> [!measure] Important Quantities > - $M_\odot \simeq 2\times 10^{30} \,\pu{kg}$ > - $R_\odot \simeq 7\times 10^8 \,\pu{m}$ > - $P_{\odot}\simeq 1 \, {\rm month}$ > - $L_\odot \simeq 3.8\times10^{26}\,\pu{W}$ ## Anatomy of the Sun The sun has a core, radiate and then covective zone. The region between the radiative and convective zones is called the tachocline and this is thought to be the origin of the magnetic field. As such, fully convective stars are not thought to have strong magnetic fields. ![[sun.jpg]] ### Internal Structure #### Core - Fusion in the sun's core utilizes the [[Proton-Proton Chain|pp chain]] ($\sim 99 \, \%$) and the [[Carbon-Nitrogen-Oxygen Cycle|CNO cycle]] ($\sim 1 \, \%$) to produce energy - While $\sim 99 \, \%$ of all energy in the Sun is produced within $0.24\;{\rm R_{\odot}}$, fusion stops at nearly $0.30\;{\rm R_{\odot}}$ - Boundary defined by the region where temperature & pressure are too low to support the [[Proton-Proton Chain|pp chain]] reactions > [!measure] Important Quantities > - Thickness: $25 \%\;R_{\odot}$ > - Volume: $1.5 \%\;V_{\odot}$ > - Mass: $50 \%\;{\rm M_{\odot}}$ > - Density: $150\;{\rm g/cm^{3}}$ > - Temperature: $15.7 \times 10^{6}\;{\rm K}$ #### Radiative Zone - Energy produced by fusion is radiated out from the [[#Core]] - The time it takes for a energy to move through the radiative zone is slow due to the photon’s small [[Optical Depth#Mean Free Path|mean free path]] - Photons emitted randomly scatter off electrons and nuclei in this region losing energy - Photons initially emitted as gamma rays, but is down-scattered to UV/visible wavelengths after the random walk/diffusion to the surface - Photons created today will take $\sim 10^{5} - 10^{6}\;{\rm years}$ to reach surface - Boundary defined by the region where temperature & density are low enough to permit atoms to retain their electrons > [!measure] Important Quantities > - Thickness: $25 \%\;R_{\odot}$ > - Volume: $30 \%\;V_{\odot}$ > - Mass: $48 \%\;{\rm M_{\odot}}$ > - Density: $0.2 - 20\;{\rm g/cm^{3}}$ > - Temperature: $7 \times 10^{6} - 2 \times 10^{6}\;{\rm K}$ #### Tachocline > [!note] Language Meaning... > ”tacho” – relating to speed > ”cline” – relating to a gradient from one extreme to another - A small layer between the [[#Radiative Zone|radiative zone]] and [[#Convective Zone|convective zone]] - Defined by a sharp regime change in uniform rotation of the [[#Radiative Zone|radiation zone]] and differential rotation of the [[#Convective Zone|convective zone]] - Large shear forces develop between the two as the horizontal layers slide past each other - Believed the Solar Dynamo is generated within this layer - “Magnetic Dyanmo” - process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time scales #### Convective Zone - Density of plasma low enough to allow convective currents to develop and act as main means of energy transfer - Motion of mass develops thermal cells that can rise to surface through heat expansion (reducing density). Once material diffusively and radiatively cools, density increases again and cell sinks back to base of convection zone. > [!measure] Important Quantities > - Thickness: $30 \%\;R_{\odot}$ > - Volume: $65 \%\;V_{\odot}$ > - Temperature: $2 \times 10^{6} - 5700\;{\rm K}$ ### Atmosphere #### Photosphere - First observationally visible layer of the sun [[#Convective Zone|convection zone]] (and below) are too opaque (must use theoretical models, helioseismology, solar neutrinos, etc.) - Change in opacity comes from the decreasing amount of hydrogen anions (that absorb light very easily), and the transmission of visible light wavelengths - Leads in to temperature minimum layer with spectral lines showcasing carbon monoxide and water “Surface Granulation” - caused by convection currents of plasma - The rising center of the granules are hotter - Once they radiatively and diffusively cool, move to edge of granule and descend rapidly “Sunspots” - regions of reduced surface temperature caused by concentrations of magnetic flux that inhibit convection - Usually appear in pairs of of opposite magnetic polarity > [!measure] Important Quantities > - Temperature: $5700\;{\rm K}$ > - Number Density: $\sim 10^{23}\;{\rm particles/m^{3}}$ #### Chromosphere - Small region above photosphere - Characteristic red color due to the electromagnetic emissions in the [[Spectral Features#Balmer Series|H-alpha spectral line]] - Has a distinct colored “flash” at the beginning and end of solar eclipses - Hair-like jets of plasma, called spicules, rise from this homogeneous region and through the chromosphere, extending up to $\sim 10,000\;{\rm km}$ into the [[#Corona|corona]] - Helium becomes ions at top of layer > [!measure] Important Quantities > Thickness: $\sim 2000\;{\rm km}$ > Temperature: $\sim 4100 - 20000\;{\rm km}$ (gradually rising with altitude) #### Transition Zone - Temperature rises rapidly from around $T \sim 20000\;{\rm K}$ in the upper chromosphere to coronal temperatures closer to $10^{6}\;{\rm K}$ - Facilitated by the full ionization of helium, reducing the radiative cooling of the present plasma - Not easily observable from Earth surface, but in easy to see in space by viewing the extreme ultraviolet portion of the EM spectrum #### Corona - No complete theory on what heats the corona, some heating is tied to magnetic reconnection - Plasma flowing from the corona expands into interplanetary space, generating the solar wind - Boundary of corona and solar wind called the “Alfvén Surface” ($\sim 10 - 20 R_{\odot}$) > [!measure] Important Quantities > Average Temperature of Low Coronal Region: $\sim 10^{6} - 2 \times 10^{6}\;{\rm K}$ > Temperature of the Hottest Regions: $\sim 8 \times 10^{6} - 20 \times 10^{6}\;{\rm K}$ ### Heliosphere The wake of the solar wind through the [[Interstellar Medium|ISM]] formed by the movement of the Sun and solar wind. The "termination shock" within is the point where the solar winds slows to subsonic speed relative to the motion of the Sun ![[heliosphere-boundary.png|align:center|600]] #### Solar Wind The speed the solar wind is emitted from the Sun is [[Fluid Mechanics#Supersonic|supersonic]] ($v_{\rm esc,\odot} > c_{\rm s} \sim 100\;{\rm km/s}$) until it reaches the [[Sun#Termination Shock|Termination Shock]]. ##### Parker Solar Wind Model If we assume that the solar wind is composed of purely ionized hydrogen acting like and ideal gas, we can use the hydrostatic equilibrium between the solar wind and ISM (instead of mass continuity as in [[Question 3]]) to find the solar wind pressure. $ \begin{align} P = \frac{n k_{\rm B} T}{\mu} = 2 \, n \, k_{\rm B} T \hspace{1cm} \left( \mu = \frac{1}{2}\;,\;\rho = n m_{\rm p} \right) \hspace{1cm} \Rightarrow \hspace{1cm} \frac{\mathrm{d} P}{\mathrm{d} r} &= - \frac{G M_{\odot} \rho}{r^{2}} \\ \frac{\mathrm{d} (2 n k_{\rm B} T)}{\mathrm{d} r} &= - \frac{G M_{\odot} (n m_{\rm p})}{r^{2}} \\ \frac{\mathrm{d} n}{\mathrm{d} r} &= - \left(\frac{G M_{\odot} m_{\rm p}}{2 k_{\rm B} T}\right) \frac{n}{r^{2}} \\ \int \frac{\mathrm{d} n}{n} &= - \lambda \int \frac{\mathrm{d} r}{r^{2}} \\ \ln \left(\frac{n}{n_{0}}\right) &= - \left(\frac{G M_{\odot} m_{\rm p}}{2 k_{\rm B} T}\right) \left( \frac{1}{r_{0}} - \frac{1}{r} \right) \\ \ln \left(\frac{n}{n_{0}}\right) &= - \underbrace{\left(\frac{G M_{\odot} m_{\rm p}}{2 k_{\rm B} T r_{0}}\right)}_{\lambda} \left( 1 - \frac{r_{0}}{r} \right) \end{align} $ $n(r) = n_{0} e^{- \lambda \left( 1 - \frac{r_{0}}{r} \right)} \hspace{1cm} \text{where} \hspace{1cm} \lambda \equiv \left(\frac{G M_{\odot} m_{\rm p}}{2 k_{\rm B} T r_{0}}\right)$ #### Current Sheet !UNFINSIHED #### Termination Shock !UNFINISHED #### Heliosheath !UNFINISHED #### Heliopause *(See [[Question 3]])* The theoretical boundary where the Sun's solar wind is stopped by the [[Interstellar Medium|ISM]]. Bounds the [[#Heliosphere]]. Location defined by pressure balance, at about $120\,\pu{AU}$ as measured by voyager. Beyond the heliopause... - There is a sharp drop in the temperature of solar wind-charged particles - Change in the direction of the magnetic field - Increase in the number of galactic cosmic rays #### Heliotail ## Solar Activity ### Solar Flare - Solar Flare is a sudden flash of light on the Sun surface (i.e. increase in brightness on the Sun) usually observed in close proximity to a sunspot group. - They are closely associated with the ejection of plasma and may cause acceleration of particles (Solar Energetic Particles, SEP) through the Sun's Corona into outer space. - Classification of solar flares are based on their X-ray brightness, in the wavelength range 1 to 8 Angstroms. Flares classes have names: - A, B, C, M, and X (A being the tiniest and X being the largest) - Each category has nine subdivisions ranging by number, with the higher number correlating to the strength (e.g. C1 to C9, M1 to M9, and X1 to X9) - These are logarithmic scales, much like the seismic Richter scale. Therefore, an M flare is 10 times as strong as a C flare. ### Coronal Mass Ejection (CME) - CME is a release of plasma and accompanying magnetic field from the solar [[#Corona|corona]]. - CMEs often follow solar flares and are normally present during a solar prominence eruption. - The energy/plasma is released into the [[#Solar Wind|solar wind]]. - SEP can be emitted and accelerated into the heliosphere.