CHINESE ASTRONOMY AND ASTROPHYSICS

PERGAMON Chinese Astronomy and Astrophysics 25 (2001) 412-415

Lithium Depletion in the Solar Atmosphere+*

Xiong Da-run’ Deng Li-cai2 1 Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008

2 National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012

Abstract Using a complete non-local convection theory, we carried out the

theoretical calculations of 7Li depletion of the solar convective envelope models

with different convective parameters cl and ~2, and got a model of the solar

convection zone consistent with the observed 7Li abundance and the depth of the

solar convection zone determined by helioseismic techniques. The overshooting

distance of effective non-local convective mixing of 7Li is very extensive, which

is about 1.07Hp or 0.09Ro. However, the super-radiative temperature zone is

much narrower, and it is only 0.20Hp or 0.016Ra.

Key words: 7 Li abundance-convection-overshooting-solar interior

1. INTRODUCTION

The Sun is observed to have 7Li abundance 7Li/H M lo-lo (by number), or [‘Li] =

log(7Li/H) + 12 M 1.0, which is less than that of the primitive solar nebula by about

two orders of magnitude. Therefore, the Sun has undergone considerable 7Li depletion after

its formation. However, the 7Li abundance of warm stars (T, > 5500K) in the young open

clusters is almost normal and very close to that of interstellar medium. This observed fact

means that 7Li depletion of solar-type stars must occur during the main sequence evolution.

There is no significant 7Li depletion during the pre-main sequence evolution.

7Li is destroyed by 7Li(p, cu)4He reactions at relatively low temperature (T 2 2.5 x

106K). 7Li depletion is a sensitive monitor for stellar convection. The mechanism of 7Li

depletion still remains unsolved. Various theories have been proposed, among them the

rotation-induced turbulent diffusion mechanism 11-‘1 is the most prevalent one. In the present

t Supported by National Natural Science Foundation and National key project Received 2001-09-04

* CAA LETTER

0275-1062/01/$-see front matter @ 2001 Elsevier Science B. V. All rights reserved PII: SO275-1062(01)00093-5

Xiong Da-run, Deng Li-cai / Chinese Astronomy and Astrophysics 25 (2001) 412-415 413

paper we probe 7Li depletion resulted from convective overshooting and try to give an

estimation of the overshooting distance.

2. NUMERICAL RESULTS

For treatment of the non-local convective mixing of elements in stellar evolution we developed a statistical theory of non-local convection[41. Mixing of species is also in- cluded in a self-consistent wayF51. It was used to calculate the evolution of massive starsL61. It can be also used to calculate 7Li depletion. 7Li is an extremely rare element in stars. Any change of 7Li abundance cannot influence the

structure of stars, namely, 7Li can be consid- ered as a passive element. Therefore, the equi- librium model of the Sun and 7Li depletion

can be calculated separately. 7Li is destroyed at relatively low temper-

ature. Hence, it is not necessary to construct the whole model of the Sun for theoretical cal- culation of 7Li depletion. Instead it is enough to construct a model of convective envelope for this subject. For the reasons mentioned above the theoretical calculations of 7Li deple- tion are divided into the following two steps:

-2

0.7 0.75 0.8 rJR0

Fig. 1 7Li abundance vs. the depth of convection zone for the solar convective

envelope models with different convective parameter Q/C,. The cross marks the ‘Li

abundance and depth of convection zone of the Sun.

1) Firstly, we constructed a set of models of solar convective envelope with different

convective parameters cl and CZ. The fundamental equations and boundary conditions can

be referred to our earlier paperf71.

2) Secondly, we carried out the calculations of 7Li depletion for these envelope models.

The 7Li abutidance of the primitive solar nebula, [7Li] = 3.3, is adopted as the initial ‘Li

abundance of the Sun, and the age of the Sun is 4.65 x 10’ years.

Table 1 7Li depletion of the solar models

Model Ml

Cl C2lCl Tc/Ro 17L4 0.64 l/l 0.716 -21.92

M2 0.62 112 0.716 -5.54 M3 0.61 l/4 0.716 0.44 M4 0.62 l/5 0.714 0.97 M5 0.62 l/8 0.709 1 .fi7

There are two adjustable parameters cl and cg in our non-local convection theory. Among

them, cl is related to the dissipation of turbulence. It determines the efficiency of convective

transfer of energy. The depth of convection zone is mainly determined by cl. The larger cl,

the deeper convection zone. The parameter c2 is concerned with non-local turbulent diffu-

sion. The overshooting distance is directly proportional to m. Overshooting increases

with increase of c2 . Therefore, the larger cl and ~2, the quicker 7Li depletion. Fig.1 displays

414 Xiong Da-run, Deng Li-cai / Chinese Astronomy and Astrophysics 25 (ZOOl) 41%4f5

the variation of 7Li abundance with the depth of convection zone for the solar model. It

can be seen that the ‘Li abundance decreases with increase of the depth of convection zone

and cz/ci. In Fig. 1 the cross marks the ‘Li abundance and depth of convection zone of the

Sun, which corresponds roughly with a model of solar convection zone with the convective

parameters cl = 0.62 and c~/ci = l/5 (Model M4 in Table 1).

, \ \

-2 - \ \ \ \

\ \

I. .:.I, . L. .,, .\

0 2 4 6 8 10

age (G Y.)

-I

-2

-- t=4.65*1Oby

_____ t=4.65*107y

0.5 0.6 0.7 0.8 0.9 I r,lR,

Fig. 2 ‘Li abundance vs. age for the solar Fig. 3 ‘Li abundance vs. depth (rc/Ra) at four

convective envelope models listed in Table 1. ages for the Model M4 of solar convective

The cross marks the ‘Li abundance and age of envelope

the Sun. Ml-M5 near the curves indicate the corresponding models listed in Table 1.

Table 1 lists the theoretical 7 Li abundance of solar convection zone models, which have

nearly the same depth of convection zone determined by helioseismology rc/Ra = 0.713181,

but different ca/ci. Fig. 2 displays the variation of ‘Li abundance with age for these models.

The cross marks the location of the present Sun on the age-7Li plane. Fig. 3 shows the

variation of ‘Li abundance with depth (rc/Ra) at four ages for Model M4. The vertical thin

line marks the position of the bottom of the solar convection zone. It can be seen that the

effective non-local convective mixing of 7Li element penetrates deeply into the convective

stable zone. The overshooting distance is about 1.07Hp or 0.090Ra for ‘Li mixing, where

Hp is the local pressure scale height and Ra is the solar radius.

It must be indicated that there is not a common overshooting distance in every sense.

It is different for different problems concerned. For example, the physical quantity measured

by helioseismology is the distribution of sound speed in the solar interior, namely, the T -

P structure. Therefore, the overshooting distance in the sense of helioseismology will be

the extension of the super-radiative temperature zone. It is 0.20Hp (or 0.016Ra) for Model

4. It is only about l/5 of the overshooting distance in ‘Li problem. The e-fold lengths of

turbulent velocity and temperature are about 0.38Hp in the bottom overshooting zone.

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