An Introduction to Modern Astrophysics 11.5, 12.1-12.2 (Carroll, Ostlie)

The rate of energy output of stars.

Luminosity

The total energy of a system of particles in equilibrium is ___ of the system's potential energy

half

Whereas electron orbits involve energies in the electron volt (eV) range, ___ processes generally involve energies millions of times larger (MeV).

nuclear

The nucleus of a particular ___ is specified by the number of protons, Z, it contains (not to be confused with the mass fraction of metals), with each proton carrying a charge of +e.

element

In a neutral atom the number of protons must ___ the number of orbital electrons.

equal

A/an ___ of a given element is identified by the number of neutrons, N, in the nucleus, with neutrons being electrically neutral.

isotope

All isotopes of a given element have the same number of:

protons

Collectively, protons and neutrons are referred to as ___, the number of ___ in a particular isotope being A = Z + N.

nucleons

The simplest isotope of hydrogen is composed of:

one proton and one electron

Energy is ___ with an accompanying loss in mass when nucleons are combined to form atomic nuclei.

released

A helium nucleus, composed of 2 protons and 2 neutrons, can be formed by a series of nuclear reactions originally involving 4 hydrogen nuclei. Such reactions are known as ___ reactions.

fusion

This type of reaction occurs when a massive nucleus is split into smaller fragments.

Fission

All nuclei are positively charged, meaning that a/an ___ must be overcome before nucleus contact can ocur.

Coulomb potential energy barrier

The potential energy curve is composed of 2 parts: the portion outside of the nucleus is the potential energy that exists between 2 positively charged nuclei, and the portion inside the nucleus forms a potential well governed by the ___ that binds the nucleus together.

strong nuclear force

A very short-range force that acts between all nucleons within an atom. It's an attractive force that dominates the Coulomb repulsion between protons.

Strong nuclear force

This relates the number density of particles with velocities between v and v + dv to the temperature of a gas.

Maxwell-Boltzmann distribution

The number of reactions per target nucleus per unit time, divided by the flux of incident particles.

Cross section

The physicist who first investigated Coulomb barrier penetration.

George Gamow

The exact sequence of steps by which one element is converted into another.

Nucleosynthesis

The process by which a chain of nuclear reactions leads to the final product can't happen in a completely arbitrary way; a series of particle ___ must be obeyed.

conservation laws

This term means a "light thing" and includes electrons, positrons, neutrinos, and antineutrinos.

Lepton

Although this is extremely rare in comparison with matter, it plays an important role in subatomic physics, including nuclear reactions. Particles of this type are identical to their matter counterparts but have opposite attributes, such as electric charge.

Antimatter

This has the characteristic that a collision with its matter counterpart results in complete annihilation of both particles, accompanied by the production of energetic photons.

Antimatter

This many photons are required to conserve both momentum and energy simultaneously.

Two

These particles are electrically neutral and have a very small but non-zero. One of the interesting characteristics of them is their extremely small cross section for interactions with other matter, making them very difficult to detect.

Neutrinos

After being produced in the deep interior, these particles always always successfully escape from a star.

Neutrinos

Since electrons and positrons have charges equal in magnitude to that of a proton, leptons will contribute to the charge conservation requirement while their total ___ must also be conserved.

lepton numbers

The total number of matter leptons minus the total number of ___ must remain constant.

antimatter leptons

Applying the conservation laws, one chain of reactions that can convert hydrogen into helium is the first:

proton-proton chain

The slowest step in the proton-proton chain sequence is the ___ one, because it involves the decay of a proton into a neutron.

initial

In an environment characteristic of the center of the sun, 69% of the time a helium-3 interacts with another helium-3 in the PPI chain, whereas 31% of the time the ___ chain occurs.

PPII

Yet another branch, the ___ chain, is possible because the capture of an electron by the beryllium-7 nucleus in the PPII chain competes with the capture of a proton (a proton is captured only 0.3% of the time in the center of the Sun).

PPIII

A second, independent cycle also exists for the production of helium-4 from hydrogen. In the ___, carbon, nitrogen, and oxygen are used as catalysts, being consumed and then regenerated during the process.

CNO cycle

As shown by the power law dependence, the CNO cycle is much more strongly ___ than is the pp chain.

temperature-dependent

Low-mass stars, which have smaller central temperatures, are dominated by the pp chains during their ___ evolution.

hydrogen burning

More massive stars, with their higher central temperatures, convert hydrogen to helium by the:

CNO cycle

When hydrogen is converted into helium by either the pp chain or the CNO cycle, the mean molecular weight of the gas:

increases

The reaction sequence by which helium is converted into carbon.

Triple alpha process

This process takes its name from the historical result that the mysterious alpha particles detected in some types of radioactive decay were shown by Rutherford to be helium-4 nuclei.

Triple alpha process

In this process, the first step produces an unstable beryllium nucleus that will rapidly decay back into 2 separate helium nuclei if not immediately struck by another alpha particle. As a result, this reaction may be thought of as a three-body interaction, and therefore.

Triple alpha process

After sufficient carbon has been generated by the triple alpha process, it becomes possible for carbon nuclei to capture alpha particles, producing this.

Oxygen

At helium-burning temperatures, the continued capture of alpha particles leading to progressively more massive nuclei quickly becomes prohibitive due to the ever higher:

Coulomb barrier

Reactions where energy is absorbed rather than released.

Endothermic

Reactions where energy is released.

Exothermic

In these reactions the product nucleus actually possesses more energy per nucleon than did the nuclei from which it formed.

Endothermic

True or false: in general, endothermic reactions are much more likely to occur than exothermic reactions under conditions that normally prevail in stellar interiors.

False

These three different energy transport mechanisms operate in stellar interiors.

Radiation, convection, conduction

This allows the energy produced by nuclear reactions and gravitation to be carried to the surface via photons, the photons being absorbed and re-emitted in nearly random directions as they encounter matter.

Radiation

This can be a very efficient transport mechanism in many regions of a star, with hot, buoyant mass elements carrying excess energy outward while cool elements fall inward.

Convection

This transports heat via collisions between particles.

Conduction

Although this can play an important role in some stellar environments, it is generally insignificant in most stars throughout the majority of their lifetimes.

Conduction

As either the flux or the opacity increases, the temperature gradient must become ___ if radiation is to transport all of the required luminosity outward. The same situation holds as the density increases or the temperature decreases.

steeper (more negative)

If the temperature gradient becomes too steep, this can begin to play an important role in the transport of energy.

Convection

Physically, this involves mass motions: hot parcels of matter move upward as cooler, denser particles sink.

Convection

The field of physics describing the motion of gases and liquids.

Fluid mechanics

Fluid mechanics relies on this complicated set of three-dimensional equations.

Navier-Stokes equations

When convection is present in a star, it is generally quite turbulent, requiring a detailed understanding of the amount of these two things.

Viscosity, heat dissipation

A characteristic length scale for convection, typically referred to in terms of this, is often comparable to the size of the star.

Pressure scale height

In the study of heat transport, conservation of energy is expressed by this, where the change in the internal energy of a mass element is given by the amount of heat added to that element minus the work done by that element on its surroundings.

First law of thermodynamics

The internal energy of a system U is a/an ___, meaning that its value depends only on the present conditions of the gas, not on the history of any changes leading to its current state.

state function

True or false: heat and work are state functions.

False

A gas composed of single particles with no ionization.

Ideal monatomic gas

In the case of an ideal monatomic gas, the internal energy is just the:

kinetic energy per unit mass

The change in heat of the mass element dQ is generally expressed in terms of the ___ of the gas.

specific heat

The amount of heat required to raise the temperature of a unit mass of a material by a unit temperature interval.

Specific heat

The volume per unit mass.

Specific volume

For a monatomic gas, the ratio of specific heats is:

5/3

As both C_p and C_v increase, the ratio of specific heats approaches:

unity

Since the change in internal energy is independent of the process involved, consider the special case of a/an ___ for which no heat flows into or out of the mass element (dQ = 0).

adiabatic process

If the star's actual temperature gradient is steeper than the adiabatic temperature gradient, the temperature gradient is said to be:

superadiabatic

If the actual temperature gradient is superadiabatic, this will result.

Convection

The amount of mass per second that crosses a unit area oriented perpendicular to the direction of the flow.

Mass flux

The derivation leading to the prescription for the convective flux. Although basically a phenomenological theory containing arbitrary constants, this is generally quite successful in predicting the results of observations.

Mixing-length theory