Rotational Evolution of Low Rotational Evolution of Low Mass StarsMass Stars

Ramiro de la Reza

Observatório Nacional - Rio de Janeiro

Compilation of 3100 observed rotation periods and some vsini for open clusters for M < 1.2 Mo (Irwin-Bouvier 2009)

Solar mass stars ~ 0.9 M/Mo 1.1

Very low mass stars M 0.4 Mo

Evolution PMS from 1 Myr. (ONC) ~30 Myrs. (ZAMS)

MS 30Myr ~ 650 Myrs (Hyades/Praesepe)

Compilation of 3100 observed rotation periods and some vsini for open clusters for M < 1.2 Mo (Irwin-Bouvier 2009)

M/M

1 My

3 My

2 My

3 My

30 My

5 My

5 My

40 My

50 My

100 My

100 My

130 My 625 My

485 My

200 My

150 My

150 My

625 My

P

M/Mo

Slowest rotators:From 1 Myr up to 5 Myr, P ~ constant= 10 d

From 5 Myr up to ~ 40 Myr, P =10 to P=8 d

Then, contraction ceases

Rapid rotators:From 1 Myr up to 5 Myr, P=1 d => P=0.6 d

This is OK with stellar contraction

Rapid rotators are much less braked

1- One operating in the PMS up to 5-10 Myr

that will maintain the rotation constant

2- One operating in the MS ( 100-600 Myr)

to produce the convergence of the rotation rates

Conclusions: We need to invoke two mechanisms of angular momentum removal

Lifetime of disks

The resulting rotation will depend on one important parameters: lifetime of disks

1- High rotators stars will result from short lifetime disks

2- Low rotators from long lifetime disks

Distribution of rotation periods for ONC with masses > 0.25 Mo

Can this be tested?

Rebull et al. 2006 presented the first statistical detection of this effect using IRAC

However, a puzzling population of slowly-rotating stars with no disks appeared later confirmed by Cieza-Baliber (2007)

Hen 3-600

Chavero 2009 (Thesis)

For the second loss of angular momentum on the MS the mechanism considered, at least for solar mass stars, is a solar-type magnetized stellar wind (Kraft 1967).

From the Hyades up to the Sun the rotation follows the famous Skumanich (1972) law : ω α t -1/2

MODELS

Bouvier (1997), Allain (1998), Irwin (2007)

Evolution with four parameters:

ω0 , K (solar type angular momentum loss), ωsat , disk lifetime

disk bracking

spin up spin down

Star solid body rotation => no good fit

Introduction of a differential rotation with a core and an envelope with different rotation velocities.

There is a coupling between these two regions shear

This coupling transporting angular momentum from the rapid core rotator to the envelope lower rotator (observable) depends on a timescale τC

τC ~ 6 Myr for rapid rotators (~ solid body rotation)

τC ~ 110 Myr for a slower rotators ( inefficient coupling)

dStellar differential rotation => better fitdiiDdi

Low mass stars => bad fit

How to measure the rotational velocities of stars in associationsHow to measure the rotational velocities of stars in associations

Ø (vsini) = Ø (y)

Method: Chose a f(v) law, where v= v eq in order that Ø (vsini) be equal to the observed distribution of vsini velocities

With these v eq we can calculate the momentum J= α2 < v eq> <M><R>

Where alpha is the total gyration stellar radius that depends on (mass, age)

Calculations for associations between 8 and 30 Myr shown that J is conserved for low and high rotators.

Rotation of post-T Tauri starsRotation of post-T Tauri stars

de la Reza & Pinzón (2004): Rotation vs X-ray radiationScholz et al. (2007): Rotation vs activity (Hα)

Both works were done for almost the same group of stellar associations:

ε Cha 6.7 Myr (Jilinski et al. 2005)

TWA 8.3 +- 0.8 Myr (de la Reza et al. 2006)

BPMG 11.3 +- 0.3 Myr (Ortega et al. 2004)

Tuc/Hor 30 Myr (Zuckerman & Song 2004)

Observed distribution of vsini for three associations

Schematic time evolution of mean LX and log LX/Lb for both LM and HM rotating modes. Open symbols represent TWA (triangles), BPMG (squares), and Tuc/HorA (large octagons). Filled squares correspond to ONC data taken from Feigelson et al. (2003). In the bottom panel, the filled circles are taken from Huélamo (2002) and represent nine PTTS belonging to Lindroos systems.

The deduced V (eq) enable us to estimate periods for the associations: X-ray radiation in the PMS is different than the radiation obtained for slow rotators in the MS (solid line)

Figure 8Figure 7

Behavior of X-ray radiation with the age of the associations (de la Reza and Pinzón 2004)

FIG. 9 FIG. 10

X-ray radiation with stellar mass: higher mass stars de-saturate faster at 30 Myr because their convective layers attaint a minimum. Even a larger vsini do not affect this (de la Reza & Pinzón 2004)

Lithium depletion in associations

(da Silva et al. 2009)

Conclusions1- Rotation is an important parameter to understand the general

evolution of stars and disks in the PMS and MS stages.

2- General rotation of very low mass stars is not yet in a total agreement with observations

3- We need to understand more the physics of the braking mechanisms

4- Rotation (together with convection) explains the Li abundance in stars and stars with planets and also the Li abundance dispersion