IOAA: The Sun

My notes to prepare Team USA for the solar portion of the 2021 IOAA.

Source: Carroll, Ostlie - chapter 11


  • spectral class G2



  • Radiative core surrounded by a convective envelope
  • Sun produces energy through the proton-proton chain
    • Produces He^3^ as an intermediate (it’s created and then destroyed)
    • He^3^ - He^3^ interactions require high temperatures
    • At greater depths, these interactions result in He^3^ being destroyed faster, so it is less abundant there
      • Explains the bump of He^3^ abundance at 0.3R


  • Bump near 0.7R is explained by changes in position of base of the surface convection zone


  • Volume of shell is given by $dV = 4\pi r^2 dr$, so shells further away from the center have more mass
  • On the other hand, going closer to the center of the sun, nuclear reactions happen more rapidly
  • Hence, maximum energy production occurs at ~0.1R

Neutrino Problem

  • “Neutrino problem” began when Raymond Davis measured neutrinos from the sun in the Homestake experiment
  • Expected a rate of 7.9 SNU, observed a rate at 2.56 SNU
    • 1 SNU = 1 solar neutrino unit = 10^-36^ reactions per target atom per second
  • Discrepancy is explained by neutrino oscillation, where neutrinos change between 3 different flavors
    • Electron, muon, tau flavors
    • Implies that neutrino have mass

Solar Rotation

  • Sun undergoes differential rotation - rate varies with latitude
  • Solar rotation period…
    • …at the equator = 24.47 days
    • …at the poles = 38 days
    • …on average = 28 days

Carrington Rotation (CR)

  • Used to follow sunspots
  • Approx. 25.38 (siderial period) or 27.2523 (synodic period)

Layers of the Sun


  • tau_500 is the optical depth at 500 nanometers


  • Region where the observed optical photons originate
  • Effective temperature = temperature of the gas at this depth: T~e~ = T~τ=2/3~ = 5777 K
  • Absorption lines (e.g. Fraunhofer lines) are produced here
  • Contains granulation, a patchwork of bright and dark regions

Optical Depth

  • Optical depth is defined as $\tau = -\ln(f)$, where $f$ is the fraction of photons originating from a layer that reach us.
  • Alternatively, $e^{-\tau} = f$.

Example: if 1% of the photons from a layer reach us, the optical depth is 4.5, since $e^{-4.5} \approx 0.01$.

On average, the solar flux is emitted from an optical depth of 2/3 (Eddington approximation).


  • Located in the photosphere
  • Plot of sunspot location as a function of time creates Manuder’s butterfly diagram:


  • Sunspots generally originate at 40 N and 40 S latitude


  • Dark central portion of sunspot = umbra

    • Darker because sunspots are cooler (3900 K vs. surface temperature of 5700 K)
  • Lighter surrounding “filamental” region = penumbra

  • Sun’s polarity and the polarity of sunspots (location of magnetic north and south) flips every 11 years, so the sun is on a 22-year cycle



  • Portion that lies above the photosphere and extends upward for approx. 1600 km
  • Density decreases and temperature increases with increasing altitude
    • 6,000 K at the base to 35,000 K at the base of the corona
  • Contains spicules, dynamic jets of plasma that appear as “hairs”
  • Contains prominences, a large gas feature extending from the surface and often loops
    • If it breaks, it releases a CME
    • When viewed against the solar disk, it’s a filament
    • When viewed from the side, it’s a prominence


  • Extends above the chromosphere
  • Extremely low density, effectively transparent to most radiation
  • Temperatures in excess of 10^6^ K

Solar Wind

  • Dark, cool regions known as coronal holes exist
    • Correspond to parts of the magnetic field where the field lines are open
    • This results in the solar field (particles can follow their way out of the sun due to lorentz force)


Radiation Pressure

  • Magnetohydrodynamics (MHD) is the study of the interaction between magnetic fields and plasmas

Using MHD, we can show that the magnetic energy density $u_m$ and magnetic pressure $P_m$ are equal:

$$u_m = P_m = \frac{B^2}{2\mu_0}$$

Alfven Waves

  • Disturbances in magnetic field lines can propgate down the line, creating an Alfven wave
  • Adiabatic sound speed is given by $v_s = \sqrt{\gamma P_g/\rho}$, so the Alfven wave should be similiar.
  • Careful analysis shows that Alfven wave speed is $v_m = B/\sqrt{\mu_0\rho}$

Solar Flares

  • Events that release trememdous amounts of energy (10^17^ J to 10^25^ J) as well as charged particles
  • Caused by reconnection of magnetic field lines
    • Field lines break and reconnect, releasing energy

Coronal Mass Ejections

  • 5 x 10^12^ kg to 5 x 10^13^ kg of mass is ejected from the corona during a CME
  • Approximately 1 per day (max of 3.5/day during high solar activity, low of 0.2/day during low solar activity)