[mesa-users] Interesting behavior at the lower edge of the main sequence

Frank Timmes fxt44 at mac.com
Sun Oct 23 23:50:01 EDT 2016

hi jon,

i’ll take a few of the numerous questions.

your results seem reasonable at a broad level, although its 
challenging to say more without seeing the inlist(s) and any 
run_star_extra.f90 .

perhaps these literature starting points will be useful to you

burrows et al, rev mod phys, 2001

hayashi & nakano, ptp, 1963

section 7.1 of paxton et al 2011


> On Oct 23, 2016, at 7:32 PM, Jon Brase <jon.brase at gmail.com> wrote:
> Greetings,
> I'm fairly certain I'm not the typical MESA user, in that I'm not using  
> MESA as part of formal academic research, but just on my free time to  
> satisfy my curiousity about stellar evolution.
> One of the things I've been looking into, which I haven't found any  
> detailed treatment of in the publicly available literature, is the exact  
> nature of the transition from the lower end of the main sequence to the  
> high-mass brown dwarves. All I've been able to discover through reading is  
> that the lower mass limit for the main sequence is around 0.08 solar  
> masses and that the transition is fairly sharp, without a lot of details  
> beyond that. I've been exploring this transition with MESA, and have  
> gotten some very interesting results.
> I'll begin with a review of the dynamics of brown dwarves and main  
> sequence stars as we approach the limiting mass from either side, then  
> I'll describe the behavior that I've found at the limiting mass, after  
> which, as I am not completely familiar with the physics involved or with  
> MESA, I will have a few questions.
> Early on, everything in within a few percent of the limiting mass looks  
> much the same: convective throughout, approaching the electron degeneracy  
> limit on denisty, a large fraction of luminosity provided by burning H  
> into He3, but still dependent on gravity to make up the balance.
> On the brown-dwarf side of the limiting mass, the object reaches the  
> degeneracy limit, convection stalls as the gas inside the object no longer  
> responds to changes in temperature with significant changes in volume, and  
> the fusion rate drops off as the object is no longer able to maintain its  
> internal temperature against losses through the surface by contracting  
> under gravity. The fusion rate falls off so rapidly and so soon after the  
> stall in convection that I thought at first that the latter was somehow  
> causing the former, but it turns out that they are independent results of  
> the rising degeneracy of the object that just happen to occur at around  
> the same time (this will be important later).
> The stall in convection begins with the formation of a radiative zone  
> around the core, which then grows swiftly inward until it reaches the  
> center of the star and more slowly outward ("swift" and "slow" here are  
> relative terms, as objects near the transition mass form a radiative shell  
> around 100 Gyr after formation). Apparently temperature gradient in the  
> core is enough to drive convection despite the rising degeneracy, and, of  
> course, outside of the radiative shell degeneracy is too low to choke off  
> convection.
> As we approach the limiting mass from below, the brown dwarf has more and  
> more of its luminosity provided by fusion before it hits the degeneracy  
> limit, and takes longer and longer to hit the limit.
> On the main-sequence side of the limiting mass, the star reaches the ZAMS  
> before it hits the degeneracy limit, then degeneracy decreases as fusion  
> heats the star up, with the HR track of the main sequence forming a more  
> and more acute angle with the pre-main sequence track and the time until  
> the star reaches the ZAMS getting longer and longer as the mass gets  
> closer to the lower limit of the main sequence.
> This is where the bit about the cessation of convection and the cessation  
> of fusion being separate consequences of increasing degeneracy in brown  
> dwarves becomes important: stars just above the main sequence limit  
> actually do see a radiative shell form, just as in brown dwarves. The  
> radiative shell actually insulates the core (far from quenching it as I  
> had first thought), and so for most stars in this mass range the radiative  
> shell is quite transient: its formation immediately brings the star to the  
> ZAMS, whereupon rising fusion output promptly reestablishes convection.  
> However, in a razor thin mass range right at the main sequence limit, the  
> formation of the shell does not bring the star to the ZAMS, but it does  
> insulate the core enough that gravitational contraction is able to make up  
> the difference between fusion luminosity and surface luminosity for a very  
> long time, during which a significant amount of fusion happens. Just as  
> with a brown dwarf, the core convection zone shrinks as the radiative zone  
> grows inward, but as the object lingers in this state for trillions of  
> years while still fusing, the shrinkage of the core causes a significant  
> composition gradient to form across the radiative zone as He3:H ratios in  
> the core rise.
> Finally, after 7 trillion years, the star reaches the ZAMS. Unlike more  
> massive red dwarves, however, reaching the ZAMS does not reinvigorate  
> convection, and the convective core continues to shrink, until the star  
> has a fully radiative core. Without convection, the hydrogen in the core  
> is not replenished, and as it is depleted, burning moves into a shell that  
> moves outward as the star ages. However, thus far, temperatures in the  
> core have been just sufficient to burn hydrogen, but have remained too low  
> to burn He3, resulting in a core that is mostly He3. As the hydrogen  
> burning shell moves outward, temperatures in the core become high enough  
> to start He3 fusion and complete the pp chain, which causes convection in  
> the core to restart for a while.
> As He3 is depleted in the core, convection dies down again, and He3  
> burning itself moves out into a shell. Through all of this, the star  
> increases gradually in luminosity, but more rapidly in temperature, so  
> that its HR track takes a wider angle to its original pre-main-sequence  
> track than a typical low-mass red dwarf. The track has a couple jogs in it  
> near events like He3 ignition, but is fairly straight. When the star  
> reaches an age of about 90 Tyr, however, the helium shell reaches  
> approximately the radius at which the radiative shell originally formed,  
> and, one of two things happens: either He3 fusion falters, followed by a  
> general cessation of fusion altogether and a transition to a layered  
> He4/He3/H white dwarf, or (actually the first case that I ran across) He3  
> fusion transitions to an abrupt thermal runaway. This presumably happens  
> because of the degenerate conditions and the fact that, unlike He3 burning  
> in more massive stars, almost all of the hydrogen in the He3 burning shell  
> has already been converted to He3, so He3 burning isn't limited by the  
> rate of He3 formation. However, it is not obvious to me why this seems to  
> suddenly develop after trillions of years of stable burning when the He3  
> shell reaches a given radius, rather than happening with the initial  
> ignition of He3 fusion in the core.
> During the runaway event, the power output of the He3 burning shell jumps  
> by a factor of around 1e10 from around 1e-4.7 L_sun to about 1e5.3 L_sun,  
> and the star begins an ascent up what I call the "green giant branch", to  
> a maximum radius of about 0.5 R_sun (the radius before the flash is about  
> 0.05 R_sun). I call it a "green giant" because the star grows continuously  
> hotter as it grows in radius and luminosity, which would suggest the term  
> "blue giant", but that already refers to something else (and the star  
> never gets bluer than a K spectral type). When the star reaches the tip of  
> the GGB, it has an inert, radiative core, is convective up from the region  
> where the He3 flash occured up to the surface (at the beginning of the  
> flash the radiative boundary is above the point where the flash takes  
> place), and reaches a maximum temperature of ~4500K and maximum surface  
> luminosity of 0.1 L_sun.
> The star then leaves the GGB on a track slightly to the right of it. It  
> contracts in several pulses, with more minor He3 flashes ending and  
> briefly reversing each contraction phase. Each contraction phase drives  
> convection deeper into the star, moving the burning region further inward  
> toward the core as previously inert regions receive fresh He3 and H.  
> Finally, the star settles down into a fully convective object at about  
> 1e-2 L_sun, beginning a sort of "second main sequence". Actually, the star  
> only becomes fully convective if I have use_Ledoux_criterion off,  
> otherwise a semiconvective region remains near the core which never fully  
> mixes, but this doesn't make much difference to the final structure of the  
> star; As with more typical red dwarves, convection eventually gives way to  
> a radiative core as hydrogen and He3 are depleted, and the star finally  
> settles into a He4 white dwarf phase, and the profile of nuclear  
> abundances from core to surface is pretty much the same in the end whether  
> full convection reached the core or not. Between the onset of the "second  
> main sequence" and the cessation of fusion, about a trillion years  
> elapses, in which time the star maintains a fairly constant luminosity,  
> moving straight left on the HR plot and crossing its previous GGB track.
> The transition from brown dwarf to minimal main-sequence star to  
> traditional red dwarf is very sharp for a given initial composition and  
> set of starting parameters, on the order of a millionth of the mass of the  
> star (meaning less than one Earth mass!). As such, the variation in the  
> mass at which the transition occurs varies with changes in the composition  
> of the star or simulation parameters such as the number of grid points by  
> an amount much greater than the width of the transition. Probing the  
> dynamics of the transition is complicated by the fact that the simulation  
> seems to be rather "noisy" with respect to changes in mass on the order of  
> the width of the transition: masses over the transition mass can be found  
> that evolve into brown dwarves in MESA, masses under the transition mass  
> can be found that evolve into traditional red dwarves, and so forth. I  
> believe the reason for this is quantization noise due to finite grid  
> density in MESA, and this brings me to my first two questions:
> First of all, given the quantization noise, how trustworthy are my  
> findings so far? I seem to be getting fairly consistent results as far as  
> what the minimal main sequence star looks like (in terms of structure,  
> evolution, and lifetime) when I change composition and simulation  
> paramaters and find the transition mass for the new setup, so I'm inclined  
> to think that what I'm finding represents something that actually happens  
> for stars on the edge of the main sequence, but I'm bothered by the  
> noisiness of the results. Even if my findings to this point are  
> trustworthy, it would be nice to be able to characterize the behavior of  
> the transition region with more resolution with respect to mass than the  
> quantization noise I'm presently encountering allows for (e.g, are there  
> masses for which the star reaches the main sequence, but He3 burning never  
> begins? In stars for which the He3 flash occurs, does it occur at  
> different depths for different masses?).
> Secondly, what's the best way to increase the fidelity of MESA's results  
> under very small changes in mass? I assume increasing the grid resolution  
> is going to be a big part of it, but is there anything else I'd need to  
> do? Are there any insurmountable obstacles I'm likely to encounter (i.e,  
> is there good reason to believe that MESA is not capable of delivering  
> good results for such small changes in mass whatever simulation parameters  
> are used?).
> Beyond these first two, I have several other questions:
> As I've stated, I've been using MESA to satisfy my curiosity because I  
> wasn't able to find much on this subject in the publicly available  
> literature. Has there been research done in this direction that just isn't  
> available to the general public or is otherwise obscure, or is this  
> something that just hasn't attracted a lot of interest (for example,  
> because the timeframe at which lower main sequence differentiates from the  
> upper brown dwarves is on the order of 10 times the current age of the  
> universe, or because the transition is sharper than currently available  
> simulational tools can resolve)?
> I'd also like to ask what physics needs to be taken into account in a star  
> such as what I described above. I assume, given the fact that the star's  
> pre-main sequence and early main sequence life is characterized by the  
> progressive failure of convection in the core, that mixing parameters like  
> semiconvection are probably important, but not being a professional  
> astrophysicist, I'm not quite sure of their importance in this scenario or  
> what sane values for them would be. In particular, whereas many parameters  
> for MESA have non-zero default values, which gives me an idea of what is  
> normal, alpha_semiconvection and thermohaline_coeff default to 0 (which I  
> take to mean "don't model these processes"), which makes determining sane  
> values for them more difficult for the non-initiated.
> Regarding the pgstar Power window, I assume that the reaction categories  
> shown are taken from the "Category" column in  
> $MESA_DIR/data/rates_data/reactions.list ? Is it safe to change category  
> names in that file, or are they used for physics as well as display (for  
> example, if I put he3 burning in its own category instead of in the "pp"  
> category, would it affect the application of mesh_dlog_pp_dlogP_extra)? I  
> ask because of the way that H->He3 burning and He3->He4 burning end up  
> happening in separate regions of the star in this scenario, which would  
> make it nice to be able to have them categorized separately in the Power  
> window.
> Finally, does my description of the evolution of a minimal main sequence  
> star pass the smell test? In other words, as a layman with interest in the  
> subject, I can identify the physical processes behind the various stages  
> the simulated star goes through, and it all seems fairly straightforward  
> from what I know of the physics, but is there anything that makes someone  
> with more expertise say "wait a minute, this process isn't modeled, and it  
> would make that phenomenon not happen, which would totally change the way  
> such an object would evolve", or something to that effect? The two things  
> that I think have the most potential to elicit that reaction are the weird  
> timing of the He3 flash (why does He 3 burning begin stably, proceed for  
> trillions of years, and then suddenly turn into a thermal runaway?) and  
> mass loss due to stellar winds (the transition region between classical  
> red dwarves and classical brown dwarves is less than an Earth mass across.  
> Is it realistic that a minimal main sequence star would lose less than an  
> Earth mass over trillions of years?).
> I look forward to hearing back,
> -- 
> Jon Brase
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