Study Notes on The Sun
PHYS 1901 – The Sun Study Notes
16 The Sun Our Parent Star
16.1 Physical Properties of the Sun
The Sun is characterized as a typical star: a glowing ball of gas held together by its own gravity and powered by nuclear fusion at its center. It is rather unremarkable, sitting in the middle of observed ranges for stars regarding mass, radius, and brightness.
Properties of the Sun:
Radius: 700,000 km (over 10 Earth radii), appearing with an angular size of 0.5° from Earth.
Mass: 2.0 \times 10^{30} kg (more than 300,000 times that of Earth).
Average density: 1400 kg/m^3 (approximately 1/4 that of Earth’s, a bit more than water).
The Sun rotates approximately once a month, as observed by tracking sunspots, exhibiting differential rotation:
Equator: about 25 days (faster).
Poles: about 31 days at latitude 60° and up to 36 days at the poles (slower).
Average surface temperature: 5800 K, with the solar radiation distribution resembling a blackbody spectrum.
The Sun does not have a solid surface. The visible part is the photosphere, about 500 km thick, giving the appearance of a sharp, well-defined edge rather than a fuzzy ball.
16.2 The Solar Interior
Describes the internal structure of the Sun:
Central core: Radius of 200,000 km, the site of nuclear reactions (fusion) that generate energy output.
Radiation zone: 300,000 km thick, where energy is transported by electromagnetic radiation.
Convection zone: 200,000 km thick, where material is in constant convective motion, transporting energy through hot gases rising and cooler gases sinking.
Photosphere: Visible surface of the Sun, approximately 500 km thick.
Chromosphere: Lower atmosphere of the Sun, around 1500 km thick.
Transition zone: Region of rapid temperature increase, situated between the chromosphere and corona.
Corona: The Sun's outer atmosphere, situated 10,000 km above the photosphere, with temperatures reaching 3 million Kelvin, transitioning into the solar wind.
Solar wind: The corona generates a solar wind that permeates the solar system, traveling in all directions.
Solar Atmosphere and Spectroscopy
The Sun's atmosphere encompasses regions above the photosphere, allowing extensive study through absorption spectral lines.
Fraunhofer absorption lines: Dark lines in the Sun's spectrum, indicating specific elements present. Analysis reveals at least 67 elements, with the top 10 including:
Hydrogen
Helium
Oxygen
Carbon
Neon
Nitrogen
Magnesium
Silicon
Iron
Sulfur
The depth from which light is observed in the atmosphere depends on its wavelength:
Photons with wavelengths far from atomic absorption features travel from deeper layers without interaction.
Photons near absorption features are more likely to be captured by atoms or ions.
Chromosphere: The inner part of the atmosphere, just above the photosphere. It emits sunlight but is usually obscured by the brighter photosphere.
Visible during a solar eclipse, appearing with a reddish hue due to the dominant H-alpha red line emission from hydrogen.
Characterized by spicules: hot jets of matter ejected into the upper atmosphere at ~100 km/s, reaching thousands of kilometers above the photosphere. They accumulate at the edges of supergranules and are results of magnetic disturbances.
Corona: Even fainter than the chromosphere, visible only during total solar eclipses.
Its spectrum shifts from absorption to emission, as it comprises hot gas against the dark background of outer space.
Coronal atoms are highly ionized due to extreme temperatures (e.g., iron atoms observed to have lost half their electrons).
Temperature Anomaly: Counterintuitively, the temperature increases significantly further from the Sun's surface, reaching 1-2 million Kelvin in the corona. This phenomenon is not fully understood but is hypothesized to be linked to magnetic disturbances in the photosphere.
Solar Wind: A constant stream of escaping charged particles from the high-temperature corona.
Coronal gas at ~10 million km from the photosphere is hot enough to escape the Sun's gravity.
While sunlight reaches Earth in 8 minutes, solar wind particles (charged) travel at ~500 km/s and take a few days to reach Earth.
The Sun sheds about 2 million tons of matter per second via solar wind, but this accounts for only ~0.1% of its total mass over 4.6 billion years
16.3 Solar Luminosity
The Sun radiates substantial energy uniformly in all directions.
Solar constant: The energy reaching the Earth's atmosphere per unit area per unit time is 1400 W/m².
Approximately 50-70% of incoming solar energy reaches Earth’s surface. Remainder is absorbed (30%) or reflected (0-20%).
Calculation of energy received during sunbathing:
Area of body = 0.5 m².
Energy received: 1400 W/m² × 70% × 0.5 m² = 525 W (similar to five 100-W lightbulbs).
Total luminosity of the Sun:
Total energy radiated each second across a sphere with radius 1 AU:
Surface area: 4 ext{π}r^2 = 4 ext{π}(1 ext{ AU})^2 = 2.8 imes 10^{23} ext{ m}^2.
Multiply by solar constant: 1400 W/m².
Luminosity = 4 x 10²⁶ W.
Energy output equivalent to detonating 10 billion 1-megaton nuclear bombs every second.
Implications: Six seconds of such energy would evaporate all of Earth’s oceans, and three minutes could melt Earth's crust.
16.4 The Interior of the Sun
Understanding the Sun's interior without direct probing involves building mathematical models integrating available data:
Models incorporate known bulk properties like mass, radius, temperature, and luminosity.
These properties are assumed to be static over observable timescales.
Hydrostatic equilibrium: The Sun is modeled as being in hydrostatic balance, where the inward pull of gravity is exactly offset by the outward forces from pressure. This ensures the Sun is neither exploding nor imploding.
This equilibrium requires extremely high internal temperatures to counteract enormous gravitational forces, leading to the early conception of nuclear fusion processes in the 1920s.
Solar Interior Profiles
Density Profile:
Highest in the core, about 20 times the density of iron.
Drops sharply, reaching the density of water at ~350,000 km from the center.
In the photosphere, it is 10,000 times less dense than Earth's air.
In the far corona, density can be as low as 10^{-23} kg/m^3, similar to a laboratory vacuum.
Approximately 90% of the Sun's mass is contained within half its radius.
Temperature Profile:
Inner core temperature is about 15 million Kelvin.
A minimum temperature of 10 million Kelvin is required for nuclear reactions to ignite in a star (e.g., Jupiter and Saturn do not reach these temperatures and thus are not stars).
Temperature gradually decreases to 5800 K at the photosphere.
Beyond the photosphere, in the transition zone and corona, the temperature dramatically increases again.
Rotation Profile (Complexity):
Exhibits differential rotation as observed at the surface.
Below the surface, zonal flows with alternating bands of higher and lower rotation rates exist.
Wide rivers of low speed occur at the equator and higher speed rotation at the poles just below the surface.
Material at the base of the convection zone oscillates with a period of 1.3 years, showing a rotation speed sometimes 10% faster or slower than the surface.
The radiative inner interior rotates more like a solid body, approximately once every 26.9 days.
Energy Transport and Photosphere Features
Energy Transport in the Interior:
Near the core, gases are completely ionized (nuclei without electrons) due to the extreme heat (15 million K). Light (electromagnetic radiation) travels freely without impedance by atoms in the core.
As temperature drops away from the core, atoms retain some electrons. These atoms can absorb and re-emit radiation, effectively impeding photon travel. By the edge of the radiation zone, all photons are absorbed.
In the convection zone, energy is transported by convection: hot solar gases move outward, cool, and then sink, forming convection cells. These cells can be tens of thousands of kilometers deep and progressively shrink closer to the surface.
At the photosphere, the gas is too thin to sustain convection. Here, atoms and ions intercept sunlight, and energy transport reverts to radiation.
Granulation and Supergranulation:
The photosphere appears granulated with bright and dark regions called granules, each about 1,000 km across, lasting 5-10 minutes. These are the visible tops of convection cells just below the photosphere.
Spectral line analysis shows Doppler shifts: bright granules move towards us (~1 km/s), while darker granules move away. Brightness variations are due to temperature differences of less than 500 K.
Supergranulation: Larger-scale flows (~30,000 km across) also exist, an imprint of deeper convective processes, where material upwells at the center, flows across the surface, and sinks at the edges.
16.5 Visiting the Sun
Key spacecraft monitoring the Sun include:
SOHO (Solar and Heliospheric Observatory): Launched in 1995, mission extended until the end of 2025, stationed at Lagrangian point L1 (1.5 million km from Earth), a stable gravitational point. SOHO uses an occulting disk to block direct sunlight, allowing observation of dimmer features.
SDO (Solar Dynamics Observatory): Orbits the Earth in geosynchronous orbit.
These observatories measure various solar phenomena in real-time, including:
Corona characteristics and magnetic fields (e.g., following expanding and breaking magnetic field loops).
Solar wind and internal vibrations.
Observed significant solar events, including coronal mass ejections and solar weather.
16.6 Testing and Refining the Standard Solar Model
The 1960s revealed the oscillation of the Sun’s surface through Doppler shifts, indicating the Sun is vibrating.
Helioseismology: The study of these vibrations, which are internal pressure waves reflecting off the photosphere and the inner parts of the Sun, capable of probing the solar interior (analogous to seismology for Earth).
GONG (Global Oscillations Network Group): Supports continuous observations from Earth to refine the standard solar model by providing data on the Sun's temperature, density, rotation, and convective state.
Observations show:
Agreement between measurement and model predictions within 0.1% accuracy for oscillation frequencies and wavelengths.
Global circulation patterns and large-scale gas flows, including a two-conveyor belt system that transports material up to 300,000 km depth. These belts transport matter at 10-15 m/s between the equator and poles, taking 40 years for one complete loop. This system is thought to regulate sunspot cycles.
16.7 Observations of Solar Neutrinos
Neutrinos produced in the Sun's fusion processes (specifically the proton-proton chain) travel without much interaction, providing direct insight into the core's conditions. They can penetrate light-years of lead without stopping.
Detectors exist on Earth designed to capture these rare neutrino interactions:
Some use large quantities of target fluids like chlorine or gallium, where neutrino interaction transforms the material (e.g., chlorine into argon), producing detectable radioactive products.
Others deploy tanks of water or heavy water (e.g., the Sudbury Neutrino Observatory, SNOW, in Canada), detecting light emitted when a neutrino interacts with the water molecules.
The probability of a neutrino interaction is extremely low (about 1 in 10^{15} passes), requiring massive detectors and immense patience (months to years between detections).
Solar neutrino problem: Early detections yielded 50-70% fewer neutrinos than predicted by models, hinting at an issue with our understanding of neutrinos or the solar model.
The solution found that neutrinos could change types (flavors) during their 8-minute journey from the Sun to Earth, a phenomenon known as neutrino oscillations. This is possible because neutrinos possess a tiny mass.
Detectors, typically sensitive to only one type of neutrino (electron neutrinos), missed those that had oscillated into other types (muon or tau neutrinos).
Confirmations of neutrino oscillations by experiments in Japan (1998) and SNOW (2001) showed that the total number of neutrinos (across all types) is consistent with solar models, resolving the problem. This research was awarded a Nobel Prize in Physics (2015).
16.8 Energy Generation in the Proton-Proton Chain
Energy Production Rate: For every kilogram of solar material, the Sun generates 0.2 milliwatts of power. While this seems tiny (e.g., burning wood generates a million times more energy), the Sun sustains this process for billions of years.
Over 5 billion years, each kilogram of solar material has produced 3 \times 10^{13} joules, demonstrating
The fundamental reaction powering the Sun is the *proton-proton chain:
Step I: Two protons combine to form deuterium.
Step II: Positrons emitted annihilate with electrons producing gamma rays. Deuterons combine with protons to generate helium-3.
Step III: Two helium-3 nuclei combine to form helium-4 and release energy.
The net effect results in four hydrogen nuclei fusing to create helium-4, emitting neutrinos and gamma rays.
The total energy produced can be calculated using Einstein’s mass-energy relationship:
E = mc^2 where the mass difference is significant enough to yield tremendous energy outputs.
16.9 Implications and Applications
Understanding solar properties influences climate and space weather predictions.
The relationship between solar activity, such as sunspots and solar flares, directly correlates to geomagnetic disturbances on Earth, affecting technology.