3. properties of stellar-mass objects (chps. 19-22)

8/10/2019 3. Properties of Stellar-Mass Objects (Chps. 19-22)

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Star formation:

Almost atoms must be accumulated in order for

their collective pull of gravity to keep them together. Even

more mass is required in the presence of heat, rotation, andmagnetism, which oppose gravitational contraction.

Star formation only begins once gravity becomes the

dominating force, causing a cloud to lose its equilibrium and

start contracting. Radical changes are made to the clouds

internal structure before equilibrium is restored.

Stage 1Interstellar cloudhuge, dense cloud that

collapses when a pocket of gas becomes gravitationally

unstable, fragmenting the cloud into smaller and smallerclumps of matter; produces anywhere from a few dozen to

hundreds of stars

Stage 2Collapsing cloud fragmentshrinks substantially

in size; fragments eventually become dense enough to trap

radiation, causing the temperature and pressure to rise, and

fragmentation to cease

Stage 3Fragmentation ceasesbegins to resemble a star;

dense, opaque region at the center called protostar; mass

grows but radius shrinks; contains a photosphere surface,

with material opaque to radiation it emits

Stage 4Protostarphysical properties can be plotted on

H-R diagram; pressure close to, but not in equilibrium with,


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gravity; evolutionary trackmotion of stars location on

diagram as it evolves, early evolutionary track called Kelvin-

Helmholtz contraction phase

T Tauri starprotostar in late stages of formation, often

exhibiting violent surface activity; T Tauri windbipolar

jets; observed to brighten significantly in short periods oftime, supporting theory of rapid evolution during final phase

of star formation; contains trace amounts of lithium, an

indicator of stellar youth; loses up to 50% of its mass before

stabilizing

Classic T Taurihas a massive accretion disk that

displays strong emission lines

Weak T Tauriweak to nonexistent disk that may haveresulted in a planetesimal

Stage 5Protostar evolutiongas is now completely

ionized, but protons do not have enough thermal energy to

undergo nuclear binding; contraction rate depends on rate at

Hayashi

track


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which protostars internal energy can be radiated away into

space

Stage 6Newborn starprotons begin fusing into helium

nuclei in the core; marked by slight contractionStage 7Main sequencepressure and gravity are balanced;

rate of nuclear energy generation equals rate at which energy

is radiated from the surface

Zero-age main sequencemain-sequence line for newborn

stars predicted by theory

The minimum mass of gas needed to generate core

temperatures high enough for nuclear fusion is about 0.08

solar masses. Brown dwarfs are failed stars with massestoo low for nuclear burning, with one example being Jupiter

Shock waveshell of gas driven outward by high

temperatures and pressures that push thin matter into dense

sheets; considered a triggering mechanism that initiates star

formation in a chain reaction; generated by emission nebulae,

planetary nebulae, supernovae, galaxy spiral-arm waves, and

interactions between galaxiesStar clustergroup of stars formed from the same parent

cloud and lying in the same region of space; usually found in

plane of Milky Way

Associationless dense cluster covering a larger area; T

associations contain T Tauri stars while OB associations

contain O- and B-type stars

Open clusterloose and irregular; distance of a few parsecs

across; typically contain from a few hundred to a few tens of

thousands of stars

Globular clusterusually outside Milky Way plane;

contains hundreds of thousands to millions of stars spread

out over about 50 pc; most are at least 10 billion years old,


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so upper-main-sequence stars have already been exhausted;

contains oldest known stars in galaxy; Classes I-XII

classification based on number of members; follows trend of

decreasing core density, decreasing presence of halo, andincreasing homogeneity

Low-mass stars are more common, because the first

massive stars to form tend to disrupt their environment and

prevent more high-mass stars from forming.

Encounters with giant molecular clouds remove cluster

stars. The lifetime of a cluster depends on its mass, and

clusters eventually dissolve into individual stars like the Sun.

Stellar Evolution:Hydrostatic equilibriumnormal situation in which outward

pressure of hot gas exactly balances inward pull of gravity in

a main sequence star

Core-hydrogen burningslow

process in which hydrogen fuses

into helium in a stars coreNo red dwarfs (low-mass

stars on bottom-right of H-R

diagram) have ever left the main

sequence. Conversely, most blue

giants (high-mass stars on top-left)

have burned out long ago.

As a main-sequence star ages,

its temperature, luminosity, and

radius increase slowly. As the

hydrogen in the core is consumed,

helium content increases (fastest at

the center), and the star begins to


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leave the main sequence. A Sun-like star begins to run out

of fuel after about 10 billion years. The outward-pushing

gas pressure weakens, and gravity forces the inner core to

start contracting. Higher temperatures are required forhelium nuclei to fuse into heavier elements due to

electromagnetic repulsion. In the

hydrogen-shell burning stage, hydrogen

is fused even more rapidly than before

and energy is generated faster, causing

the star to brighten.

The overlying layers expand and

cool. As the surface temperature falls,the star follows the horizontal path from its main-sequence

location known as the subgiant branch. The interior

becomes mostly opaque, and convection carries the cores

energy output to the surface, dramatically increasing its

temperature. Here the star follows the vertical path known

as the red-giant branch.

About 100 million years after a solar-mass star leavesthe main sequence, the central density has reached about

kg/m3and the temperature has reached about K, which

is high enough for helium to fuse into carbon. Three helium-

4 nuclei (alpha particles) are combined into carbon-12 in the

triple-alpha process.

The Pauli exclusion principle prohibits electrons in the

core of the star from being squeezed too close together.Electron degeneracy describes the

condition in which they have reached the

state of becoming incompressible, and

contact between electrons is called

electron degeneracy pressure. This sort


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of pressure is independent of temperature, so nuclear

reaction rates increase, and the temperature increases rapidly

in a helium flash. Soon, the core is heated to the point where

normal thermal pressure is restored. Now, the star is stablyburning both helium and hydrogen in what is called the

horizontal branch of the H-R diagram.

As the carbon core shrinks but grows in radius, the

outer envelope expands yet again, and the star becomes a red

supergiant on the asymptotic-giant branch.

At a density of about kg/m3, the electrons in the

core once again become degenerate. The helium-burning

shell becomes subject to a series of explosive helium-shellflashes caused by enormous pressure and extreme sensitivity

of the triple-alpha burning rate to small changes in

temperature. The unstable outer layers increasingly fluctuate

in size until the envelope is ejected and forms a planetary

nebula, a shell of warm, glowing gas completely surrounding

the core. Over time, it spreads out and cools before

dispersing.The hot, small, and dim carbon core that remains is now

called a white dwarf. A DA white dwarf retains hydrogen in

its outer envelope, while a low mass star that never reaches

helium fusion or a

binary member

whose envelope

has been stripped

away by its

companion forms a

helium/DB white

dwarf. A high-

mass, high-


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temperature star may instead form a neon-oxygen white

dwarf. After a while, the white dwarf completely burns out

and becomes a black dwarf, with a temperature of absolute

zero.

Stellar evolution differs based

on mass. The dividing line between

high-mass and low-mass stars is

usually around 8 solar masses whenthe carbon core forms. High-mass

stars are able to fuse up to oxygen

and even higher elements, and

usually end in a supernova. No

helium flash occurs for stars more

massive than about 2.5 solar masses.

To the left are evolutionary tracks

for higher-mass stars.

In star clusters, the main

sequence turnoff is the high-

luminosity end of the stars that are

just about to leave the main


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Novaincrease in brightness of white dwarf by a factor of

10,000 or more in a matter of days, then returns to original

luminosity; results from explosion caused by matter falling

onto surface from atmosphere of binary companion; lightcurve shows rapid rise and slow decline

Classical novaone outburst of 8-15 magnitudes with

quick brightening but slow recession to original amplitude;

caused by thermonuclear runaway of hydrogen on white

dwarfDwarf novafrequent (10-1000 day period) outbursts

of 2-6 magnitudes; caused by accretion as explained in the

disk instability model or the mass transfer burst model

Recurrent nova4-9 magnitudes; 10-100 year period of

outbursts that eject

discrete shells at

velocities comparable

to those of classical

novae; type Acloser

to classical nova, type

Bcloser to dwarf

nova


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Accretion diskswirling, flattened disk of matter revolving

around white dwarf; formed by material leaving companion;

hot inner part radiates in visible, ultraviolet, and X-ray parts

of spectrum; hot spot is point at which stream of matterstrikes accretion disk

The more massive a star is, the heavier elements it can

fuse. A star of 20 solar masses burns hydrogen for 10

million years, helium for 1 million years, carbon for 1000

years, oxygen for 1 year, and silicon for a week; the iron

core grows for less than a day. Iron is the most stable

element (it has the greatest nuclear binding energy), and

energy cannot be obtained from either its fusion or its fission.Photodisintegrationprocess in which individual photons

are able to split iron into lighter nuclei repeatedly until only

protons and neutrons remain; occurs when star temperature

reaches nearly 10 billion K

Neutronizationas core density rises, protons and electrons

collide to form neutrons and neutrinos, nearly massless and

chargeless particles moving almost at the speed of lightNeutron degeneracy pressuretakes place in shrinking core

when contact between neutrons prevent further gravitational

collapse

The entire collapse of the iron core takes only about a

second. Then the core rebounds, sending an enormous shock

wave that blasts all the overlying layers into space. The star

explodes in a core-collapse supernova (Type II), whose

brightness may rival that of its entire galaxy.

Supernovaprogenitors iron core implodes; protons and

electrons fuse to form neutrons and neutrinos; characterized

by dramatic increase of brightness and fading; form neutrons

stars and black holes


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Type I supernovahydrogen-

poor; light curve similar in

shape to that of a nova

Type II supernovalightcurve shows hydrogen;

usually has a plateau in the

curve a few months after

maximum; equally as common as Type I

Chandrasekhar mass1.4-solar-mass limit for white dwarfs

Carbon-detonation supernova (Type I)takes place when an

accreting white dwarf exceeds Chandrasekhar mass, or when

two white dwarfs in binary system collide and merge;pressure of degenerate electrons cannot withstand pull of

gravity; internal temperature rapidly rises and carbon fuses

into heavier elements; used as standard candles because of

small luminosity range, which can be derived from rate

Stellar nucleosynthesisnuclear fusion that forms the rest of

the elements in the universe

Heavier elementswhose atomic masses are

multiples of 4 usually form

through helium capture.

Neutron capture, or the

s(slow)-process, involves

adding neutrons to a

nucleus, causing it to

become unstable and decay

radioactively into a stable

nucleus of a different

element. The r(rapid)-

process only occurs during


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supernova explosions, and produces

the heaviest elements known in the

universe. Each new generation of

stars increases the concentration ofthe heaviest elements in the

universe, passing them on to the

next generation. Because of this,

the spectra of the youngest stars

usually show the heaviest elements,

and their abundance is continually increasing.

Degenerate gasexists in core remnant; follows laws of

quantum mechanics, i.e. pressure depends on particle speed,not temperature; degenerate particles (electrons for white

dwarfs, neutrons for neutron stars) fill lower energy levels

first, making compression extremely difficult; increasing

mass increases compression and reduces volume

Neutron stars:

Neutron starextremely small, dense, solid innermost partof the core that remains as a supernova remnant; composed

purely of neutrons; produces no nuclear reactions; rotates

extremely rapidly, following

conservation of angular

momentum; very strong

magnetic fields whose lines

are squeezed closer together

by contracting material;

rotation slows and then ceases

as energy is radiated into space;

have theoretical mass limit of

3 solar masses, which does not


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take magnetism and rotation into account

Pulsarneutron star with stable pulse period of 0.03-0.3

seconds and duration caused by radiation (usually radio, but

sometimes visible, X-ray, and gamma-ray) emitted in narrowsearchlight pattern, often described as lighthouse model;

usually has high velocity because

energy from asymmetrical

supernova caused it to recoil in

opposite direction; glitches or

sudden increases in angular velocity

occur from decrease in volume

X-ray burstersudden period ofrapid nuclear burning and release of

energy in the form of X-ray

radiation lasting only a few seconds; occurs when neutron

star in binary system accretes matter onto surface, raising

temperature until hydrogen fusion is able to take place

Millisecond pulsarrotates very rapidly and has

millisecond-long pulse period; paradoxically found inglobular clusters, which usually contain older stars; possible

explanation involves companion star providing matter that

strikes almost parallel to neutron stars surface, causing it to

spin faster

Gamma-ray burstirregular flashes of gamma rays that

release tremendous amounts of energy within seconds from

cosmological distances; light curve changes instantaneously

(not blurred like that of a larger object), implying that the

source of gamma-ray bursts come from sources no larger

than a few hundred kilometers across; pictured as relativistic

fireballs, or expanding regions of superhot gas


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becomes stretched and squeezed, which produces a high

amount of friction. Gravitational redshift is induced by the

black holes gravitational field and causes light to be

redshifted to infinitely long wavelengths.

Variable stars:

Variable starstar whose luminosity changes with time

Cataclysmic/explosive variablenova or supernova

Intrinsic variablevariability is a

basic trait and not dependent on

being part of binary system

Eruptive variableusually a pre-main sequence star that is still

condensing and is much larger or

smaller than average main sequence

star; sometimes is red giant that

easily loses gas or is part of binary

system

Symbiotic novaslow irregular eruptive variablescomposed of red giant (usually a Mira variable) and white

dwarf below Chandrasekhar limit

Pulsating variable starsclass of intrinsic variables whose

luminosity varies cyclically because of rising and falling in

opacity and internal pressure; experiencing period of

instability; includes (a) RR Lyrae and (b) Cepheid variables,

whose light curves are shown below

Cepheids follow the

period-luminosity


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relationship. Type I and Type II Cepheids differ in the fact

that Type I Cepheids are usually younger stars with higher

metallicities and shorter pulsation periods, while Type II

Cepheids are usually Population II stars. Type IIs arefainter by about 1.6 magnitudes and are divided into the BL

Herculis (periods of 1-4 days), W Virginis (10-20 days), and

RV Tauri (>20 days) subclasses.

All RR Lyrae stars have

about the same luminosity of

about 100 solar luminosities. RR

Lyrae variables are commonly

found in globular clusters andoften used as standard candles.

The instability strip is a

near-vertical region on the H-R

Diagram that consists of

internally unstable, post-main-

sequence stars, such as those described above.

Mira variablered giant on asymptotic branch, periodlonger than 100 days, amplitude greater than 1 order of

magnitude in infrared and 2.5 magnitudes in visible; has

already lost about half of initial mass and is at about 2 solar

masses; 75% not spherically symmetric; period increases or

decreases by factor of 3 over long periods of time due to

thermal pulsesevents in which helium shell near core

temporarily undergoes nuclear fusion

Semiregular variablename refers to period; giant or

supergiant with period between 20-2000 days and irregular

light curve shape

SRAlate-type giants, persistent periodicity and

similar to Mira variables, but with smaller amplitudes


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SRBalternating intervals of periodic and slow

irregular changes; described by mean period

SRCamplitudes on 1 order of magnitude, periods of

about 30 to several thousand daysSRDF, G, or K spectral types; amplitudes range from

0.1 to 4 magnitudes, periods from 30-1100 days

RV Tauri variablevaries in luminosity (by up to 4

magnitudes) and spectral type (anywhere from F to M) with

periods of 30-150 days; exhibits alternating, changing

primary and secondary minima

RVaconstant mean luminosity

RVbperiodic variations in mean brightness; includesthe prototype RV Tauri

ZZ Ceti / DAV variablewhite dwarf with small luminosity

variations of 0.001 to 0.2 magnitudes and short periods of

30-1200 seconds due to ionization and hydrogen

recombination in the outer envelope

3. properties of stellar-mass objects (chps. 19-22)

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