Astrophysics: Stars and the Universe

A star glows because it's hot, like the coil of a toaster. Hot objects give off light across a range of wavelengths, and the hotter the object, the shorter the wavelength where it shines brightest. This is Wien's law:

λ_peak = b ÷ T, with b = 2.898 × 10⁻³ m·K

The Sun's surface is about 5 800 K, so it peaks near 500 nm, in the middle of the visible range. Cooler stars peak in the red or infrared and look orange or red. Hotter stars peak in the ultraviolet and look blue-white. A star's color is a thermometer.

When starlight is spread into a spectrum, it's crossed by thin dark lines. Atoms in the star's outer layers absorb light only at certain wavelengths, the same ones they'd give off if heated in a lab. Matching the lines tells us which elements a star contains. Almost every star turns out to be mostly hydrogen and helium.

If you plot stars by luminosity and surface temperature, they don't land just anywhere. This plot is the Hertzsprung–Russell (HR) diagram. By tradition, temperature runs backward, hot on the left and cool on the right.

About 90% of stars lie on a band from hot and bright to cool and dim: the main sequence. Where a star sits on it depends mainly on its mass. Heavy stars are hot, blue and thousands of times more luminous than the Sun; light ones are cool, red and dim. Above the band are giants and supergiants, cool but enormous, so they still give off lots of light. Below it are white dwarfs, hot but about the size of Earth, so they're dim.

A star begins in a nebula, a cloud of gas and dust. Gravity pulls a clump together and it heats up. When the core reaches about 10 million K, hydrogen starts fusing into helium, and the outward push from that energy balances gravity. The star is now on the main sequence, where it spends most of its life. The Sun has been there for about 4.6 billion years and has roughly 5 billion to go.

When the core runs out of hydrogen, the star swells into a red giant. What happens next depends on mass:

• Sun-like stars gently shed their outer layers as a glowing planetary nebula. The core left behind is a white dwarf, which slowly cools. A white dwarf can't be more than about 1.4 solar masses.
• Stars above about 8 solar masses become red supergiants and fuse elements up to iron. Then the core collapses in a fraction of a second and the star explodes as a supernova. The core becomes a neutron star, about 20 km across, or for the heaviest stars, a black hole.

Supernovae scatter heavy elements into space. The iron in your blood and the calcium in your bones were made inside stars.

A star sends its light out equally in all directions. At distance d, that light is spread over a sphere of area 4πd², so the brightness we measure is

b = L ÷ (4πd²)

Double the distance and the same light covers four times the area, so the star looks a quarter as bright. Triple it and it looks a ninth as bright. This is the inverse-square law. Comparing two distances, b₂ = b₁ × (d₁ ÷ d₂)².

It's why a dim-looking star might be very luminous but far away. If astronomers know a star's luminosity, for example from a Cepheid variable star whose pulsing rate reveals it, they can measure its brightness and work out how far away it is.

Throw a ball up and it falls back. Throw it faster and it goes higher. Throw it at the escape velocity and it slows down forever but never stops and never returns. Setting its kinetic energy equal to the energy needed to climb out of gravity gives

v_esc = √(2GM ÷ r)

For Earth that's 11.2 km/s. Squeeze the same mass into a smaller radius and the escape velocity goes up. If an object is squeezed so small that the escape velocity reaches the speed of light, nothing, not even light, can get out. It's a black hole. The radius where this happens is the event horizon, at r = 2GM/c². For a mass equal to the Sun's, that's only about 3 km.

We can't see black holes directly, but we see what they do: stars whipping around an unseen mass at the center of our galaxy, hot gas glowing as it falls in, and gravitational waves from black holes merging.

The spectral lines of distant galaxies are shifted toward the red end: they're redshifted, so the galaxies are moving away from us. In 1927 Georges Lemaître predicted from Einstein's equations, and in 1929 Edwin Hubble showed from observations, that the farther away a galaxy is, the faster it recedes. This is the Hubble–Lemaître law:

v = H₀ × d

H₀ is the Hubble constant, about 70 km/s per megaparsec. Measurements range from about 67 to 73, and the gap is an open question. A galaxy 200 Mpc away moves away at about 14 000 km/s. It isn't that we're at the center: space itself is stretching, so every galaxy sees the others moving away, like raisins in rising dough.

Run the expansion backward and everything was once packed together, hot and dense. That's the Big Bang, about 13.8 billion years ago. Three main pieces of evidence support it:

• The expansion itself, measured by Hubble's law.
• The cosmic microwave background (CMB): a faint glow from every direction, released about 380 000 years after the Big Bang when the universe cooled enough to become transparent. The expansion has stretched it into microwaves at just 2.725 K.
• Light elements: the early universe was hot enough for fusion for a few minutes, which predicts about 25% helium by mass, close to what we measure in the oldest stars and gas clouds.

For most of history, the stars were points of light whose nature could only be guessed. Splitting their light into spectra turned astronomy into astrophysics, and within a century it had revealed how stars work and that the universe has a history.