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Ely Rajo
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When can I say that the system is in equilibrium?
How can I estimate how quickly it takes to the system to reach equilibrium?
Thanks.
How can I estimate how quickly it takes to the system to reach equilibrium?
Thanks.
Soul Surfer said:If I remember right the reaction speed varies extremely quickly once the temperature threshold for its initiation has been reached.
so the extra heat could possibly run away before the negative feedback and cooling happens.
Your interest was in how long it takes to reach an equilibrium again you will have to look up textbooks on this but radiative transfer of energy in stars is quite slow and convective transfer by motion of the less dense heated plasma can be much quicker.
lot of the time when a star is in the main sequence necleosynthesis energy generation is going on in the core
Ely Rajo said:When can I say that the system is in equilibrium?
How can I estimate how quickly it takes to the system to reach equilibrium?
and:Ely Rajo said:When can I say that the system is in equilibrium?
How can I estimate how quickly it takes to the system to reach equilibrium?
Thanks.
Actually, I believe the answer to both above is that there is never an "equilibrium". the OP mentioned CNO cycle (Stars greater than ~1.1 Ms) but for H fusion the Proton-Proton chain would be the same in as far as H fusion/equilibrium is concerned so we can use our Sun as an example. There will always be changes in both the core and envelope layers as evidenced by the observed photosphere pulsation and magnetic and acoustic variations throughout the whole star. A star using predominately the P-P chain might be less active as far as the oscillations are concerned because of the lower T=P=lifespans, but oscillations are oscillations. Predominant because there is always at least a little bit of both P-P and CNO in any star, they aren't mutually exclusive.Space Tiger said:Which equilibrium are you referring to, exactly? Local thermodynamic equilibrium in the core? Pressure equilibrium?
That may be, but no core ever actually reaches an actual equilibrium, it changes continuously. ST's mention was pressure equilibrium with a question mark, not as an answer.neurocomp2003 said:i eblieve the equilbrium he's looking for is across one of the radial cores ...that maintains the pressure equilbrium that spacetiger mentioned. Either its from the core expanding or before changing to another burning.
Labguy said:and:Actually, I believe the answer to both above is that there is never an "equilibrium".
In this case a star's imbalances are on a much higher scale than water pressure "fluctuating wildly" from minor disturbances. Too many people are given information that leads them to think that stars/evolution is an orderly process, when the variables would actually take volumns of books to describe.Space Tiger said:If we agree that equilibrium can be a useful concept, it's then a matter of determining how much precision the OP really wanted and over what length and time scales. Depending on their response, it may turn out that they shouldn't approximate it as being in equilibrium, in which case your answer could be the best.
Labguy said:In this case a star's imbalances are on a much higher scale than water pressure "fluctuating wildly" from minor disturbances. Too many people are given information that leads them to think that stars/evolution is an orderly process, when the variables would actually take volumns of books to describe.
On some posts I give a "generic", good-enough answer and someone comes along and pounces in with great detail. Next post I put up some detail and then it is criticized as not generic enough.
A perfect example, ST, was your statement to someone a few weeks ago that:(approximate quote from memory)...
SpaceTiger said:The best way to destroy a degenerate object is to give it mass until it passes the Chandrasekhar Limit. When you do this to a white dwarf, you get a Type Ia supernova.
I hope you know that this description was so broad and innacurate as to be essentially meaningless, much less misleading to any newcomer who might then go around quoting that as gospel because Space Tiger said so.
NOT!
If anyone would like, I'll post for about the fifth time what is really necessary for a Type Ia supernova
Fundamentals maybe, but is that enough to correctly answer questions on PF? To me it isn't; someone always asks for more and then the "fundamental" guy has to search for a bunch of links. Bummer.SpaceTiger said:I'm sorry, but I don't agree that one needs to read many volumes of books to have a grasp of stellar evolution. In fact, I think the fundamentals are very easily communicated in a few chapters and I think this is the most important thing for people to understand. Helioseismology is, I believe, correctly treated as a side subject, good for probing the interiors of stars, but not particularly important for getting a qualitative understanding of stars like the sun.
Examples of what? How different cores act/react based on mass and chemical composition? Stellar pulsations? Main sequence and off-main sequence movement? End-life based on original masses? Radiative and convective zones? Why some stars have radiative cores and others have convective cores? Why PP chain and CNO cycle can, and do, occur at the same time? Stellar acoustics? What were the two different "limits" calculated by Chandrasekhar? Difference between Chandra's mass and Chandra's limit(s)? Significance of the 1.39 mass limit? Dozens of other differences? This doesn't lead me to believe that the "fundamentals are very easily communicated in a few chapters."SpaceTiger said:Furthermore, the fluctuations we see on the surface of the sun are of very low amplitude and I've never seen them incorporated into a solar model. Could you please cite some examples of this?.
More information doesn't usually bother me because any reader can just peruse the parts needed for his satisfaction. It is the oversimplifications that do, as in your statement about Type Ia supernovae below.SpaceTiger said:I haven't had any problem with your posts. Perhaps you're just being oversensitive. Just because someone decides to give more information doesn't mean that they're criticizing or correcting the information you provided.
I already qualified that in my statement that it was approximate based on memory, no search. Let your fingers do the walking.SpaceTiger said:The proper quote is (please do the search in the future):
Actually it was very inaccurate. Does 1.39 Ms ring a bell? Chandra's "limit" of 1.44 Ms doesn't apply. Carbon deflagration and detonation? Assymetric detonation? Specific chemical composition? S.E Woosley is considered about the foremost stellar physicist working today, and he (and friends) does a very nice job in explaining why so very few accreting white dwarf stars ever result in a Type Ia supernova. Check out some of his books/papers.SpaceTiger said:Again, I disagree that what I said was inaccurate. I think you'd be hard-pressed to find an astronomer who didn't think that accreting past the Chandrasekhar limit of a white dwarf would lead to a Type Ia supernova. There's serious debate about whether this is the only source of Type Ia's, but for the purpose of the post (found https://www.physicsforums.com/showpost.php?p=843864&postcount=24"), I hardly think it was necessary to get into that.)
I'm always civil; just sometimes hostile.SpaceTiger said:Let's try to be civil here.
Again I would point out the work of Woosley and friends, in books and some on the internet.SpaceTiger said:If you know, you better alert the astronomical community, cause the rest of us are still pretty unsure about it.
Labguy said:Fundamentals maybe, but is that enough to correctly answer questions on PF? To me it isn't; someone always asks for more and then the "fundamental" guy has to search for a bunch of links. Bummer.
Examples of what?
...This doesn't lead me to believe that the "fundamentals are very easily communicated in a few chapters."
Actually it was very inaccurate. Does 1.39 Ms ring a bell? Chandra's "limit" of 1.44 Ms doesn't apply.
Carbon deflagration and detonation? Assymetric detonation? Specific chemical composition?
S.E Woosley is considered about the foremost stellar physicist working today, and he (and friends) does a very nice job in explaining why so very few accreting white dwarf stars ever result in a Type Ia supernova. Check out some of his books/papers.
I'm always civil; just sometimes hostile.
Again I would point out the work of Woosley and friends, in books and some on the internet.
If "the fundamentals are very easily communicated in a few chapters" I wouldn't have 26 folders with 224 files saved in "favorites" just on stellar evolution and another 9 folders and 80 files on stellar composition (chemical) and H-R diagrams.
And after reading them all, I'm still not even close to being considered an expert on stellar evolution but am probably more versed on that particular subject than your above-average PF reader.
Labguy said:I totally agree that readers don't come here to read textbooks and that bite-sized comments are sufficient unless innacurate.
However, when someone mentions the "Chandrasekhar Limit" almost everyone thinks about the famous 1.44 Msolar and if the number needed for an answer is something different I think that should be noted.
On PF, I don't think that this is too complicated to post and certainly not "incomprehensible to the novice". We should note the differences for any reader and I don't see that as too complicated.
EDIT: You have no idea how long that took.
On this last point only, and my last point only, is that "a white dwarf star that passes the Chandrasekhar limit will become a Type Ia supernova" (approximation quote) is not correct and that Ia's are rare. This is only because so many specific conditions/properties of the WD have to be so precise that only a very few >massChandra go Type Ia.Space Tiger said:I did a lot of reading on Type Ia supernovae last night and, although I learned a number of new things, nothing suggested that what I said was inaccurate.
I added the italics and bold. The point is that so many specifics have to occur that most white dwarfs, regardless of high mass, don't make it to a Type Ia.Only the prompt detonation mechanism is agreed to be inconsistent with SN Ia spectra, as it fails to produce sufficient amounts of intermediate mass elements (Arnett 1969, Arnett et al 1971). This apparently slow progress is essentially a consequence of the overwhelming complexity of turbulent flame physics and deflagration-detonation transitions (DDTs) (Williams 1985, Zeldovich et al 1985) that makes first-principle predictions based on Mchan explosion models nearly impossible. The close analogy with thin chemical premixed flames has been exploited to develop a conceptual framework that covers all scales from the white dwarf radius to the microscopic flame thickness and dissipation scales (Khokhlov 1995, Niemeyer & Woosley 1997).
Laminar thermonuclear carbon and oxygen flames at high to intermediate densities were investigated by Buchler et al (1980), Ivanova et al (1982), and Woosley & Weaver (1986b), and, using a variety of different techniques and nuclear networks, by Timmes & Woosley (1992).
The ratio of the laminar flame speed and the turbulent velocity on the
scale of the flame thickness, K D Sl=v._/, plays an important role: If K _ 1, the laminar flame structure is nearly unaffected by turbulent fluctuations. Inserting the results of Timmes & Woosley (1992) for Sl and _ as functions of density, and using a typical turbulence velocity v.106cm/_107 cm s−1, the transition from flamelet to distributed burning can be shown to occur at a density of _dis _ 107 g cm−3 (Niemeyer & Kerstein 1997).
Given no time to expand prior to being burned, the CCO material in this scenario is transformed almost completely into iron-peak nuclei and thus fails to produce significant amounts of intermediate mass elements, in contradiction to observations (Filippenko 1997a,b). It is for this reason that prompt detonations are generally considered ruled out as viable candidates for the SN Ia explosion mechanism. In addition to the empirical evidence, the ignition of a detonation in the highdensity medium of the white dwarf core was argued to be an unlikely event. In spite of the smallness of the critical mass for detonation at _ _ 2 _ 109 g cm−3 (Niemeyer & Woosley 1997, Khokhlov et al 1997) and the correspondingly large number of critical volumes in the core (_1018), the stringent uniformity condition for the temperature gradient of the runaway region (Blinnikov & Khokhlov 1986, 1987) was shown to be violated even by the minute amounts of heat dissipated by convective motions (Niemeyer & Woosley 1997).
A different argument against the occurrence of a prompt detonation in CCO white dwarf cores was given by Kriminski et al (1998), who found that CCO detonations may be subject to selfquenching at high material densities ( _ > 2_107 g cm−3) (see also Imshennik et al 1999).
One of the most successful examples, model W7 of Nomoto et al (1984), clearly demonstrates the excellent agreement of “fast” deflagration models
with SN Ia spectra and light curves. St has been parameterized differently
by different authors, for instance as a constant fraction of the local sound speed (Hoeflich & Khokhlov 1996, Iwamoto et al 1999), using time-dependent convection theory (Nomoto et al 1976, 1984; Buchler & Mazurek 1975; Woosley et al 1984), or with a phenomenological fractal model describing the multiscale character of the wrinkled flame surface (Woosley 1990, 1997b). All these studies essentially agree that very good agreement with the observations is obtained if St accelerates up to roughly 30% of the sound speed.
Labguy said:Boring for PF readers and "too specific" but it contains:
I added the italics and bold. The point is that so many specifics have to occur that most white dwarfs, regardless of high mass, don't make it to a Type Ia.
the ignition of a detonation in the highdensity medium of the white dwarf core was argued to be an unlikely event.
Equilibrium refers to a state of balance or stability in a system, where all forces and processes are in equal and opposite quantities, resulting in no net change over time.
Equilibrium is reached when the rates of forward and reverse reactions in a system are equal, resulting in a constant concentration of reactants and products. This can occur spontaneously or through external interventions.
The time it takes for a system to reach equilibrium can be influenced by factors such as temperature, pressure, concentration of reactants and products, and the presence of catalysts or inhibitors.
The time to reach equilibrium can be estimated by using mathematical models, such as the equilibrium constant equation, to calculate the rate of the forward and reverse reactions. Additionally, experiments can be conducted to measure the rate of reaction and extrapolate the time to equilibrium.
Estimating the time to reach equilibrium is crucial for understanding the behavior of chemical and physical systems. It allows for better control and optimization of processes, prediction of outcomes, and identification of potential issues or limitations. It also helps in the development and improvement of scientific theories and models.