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BigDon
2008-Apr-03, 06:23 AM
What's the longest a star can stay in the main sequence?

I recall reading a smaller than Sun sized star, about .6 the mass, can last for trillions of years. I know info changes in twenty odd years and wondered what you thought.

EndeavorRX7
2008-Apr-03, 06:28 AM
BigDon,

I hear scientist throwing around numbers as if there is some accuracy to it. They say trillions, but seriously, how the heck does anyone know for sure?? Think about how long a trillion years is and how long we've been civilized. I mean how do we know if its 1 trillion or 100 trillion? The only thing that is certain is it lasts a long time in comparison to us.

Spaceman Spiff
2008-Apr-03, 02:03 PM
Ok - so we have fewer observational constraints on low mass star evolution. That's not to say that we're in the dark and it's anybody's guess. In fact their lack of observed MS/post-MS evolution already makes an important statement. And we can observe in a statistical sense the pre-main sequence evolution of these stars (they're laggards - the last ones to arrive on the main sequence in any particular star cluster). In any case, I suggest taking a look at this paper (http://adsabs.harvard.edu/abs/1997ApJ...482..420L).

I think the paper is probably old enough that you can access it even if you don't have an ApJ subscription. If not, and you'd like to read it, let me know.

Tim Thompson
2008-Apr-03, 04:29 PM
... In any case, I suggest taking a look at this paper (http://adsabs.harvard.edu/abs/1997ApJ...482..420L). I think the paper is probably old enough that you can access it even if you don't have an ApJ subscription. If not, and you'd like to read it, let me know.
It is old enough, you can tell by the green links on the ADS page that the paper can be downloaded. There are other papers by Adams & Laughlin along the same lines ...

Red Dwarfs and the End of the Main Sequence (http://adsabs.harvard.edu/abs/2004RMxAC..22...46A); Adams, Graves & Laughlin; Revista Mexicana de Astronomía y Astrofísica (Serie de Conferencias) Vol. 22, pp. 46-49, Dec 2004.
A dying universe: the long-term fate and evolution of astrophysical objects (http://adsabs.harvard.edu/abs/1997RvMP...69..337A); Adams & Laughlin; Reviews of Modern Physics, Volume 69, Issue 2, April 1997, pp.337-372.

They also wrote a book about the same time on the same topic, The five ages of the universe: inside the physics of eternity (http://www.amazon.com/Five-Ages-Universe-Physics-Eternity/dp/0684865769/ref=sr_1_1?ie=UTF8&s=books&qid=1207239983&sr=1-1). Their work is a follow-up to a 1979 paper by Freeman Dyson, Time without end: Physics and biology in an open universe (http://adsabs.harvard.edu/abs/1979RvMP...51..447D); Reviews of Modern Physics, Volume 51, Issue 3, July 1979, pp.447-460 (which is not available online without a subscription).

The lowest mass for a main sequence star is about 0.08 solar masses, and Adams & Laughlin give both 1013 (10 trillion) and 1014 (100 trillion) years as a main sequence lifetime in different papers. That lifetime is calculated from models of stellar evolution, and clearly depends on assumptions in the model. There are details of stellar models, especially convection, that still need to be worked out. So the bottom line for numbers this big, or so I think, is that the order of magnitude is reliable, but I wouldn't assume a lot of reliability in more than 1 or 2 significant figures.

A really great number that comes from Dyson's paper is the biggest number I have ever seen which had any claim to physical significance. According to Dyson, it takes about 101075 years for all the matter in the universe to spontaneously collapse to black holes (it may by 79 or 72, I can't remember the top exponent for sure at the moment, but it's a big number anyway).

Of course Dyson, and Adams & Laughlin write before the accelerated expansion became a real part of cosmology. So one might argue now that such time scales are rendered unachievable by a Big Rip.

Cougar
2008-Apr-03, 05:53 PM
The lowest mass for a main sequence star is about 0.08 solar masses, and Adams & Laughlin give both 1013 (10 trillion) and 1014 (100 trillion) years as a main sequence lifetime in different papers.
I think we should start looking for one of these to move to. I'm getting kind of claustrophobic in this neighborhood with only a couple billion years left on our heater's warranty....

jlhredshift
2008-Apr-03, 06:04 PM
A really great number that comes from Dyson's paper is the biggest number I have ever seen which had any claim to physical significance. According to Dyson, it takes about 101075 years for all the matter in the universe to spontaneously collapse to black holes (it may by 79 or 72, I can't remember the top exponent for sure at the moment, but it's a big number anyway).



Roger Penrose might say at this point that it is not the first exponent (10) but the second one (75) that worries him.

BigDon
2008-Apr-03, 07:52 PM
Thanks Mr. Spiff, Mr. Thompson

Spaceman, I'm in the middle of chapter two, but I have one maybe two cubic ****loads of stuff to do today. I was just skimming without logging in so I wouldn't get caught up in a discussion and spend all damn day posting instead of what I should be doing. But your link is so what I'm looking for I had to log in to thank you.

Mr. Thompson! You're a psychic! Get out of my head! I was going to use the info from the first question I asked to basically be able to ask intelligent questions regarding "deep time" as I heard it refferred to once. And your links go right to the spot.

Good one Cougar. I bet when future civs form around them they will have strong theories why life can't form around stars heavier than .8 solar masses. 20 bucks and a case of Full Sail. When we join the Choir Invisible, I'll be in the baratone section.

Spaceman Spiff
2008-Apr-03, 10:16 PM
Glad to have been some help!

m1omg
2008-Apr-04, 07:18 AM
It is old enough, you can tell by the green links on the ADS page that the paper can be downloaded. There are other papers by Adams & Laughlin along the same lines ...

Red Dwarfs and the End of the Main Sequence (http://adsabs.harvard.edu/abs/2004RMxAC..22...46A); Adams, Graves & Laughlin; Revista Mexicana de Astronomía y Astrofísica (Serie de Conferencias) Vol. 22, pp. 46-49, Dec 2004.
A dying universe: the long-term fate and evolution of astrophysical objects (http://adsabs.harvard.edu/abs/1997RvMP...69..337A); Adams & Laughlin; Reviews of Modern Physics, Volume 69, Issue 2, April 1997, pp.337-372.

They also wrote a book about the same time on the same topic, The five ages of the universe: inside the physics of eternity (http://www.amazon.com/Five-Ages-Universe-Physics-Eternity/dp/0684865769/ref=sr_1_1?ie=UTF8&s=books&qid=1207239983&sr=1-1). Their work is a follow-up to a 1979 paper by Freeman Dyson, Time without end: Physics and biology in an open universe (http://adsabs.harvard.edu/abs/1979RvMP...51..447D); Reviews of Modern Physics, Volume 51, Issue 3, July 1979, pp.447-460 (which is not available online without a subscription).

The lowest mass for a main sequence star is about 0.08 solar masses, and Adams & Laughlin give both 1013 (10 trillion) and 1014 (100 trillion) years as a main sequence lifetime in different papers. That lifetime is calculated from models of stellar evolution, and clearly depends on assumptions in the model. There are details of stellar models, especially convection, that still need to be worked out. So the bottom line for numbers this big, or so I think, is that the order of magnitude is reliable, but I wouldn't assume a lot of reliability in more than 1 or 2 significant figures.

A really great number that comes from Dyson's paper is the biggest number I have ever seen which had any claim to physical significance. According to Dyson, it takes about 101075 years for all the matter in the universe to spontaneously collapse to black holes (it may by 79 or 72, I can't remember the top exponent for sure at the moment, but it's a big number anyway).

Of course Dyson, and Adams & Laughlin write before the accelerated expansion became a real part of cosmology. So one might argue now that such time scales are rendered unachievable by a Big Rip.

Big Rip is just a theory, I think that universe will accelerate expanding but not rip.
And baryonic matter will be decayed in 1039 years anyways.
Wanna see bigger physically significant number?, just look;
http://www.fpx.de/fp/Fun/Googolplex/GetAGoogol.html
And this; http://en.wikipedia.org/wiki/Poincaré_recurrence_theorem ,
yelds MUCH greater numbers.
http://www.mpipks-dresden.mpg.de/mpi-doc/kantzgruppe/wiki/projects/Recurrence.html

And it is significant to physics.
Everything will happen again.....after a long time.

Vanamonde
2008-Apr-04, 09:55 AM
...And baryonic matter will be decayed in 1039 years anyways...

It that due to the half life of the proton? I have heard anything about that in awhile - has there been evidence of this?

Hornblower
2008-Apr-04, 11:14 AM
Sky and Telescope had a brief report on this topic in the November 1997 issue. A team headed by Gregory Laughlin at the University of Michigan performed a computer simulation of the evolution of a 1/10 solar mass star. Their calculations predicted about 2 billion years in the pre-main-sequence contraction, 5.7 trillion years on the main sequence, and about 0.6 trillion years of contracting into a helium-rich white dwarf. There would be no red giant stage, as convection throughout the star would prevent the layering that is necessary for such a stage.

Spaceman Spiff
2008-Apr-04, 02:21 PM
Sky and Telescope had a brief report on this topic in the November 1997 issue. A team headed by Gregory Laughlin at the University of Michigan performed a computer simulation of the evolution of a 1/10 solar mass star. Their calculations predicted about 2 billion years in the pre-main-sequence contraction, 5.7 trillion years on the main sequence, and about 0.6 trillion years of contracting into a helium-rich white dwarf. There would be no red giant stage, as convection throughout the star would prevent the layering that is necessary for such a stage.

Yep. That S&T article was an overview of the work already linked here (http://adsabs.harvard.edu/abs/1997ApJ...482..420L) (see post number 3).

m1omg
2008-Apr-04, 05:40 PM
It that due to the half life of the proton? I have heard anything about that in awhile - has there been evidence of this?

Well no evidence, yes proton decay, but it is predicted by GUT theory and I am not sure how would you discover evidence for that.

Hornblower
2008-Apr-04, 07:01 PM
Yep. That S&T article was an overview of the work already linked here (http://adsabs.harvard.edu/abs/1997ApJ...482..420L) (see post number 3).
Thanks for the link. In my haste I had not yet browsed the posted links.

Tim Thompson
2008-Apr-05, 05:11 AM
Well no evidence, yes proton decay, but it is predicted by GUT theory and I am not sure how would you discover evidence for that.
You find evidence by having lots of protons to study. The product of the decay probability per unit tiime times the number of protons times the time span of the observation gives you the number of decay events you expect. So, you look at a big pile of protons for a long time. If you don't see anything unambiguously identifiable as a proton decay, then you can set a lower limit on the proton lifetime. This has been done, and there are a few groups working on the problem, which requires a lot of people and a really big detector. Hayato, et al., 1999 (http://adsabs.harvard.edu/abs/1999PhRvL..83.1529H) (123 authors) set a lower limit for the lifetime of a proton at 6.7x1032 years. More recently, Kobayashi, et al., 2005 (http://adsabs.harvard.edu/abs/2005PhRvD..72e2007K) (137 authors) found a maximum lower limit of 2.3x1033 years. So far no proton decay events have been reported, that I know of.

Vanamonde
2008-Apr-06, 04:50 AM
Wow! Decaying protons will produces neutrinos of a certain power. So, Super-Kamiokande in Japan and other neutrinos detectors should detect it, maybe someday. "Therefore a lower limit on the partial lifetime of the proton τ/B\(p-->ν¯K+\) was found to be 6.7×10^32 years at 90% confidence level.

The abstract of the second papers says, "We set lower limits of partial nucleon lifetime 2.3×10^33, 1.3×10^32, 1.3×10^33, and 1.0×10^33 years at 90% confidence level for p→ν¯K+, n→ν¯K0, p→μ+K0, and p→e+K0 modes, respectively. These results give a strong constraint on supersymmetric grand unification models. "

No maximum lower limit - different ones for different decay modes.

Hornblower
2008-Apr-06, 01:23 PM
Here are some responses to discussion since my last post, in no particular order.

Most of my observations of projected images of the Sun were during solar eclipses, with the Sun high in a clear blue sky. I would describe the general appearance of the image as "warm" white, with the limb and sunspots having a slight brownish tinge. That is not a surprise considering the contribution of the blue sky to the ambient light that dominated my vision under these conditions. I probably would not have noticed that tint had I not been looking for it.

George, did the McMath room have any ambient light other than the projected solar image? If so, what type?

If asked about the intrinsic color of a reflective object such as a piece of paper, I would define it in terms of the difference, or lack thereof, between the spectral luminance of the reflected light and that of the incident light. This can be done readily with a suitable spectrometer, and can be considered independent of the exact color of the incident light, provided that light has a broad continuous spectrum over the whole range and can be held reliably constant. For supercritical work I would look for the possibility of varying tint with changes in the angle of incidence, depending on the surface texture of the object. If the spectrum of the reflected light matches that of the incident light, and the albedo is close to 100%, I would call the object white by definition. If it is darker, I would call it neutral gray.

As I write this, I am looking at a sheet of paper under a typical tungsten lamp, and it looks pure white as long as that lamp dominates my vision and I have no other white objects for comparison. However, when I hold the paper up and compare it side by side with a white house across the street, while keeping the paper illuminated only by the lamp, the paper looks distinctly beige. I am far enough from the window that the lamp is still dominating my vision. The house, under an overcast sky, looks "cold" white in this view. My experience in photographing snow with color film indicates that this cloudy sky has virtually the same color balance as the combination of the Sun and a clear blue sky.

It has been mentioned that the solar luminance is roughly equal at the red and blue ends of the spectrum, and somewhat stronger in the green range in the center. This is true if we analyze the luminance as a function of wavelength. However, if we analyze it as a function of frequency, it will appear to be strongest at the red end and much weaker elsewhere. See the following Wikipedia article which discusses these mathematical methods. The respective equations can be crunched in a spreadsheet with a little practice.
http://en.wikipedia.org/wiki/Planck's_law_of_black_body_radiation
Our eyes and visual cortex respond as they do for natural reasons, independently of our choice of a mathematical technique for analyzing the spectrum. The wavelength function appears to be a pretty good choice for making sense of it.

Suppose we wish to ascertain what our astronauts would see in a neutrally attenuated image of the Sun in space. No fancy stuff would be needed. A pinhole projection onto a neutral screen in a darkened cabin would be sufficient. If necessary the window's tint, if any, could be evaluated on the ground. I stand by my prediction that the spot would resemble a defocused image of an F0 star as seen from sea level, that is, neutral white.