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Creation of Li-7 and Destruction of He-3, Be-9, B-10, and B-11 in Low Mass Red Giants, Due

Creation of Li-7 and Destruction of He-3, Be-9, B-10, and B-11 in Low Mass Red Giants, Due
Creation of Li-7 and Destruction of He-3, Be-9, B-10, and B-11 in Low Mass Red Giants, Due

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preprint astro-ph/9512122;ApJ,in press Creation of 7Li and Destruction of 3He,9Be,10B,and 11B in Low Mass Red Giants,Due to Deep Circulation I.-Juliana Sackmann W.K.Kellogg Radiation Laboratory 106-38,California Institute of Technology,Pasadena,CA 91125and Arnold I.Boothroyd 1Dept.of Mathematics &Statistics,Monash University,Clayton,VIC 3168,Australia ABSTRACT It has been demonstrated that 7Li can be created in low mass red giant stars via the Cameron-Fowler mechanism,due to extra deep mixing and the associated “cool bottom processing ”.Under certain conditions,this 7Li creation can take the place of the 7Li destruction normally expected.Note that such extra mixing on the red giant branch (RGB)has previously been invoked to explain the observed 13C enhancement.This new 7Li production can account for the recent discovery of surprisingly high lithium abundances in some low mass red giants (a few of which are super-rich lithium stars,with abundances higher than that in the interstellar medium).The amount of 7Li produced can exceed log ε(7Li)~4,but depends critically on the details of the extra mixing mechanism (mixing speeds,geometry,episodicity).If the deep circulation is a relatively long-lived,continuous process,lithium-rich RGB stars should be completely devoid of beryllium and boron.

Cool bottom processing leads to 3He destruction in low mass stars;in contrast to the 7Li creation,the extent of 3He depletion is largely independent of the details of the extra mixing mechanism.The overall contribution from solar-metallicity stars (from 1to 40M ⊙)is expected to be a net destruction of 3He,with an overall 3He survival fraction g 3≈0.9±0.2(weighted average over all stellar masses);this is in contrast to the conclusion from standard dredge-up theory,which would predict that stars are net producers of 3He (with g dr 3~2.4±0.5).Population II stars experience even more severe 3He depletion,with 0.3~

0.7.Destruction of 3

He in low mass

stars is consistent with the requirements of galactic chemical evolution models;it would also result in some relaxation of the upper bound on the primordial (D+3He)/H

abundance,thus relaxing the lower bound on the cosmic baryon density?b from Big

Bang nucleosynthesis calculations.

For reference,we also present the e?ects of standard?rst and second dredge-up on the helium,lithium,beryllium,and boron isotopes.

Subject headings:Galaxy:abundances—nuclear reactions,nucleosynthesis,

abundances—stars:abundances—stars:AGB and Post-AGB—stars:giants

1.Introduction

For some time,it has been known that stars super-rich in lithium exist,with abundances much higher than they could have been endowed with at birth,i.e,larger than the present interstellar medium value.A much clearer understanding of these super-rich lithium stars was provided by the recent Magellanic Cloud observations of Smith&Lambert(1989,1990),who obtained for the ?rst time a luminosity range for lithium-rich asymptotic giant branch(AGB)stars.They found that the most luminous AGB stars were lithium-rich,in excellent agreement with the predictions of theoretical models of hot bottom burning(Sackmann,Smith,&Despain1974;Scalo,Despain,& Ulrich1975;Sackmann&Boothroyd1992,1995,1998).Hot bottom burning is predicted to occur occur only in the most massive AGB stars(between~4and~7M⊙),which are also the most luminous ones(Iben1975;Bl¨o cker&Sch¨o nberner1991;Lattanzio1992;Sackmann&Boothroyd 1992,1995,1998;Boothroyd&Sackmann1992;Boothroyd,Sackmann,&Ahern1993).However, some lithium-rich stars do not?t into the above scenario.

During most of the evolution of a star,lithium is destroyed,as it burns at relatively low temperatures.During the pre-main sequence phase,there can be signi?cant lithium destruction for stars of masses~<1M⊙(see,e.g.,D’Antona&Mazzitelli1984;Pro?tt&Michaud1989; VandenBerg&Poll1989;Michaud&Charbonneau1991).During the main sequence phase, considerable lithium destruction is observed in low mass stars(~<1.2M⊙),e.g.,by two orders of magnitude for the Sun;this is generally explained by rotation-induced slow mixing,with some di?usion(see,e.g.,Schatzman1977;Baglin,Morel,&Schatzman1985;Vauclair1988;Pinsonneault et al.1989;Michaud&Charbonneau1991;Pro?tt&Michaud1991;Charbonnel,Vauclair,& Zahn1992;Chaboyer,Demarque,&Pinsonneault1995),though part of this e?ect might possibly be due to early main sequence mass loss(Boothroyd,Sackmann,&Fowler1991;Swenson& Faulkner1992;Whitmire et al.1995;Guzik&Cox1995).As stars approach the base of the red giant branch(RGB),the surface lithium abundance declines further by two orders of magnitude, as the deepening convective envelope reaches into lithium-depleted interior layers.Thus RGB stars,and AGB stars of~<4M⊙,are expected to have surface lithium abundances from two to four orders of magnitude below the present interstellar medium value of logε(7Li)~3.3(where logε(7Li)≡log[n(7Li)/n(H)]+12).

In general,this is observed to be the case;Population I red giants usually have lithium abundances lying in the range?1~

Another problem concerns3He.It is well known that deuterium(D)and3He are created in the Big Bang.Stars burn their initial D to3He while still on the pre-main sequence.Low mass stars create3He pockets in their interior during main sequence burning,as?rst pointed out by Iben (1967),which will subsequently be dredged up to the surface on the RGB,and injected into the interstellar medium via stellar mass loss on the RGB and AGB.Recent measurements of3He mass fractions of~0.001in the low-mass planetary nebulae NGC3242and IC289con?rm that this does indeed occur in at least some stars(Galli et al.1997).The sum of D+3He in the interstellar medium was predicted to increase with time,due to this stellar processing.The observed solar ratio (D+3He)/H≈4×10?5has thus been used as an upper bound on the primordial ratio,in order constrain Big Bang nucleosynthesis models(see,e.g.,Steigman1985);it provides the strongest lower limit on the baryon to photon number ratioη≥3×10?10,and thus to the baryon density of the universe?b≥0.01h?2(where h is the Hubble constant in units of100km s?1Mpc?1).

Rood,Bania,&Wilson(1984)pointed out that the apparent observed trend with galactocentric radius of the3He abundances in H II regions was the opposite of what one would expect if the galactic3He abundance was increasing with time due to stellar processing.More recent data(Rood et al.1997;Bania et al.1997)show no signi?cant trend of the3He abundance in H II regions as a function of either galactocentric radius or metallicity,with an average abundance of3He/H=1.5+1.0

×10?5.Some extragalactic measurements of deuterium have recently appeared;

?0.5

a high ratio D/H≈2×10?4recently observed in a high-redshift(z=3.32)absorption system in the quasar Q0014+813(Songaila et al.1994;Carswell et al.1994;Rugers&Hogan1996a)has sparked new interest in deuterium and3He,since this observation implied a much larger primordial (D+3He)/H value than had been inferred from the galactic observations.More recently,Rugers

×10?4in another absorber of Q0014+813(at redshift &Hogan(1996b)measured D/H=1.9+1.6

?0.9

z=2.798).If the observed absorption lines do indeed correspond to deuterium and not some coincidental interloper cloud happening to lie at the corresponding velocity,then this leads to correspondingly lower values ofη~<1.7×10?10and?b~<0.006h?2,close to the baryon density ?b≈0.003observed in stars and gas,eliminating the need for the existence of large amounts of baryonic dark matter.These observations also imply a decline by a factor of order6from the primordial(D+3He)/H value to the presolar value.Galactic chemical evolution models can obtain such a decline only if low mass stars destroy3He,instead of creating it;even a low primordial D/H value tends to result in excessive amounts of3He at the present epoch if stars create3He(see,e.g., Yang et al.1984;Walker et al.1991;Steigman&Tosi1992;Vangioni-Flam,Olive,&Prantzos1994; Galli et al.1994,1995)—note that a low value of D/H=(2.3±0.3[stat]±0.3[syst])×10?5has been measured in an absorber at redshift z=3.572of the quasar1937?1009(Tytler&Fan1994; Tytler,Fan,&Burles1996),and that deuterium abundances in quasar absorbers are still being debated(see,e.g.,Tytler,Burles,&Kirkman1996;Rugers&Hogan1997;Webb et al.1997).Galli et al.(1994,1995)suggested that a low-energy resonance in the3He+3He reaction could increase this rate su?ciently for low mass stars to become net destroyers of3He.Hogan(1995)suggested a less speculative mechanism,namely,the extra deep mixing below the conventional convective envelope on the RGB,which is generally invoked to explain the anomalously low12C/13C ratios observed in low mass stars(below the12C/13C values resulting from?rst dredge-up).

Over the last two decades,the need for some such deep mixing process on the RGB has been pointed out by many investigators,in order to understand the puzzle of the low12C/13C ratios observed in low mass Population I RGB stars,and the12C depletion and the[O/Fe]–[Na/Fe] anticorrelation discovered in low mass Population II RGB stars(see,e.g.,Dearborn,Eggleton,& Schramm1976;Genova&Schatzman1979;Sweigart&Mengel1979;Gilroy1989;Gilroy&Brown 1991;Dearborn1992;Smith&Tout1992;Charbonnel1994,1995a,b;Boothroyd,Sackmann,& Wasserburg1995,hereafter BSW95;Wasserburg,Boothroyd,&Sackmann1995,hereafter WBS95; Denissenkov&Weiss1996;Charbonnel,Brown,&Wallerstein1998).Recently,BSW95and WBS95 suggested that such deep circulation might also occur in AGB stars of low mass,in order to account for the anomalously low18O abundances observed in these stars.

In this paper,we present consistent computations of the e?ects of standard?rst and second dredge-up(in RGB and AGB stars,respectively)on7Li and3He.In addition,we have included 9Be,10B,and11B in our calculations,since they are also destroyed at relatively low temperatures in stars,and therefore can provide additional signatures of stellar mixing.For completeness,we include the results for4He.We also present calculations of the e?ects on these isotopes of“cool bottom processing”(CBP).In this process,deep extra mixing transports envelope material into the outer wing of the hydrogen-burning shell,where it undergoes partial nuclear processing,and then transports the material back out to the envelope.We have modelled CBP by a deep circulation process,determining some of the free parameters of our model by requiring that our computations yield results that agree with the observed RGB12C/13C ratios.The CNO isotopes for these models are discussed in detail in Boothroyd&Sackmann(1998).

2.Methods

We considered stars of29di?erent masses from0.85to9.0M⊙,evolving them self-consistently from the pre-main sequence through?rst dredge-up up to either the helium core?ash(which terminates the RGB for low mass stars),or through second dredge-up to the?rst helium shell?ash (for intermediate mass stars and some low mass stars),or to core carbon ignition during second dredge-up(for higher masses).For evolutionary program details,see Boothroyd&Sackmann (1988),Sackmann,Boothroyd,&Fowler(1990),and Sackmann,Boothroyd,&Kraemer(1993).

For solar metallicity,we used a helium mass fraction Y=0.28,with solar CNO abundances. For lower metallicities,we reduced Y(taking?Y/?Z≈2),and increased the oxygen content, approximating the observed trend by[O/Fe]∝?0.5[Fe/H]for[Fe/H]≥?1,and constant [O/Fe]=+0.5for[Fe/H]

A fuller discussion of the CNO elements is given in Boothroyd&Sackmann(1998).In addition to solar metallicity(Z=0.02),we considered metallicities appropriate to the Magellanic Clouds (Z=0.012and0.007,with[Fe/H]≈?0.35and?0.7,respectively),an intermediate value of Z=0.003([Fe/H]≈?1.2),a Population II metallicity of Z=0.001([Fe/H]≈?1.7),and an extreme Population II metallicity of Z=0.0001([Fe/H]≈?2.7).Since stars convert deuterium to3He on the pre-main sequence,our program lumps deuterium in with3He;our initial3He abundance is actually the sum of deuterium and3He.Since the variation of(D+3He)as a function of time(or metallicity)is not well known,we generally chose an initial ratio3He/4He=4×10?4 by number(solar abundances),but also considered extreme values of this ratio,namely,4×10?3 and4×10?5.For solar metallicity we used a7Li abundance logε(7Li)=3.0,close to that of the present interstellar medium(logε(7Li)ISM≈3.3);for Population II metallicities,we reduced the initial7Li abundance to logε(7Li)=2.6,a factor of5below the present cosmic abundance.Note that stellar models which include microscopic di?usion of7Li suggest that this is a reasonable initial value to match the observations of Spite plateau lithium abundances in Population II stars(Vauclair&Charbonnel1995),as do models which include rotational e?ects(Pinsonneault, Deliyannis,&Demarque1992;Deliyannis,Boesgaard,&King1995;Vauclair&Charbonnel 1995);it is hard to avoid some main sequence7Li depletion in these stars.Beryllium and boron isotopes were considered only for the cases Z=0.02and Z=0.001;we used solar abundances (Be/H=1.3×10?11,B/H=4×10?10,and11B/10B=4.0,by number:Grevesse[1984]),scaled linearly with metallicity.Note that initial abundances of the light elements are generally not critical, as the depletion factors that we report in this paper are insensitive to the absolute starting value.

Mass loss on the RGB and AGB was included via a Reimers’(1975)wind,with mass loss parameterη≈0.6,as discussed in Boothroyd&Sackmann(1998)(see also Sackmann et al.1993); values up toη=1.4for Population I cases with masses>2.5M⊙were tested,but the amount of mass lost was still insigni?cant at the points where?rst and second dredge-up take place.We used the OPAL1995interior opacities(Iglesias&Rogers1996),and Alexander molecular opacities (Alexander&Ferguson1994)at low temperatures;these latter require a value ofα=1.67(whereαis the ratio of the convective mixing length to the pressure scale height)in order to obtain a correct

model of the Sun(Sackmann et al.1990,1993).Tests were made using older opacity https://www.doczj.com/doc/ea5878893.html,e of the interior opacities from the Los Alamos Opacity Library(LAOL:from Keady[1985])yielded only slightly di?erent amounts of dredge-up(Boothroyd&Sackmann1998),while use of molecular opacities from Sharp(1992)required a value ofα=2.1but had no e?ect on dredge-up.(Note that the value ofαhas almost no e?ect on the depth of dredge-up,as has already been noted by Charbonnel[1994]).Nuclear reaction rates from Caughlan&Fowler(1988)were used,except for the17O-destruction reactions17O(p,α)14N and17O(p,γ)18F(e+ν)18O,where the rates of Blackmon (1996)(from measurements of Blackmon et al.[1995])or of Landr′e et al.(1990)were used.

For cool bottom processing(CBP),parametric computations were performed,with envelope structures obtained from full evolution models of a1M⊙star in the appropriate stages of evolution. Two types of models were considered.In the?rst type,as described in WBS95,the star’s structure was taken to be unchanging in time(“single episode”);it was taken at the point on the RGB where CBP is expected to begin(when the hydrogen shell erases the composition discontinuity left behind by?rst dredge-up).The CBP was then computed over time period less than or comparable to the RGB lifetime.In the second type of model,the change in envelope structure as the star climbs the RGB was taken into account by interpolating between full evolution models at15points on the RGB (“evolving RGB”).The CBP was assumed to start when the hydrogen shell erases the composition discontinuity from?rst dredge-up,and continue until the tip of the RGB was reached.For these “evolving RGB”cases,metallicities Z=0.02,0.007,0.001,and0.0001were considered(taking structures from the relevant full evolution models),and higher masses were simulated by adding envelope mass,and starting at the appropriate(higher-luminosity)RGB position(this should be a good approximation,since the structure near the burning shell on the RGB is almost independent of the envelope mass).Isotopic abundances were taken from full evolutionary models,except for 7Li,where an additional main sequence depletion by a factor of50was assumed for the1M⊙case(note that the observed main sequence7Li depletion in low mass stars cannot be predicted by standard stellar models).

In our two-stream“conveyor-belt”circulation model for CBP,matter from the bottom of envelope convection streamed downward,reaching a maximum temperature T P,then returned upward and was mixed with the convective envelope(i.e.,a composition advection equation with nuclear burning,and no mixing between downward and upward streams).Envelope and stream compositions were followed through time.We assumed that the temperature di?erence ?log T=log T P?log T H between the bottom of mixing and the bottom of the hydrogen-burning shell was constant,and treated it as a free parameter;values selected for discussion were those satisfying the observational data,as discussed in WBS95and Boothroyd&Sackmann(1998).For a thin H-burning shell,assuming constant?log T is roughly equivalent to assuming extra mixing always reaches down to the same value of the molecular weight gradient?μ.

For CBP in the“single episode”circulation models,?log T≈0.17yielded a reasonable match to the observed12C/13C ratio on the RGB(~13±3for a1.2M⊙star,or~11for a1.0M⊙star: see Gilroy[1989]),after a processing time t mix:RGB≈1.25×107yr(see Fig.7).During this time,

the star’s luminosity increases by only60%(Sackmann et al.1993),so the assumption of static envelope structure is not unreasonable(the luminosity increase is by a factor of100at the tip of the RGB,after a timeτRGB~7×107yr).For CBP in the“evolving RGB”circulation models,?log T=0.262±0.010matched the above observed carbon isotope ratios on the RGB(Fig.9a; see also Boothroyd&Sackmann1998).

The other key free parameter was the stream mass?ow rate˙M p.This must be slower than that of convection in RGB or AGB envelopes(˙M p?˙M conv~1M⊙/yr),while the streams must move faster than the speed with which the H-shell burns its way outward(˙M p~>˙M c).We explored a wide range of˙M p values.For equal downward and upward velocities,the fractional areas at the base of the convective envelope occupied by downward and upward streams are equal.The downward stream then spends a time?t d=0.5?M r/˙M p in a layer?M r,the upward stream spending the same time?t u there on its way out.When downward and upward velocities(and respective fractional areas f d and f u)are not equal,these times become?t d=f d?M r/˙M p and ?t u=f u?M r/˙M p.The total time spent in any mass layer is independent of f d and f u,for f d+f u=1;thus the total amount of nuclear burning is generally independent of f u/f d.The7Li production via the Cameron-Fowler mechanism(Cameron1955;Cameron&Fowler1971)is an exception;it does depend on f u,which a?ects the speed with which7Be is transported upwards, and thus the amount which survives to reach cool layers before decaying into7Li.Let f≡f u/f d; besides f=1(i.e.,f d=f u=0.5),we considered f=9and99.

3.Results

We present?rst and second dredge-up results from standard stellar models,and cool bottom processing(CBP)results from our“single episode”and“evolving RGB”circulation models of extra mixing.Note that some results for4He,3He,and the CNO isotopes are tabulated in Boothroyd& Sackmann(1998);more detailed tables are available from the authors1.

3.1.Standard First and Second Dredge-up

Figure1a presents the mass layer M r/M down to which the convective envelope reaches,at its deepest penetration during standard?rst and second dredge-up(for stars of>7M⊙,the depth of second dredge-up is shown at the moment when the program failed during core carbon ignition). Note that we de?ne“second dredge-up”in low mass stars as the stage of deepest convective penetration on the early AGB,even if this is shallower than?rst dredge-up.Figure1b displays the corresponding temperatures T ce at the base of the convective envelope.For Z=0.02stars of mass

Fig.1.—(a)Maximum depth in mass of the convective envelope(M dr r),relative to the initial stellar mass M,of?rst and second dredge-up(solid and dashed curves,respectively)as a function of stellar mass M.The metallicities are indicated on the curves for?rst dredge-up;the second dredge-up curves are in the same order.For Z=0.02,0.007,and0.0001,the dotted continuations of the dashed curves show the depth reached by second dredge-up at the point where the program failed during core carbon ignition.(b)The maximum temperature T ce at the bottom of the convective envelope during?rst and second dredge-up(solid and dashed curves,respectively)for the same metallicities as(a);for Z=0.02,the value of T ce is also shown at the time of core carbon ignition, for stars of mass>7M⊙(dotted continuation of dashed curve).

≤1M⊙,there is some burning of7Li during?rst dredge-up,when T ce reaches nearly4×106K. Higher temperatures are attained during second dredge-up in intermediate mass stars,but no7Li burning takes place in any but the highest mass stars(~6?7M⊙),as the timescales are too short.

Figure2illustrates where in a star’s envelope7Li,9Be,10B,and11B are destroyed,and where in the interior the pocket of3He has been created,prior to?rst dredge-up.One sees that7Li is burned up?rst,followed by9Be;further in,11B and10B burn at similar depths(11B slightly before10B).The pocket of3He peaks considerably deeper in the interior.First dredge-up will dilute the pockets of7Li,9Be,11B,and10B,and will enrich the surface with3He from the pocket

Fig.2.—The abundance pro?les of the light elements as a function of the mass coordinate M r/M at the end of the main sequence for Z=0.02stars(a)of1M⊙,and(b)of6M⊙.The depth of standard?rst dredge-up on the RGB is shown by the arrows.

below.Table1illustrates the depths of these pockets in stars of di?erent masses and metallicities, prior both to?rst dredge-up on the RGB and to second dredge-up on the AGB.

Figure3displays the envelope4He enrichment produced by?rst and second dredge-up.There is little metallicity dependence;?rst dredge-up in low mass stars increases the helium mass fraction by?Y~0.02,while second dredge-up in~7M⊙stars yields?Y~0.1.One can compute the contribution of these stars to the4He enrichment of the interstellar medium(similar estimates for CNO isotopes are discussed in more detail in Boothroyd&Sackmann[1998]).Using the initial–?nal mass relationship(Weidemann&Koester1983;Weidemann1984),one can estimate the envelope mass ejected for a given initial stellar mass.Multiplying mass ejected by the mass fraction of 4He from Figure3,and weighting the results by an initial mass functionφ(M)∝M?2.3(Salpeter 1955),one can estimate the contribution to the interstellar https://www.doczj.com/doc/ea5878893.html,paring with similar4He computations for supernovae(Weaver&Woosley1993),one?nds that low and intermediate mass stars(1?12M⊙)inject nearly as much4He into the interstellar medium as do supernovae.

Figure4is a key diagram.It illustrates the conventional viewpoint that low mass stars

(M~<4M⊙)should be a considerable source of3He in the universe,according to the predictions of standard dredge-up theory.Note that the?rst and second dredge-up results of Figure4are in good agreement(~10%)with the low mass star results of Charbonnel(1995a,b),the low and intermediate mass star results of Dearborn,Steigman,&Tosi(1996),and the intermediate mass star results of Weiss,Wagenhuber,&Denissenkov(1996)(though the latter?nd~30%less3He dredge-up than the other authors,for stellar masses below1.5M⊙).Figure4also illustrates the3He depletion that is expected due to extra mixing in low mass stars,as computed via our “evolving RGB”CBP models(diamonds on long-dashed curves).For low enough stellar masses, overall depletion of3He is obtained,relative to its initial abundance.On average,one?nds that stars are net destroyers of3He in the universe,particularly low-metallicity stars;this is discussed below in§3.2.(Note that Fig.4does not show the e?ect of hot bottom burning in intermediate mass AGB stars,which would destroy almost all the3He in Population I stars of4?7M⊙,and in Population II stars of3.5?6M⊙[Boothroyd&Sackmann1992;Sackmann&Boothroyd1998].) Figure5summarizes the reduction of the surface7Li abundance due to pre-main sequence burning and?rst and second dredge-up.Pre-main sequence burning(dot-dashed curve in Fig.5) is important only for masses~<1.2M⊙at near-solar metallicity;there is no signi?cant pre-main

Table1:Size of the Pockets of7Li,9Be,10B,and11B Prior to First and Second Dredge-up a

3He p d Z&M...........................(M?M r)/M...........................

stage(M⊙)dr b7Li9Be10B11B3He3He p c

0.02, 1.00.7560.0370.0600.1940.1520.8260.39149. RGB 2.50.8580.01480.03120.11720.08720.7770.369 5.8

6.00.7690.01320.02750.10550.07700.6040.327 1.37 0.001, 1.00.6890.0240.0550.1760.1390.7240.33654. RGB 2.50.7460.01040.02400.09320.06960.7510.2838.0

6.00.00080.00800.02050.07880.05750.5100.260 1.69 0.02, 2.50.7880.6690.7170.7600.7530.7830.778 1.10 AGB 6.00.8450.5590.6470.7080.6910.7540.741 1.01 0.001, 2.50.7290.2550.3240.5080.4640.6590.627 1.08 AGB 6.00.8370.00790.02040.07870.05740.5120.260 1.68

a Bottom of pocket is de?ned as point where abundance drops by a factor of2.

b Fraction of the star’s mass contained in the convective envelope at the time of deepest dredge-up.

c Depth of the3He peak.

d Peak3H

e abundance,relative to its surface abundance.Note that the peak subsequently grows somewhat higher than the values quoted here,before it is actually dredged up.

Fig. 3.—Envelope4He mass fraction Y due to standard?rst and second dredge-up(solid and dashed curves,respectively),or at core carbon ignition during second dredge-up(dotted continuation of dashed curves),as a function of initial stellar mass M for various input metallicities Z.The initial stellar abundance is given by the dot-dashed lines.

sequence7Li burning in Population II stars of≥0.85M⊙.Possible e?ects of main-sequence7Li depletion on the?rst dredge-up depletion factors of Figure5are discussed below.

The7Li depletion due to?rst and second dredge-up is usually due entirely to dilution(by a factor of~60)of the surface lithium pocket,and this dilution is relatively insensitive to the stellar mass and metallicity(varying by less than a factor of3).In addition to dilution,however,there are some cases where7Li also burns during dredge-up,at the bottom of the(standard)deep convective envelope.This occurs during?rst dredge-up only for Population I stars of masses≤1M⊙,and during second dredge-up only for Population I stars of~7M⊙and Population II stars of~6M⊙.

Extra mixing on the main sequence can destroy lithium there;one may question whether this would a?ect the?rst dredge-up dilution factors.Low mass stars are observed to experience

considerable7Li depletion on the main sequence(see,e.g.,Hobbs&Pilachowski1988,and references

Fig. 4.—Envelope3He abundance due to standard?rst and second dredge-up(solid and dashed curves,respectively),or at core carbon ignition(dotted continuation of dashed curves);dot-dashed lines show initial stellar3He abundances.Heavy(central)curves are for our standard initial ratio 3He/4He=4×10?4by number;light curves are for extreme cases4×10?3and4×10?5.Diamonds connected by long-dashed curves show the e?ect of cool bottom processing(CBP)on the RGB, from our“evolving RGB”CBP models.

therein).This will a?ect the RGB abundances,but not the dilution factor(since the size of the lithium pocket on the main sequence cannot be reduced signi?cantly—it does not extend much below the main sequence convective envelope,at least for stars~<1M⊙).Stars of mass~>1.4M⊙do not exhibit reduced surface lithium abundances while on the main sequence(see,e.g.,Boesgaard &Tripicco1987;Balachandran1991).However,there may be some evidence that extra mixing can cause additional lithium depletion in the interior,reducing the size of the lithium pocket(and thus increasing the?rst dredge-up dilution factor).For the Hyades,there is no such evidence:the lithium abundances on the RGB are completely explainable by?rst dredge-up dilution alone,as pointed out by Duncan et al.(1998).Possible evidence for additional lithium depletion comes from Gilroy’s(1989)observations of7Li in open cluster giants of intermediate mass;non-LTE corrections to the observed lithium abundances(Carlsson et al.1994)may reduce the e?ect,but probably will not eliminate it.

Fig.5.—Envelope7Li abundance changes due to standard?rst and second dredge-up(solid and dashed curves,respectively),or at core carbon ignition(dotted continuation of dashed curves), relative to the values at the end of the main sequence(depletion during the main sequence is not shown).Dot-dashed curves show the pre-main sequence7Li burning,relative to the initial (interstellar medium)value.Separated symbols show the e?ect of AGB hot bottom burning for Z=0.02and0.001:the minimum AGB7Li abundance at the start of hot bottom burning(open circles),peak AGB7Li abundance(solid circles),and?nal equilibrium hot bottom burning7Li abundances(solid diamonds—note that this equilibrium may not be reached by Population I stars and lower mass Population II stars).Arrows indicate directions of possible shifts in values, as expected from variations in AGB mass loss rates,or from continuation of an incomplete model run(see Sackmann&Boothroyd1995,1998).

Figure5also summarizes the7Li creation in AGB stars of~4?7M⊙due to hot bottom burning(Sackmann&Boothroyd1992,1995,1998).First,7Li is burned,being depleted by several orders of magnitude.As hot bottom burning becomes stronger,the Cameron-Fowler mechanism (Cameron1955;Cameron&Fowler1971)yields a large increase in the envelope7Li abundance. Independent of past7Li history,such super-rich lithium stars attain peak7Li abundances10?20 times the present interstellar7Li abundance,and may contribute signi?cant amounts of7Li to the interstellar medium(Sackmann&Boothroyd1995,1998).The envelope7Li is produced from3He; as3He is burned,the7Li abundance declines again.If hot bottom burning continues long enough,

Fig.6.—Envelope9Be,10B,and11B depletions due to standard?rst and second dredge-up,as a function of initial stellar mass M,for solar(Z=0.02)and Population II(Z=0.001)metallicities.

3He destruction reaches equilibrium with its creation via the p-p chain,and the7Li abundance reaches a?nal value4?5orders of magnitude below the interstellar abundance(see5and6M⊙Z=0.001cases in Fig.5);stellar runs for Population I stars were terminated before this stage was reached,since they approach this?nal equilibrium much more slowly than Population II stars(and may in fact never reach it at all,depending on the point of onset of the AGB“superwind”).

Figure6shows the e?ect of?rst and second dredge-up on the surface abundances of9Be,10B, and11B,for both solar and Population II compositions.For?rst dredge-up,the abundance changes are entirely due to dilution;since the extent of the pockets being diluted is greater than for7Li, the dilution is less.For solar metallicity,this dilution is a factor of~30for9Be,and a factor of~10for10B and11B;this dilution is fairly independent of stellar mass except for M<2M⊙(as was the case for7Li).The e?ect of second dredge-up is minor compared to that of?rst dredge-up; there is burning of9Be during second dredge-up by as much as several orders of magnitude in stars of~7M⊙,but relatively little burning of11B,and no signi?cant burning of10B.

There is very little data published on beryllium and boron observations in evolved stars of low or intermediate mass.Boesgaard,Heacox,&Conti(1977)searched for beryllium in four giants in the Hyades cluster,and were only able to obtain upper limits,namely,Be/H≤3.1×10?13.

For eight Hyades dwarfs,they measured Be/H≈1.0×10?11(Boesgaard et al.1977;Boesgaard& Budge1989).This implies that the giants had a beryllium dilution factor of≥32.From Gilroy (1989),the turn-o?mass of the Hyades is about2.2M⊙;for this mass,our work shows that standard ?rst dredge-up would give a dilution factor of about28,which is consistent.Note that possible non-LTE e?ects were not considered in the above observations.

Note that boron abundances on the RGB should be at least a factor of~30higher than beryllium abundances there,due to its higher initial abundance.If there were no reduction of the main sequence pockets from extra mixing,there would be an additional factor of3from the fact that the boron pocket is three times as big(in mass extent)as the beryllium pocket(see Table1or Fig.2,or the?rst dredge-up dilution factors from Fig.6).On the other hand,it is more di?cult to observe boron:the2498?A line can only be observed from space,and in addition red giant stars have very little?ux in the UV(compare to beryllium,where the3130?A line can be observed using ground-based telescopes,and there is somewhat more?ux).Recently,Duncan et al.(1994, 1998)made the?rst observations of boron abundances in two red giants in the Hyades.They?nd [B/H]=?1.1±0.2in the giants,as opposed to[B/H]=?0.1±0.2on the main sequence,yielding a boron depletion of order10,consistent with?rst dredge-up predictions.They point out that corrections for non-LTE e?ects for boron in giants are yet to be calculated.

3.2.Deep Circulation on the RGB and AGB

Observations indicate that surface13C abundances continue to change on the RGB after the end of conventional?rst dredge-up(Gilroy&Brown1991;Charbonnel1994;Charbonnel et al. 1998),suggestive of nuclear processing resulting from extra mixing below the base of the convective envelope,i.e.,cool bottom processing(CBP).Slow deep circulation tends to be opposed by a gradient in the mean molecular weightμ.A largeμ-discontinuity is left behind by?rst dredge-up. For Population I stars,the post-dredge-up decrease in12C/13C is observed to commence on the RGB only after the point where the hydrogen shell has subsequently burned its way out to(and destroyed)this“μ-barrier”(see,e.g.,Charbonnel1994;Charbonnel et al.1998).As discussed in Boothroyd&Sackmann(1998),the12C/13C observations suggest that CBP begins when the “μ-barrier”is erased,and then“tails o?”in a manner intermediate between the behavior assumed in our“single episode”and“evolving RGB”CBP models.Unfortunately,the data are su?ciently sparse that this scenario is not completely certain—for example,an earlier starting point for CBP cannot be completely ruled out,though it seems unlikely.Note that the depth of extra mixing in our CBP models was normalized to reproduce the observed ratio12C/13C~13in the galactic open cluster M67,which has a turn-o?mass of~1.2M⊙(see§2).

The relatively sparse observations of?eld Population II stars are consistent with the scenario in which CBP does not begin until theμ-barrier is erased(Sneden,Pilachowski,&VandenBerg 1986;Pilachowski et al.1993,1997),and are also consistent with our“evolving RGB”CBP models. However,as discussed in Boothroyd&Sackmann(1998),Population II stars in globular clusters

exhibit signs of continuous CBP throughout most or all of the RGB evolution,starting well before the hydrogen shell has erased theμ-barrier(possibly even before deepest?rst dredge-up),and exhibit more processing at a given metallicity than?eld Population II stars(see,e.g.,Carbon et al.1982;Trefzger et al.1983;Langer et al.1986;Suntze?&Smith1991;Boothroyd&Sackmann 1998).Since our models made the assumption that no CBP took place until theμ-barrier was erased,they may be expected to underestimate the amount of processing in globular cluster stars.

The“evolving RGB”models make the reasonable assumption that the extra mixing process continues throughout the subsequent RGB evolution;note that if this is the case,then extra mixing and CBP might occur on the AGB as well.The stellar structure on the AGB of a low mass star is similar to the structure near the tip of the RGB,and thus lithium abundances on the AGB might be produced at a level similar to those predicted at the tip of the RGB by the“evolving RGB”model.On the other hand,the“single episode”models assume that extra mixing terminates before the star’s luminosity increases much(e.g.,due to spin-down resulting from the RGB mass loss). This is also a possible scenario,but little or no CBP would be expected on the AGB in this case (the driving mechanism being exhausted on the RGB).The post-RGB lithium abundance in this case would be expected to be nearly constant,at whatever value was left behind when CBP turned o?on the RGB(probably a low lithium abundance,as the mixing would presumably slow down before stopping,and low˙M p values yield low lithium abundances—see Figs.8and9c).

For stellar masses above~2.3M⊙,the RGB ends before the hydrogen shell reaches the μ-barrier,and thus no CBP is expected on the RGB;even if some CBP did take place,these stars spend little time on the RGB,and processing should be negligible.On the early AGB,CBP cannot be extensive,as the hydrogen shell largely stops burning;CBP might take place later on the thermally pulsing AGB,when the hydrogen shell burns strongly(albeit interrupted intermittently by the helium shell?ashes).For a fuller discussion,see Boothroyd&Sackmann(1998).

In the present work,extra mixing in both Population I and Population II stars are modelled via a conveyor-belt model of deep circulation similar to that of WBS95,as discussed in§2.Charbonnel (1995a,b)and Denissenkov&Weiss(1996)have modelled such mixing in Population II stars using a di?usion algorithm.As discussed in WBS95,these two approaches should yield similar results for the CNO isotopes,since the nuclear processing of CNO isotopes should be insensitive to the speed or geometry of mixing.However,as discussed below,the lighter elements are more dependent on the mixing speed,especially7Li.They are discussed in detail in the following sections.

3.2.1.7Li

Figure7shows the abundances of the light elements(and12C/13C)as a function of time on the RGB,for one of our“single episode”CBP models(note that12C/13C reaches the observed value after1.25×107yr,but most of the activity in the light elements takes place much earlier; computations were terminated after5×107yr).It is a key diagram,demonstrating that under

Fig.7.—The e?ect of CBP in our“single episode”models,as a function of time on the RGB. These are for a solar metallicity1M⊙star with an envelope mass M env=0.7M⊙and a mixing rate of deep circulation˙M p=10?3M⊙/yr;circulation was assumed to reach to?log T=0.17from the base of the hydrogen-burning shell,such that the envelope12C/13C ratio reaches the observed value of~11after a time t mix:RGB~1.25×107yr(vertical line),although the computations were continued for5×107yr.The quantities plotted are the log of the12C/13C number ratio,the log of the3He mass fraction,and logεvalues for the other light elements.Hatched regions of7Li curves emphasize cases where abundances are higher than the upper bound of typical RGB?eld stars. certain conditions a major amount of7Li can be created on the RGB due to CBP in a1M⊙star of solar metallicity.Figure8a shows the7Li abundances similarly,for various mixing speeds˙M p.One sees that7Li is enhanced for models with rapid enough circulation(namely,˙M p~>10?4M⊙/yr); lower mixing speeds yield lithium destruction.

Figure9shows the abundances of the light elements(and12C/13C)as a function of luminosity on the RGB,for our“evolving RGB”CBP models with various mixing speeds˙M p.Note that in these models the total mass drops from0.984to0.710M⊙(due to mass loss on the RGB),the

Fig.8.—(a)Dependence of the7Li creation and depletion on the mixing speed˙M p and on our geometry factor f≡f u/f d in our“single episode”CBP models on the RGB.Curves are labelled by log˙M p,and by f for cases with f=1;hatched regions of curves emphasize high lithium abundance cases(as in Fig.7).Note that models with˙M p<10?7M⊙/yr do not produce enough13C to match the observations by the time t mix:RGB is reached(indicated by vertical line).(b)Dependence of 9Be destruction,similarly.Note that boron isotope destruction curves would have the same form, except for having higher initial abundance.

core mass grows from0.243to0.462M⊙,and the convective envelope mass M env thus drops from 0.718to0.246M⊙(for lower metallicities or higher stellar masses,these changes are smaller).In these models,the value reached by12C/13C at the tip of the RGB agrees with the observed values (i.e.,the circulation was assumed to operate throughout the RGB);it is essentially independent of the mixing speed or geometry(see Fig.9a).As in the“single episode”cases,the7Li abundance is rapidly enhanced for˙M p~>10?4M⊙/yr;but even at lower mixing speeds(˙M p~>10?6M⊙/yr), signi?cant7Li enhancements occur as the star climbs the RGB.

The present work shows for the?rst time that low mass RGB stars can also become super-rich

Fig.9.—The e?ect of CBP(for various mixing speeds˙M p)in our“evolving RGB”solar metallicity 1M⊙CBP models as a function of luminosity on the RGB;curves are labelled by log˙M p.Initial and?rst dredge-up abundances are shown schematically in the left portion of each panel(open circles).(a)The12C/13C number ratio;the initial ratio(o?scale)was90.(b)The log of the3He mass fraction.(c)The logε(7Li)values.The?lling between cases with geometry factors f=1 (solid curves)and f=9(dotted curves)having the same˙M p indicates the e?ect of varying the circulation geometry(see text).Hatched regions of curves and heavy?lled regions emphasize high lithium abundance cases,as in Fig.7.(d)Values of logε(9Be)(solid curves),logε(10B)(dotted curves),and logε(11B)(dashed curves);low-˙M p cases are omitted for clarity.Curves for Be and B having the same˙M p value are connected by?lled regions.

lithium stars.This allows one to understand the“K Giant Lithium Problem”(de la Reza&da Silva 1995),of anomalously high lithium abundances discovered in otherwise normal low-mass K giants of relatively low luminosity(Wallerstein&Sneden1982;Hanni1984;Brown et al.1989;Gratton &D’Antona1989;Pilachowski et al.1990;Pallavicini et al.1990;Fekel&Marschall1991;Fekel& Balachandran1993;da Silva et al.1995a,b;de la Reza&da Silva1995;de la Reza et al.1996,1997; Fekel et al.1996).The presence and amount of lithium creation are critically dependent on the assumed speed˙M p of extra mixing,as well as on the geometry of mixing(as measured by our factor

f≡f u/f d,the fractional area of upward streams relative to downward streams in our conveyor-belt

circulation model).Deeper extra mixing yields higher lithium enhancements for a given(rapid) mixing rate(as may be seen by comparing peak7Li values from Fig.8with the values attained in Fig.9c near log L=1.5).However,it is noteworthy that the amount of7Li created does not depend on the previous lithium abundance,i.e.,on the lithium history of the star.A qualitative understanding of this mechanism for RGB lithium enrichment is relatively straightforward.

In order to produce the observed additional13C,the extra mixing must reach temperatures high enough that3He is also burned(as shown in Figs.7and9),resulting in7Be creation via 3He(α,γ)7Be.If the extra mixing is slow,this7Be is destroyed while still at high temperatures via7Be(p,γ)8B(e+ν)8Be→2αor7Be(e?,ν)7Li,and any7Li produced from7Be electron capture is immediately burned up via7Li(p,α)4He.However,for su?ciently high mixing speeds,7Be can be transported out to cooler regions before the electron capture takes place,where the resulting 7Li can survive and enrich the stellar envelope.In other words,under special conditions the Cameron-Fowler mechanism can work in low-mass,low-luminosity RGB stars.The resulting envelope7Li abundance is determined by the balance between7Be being transported out(to form7Li),and7Li being transported back inwards(and being destroyed).The envelope7Li abundance reaches equilibrium relative to the abundance of3He on a timescale t proc~M env/˙M p, the time required for circulation to process the entire envelope;t proc is the timescale on which the 7Li abundance reaches its peak values in Figures7,8a,and9c.

The e?ect on the envelope7Li abundance of changing the mixing speed˙M p or the relative areas of upward and downward streams f≡f u/f d can be readily understood.For mixing speeds ˙M

>10?7M⊙/yr,only a small fraction of the3He in a circulating blob of matter is destroyed p

during a single circulation pass,and the total3He burning rate per unit time is then independent of˙M p(see Fig.9b):the amount burned per circulation pass is then inversely proportional to˙M p, and the number of circulation passes per unit time is proportional to˙M p.The amount of7Be produced per unit time is thus independent of˙M p,but the amount that survives to reach cool temperatures is not.If one increases˙M p,at?rst the amount of surviving7Be increases,as does the resulting7Li production.However,as˙M p increases still more,there comes a point where essentially all the7Be survives;the7Li production rate cannot increase further.The7Li destruction rate, however,still increases with increasing˙M p(since all7Li transported down is burned),and the resulting envelope7Li abundance decreases with increasing˙M p.The value of˙M m p which yields the maximum7Li production depends on the temperature at the base of the circulation(as may be seen from Fig.9c,where this temperature grows as the star ascends the RGB).If the circulation speed is less than˙M m p,then changing the stream geometry will a?ect the7Li abundance.Increasing f u/f d yields a wider and slower upward stream;less of the7Be produced at the base of the circulation survives out to cool regions,yielding a lower7Li abundance(see Fig.9c).

Figures7and9show that the peak7Li abundance can be attained prior to any signi?cant13C enrichment,but that the7Li abundance can remain high or even grow during the13C enrichment process.These preliminary models would thus predict that low mass super-rich lithium stars could occur with12C/13C ratios throughout the range from~30to~4.This is in reasonable agreement

脐带干细胞综述

脐带间充质干细胞的研究进展 间充质干细胞(mesenchymal stem cells,MSC S )是来源于发育早期中胚层 的一类多能干细胞[1-5],MSC S 由于它的自我更新和多项分化潜能,而具有巨大的 治疗价值 ,日益受到关注。MSC S 有以下特点:(1)多向分化潜能,在适当的诱导条件下可分化为肌细胞[2]、成骨细胞[3、4]、脂肪细胞、神经细胞[9]、肝细胞[6]、心肌细胞[10]和表皮细胞[11, 12];(2)通过分泌可溶性因子和转分化促进创面愈合;(3) 免疫调控功能,骨髓源(bone marrow )MSC S 表达MHC-I类分子,不表达MHC-II 类分子,不表达CD80、CD86、CD40等协同刺激分子,体外抑制混合淋巴细胞反应,体内诱导免疫耐受[11, 15],在预防和治疗移植物抗宿主病、诱导器官移植免疫耐受等领域有较好的应用前景;(4)连续传代培养和冷冻保存后仍具有多向分化潜能,可作为理想的种子细胞用于组织工程和细胞替代治疗。1974年Friedenstein [16] 首先证明了骨髓中存在MSC S ,以后的研究证明MSC S 不仅存在于骨髓中,也存在 于其他一些组织与器官的间质中:如外周血[17],脐血[5],松质骨[1, 18],脂肪组织[1],滑膜[18]和脐带。在所有这些来源中,脐血(umbilical cord blood)和脐带(umbilical cord)是MSC S 最理想的来源,因为它们可以通过非侵入性手段容易获 得,并且病毒污染的风险低,还可冷冻保存后行自体移植。然而,脐血MSC的培养成功率不高[19, 23-24],Shetty 的研究认为只有6%,而脐带MSC的培养成功率可 达100%[25]。另外从脐血中分离MSC S ,就浪费了其中的造血干/祖细胞(hematopoietic stem cells/hematopoietic progenitor cells,HSCs/HPCs) [26, 27],因此,脐带MSC S (umbilical cord mesenchymal stem cells, UC-MSC S )就成 为重要来源。 一.概述 人脐带约40 g, 它的长度约60–65 cm, 足月脐带的平均直径约1.5 cm[28, 29]。脐带被覆着鳞状上皮,叫脐带上皮,是单层或复层结构,这层上皮由羊膜延续过来[30, 31]。脐带的内部是两根动脉和一根静脉,血管之间是粘液样的结缔组织,叫做沃顿胶质,充当血管外膜的功能。脐带中无毛细血管和淋巴系统。沃顿胶质的网状系统是糖蛋白微纤维和胶原纤维。沃顿胶质中最多的葡萄糖胺聚糖是透明质酸,它是包绕在成纤维样细胞和胶原纤维周围的并维持脐带形状的水合凝胶,使脐带免受挤压。沃顿胶质的基质细胞是成纤维样细胞[32],这种中间丝蛋白表达于间充质来源的细胞如成纤维细胞的,而不表达于平滑肌细胞。共表达波形蛋白和索蛋白提示这些细胞本质上肌纤维母细胞。 脐带基质细胞也是一种具有多能干细胞特点的细胞,具有多项分化潜能,其 形态和生物学特点与骨髓源性MSC S 相似[5, 20, 21, 38, 46],但脐带MSC S 更原始,是介 于成体干细胞和胚胎干细胞之间的一种干细胞,表达Oct-4, Sox-2和Nanog等多

高级英语写作黄金句型和新词

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