Compact Objects & High-Energy Astrophysics: The Densest Things and the Hardest Light

On 17 August 2017 two detectors in the United States and one in Italy shook, very slightly, for about a minute and a half. Less than two seconds later a gamma-ray satellite flagged a short flash from the same patch of sky. Within hours telescopes in Chile had found a new point of light in a galaxy 130 million light-years away, and over the next weeks that light faded from blue to red. Two neutron stars, each the leftover of an exploded star and each about as wide as a city, had spiralled together and merged.

That one event showed ripples in spacetime, a burst of light, a glowing cloud of freshly made heavy elements, and a new way to measure how fast the universe expands. It is the whole subject in miniature: compact objects are the dead stars (white dwarfs, neutron stars, black holes), and high-energy astrophysics is what they do to the gas, the magnetic fields and the particles around them.

Nobody has been near any of this. A graduate does it by scaling arguments: if the flicker lasts a millisecond, the thing is smaller than a country; if the period is 33 milliseconds and slowing, here is its magnetic field. This piece lets you do those sums yourself.

Degeneracy: what holds up a dead star

A star avoids collapse because hot gas pushes back. When the fuel is gone and the heat leaks away, something else must push, and it is not heat. It is a quantum rule: no two electrons may occupy the same state. Squeeze electrons into a smaller space and each one's momentum must rise, because confining a particle makes its momentum uncertain. That momentum is a pressure, and it does not need any temperature. This is degeneracy pressure.

It has a strange consequence. For ordinary (slow) electrons, the pressure rises as density to the power 5/3. Work through the balance with gravity and a heavier white dwarf is a smaller one:

Near the top of the range the electrons move at nearly the speed of light, the pressure law softens to density to the power 4/3, and that exactly matches gravity's pull: no radius is stable at any mass beyond a critical value, the Chandrasekhar mass of about 1.4 Suns for a carbon–oxygen star. Subrahmanyan Chandrasekhar worked it out in 1930–31 on a ship to England. The practical form is a curve you can plot. A good fit to his full calculation (Nauenberg 1972) is R = 0.0112 R_☉ √(x^−2/3 − x^2/3), with x = M/1.44 M_☉.

Without JavaScript: at 0.6 Suns the curve gives a radius of about 8,700 km (a little more than Earth); at 1.0 Sun, 5,500 km; at 1.4 Suns, about 1,500 km, and the radius falls toward zero as the mass approaches 1.44.

Why does this matter beyond textbooks? A white dwarf in a binary that gathers gas toward the limit can explode as a Type Ia supernova. Because the trigger mass is nearly the same each time, the explosions are similar enough to be used as distance markers (the rung in Astrophysics & Cosmology, 34/88), though they need a calibration based on how fast each one fades. Note the honest caveat: whether the usual parent is a white dwarf growing by accretion or two white dwarfs merging is still argued, and likely both happen.

Pulsars: a lighthouse that tells you its field and its age

Past the limit, electrons and protons are crushed into neutrons, and neutron degeneracy plus the strong force holds the star up: a neutron star of roughly 1.2 to 2.3 Suns (perhaps a little more) and a radius near 12 km. The density is about 4 × 10¹⁷ kg/m³, a mountain's mass in a thimble. A neutron star's gravity gives a compactness GM/Rc² of about 0.17: the escape speed is 59% of the speed of light. Among the heaviest measured is PSR J0952−0607, about 2.35 solar masses with an uncertainty near 0.17 (Romani et al. 2022). Radii from NASA's NICER X-ray telescope fall near 12–13 km. The upper limit for neutron stars is not known exactly because the physics of matter at that density is not.

Squeeze a spinning star from the size of the Sun to 12 km and it spins up enormously (angular momentum is conserved), and its magnetic field is squeezed too. The beam of radio waves from the magnetic poles sweeps the Earth like a lighthouse: a pulsar, discovered in 1967 by Jocelyn Bell Burnell and Antony Hewish. The pulses are extremely regular, but the period slowly grows because the rotating magnet radiates away spin energy. Just two measured numbers, the period P and how fast it grows (Ṗ), give three things:

Worked for the Crab pulsar, the core left by the supernova that Chinese and other astronomers recorded in 1054: P = 33.4 ms, Ṗ = 4.2 × 10⁻¹³. That gives B near 4 × 10¹² gauss, a characteristic age of 1,260 years (the true age is about 970; the formula assumes the star started spinning infinitely fast and braking in a particular way, so treat it as a rough guide), and a spin-down power of 4.5 × 10³¹ watts, about 100,000 Suns, which is what lights the whole Crab Nebula.

Without JavaScript: the Crab (33 ms) has B near 4 × 10¹² G; the millisecond pulsar B1937+21 (1.56 ms) has about 4 × 10⁸ G and is hundreds of millions of years old; the magnetar SGR 1935+2154 (3.2 s) has about 2 × 10¹⁴ G.

Slide it. Young, strong-field pulsars sit at the top; they slow, drift to the right and down, and fade out of the radio as the period reaches several seconds. Some are rejuvenated: a neutron star in a binary can be spun back up by gas from its companion into a millisecond pulsar, which is why the lower left fills with old stars with weak fields. The fastest known spins 716 times a second; its equator moves at about 18% of light speed. At the top right, with fields of 10¹⁴–10¹⁵ G, are the magnetars. In April 2020 one of them, SGR 1935+2154, emitted a radio burst resembling the mysterious fast radio bursts, the first such burst traced to a known object in our own galaxy.

Accretion: the best engine, and the speed limit on it

Fusion turns 0.7% of hydrogen's mass into energy. Dropping gas onto a compact object does far better. A kilogram that falls onto a neutron star's surface releases about GM/R in energy per kilogram, which is 0.17 of its rest energy. Onto a black hole there is no surface, so the gas swirls in a disk and radiates as it spirals in until it reaches the innermost stable circular orbit (ISCO), after which it plunges in without radiating much. How much it radiates depends on how close the ISCO is, and that depends on the black hole's spin:

With no spin, η = 5.7%. At maximum spin it reaches 42%, and an astrophysical limit near 32% (Thorne 1974) is more realistic, because the hole's own radiation tends to cap its spin. That is eight to sixty times better than fusion, and it is why a quasar can outshine all the stars of its host galaxy from a region not much bigger than our solar system.

There is a ceiling. Light carries momentum, and the infalling gas is ionised. If the luminosity is too large, the light pushes outward on the electrons harder than gravity pulls the matching protons inward, and the inflow stalls. Setting the two forces equal gives the Eddington luminosity, which depends only on mass:

The limit gives a speed limit on growth. A hole shining at the Eddington rate grows by a factor of e (2.7) in a time t = 0.45 Gyr × η / (1 − η), about 50 million years for η = 0.1 (the Salpeter time). That clashes with a surprise: quasars with a billion Suns already existed when the universe was less than 700 million years old. ULAS J1342+0928 (redshift 7.54, about 800 million Suns; Bañados et al. 2018) and J0313−1806 (redshift 7.64, about 1.6 billion Suns; Wang et al. 2021) are examples. Start from a 100-Sun remnant of an early star and you need ln(10⁷) = 16 e-folds. Try it.

Without JavaScript: η is 5.7% for no spin, about 15.6% at spin 0.9, 32% at 0.998. A 100-Sun seed shining at Eddington needs about 0.44 Gyr to reach a billion Suns if η = 5.7% and 0.81 Gyr if η = 10%, against 0.59 Gyr available.

Notice the twist: a faster spin makes the engine more efficient, so more of the infalling mass is turned into light and less is kept, and the black hole grows slower at a given brightness. Astronomers therefore consider massive seeds (direct collapse of a gas cloud into a black hole of 10,000 or more Suns), super-Eddington bursts and mergers. Which wins is open, and the James Webb Space Telescope keeps finding black holes that look heavy for their age.

Timing and beaming: size and speed from light alone

Take a source that doubles its brightness in a time Δt. Its parts can only act in step if light has time to cross it, so it cannot be much larger than cΔt. The reasoning needs nothing else. A flicker of 1 millisecond means a region under 300 km, which is smaller than a country, so it can only be a compact object. Quasars brightening in a few days are smaller than the solar system. This is how the central engines were known to be tiny long before anyone could see them.

Now suppose the source is a blob moving close to the speed of light almost toward you. It nearly catches up with its own light, so the time between two flashes it emits is squeezed when you receive them, and it seems to cross the sky faster than light:

Nothing travels faster than light. The illusion is geometry, and it is a measurement tool: the apparent speed and the brightening together give Γ and θ. Mirabel and Rodríguez saw blobs from the X-ray binary GRS 1915+105 in 1994 move at an apparent 1.25 c; with β = 0.92 and θ = 70° the formula gives 1.26. The effect is strong in jets of galaxies (apparent speeds up to several times c in M87 and in many quasars), and in 2018 radio images of the GW170817 afterglow showed motion of about four times c, which constrained the jet's angle.

Without JavaScript: a 1 ms flicker bounds the size at about 300 km, a day at about 173 AU (one light-day), a year at one light-year. A jet with Γ = 10 seen at 6° looks about 9.9 times faster than light.

The other half of this is the counter-jet. The blob heading away is dimmed by the same factor, so a jet that shows up on one side only tells you it is moving fast. For Γ = 10 at 6° the approaching side is brighter by a factor of several million.

Cosmic accelerators: how big, how strong

Cosmic rays are charged particles, mostly protons, that arrive from space with energies up to tens of millions of times the energy of a Large Hadron Collider beam. Because magnetic fields bend them, they do not point back to their source, and for a century their origin was a mystery. A graduate has one neat sum for what an accelerator would need. A particle of charge Ze and energy E in a field B moves in a circle of radius E / (ZecB). If that is larger than the accelerator, the particle leaves. So the biggest energy that a region of size R and field B can hold is the Hillas limit (A. M. Hillas, 1984):

Check it on the LHC. Its bending magnets are 8.33 tesla over a bending radius of 2,804 m. The formula gives 7.0 TeV, the design energy per beam. Now plug in the sky: a supernova-remnant shock, with a field of about 10 microgauss (1 nanotesla) over a few parsecs, is one of the presets below. The result is a ceiling, not a prediction: real accelerators lose energy to radiation and rarely reach it.

Without JavaScript: the LHC sum gives 7.0 TeV; a supernova shock (1 nT, 5 pc, β = 0.03) gives about 1.4 PeV, the right region for the knee; a radio-galaxy lobe (10 nT, 10 kpc, β = 0.1) gives about 90 EeV.

The results are the story. Supernova remnants can reach the knee at about 3 × 10¹⁵ eV, and they are widely thought to supply most Galactic cosmic rays. The highest-energy particles, near 10²⁰ eV, need something far bigger or stronger, such as the lobes and jets of active galaxies, or something exotic; the Pierre Auger Observatory in Argentina reported in 2017 that cosmic rays above 8 EeV arrive preferentially from a direction pointing outside our galaxy. Their sources are not yet identified. Neutrinos have no charge, so they point straight back: IceCube traced one 2017 event to the blazar TXS 0506+056 (2018) and found a Seyfert galaxy, NGC 1068, in 2022.

Mergers: gravitational waves plus light

Chirps from black holes show that the waves are there. A neutron-star merger adds light, and the pair together does what neither can alone. The chirp gives the masses and, because the strain h (the stretch of space) drops as 1/d, the distance as well: the waveform tells you its own loudness at the source, so the observed loudness gives how far it is. That is a standard siren, with no distance ladder. The light gives the galaxy, and the galaxy gives the redshift.

For GW170817 the numbers were: chirp mass 1.188 solar masses, a distance of about 40 Mpc (43.8 Mpc is the central value of the best-fit analysis, with a large lopsided error because the tilt of the orbit and the distance are partly degenerate), and a host galaxy, NGC 4993, receding at about 3,000 km/s. That gives H₀ near 70 km/s/Mpc, with a range of +12 and −8 from a single event (later narrowed to roughly ±5 with radio images of the jet). Slide the numbers.

Without JavaScript: 3,017 km/s over 43.8 Mpc is 68.9 km/s/Mpc. A distance 15% smaller gives 81; 15% larger, 60. One merger cannot decide between 67 and 73; dozens could.

The rest of the event was a gift. The gamma-ray burst came 1.74 s after the merger, from a journey of 130 million years. That fixes the speed of gravity equal to the speed of light to about one part in 10¹⁵, which killed a family of alternative gravity theories. The glow that followed, a kilonova, was powered by the radioactive decay of newly made heavy elements, evidence that neutron-star mergers are one of the places where gold, platinum and many other heavy nuclei are made; how much of the universe's supply they account for is still being worked out. And the masses are changing the picture of the stellar graveyard: in 2024 the LIGO–Virgo–KAGRA team announced a merger seen in May 2023, GW230529, with a partner of 2.5 to 4.5 Suns, in the gap between the heaviest neutron stars and the lightest known black holes.

What a graduate just sees

• Degenerate stars shrink as they gain mass, and there is a mass beyond which no radius is stable.
• A pulsar's period and its slowdown give its field, its rough age and its power; a plot of the two is a family tree of neutron stars.
• Falling onto a compact object releases about 6 to 40 per cent of the rest mass as light, eight to sixty times more than fusion.
• Light pushes back: Eddington luminosity is about 10³¹ W per solar mass, and growth time is tens of millions of years at best.
• A flicker of Δt means a size under cΔt, and an apparent speed above c is a clue to a nearly head-on jet.
• An accelerator cannot hold a particle whose gyro-radius exceeds the accelerator: size times field is the budget.
• A merger with a chirp and a flash gives a distance and a redshift together.

Where it shows up next

• Galaxies & the Milky Way (36/42): the supermassive black hole at a galaxy's centre, its jets and the Eddington-limited growth shape the galaxy around it.
• Astrophysics & Cosmology (34/88): Type Ia supernovae, standard sirens and the Hubble tension all rest on compact-object physics.
• Astronomical Data & Computation (36/44): pulsar searches, transient alerts and the Event Horizon Telescope are signal-processing problems.
• Particle & Nuclear Physics (34/86): nuclear matter at neutron-star density, and the origin of heavy elements.
• In the world: pulsar timing arrays, which clock dozens of millisecond pulsars and in 2023 reported evidence of a background hum probably from pairs of supermassive black holes, X-ray space telescopes, the Pierre Auger and IceCube observatories, and the LIGO–Virgo–KAGRA network.

If you want to go deeper

• 📘 Textbook. Malcolm Longair, High Energy Astrophysics (Cambridge, 3rd edition 2011). The standard single-volume course, from radiation processes to cosmic rays and black holes.
• 📘 Textbook. Juhan Frank, Andrew King and Derek Raine, Accretion Power in Astrophysics (Cambridge, 3rd edition 2002), the classic on discs; and Stuart Shapiro and Saul Teukolsky, Black Holes, White Dwarfs, and Neutron Stars (Wiley, 1983), the standard on the stars themselves.
• 📘 Gentler. Janna Levin, Black Hole Blues and Other Songs from Outer Space (Knopf, 2016), the human story of LIGO; Kip Thorne's Black Holes and Time Warps (1994) covers the ideas.
• 🌐 Free course. MIT OpenCourseWare 8.901 Astrophysics I (Spring 2006, Deepto Chakrabarty), a graduate introduction to stellar astrophysics and galactic dynamics.