PRE-MAIN-SEQUENCE STELLAR EVOLUTIONARY TRACKSPRE-MAIN-SEQUENCE STELLAR EVOLUTIONARY TRACKS

The paths followed by a newly-formed star as it approaches the main sequence on the HR diagram:

“Vertical”: Hayashi track

“Horizontal”: Henyey track

From Protostars to Stars

Ignition of H He fusion processes

Star emerges from the enshrouding dust cocoon

HAYASHI TRACKHAYASHI TRACK

PMS begin the evolution at the upper right of the HR diagram: Low T Large R (and L)Luminosity is supplied by contraction (i.e. from Eg, see “virial theor.”)

At the beginning, isothermal collapse: released Eg, freely radiated away

Later on: hydrostatic core+envelope of increasing density: released Eg increasingly hard to be radiated outside: Luminosity decreases Temperature at the outer edge, roughly constant

HAYASHI TRACK IS ROUGHLY VERTICALLY DOWNWARDS ON THE HR DIAGRAM

Hydrostatic core contracts quasi-statically: Kelvin-Helmholtz contraction

Kelvin-Helmholtz time scale kh Eg/L GM2/RL

Henyey tracksHenyey tracks

Contraction at nearly constant T stops when the star develops a radiative core

The star moves to the MS along nearly horizontal paths in the HR diagram:

Henyey tracks

Radiative transfer of energy: diffusion equation:

L(r) = -(64r2)/3 dT4/dr

(1/ dT4/dr ~ 1/<> T4/R* ~ L */(R *)2

From:Hydro- equilibrium:

GM/R = kT/mH --------------- <T> ~ M*/ R * ; <> ~ M */(R *)3

Results: (M *)3 <> -1 ~ L *

High-mass stars: (electron scattering dominated) <> ~ cte L * ~ (M *)3

Low-mass stars <> (b-b,b-f transitions) L * ~ (M *)3 <> -1

As a PMS becomes increasingly radiative, this mass-luminosity scaling becomesmore relevant, and contraction to the MS occurs at nearly constant luminosity

THEORETICAL PREDICTIONS OF HOW PROTOSTAR EVOLVES FROM CORETHEORETICAL PREDICTIONS OF HOW PROTOSTAR EVOLVES FROM CORETO MAIN SEQUENCE IN HR DIAGRAMTO MAIN SEQUENCE IN HR DIAGRAM

Ex. Evolutionary tracks calculations D´Antona & Mazzitelli 1994, ApJS, 90, 467

Ex.: For M= 0.8 Msol; R=2Rsol and L=1Lsol k-h 4.3 106 yr Hayashi track ~

1.4 106 yr

(Evolutionary tracks for different masses, separated in Teff partially due to differentgravities affect to the outer atmospheric opacities.)

THE BIRTH LINE: THEROY VS. OBSERVATIONSTHE BIRTH LINE: THEROY VS. OBSERVATIONS

FROM CALVET (2004)

Line on the HR diagram beyond which no PMS are observed. This BIRTH LINE BIRTH LINE cut cut across the Hayashi trackacross the Hayashi track

The birth line: stars are not observed in the top right-hand side of the HR diagram, where the theory predicts the start of Hayashy track.

HR diagram is normally plotted for optical colours the start of Hayashi track corresponds to the youngest PMS surrounded by gas and dust optical/nir radiation cannot escape undetectable