eff < 10 000 K • Non magnetic • Abundance anomalies => Slow

Typical abundance patterns

underabundances : Li, CNO, Ca, Sc overabundances : Iron peak elements (2-5) Rare earths (10 or more) • Fm’s are expected to have the same patterns Gebran et al., 2007 (poster 05)

The Basic Model

• Michaud (1970): separation in radiative zone leads to observed abundance anomalies • Anomalies predicted by purely diffusive models are larger than those observed • Other processes?

1.4M

 :

Diffusion only (black), mass loss ( green ), turbulence ( orange

).

red , blue ,

Transport Processes

• Competition between

g

and

g

rad approx. determines movement of elements • Position of BSCZ and

g

=

g

rad (

v

drift = 0) Mass Loss • Large scale effects can hinder diffusion • Diffusion time scales grow with increasing density

Models with Turbulence

Richer et al (2000): • Sirius A: – 1 free parameter (mixed mass)

Can mass loss do the same?

observed are well reproduced Other papers: Richard et al. (2001) Michaud et al. (2005)

Implementation of Mass Loss

Physical considerations: 1.

t

diff >>

t

conv

Homogeneous abundances in CZ 2. Convective overshoot mixes the atmosphere and links H-He CZ (Latour et al. ,1981) • • • The mass loss rates considered are: chemically homogenous (with the same composition as the SCZ) spherically symmetrical weak enough not to influence nuclear burning in the core or the stellar structure

Implementation of Mass Loss

  

t c

        

D

 ln

c

   U

c

  

U w



v w e

ˆ

r

(many numerical problems encountered)  (

S

nuc )

c



U

• But with simple hypotheses these problems can be avoided: (1) homogeneous CZ (2) Mass lost has same composition as SCZ • Mechanism is not important

Implementation of Mass Loss

 

c



t

        

D

 ln

c

  ( 

U

 

U

w )

c

   (

S

nuc 

S

w )

c



U w

0

v w

ˆ

r

• where:

U



w

   

v w

0

e

ˆ

r

In SCZ Under SCZ

M SCZ

0    

S w

Models with Mass Loss

• The evolutionary calculations take into detailed account time-dependant abundance variations of 28 chemical species and include all effects of atomic diffusion and radiative accelerations.

• These are the first fully self-consistent evolutionary models which include mass loss.

• Models were calculated for 1.35, 1.40, 1.45 and 1.50

M  .

• All the models have evolved from the homogenous pre main sequence phase with a solar metallicity (Z=0.02).

• The mass loss rates considered varied from 1 x 10 -14 3 x 10 -13 M  yr-1.

to

Results: 1.5 M



model

• Observation: t UMa (Hui-Bon-Hoa, 2000) Age~500 Myr,

T

eff ~7000 K • Turbulence and mass loss have slightly different effect on certain Fe convection zone appears naturally!

Results (cont.)

• Anomalies appear with decreasing importance down to stars of 1.35M

 . • Reasonable mass loss rates can reduce anomalies to the desired levels

Conclusions

• With a mass loss rate of the order of the solar mass loss rate we can successfully reproduce the observed anomalies of t UMa.

• It is shown that turbulence and mass loss affect anomalies differently. It is thus possible that additional observations (and more massive models) could help constrain the relative importance of each process.

• Observations of elements between Al and Ar could allow us to determine if there is separation between the Fe and H-He convection zones.

• In any case, it is seen that mass loss can effectively reduce the predicted anomalies to observed levels.