2. Observational constraints
During the past years, many observational campaigns have been conducted to obtain new accurate measurements of the rotation rates of low mass stars of various ages. Efforts were made both to determine and rotational periods, and were especially conducted to determine rotational velocities of slow rotators, during pre-main sequence phase and in young clusters. For our computations I use a census of both and period determinations from various authors.
I divide our observational sample in three mass bins: 0.9 to 1.1 stars are compared to 1 model. 0.6 to 0.9 stars are compared to 0.8 and 0.6 models. And masses lower than 0.6 are compared to 0.5 model.
For T Tauri stars I used period determinations when available, or when star's radius is known (Bouvier et al. 1986, 1990, Hartmann et al. 1997, Hartmann & Stauffer 1989, Walter et al. 1988). In the case of T Tauri stars, the sample is too small to be divided, and I use the same initial conditions over the full mass range. This leads to angular velocities for CTTS at the age of 106 yr, between 2 and 10 , i.e 10 and 30 km .
Recent observations of post TTS (PTTS or naked TTS), discovered in the Chameleon and Lupus star forming regions from the ROSAT all-sky survey show a widening of the distribution of velocities with age (Wichmann et al. 1997, Covino et al, 1997, Bouvier et al. 1997a). The maximum velocity increases during the pre-main sequence and up to the arrival on the main-sequence (ZAMS). The PTTS cover an age spread between 1 Myr and a few 10 Myr. An interesting issue, in the case of PTTS, is the existence of a bias among X-ray selected observations against slow rotators, as activity is directly correlated to rotation. If this is the case, this bias would lead to an apparent lack of slow rotators during the PTTS phase. It is especially true for 0.6 to 0.9 stars (see Fig. 13). How serious is this problem cannot be investigated for the moment, because of the poorness of the sample of post-TTS for which is known.
Among young clusters there is a large dispersion of velocities: IC2602, IC2391 (30 Myr,Stauffer et al. 1997b), Alpha Persee (50 Myr, Prosser 1992, 1994, Stauffer et al. 1989, 1993), and the Pleiades (80-100 Myr, Soderblom et al. 1993, Queloz et al. 1997a, 1997b). In Alpha Per , velocities of 1 stars extend from a few km up to 200 km , while in the Pleiades maximum velocity has decreased down to 50 km . In Alpha Per the fraction of very slow rotators ( 10 km ) is around 30 % (Allain et al. 1997). In the Pleiades this fraction is (Allain et al. 1996).
M 34 (250 Myr, Jones et al. 1997), and M 7 (220 Myr Prosser et al. 1995) are intermediate clusters between the Pleiades and the Hyades ages (600 Myr, Radick et al. 1987, Stauffer et al. 1997c). On the main sequence, solar-type stars all have low rotation rates.
Important differences from one mass bin to another occur in young clusters and later. The time of the arrival on the main sequence depends on mass, and at the age of the M 34/M 7 clusters a one solar mass star is already on the main sequence, while a 0.5 has just arrived on the ZAMS. In the Pleiades, the maximum velocity for 1 stars is 50 km , while it is 100-150 km for lower masses. The studies in this cluster show that the distribution of velocities is also mass-dependent: for spectral types later than G0, the minimum rotation rate increases with decreasing mass (Stauffer et al. 1997c). In the Pleiades cluster the proportion of stars with velocities lower than 10 km is about 35% for solar-mass stars, and is about 65% in th 0.6-0.9 mass range. (Allain et al, 1996, Queloz et al. 1997a, 1997b). In the cluster M 34, there is more spread in the velocities in the 0.6-0.9 mass range than in the 0.9-1.1 mass range (7 - 45 km , 5 - 15 km , respectively). For the Hyades cluster, differences are even more striking and Radick et al. (1987) found a tight relationship between rotation period and mass down to 0.6 : the lower the mass, the lower the velocity. For masses lower than 0.6 , the Hyades stars still exhibit a dispersion of velocities comparable to the dispersion in M 34 for 0.6-0.9 stars (Stauffer et al., 1997a), meaning that very low-mass stars still undergo a significant braking.
Most of the angular velocities presented here (see e.g Fig. 11) come from measurements, and are thus lower limits to the true angular velocities.
© European Southern Observatory (ESO) 1998
Online publication: April 20, 1998