Pre-supernova evolution of massive stars

Ch. 12 of Notes by Onno Pols. HKT Chapter 2.

Day 17 - October, 23, 2025

Agenda:

• Reminders - HW3 - Due: Nov. 4, before class (2m)
• Lecture (25m)
• ICA 15 - 3/4 Groups - Due: Not for credit (25m)
• ICA 15 Report out (10m)

Recap -

The Horizontal Branch (HB)

• Described as the location in the HR diagram for stars that have just undergone helium flash and settled into stable burning and thermodynamic equilibrium.

  • For a fixed helium core ignition mass, the radius and effective temperature depends on the envelope mass.

• Stars with less envelope mass at the ZAHB can be substantially hotter than those with much more of their envelope remaining.

Recap -

• Recall that helium burning begins when the temparature in the core has reached K via the triple- reaction.

• Core helium burning proceeds in a stable fashion, causing a large focus of energy production near the center that leads to formation of a convective core that grows with time.

• These stars undergo a blue loop during core He-burning.

• Massive stars reach temperatures of K

  • allowing them to ignite Carbon under non-degenerate conditions.
  • a critical core mass () is required to reach these ignition conditions, this critical mass is usually reached for stars with initial mass greater than but this is subject to uncertainties in mixing etc.

• Stars with initial mass greater than will go on to burn elements heavier than Carbon up to the formation of an iron core.

• The central regions of massive stars in the plane showing these proceed through early burning phases under non-degenerate conditions - ideal gas.

• For stars with initial mass greater than mass loss by stellar winds becomes of significant importance.
  • At , the mass loss timescale () can become comparable to the nuclear timescale.

Q: Blue loop where?

Stellar wind mass loss

• Observations in the ultraviolet and infrared part of the spectrum show that luminous stars, with masses above 15 under rapid mass loss outflows. Using these data, empirical fits have been for stars and roughly solar metallicity:

The mechanism causing the strong mass loss depends on the location of the star in the HR diagram.

Radiation-driven stellar winds in massive stars

Hot, luminous stars (OB-type main-sequence stars and blue supergiants, BSG) undergo a fast radiation-driven stellar wind.

• Radiation pressure at frequencies corresponding to absorption lines suggest strong interactions between the photons and matter that leads to an outward acceleration.

Schematic HR diagram

Radiation-driven stellar winds in massive stars

You can compute an upper limit for this mass loss making an assumption that the photon imparts all of its momentum during the interaction:

where, is the terminal wind velocity at large distance from the star (‘infinity’) with typical values that are 1,000 to 3,000 (km s) for O-type stars.

Radiation-driven stellar winds in massive stars

• Empirical rates suggest about 1/3 to 1/6 of the momentum is actually transferred.

  • Doppler broadening of the spectral lines that allows the outflowing atoms to then be able to absorb photons at a different, higher frequency leading to a positive feedback mechanism driving the wind.

• Uncertainties due to clumping can also effect rate estimates. Moreover, the mass loss rate is depends on the metallicity of the star, due to the heavier elements being the main elements that contribute to the line driving .

Red supergiant mass loss

Red Supergiants (RSG): are cool, luminous stars that experience slow but significant mass loss similar to the AGB superwinds -- driven by a combination of radial stellar pulsations and radiation pressure on dust particles in the cool atmosphere.

• Stars with spend a large fraction of their core He-burning evolution as RSG losing part of their H-envelope.
  • In the case of complete removal of the H-envelope, the He-core is exposed as a Wolf-Rayet (WR) star.

The Humphreys-Davidson limit

• Observations of the most luminous stars suggest an upper limit to the luminosity of a RSG.

• there are no RSGs with (),

• expected luminosity of a RSG with initial mass of This limit is known as the Humphreys-Devidson as comprised of two parts.

The Humphreys-Davidson limit

A -dependent part that is essentially a generalization of the Eddington Luminosity.

• The actual opacity near the surface is larger than electron scattering and decreases with increasing temperature. Above this limit the surface of the star becomes unstable.

The Humphreys-Davidson (HD) limit

• A -independent component (horizontal part) where the Eddington Luminosity reaches a minimum
  • due to the fact that stars in this regime are dominated by electron scattering opacity, which has no dependence.

Luminous Blue Variables (LBVs)

• Very luminous stars near the HD limit are unstable and experience episodic mass loss of during outburst -- known as Luminous Blue Variables.

• Stars experienceing strong mass loss via LBV outbursts will eventually become WR stars and never RSGs.

Example LBV: Carinae ( Car): binary star system with a LBV

Credit: Nathan Smith (UA Professor), NASA.

• binary stay systen,
• Great eruption in 1837 and becoming the second brigthest star in the sky 11-14 March 1843
• secondary star is about

Evolution of massive stars with mass loss in the HR diagram

Evolution tracks of massive stars () with mass loss.

• The shaded regions correspond to long-lived evolution phases on the main sequence, and during core He burning as a RSG (at ) or as a WR star (at )

Evolution of massive stars in the HR diagram

We can identify 4 main catagories defining the phases of these stars:

Wolf-Rayet stars ()

Very hot, luminous stars with with bright emission lines in their spectra, mass loss rates of to .

WNL stars: some H present on their surface () and increased He and N abundances consistent with CNO cycle burning.

WNE stars: similar to WNL but they lack hydrogen ()

WC stars: no H, little or no N, some He/C/O suggest partial H burning

WO stars: similar to WC stars but strongly increased O suggesting nearly complete helium burning

Advanced evolution of massive stars

• In the advanced phases of burning in the core of a massive star, the temperatures can exceed K at which point neutrino losses from various sources become a significant energy leak, greater than that carried away by photons.

Advanced evolution of massive stars

• The intersections of the nuclear burning lines with the neutrino loss line define the burning temperature of the corresponding fuel to maintain equilibrium.

• burning evolutionary timescales shrink significantly

• the "core" and envelope star become essentially decoupled to what is occuring at the surface

Advanced evolution of massive stars

Pre-supernova structure

Kippenhahn diagram showing the interior of a 15 star towards core-collapse.

In-Class Assignment 15

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.