Mem. S.A.It. Vol. 80, 180c© SAIt 2009 Memorie della

Hints from chromospheric activity to constrainstellar modelling

D. Cardini and M. P. Di Mauro

INAF – Istituto di Astrofisica Spaziale e Fisica Cosmica–Roma, Via del Fosso del Cavaliere100, 00133 Roma, Italy

Abstract. We discuss on the possibility to use measurements of chromospheric activity androtation period as indicator of the age and location of the base of the convective envelopein low-mass main sequence stars. This is expected to have strong impact on studies ofpulsations and modelling of solar-type stars.

1. Introduction

It is generally accepted that the rotational ve-locities of low main–sequence single stars de-cline with increasing age (Kraft 1967), dueto angular momentum loss through magnetizedwinds (Schatzman 1962) and/or sporadic massejection from stars with deep surface convec-tion zone.

Analysis of data of mass, rotation period,and age in a large sample of cluster and fieldstars allowed Cardini & Cassatella (2007) todetermine that the rotation period Prot of a starcan be expressed as:

P(t,M) = (25.6 ± 2.5) × t0.45±0.06(1.4 − M/M�)

where t and M/M� are respectively the age (inGyr) and the mass of the star (in solar masses).The expression applies to stars with mass from0.25 M� to 1.3 M�.

2. Evolution with age of thechromospheric activity

It has been known for a long time that age,rotation, and the level of magnetic activity

are related each other in main–sequence stars(Smith 1979).

Analysis of the level of chromospheric ac-tivity, as measured by the Mg II line surfaceflux, for a sample of stars with different massesand ages allowed Cardini (2007) to concludethat the chromospheric emission of late main–sequence stars is linearly correlated, in logvariables, to the rotation period and hence toage. However this correlation is valid up tosome ”critical ages”, different for each stel-lar mass, after which the correlation rotation–activity ends and the activity suddenly drops.

From the comparison of the chromosphericactivity evolution with the evolution of vari-ous structural parameters in stars with differ-ent masses, we have found that the convec-tive envelope depth should be the parameterwhose rapid change can determine the drop ofthe level of activity. Figure 1 (bottom panels)shows the time evolution of chromospheric ac-tivity for stars with mass 0.45 < M/M� < 0.75(left) and 1.14 < M/M� < 1.3 (right) and(top panels) the time evolution of the depth ofconvective envelope, relative to the total starradius, for two evolutive models of 0.6 M�(left) and 1.2 M� (right) calculated with the

Cardini and Di Mauro: Hints from chromospheric activity 181

Fig. 1. Top: The width of the convective envelope, relative to the total star radius, versus age for twoevolutive models. Bottom: Evolution with age of FMg II for stars in two mass bins. The solid lines show thefunctional dependence, derived by a fitting procedure, of FMg II on age in the early evolutive stages.

code by Christensen-Dalsgaard (2007). As canbe seen, for what concerns lower mass stars,which have a slow evolutionary time, the chro-mospheric activity is proportional, in log vari-ables, to the stellar age along all their life timeup to now. Actually their convective zone depthdoes not undergo any significant change alongthis time. Vice versa, in higher mass stars,which evolve very rapidly, the decline in ac-tivity is correlated to the age, and hence tothe loose of rotation velocity, only for a littlespan of time after which a qualitative changein chromospheric behavior appears in corre-spondence with the onset of the deepening ofthe convective envelope. The authors are ac-tually working to explicit the relationship be-tween the level of chromospheric activity andthe depth of convective envelope.

3. Implications for studies ofsolar–type stars

It is well known that the potential of astero-seismology strongly depends on the availabil-ity of accurately identified pulsation frequen-cies and global parameters in order to con-strain stellar structure properties. Here we haveshown a preliminary study on the possibility ofusing measurements of chromospheric activity

and rotation period, as obtained from photo-metric and spectroscopic observations, to de-termine the age and the location of the base ofthe convective envelope in a number of main–sequence stars with mass M < 1.4M�. We be-lieve that the scenario outlined in this paperhas large consequences on studies of main–sequence solar–type stars and on the progressof our understanding of stellar structure andevolution. The idea is to combine asteroseis-mic data and measurements of magnetic activ-ity and rotation period in order to better con-strain stellar properties such as age and exten-sion of the convective region. In the next fu-ture we plan to apply this method to a numberof well known targets of asteroseismic stud-ies (e.g. β Hyi, α Cen A, α Cen B, ε Eri) forwhich measurements of period and chromo-spheric activity are available in literature.

References

Cardini, D. 2007, ApJ, submittedCardini, D., & Cassatella, A. 2007, ApJ, 666,

393Christensen-Dalsgaard, J. 2007, Ap&SS, 461Kraft, R. P. 1967, ApJ, 150, 551Schatzman, E. 1962, Ann. d’Astroph., 25, 18Smith, M. A. 1979, PASP, 91, 737