20.4 Thermodynamics in astrophysics and cosmology

Stars are cosmic engines, converting matter into energy through nuclear fusion. This process, governed by thermodynamics, shapes a star's life from birth to death. Understanding stellar evolution helps us grasp the universe's past and future.

Thermodynamics extends beyond stars to galaxies, clusters, and the cosmos itself. From the hot gas in galaxy clusters to the cosmic microwave background, these principles explain the universe's structure and evolution on the grandest scales.

Stellar Evolution and Thermodynamics

Thermodynamics of stellar evolution

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• Gravitational contraction and hydrostatic equilibrium maintain balance between inward gravitational force and outward pressure
  • Protostar formation occurs when molecular clouds collapse under their own gravity (Orion Nebula)
  • Virial theorem states that the balance between gravitational potential energy and internal kinetic energy determines stellar stability
• Nuclear fusion generates energy in the stellar core
  • Proton-proton chain reaction fuses hydrogen into helium in low-mass stars (Sun)
  • CNO cycle dominates energy production in high-mass stars (Betelgeuse)
  • Energy production rate determines the star's luminosity
• Energy transport mechanisms distribute energy from the core to the surface
  • Radiation transports energy through photon diffusion in the stellar interior
  • Convection transports energy through bulk motion of plasma in outer layers (granulation on the Sun's surface)
• Stellar structure and stability depend on the balance between energy production and transport
  • Main sequence represents the stable phase of hydrogen burning (Sun)
  • Red giant phase occurs when the star expands and cools after exhausting hydrogen in its core (Aldebaran)
  • White dwarf forms when electron degeneracy pressure supports the core after nuclear fusion ceases (Sirius B)
• Stellar remnants and end states depend on the initial mass of the star
  • Chandrasekhar limit $(\approx 1.4 M_{\odot})$ determines the maximum mass for white dwarfs
  • Neutron stars form when neutron degeneracy pressure supports the core after supernova explosion (Crab Pulsar)
  • Black holes form from the collapse of massive stars when no known force can counteract gravity (Cygnus X-1)

Thermodynamics in Galaxies, Clusters, and Cosmology

Thermodynamics in galactic structures

• Virial theorem applies to galaxies and clusters relating kinetic energy and gravitational potential energy
  • Estimating total mass of galaxies and clusters includes dark matter (Milky Way, Coma Cluster)
• Intracluster medium (ICM) exhibits high-temperature properties
  • Hot, ionized gas in galaxy clusters has temperatures $T \approx 10^7 - 10^8$ K (Perseus Cluster)
  • X-ray emission from the ICM arises from bremsstrahlung and line emission processes
  • Sunyaev-Zel'dovich effect distorts the cosmic microwave background (CMB) through inverse Compton scattering (Bullet Cluster)
• Cooling flows and feedback mechanisms regulate the ICM
  • Radiative cooling of the ICM can lead to cooling flows in cluster centers
  • AGN feedback heats the ICM through jets and outflows from supermassive black holes (M87)
  • Star formation and supernova feedback also contribute to the energy balance in galaxies (starburst galaxies)

Early universe thermodynamic properties

• Cosmic microwave background (CMB) radiation represents relic photons from the early universe
  • CMB has a blackbody spectrum with $T \approx 2.7$ K
  • Temperature anisotropies in the CMB serve as seeds for structure formation (WMAP, Planck maps)
• Big Bang nucleosynthesis (BBN) describes the formation of light elements in the early universe
  • BBN produces hydrogen, helium, and lithium in the first few minutes after the Big Bang
  • Primordial abundances depend on the baryon-to-photon ratio $(\eta \approx 6 \times 10^{-10})$
• Cosmic inflation and thermalization shape the early universe
  • Exponential expansion during inflation leads to a homogeneous and isotropic universe on large scales
  • Reheating transfers energy from the inflaton field to particles, thermalizing the universe
• Structure formation and growth arise from gravitational instability
  • Density perturbations grow through gravitational instability (Cosmic Web)
  • Jeans criterion determines the minimum scale for collapse based on gas pressure and gravity
  • Hierarchical clustering describes the formation of smaller structures first, which then merge into larger ones (galaxy filaments and clusters)

Dark energy and cosmological thermodynamics

• Accelerating expansion of the universe indicates the presence of dark energy
  • Observations from Type Ia supernovae, baryon acoustic oscillations (BAO), and the CMB support cosmic acceleration
  • Dark energy requires negative pressure to drive the accelerated expansion
• Cosmological constant $(\Lambda)$ represents the simplest form of dark energy
  • $\Lambda$ has a constant energy density and an equation of state $w = -1$
  • Quantum vacuum energy is a possible origin for the cosmological constant
• Dynamical dark energy models propose alternative explanations
  • Quintessence involves a scalar field with a time-varying equation of state
  • Phantom energy has an equation of state $w < -1$, leading to exotic consequences
  • Modified gravity theories, such as $f(R)$ gravity, can mimic the effects of dark energy
• Thermodynamic implications of dark energy and the expanding universe
  • Entropy of the universe and the arrow of time are connected to the expansion history
  • Generalized second law of thermodynamics states that the total entropy of the universe never decreases $dS_{\text{universe}} \geq 0$
  • Holographic principle and the entropy bound limit the maximum entropy content of a region of space