1. PRE-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

3. From Protostars to Stars
Star emerges from the enshrouding dust cocoon
Ignition of H  He fusion processes

4. HAYASHI 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 tkh Eg/L GM2/RL

5. (1/kr) dT4/dr ~ 1/<kr> T4/R* ~ L */(R *)2
Henyey 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) = -(64psr2)/3kr dT4/dr
(1/kr) dT4/dr ~ 1/<kr> T4/R* ~ L */(R *)2
From:
Hydro- equilibrium:
GM/R = kT/mmH <T> ~ M*/ R * ; <r> ~ M */(R *)3
Results: (M *)3 <k> -1 ~ L *

6. Low-mass stars <k> (b-b,b-f transitions)
High-mass stars: (electron scattering dominated) <k> ~ cte
L * ~ (M *)3
Low-mass stars <k> (b-b,b-f transitions)
L * ~ (M *)3 <k> -1
As a PMS becomes increasingly radiative, this mass-luminosity scaling becomes
more relevant, and contraction to the MS occurs at nearly constant luminosity

8. THEORETICAL PREDICTIONS OF HOW PROTOSTAR EVOLVES FROM CORE
TO MAIN SEQUENCE IN HR DIAGRAM
Ex. Evolutionary tracks calculations  D´Antona & Mazzitelli 1994, ApJS, 90, 467

9. Ex. : For M= 0. 8 Msol; R=2Rsol and L=1Lsol tk-h 4
Ex.: For M= 0.8 Msol; R=2Rsol and L=1Lsol tk-h yr  Hayashi track ~ yr
(Evolutionary tracks for different masses, separated in Teff partially due to different
gravities affect to the outer atmospheric opacities.)

13. THE BIRTH LINE: THEROY VS. OBSERVATIONS
Line on the HR diagram beyond which no PMS are observed. This BIRTH LINE cut across the Hayashi track
FROM CALVET (2004)

14. 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