Astronomy & Astrophysics manuscript no. rotation c ESO 2018 October 18, 2018 Scenarios to explain extreme Be depletion in solar-like stars: accretion or rotation effects? M. Viallet, I. Baraffe Physics and Astronomy, University of Exeter, Stocker Road, Exeter, UK EX4 4QL e-mail: [email protected], [email protected] Received; accepted ABSTRACT Studies of beryllium abundance in large samples of solar-type stars show a small fraction of extremely beryllium- deficient stars, which challenges our current understanding of light element depletion in these stars. We suggest two possible scenarios that may explain this high level of Be depletion: early accretion and rotational mixing. We show that in both cases, the conditions required to reach the observed level of Be depletion are quite extreme, which explains the very small fraction of detected Be outliers. We suggest that substantial Be depletion can be obtained in stars if they were fast rotators in the past, with high initial rotational velocities and short disc lifetimes. Our analysis suggests that rotational mixing may not be efficient enough to deplete Be in less than 10 Myr. Consequently, the detection of strongly Be-deficient stars in clusters younger than ∼ 10 Myr may provide a genuine signature of accretion process and the proof that some protostars may undergo many extreme bursts of accretion during their embedded phases of evolution. Key words. stars: rotation - stars: solar-type - stars: abundances - stars: pre-main sequence - accretion, accretion disks - hydrodynamics 1. Introduction v sin i of these stars, their rotation rate is similar to that of the Sun, and their estimated ages are between 1 and 2 The light chemical elements lithium, beryllium and boron Gyr. Takeda et al. (2011) found four strongly Be-depleted provide good tracers of internal mixing processes in stel- objects within their sample of 118 stars: HIP 17336, HIP lar interiors. A huge amount of observational and theoret- 32673, HIP 64150, and HIP 75676. These objects have sim- ical works has been devoted to the analysis of their abun- ilar properties as those of the Santos et al. (2004) sam- dances at the surface of various types of stars. Interest ple: strong Li depletion, an age of ∼ 3 − 5 Gyr, and low in these elements has recently increased within the con- v sin i ∼ 2 km/s. The properties of these seven objects are text of exoplanet discoveries because of possible links be- summarised in Table 1. Existing calculations for Be deple- tween Li depletion in a star and the presence of a planet tion in this mass range, based on rotational mixing scenar- orbiting this star (see e.g Sousa et al. 2010 and refer- ios (Pinsonneault et al. 1989) or mixing by internal waves ences therein). This suggestion motivated extensive stud- (Montalb´an & Schatzman 2000), cannot explain these low ies of solar-type stars with the main goal of analysing Be abundances (see e.g Fig. 4 of Delgado Mena et al. 2012). Li and Be in planet hosting stars and of confirming or refuting the above-mentioned link (Takeda et al. 2011; G´alvez-Ortiz et al. 2011; Delgado Mena et al. 2012). This has yielded large samples of homogeneous data, which pro- vide excellent opportunities to study properties and trends In this paper, we explore two scenarios that may ex- of light-element depletion. One striking property resulting plain these Be-deficient outliers, which are observed in arXiv:1209.1812v1 [astro-ph.SR] 9 Sep 2012 from these studies is a small fraction of highly Be-deficient an effective temperature range 5000 − 6000 K and corre- stars in sufficiently large samples, which questions our cur- spond to a mass range 0.8 − 1.1 M⊙. The first scenario rent understanding of Be destruction in solar-type and low- is based on episodic accretion at early stages of evolution mass stars. (§2), which can strongly affect the internal structure of In a sample of 82 stars, Santos et al. (2004) found three young accreting objects and enhance the depletion of light abnormally Be-depleted objects, namely HD 4391, HD elements, following the ideas of Baraffe et al. (2009) and 20766 and HD 280807. These Be-deficient stars are dwarfs Baraffe & Chabrier (2010). The second scenario is based with Teff in the range 5700 - 5900 K. Lithium depletion on rotational mixing. We adopt a simplified treatment of is poorly constrained but is also significant, with Li abun- rotational mixing in stellar interiors, which we describe and 1 dances A(Li) < 1 (upper limit). According to the measured validate in §3. We quantitatively show (§4) that substantial Be depletion can be obtained in stars if they were fast rota- 1 The notation A(E) defines the abundance of element E and tors in the past. This idea was mentioned in Takeda et al. is equal to log[N(E)/N(H)] + 12, where N(E) and N(H) are the (2011), but no quantitative studies exist to confirm it. mole fraction of element E and of hydrogen, respectively. Discussion and conclusion follow in Sect. 5. 1 M. Viallet & I. Baraffe: Extreme Be depletion in solar-type stars Table 1. Parameters of strongly Be-depleted objects. Star Teff A(Be) A(Li) Age v sin i (K) (Gyr) (km/s) a HD 4391( ) 5878 0.64 < 1.09 1.2 2.72 a HD 20766( ) 5733 < −0.09 < 0.97 1.6 1.98 a HD 20807( ) 5843 0.36 < 1.07 2.1 1.74 b HIP 17336( ) 5671 < −0.85 < 0.8 3.89 2.07 b HIP 32673( ) 5724 < −0.78 < 1.0 3.16 2.83 b HIP 64150( ) 5800 < −0.88 < 1.0 4.2 2.21 b HIP 75676 ( ) 5772 < −0.96 < 1.1 4.16 2.18 a b Notes. ( ) From Santos et al. (2004) ( ) From Takeda et al. (2010) and Takeda et al. (2011). 2. Episodic accretion scenario Baraffe et al. (2009) and Baraffe & Chabrier (2010) re- Fig. 1. Abundance of Be (divided by the initial abun- cently investigated the effect of episodic accretion at very dance Be0) versus time (in yr) in stars that have under- early stages of evolution on the structure and Li deple- gone a given number Nburst of accretion bursts with M˙ =5 −4 −1 tion of low-mass objects. Baraffe et al. (2009) showed that 10 M⊙yr and duration ∆tburst = 100 yr. The blue bursts of accretion can produce objects significantly more solid line corresponds to an accreting sequence with final compact than their non-accreting counterpart of same mass mass 1 M⊙ with Nburst=20 bursts. The red dashed line and age. These authors suggested that non-steady accre- corresponds to a final mass 0.8 M⊙ with Nburst=16. The tion during the embedded phase of protostar evolution pro- accretion process starts from an initial seed mass of 10 MJ duces the observed spread in luminosity in the Herzsprung- (see Baraffe & Chabrier 2010 for details). The black dotted Russel diagram (HRD) of young clusters. As a consequence line indicates the Be abundance for non-accreting models of the more compact structure, Baraffe & Chabrier (2010) of 0.8 M⊙ or 1 M⊙, which are the same for both masses showed that objects undergoing very strong accretion since Be is not depleted in those models. bursts have significantly higher central temperatures and can be severely Li-depleted. This scenario provides an ex- planation for the unexpected level of Li depletion observed in a few low-mass members of young clusters (∼ a few Myr). Based on the same calculations as in Baraffe & Chabrier (2010), we find that significant Be depletion can take place 3. Rotational mixing scenario: the model in stars that have undergone short and very intense bursts −4 −1 of accretion with M˙ ∼ 5 10 M⊙yr . Those results are In the following, we explore quantitatively whether rota- illustrated in Fig. 1, which displays the abundance of Be tion can explain extreme Be depletion, based on the im- as a function of time at early stages of evolution of low- plementation of rotation effects in the same stellar evo- /solar-mass stars. These calculations show that the early lution code as in the previous section to study accretion history of accretion can significantly deplete Be in stars effects (see Baraffe et al. 2009 and references therein). in the mass range of interest. Note that Li is totally de- Different parametrisations for the treatment of rotational stroyed in the models displayed in Fig. 1. As explained in effects in 1D stellar evolution codes exists in the lit- Baraffe & Chabrier (2010), the more compact and hotter erature, see e.g. Pinsonneault et al. (1989); Heger et al. structure of accreting models increases the maximum tem- (2000); Denissenkov & Tout (2000); Maeder & Meynet perature reached at the bottom of the convective envelope, (2010) and references therein. These formalisms are usu- which increases the level of Li and Be destruction com- ally based on the treatment of Endal & Sofia (1978) (e.g. pared to the non-accreting counterparts of same mass. We Pinsonneault et al. 1989) or on the model of Zahn (1992) find that substantial depletion of Be only happens if the and its subsequent developments (see e.g. Maeder & Zahn protostar undergoes several bursts (more than ten) of ex- 1998). All these formalisms contain free parameters that −4 −1 treme intensities with rates ≫ 10 M⊙yr . According are calibrated to reproduce observations (e.g solar surface to numerical simulations of collapsing cloud cores, typical rotational velocity, surface abundances of light elements) mass accretion rates onto the protostar vary in the range and yield very different results when applied to the same −6 −1 −4 −1 10 M⊙yr − 10 M⊙yr (Vorobyov & Basu 2010; case study, as recently illustrated by Potter et al.