Stellar Evolution and the Universe
Star Formation and the Interstellar Medium (ISM)
The Interstellar Medium
The ISM, composed of gas and dust between stars, plays a crucial role in star formation. Dust, constituting about 1% of the ISM, emits light depending on its temperature. This dispersed material, particularly the solid dust grains, blocks visible light, causing interstellar extinction. Larger particles, around 300nm in size, preferentially block shorter wavelengths, leading to the reddening of light. The position of absorption lines remains unaffected by this phenomenon. Dust, heated by starlight, emits radiation in the infrared or even X-ray spectrum if extremely hot.
Gas and dust concentrate in interstellar clouds, with “forbidden” emission lines like the 21cm line from hydrogen atoms revealing their presence. Molecular clouds, cold and dense enough for H2 and other molecules to form, appear dark and emit infrared radiation. These vast structures collapse into molecular cores and subsequently protostars surrounded by disks.
Star Formation and Evolution
As a protostar shrinks, radiating energy outward, its core pressure rises until hydrogen fusion ignites, marking its entry into the main sequence. Very low-mass stars, unable to initiate fusion, become brown dwarfs, objects that are neither stars nor planets.
Stars follow evolutionary tracks on the Hertzsprung-Russell (HR) diagram. Low-mass stars, like our Sun, follow the Hayashi track to reach the main sequence. Protostars appear more luminous due to their larger size. Material ejected from protostars forms bipolar outflow jets.
Star clusters, groups of stars born from the same molecular cloud, provide insights into stellar evolution.
Low Mass Star Evolution
Main Sequence and Beyond
Luminosity, the rate of energy radiation from a star, is directly related to mass. Higher mass stars are more luminous and consume fuel faster, resulting in shorter main sequence lifetimes. The main sequence phase is characterized by hydrogen fusion in the core.
As helium accumulates in the core, hydrogen fusion ceases, and the core collapses into an electron degenerate state. This shrinking core increases the fusion rate and luminosity, causing the star to expand and cool, becoming a red giant.
Hydrogen shell fusion continues until sufficient heat and pressure trigger helium fusion into carbon in the core through the triple-alpha process. This helium flash leads to steady helium fusion, placing the star on the horizontal branch of the HR diagram, smaller and hotter than before.
End Stages of Low Mass Stars
With carbon building up in the core, the star becomes more luminous and cooler, entering the asymptotic giant branch. It expands further than a red giant and cools significantly, shedding its outer layers to form a planetary nebula. The remaining core becomes a white dwarf, a dense, Earth-sized object composed of electron degenerate carbon. White dwarfs slowly cool over time.
Planet migration may occur during the red giant phase. In binary star systems, mass transfer can occur as the larger star expands and fills its Roche lobe, transferring material to the smaller companion. The larger star eventually becomes a white dwarf, while the smaller star gains mass and evolves into a red giant, potentially leading to various outcomes:
- Novae: Pressure on the white dwarf triggers hydrogen fusion from the accreted material, resulting in a brief but intense increase in luminosity.
- Type Ia Supernovae: If the mass accreted onto the white dwarf exceeds the Chandrasekhar limit (1.4 solar masses), carbon fusion ignites, causing a catastrophic explosion that leaves no remnant behind. These events are extremely bright, reaching about 10 billion times the luminosity of the Sun and enriching the interstellar medium with heavier elements, including “iron peak” elements.
Metallicity and Stellar Properties
Elements heavier than hydrogen and helium are considered metals in astronomy. Metallicity, the ratio of metals to the total mass of a star, is often expressed as [Fe/H], scaled to the Sun’s metallicity (Fe/H = 0) on a logarithmic scale. A positive value indicates a higher iron abundance compared to the Sun, while a negative value signifies a lower abundance.
High iron content suggests an origin from a Type Ia supernova, like our Sun. Higher metallicity generally leads to redder and cooler stars, potentially with shorter lifetimes.
High Mass Star Evolution
Main Sequence and Beyond
Stars exceeding 3 solar masses are considered high-mass stars. They are brighter and have shorter lifespans than low-mass stars. During their main sequence phase, they utilize the carbon-nitrogen-oxygen (CNO) cycle for hydrogen fusion, with carbon acting as a catalyst.
Intermediate-mass stars also employ the CNO cycle but may eventually fuse carbon and follow a similar fate as low-mass stars.
Luminous blue variables (LBVs) are extremely massive stars burning hydrogen with such intensity that they eject mass outward, making them unstable.
Convection efficiently mixes hydrogen in the cores of high-mass stars. When hydrogen is depleted, helium burning occurs in a non-degenerate core, unlike in low-mass stars. These stars evolve into supergiants, moving to the upper right region of the HR diagram.
Instability Strip and Variable Stars
As high-mass stars cool, they pass through the instability strip on the HR diagram, causing them to pulsate and exhibit periodic variations in luminosity. These pulsating variable stars serve as valuable distance indicators. Two main types exist:
- Cepheid Variables: High-mass stars evolving into supergiants, with more luminous stars exhibiting longer pulsation periods.
- RR Lyrae Variables: Low-mass stars on the horizontal branch, less luminous than Cepheids.
Fusion of Heavier Elements and Supernovae
High-mass stars can fuse progressively heavier elements in their cores, forming a nested shell structure. This process continues until iron, which requires more energy to fuse than it releases. The net energy of a nuclear reaction is determined by the difference in binding energy between the products and reactants.
Each fusion stage becomes progressively shorter, and neutrino production increases, leading to energy loss through neutrino cooling. Eventually, electron degeneracy pressure becomes insufficient to support the iron core, causing it to collapse and rebound in a Type II supernova explosion.
The shockwave from the supernova triggers the synthesis of elements heavier than iron (nucleosynthesis). The kinetic energy heats the surrounding ISM, enriching it with newly formed elements.
Neutron Stars and Pulsars
The remnant of a Type II supernova can be a neutron star, an extremely dense object with a mass between 1.4 and 3 solar masses and a radius of about 10 kilometers.
X-ray binaries consist of a neutron star accreting matter from a companion star, emitting X-rays in the process.
Pulsars are rapidly rotating neutron stars with strong magnetic fields. They emit beams of radiation from their magnetic poles, appearing to pulse as they rotate.
Galaxies
Classification and Properties
Galaxies are vast collections of stars, gas, dust, and dark matter. Astronomers use various methods, including observations of novae and Cepheid variable stars, to determine their distances.
Galaxies are classified into three main types:
- Spiral Galaxies: Characterized by a flattened disk with spiral arms, appearing flat when viewed edge-on and round when viewed face-on.
- Elliptical Galaxies: Exhibit an elliptical shape from all viewing angles.
- Irregular Galaxies: Galaxies that do not fit into the spiral or elliptical categories.
The tuning fork diagram illustrates the different types of spiral and elliptical galaxies. Spiral galaxies are further categorized based on the prominence of their central bulge and the tightness of their spiral arms. Elliptical galaxies are classified according to their degree of ellipticity, ranging from E0 (spherical) to E9 (highly elongated).
Spiral vs. Elliptical Galaxies
Spiral galaxies have a central bulge with stars orbiting in various directions, while elliptical galaxies have hot gas and no ongoing star formation. Spiral arms are regions of active star formation, triggered by density waves that compress gas and dust.
Galactic disks can be warped, and their rotation curves, which plot rotational velocity against distance from the center, often reveal the presence of dark matter. The observed velocities do not decrease as expected with increasing distance, suggesting the existence of additional, unseen mass.
Dark Matter and Active Galactic Nuclei (AGN)
Gravitational lensing, the bending of light by massive objects, provides further evidence for dark matter. The cosmic microwave background (CMB) radiation also suggests that dark matter constitutes about 5/6 of the total mass in the universe.
Galaxies are surrounded by halos of dark matter. Active galactic nuclei (AGN) are extremely luminous galactic centers powered by supermassive black holes accreting matter. Quasars are the brightest type of AGN, emitting trillions of times the luminosity of the Sun. AGN often exhibit jets of material ejected from the poles of the black hole.
Weakly interacting massive particles (WIMPs) are a leading candidate for dark matter.
The Milky Way Galaxy
Structure and Composition
The Milky Way is a barred spiral galaxy (SBbc) with a central bulge, a disk containing spiral arms, and a surrounding halo of stars and globular clusters. Globular clusters, dense collections of up to millions of stars, are predominantly found in the halo and tend to be older than stars in the disk.
The Sun is located about 8.3 kiloparsecs (kPc) from the galactic center, and the Milky Way has a diameter of approximately 30 kPc. The dark matter halo extends much further, with an outer diameter of around 90 kPc.
Stellar Populations and Dynamics
Doppler shift measurements of neutral hydrogen gas reveal the orbital velocities of stars in the Milky Way. The rotation curve is nearly flat, indicating a significant amount of dark matter (around 90%).
Globular clusters in the halo are older than those in the disk, and no young globular clusters have been observed. Younger stars generally have higher metallicity. Metal-rich stars near the Sun belong to Population I, while more distant, metal-poor stars belong to Population II. The oldest stars, with virtually zero metallicity, would belong to the hypothetical Population III, which has not yet been discovered.
The ages of stars in the Milky Way follow a general trend: Halo stars are the oldest, followed by stars in the bulge, thick disk, and thin disk. Some nearby stars with high velocities belong to the halo population.
The high metallicity in the galactic center is attributed to rapid star formation during the early stages of the galaxy’s formation. The Milky Way has a peanut-shaped bulge and exhibits asymmetric drift, with more stars near the Sun originating from inner orbits than outer orbits.
Outer Regions and Cosmic Rays
Beyond the thin disk lies an extended gas disk, not dense enough for star formation. Cosmic rays, high-energy charged particles, permeate the galaxy but are deflected by the Milky Way’s magnetic field.
The halo contains some heavy elements, likely originating from supernovae and stellar winds. Tidal streams, remnants of dwarf galaxies disrupted by the Milky Way’s gravity, provide evidence of ongoing galactic interactions.
The shape and dynamics of the Milky Way are influenced by the distribution of dark matter. Hypervelocity stars, exceeding the galactic escape velocity, have been observed, suggesting they were ejected from the galaxy’s center.
The Local Group
Galaxy Groups and Clusters
Galaxy groups are small collections of galaxies, typically containing a few dozen large members. The Milky Way belongs to the Local Group, along with the Andromeda Galaxy and the Triangulum Galaxy as the three largest members.
Large clusters of galaxies are known as galaxy clusters, and collections of groups or clusters form superclusters. The Local Group is part of the Virgo Supercluster.
Members of the Local Group
The Andromeda Galaxy is the largest member of the Local Group and is approaching the Milky Way. The Triangulum Galaxy is smaller than the Milky Way. The Large and Small Magellanic Clouds are satellite galaxies of the Milky Way.
Dwarf galaxies, smaller and less massive than typical galaxies, are common in the universe. They are classified into several types:
- Dwarf Irregulars
- Dwarf Ellipticals
- Dwarf Spheroidals (most common)
- Ultra-faint Dwarfs
Dwarf galaxies can be faint but massive if dominated by dark matter. Smaller galaxies in groups or clusters are often absorbed by larger galaxies over time. Dwarf galaxies can also stir up gas in larger galaxies, triggering star formation.
Relativity and Black Holes
Neutron Stars and Black Holes
Neutron stars exceeding 3 solar masses can collapse into black holes. Black holes can also form from the collapse of massive stars in Type II supernovae or through accretion processes in binary systems.
Special and General Relativity
Inertial reference frames and Newtonian physics break down near black holes and at relativistic speeds (a significant fraction of the speed of light). Relativity, developed by Albert Einstein, postulates that the laws of physics are the same for all observers, regardless of their motion, and that the speed of light is constant for all observers.
Special relativity deals with objects moving at constant velocities, while general relativity describes the effects of gravity and acceleration on spacetime.
Implications of Special Relativity
Special relativity has several important consequences:
- Mass-Energy Equivalence (E=mc^2): Mass and energy are equivalent and interchangeable.
- Universal Speed Limit: The speed of light is the ultimate speed limit in the universe.
- Relativity of Simultaneity: The concept of “at the same time” is relative and depends on the observer’s frame of reference.
- Time Dilation: Time runs slower for objects moving at high speeds relative to a stationary observer.
- Length Contraction: Objects appear shorter in the direction of their motion at high speeds.
The Lorentz factor, a mathematical term in special relativity, quantifies these relativistic effects. The twin paradox illustrates time dilation: a twin who travels at high speed will age slower than their stationary twin.
General Relativity and Spacetime
General relativity describes how mass and energy warp the geometry of spacetime, causing gravity. It explains phenomena such as the bending of light by gravity and the existence of black holes.
The Expanding Universe
Hubble’s Law and the Distance Ladder
Edwin Hubble’s observations of Cepheid variable stars in the Andromeda Galaxy led to the first accurate measurement of its distance. The distance ladder, a series of methods for determining distances to astronomical objects, relies on overlapping distance ranges and standard candles (objects with known luminosities).
Cosmology and the Cosmological Principle
Cosmology is the study of the universe’s structure, evolution, origin, and fate. The cosmological principle assumes that the universe is homogeneous (the same in all places) and isotropic (appearing the same in all directions) on large scales, and that the laws of physics are universal.
Redshift and Expansion
Observations show that galaxies are moving away from each other with velocities proportional to their distances. This phenomenon, known as Hubble’s Law, is evident in the redshift of light from distant galaxies. The Hubble constant (H0) quantifies the rate of expansion.
The expansion of the universe implies that there is no center to the cosmos. Distant galaxies have a large lookback time, meaning we see them as they were in the past. The Hubble time is the estimated age of the universe based on the current expansion rate.
Cosmological Redshift and the CMB
Cosmological redshift is the stretching of light waves due to the expansion of space. The longer the light travels, the greater the redshift. The cosmic microwave background (CMB) radiation is a faint glow of microwave radiation that permeates the universe. It is a remnant of the early universe, when it was hot and dense, and has been redshifted to a temperature of 2.73 Kelvin.
Recombination and Big Bang Nucleosynthesis
Recombination, the era when electrons combined with protons to form neutral hydrogen atoms, allowed light to travel freely through the universe. Before recombination, the universe was opaque to radiation.
Big Bang Nucleosynthesis, which occurred in the first few minutes after the Big Bang, produced light elements, primarily hydrogen and helium. About 24% of the ordinary matter in the universe is helium, a result of this process.
