Mažos masės žvaigždės: Raudonieji milžinai ir baltieji nykštukai

Low-mass stars: Red giants and white dwarfs

The evolutionary path followed by Sun-like stars after core hydrogen exhaustion, ending as compact white dwarfs

When a Sun-like star or another low-mass star (roughly ≤8 M⊙) finishes its main sequence life, it does not end as a supernova. Instead, it follows a gentler but still dramatic path: expanding into a red giant, igniting helium in its core, and eventually shedding its outer layers, leaving behind a compact white dwarf. This process determines the fate of most stars in the universe, including our Sun. Below, we will examine each stage of low-mass star evolution after the main sequence, revealing how these changes reshape the star's internal structure, luminosity, and final fate.

1. Overview of low-mass star evolution

1.1 Mass limits and lifetimes

Stars considered “low mass” typically range from about 0.5 to 8 solar masses, though exact boundaries depend on details of helium ignition and final core mass. Within this mass range:

  • Core-collapse supernova is very unlikely; these stars are not massive enough to form an iron core that would later collapse.
  • White dwarf remnants are the final outcome.
  • Long main sequence lifetime: Lower-mass stars near 0.5 M⊙ can spend tens of billions of years on the main sequence, while a 1 M⊙ star like the Sun lasts about 10 billion years [1].

1.2 Post-main sequence evolution briefly

After core hydrogen exhaustion, the star passes through several important stages:

  1. Hydrogen shell burning: The helium core contracts, and the hydrogen-burning shell pushes the outer layers into a red giant.
  2. Helium ignition: When the core temperature rises sufficiently (~108 K), helium fusion begins, sometimes explosively – the so-called “helium flash.”
  3. Asymptotic giant branch (AGB): Later burning stages, including helium and hydrogen burning in shells above the carbon–oxygen core.
  4. Planetary nebula ejection: The star's outer layers are gently ejected, forming a beautiful nebula, leaving the core as a white dwarf [2].

2. Red giant phase

2.1 Leaving the main sequence

When a Sun-like star exhausts its core hydrogen, fusion moves to the surrounding shell. Since fusion does not occur in the inert helium core, it contracts due to gravity, causing the temperature to rise. Meanwhile, the star's outer layer expands significantly, making the star:

  • Larger and brighter: the radius can increase by tens or hundreds of times.
  • Having a cool surface: the expanded layer's temperature decreases, giving the star a red hue.

Thus, the star becomes a red giant on the H–R diagram's red giant branch (RGB) [3].

2.2 Hydrogen shell burning

At this stage:

  1. Helium core contraction: The helium ash core shrinks, and the temperature rises to ~108 K.
  2. Shell burning: Hydrogen burns intensely in a thin shell near the core, often causing strong radiation.
  3. Expansion of the outer layer: Additional energy from shell burning pushes the outer layers outward, and the star ascends the red giant branch.

A star can spend hundreds of millions of years on the red giant branch, gradually forming a degenerate helium core.

2.3 Helium flash (for stars ~2 M⊙ or lower)

In stars with masses ≤2 M⊙, the helium core becomes electron degenerate – meaning the quantum pressure of electrons resists further compression. When the temperature reaches a critical threshold (~108 K), helium fusion ignites explosively in the core – this is the helium flash, releasing a burst of energy. This flash removes degeneracy and restructures the star without catastrophic outer layer ejection. Higher mass stars ignite helium more gently, without a flash [4].

3. Horizontal branch and helium burning

3.1 Core helium fusion

After the helium flash or mild ignition, a stable helium burning core forms, where 4He → 12C, 16O synthesis occurs, mainly through the triple‐alpha process. The star adjusts to a new stable state on the horizontal branch (in stellar group H–R diagrams) or the red clump in slightly lower mass cases [5].

3.2 Duration of helium burning

The helium core is smaller and occurs at a higher temperature than the hydrogen burning phase, but helium fusion is less efficient. As a result, this stage typically lasts about 10–15% of the star's main sequence lifetime. Over time, an inert carbon–oxygen (C–O) core forms, which eventually prevents the synthesis of heavier elements in low-mass stars.

3.3 Ignition of the helium burning shell

When the central helium reserves are exhausted, the helium burning shell ignites outside the already formed carbon–oxygen core, pushing the star toward the asymptotic giant branch (AGB), known for its bright, cool surfaces, strong pulsations, and mass loss.

4. Asymptotic giant branch and outer layer ejection

4.1 AGB evolution

During the AGB phase, the star's structure features:

  • C–O core: An inert, degenerate core.
  • Helium and hydrogen burning shells: Burning shells that cause pulsational behavior.
  • With a huge outer layer: The star's outer layers expand to enormous radii, having relatively low surface gravity.

Thermal pulses in the helium shell can cause dynamic expansion processes, resulting in significant mass loss through stellar winds. This outflow often enriches the interstellar medium with carbon, nitrogen, and s-process elements formed during shell flashes [6].

4.2 Planetary nebula formation

Eventually, the star can no longer hold onto its outer layers. The final superwind or pulsation-driven mass loss reveals the hot core. The ejected outer layer shines in UV radiation emitted from the hot stellar core, creating a planetary nebula – often a complex shell of ionized gas. The central star essentially becomes a proto–white dwarf, shining intensely in UV radiation for tens of thousands of years as the nebula continues to expand.

5. White dwarf remnant

5.1 Composition and structure

When the ejected outer layer dissipates, the remaining degenerate core appears as a white dwarf (WD). Typically:

  • Carbon–oxygen white dwarf: The final stellar core mass is ≤1.1 M⊙.
  • Helium white dwarf: If the star lost its outer layer early or was in a binary interaction.
  • Oxygen–neon white dwarf: In slightly more massive stars near the upper mass limit required for WD formation.

Electron degeneracy pressure supports the WD from collapse, setting typical radii roughly the size of Earth, with densities from 106 up to 109 g cm−3.

5.2 Cooling and WD lifetimes

The white dwarf radiates residual thermal energy over billions of years, gradually cooling and fading:

  • Initial brightness is moderate, mostly radiating in optical or UV bands.
  • Over tens of billions of years it fades to a “black dwarf” (hypothetical, since the universe is not old enough for WDs to cool completely).

Besides nuclear fusion, WD luminosity decreases as stored heat is released. Observing WD sequences in star clusters, astronomers calibrate cluster ages since older clusters have cooler WDs [7,8].

5.3 Binary interactions and nova / Type Ia supernova

In close binary systems, the white dwarf can accrete material from the companion star. This can cause:

  • Classical nova: Thermonuclear runaway on the WD surface.
  • Type Ia supernova: If the WD mass approaches the Chandrasekhar limit (~1.4 M⊙), carbon detonation can completely destroy the WD, creating heavier elements and releasing enormous energy.

Therefore, the WD phase may have further dramatic consequences in multiple star systems, but in isolation it simply cools indefinitely.

6. Observational evidence

6.1 Color–magnitude diagrams of star clusters

Open and globular cluster data show distinct “red giant branch,” “horizontal branch,” and “white dwarf cooling sequence,” reflecting the evolutionary path of low-mass stars. By measuring main sequence turnoff ages and WD luminosity distributions, astronomers confirm theoretical lifetimes of these stages.

6.2 Planetary nebula surveys

Imaging surveys (e.g., with the Hubble telescope or ground-based telescopes) reveal thousands of planetary nebulae, each with a hot central star rapidly becoming a white dwarf. Their morphological diversity—from ring-shaped to bipolar forms—shows how wind asymmetries, rotation, or magnetic fields can shape the ejected gas structures [9].

6.3 White dwarf mass distribution

Large spectroscopic surveys show that most WDs cluster around 0.6 M⊙, consistent with theoretical predictions for intermediate-mass stars. The rarity of WDs near the Chandrasekhar limit also matches the mass limits of stars that form them. Detailed WD spectral lines (e.g., from DA or DB types) provide information about core composition and cooling ages.

7. Conclusions and future research

Low-mass stars, such as the Sun, follow a well-understood path after hydrogen exhaustion:

  1. Red giant branch: The core contracts, the outer layer expands, the star reddens and brightens.
  2. Helium burning (horizontal branch / red clump): The core ignites helium, and the star reaches a new equilibrium.
  3. Asymptotic giant branch: A double shell-burning cycle around a degenerate C–O core, ending with strong mass loss and planetary nebula ejection.
  4. White dwarf: A degenerate core remains as a compact stellar remnant that cools and fades over the ages.

Ongoing work refines AGB mass loss models, the characteristics of helium flashes in low-metallicity stars, and the complex structure of planetary nebulae. Observations from multiwavelength surveys, asteroseismology, and improved parallax data (e.g., from Gaia) help confirm theoretical lifetimes and internal processes. Meanwhile, studies of close binary systems reveal the causes of novae and type Ia supernovae, emphasizing that not all WDs quietly cool—some undergo explosions.

Essentially, red giants and white dwarfs describe the final chapters of most stars, showing that hydrogen exhaustion is not the end of a star but a rather dramatic turn toward helium burning and, ultimately, the gentle fading of a degenerate core. Since our Sun is approaching this path over several billion years, it reminds us that these processes shape not only individual stars but entire planetary systems and the broader chemical evolution of galaxies.

Šaltiniai ir tolesni skaitymai

  1. Eddington, A. S. (1926). The Internal Structure of the Stars. Cambridge University Press.
  2. Iben, I. (1974). “Stellar Evolution on the Main Sequence and Beyond.” Annual Review of Astronomy and Astrophysics, 12, 215–256.
  3. Reimers, D. (1975). “Circumstellar Shells and Mass Loss of Red Giants.” Mem. Soc. R. Sci. Liège, 8, 369–382.
  4. Thomas, H.-C. (1967). “Helium Flash in Red Giant Stars.” Zeitschrift für Astrophysik, 67, 420–428.
  5. Sweigart, A. V., & Gross, P. G. (1978). “Helium Mixing in Red Giant Evolution.” The Astrophysical Journal Supplement Series, 36, 405–436.
  6. Herwig, F. (2005). “Evolution of the Asymptotic Giant Branch.” Annual Review of Astronomy and Astrophysics, 43, 435–479.
  7. Koester, D. (2002). “White Dwarfs: Research in the New Millennium.” Astronomy & Astrophysics Review, 11, 33–66.
  8. Winget, D. E., & Kepler, S. O. (2008). “A Look Inside the Star: The Astrophysics of White Dwarfs.” Annual Review of Astronomy and Astrophysics, 46, 157–199.
  9. Balick, B., & Frank, A. (2002). “Shapes of Planetary Nebulae and Their Formation.” Annual Review of Astronomy and Astrophysics, 40, 439–486.
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