Stars on the main sequence follow predictable patterns in mass, luminosity, and temperature. These relationships help us understand stellar evolution and lifespans. The Hertzsprung-Russell diagram visually represents these connections, showing where different types of stars fall based on their properties.

Nuclear fusion powers main sequence stars, with different processes dominating based on stellar mass. The proton-proton chain fuels smaller stars like our Sun, while the CNO cycle drives fusion in larger stars. These reactions, along with other factors, determine how long a star will shine on the main sequence.

Main Sequence Stars

Stellar mass-luminosity-temperature relationships

• Mass-luminosity relation describes more massive stars exhibiting higher luminosity approximated by $L \propto M^{3.5}$ (Sun, Sirius)
• Mass-temperature relation shows more massive stars have higher surface temperatures (Rigel, Betelgeuse)
• Mass-radius relation indicates more massive stars possess larger radii (VY Canis Majoris, UY Scuti)
• Stefan-Boltzmann law $L = 4\pi R^2 \sigma T^4$ connects luminosity, radius, and temperature of stars
• Main sequence lifetime inversely proportional to mass $t_{MS} \propto M^{-2.5}$ shorter lifespans for massive stars (O-type stars)

Interpreting Hertzsprung-Russell diagrams

• H-R diagram axes plot spectral type or temperature (x-axis) against luminosity or absolute magnitude (y-axis)
• Main sequence forms diagonal band from top-left to bottom-right containing majority of stars (Sun, Alpha Centauri A)
• Other regions include giants, supergiants (Betelgeuse, Antares) and white dwarfs (Sirius B)
• Stellar evolution paths on H-R diagram show pre-main sequence and post-main sequence stages
• Isochrones represent lines of constant age on H-R diagram useful for determining cluster ages
• Determining stellar properties from H-R diagram position reveals mass on main sequence and radius using luminosity and temperature

Stellar Physics

Nuclear fusion in main sequence stars

• Proton-proton (p-p) chain dominates in low-mass stars (< 1.3 solar masses)
  • Net reaction: $4^1H \rightarrow ^4He + 2e^+ + 2\nu_e + \gamma$
  • Primary fusion process in Sun and red dwarfs
• CNO cycle prevails in higher-mass stars (> 1.3 solar masses)
  • Catalytic cycle utilizing carbon, nitrogen, and oxygen
  • More efficient at higher temperatures (Sirius, Vega)
• Energy production rates vary
  • p-p chain: $\epsilon_{pp} \propto T^4$
  • CNO cycle: $\epsilon_{CNO} \propto T^{18}$
• Neutrino production occurs as byproduct of fusion reactions carrying away some energy
  • Detected on Earth using specialized underground detectors (Super-Kamiokande)

Factors of stellar main sequence lifespans

• Initial mass serves as primary factor determining lifespan more massive stars have shorter lifespans (O and B type stars)
• Metallicity affects opacity and energy transport influences main sequence turnoff point
• Rotation rate can extend lifespan faster rotation induces mixing bringing fresh fuel to the core
• Magnetic fields impact stellar structure and evolution creating starspots and flares
• Mass loss more significant in massive stars shortens main sequence lifetime (Wolf-Rayet stars)
• Convection vs radiative energy transport depends on stellar mass affects efficiency of energy transport from core to surface
  • Convective cores in massive stars (O and B types)
  • Radiative cores in lower-mass stars (G and K types)