List of most massive stars
Encyclopedia
This is a list of the most-massive star
s so far discovered. The list is ordered by solar mass
(1 solar mass = the mass of Earth's Sun
).
Stellar mass is the most important attribute of a star. Combined with chemical compositions, mass determines a star’s luminosity
, its physical size, and its ultimate fate. Due to their mass, most of the stars below will eventually go supernova
or hypernova
, and form black hole
s.
The masses listed in the table below are inferred from theory, using difficult measurements of the stars’ temperatures and absolute brightnesses. All the listed masses are uncertain: both the theory and the measurements are pushing the limits of current knowledge and technology. Either measurement or theory, or both, could be incorrect. An example is VV Cephei
, which, depending on which property of the star is examined, could be between 25 to 40, or 100 solar masses.
Massive stars are rare; astronomer
s must look very far from the Earth
to find one. All the listed stars are many thousands of light years away, and that alone makes measurements difficult. In addition to being far away, it seems that most stars of such extreme mass are surrounded by clouds of outflowing gas; the surrounding gas obscures the already difficult-to-obtain measurements of the stars’ temperatures and brightnesses, and greatly complicates the issue of measuring their internal chemical compositions. For some methods, different chemical composition leads to different mass estimates.
In addition, the clouds of gas obscure observations of whether the star is just one supermassive star, or instead a multiple star
system. A number of the stars below may actually consist of two or more companions in close orbit, each star being massive in itself, but not necessary supermassive. Alternatively, it is possible for a multiple-star system to still have one (or more) supermassive star, with one (or more) much smaller companion(s). Without being able to see inside of the surrounding cloud, it is difficult to know which scenario might be the case.
Amongst the most reliable listed masses are NGC 3603-A1 and WR20a+b
, which were obtained from orbital measurements. They are both members of (different) binary star
systems, and it is possible to measure in both cases the individual masses of the two stars by studying their orbital motion, via Kepler's laws of planetary motion
. This involves measuring their radial velocities
and also their light curves, as both stars are eclipsing binaries.
Also there are a number of supernovae and hypernovae remnants whose precursor stars' masses can be estimated based on pre-super/hypernova observations, the energy of the super/hypernova, and the type of super/hypernova event. These stars (if they had not exploded) would have easily made appearances in this list (however they are not shown below).
es. Masses are their current assumed mass, not their initial (formation) mass:
s are the end point evolution of massive stars. Technically they are not stars, as they no longer generate heat and light via nuclear fusion in their cores.
grows to a size beyond 120 solar mass
es, something drastic must happen. Although the limit can be stretched for very early Population III stars, if any stars existed above 120 solar mass, they would challenge current theories of stellar evolution
.
The limit on mass arises because stars of greater mass have a higher rate of core energy generation, which is higher far out of proportion to their greater mass. For a sufficiently massive star, the outward pressure
of radiant energy
generated by nuclear fusion
in the star’s core exceeds the inward pull of its own gravity. This is called the Eddington limit. Beyond this limit, a star ought to push itself apart, or at least shed enough mass to reduce its internal energy generation to a lower, maintainable rate. In theory, a more massive star could not hold itself together, because of the mass loss resulting from the outflow of stellar material.
Studying the Arches cluster
, which is the densest known cluster of stars in our galaxy, astronomers have confirmed that stars in that cluster do not occur any larger than about 150 solar masses.
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
s so far discovered. The list is ordered by solar mass
Solar mass
The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...
(1 solar mass = the mass of Earth's Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
).
Stellar mass is the most important attribute of a star. Combined with chemical compositions, mass determines a star’s luminosity
Luminosity
Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...
, its physical size, and its ultimate fate. Due to their mass, most of the stars below will eventually go supernova
Supernova
A supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...
or hypernova
Hypernova
Hypernova , also known as a type 1c Supernova, refers to an incredibly large star that collapses at the end of its lifespan...
, and form black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
s.
Uncertainties and caveats
Most of the masses listed below are contested, and being the subject of current research, are constantly being revised.The masses listed in the table below are inferred from theory, using difficult measurements of the stars’ temperatures and absolute brightnesses. All the listed masses are uncertain: both the theory and the measurements are pushing the limits of current knowledge and technology. Either measurement or theory, or both, could be incorrect. An example is VV Cephei
VV Cephei
VV Cephei, also known as HD 208816, is an eclipsing binary star system located in the constellation Cepheus, approximately 2,400 light years from Earth.Size, mass and luminosity estimates are all considerably uncertain due to insufficient knowledge of the Cephei star system: Professor Kaler writes...
, which, depending on which property of the star is examined, could be between 25 to 40, or 100 solar masses.
Massive stars are rare; astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
s must look very far from the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
to find one. All the listed stars are many thousands of light years away, and that alone makes measurements difficult. In addition to being far away, it seems that most stars of such extreme mass are surrounded by clouds of outflowing gas; the surrounding gas obscures the already difficult-to-obtain measurements of the stars’ temperatures and brightnesses, and greatly complicates the issue of measuring their internal chemical compositions. For some methods, different chemical composition leads to different mass estimates.
In addition, the clouds of gas obscure observations of whether the star is just one supermassive star, or instead a multiple star
Multiple star
A multiple star consists of three or more stars which appear from the Earth to be close to one another in the sky. This may result from the stars being physically close and gravitationally bound to each other, in which case it is physical, or this closeness may be merely apparent, in which case...
system. A number of the stars below may actually consist of two or more companions in close orbit, each star being massive in itself, but not necessary supermassive. Alternatively, it is possible for a multiple-star system to still have one (or more) supermassive star, with one (or more) much smaller companion(s). Without being able to see inside of the surrounding cloud, it is difficult to know which scenario might be the case.
Amongst the most reliable listed masses are NGC 3603-A1 and WR20a+b
Westerlund 2
Westerlund 2 is a young massive obscured star cluster with an estimated age of about one or two million years. It contains some of the hottest, brightest, and most massive stars known...
, which were obtained from orbital measurements. They are both members of (different) binary star
Binary star
A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...
systems, and it is possible to measure in both cases the individual masses of the two stars by studying their orbital motion, via Kepler's laws of planetary motion
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....
. This involves measuring their radial velocities
Radial velocity
Radial velocity is the velocity of an object in the direction of the line of sight . In astronomy, radial velocity most commonly refers to the spectroscopic radial velocity...
and also their light curves, as both stars are eclipsing binaries.
Stellar evolution
A number of the stars may have started out with even greater masses than those currently estimated, but due to the huge amount of gas they outflow, and sub-supernova and supernova impostor explosion events, have lost many tens of solar masses of material.Also there are a number of supernovae and hypernovae remnants whose precursor stars' masses can be estimated based on pre-super/hypernova observations, the energy of the super/hypernova, and the type of super/hypernova event. These stars (if they had not exploded) would have easily made appearances in this list (however they are not shown below).
List of the most massive stars
Known stars with an estimated mass of 25 or greater solar massSolar mass
The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...
es. Masses are their current assumed mass, not their initial (formation) mass:
| Star name | Solar mass |
|---|---|
| R136a1 R136a1 R136a1 is a blue hypergiant star and the most massive star known. It is an estimated 265 solar masses. The star is also the most luminous at 8,700,000 times the luminosity of the Sun.... |
265–320 |
| WR 101e | 150–160 |
| HD 269810 HD 269810 |- style="vertical-align: top;"| Distance | 170,000 LyHD 269810 or HDE 269810 or R 122 in the Large Magellanic Cloud is a blue star. It is one of the most massive stars known, at 150 solar masses.-External links:****... |
150 |
| Peony Nebula Star WR 102ka WR 102ka also known as the Peony Nebula Star or Peony star is a Wolf-Rayet star that is one of several candidates for the most luminous known star in our Milky Way Galaxy. Peony nebula star is a hypergiant luminous blue variable star... |
150 |
| LBV 1806-20 | 130–200 |
| HD 93129 A HD 93129A HD 93129A is one of the most luminous stars in the Milky Way. This very young blue hypergiant is an O-type hypergiant located about 7500 light-years from Earth in the bright nebula NGC 3372, the same nebula that harbors other super luminous stars, like Eta Carinae.HD 93129A is actually the brighter... + B |
A=120–127, B=80 |
| HD 93250 HD 93250 HD 93250 is a blue main sequence star in cluster .... |
118 |
| NGC 3603-A1 | A=116, B=89 |
| Pismis 24-1 Pismis 24-1 Pismis 24-1 is part of the open cluster Pismis 24 within the nebula NGC 6357 about 8150 light-years away. Pismis 24-1 is the largest and more brilliant of the visible stars of this cluster, and is one of the most massive and luminous stars known... A + B |
A=100–120, B=100 |
| Arches cluster Arches Cluster The Arches Cluster is the densest known star cluster in the Milky Way, and islocated about 100 light years away from the center of our galaxy, in the constellation Sagittarius.... |
Many stars, 100–130 |
| Pismis 24-17 Pismis 24-1 Pismis 24-1 is part of the open cluster Pismis 24 within the nebula NGC 6357 about 8150 light-years away. Pismis 24-1 is the largest and more brilliant of the visible stars of this cluster, and is one of the most massive and luminous stars known... |
100 |
| Hineliun | 100 |
| S Doradus S Doradus S Doradus is the brightest star in the Large Magellanic Cloud, a satellite of the Milky Way. A hypergiant, it is one of the most luminous stars known , but so far away that it is invisible to the naked eye.This star belongs to its own eponymous S Doradus class of variable stars S Doradus is the... |
100 |
| Eta Carinae | 90–100 |
| Cygnus OB2-12 Cygnus OB2-12 Cygnus OB2-12 is an extremely bright blue hypergiant with an absolute bolometric magnitude of -12.2, which approaches the upper limit believed possible for normal single stars.... |
92 |
| WR20 a + b Westerlund 2 Westerlund 2 is a young massive obscured star cluster with an estimated age of about one or two million years. It contains some of the hottest, brightest, and most massive stars known... |
A=83, B=82 |
| The Pistol Star | 80–150 |
| Melnick 42 Melnick 42 Melnick 42 is a supermassive blue giant star in the Tarantula Nebula in the Large Magellanic Cloud, located in the constellation Dorado. With its bolometric luminosity of ca. 2,000,000 it's one of the most luminous stars of the Tarantula Nebula, being outshined by the hypermassive star R136a1.... |
80–100 |
| HD 97950 HD 97950 HD 97950, is a multiple system consisting of a core of 4 stars A1-A3 and B, plus 5 other stars. The system is sometimes considered a stellar cluster.... |
80 |
| Sk-71 51 | 80 |
| R 126 | 70 |
| Companion to M33 X-7 | 70 |
| LY Aurigae LY Aurigae LY Aurigae is an eclipsing binary hypergiant of Beta Lyr type in the constellation Auriga.-References:* * * *... |
64 |
| LH54-425 A + B | A=62, B=37 |
| Var 83 Var 83 Var 83 is a blue hypergiant in the constellation Triangulum, in the Triangulum Galaxy. With its bolometric luminosity of ±2,240,000 it is one of the most luminous stars known.... in M33 M33 M33, M-33, or M.33 may refer to:* M-33 , a state highway in Michigan* M33 cluster bomb, a Cold War-era U.S. biological cluster bomb* HMS M33, an M29-class monitor warship of the Royal Navy... |
60–85 |
| Sher 25 Sher 25 Sher 25 is an old blue supergiant star located approximately 20,000 light years from the Sun in the H II region NGC 3603 of the Milky Way galaxy. It's a spectral type B1.5Iab star with an apparent magnitude is 12.2, and located at right ascension , declination in the constellation Carina... in NGC 3603 |
60 |
| Zeta-1 Scorpii | 60 |
| Zeta Puppis Zeta Puppis Zeta Puppis is a star in the constellation of Puppis. It is also known by the traditional names Naos and Suhail Hadar in Arabic.... |
59 |
| WR22 | 55–74 |
| Plaskett A + B Plaskett's star Plaskett's Star is a spectroscopic binary at a distance of around 6600 light-years... |
A=43, B=51 |
| AG Carinae AG Carinae AG Carinae is a star in the constellation Carina. It is classified as a luminous blue variable and is one of the most luminous stars in the Milky Way. The large distance and intervening dust mean that the star is not visible to the naked eye; its apparent brightness varies irregularly between... |
50 |
| WR102c | 45–55 |
| IRS-8* | 44.5 |
| HD 5980 HD 5980 HD 5980 is a binary star in NGC 346 nebula. It is one of the brightest stars in the Small Magellanic Cloud, and one of the most luminous stars known. HD 5980 A is probably a luminous blue variable of about 40–60 solar masses, while HD 5980 B is an evolved Wolf–Rayet star of about 30 solar masses.... A + B |
A=40–62, B=30 |
| DL Crucis DL Crucis DL Crucis is a variable star in the constellation Crux.-References:*... |
40–50 |
| Epsilon Orionis Epsilon Orionis Alnilam is a large blue supergiant star in the constellation of Orion. Its Flamsteed designation is 46 Orionis.... |
40 |
| HD 148937 | 40 |
| IRAS 05423-7120 | 40 |
| Rho Cassiopeiae Rho Cassiopeiae Rho Cassiopeiae is a yellow hypergiant star in the constellation Cassiopeia. It is about away from Earth, yet can still be seen by the naked eye , as it is 550,000 times as luminous as the Sun. On average, it has an absolute magnitude of −7.5, making it one of the most luminous stars known... |
40 |
| RW Cephei RW Cephei RW Cephei is an M-class red hypergiant star in the constellation Cepheus. One of the largest stars known, RW Cephei is estimated at 1650 solar radii. RW Cephei, while nearly as large as the orbit of Jupiter, is not as large as other stars in the constellation of Cephus, namely V354 Cephei and VV... |
40 |
| Theta1 Orionis C | 40 |
| Xi Persei Xi Persei Xi Persei is a star in the constellation Perseus. It has the traditional name Menkib . Menkib has an apparent magnitude of +4.042 and is classified as a blue giant . It is approximately 1800 light years from Earth.Its apparent luminosity is 13,500 times that of the Sun... |
40 |
| V382 Carinae V382 Carinae V382 Carinae, also known as x Carinae , is a star in the constellation Carina.V382 Carinae is a yellow G-type hypergiant with a mean apparent magnitude of +3.93. It is 5930.90 light years from Earth. It is classified as a Cepheid variable star and its brightness varies from magnitude +3.84 to... |
39 |
| Companion to NGC300 X-1 | 38 |
| Cluster R136a R136a R136, formally known as RMC 136, is a super star cluster near the center of the 30 Doradus complex , in the Large Magellanic Cloud. It is a young star cluster, 1-2 million years old, of giant and supergiant stars. The majority of its stars are of spectral type O3, with 39 confirmed O3-type stars... |
12 stars, all 37–76 |
| Chi2 Orionis | 35–40 |
| Companion to IC10 X-1 | 35 |
| Nu Aquilae Nu Aquilae Nu Aquilae is a star in the constellation Aquila.Nu Aquilae is a yellow-white F-type supergiant with an apparent magnitude of +4.64. It is at least 3000 light years from Earth and lies close to the celestial equator.-References:... |
30-45 |
| VY Canis Majoris VY Canis Majoris VY Canis Majoris is the largest known star and also one of the most luminous. Located in the constellation Canis Major, it is a red hypergiant, between 1800 and 2100 solar radii, 8.4–9.8 astronomical units in radius, about 3.0 billion km or 1.9 billion miles in diameter, and about 1.5 kiloparsecs ... |
30–40 |
| 19 Cephei 19 Cephei 19 Cep is a triple star.-References:*... |
30–35 |
| Gamma Velorum Gamma Velorum Gamma Velorum is a star system in the constellation Vela. At magnitude +1.7, it is one of the brightest stars in the night sky. It has the traditional names Suhail and Suhail al Muhlif, which confusingly also apply to Lambda Velorum... A |
30 |
| P Cygni P Cygni P Cygni is a variable star in the constellation Cygnus. The designation "P" was originally assigned by Johann Bayer in Uranometria as a nova.... |
30 |
| R 66 | 30 |
| Eta Canis Majoris Eta Canis Majoris Eta Canis Majoris is a star in the constellation Canis Major. It has the traditional name Aludra.The name Aludra originates from the Arabic: عذرا al-‘aðrā "the virgin"... |
30 |
| Zeta Orionis | 28 |
| IRS 15 | 26 |
| VV Cephei VV Cephei VV Cephei, also known as HD 208816, is an eclipsing binary star system located in the constellation Cepheus, approximately 2,400 light years from Earth.Size, mass and luminosity estimates are all considerably uncertain due to insufficient knowledge of the Cephei star system: Professor Kaler writes... |
25–40 |
| Alpha Camelopardalis Alpha Camelopardalis Alpha Camelopardalis is an O-type supergiant star, with an apparent visual magnitude of approximately 4.301. It is the third brightest star in the constellation of Camelopardalis, the first and second brightest being β Camelopardalis and CS Camelopardalis, respectively... |
25–30 |
| 6 Cassiopeiae 6 Cassiopeiae 6 Cassiopeiae is an A type bright supergiant or hypergiant. It is about 25 times as massive as the Sun.... |
25 |
| EZ Canis Majoris EZ CMa EZ Canis Majoris is a Wolf-Rayet star in the constellation of Canis Major. It has an apparent visual magnitude which varies between 6.71 and 6.95.... |
25 |
| KY Cygni KY Cygni KY Cygni is a red supergiant star located in the constellation Cygnus. It is one of the largest stars known, at about 1,420 or more times the Sun's diameter, and is also one of the most luminous, with about 300,000 or more times the Sun's luminosity... |
25 |
| Mu Cephei Mu Cephei Mu Cephei , also known as Herschel's Garnet Star, is a red supergiant star in the constellation Cepheus. It is one of the largest and most luminous stars known in the Milky Way... |
25 |
| V509 Cassiopeiae V509 Cassiopeiae V509 Cassiopeiae is a star in the constellation Cassiopeia.V509 Cassiopeiae is a yellow-white G-type hypergiant with a mean apparent magnitude of +5.10. It is at least 7800 light years from Earth. It is classified as a semiregular variable star and its brightness varies from magnitude +4.75 to... |
25 |
| NGC 7538 NGC 7538 NGC 7538, near the more famous Bubble Nebula, is located in the constellation Cepheus. It is located about 9,100 light years away from earth. It is home to the biggest yet discovered protostar which is about 300 times the size of our Solar System. It is located in the Perseus Spiral Arm of the... S |
20–40 |
| S Monocerotis A S Monocerotis S Monocerotis, also known as 15 Monocerotis, is a massive variable star system located in the constellation Monoceros. It is a spectroscopic binary system with an orbital... |
18–30 |
| WR47 | 8–48 |
Black holes
Black holeBlack hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
s are the end point evolution of massive stars. Technically they are not stars, as they no longer generate heat and light via nuclear fusion in their cores.
- Micro black holeMicro black holeMicro black holes are tiny black holes, also called quantum mechanical black holes or mini black holes, for which quantum mechanical effects play an important role....
s are hypothetical black holes. They can be created by particle accelerators. - Stellar black holeStellar black holeA stellar black hole is a black hole formed by the gravitational collapse of a massive star. They have masses ranging from about 3 to several tens of solar masses...
s are objects with approx. 4-15 times the mass of our Sun. - Intermediate-mass black holeIntermediate-mass black holeAn Intermediate-mass black hole is a black hole whose mass is significantly more than stellar black holes yet far less than supermassive black holes...
s range from 100-10000 times the mass of our Sun. - Supermassive black holeSupermassive black holeA supermassive black hole is the largest type of black hole in a galaxy, in the order of hundreds of thousands to billions of solar masses. Most, and possibly all galaxies, including the Milky Way, are believed to contain supermassive black holes at their centers.Supermassive black holes have...
s are in the range of millions or billions of solar masses.
Eddington's size limit
Astronomers have long theorized that as a protostarProtostar
A protostar is a large mass that forms by contraction out of the gas of a giant molecular cloud in the interstellar medium. The protostellar phase is an early stage in the process of star formation. For a one solar-mass star it lasts about 100,000 years...
grows to a size beyond 120 solar mass
Solar mass
The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...
es, something drastic must happen. Although the limit can be stretched for very early Population III stars, if any stars existed above 120 solar mass, they would challenge current theories of stellar evolution
Stellar evolution
Stellar evolution is the process by which a star undergoes a sequence of radical changes during its lifetime. Depending on the mass of the star, this lifetime ranges from only a few million years to trillions of years .Stellar evolution is not studied by observing the life of a single...
.
The limit on mass arises because stars of greater mass have a higher rate of core energy generation, which is higher far out of proportion to their greater mass. For a sufficiently massive star, the outward pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
of radiant energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
generated by nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
in the star’s core exceeds the inward pull of its own gravity. This is called the Eddington limit. Beyond this limit, a star ought to push itself apart, or at least shed enough mass to reduce its internal energy generation to a lower, maintainable rate. In theory, a more massive star could not hold itself together, because of the mass loss resulting from the outflow of stellar material.
Studying the Arches cluster
Arches Cluster
The Arches Cluster is the densest known star cluster in the Milky Way, and islocated about 100 light years away from the center of our galaxy, in the constellation Sagittarius....
, which is the densest known cluster of stars in our galaxy, astronomers have confirmed that stars in that cluster do not occur any larger than about 150 solar masses.
See also
- Luminous blue variableLuminous blue variableLuminous blue variables, also known as S Doradus variables, are very bright, blue, hypergiant variable stars named after S Doradus, the brightest star of the Large Magellanic Cloud. They exhibit long, slow changes in brightness, punctuated by occasional outbursts in brightness during substantial...
- Wolf-Rayet starWolf-Rayet starWolf–Rayet stars are evolved, massive stars , which are losing mass rapidly by means of a very strong stellar wind, with speeds up to 2000 km/s...
- HypergiantHypergiantA hypergiant is a star with a tremendous mass and luminosity, showing signs of a very high rate of mass loss.-Characteristics:...
- List of least massive stars
- List of largest known stars
- List of most luminous stars
- List of brightest stars
- Lists of stars
- SupergiantSupergiantSupergiants are among the most massive stars. They occupy the top region of the Hertzsprung-Russell diagram. In the Yerkes spectral classification, supergiants are class Ia or Ib . They typically have bolometric absolute magnitudes between -5 and -12...