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

_Source: Carroll, Ostlie - chapter 11_

- spectral class G2

## Composition

![Composition](composition.png)

- 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

![Helium Abundance](helium-abundance.png)

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

![Luminosity Profile](luminosity-profile.png)

- 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

![Sun Layers](sun-layers.png)

- 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**:

![Butterfly Diagram](butterfly-diagram.png)

- Sunspots generally originate at **40 N** and **40 S** latitude

![Sunspot](sunspot.png)

- 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

![Sunspot Polarity](sunspot-polarity.png)

### 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)

![Coronal Holes](coronal-holes.png)

#### 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)