IOAA: The Sun

2021-11-15 747 words 4 minutes

Contents

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

Source: Carroll, Ostlie - chapter 11

Sun

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” 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

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

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 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:

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

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)

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:

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

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 $v_m = B/\sqrt{\mu_0\rho}$

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

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)