Eddington limit

The Eddington limit, or Eddington luminosity was first worked out by Arthur Eddington. It is a natural limit to the normal luminosity of stars. The state of balance is a hydrostatic equilibrium. When a star exceeds the Eddington limit, it loses mass with a very intense radiation-driven stellar wind from its outer layers.

Eddington's models treated a star as a sphere of gas held up against gravity by internal thermal pressure. Eddington showed that radiation pressure was necessary to prevent collapse of the sphere.^[1]

Most massive stars have luminosities far below the Eddington luminosity, so their winds are mostly driven by the less intense line absorption.^[2] The Eddington limit explains the observed luminosity of accreting black holes such as quasars.

Super-Eddington luminosities

Eddington limit explains the very high mass loss rates seen in the outbursts of η Carinae in 1840–1860.^[3] The regular stellar winds can only stand for a mass loss rate of about 10⁻⁴–10⁻³ solar masses per year. Mass loss rates of up to 0.5 solar masses per year are needed to understand the η Carinae outbursts. This can be done with the help of the super-Eddington broad spectrum radiation driven winds.

Gamma-ray bursts, novae and supernovae are examples of systems exceeding their Eddington luminosity by a large factor for very short times, resulting in short and highly intensive mass loss rates. Some X-ray binaries and active galaxies are able to maintain luminosities close to the Eddington limit for very long times. For accretion powered sources such as accreting neutron stars or cataclysmic variables (accreting white dwarfs), the limit may act to reduce or cut off the accretion flow. Super-Eddington accretion onto stellar-mass black holes is one possible model for ultraluminous X-ray sources (ULXs).

For accreting black holes, all the energy released by accretion does not have to appear as outgoing luminosity, since energy can be lost through the event horizon, down the hole. Effectively, such sources may not conserve energy.

Most luminous known K- and M-type supergiants

Name	Luminosity (L☉)	Effective temperature (K)	Spectral type	Notes	References
LGGS J013312.26+310053.3	575,000	4,055			[4]
LGGS J004520.67+414717.3	562,000	–	M1I	Likely not a member of the Andromeda Galaxy, should be treated with caution in regards to the H–D limit.[5]	[5]
LGGS J013339.28+303118.8	479,000	3,837	M1Ia		[4]
Stephenson 2 DFK 49	390,000	4,000	K4	Another paper estimate a much lower luminosity (245,000 L☉)[6]	[7]
HD 269551 A	389,000	3,800	K/M		[8]
WOH S170	380,000	3,750	M	Large Magellanic Cloud membership uncertain.	[8]
RSGC1-F02	363,000	3660	M2		[9]
LGGS J013418.56+303808.6	363,000	3,837			[4]
LGGS J004428.12+415502.9	339,000	–	K2I		[5]
AH Scorpii	331,000	3,682	M5Ia		[10]
SMC 18592	309,000[11] - 355,000[8]	4,050[8]	K5–M0Ia
LGGS J004539.99+415404.1	309,000	–	M3I		[5]
LGGS J013350.62+303230.3	309,000	3,800			[8]
HV 888	302,000	3,442[12]–3,500[13][14]	M4Ia		[11]
RW Cephei	300,000	4,400	K2Ia-0		[15]
LGGS J013358.54+303419.9	295,000	4,050			[8]
GCIRS 7	295,000	3,600[16]	M1I		[17]
SP77 21-12	295,000	4,050	K5-M3		[8]
EV Carinae	288,000	3,574[18]	M4.5Ia		[19]
HV 12463	288,000	3,550	M	Probably not a LMC member.	[8]
LGGS J003951.33+405303.7	288,000	–			[5]
LGGS J013352.96+303816.0	282,000	3,900			[8]
RSGC1-F13	282,000	3,590			[9]
WOH G64	282,000	3,400	M5I	Likely the largest known star.	[20]
Westerlund 1 W26	275,000	3,782	M0.5-M6Ia		[21]
LGGS J004731.12+422749.1	275,000	–			[5]
VY Canis Majoris	270,000	3,490	M3–M4.5		[22]
Mu Cephei	269,000+111,000 −40,000	3750	M2 Ia		[23]
LGGS J004428.48+415130.9	269,000		M1I		[5]
RSGC1-F01	263,000	3,450	M5		[9]
LGGS J013241.94+302047.5	257,000	3,950			[8]
LMC 145013	251,000[11] - 339,000[8]	3,950[8]	M2.5Ia–Ib
LMC 25320	251,000	3,800	M		[8]