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

#Composition

• 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

#Photosphere

• 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).

Sunspots

• 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

#Chromosphere

• 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

#Corona

• 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)