How Big Black Holes Are, and Why Their Waves Reach Us

A gravitational wave detector on Earth registered two black holes colliding more than a billion light-years away. The obvious reaction to that sentence is that the objects involved must have been staggering in size — otherwise nothing about them could possibly still matter at that range.

They were about 210 and 170 kilometers across. Smaller than the drive from Los Angeles to San Diego.

The gap between those two facts is the whole subject of this article. The signal reached us not in spite of the objects being small but because they were, and following that inversion is what makes the rest of gravitational-wave astronomy legible: why the galaxy’s own enormous black hole is silent, why the detectors are shaped the way they are, and why the largest black holes in the universe need an instrument the size of the Milky Way to hear.

Where this came from

The starting question was one of scale: how large is the black hole at the center of the Milky Way, expressed in units that mean something — a number of Suns, or measured against the solar system.

Behind it sat a harder one. A gravitational wave had been detected from two black holes merging elsewhere in the universe, and a billion light-years is far enough that whatever happened out there should not be able to touch anything here. Something about that source has to be extreme enough to account for it. The natural guess is that the black holes were enormous — perhaps the size of the solar system, which would make them very large objects indeed.

That guess, and the reasoning that produces it, is where the article starts.

Checking the solar-system figure

The two black holes that produced the detected signal were roughly 210 and 170 kilometers across. Measuring the solar system out to Neptune’s orbit — about 9 billion kilometers — the solar-system figure overshoots by a factor of around 40 million.

“The black holes must be pretty big” is the firmer half of the guess, and it is directionally fine: 36 and 29 solar masses is heavy. The scale attached to it is what misses, and it misses by a lot.

The reasoning is worth separating from the conclusion, because the reasoning is the part that survives. Intensity falls off with distance, so a signal still detectable at extreme range implies an extreme source. For light, for sound, for nearly anything in ordinary experience, that inference holds — and it holds here too. The source was extreme.

The error is in which quantity was extreme. Not size. Compactness — which runs the opposite direction, because the objects had to be small for the event to be loud enough to cross a billion light-years at all. That inversion is the load-bearing idea in the rest of this article.

Solar-system-sized black holes do exist, and section 12 is about them. That is a separate fact rather than a partial rescue of the guess: they are not what this detector heard, and nothing in the detection points toward them.

The short answers

Sagittarius A*, the black hole at the center of the Milky Way, holds about 4.3 million Suns’ worth of mass in a ball roughly 25 million kilometers across. That is about 18 Suns lined up edge to edge, or about a sixth of the distance from Earth to the Sun. Drop it where the Sun is and it would swallow the Sun many times over — but it would not reach Mercury. Mercury’s orbit is about 116 million km across; the black hole spans roughly a fifth of that.

The two that merged were about 36 and 29 solar masses, making them roughly 210 and 170 km across. City scale, not solar-system scale.

The wave reached us because extreme compactness let two very heavy objects get within a few hundred kilometers of each other and orbit at nearly half the speed of light — and because essentially nothing in the universe absorbs a gravitational wave.

What “size” means for a black hole

A black hole has no surface. There is no shell of material to touch. What gets called its size is the event horizon: the boundary where escaping would require moving faster than light. Cross it and every available path, including every path a light beam could take, leads further in. It is a one-way surface in the geometry, not an object.

The radius of that boundary follows a rule simple enough to be suspicious:

About 3 kilometers of radius for every solar mass. Exactly linear. Double the mass, double the radius. That one number gives the size of any non-spinning black hole in the universe.

Why bigger black holes are thinner

Radius grows in proportion to mass, but volume grows as the cube of radius. So the average density inside the horizon falls off as one over mass squared. Following that out:

• A 36-solar-mass black hole packs roughly 10^16 kg into every cubic meter — about ten trillion times the average density of the Sun.
• Sagittarius A*, despite being 120,000 times heavier, sits at roughly 10^6 kg per cubic meter: only about 700 times the Sun’s average density, around 1,000 times water.
• Above roughly 140 million solar masses, the average density inside the horizon drops below water. Above a few billion, it drops below air.

This dismantles the usual mental image. “Black hole” does not mean “infinitely crushed thing” at the scale of the horizon. For the largest ones, if the mass were spread evenly through the interior volume, it would be thinner than the atmosphere in the room.

It also sets up the real point. Mass and size are not what make something a strong gravitational-wave source. The biggest black hole in this galaxy is, by the measure that actually matters, one of the least extreme objects in the discussion.

What a gravitational wave actually is

Newton’s picture: gravity is a force that mass exerts across empty space on other mass. Einstein’s replacement discards the force entirely.

In Einstein’s picture there is a four-dimensional fabric — space and time woven together — and mass and energy bend it. Anything moving “straight” through a bent region follows a curved path. The Earth is not being pulled by the Sun. The Earth is coasting in a straight line through a region the Sun has curved, and a straight line through curved geometry is an orbit.

Then the follow-up question that produces waves. If the shape of the fabric depends on where the mass is, and the mass moves, the shape has to update. That update is not instantaneous. It travels outward at exactly the speed of light.

A gravitational wave is that update, in transit. It is not something traveling through space. It is a change in the shape of space, traveling.

What it does on arrival is change distances. A passing wave stretches space along one axis while squeezing the perpendicular axis, then reverses, alternating at the wave’s frequency. Picture a ring of marbles floating freely. As the wave passes, the ring pulses — taller and narrower, then wider and shorter, then back. Nothing pushes the marbles. Each one sits exactly where it was. The distance between them is what changes.

One more requirement, and it explains why the universe is not saturated with these waves: a perfectly symmetric arrangement radiates nothing. A spherical star pulsing in and out while staying spherical emits zero. A perfect sphere spinning on its axis emits zero. What is needed is mass distributed lopsidedly and changing — the archetype being two objects whirling around each other, which drags a rotating lopsidedness around a circle and throws off a wave at twice the orbital frequency.

Why the signal comes from compactness, not size

The power a two-body system radiates in gravitational waves scales as the masses squared, divided by the separation to the fifth power. Two things matter — how much mass, and how close together — and closeness dominates violently. Halve the separation and the power rises 32-fold. Divide it by ten and the power rises 100,000-fold.

Here is the anchor that makes this concrete. The Earth orbiting the Sun is a genuine gravitational-wave source. Its output is about 200 watts — two bright light bulbs, radiated into the entire universe. At that rate the Earth’s orbit shrinks by less than the width of an atomic nucleus per lap. The Sun and Earth are not short on mass. They are simply too far apart and moving too slowly for the geometry to care.

Now change one variable. Keep tens of solar masses, but bring the two objects within a few hundred kilometers of each other.

This is where compactness becomes the entire story. A star of 30 solar masses is well over a million kilometers wide, so two of them physically cannot get closer than about a million kilometers — they would have collided and merged as gas long before. Their own bulk sets a floor on how close they can get, and that floor is far too high to radiate anything. Collapse each into a 200-km black hole and the floor collapses with it, by four orders of magnitude. A separation of a few hundred kilometers becomes geometrically permitted, and the fifth-power law pays out.

At that separation, orbital speed becomes a serious fraction of light speed. In its final moments the pair was circling roughly a hundred times per second at nearly half the speed of light.

This is the answer to the original puzzle. The event was loud because it was small. Compactness is what permits the extreme closeness; closeness is what the power law rewards. Two objects the size of the solar system carrying the same mass would drift around each other slowly and far apart, and radiate almost nothing — for the same reason the Earth and Sun manage only 200 watts.

The brightest thing in the universe, for a fifth of a second

Adding up the ledger: 36 plus 29 solar masses went in, about 62 came out. The missing three solar masses did not become light, heat, or debris. It converted directly into the energy of rippling spacetime, over roughly two tenths of a second.

Peak power: 3.6 × 10^49 watts, about 10^23 times the Sun’s output. Roughly the combined light of every star in the observable universe, and by some estimates several times more.

For a fraction of a second, inside a region 400 km wide, that collision was the most luminous event in existence. It emitted essentially no light at all.

There is a ceiling here worth knowing about, because it is what makes this class of event special rather than merely large. Combining the constant of gravity with the speed of light yields a natural unit of power — around 3.6 × 10^52 watts — that nothing in general relativity exceeds. It does not depend on the mass involved; it is a property of the theory. A black hole merger reaches within a factor of about a thousand of that ceiling. Nothing else known comes close.

Why a billion light-years doesn’t weaken it much

Two independent reasons, and both are needed.

It falls off as 1/distance, not 1/distance². Light dims by the inverse square because a telescope collects the wave’s energy, and energy spreads over a sphere whose area grows as radius squared. A gravitational-wave detector collects no energy. It measures the wave’s amplitude — the fractional stretch — and amplitude falls one power slower. Over a billion light-years, that single power of difference is worth an enormous factor in what survives the trip. The practical consequence: doubling a detector’s sensitivity multiplies the volume of universe it can survey by eight, not by 2.8.

Nothing absorbs it. This is the deeper reason, and it inverts the intuition the question started from. Gravitational waves are almost undetectable because matter barely responds to them — which is exactly why they arrive intact. Light leaving that region would have been scattered by gas, absorbed by dust, and reprocessed by plasma across a billion light-years of intervening universe. The gravitational wave passed through all of it, then through the Earth, then through everyone on it, essentially unchanged. The planet is transparent to it.

Crossing the universe does not require strength. It requires not being stopped. The same weakness that makes these waves nearly impossible to measure is what makes them nearly impossible to block — which is also why they carry information out of places light cannot escape from at all.

What actually arrived here

The strain — the fractional change in distance — was about one part in 10^21. A billion trillion.

Concretely: every distance in the room you are sitting in briefly changed by that ratio. Measured across a person’s shoulders, half a meter, the change was about 5 × 10^-22 meters. That is vastly smaller than a proton, far below any scale a body or an atom has means to respond to. Nothing happened to anyone. And yet it is literally true that the space in that room was stretched and squeezed by a collision a billion light-years away — which is the sense in which the event “reaches” us at all.

Across LIGO’s 4-kilometer arms, the same ratio produces a length change of roughly 10^-18 meters: about a thousandth of a proton’s width. That is the entire measurement.

That it is readable at all comes down to three tricks stacked together. A laser is split down two perpendicular 4-km arms. Each beam bounces about 300 times before returning, building an effective path of over a thousand kilometers. The two beams are then recombined so that when the arms are equal they cancel, leaving the output port dark. A passing wave stretches one arm while squeezing the other, the cancellation breaks, and light leaks out.

The design idea worth extracting: the instrument never measures a length. It measures the difference between two lengths. Anything affecting both arms equally — thermal drift, laser wobble, the ground settling — cancels out of the answer. On top of that, two detectors 3,000 km apart in Louisiana and Washington must record the same waveform with the correct light-travel delay between them, which is how a real signal gets separated from a truck driving past.

Why the galaxy’s own black hole is silent

Here is the rule that unifies everything above.

Black hole radius scales up with mass. Merger frequency scales down with mass. Heavier black holes are larger, so they touch at greater separations, so their final orbits are slower. The mass of the source sets the pitch of the wave it emits.

Stellar-mass mergers land squarely in the audio band, which is why the detections can be played through speakers as an audible chirp. Sagittarius A*‘s weight class, were it to merge, would produce a wave with a period of minutes to hours — completely invisible to a 4-km instrument. That is why LISA is being built with arms 2.5 million kilometers long.

Two further reasons Sagittarius A* specifically produces nothing: it is not currently merging with anything, and a lone black hole sitting still radiates nothing regardless of mass. Mass by itself does not generate gravitational waves. Changing, lopsided mass distributions do.

So how big should the black holes be?

Signal strength scales roughly as total mass to the 5/3 power, divided by distance — so doubling the mass roughly triples the strain. More mass really is louder. But the frequency constraint pulls the other way, which means every detector has a window rather than a bigger-is-better rule:

• Below ~5 solar masses (neutron stars): quiet. Detectable only relatively nearby — hundreds of millions of light-years rather than billions.
• 20–200 solar masses total: the ground-detector sweet spot. Heavy enough to be loud, light enough that the merger still happens inside the audio band.
• Above ~200 solar masses: louder in absolute terms, but the merger frequency slides below the instrument’s floor. The event falls off the bottom of its hearing.

The pair behind the first confident detection sat near the optimum for the instrument that heard them — not entirely a coincidence, since a detector finds first whatever it is best shaped to find.

The solar-system-scale black holes

Section 1 set this aside as a separate fact. Here it is.

At the centers of the largest elliptical galaxies sit black holes of tens of billions of solar masses, with event horizons several times wider than Neptune’s orbit. Genuinely solar-system-scale objects. When two of those merge — which happens when their host galaxies collide — it is the most energetic event the universe is capable of producing.

Finding one involves no laser at all. It means measuring the arrival times of pulsars across the galaxy for fifteen or twenty years and watching for a correlated wobble in when their pulses land, as the passing wave stretches and squeezes the space between them and us. A detector the size of the Milky Way, listening for a note that takes a decade to complete a single cycle.

So solar-system scale does describe a real class of black hole. But arriving at it from the distance argument was a coincidence, not a derivation: these objects are not large because their signals travel far. They are large because they spent billions of years growing, and their mergers are detectable for the same compactness reason as everything else here — just played at a frequency a million times lower.

What this leaves open

• The intermediate-mass gap. Between roughly 100 and 100,000 solar masses, detections are sparse. Whether black holes populate that range in numbers, and how they would form, is unsettled.
• How the merging pairs got close in the first place. Two black holes have to lose an enormous amount of orbital energy to reach the separation where gravitational waves take over. Whether that happens through a shared gas envelope, through gravitational encounters in dense star clusters, or some mix, is an open question.
• The nanohertz background. Pulsar timing arrays have found evidence of a low-frequency hum consistent with many supermassive pairs across the sky. Attributing it confidently to those pairs — rather than to something from the early universe — is ongoing work.

Sources

• Sagittarius A* — Britannica and Space.com — mass and event horizon scale
• GW150914 press release — LIGO Caltech — masses, distance, three solar masses radiated, near-half-light-speed collision
• Properties of the Binary Black Hole Merger GW150914 (arXiv:1602.03840) — peak luminosity 3.6 × 10^56 erg/s, source-frame masses, 410 Mpc luminosity distance
• LIGO Facts — Caltech and LIGO: The Laser Interferometer Gravitational-Wave Observatory (arXiv:0711.3041) — strain sensitivity, arm-length displacement, proton-width comparison
• Fun with Gravitational Waves — Scientific American — the ~200 watt Earth–Sun figure
• LIGO on the pulsar timing array detection and Gravitational wave physics with LISA and pulsar timing arrays — detector frequency bands
• Merging Supermassive Black Holes Will Become The Most Energetic Events Of All — Forbes — brightness relative to all starlight in the observable universe