in the solar wind? Is the mass which falls into the sun ignored or subtracted to get a net loss of mass?
My guess is significant numbers of photons are absorbed in the the sun's plasma even beyond the photosphere in the corona = energy converted back to matter and significant fission also occurs outside the core of the Sun; does this affect the 4.289 ?
Why do we think the fusion of hydrogen to helium occurs mostly on the outer surface of the core, instead of distributed throughout the core? Neil

It should mostly just be the solar luminosity converted back to mass. Energy flux at Earth time area of a sphere 1 AU in radius. Everything else is pretty trivial.

Also, there isnt really any photon absorption above the photosphere. The photosphere is defined as where re-absorption of solar radiation ends. The net effect of the solar atmo above that is pretty small.

neilzero
2009-Dec-05, 12:21 PM
Yes, trivial in recent centuries. At the time that fusion of hydrogen to helium began, the sun was more luminous and thus lower average density. The sun cooled for about a million years, and has been warming very slowly ever since. Why is the sun warming? Also, there was more matter falling into the sun, 4.6 billion years ago. So bigger, but about the same mass. Neil

George
2009-Dec-05, 03:22 PM
Yes, trivial in recent centuries. At the time that fusion of hydrogen to helium began, the sun was more luminous and thus lower average density. Once it reached the point of Zero-Age Main Sequence (ZAMS), ~ 50 Myr from the time the cloud contracted, the Sun was about 70% the luminosity it is today and with a Planck temp. of about 5586K.


Why is the sun warming? The density of the core is constantly increasing as hydrogen converts into the more dense helium. This causes it to run hotter as it maintains hydrostatic equilibrium.

Spaceman Spiff
2009-Dec-05, 04:40 PM
Here are a couple of recent papers delving into the past, present, and future evolution of our Sun:

Solar Models: current epoch and time dependencies, neutrinos, and helioseismological properties (http://arxiv.org/abs/astro-ph/0010346)
and
Distant Future of the Sun Revisited (http://arxiv.org/abs/0801.4031)

The most important underlying reason for the Sun's evolution has to do with the increasing mean molecular weight of its core (hydrogen is fusing into helium). The core's T and L increase as a result of maintaining hydrostatic equilibrium.

Please substantiate:


Yes, trivial in recent centuries. At the time that fusion of hydrogen to helium began, the sun was more luminous and thus lower average density. The sun cooled for about a million years, and has been warming very slowly ever since. Why is the sun warming? Also, there was more matter falling into the sun, 4.6 billion years ago. So bigger, but about the same mass.

chornedsnorkack
2009-Dec-05, 06:56 PM
What is the actual ratio of Sunīs present mass loss through radiation and mass loss through solar wind?

The luminosity of quiet Sun and active Sun differs by just 0,1 %. What is the range of solar wind mass loss?

The young Sun emitted less light. Was the solar activity and wind weaker or stronger?

neilzero
2009-Dec-05, 07:42 PM
Perhaps someone else can substantiate, the portion (if any) of what I typed that is still true. I don't know where I read it, but it seemed logical except the fusion occurring at the surface of the core. As the protosun (4.6 billion years ago) gathered mass it became very hot and bright due to compression heating. Early fusion was less than today for T and L reasons (what ever that means), but there was an overlap period (perhaps much shorter than the million years I suggested when the photosphere with more area, released as much (more perhaps) energy than the present sun. The sun possibly ran out of lithium to fuse during the over lap period. Main stream opinion seems to be that the sun was dimmer 4.5 billion years ago to one million years ago. The fossil record casts doubt on lots dimmer as ice ages began quite recently. Please correct any errors.
Assuming Korjik is correct, the mass of the solar wind and the mass of the present in falling matter are each less than 1% of the mass converted to energy. If I understood correctly, the solar wind and CMEs = corona mass ejections were stronger (than now) just before and just after the sun began fusing hydrogen to helium, but perhaps still insignificant compared to the mass converted to energy. Possibly weak solar wind and rare CMEs from 4.5 billion to one million years ago.
I lack the back ground to understand much of the first link (an abstract?) that Spaceman Spiff gave, but thank you anyway. Neil

George
2009-Dec-05, 07:57 PM
As the protosun (4.6 billion years ago) gathered mass it became very hot and bright due to compression heating. Yes. [Lord Kelvin, I think, was one who calculated the age of the Sun based on how much energy could be produced by the Sun as it contracted from a glob of gas into a hot tight ball converting gravitational energy into kinetic energy. They did not know about fusion at the time.]


Early fusion was less than today for T and t reasons (what ever that means) The "T" might stand for Tritiumm which would have fused with deuterium to produce helium, but only in the earliest phase of fusion for a star because it burns lithium to make tritium (and there's not much lithium to begin with). The little "t" might stand for temperature since the temperature required for this fusion is considerably less than today's fusion process.



...but there was an overlap period (perhaps much shorter than the million years I suggested when the photosphere with more area, released as much (more perhaps) energy than the present sun. Perhaps so. Do you have any references for this? [I probably should know this, but I forget things. :)]


The sun possibly ran out of lithium to fuse during the over lap period. Main stream opinion seems to be that the sun was dimmer 4.5 billion years ago to one million years ago. Yes, but I think you'll find that this lower luminosity begins with the point in time when the protosun became a full-fledged star (ie hydrogen fusion point or ZAMS).

Prior to the ZAMS point, I would assume the Solar radius could be larger because of the lower fusion temperature, which would have made the Sun more luminous since it would have been larger in diameter.

chornedsnorkack
2009-Dec-05, 08:53 PM
What defines ZAMS?

At present, Sun is steadily expanding, so the fusion energy generation is about 100,04% of the radiation output . So there would have been a time in Sunīs history where fusion was significant, but considerably less than 100 % radiation output. Where is the dividing line between pre-main-sequence and main sequence drawn?

Hornblower
2009-Dec-05, 09:24 PM
What defines ZAMS?

At present, Sun is steadily expanding, so the fusion energy generation is about 100,04% of the radiation output . So there would have been a time in Sunīs history where fusion was significant, but considerably less than 100 % radiation output. Where is the dividing line between pre-main-sequence and main sequence drawn?

If I am not mistaken, it is when the fusion comes up to full power and generates enough energy to halt further gravitational contraction. Counterintuitively, the star was more luminous just before this point, because of the gravitational potential energy that was being transformed into heat. It stabilizes with the fusion at a somewhat lower output.

chornedsnorkack
2009-Dec-05, 09:36 PM
If I am not mistaken, it is when the fusion comes up to full power
What is "full power", considering that fusion energy output keeps increasing while on main sequence?

Cougar
2009-Dec-05, 10:32 PM
Can someone give details on the 4.289 billion kilograms per second? Is that the calculated amount of mass converted to energy in the Sun's core?

Apparently so. Although the book I'm reading has a slightly different figure - 4.4 million tons/sec, which is 4.4 billion kg/sec, as the Sun's mass being converted to energy every second.

Four billion kilograms sounds like a lot, until you consider how many kilograms are in the Sun....

Take 1030 kg, and then take another 1030 kg. The Sun's got a heck of a lot of kilograms.

Spaceman Spiff
2009-Dec-05, 11:39 PM
Perhaps someone else can substantiate, the portion (if any) of what I typed that is still true. I don't know where I read it, but it seemed logical except the fusion occurring at the surface of the core. As the protosun (4.6 billion years ago) gathered mass it became very hot and bright due to compression heating. Early fusion was less than today for T and L reasons (what ever that means), but there was an overlap period (perhaps much shorter than the million years I suggested when the photosphere with more area, released as much (more perhaps) energy than the present sun. The sun possibly ran out of lithium to fuse during the over lap period. Main stream opinion seems to be that the sun was dimmer 4.5 billion years ago to one million years ago. The fossil record casts doubt on lots dimmer as ice ages began quite recently. Please correct any errors.
Assuming Korjik is correct, the mass of the solar wind and the mass of the present in falling matter are each less than 1% of the mass converted to energy. If I understood correctly, the solar wind and CMEs = corona mass ejections were stronger (than now) just before and just after the sun began fusing hydrogen to helium, but perhaps still insignificant compared to the mass converted to energy. Possibly weak solar wind and rare CMEs from 4.5 billion to one million years ago.
I lack the back ground to understand much of the first link (an abstract?) that Spaceman Spiff gave, but thank you anyway. Neil

Look in the upper right corner of the web pages I linked to for links to the pdf files of the full papers.

Spaceman Spiff
2009-Dec-05, 11:45 PM
What is "full power", considering that fusion energy output keeps increasing while on main sequence?

He probably means that ZAMS is defined to have occurred about ~1 thermal timescale after the time the Sun came into thermal energy equilibrium, i.e., power from nuclear fusion (energy in) equals surface luminosity (energy out). But keep in mind that evolution onto ZAMS isn't an on-off switch, but rather a transition.

Spaceman Spiff
2009-Dec-05, 11:52 PM
Here (http://homepages.wmich.edu/~korista/snotes106/Sun-evolution.gif) is an annotated illustration of the evolution of our Sun. It is schematic only, but hits many of the highlights. (It's meant to be consumable by an astro 100 student -- do not mistake it for a state of the art model evolution, which the links I gave above are.)

George
2009-Dec-06, 12:26 AM
Here (http://homepages.wmich.edu/~korista/snotes106/Sun-evolution.gif) is an annotated illustration of the evolution of our Sun. It is schematic only, but hits many of the highlights. (It's meant to be consumable by an astro 100 student -- do not mistake it for a state of the art model evolution, which the links I gave above are.) I sure like your links. Thanks. [This last one seems a little off, as you suggest, but it is a nice layout of its history, better than others I've seen.]

As for ZAMS, I think it is when hydrogen fusion takes over. At this point, the mass of the star is well established because the stellar wind will prevent further accumulation of infalling mass. I could be wrong since deterium fusion might do the same thing.

Hornblower
2009-Dec-06, 01:16 AM
What is "full power", considering that fusion energy output keeps increasing while on main sequence?

I was using "full power" in a short term sense. As the core of the contracting protostar reaches a few million degrees, it induces fusion which goes at a rapidly increasing rate as the temperature continues to rise. When the heat and radiation from the fusion become intense enough to halt the contraction, the fusion rate levels off. The subsequent rate increase as the helium "ash" builds up is very slow by comparison.

neilzero
2009-Dec-06, 04:52 AM
Hi Hornblower: It seems the total fusion would increase with pressure and heat. When contraction of the core stopped, the average spacing of the atom nuclii would level off, but the heat and pressure should rise even faster, preventing the total number of atoms fusing per second from leveling off. What am I missing? Dropping density outside the core should allow the energy to reach the photo sphere sooner, thus making the photosphere hotter. Are we perhaps thinking visable spectrum instead of IR to gamma? Neil

George
2009-Dec-06, 05:54 AM
Hi Hornblower: It seems the total fusion would increase with pressure and heat. When contraction of the core stopped, the average spacing of the atom nuclii would level off, but the heat and pressure should rise even faster, preventing the total number of atoms fusing per second from leveling off. What am I missing? The contraction of the core would increase the pressure and temperature until equilibrium is reached.


Dropping density outside the core should allow the energy to reach the photo sphere sooner, thus making the photosphere hotter.If the core contracts, the outer region will contract also. [In the latter stages of a stars life, this isn't quite the case, however.] There is some variation in the density and temperature profile during the early pre-main sequence period because the convective zone, which transports heat faster, can be larger in size than during the main sequence life.

chornedsnorkack
2009-Dec-06, 08:25 AM
So ZAMS comes when Henyey track meets the main sequence. What exactly defines ZAMS point?

Spaceman Spiff
2009-Dec-06, 03:50 PM
So ZAMS comes when Henyey track meets the main sequence. What exactly defines ZAMS point?

It's been mentioned (http://www.bautforum.com/space-astronomy-questions-answers/97614-how-big-sun-when-first-ignited.html#post1637092) at least once above. But as also mentioned the definition of ZAMS is arbitrary -- there is no precise "point" (or threshold) in time, but several criteria which are met in transition.

Spaceman Spiff
2009-Dec-06, 04:13 PM
The contraction of the core would increase the pressure and temperature until equilibrium is reached.

If the core contracts, the outer region will contract also. [In the latter stages of a stars life, this isn't quite the case, however.] There is some variation in the density and temperature profile during the early pre-main sequence period because the convective zone, which transports heat faster, can be larger in size than during the main sequence life.

Actually, no, that's not necessarily the case. If the star has no means of replacing energy lost at its surface as emitted light (other than gravitational contraction), then yes the whole star will undergo contraction to maintain hydrostatic equilibrium, as it did early pre-MS. This "whole star" contraction also occurs in stars more massive than about 2 solar masses just after leaving the MS**. Otherwise, the density and temperature profiles adjust to maintain hydrostatic (dynamical) equilibrium in the face of a rising mean molecular weight within the core, as H (wt. 1 unit) is converted into He (wt. 4 units).




**Because these stars burn H to He via the highly temperature-sensitive CNO cycle, the required temperature gradient in the central regions of the star drive it into convective energy transport. The H-burning core thus remains well mixed (and need not adjust its structure as much as lower mass MS stars as H is converted to He), resulting in the star "emptying its gas tank" before another fuel supply has been identified.

George
2009-Dec-06, 05:20 PM
Actually, no, that's not necessarily the case. If the star has no means of replacing energy lost at its surface as emitted light (other than gravitational contraction), then yes the whole star will undergo contraction to maintain hydrostatic equilibrium, as it did early pre-MS. But the source of energy that would stop contraction must come from the core. So if the core contracts it must not have enough energy production to sustain itself thus not enough energy to maintain the size of the upper levels. I suppose there is a time factor since any radiative zone would delay the energy transport to the convective zone, but eventually the core contraction would necesitate the contraction of the outer layers, unless the outer layers become active in fusion.

Perhaps the relative sizes of the zones change, which might explain the lack of contraction of the star itself, though the core is shrinking. Is this the ticket?

chornedsnorkack
2009-Dec-06, 05:46 PM
So, the core of the star is contracting and heating before main sequence, on Henyey track - and it is contracting and heating when on the main sequence.

Spaceman Spiff
2009-Dec-06, 08:53 PM
But the source of energy that would stop contraction must come from the core. So if the core contracts it must not have enough energy production to sustain itself thus not enough energy to maintain the size of the upper levels. I suppose there is a time factor since any radiative zone would delay the energy transport to the convective zone, but eventually the core contraction would necesitate the contraction of the outer layers, unless the outer layers become active in fusion.

Perhaps the relative sizes of the zones change, which might explain the lack of contraction of the star itself, though the core is shrinking. Is this the ticket?

The reason the core adjusts its structure (temperature and density profile) while on the main sequence is because hydrogen is being converted into helium. The mean molecular wt is increasing, so that if NOTHING happened otherwise, the core pressure would fall beneath that required by hydrostatic equilibrium. Core 'shrinkage' while on the main sequence occurs not on a thermal time scale (as it would if there were a major energetics problem -- as during pre-MS stages), but on a much longer nuclear time scale (time to convert H into He). It's a gradual/quasi-static adjustment of the core's structure to maintain hydrostatic (more colloquially, pressure-gravity) equilibrium in the face of an increasing mean molecular wt.

This is a bigger issue for stars of our Sun's mass and less, because they convert H into He via the less temperature sensitive pp-chain, and their cores thus remain in radiative equilibrium. The result is that such stars gradually "burn" a helium "hole" in their cores' center (where T and density are greatest and so the nuclear reactions fastest). Here are some hard numbers to illustrate. In the 4.55 billion years since the Sun arrived onto the ZAMS, the temperature in at its center has risen from a bit over 13 million to nearly 16 million K, and the density there has nearly doubled to about 150 g per cc. The hydrogen mass fraction in the very center is now just ~32%, while that of helium has risen to something like 66%. H then goes up and He goes down moving away from the Sun's center. This is in contrast to the nearly homogeneous mix of 71% H and 27% He at ZAMS.

There IS a time period, post-MS (http://www.bautforum.com/space-astronomy-questions-answers/97614-how-big-sun-when-first-ignited.html#post1637435), that stars more massive than about twice that of our Sun DO undergo overall contraction, and this IS an energetics problem, as you describe.

Does that make more sense?

George
2009-Dec-07, 05:21 AM
Does that make more sense? That's nice info on the core, but what would explain the outer region not contracting when the core contracts, other than reasons I mentioned?

Tim Thompson
2009-Dec-07, 05:58 AM
So if the core contracts it must not have enough energy production to sustain itself thus not enough energy to maintain the size of the upper levels. ... but eventually the core contraction would necesitate the contraction of the outer layers, unless the outer layers become active in fusion.
Not really. When the core contracts it actually heats up, generating more energy, not less. This means the outer layers are sitting on a hotter core. Hence, the outer layers expand while the inner layers (core) contract, so as to maintain thermal equilibrium (the larger surface area cools more efficiently). That's how stars like Betelgeuse get to be nearly 10 AU across!

chornedsnorkack
2009-Dec-07, 02:10 PM
So, when Sun is on the pre-main-sequence Henyey track, the core is contracting and heating, it is already hot enough to be radiative and undergo some protium fusion as well as lithium and deuterium fusion, and therefore have composition gradients, and the fusion output is increasing.

When the Sun is already on main sequence, all of the above still apply.

The only apparent difference seems to be that on Henyey track, the exterior is contracting, but on the main sequence, the exterior is expanding even as the core contracts...

Spaceman Spiff
2009-Dec-07, 05:42 PM
That's nice info on the core, but what would explain the outer region not contracting when the core contracts, other than reasons I mentioned?

The power from fusion steadily increases, especially in the Sun-like stars, over time while on the main sequence for reasons I briefly mentioned here (http://www.bautforum.com/space-astronomy-questions-answers/97614-how-big-sun-when-first-ignited.html#post1636871).

Spaceman Spiff
2009-Dec-07, 05:56 PM
So, when Sun is on the pre-main-sequence Henyey track, the core is contracting and heating, it is already hot enough to be radiative and undergo some protium fusion as well as lithium and deuterium fusion, and therefore have composition gradients, and the fusion output is increasing.

When the Sun is already on main sequence, all of the above still apply.

The only apparent difference seems to be that on Henyey track, the exterior is contracting, but on the main sequence, the exterior is expanding even as the core contracts...

Just so that other readers are on the same track :): The Henyey track for a sun-like star represents its final approach to the ZAMS, with its interior transferring energy largely via radiation transfer (due to the reduced gas opacities at the higher T), rather than by convection. During this time period the star is not in energy equilibrium (surface L still greater than the power generated via fusion, so gravitational contraction must supply the rest), but as the proto-star thus continues to contract, the increasing temperatures and densities drive up the power generated via fusion.

Now to answer chornedsnorkack's questions -- the differences are more significant:

1) The time scale for changes in stellar structure for stars on the main sequence is far longer than that during that star's approach onto the main sequence.

2) By definition, we say that a main sequence star is in energy equilibrium, while as I just mentioned proto-stars are not.

chornedsnorkack
2009-Dec-07, 08:12 PM
Just so that other readers are on the same track :): The Henyey track for a sun-like star represents its final approach to the ZAMS, with its interior transferring energy largely via radiation transfer (due to the reduced gas opacities at the higher T), rather than by convection. During this time period the star is not in energy equilibrium (surface L still greater than the power generated via fusion, so gravitational contraction must supply the rest), but as the proto-star thus continues to contract, the increasing temperatures and densities drive up the power generated via fusion.

Now to answer chornedsnorkack's questions -- the differences are more significant:

1) The time scale for changes in stellar structure for stars on the main sequence is far longer than that during that star's approach onto the main sequence.

2) By definition, we say that a main sequence star is in energy equilibrium, while as I just mentioned proto-stars are not.

But there is no energy equilibrium. The contraction of the core goes on on the Henyey track, and it continues (at a slower speed) on main sequence. Then what marks the zero age main sequence point?

Tim Thompson
2009-Dec-07, 10:37 PM
One of the difficulties with Q&A sessions like this is that seemingly simple things can get complicated rather quickly. So let me start by advocating reference to the standard literature, to the extent this can be done. Therefore I advise that anyone interested in the problems of star formation seek out the book The Formation of Stars by Steven W. Stahler & Francesco Palla, Wiley-VCH, 2004. This is an 852 page textbook on star formation. Knowing something about physics & math helps a lot in reading it, but one can get a lot out of the text and tables even if weak on the technical end. And I can even suggest published papers that extend the basic features of the book to the latest wrinkles of research: Theory of Star Formation (http://adsabs.harvard.edu/abs/2007ARA%26A..45..565M), Cold Dark Clouds: The Initial Conditions for Star Formation (http://adsabs.harvard.edu/abs/2007ARA%26A..45..339B) and Toward Understanding Massive Star Formation (http://adsabs.harvard.edu/abs/2007ARA%26A..45..481Z), all 3 of which appear in the 2007 issue of Annual Review of Astronomy and Astrophysics.

Now, we can reference the Stahler & Palla book, chapter 16, where they discuss the physics of contraction and both the Hayashi & Henyey tracks. If I understand all this correctly, Hayashi track protostars are fully convective and the transition from convective to radiative cooling is the principle feature of the transition from Hayashi track to Henyey track. The result is that in the Henyey track the contraction of the core actually accelerates and the luminosity and surface temperature both rise (at least for objects greater than about 0.2 solar masses). The zero age main sequence (ZAMS) is where the onset of PP fusion generates enough energy to balance the energy lost through surface radiative cooling so the radius stabilizes and rapid contraction stops.

We can also answer the original question of the thread by looking at Stahler & Palla tables 16.1 and 16.2. A 1 solar mass star starts out on the birthline at 4.92 solar radii and about 7.1 solar luminosities (where I mean today's "solar"). It takes about 32,000,000 years to reach the ZAMS, steadily shrinking all the way. Somewhere between 1,000,000 and 3,000,000 years along it stops being 100% convective and the convective zone begins to thin. Once it reaches the ZAMS its radius is 1.01 solar radii (of course these are model calculations not observed protostar properties; I don't think the observational end can achieve that kind of precision at the moment).

George
2009-Dec-08, 12:59 AM
Not really. When the core contracts it actually heats up, generating more energy, not less. This means the outer layers are sitting on a hotter core. Hence, the outer layers expand while the inner layers (core) contract, so as to maintain thermal equilibrium (the larger surface area cools more efficiently). Yet additional heat expands the core, not contracts it, except in the case when the core has converted more and more hydrogen into helium as others, including me, have stated. I'm sure this is what you meant, but as you say, these things can get a little confusing.


That's how stars like Betelgeuse get to be nearly 10 AU across! I suspect the better explanation is that the outer layers are at a temperature and pressure that allow fusion, which generates the needed heat for the swelling, though what you are saying is still correct.

My focus was more on the pre-main sequence events and not the late stages, but it is worth discussing them as well.


But there is no energy equilibrium. The contraction of the core goes on on the Henyey track, and it continues (at a slower speed) on main sequence. But that is during the pre-main sequence period and not the main sequence period where equilibrium is found.


Then what marks the zero age main sequence point? I suspect it is when hydrostatic equilibrium is established during hydrogen fusion. This is also the time when the star is essentialy no longer gaining mass.

George
2009-Dec-08, 01:04 AM
We can also answer the original question of the thread by looking at Stahler & Palla tables 16.1 and 16.2. A 1 solar mass star starts out on the birthline at 4.92 solar radii and about 7.1 solar luminosities (where I mean today's "solar"). This is interesting. I'm guessing the 7.1x Solar luminosity is bolometric and not near so bright in the visible range. If so, any idea of its visible brightness?

Spaceman Spiff
2009-Dec-08, 03:32 AM
But there is no energy equilibrium. The contraction of the core goes on on the Henyey track, and it continues (at a slower speed) on main sequence. Then what marks the zero age main sequence point?

Read again what I've already said. If the Sun were not replacing the energy lost at its surface via its surface luminosity, then it would need to settle the bill with the release of gravitational potential energy of contraction. It is not presently doing so, and it is around this event of energy in = energy out that the Sun arrived on the ZAMS.

I'll say it another way. If the Sun were not presently in energy equilibrium (by any useful definition) it would be evolving -- contracting or expanding -- on a thermal timescale (millions of years for our Sun). It is not. Energetically (and in bulk structurally), the Sun is evolving on a nuclear timescale ~1000x longer (billions of years for our Sun) because it is on this timescale that H is converted into He, thus changing the mean molecular weight of the gas there. The most important source of pressure in our Sun's core is directly proportional to density and temperature, but inversely proportional to the mean molecular weight. So the core's density and temperature profiles must change very gradually over time, and along with them the power generated by fusion with the increasing contribution of Helium to the core's composition. These changes are quasi-static -- a shifting energy equilibrium.

Crude analogy:
The valves of your car's tires have a slow air leak. For the sake of argument, they all leak at 1 molecule per second (a very slow leak, but never mind). Now, there is a pressure (difference**) monitoring device within the tire that monitors the pressure and for every molecule that leaves the valve, another one is introduced via this device. If the device under-corrects or over-corrects, a negative feedback loop is invoked to match the proper target tire pressure. As the tire ages, the rate of the leak increases to 3 and then later 10 molecules per second, but the device keeps tabs and ascertains that air molecules are introduced at the same rate they leave. As long as that is true, your tires will always have the proper tire inflation. Going much beyond this, the analogy stretches thin.



**What you measure with a tire "pressure" gauge is a pressure difference between the pressure of the air inside the tire and that of the local ambient atmospheric pressure. After a blowout, this pressure difference is zero. But otherwise this pressure difference scaled in proportion to the footprint area of the tire on the ground equates with the weight bearing down on that axle. You can get a usefully accurate measure the weight of your car this way.

Spaceman Spiff
2009-Dec-08, 03:52 AM
I suspect it is when hydrostatic equilibrium is established during hydrogen fusion. This is also the time when the star is essentialy no longer gaining mass.

The Sun was in hydrostatic equilibrium for ~50 million years before it arrived on the main sequence. It is not established, as you say, "during hydrogen fusion".

If H fusion were not in operation (or weakly operating) within our Sun, much as during our Sun's early protostar stage, it can be (and was) in hydrostatic equilibrium. In this case because the sources of pressure within the star are dependent on T, the star can release gravitational potential energy via slow contraction -- half of it replacing the energy lost each second at the protostar's surface, and the other half in increasing the thermal energy content of the gas. So as the protostar radiates energy away from its surface, it sinks into a deeper potential well as it contracts, becoming hotter (and of course denser) to maintain a balance between pressure and gravity (in colloquial terms). This balance shifts quasi-statically on the thermal (or Kelvin-Helmholtz) time scale. Star's (and all bound systems) in dynamical equilibrium have negative heat capacities!

If the Sun or protostar (or some major mass shells within) were to suddenly find itself out of hydrostatic equilibrium, it would quickly adjust its structure to move toward re-establishing this dynamical equilibrium by rapidly collapsing or expanding on what is usually referred to as the dynamical time scale (~sound crossing time scale, or ~free-fall time scale). For our Sun this time scale is minutes.

So stars have 3 important time scales. These are (with values pertaining to our Sun):

1) dynamical time scale = time to establish hydrostatic equilibrium: minutes
2) thermal time scale = time for the star to dump its present thermal energy supply (or to thermally relax after a burp or hiccup in energy): 107 years (also referred to as the Kelvin-Helmholtz contraction time scale).
3) nuclear time scale = time for fusion to change significantly the elemental composition of the star's core: a fair fraction of its main sequence life span of 10 billion years.

chornedsnorkack
2009-Dec-08, 09:30 AM
Read again what I've already said. If the Sun were not replacing the energy lost at its surface via its surface luminosity, then it would need to settle the bill with the release of gravitational potential energy of contraction. It is not presently doing so, and it is around this event of energy in = energy out that the Sun arrived on the ZAMS.

I'll say it another way. If the Sun were not presently in energy equilibrium (by any useful definition) it would be evolving -- contracting or expanding -- on a thermal timescale (millions of years for our Sun). It is not. Energetically (and in bulk structurally), the Sun is evolving on a nuclear timescale ~1000x longer (billions of years for our Sun) because it is on this timescale that H is converted into He, thus changing the mean molecular weight of the gas there. The most important source of pressure in our Sun's core is directly proportional to density and temperature, but inversely proportional to the mean molecular weight. So the core's density and temperature profiles must change very gradually over time, and along with them the power generated by fusion with the increasing contribution of Helium to the core's composition. These changes are quasi-static -- a shifting energy equilibrium.



But the slow (nuclear timescale) evolution of the structure of Sun does still cause release of energy from the contraction of solar core. This energy release must be a (small) contributor to the energy budget of the Sun. The nuclear timescale evolution may be 1000x slower than thermal timescale. But if the Sun on main sequence were to get 99,90 % of it energy from fusion and 0,10% of energy from contraction whereas a Sun getting just 50% of energy from fusion was still contracting on a roughly thermal timescale on Henyey track, where precisely does the ZAMS point go? At the spot where the energy from fusion is 90,0% total? Or 99,0% total?

George
2009-Dec-08, 03:46 PM
The Sun was in hydrostatic equilibrium for ~50 million years before it arrived on the main sequence. It is not established, as you say, "during hydrogen fusion".

If H fusion were not in operation (or weakly operating) within our Sun, much as during our Sun's early protostar stage, it can be (and was) in hydrostatic equilibrium. In this case because the sources of pressure within the star are dependent on T, the star can release gravitational potential energy via slow contraction -- half of it replacing the energy lost each second at the protostar's surface, and the other half in increasing the thermal energy content of the gas. So as the protostar radiates energy away from its surface, it sinks into a deeper potential well as it contracts, becoming hotter (and of course denser) to maintain a balance between pressure and gravity (in colloquial terms). This balance shifts quasi-statically on the thermal (or Kelvin-Helmholtz) time scale. I would still be a little surprised that if both hydrostatic equilibrium and hydrogen fusion were found that the star would not be considered to be on the main sequence. [I did state both conditions.]


Star's (and all bound systems) in dynamical equilibrium have negative heat capacities! This is intriguing. What does it mean? Adding more heat will release a greater amount of heat?

Tim Thompson
2009-Dec-08, 04:23 PM
Star's (and all bound systems) in dynamical equilibrium have negative heat capacities!

This is intriguing. What does it mean? Adding more heat will release a greater amount of heat?
Here is what Stahler & Palla have to say (emphasis as in the original text) ...

The Formation of Stars, Stahler & Palla, page 584, section 16.2.1 ...
"Radiation drains away internal energy. Since the object is gravitationally bound, its total energy, Etot, is negative and becomes more so with the passage of time. The virial theorem tells us, however, that the thermal contribution, U, is -Etot. Thus, U actually increases, as does the internal temperature. A pre-main-sequence star is therefore an object with negative heat capacity, one whose temperature rises as a result of heat loss. This behavior, odd by terrestrial standards, occurs because of the increased gravitational binding."

I think you will find that this is true of stellar cores in all, or virtually all cases. So earlier, when you said ... "Yet additional heat expands the core, not contracts it, ..." you were saying something that looks like it makes sense but in fact does not actually happen. Stellar cores invariably contract, albeit slowly, during main sequence evolution. The result is a loss of heat energy but an increase in temperature, where one would expect an increase in temperature to indicate an increase in heat energy. I don't know of any example of a stellar core actually expanding, although there may be nuclear instabilities in some classes of variable star that will do this; most variable stars, Cepheids for instance, vary because of changing ionization states in the "mantle" of the star, well outside the core.

While the temperature of the solar core is around 15,000,000 Kelvins, the temperature of a core in advanced nuclear burning stages can be about 3,000,000,000 Kelvins. That's what the core of Betelgeuse certainly is like, an extremely tiny nuclear furnace probably smaller than our own sun, surrounded by an atmosphere nearly 5 AU in radius, required to cool the star and maintain at least quasi-equilibrium.

Spaceman Spiff
2009-Dec-08, 05:11 PM
I would still be a little surprised that if both hydrostatic equilibrium and hydrogen fusion were found that the star would not be considered to be on the main sequence. [I did state both conditions.]


Maybe we're talking past one another. Yes, a main sequence star is in hydrostatic equilibrium, but that's not the criterion to establish when star arrives on the ZAMS. In the case of the Sun, it was in hydrostatic equilibrium (HE) for ~50 million (5 x 107) years before arriving onto the ZAMS. In the big picture, the protostellar sun slowly contracted onto the ZAMS -- maintaining HE all along the way. It became hotter and denser until the fusion reaction rates became high enough to replace the energy lost as the star's surface luminosity.



This is intriguing. What does it mean? Adding more heat will release a greater amount of heat?

If you add energy to a star initially in hydrostatic equilibrium, it will find a new equilibrium in an expanded, cooler state. If you suck energy out, it will find a new equilibrium in a contracted, hotter state. This is true as long as pressure and temperature are strongly coupled.

George
2009-Dec-08, 05:16 PM
Here is what Stahler & Palla have to say (emphasis as in the original text) ...

The Formation of Stars, Stahler & Palla, page 584, section 16.2.1 ...
"Radiation drains away internal energy. Since the object is gravitationally bound, its total energy, Etot, is negative and becomes more so with the passage of time. The virial theorem tells us, however, that the thermal contribution, U, is -Etot. Thus, U actually increases, as does the internal temperature. A pre-main-sequence star is therefore an object with negative heat capacity, one whose temperature rises as a result of heat loss. This behavior, odd by terrestrial standards, occurs because of the increased gravitational binding."
Thanks Tim. I'm unclear why a protostar is seen as having negative total energy unless the negative refers only to the change in energy (ie rate of energy), perhaps. A rise in temperature due to heat loss, however, does explain the negative heat capacity idea. Yet I would expect this only in a PMS star and not an MS star, right? There's something about the gas law that I find ideal. [ok, bad pun. ;)]


Stellar cores invariably contract, albeit slowly, during main sequence evolution. The result is a loss of heat energy but an increase in temperature, where one would expect an increase in temperature to indicate an increase in heat energy. I don't know of any example of a stellar core actually expanding,... Yes, but if we eliminate the causal condition of changes to the core density -- increasing the helium to hydrogen ratio -- then I don't see this being possible. [I was trying to look for another factor in contraction. Is there one, assuming equilibrium?]


...although there may be nuclear instabilities in some classes of variable star that will do this; most variable stars, Cepheids for instance, vary because of changing ionization states in the "mantle" of the star, well outside the core. Yes, the behavior of the hydrogen and helium ionization layers is fascinating, but I haven't had the time to enjoy this facet of stellar physics. I can see why variable star astronomers (eg Pamela Gay) enjoy these jewels.


While the temperature of the solar core is around 15,000,000 Kelvins, the temperature of a core in advanced nuclear burning stages can be about 3,000,000,000 Kelvins. That's what the core of Betelgeuse certainly is like, an extremely tiny nuclear furnace probably smaller than our own sun, surrounded by an atmosphere nearly 5 AU in radius, required to cool the star and maintain at least quasi-equilibrium. I wonder what the luminosity is of just the inner core? Perhaps all the other layers -- the ones also engaged in fusion -- are the greater contributors.

Spaceman Spiff
2009-Dec-08, 05:33 PM
But the slow (nuclear timescale) evolution of the structure of Sun does still cause release of energy from the contraction of solar core. This energy release must be a (small) contributor to the energy budget of the Sun. The nuclear timescale evolution may be 1000x slower than thermal timescale. But if the Sun on main sequence were to get 99,90 % of it energy from fusion and 0,10% of energy from contraction whereas a Sun getting just 50% of energy from fusion was still contracting on a roughly thermal timescale on Henyey track, where precisely does the ZAMS point go? At the spot where the energy from fusion is 90,0% total? Or 99,0% total?

By the time the Sun arrived on the main sequence (a somewhat arbitrary point in time), 99.9%+ of its luminosity was generated by H-fusion. Averaged over its full MS life span, H fusion will supply ~99.99% of its luminosity.

As they say, a picture is worth a 1000 words (http://homepages.wmich.edu/%7Ekorista/approach_to_ZAMS_1M_Z02.pdf). Shown is a 1 solar mass star's approach (with the listed composition in H, He and heavy elements) onto the ZAMS. The horizontal axis is time in log10 units (107 -- 108 years) since establishing hydrostatic equilibrium, increasing to the right. The vertical axis is the fraction of the star's luminosity L(t) at some time t supplied by either fusion or gravitational potential (Gravo-Thermal) energy. While this is a detailed stellar evolution computation, it is not state of the art for our Sun in particular.

Notice how the contributions of gravo-thermal power and H-fusion power switch places about 30,000,000 years in -- roughly half of a Kelvin-Helmholtz contraction timescale for a 1 solar mass star with the ZAMS radius (0.87 Rsun) and luminosity (0.60 Lsun). It then takes roughly 1 more of those for the star to stabilize its structure with its newly found source of energy that will maintain it on the MS for ~1010 years. There are small oscillations in L(H-fusion)/L(star) out to ~108 years at the 0.1%-0.2% level, damped by the pressure-temperature thermostat, which then fall to a more constant level of ~0.01% for the remainder of the MS life span (according to these computer simulations).

George
2009-Dec-08, 05:43 PM
Maybe we're talking past one another. Yes, a main sequence star is in hydrostatic equilibrium, but that's not the criterion to establish when star arrives on the ZAMS. In the case of the Sun, it was in hydrostatic equilibrium (HE) for ~50 million (5 x 107) years before arriving onto the ZAMS. In the big picture, the protostellar sun slowly contracted onto the ZAMS -- maintaining HE all along the way. It became hotter and denser until the fusion reaction rates became high enough to replace the energy lost as the star's surface luminosity. I assumed that a contraction would mean HE is not being maintained. An analgoy would be a tiny hole in a balloon causing the balloon to contract yet, apparently, it is still considered to be in HE. Is this a correct analogy?


If you add energy to a star initially in hydrostatic equilibrium, it will find a new equilibrium in an expanded, cooler state. If you suck energy out, it will find a new equilibrium in a contracted, hotter state.This is georgeeze, and I like it! :)

Spaceman Spiff
2009-Dec-08, 06:03 PM
I assumed that a contraction would mean HE is not being maintained. An analgoy would be a tiny hole in a balloon causing the balloon to contract yet, apparently, it is still considered to be in HE. Is this a correct analogy?

In a word, 'no'.

If Dr. Evil's thermal sucking machine could instantaneously extract 99% (just to pick a number) of our Sun's present total thermal energy content, it would rapidly fall in on itself to a white dwarf (about 1% of its present size) in ~30 minutes. That is what I call a collapse, which is not the same as gravitational contraction. Consider again my car tire analogy (http://www.bautforum.com/space-astronomy-questions-answers/97614-how-big-sun-when-first-ignited-2.html#post1638390). If instead of a very slow leak in the valves, you and 3 friends blow out the side walls of the tires, at which point the car would fall freely under its own (gravity) weight until the axles hit the ground in a fraction of a second. Why? Because the tire could no longer maintain or find a new pressure-gravity balance.

Thermal Equilibrium -- the thermal energy content of the star is maintained by H fusion, so no gradual contraction or gradual expansion on the thermal time scale.

Hydrostatic Equilibrium -- pressure/gravity are in balance, so no rapid collapse or rapid expansion on the dynamical time scale.

As I mentioned here (http://www.bautforum.com/space-astronomy-questions-answers/97614-how-big-sun-when-first-ignited-2.html#post1638399), these two time scales differ by many, many orders of magnitude.

chornedsnorkack
2009-Dec-08, 06:15 PM
Thanks Tim. I'm unclear why a protostar is seen as having negative total energy unless the negative refers only to the change in energy (ie rate of energy), perhaps.


Because it is gravitationally bound.

All gravitationally bound systems, whether protostars, stars, planets or whatever else have negative energy because the zero point of energy is when the entire contents of the star or planet are scattered to infinity.

George
2009-Dec-08, 06:30 PM
Thermal Equilibrium -- the thermal energy content of the star is maintained by H fusion, so no gradual contraction or gradual expansion on the thermal time scale.

Hydrostatic Equilibrium -- pressure/gravity are in balance, so no rapid collapse or rapid expansion on the dynamical time scale. Yes, I think I get it. It would be like the balloon if we assign the balance between the elastic tensile strength of the balloon and pressure, but allow the size of the balloon to vary by simply heating it or cooling it. In both cases, their balance (pressure and hoop stress(?) ) is maintained.


All gravitationally bound systems, whether protostars, stars, planets or whatever else have negative energy because the zero point of energy is when the entire contents of the star or planet are scattered to infinity. Well, getting one (hopefully) out of two is something, but not great. :( A scattered star to infinity is potential energy to me and not all that negative.

nokton
2009-Dec-08, 06:51 PM
Here are a couple of recent papers delving into the past, present, and future evolution of our Sun:

Solar Models: current epoch and time dependencies, neutrinos, and helioseismological properties (http://arxiv.org/abs/astro-ph/0010346)
and
Distant Future of the Sun Revisited (http://arxiv.org/abs/0801.4031)

The most important underlying reason for the Sun's evolution has to do with the increasing mean molecular weight of its core (hydrogen is fusing into helium). The core's T and L increase as a result of maintaining hydrostatic equilibrium.

Please substantiate:
At last, reason, logic, and deduction. May I make a point that our sun is creating mass
as fast as it is losing it, Spaceman dosen't have to delve into papers to prove a point,
the point is self evident to those who would but grasp the concept.
Where am I coming from? The current trotted out description of a black hole in two
dimensions, portrayed as a sink hole in spacetime, is trash science.
That scientists of reason and logic do not challenge this view, am disappointed.
A gravity well has three dimensions, space, mass, and direction.
I can stand anywhere on this little world, the pumpkin I drop falls the same,
in two dimensions it would not.
Is there anyone to contest this?
For what it's worth, I love this site, and the people in it.
Peter

Spaceman Spiff
2009-Dec-08, 07:17 PM
At last, reason, logic, and deduction. May I make a point that our sun is creating mass
as fast as it is losing it, Spaceman dosen't have to delve into papers to prove a point,
the point is self evident to those who would but grasp the concept.
Where am I coming from? The current trotted out description of a black hole in two
dimensions, portrayed as a sink hole in spacetime, is trash science.
That scientists of reason and logic do not challenge this view, am disappointed.
A gravity well has three dimensions, space, mass, and direction.
I can stand anywhere on this little world, the pumpkin I drop falls the same,
in two dimensions it would not.
Is there anyone to contest this?
For what it's worth, I love this site, and the people in it.
Peter

Errr...uhhh....I'll take the compliment, but the Sun isn't gaining mass. It's losing mass, both from fusion (E = mc2) and the wind it is blowing, although both rates are tiny. But we had best not go any further with that here.

As for the rest, I could not make heads or tails, except that it appears you've mistaken a strawman (or at best a limited analogy) for general relativity. And again, I don't see the relevance to the OP.

neilzero
2009-Dec-08, 08:00 PM
I still think the radius of the sun was slightly greater and the mass slightly less = lower average density, one second after the first few atoms of hydrogen fused to helium. The beginning fusion would have occured in a microscopic portion of the core. Shock waves would have moved out at perhaps 1% of c, inducing fusion over a wide area a few seconds later. It may have taken days for the fusion to ramp up to the steady state value and more days (centuries perhaps) for the energy (except the neutrinos) released by fusion to reach the photosphere, almost 400,000 miles away. Portions of the outer layers of the sun would continue the collapse = falling toward the core until the fusion energy flux reached the photosphere. Then raduis expansion would begin followed by compression = oscillation until the shock waves dissapated. The solar wind would divert some of the infalling mass, but enough would fall in to more than offset the mass being expelled plus the mass being converted to energy by fusion. This mass gaining likely will persist for years, perhaps a billion years. Please correct my erroneous thinking. Neil

Spaceman Spiff
2009-Dec-08, 09:00 PM
I still think the radius of the sun was slightly greater and the mass slightly less = lower average density, one second after the first few atoms of hydrogen fused to helium. The beginning fusion would have occured in a microscopic portion of the core. Shock waves would have moved out at perhaps 1% of c, inducing fusion over a wide area a few seconds later. It may have taken days for the fusion to ramp up to the steady state value and more days (centuries perhaps) for the energy (except the neutrinos) released by fusion to reach the photosphere, almost 400,000 miles away. Portions of the outer layers of the sun would continue the collapse = falling toward the core until the fusion energy flux reached the photosphere. Then raduis expansion would begin followed by compression = oscillation until the shock waves dissapated. The solar wind would divert some of the infalling mass, but enough would fall in to more than offset the mass being expelled plus the mass being converted to energy by fusion. This mass gaining likely will persist for years, perhaps a billion years. Please correct my erroneous thinking. Neil

Very little of this is relevant to our universe. :)

But lucky for you, one of the great things about science is that we don't always have to guess. Tim Thompson and I have had several posts with several links to papers provided. I suggest starting with those.

neilzero
2009-Dec-08, 10:40 PM
~My comments are enclosed with a~ our sun is creating mass
as fast ~why do you think that?~ as it is losing it, Spaceman doesn't have to delve into papers to prove a point,
the point is self evident to those who would but grasp the concept. ~ self evident is the result of grasping?~
Where am I coming from? The current trotted out description of a black hole in two
dimensions, portrayed as a sink hole in spacetime, is trash science. ~likely, but what alternative do you suggest?~
That scientists of reason and logic do not challenge this view, am disappointed.
A gravity well has three dimensions, space, mass, and direction. ~space = length, width and height? but these approach zero as an asentote; direction with respect to what? Surely you don't believe in a universal stationary?~
Is there anyone to contest this? I'll try, but you need to explain the relvence of pumpkins falling toward the center of Earth. Neil

Spaceman Spiff
2009-Dec-08, 11:00 PM
May I make a point that our sun is creating mass
as fast as it is losing it, ....
the point is self evident to those who would but grasp the concept.
Where am I coming from? The current trotted out description of a black hole in two
dimensions, portrayed as a sink hole in spacetime, is trash science.
That scientists of reason and logic do not challenge this view, am disappointed.
A gravity well has three dimensions, space, mass, and direction.
I can stand anywhere on this little world, the pumpkin I drop falls the same,
in two dimensions it would not.
Is there anyone to contest this?
For what it's worth, I love this site, and the people in it.
Peter

If you'd like to develop your thoughts along these lines, may I suggest taking them to the ATM forum? And you might keep in mind that it's not the job of scientists to "prove" all ideas false. The burden is actually on you to demonstrate a model's usefulness in predicting and explaining measurable phenomena. Good luck!

Spaceman Spiff
2009-Dec-09, 04:01 AM
My apologies to neilzero for my mis-attributing statements made by nokton in my post just above, as it originally appeared.

chornedsnorkack
2009-Dec-09, 09:12 AM
I still think the radius of the sun was slightly greater and the mass slightly less = lower average density, one second after the first few atoms of hydrogen fused to helium. The beginning fusion would have occured in a microscopic portion of the core. Shock waves would have moved out at perhaps 1% of c, inducing fusion over a wide area a few seconds later.
Please correct my erroneous thinking.

It is indeed erroneous.

Fusion never can occur as a chain reaction on a microscopic scale. When energy is released in a fusion reaction, this is like a radioactive decay. The energetic particles are very unlikely to cause another fusion reaction in their first few collisions. The energy of each fusion event is rapidly dissipated as heat in the following collision cascade.