Star Properties, Classification, and Formation: Astrophysics Key Concepts

Large parallax

Star is closer to Earth

Small parallax

Star is farther from Earth

1 arcsecond parallax

Equals 1 parsec of distance

Milli-arcsecond conversion

1000 mas = 1 arcsec

Luminosity definition

Total energy a star emits per second

Apparent brightness

How bright a star appears from Earth; depends on distance

Absolute magnitude

Brightness a star would have at 10 pc

Magnitude scale change

5 magnitudes = 100× brightness change

Magnitude 1 difference

Brightness ratio of 2.512

Smaller B-V color index

Hotter star

Larger B-V color index

Cooler star

Spectral class order

O B A F G K M (hot → cool)

Spectral class numbers

0 = hottest, 9 = coolest

Main-sequence trends

Hotter stars are more massive, luminous, larger, shorter-lived

HR Diagram x-axis

Temperature or spectral class (hot left, cool right)

HR Diagram y-axis

Luminosity or absolute magnitude

Main sequence location

Diagonal band of hydrogen-fusing stars

White dwarf region

Hot but dim (lower-left of HR diagram)

Red giant region

Cool but bright (upper-right of HR diagram)

Luminosity-radius-temperature

L = R²T⁴

Radius doubles

Luminosity increases by factor of 4

Temperature doubles

Luminosity increases by factor of 16

Luminosity classes

I = supergiant, III = giant, V = main sequence

Broad spectral lines

Indicate high gravity (e.g., white dwarfs)

Narrow spectral lines

Indicate low gravity (e.g., supergiants)

Spectroscopic parallax

Spectrum → spectral type → luminosity class → distance

Stellar mass measurement

Only measured accurately using binary stars and Kepler's law

Main-sequence lifetime

Lifetime ∝ 1/mass²·⁵

High mass star lifetime

Shorter main-sequence life

Low mass star lifetime

Longer main-sequence life

Cepheid variables

Period gives luminosity; used as standard candles

Henrietta Leavitt

Discovered Cepheid period-luminosity law

ISM definition

Gas and dust that fills the space between stars

ISM gas composition

Mostly hydrogen: HI, HII, H₂

Gas-to-dust ratio

100 : 1

HI detection

21 cm radio emission

Molecular cloud detection

CO tracer molecules

Extinction

Dust makes stars appear dimmer (magnitude increases)

Reddening

Dust removes blue light more than red light

Emission nebula

HII region glowing from hot O and B stars

Reflection nebula

Blue light from scattering by dust

Dark nebula

Cold molecular gas blocking background light

Molecular clouds

Coldest, densest ISM structures; star formation sites

Hydrostatic equilibrium

Gravity pulling inward = pressure pushing outward

Two stages of star formation

Cloud fragmentation → protostar contraction

Mass vs formation time

High-mass stars form faster

Protostar equilibrium

Not in hydrostatic equilibrium; gravity > pressure

Hayashi track

Evolutionary contraction path of low-mass protostar

Triggered formation

Shockwaves from O/B stars or supernovae trigger star birth

Open cluster

Young, 100s-1000s stars, few parsecs wide

Globular cluster

Old (10-12 Gyr), 10⁵-10⁶ stars in Milky Way halo

Main-sequence turnoff

Hottest star still on MS → determines age

Mass → evolution speed

Higher mass = faster evolution

High-mass star death

Core-collapse (Type II) supernova

Low-mass star death

Planetary nebula → white dwarf

End of main sequence

Core hydrogen exhausted → helium ash core forms

Fusion ash

Material left behind when fusion ends in core

Shell burning

Fusion occurring in layers around core

Helium ignition temperature

~100 million K

Carbon ignition temperature

~600 million K

Triple-alpha process

Helium fusion producing carbon

Main Sequence core

Hydrogen fusion; helium ash buildup

Subgiant Branch core

Helium ash core; hydrogen shell burning

Red Giant Branch core

Inert helium core; strong hydrogen shell burning

Horizontal Branch core

Helium fusion core; hydrogen shell burning continues

AGB core

Carbon-oxygen core; two fusion shells (H + He)

Planetary Nebula core

Hot C/O core ionizing ejected gas

White Dwarf core

Carbon-oxygen degenerate core; no fusion

Fusion limit

Stars cannot fuse elements heavier than iron

Photodisintegration

Gamma rays break iron into helium nuclei during collapse

Neutronization

Electrons + protons → neutrons + neutrinos

Core-collapse rebound

Shockwave produces Type II supernova

Type II supernova

Death of high-mass star; hydrogen present in spectrum

Type Ia supernova

Exploding white dwarf; no hydrogen in spectrum

Chandrasekhar limit

1.4 M☉ maximum white dwarf mass

Type Ia remnant

No remnant left (white dwarf destroyed)

Type Ia brightness

All Type Ia supernovae have same absolute magnitude (M = -19.3)

Big Bang nucleosynthesis

Forms hydrogen, helium, small lithium

Stellar nucleosynthesis

Low mass stars → carbon; high mass stars → iron

s-process

Slow neutron capture in AGB stars

r-process

Rapid neutron capture in supernovae or neutron star mergers

Neutron star formation

Remnant core of Type II supernova

Neutron star size

Radius ~10 km

Neutron degeneracy pressure

Supports neutron stars against gravity

Pulsar

Rotating neutron star with lighthouse-like beams

Black hole formation

Collapse of >3 M☉ core when neutron degeneracy fails

Schwarzschild radius

Distance where escape speed = speed of light

Event horizon

Boundary beyond which nothing escapes

Relativity postulate 1

No absolute reference frame

Relativity postulate 2

Speed of light is constant for all observers

Time dilation

Moving clocks run slower

Gravitational time dilation

Clocks run slower near massive objects

Equivalence principle

Acceleration and gravity are indistinguishable

Gravitational lensing

Light bends around massive objects

Evidence for relativity

Starlight bending, GPS corrections, muon survival, gravitational waves

Spacetime concept

Mass and energy curve spacetime; objects follow curvature