# How Bright Can a Source in the Sky Be?

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Is there a limit to how bright a light bulb can be?

Two simple considerations set that limit. First, the source cannot emit more than the energy equivalent of its entire mass, E=Mc^2. Second, the source cannot emit the energy over a timescale shorter than the time it takes light to cross its size, because according to Einstein’s Special Relativity — energy cannot propagate faster than light. Moreover, the smallest size that the source can have is the horizon scale of the smallest black hole of its mass, GM/c^2, since no energy can escape from the interior of that horizon according to Einstein’s General Relativity.

Because the entire energy, Mc^2, and the shortest timescale over which it can be released, GM/c^3, are both proportional to the source mass, M, the ratio between them — which gives the largest luminosity possible — is a universal constant independent of mass. It equals the speed of light to the fifth power divided by Newton’s constant, c^5/G, nearly 10^{26} times larger than the luminosity of the Sun. This universal limit is rooted in classical physics with no reference to quantum mechanics.

No light bulb can be brighter than this luminosity throughout the entire Universe. This limit applies not only to light but to all possible energy carriers, namely all types of radiation — including gravitational waves, and all particles — including neutrinos.

In a new paper, I showed that the above limit translates to a maximum flux that we should expect to observe for any source in the universe as a function of its distance or cosmological redshift. This realization can also be used to set a limit on the maximum distance or redshift of any source with an observed flux but an unknown origin. In general, the redshift of a cosmological source can be inferred from the spectral lines of its host galaxy or from the absorption imprinted on its spectrum by intervening hydrogen in the intergalactic medium.

For a source with a redshift of 6, emitting when the universe was only a billion years old, the limiting observable flux happens to be similar to that emanating from a blackbody radiation bath at a temperature of ten degrees Kelvin above absolute zero, merely a few times hotter than the cosmic microwave background. The flux limit for such a source is about a million times fainter than the flux of energy we receive on Earth from the Sun, and a few times fainter than the flux from a full Moon.

In general, the highest source luminosities are expected to be emitted during the formation of compact objects, in the form of gravitational waves or a gamma-ray burst during the birth of a black hole or neutrinos when a neutron star is born out of the collapse of a star.

We observe such events, but so far all known sources, including gravitational wave signals from black hole collisions observed by LIGO-Virgo-KAGRA, fall short of the universal flux limit by orders of magnitude. A future discovery of a source that is brighter than this limit would signal new physics.

Interestingly, a similar argument can be used to describe fainter systems. For any gravitationally-bound system of mass M and size R, the characteristic velocity v provides a total kinetic energy Mv^2 of order the gravitational binding energy, GM^2/R. The minimum timescale for energy release is R/v. The ratio between the total kinetic energy and shortest time provides again a limit on the output luminosity of v^5/G, smaller by a factor of (v/c)^5 than the universal limit derived for the speed of light. This explains why most astrophysical sources radiate well below the universal luminosity limit of c^5/G.

But nature is sometimes more imaginative than we are. The good news in this context is that the flux limit applies to the brightest sources in the sky, which are the easiest for us to detect. These sources may be transient and to find them we may need to monitor the sky continuously. Within a year, the Legacy Survey of Space and Time (LSST) by the Vera C. Rubin Observatory will start taking the most detailed video of the sky with its 3.2 billion pixel camera. It would be particularly interesting to seek the brightest points of light in this amazing video archive of the Universe. The sky’s the limit.