Knowt
IB PHYSICS Option D: Astrophysics
D.1 Stellar Quantities
Objects in the Universe
The solar system includes the Sun, eight planets, dwarf planets, moons, asteroids, and comets.
The universe is vast; our solar system is a mere speck.
Types of Celestial Bodies
Single star: Luminous plasma sphere held by gravity.
Binary star: Two stars orbiting a common center.
Black hole: Singularity in space-time.
Cepheid variable: Star with varying luminosity, aiding distance measurement.
Clusters of galaxies: Gravitationally affected groups of galaxies.
Constellation: Pattern of unbound stars visible from Earth.
Dark matter: Cold, non-radiating matter inferred from physics.
Galaxies: Stars, gas, and dust bound by gravity.
Main sequence star: A normal star undergoing hydrogen fusion in order to turn into helium.
Neutron stars: Dense stars with uncharged neutrons.
Nebula: Cloud of dust, gasses, helium, and hydrogen.
Planets: Celestial bodies orbiting a star.
Supernova: Highly energetic stellar explosions marking the end of a star's life cycle.
Type Ia Supernova: Results from the explosion of a white dwarf in a binary star system.
Type Ib/c Supernova: Associated with the collapse of massive, hydrogen-poor stars.
Type II Supernova: Arises from the collapse of massive stars with a significant hydrogen envelope.
White dwarfs: The remnants of low to medium-mass stars after they have exhausted their nuclear fuel.
The Nature of Stars
Stability and Equilibrium
Star stability depends on the equilibrium between gravity and radiation pressure.
Nuclear fusion maintains equilibrium, preventing collapse.
Units in Astrophysics
Lightyear (ly): Distance light travels in one year in the vacuum of space. Approximately 9.461 × 1012 kilometers.
Parsec (pc): Parallax arcsecond, a unit based on stellar parallax. Approximately 3.09 × 1013 kilometers.
Astronomical Unit (AU): Average distance from Earth to the Sun. Approximately 1.496 × 108 kilometers.
Megaparsec (Mpc): One million parsecs, often used in cosmological distance measurements. Approximately 3.09 × 1019 kilometers.
Solar Radius (R☉): The radius of the Sun, used to express the size of stars. Approximately 6.96 × 105 kilometers.
Solar Mass (M☉): The mass of the Sun, frequently used for stellar mass comparisons. Approximately 1.989 × 1030 kilograms.
Light-Minute (lmin): Distance light travels in one minute. Approximately 1.8 × 1010 kilometers.
Astronomical Distances
The universe is mostly empty; a light year measures ultra-solar system distances.
Example: Proxima Centauri - 4.31 light years or 1.3 parsecs away.
Average distance between stars in a galaxy: 1 pc (3.26 light-years).
Average distance between galaxies in a cluster: 100 kpc to several Mpc.
Stellar Parallax and Limitations
Stellar parallax measures space distances using Earth's orbit.
The parallax of one arcsecond equals one parsec (3.26 light-years).
There is limited accuracy for distant stars due to small parallax.
Luminosity and Apparent Brightness
Luminosity: Total power radiated by a star in all directions (measured in watts).
Apparent brightness: Power received per unit area (measured in W/m²).
Luminosity decreases with distance following the inverse square law.
Inverse square law: I = k / r2. States that a physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity.
I = the intensity or strength of a physical quantity,
k = a constant
r = the distance from the source of the physical quantity.
D.2 Stellar Characteristics and Stellar Evolution
Stellar Spectra
The absorption spectra can identify elements in stars.
There are seven spectral classes (O, B, A, F, G, K, M) based on temperature.
Hertzsprung–Russell (HR) Diagram
It is a graph relating absolute magnitude, luminosity, classification, and temperature.
Main sequence stars burn hydrogen; used to estimate star distances.
Mass–Luminosity Relation for Main Sequence Stars
Luminosity increases with mass for main sequence stars.
Cepheid Variables
Stars with varying luminosity correlated to period.
Used as “standard candles” for distance estimation.
Stellar Evolution on HR Diagrams
Stars form from nebulae, and then undergo nucleosynthesis.
Main-sequence lifetime: Hydrogen fusion into helium.
Red giants, white dwarfs, neutron stars, and black holes follow fuel depletion.
Chandrasekhar and Oppenheimer–Volkoff Limits
Chandrasekhar limit: Maximum mass for a white dwarf (about 1.4 solar masses).
Oppenheimer–Volkoff limit: Maximum mass for a neutron star (2-3 solar masses).
Wien’s Displacement Law
Describes the relationship between the temperature of a blackbody and the wavelength at which it emits the maximum intensity of radiation.
Mathematically expressed as λmax ⋅T = constant where λmax is the peak wavelength, and T is the temperature in Kelvin.
Implies that as the temperature of a blackbody increases, the peak emission shifts to shorter (cooler) or longer (hotter) wavelengths.
Crucial in understanding the color of stars; hotter stars appear bluer, while cooler stars appear redder.
D.3 Cosmology
Big Bang Model
It is the origin of space and time from singularity expansion.
It redshifted galaxy observation and Cosmic Microwave Background radiation support.
Cosmic Microwave Background (CMB) Radiation
It is thermal radiation from the early universe, supporting the Big Bang theory.
Hubble’s Law
v = Hd describes velocity-distance relationship.
It is used to estimate the age of the universe.
The Hubble Constant: denoted as H0; quantifies the present rate of expansion of the universe, approximately 70 km/s/Mpc.
Accelerating Universe and Redshift (z)
Supernovae observations show universe expansion acceleration.
Redshift (z) is determined by the ratio of the observed (λobserved) to (λemitted) emitted wavelengths, expressed as 1+z = (λobserved / λemitted), or in cosmological contexts, z = (Δλ / λemitted) = (c⋅Δt)/(λemitted), where c is the speed of light and t is time.
Redshift factor (1+z) affects apparent brightness.
Cosmic Scale Factor (R)
The cosmic scale factor (R) is a fundamental concept in cosmology, serving as a mathematical representation of the relative expansion or contraction of the universe as a function of cosmic time.
R is a dynamic parameter that evolves over time, capturing the changing size of the universe. As the universe expands, R increases, reflecting the overall growth of cosmic structures.
R(t) represents the relative expansion of the universe.
Einstein’s Theory of General Relativity: Astrophysicists employ Einstein's theory of general relativity to understand the behavior of R in the context of gravitational interactions on cosmic scales.
Connection to Redshift: The concept of R is intimately connected to the observed redshift (z) in astrophysics. The relationship is expressed by 1+z= 1/R, offering a crucial link between observational data, such as the redshift of distant galaxies, and the underlying dynamics of the expanding universe.