The Final States

Section 5 of 6

Observational Evidence

Part 5: Observational Evidence

How do we know neutron stars and black holes are real?

Neither object is easy to observe directly: neutron stars are tiny and often faint, and black holes emit no light from inside the event horizon. So the evidence is mostly indirect — but indirect does not mean weak. It is strong because many independent observations point to the same physical models.

Evidence for neutron stars

Observable	Model	Inference
Regular radio or X-ray pulses	rotating magnetized neutron star	pulsars are compact, rapidly rotating remnants
Millisecond periods	radius must be tens of km or less	normal stars are ruled out
Pulsar glitches	solid crust coupled to fluid/superfluid interior	neutron stars have internal structure
X-ray bursts in binaries	accretion onto a compact surface	some compact objects have surfaces
Neutron-star mergers	gravitational waves from dense-object inspiral	neutron stars merge and constrain dense matter

Observable

A radio source pulses every few milliseconds

Extremely regular pulses, fast enough to act as a clock.

Model

A rotating lighthouse beam

A beam sweeps across Earth once per rotation of a magnetized neutron star.

Inference

The source must be compact enough to rotate that fast

A neutron star explains the period, compactness, magnetic field, and stability.

Evidence for black holes

Observable	Model	Inference
X-ray binaries with compact objects above $\sim 3\,M_\odot$	accretion onto an object too massive to be a neutron star	stellar-mass black hole
No surface emission from the compact object	event horizon rather than material surface	black-hole model favored
Stellar orbits around Sgr A*	Keplerian orbits around an unseen compact mass	$\sim 4 \times 10^6\,M_\odot$ inside a tiny region
Gravitational waves from mergers	inspiral, merger, and ringdown predicted by GR	black-hole binaries exist
Event Horizon Telescope images	horizon-scale emission and shadow	strong-field GR near supermassive black holes

Artist's rendering of the Cygnus X-1 system showing a large blue supergiant star on the right with gas streaming toward a black hole on the left. The gas forms a glowing orange-red accretion disk spiraling inward, with narrow blue-white jets shooting perpendicular to the disk from near the black hole. — Figure 9Cygnus X-1, the first strong black-hole candidate. A stellar-mass black hole (~21 solar masses) accretes gas from its blue supergiant companion (HDE 226868). The infalling matter forms a swirling accretion disk heated to millions of kelvin, producing intense X-rays, with relativistic jets perpendicular to the disk. The black hole is inferred from the X-ray luminosity and the companion's orbit.NASA/CXC

Cygnus X-1 is a classic black-hole candidate. We do not see the black hole directly; we infer it from the companion star’s orbit, the mass of the compact object, and the intense X-ray emission from accretion of gas.

Accretion

The process in which gas falls onto a compact object. As the gas loses gravitational potential energy it heats up and can emit X-rays — the glow that lets us detect otherwise-invisible neutron stars and black holes in binaries.

Observable

A gravitational-wave signal that swept up in frequency and amplitude

LIGO detected a chirp whose frequency and amplitude changed rapidly with time.

Model

Two black holes spiraling together (GR waveform)

General relativity predicts the inspiral-merger-ringdown waveform of a binary black hole.

Inference

A binary black-hole merger

The initial black holes had masses of tens of solar masses, and several solar masses of energy were radiated as gravitational waves.

Worked Example 2Sgr A* — the Milky Way's Supermassive Black Hole

Problem

The black hole at the Galactic center has $M \approx 4 \times 10^6\,M_\odot$ . Find its Schwarzschild radius and compare it to the Sun’s radius and to 1 AU.

StepSchwarzschild radius by scaling

$R_s \approx 3.0\,\mathrm{km}\,(4 \times 10^6) = 1.2 \times 10^7\,\mathrm{km}$

StepCompare to the Sun and to 1 AU

$\frac{R_s}{R_\odot} = \frac{1.2 \times 10^7}{7 \times 10^5} \approx 17, \qquad \frac{R_s}{1\,\mathrm{AU}} = \frac{1.2 \times 10^7}{1.5 \times 10^8} = 0.08$

Dimensional check

Both comparisons are ratios of kilometers to kilometers, so they are dimensionless ✓.

Result

$R_s \approx 0.08\,\mathrm{AU}.$ Even a four-million-solar-mass black hole has an event horizon smaller than Mercury’s orbit — about 17 solar radii.

Quick check

An unseen object has mass $M = 8\,M_\odot$ , strong X-ray emission from accretion, no evidence for a surface, and a rapidly orbiting companion. Why is the black-hole model favored over a neutron star?