Low and intermediate mass stars (ranging from 0.6 M{\odot} to 8 M{\odot}) progress through the Red Giant Branch (RGB), Horizontal Branch (HB), and Asymptotic Giant Branch (AGB) phases.
During the AGB phase, these stars feature a contracting inert carbon-oxygen (C-O) core along with two shell burning layers, one for hydrogen (H) and the other for helium (He).
AGB stars lack the mass required to initiate carbon core burning and, as a result, undergo a series of thermal pulses because of runaway flare-ups in the helium burning shell.
Each thermal pulse leads AGB stars to shed portions of their outer envelope, causing them to lose a significant amount of mass.
Thermal pulses persist until the AGB stars completely shed their outer envelope.
The expelled outer envelope transforms into an expanding cloud of ionized gas, known as a planetary nebula.
Planetary nebulae are ionized and glow due to intense ultraviolet (UV) radiation emitted from the very hot, exposed core at the nebula's center.
The exposed core eventually becomes a carbon-oxygen white dwarf.
Typical mass of planetary nebulae ranges from 0.1 to 1 M_{\odot}.
Typical radius is around 1 light-year (ly).
Typical lifetime is approximately 10,000 years.
Given that planetary nebulae expand at roughly the same rate, their size can be used to estimate their age.
Planetary nebulae are enriched with elements heavier than hydrogen and helium, referred to as "metals" (such as carbon, nitrogen, and oxygen), enriching the interstellar medium (ISM) and subsequent generations of stars.
In the late 1700s, many astronomers mistakenly identified planetary nebulae as faint planets.
Charles Messier was among the first to observe a planetary nebula (the Dumbbell Nebula) using a telescope on July 12, 1764.
William Herschel, upon observing the Saturn Nebula in 1782, described it as having “a faint disk that is like a planet,” which led him to coin the term “planetary nebula.”
Examples of planetary nebulae include the Ring Nebula (M57), Helix Nebula (NGC 7293), Dumbbell Nebula (M27), and Saturn Nebula (NGC 7009), among others like NGC 2818, Abell 39, Twin Jet Nebula, and Engraved Hourglass Nebula.
Planetary nebulae exhibit incredibly diverse shapes and structures.
The reasons for their diverse appearances are not yet fully understood.
Possible factors influencing their shapes include binary systems, stellar winds, and magnetic fields.
Dying AGB stars that are part of binary systems can produce highly complex structures in planetary nebulae.
White Dwarfs
White dwarfs are remnants of stellar cores left behind by very low to intermediate mass stars (with masses between 0.08 M{\odot} and 8 M{\odot}).
Approximately 97% of all stars in the Milky Way will eventually become white dwarfs.
White dwarfs are very faint due to their small size.
Classification of stars by luminosity include: Hypergiant (0 or Ia+), Luminous Supergiant (Ia), Normal Supergiant (Iab), Less Luminous Supergiant (Ib), Bright Giant (II), Normal Giant (III), Subgiant (IV), Main Sequence (V), Subdwarf (sd or VI), White Dwarf (D or VII).
Examples of white dwarfs include Sirius B, Van Maanen’s Star, and Procyon B.
Sirius B has a mass of 1.018 M{\odot} and a radius of 0.008 R{\odot} (or 0.87 RE, where RE is the radius of Earth).
Van Maanen’s Star has a mass of 0.67 M{\odot} and a radius of 0.011 R{\odot} (or 1.20 R_E).
Procyon B has a mass of 0.592 M{\odot} and a radius of 0.012 R{\odot} (or 1.31 R_E).
Once a stellar core becomes a white dwarf, it can no longer generate energy through stellar nucleosynthesis.
Gravity crushes the core into a small, incredibly dense object composed of plasma of unbounded nuclei and electrons, supported by electron degeneracy pressure.
The Pauli exclusion principle dictates that no two electrons can occupy the same state.
Each quantized energy state, from the lowest to the highest, is filled with a single electron, resulting in an extremely dense configuration of particles.
A cubic centimeter of white dwarf material can weigh approximately 1 metric ton.
More massive white dwarfs experience greater gravitational force, compressing them into smaller sizes, with particles packed even more tightly.
The maximum mass a white dwarf can have is approximately 1.44 M_{\odot}, known as the Chandrasekhar limit.
Beyond this limit, electron degeneracy pressure can no longer support the white dwarf against gravitational collapse.
Subrahmanyan Chandrasekhar, an Indian-American theoretical physicist, made significant contributions to the astrophysical field and was awarded the 1983 Nobel Prize in Physics for his mathematical treatments leading to the discovery of the upper mass limit of white dwarfs.
The range of known masses for white dwarfs is 0.17 to 1.33 M{\odot}, with typical masses falling between 0.5 and 0.7 M{\odot}.
Estimated radii range from 0.008 to 0.02 R{\odot} (or 0.9 to 2.2 RE).
Known temperatures range from 3,050 to 150,000 K.
The initial temperature after formation is approximately 100,000,000 K, but white dwarfs cool slowly over time.
They may eventually become black dwarfs in trillions of years, but black dwarfs are currently hypothetical as none have existed yet.
Lower mass white dwarfs tend to be helium (He) white dwarfs, which are left behind by stars not massive enough to burn helium.
Higher mass white dwarfs are typically carbon-oxygen (C-O) white dwarfs, left behind by stars not massive enough to burn carbon.
Even more massive white dwarfs may be oxygen-neon-magnesium white dwarfs, potentially left behind by stars near the boundary between carbon burning and neon burning limits.
Novae
A cataclysmic variable is a binary system where a white dwarf accretes material from a companion star, resulting in intense brightening over a short period.
An evolved star can lose part of its hydrogen envelope onto a white dwarf, leading to mass transfer between the two stars.
The transferred material, mostly hydrogen, forms an accretion disk and atmosphere surrounding the white dwarf.
The intense heat from the white dwarf can trigger runaway hydrogen burning in the accreted material.
The intense energy from the runaway burning expels the accreted material into the interstellar medium (ISM).
This explosive event causes a significant increase in brightness, known as a nova.
Novae are typically periodic, with time intervals ranging from a few decades to thousands of years, depending on the orbital period of the binary system.
Fainter novae have shorter time intervals between outbursts, while brighter novae have longer time intervals.
Type 1a Supernovae
Several types of supernovae exist.
Type Ia, Ib, and Ic supernovae do not have hydrogen Balmer lines in their spectra.
Type II supernovae do have hydrogen Balmer lines in their spectra.
Type Ia supernovae are caused by a white dwarf exceeding its mass limit.
Type Ib, Ic, and II supernovae are core-collapse supernovae.
Type II supernovae are considered classic cases of core-collapse supernovae.
Type Ib and Ic supernovae likely originate from Wolf-Rayet stars.
Each nova event results in the white dwarf gaining mass.
Eventually, the white dwarf exceeds the Chandrasekhar limit.
Once this occurs, the white dwarf undergoes a very explosive runaway carbon burning event.
The white dwarf explodes as a Type Ia supernova and is completely destroyed.
Heavier metals, such as iron, cobalt, and nickel, are produced and dispersed into the ISM during the explosion.
The peak luminosity and absolute magnitude of Type Ia supernovae tend to be very consistent.
This consistency makes them useful as standard candles for distance measurements, allowing us to determine distances to distant galaxies.
Examples include Supernova 1994D in NGC 4526.
Expelled materials can travel as fast as 10% the speed of light.
A strong shock wave forms ahead of the expelled materials, causing them to become superheated to at least a few million Kelvin.
Supernova remnants expand, cool, and slow down over time.
This process can last for thousands to tens of thousands of years before fading away.
This applies to both Type Ia and core-collapse supernovae.
Examples of Type Ia supernovae remnants include Kepler's Supernova (SN 1604) and G299 Supernova Remnant.
Core-Collapse Supernovae
Near the end of their lifetimes, massive stars produce and accumulate iron (Fe) in their core.
When the iron core becomes very massive (exceeding the Chandrasekhar limit of 1.44 M_{\odot}), the electron degeneracy pressure can no longer support it.
The core collapses rapidly under its own weight, with electrons and protons fusing into neutrons.
The core stops contracting when it reaches neutron degeneracy, causing the implosion to rebound violently.
This violent rebound produces a shock wave strong enough to blast the envelope off the core, creating an extremely bright explosive event known as a Type II supernova.
Supernovae are extremely luminous and can be seen over vast distances, even from other galaxies.
Extreme temperature and pressure from a supernova create elements heavier than iron (e.g., gold, lead, uranium), which are then dispersed into the ISM.
For stars less than 20 M_{\odot}, the collapsed core becomes a neutron star.
For stars greater than 20 M_{\odot}, the collapsed core becomes a black hole.
Stars greater than 40 M_{\odot} may be too massive for a supernova and instead collapse directly into black holes (though this is not confirmed).
Examples of core-collapse supernovae remnants include the Crab Nebula (M1), Cassiopeia A, and the remnant of SN 1987A.
Neutron Stars
Neutron stars are remnants of stellar cores left behind by massive stars (with masses between 8 M{\odot} and 20 M{\odot}).
Once a stellar core becomes a neutron star, it can no longer generate energy via stellar nucleosynthesis.
Gravity crushes the core into a small, incredibly dense object composed of neutrons, supported by neutron degeneracy pressure.
One cubic centimeter of neutron star material can weigh approximately 1 billion metric tons.
The range of known masses for neutron stars is 0.77 to 2.35 M_{\odot}.
Typical masses tend to be around 1.35 M_{\odot}.
Typical sizes range from 15 to 30 km (10 to 20 miles).
Known temperatures range from 42,000 to 3,100,000 K.
The initial temperature after formation is approximately 1,000,000,000,000 K, but they cool over time.
Extremely high temperatures mean neutron stars radiate mostly in X-rays or gamma rays.
Unlike white dwarfs, more massive neutron stars may actually be bigger than less massive neutron stars.
The maximum mass a neutron star can have is between 2.2 and 2.9 M_{\odot}, known as the Tolman–Oppenheimer–Volkoff limit.
Beyond this limit, neutron degeneracy pressure can no longer support the neutron star.
The most massive neutron star known is PSR J0952–0607, with a mass of 2.35 M_{\odot}.
Neutron stars have extremely strong magnetic fields, ranging from 10^4 to 10^{11} T (much stronger than Earth's).
These magnetic fields are so strong they would "atomize" lifeforms that wander within a few thousand kilometers.
Different types of neutron stars include:
Pulsars: emit twin beams of radiation from their magnetic poles. The beams sweep across the sky as the neutron star spins. Most of the roughly 3,000 known neutron stars are pulsars.
Magnetars: neutron stars with particularly strong magnetic fields, about 1,000 times stronger than normal neutron stars. Only about 30 magnetars have been discovered so far.
There are now six known neutron stars that are both pulsars and magnetars
The beam from a pulsar can only be seen when it travels along the observer's line of sight, similar to a lighthouse.
The magnetic poles do not necessarily align with the rotation axis; otherwise, we would not see the