Stellar Remnants

What stellar objects are the end stage of evolution for stars with initial masses less than approximately 8 solar masses?

White dwarfs.

What is the primary source of pressure that supports a white dwarf against gravitational collapse?

Electron degeneracy pressure.

How does the radius of a white dwarf change as its mass increases?

The radius decreases; more massive white dwarfs are smaller and denser.

The empirically determined mass-radius relation for a white dwarf is approximately $R \approx 0.01 R{\odot} (M / 0.7 M{\odot})^{-1/3}$.

This formula shows that as the mass (M) of a white dwarf increases, its radius (R) decreases.

What is the Chandrasekhar mass?

The maximum mass for a stable white dwarf, approximately 1.4 solar masses, above which electron degeneracy pressure is insufficient to prevent collapse.

What physical phenomenon prevents electron degeneracy pressure from supporting a white dwarf above the Chandrasekhar mass?

The electrons become relativistic, which changes the pressure-density relationship, making it insufficient to counteract gravity.

In a binary star system, what is the term for the teardrop-shaped region of gravitational influence around each star?

The Roche lobe.

What process occurs when a star in a binary system expands beyond its Roche lobe, causing matter to be transferred to its companion?

Roche lobe overflow.

What is a nova?

A transient astronomical event caused by runaway hydrogen fusion on the surface of a white dwarf that is accreting matter from a companion star.

How do Type Ia supernovae differ from novae in terms of the fate of the white dwarf?

In a nova, the white dwarf survives and can erupt again, whereas in a Type Ia supernova, the white dwarf is completely destroyed.

What is the 'single degenerate' scenario for a Type Ia supernova?

A white dwarf accretes material from a non-degenerate companion (like a main-sequence star) until its mass exceeds the Chandrasekhar limit, triggering its explosion.

What is the 'double degenerate' scenario for a Type Ia supernova?

Two white dwarfs in a binary system merge, and their combined mass exceeds the Chandrasekhar limit, leading to a thermonuclear explosion.

Why are Type Ia supernovae particularly useful as 'standard candles' for measuring cosmic distances?

They have very consistent peak luminosities, allowing astronomers to calculate their distance based on their apparent brightness.

The core collapse of a massive star ($\sim$8 to 20 $M_{\odot}$) results in the formation of what type of stellar remnant?

A neutron star.

What is the main source of pressure that supports a neutron star against gravity?

Neutron degeneracy pressure.

How does the typical radius of a neutron star compare to that of a white dwarf?

A neutron star is significantly smaller, with a radius of about 10-15 km, compared to a white dwarf which is roughly the size of Earth.

A rapidly rotating, highly magnetized neutron star that emits beams of electromagnetic radiation is known as a _.

pulsar

What is the physical mechanism responsible for the radiation beams emitted by pulsars?

Synchrotron radiation, produced by charged particles accelerated to relativistic speeds along the star's magnetic field lines.

What is a magnetar?

A type of neutron star with an exceptionally strong magnetic field, orders of magnitude stronger than a typical neutron star.

What is the theoretical upper mass limit for a neutron star, beyond which it will collapse into a black hole?

The Oppenheimer-Volkov limit, which is approximately 3 solar masses.

A stellar remnant becomes a black hole when its escape velocity exceeds _.

the speed of light

What is the term for the boundary around a black hole from which nothing, not even light, can escape?

The event horizon.

The radius of the event horizon of a non-rotating black hole is called the _.

Schwarzschild radius

How can stellar-mass black holes be detected if they don't emit light?

By observing their gravitational effects on a companion star (radial velocity shifts) or by detecting X-rays from an accretion disk of matter falling into them.

What is gravitational microlensing in the context of detecting black holes?

The temporary brightening of a background star when a black hole passes in front of it, bending the star's light through its gravitational field.

What evidence confirmed the existence of a supermassive black hole (Sgr A*) at the center of the Milky Way?

Tracking the orbits of stars near the galactic center over many years, which revealed they were orbiting a massive, unseen object.

What types of events are the primary sources of gravitational waves detectable by current instruments like LIGO?

The mergers of compact object binaries, such as two black holes, two neutron stars, or a black hole and a neutron star.

What was the significance of the gravitational wave event GW170817?

It was the first detection of gravitational waves from a binary neutron star merger, and it was accompanied by an electromagnetic counterpart (a kilonova).

What is a kilonova?

An electromagnetic transient powered by the radioactive decay of heavy elements synthesized via the r-process during a neutron star merger.

What key information can be measured from gravitational wave signals?

The masses and spins of the merging objects, the distance to the source, and properties of the binary orbit.

Gravitational wave sources can be used as 'standard sirens,' analogous to what type of electromagnetic distance indicator?

Standard candles (like Type Ia supernovae).

What process is responsible for creating elements heavier than iron, such as gold and platinum?

The r-process (rapid neutron capture), which primarily occurs in neutron star mergers (kilonovae).

How does the s-process of nucleosynthesis differ from the r-process?

The s-process ('slow') involves neutron capture on a timescale longer than beta-decay, while the r-process ('rapid') involves capture on a much shorter timescale.

Where does the s-process primarily take place?

In AGB (Asymptotic Giant Branch) stars, between the hydrogen and helium-burning shells.

According to the 2006 IAU definition, what are the three criteria for a celestial body to be classified as a planet in our Solar System?

It must (a) be in orbit around the Sun, (b) have sufficient mass to be nearly round (hydrostatic equilibrium), and (c) have cleared the neighborhood around its orbit.

Why was Pluto reclassified from a planet to a dwarf planet?

It does not meet the third IAU criterion, as it has not 'cleared the neighborhood around its orbit' (its orbit intersects with Neptune's).

According to the IAU working definition, what is the key physical distinction between a brown dwarf and a planet?

A brown dwarf has sufficient mass (above ~13 Jupiter masses) to undergo thermonuclear fusion of deuterium, while a planet does not.

What are the two most successful methods for discovering exoplanets, accounting for the majority of detections?

The transit method and the radial velocity method.

How does the transit method detect exoplanets?

By measuring the slight, periodic dimming of a star's light as a planet passes in front of it from our point of view.

How does the radial velocity method detect exoplanets?

By measuring the periodic Doppler shift in a star's spectrum caused by the gravitational 'wobble' induced by an orbiting planet.

The first exoplanet discovered orbiting a sun-like star, 51 Pegasi b, was the first example of a class of planets known as _.

Hot Jupiters

What are 'super-Earths' and 'sub-Neptunes'?

They are the most common types of exoplanets found, with sizes between that of Earth and Neptune, a class of planet not present in our Solar System.

What is the pulsar timing method for detecting exoplanets?

It detects slight, regular variations in the arrival time of a pulsar's pulses, caused by the gravitational pull of orbiting planets.

For which types of exoplanets is the direct imaging detection method most effective?

Young, hot, massive giant planets that are far from their host star, as they emit enough infrared radiation to be seen directly.

What is the function of a coronagraph in the direct imaging of exoplanets?

It blocks out the overwhelming light from the host star, making it possible to see the much fainter light of an orbiting planet.

A periodic table showing the origin of elements indicates that merging neutron stars are the primary source of many elements like , , and _.

gold (Au), platinum (Pt), silver (Ag)

Where were the lightest elements (hydrogen, helium, and some lithium) created?

During Big Bang nucleosynthesis, shortly after the universe formed.

Stellar fusion in the cores of massive stars can produce elements up to _, which has the most tightly bound nucleus.

iron (Fe)

The escape velocity at the surface of a neutron star can be a significant fraction of what fundamental constant?

The speed of light (c).

What happens to the rotation rate of a star's core when it collapses to form a neutron star, and why?

The rotation rate increases dramatically due to the conservation of angular momentum as the radius shrinks.

What is the 'no-hair' theorem for black holes?

It states that a black hole is characterized by only three external properties: its mass, rotation (angular momentum), and electric charge.

In the context of stellar remnants, a binary system where at least one component is a white dwarf, neutron star, or black hole is called a _.

compact object binary

What instrument, a successor to ground-based interferometers, is a space-based observatory designed to detect low-frequency gravitational waves from sources like supermassive black hole mergers?

LISA (Laser Interferometer Space Antenna).

The _ mission was a space observatory that discovered thousands of exoplanets using the transit method.

Kepler

Why do white dwarfs have highly pressure-broadened spectral lines?

Due to their extremely high surface gravity, which creates a high-pressure atmosphere.

What is a 'black dwarf'?

A theoretical stellar remnant, a white dwarf that has cooled so much that it no longer emits significant heat or light.

Why is the interior of a white dwarf described as being nearly isothermal?

Energy is transported very efficiently via electron conduction, which keeps the temperature relatively uniform throughout the degenerate core.

Which two elements are synthesized in large quantities during a Type Ia supernova and subsequently decay into iron?

Nickel-56 ($^{56}$Ni) and Cobalt-56 ($^{56}$Co).

What process produces neutrons and neutrinos when the iron core of a massive star collapses?

The combination of protons and electrons ($p^+ + e^- \rightarrow n + \nu_e$), also known as electron capture or inverse beta decay.

How is the magnetic field of a neutron star thought to become so strong?

Through the conservation of magnetic flux as the massive progenitor star's core collapses to a much smaller radius.

According to the IAU, free-floating objects in young star clusters with masses below the deuterium-burning limit are not planets, but are called _.

sub-brown dwarfs

Exoplanet designations consist of the host star's name followed by a lowercase letter starting with 'b'. What does the order of the letters signify?

The order of discovery, not the distance from the host star.

The discovery of what type of exoplanet challenged initial theories of planet formation, which were based on our Solar System?

Hot Jupiters, because these giant planets were found orbiting extremely close to their stars, unlike Jupiter.

What is the name for a binary system where both stars are larger than their Roche lobes and share a common atmosphere?

A contact binary.

What is the primary composition of most white dwarfs?

Ionized carbon and oxygen.