ZAMS and Evolution On The Main-Sequence

Ch. 9.2/9.3 of Notes by Onno Pols. HKT Chapter 2.

Day 14 - October, 14, 2025

Agenda:

• Reminders - Final Project Report Draft - Due: Nov. 11 (2m)
• Lecture (15m)
• ICA 13 - 4 Groups - Due: Not for credit (30m)
• ICA 13 Group Discussion (10m)

Single Stars On and Near the Main Sequence

A star has reached the main-sequence if the following is true:

• chemically homogeneous with identical or very similar compositions
• hydrostatic and thermal balance
• energy is derived solely from nuclear burning

We can also define the Zero-Age Main-Sequence (ZAMS) as the time at which the stellar model satisfies these requirements.

The Zero-Age Main Sequence (ZAMS)

HRD for ZAMS models showing effect of initial composition. Pols 9.6.

• Metal-poor main sequence stars are hotter and have smaller radii.
• relatively low-mass stars are also more luminous than their metal-rich counterparts.
• lower bound-free opacity at lower for up to , above that electron scattering opacity dominated.

The Zero-Age Main Sequence (ZAMS)

Central versus central for detailed ZAMS models. Pols 9.7.

• central temperature to increase with mass ( and )
• comparing solar to metal poor, the luminosity of two stars with the same mass is similar, but their central temperature is higher

The Zero-Age Main Sequence (ZAMS)

We can distinguish three types of ZAMS star:

• completely convective, for
• radiative core + convective envelope, for ,
  • -chain dominates, energy production is then distributed over a larger area, which keeps the energy flux low in the center and the core remains radiative
• convective core + radiative envelope, for .
  • CNO dominates, energy production is concentrated, the energy flux is high in the center and the core is convective.

Evolution during central hydrogen burning

• Evolve away from ZAMS towards higher luminosities and larger radii.
• Hydrogen is converted into helium, the increases in the core.
• Since the increases and at the same time the H decreases, must increase somewhat to keep up the energy production, but the required increase in Tc is very small.

Single Stars On and Near the Main Sequence

• Note: ZAMS solutions for stars with identical mass or composition in stellar modeling are not unique due to many uncertainties from:

  • equations of state,
  • opacities, and
  • nuclear reaction rates.

• Evolution off of the main sequence will depend on the initial mass. We can categorize them in various ways.

Evolution of Single Stars Off the Main Sequence

Unevolved Lower ZAMS ( 0.8):

• Using HKT Eq. 1.88 Gyr, greater than a Hubble time for stars 0.8.

Lower ( to ):

• Depends on composition, this range undergoes helium ignition in the electron degenerate regime (to the right of the ). Models to the left are non-degenerate and obey ideal gas laws.

Evolution of Single Stars Off the Main Sequence

Intermediate (3 to about 8-9):

• Helium ignition occurs in a nondegenerate scenario leading to the build up of a primarily degenerate carbon (C) and (O) core.

Upper (aka Massive, or greater):

• The main distinction from intermediate masses being that a non-degenerate CO core is formed and maintained until C-ignition.

Evolution of Single Stars Off the Main Sequence

Evolution of stars off of the main sequence for three stellar tracks.

• hydrogen depletion/growth of the helium core is surrounded by an active H-burning shell which provides a power source.

• The helium core continues to contract, due to the lack of a burning source.

Evolution of Single Stars Off the Main Sequence

• The contraction and heating of the He-core and the H-shell drives expansion of the stellar envelope. The star becomes evolve towards the red giant branch (3-6).

Where the red giant branch (RGB) is characterized by a continual expansion and reddening of the star to lower effective temperatures.

In-Class Assignment 13

In class: Work on ICA here with groups per usual. Discuss conceptual questions together and prepare answers to share at the end of class.

• Choose someone that will report out the groups responses ahead of time!

After Class: Due: Not for credit

Note: ICAs will be shorter with the goal of: reducing focus on coding, increasing time for discussion and interpretation of results / plots in groups and as a class.