All told, the rate of
nuclear fusion in the core of a star is
roughly proportional to the fourth power of its mass.
(2008-08-17) Brown dwarves are substellar objects
Nuclear fusion won't ignite in bodies whose mass is less than 8% the mass of the Sun.
A brown dwarf
is a "failed star" whose mass is too small to generate
a core temperature high enough to ignite nuclear fusion.
However, gravitation can still release directly enough energy to provide a
brown dwarf with a definite glow of its own.
(Such processes were thought to provide all
the energy of stars before the discovery of nuclear reactions.)
Lord Kelvin (1824-1907)
advocated a very young Solar System using that argument. He
showed thermodynamically that the Sun could not be much more than a few million years old
"unless sources now unknown to us are prepared in the great storehouse of creation".
Kelvin lived to get a glimpse of what those other sources of energy are:
In 1896, the discovery of natural radioactivity (nuclear fission)
by Henri Becquerel (1852-1908;
paved the way for a detailed explanation of the nuclear processes
(fusion) powering ordinary stars, as first given in 1938 by Hans Bethe (1906-2005;
and Carl von Weizsäcker (1912-2007).
The Sun and the Earth were formed essentially together, about 4.54 billion years ago.
All brown dwarves are roughly the same size,
because the density of a brown dwarf is proportional to its mass.
They are roughly the same size as Jupiter, although
brown dwarves can be 15 to 80 times more massive
The density of a brown dwarf can't be much more than 70 g/cc, which is
13 times the average density of the Earth (5.515 g/cc)
or 50 times the average density of Jupiter itself (1.33 g/cc).
Beyond that point, fusion ignites.
I remember seeing the French term (naine brune)
used well before 1975, but this could very well be a case of
I am told that the term "brown dwarf" was actually coined in 1975 by
Jill Tarter (1944-)
in her doctoral dissertation (to lift the ambiguity of the prior term "black dwarf",
which is still used to denote the ultimate cold fate
of an ordinary star).
(2011-08-12) Red dwarfs are the smallest proper stars.
Stars that can live trillions of years.
The glow of a red dwarf comes from nuclear fusion and is thus very different
from the glow of a young brown dwarf (powered by fairly recent gravitational collapse).
However, both types of object may look alike and can be difficult to tell apart
without a deep anaysis of observational data.
(2008-08-17) The Jeans Mass (1902)
The mass above which a gas at temperature T collapses gravitationally.
In 1902, Sir James Jeans (1877-1946)
derived a formula for the concept which is now named after him.
He used a simplifying assumption which became known as the Jeans swindle
because it's not self-consistent (if a cloud is large enough to collapse,
it cannot be embedded in a larger cloud which is not itself collapsing).
This flaw was corrected by C. Hunter in 1962.
(2006-11-28) The Main Sequence
How average stars are born, burn and die.
(2011-09-05) Metallicity (Z)
The abundance of elements heavier than hydrogen and helium (by mass).
astronomers use the blanket term metal for any chemical
element other than hydrogen and helium (which are essentially the only
two primordial elements manufactured just after the
Big Bang, ignoring trace amounts of primordial lithium).
The metallicity (Z) of an astronomical object is defined as the fraction
of its total mass which comes from elements heavier than helium.
For example, the metallicity of the Sun is Z = 0.02
because 98% of the mass of the Sun comes from hydrogen and helium.
Eta Carinae (HST, 1996)
120 solar masses, 8000 light-years away.
Eta Carinae & Hypergiants
Stable stars cannot be more massive than Eddington's limit.
Conceivably, a very massive star could be so bright as to produce an outward
large enough to overcome the inward pull exerted by gravity on its
outer layers of gas. Such a star would expel its own outer shell;
it simply wouldn't be stable.
Shown at left is a star which is thought to approach Eddington's limit.
On July 21, 2010, the discovery of a monstrous hypergiant,
dubbed R136a1, was announced
by a team led by Paul Crowther
(University of Sheffield).
R136a1 is, by far, the most massive star ever observed.
Its mass is estimated to be 265 times that of the Sun,
which makes it about twice the previous estimate of Eddington's limit
(i.e., 150 solar masses ).
R136a1 is 165 000 light-years away, in a compact young star cluster
(RMC 136a) at the core of the
on the leading edge of the
Large Magellanic Cloud.
R136a1 is only a million years old and has already shed 20% of its initial mass
(it will survive only for another million years).
R136a1 is 10 million times brighter than the Sun.
A star more massive or more luminous is unlikely to be discovered in the near future, or ever...
At right is a UV picture of Betelgeuse taken by
the Hubble Space Telescope in March 1995.
It was the first image ever obtained that revealed
the spatial extent of a star other than the Sun.
Betelgeuse is a red supergiant.
The variability of its size and luminosity
explain why Betelgeuse appears in celestial maps as
(at the right shoulder of Orion) although it's technically less
bright than the blue giant Rigel
also belongs to the constellation of Orion
(Rigel is at the "left foot" of Orion, the hunter).
According to Hipparcos parallax data, Betelgeuse
is 427 light-years away (give or take 92 light-years).
However, the distance of Betelgeuse is still widely quoted to be
between 300 and 650
Betelgeuse is one of the two stars with the largest apparent diameter
(besides the Sun, of course).
It's virtually tied with R-Doradus, a southern star with an apparent
optical diameter of 57 mas.
The apparent diameter of Betelgeuse is about 55 mas in the optical
spectrum (at 720 nm) but it's around 125 mas in the
near-UV spectrum and about 270 mas in the far UV.
The symbol "mas" stands for "milli-arcsecond",
a unit of angular measure of
which there are 3600000 in a degree (or 1296000000 in a full turn).
1 mas is about 4.848 nrad ("nrad" = nanoradian).
Francis Gladheim Pease and Albert A. Michelson
used optical interferometry to
obtain the first determination of the size of a star.
They found the angular diameter of Betelgeuse to be
(the average value of 55 mas is now commonly accepted).
The actual diameter of the star does vary by 60% or more,
as Betelgeuse shows an unstability indicative of its ripeness
to explode into a supernova (in a matter of centuries, at most).
An angle of 55 mas
at 427 light-years corresponds to a linear distance of
7.2 astronomical units (au).
This translates into a radius of 3.6 au,
which is larger than the orbit of Mars (3.06 au).
Larger estimates for the distance of Betelgeuse and/or its angular diameter
would even make Betelgeuse's equator commensurate with the orbit of Jupiter
The mass of Betelgeuse cannot be much more 20 solar masses.
Therefore, its density is extremely low...
A ball whose radius is 3 au (650 times as big as the sun)
and whose mass is 20 solar masses has
an average density of only 0.0001 g/L.
This is just a rarefied gas, which is about ten thousand times less dense than air
The temperature of Betelgeuse has been estimated to be around 3900 K
(Tsuji, 1979). Cooler supergiants are larger.
The record is currently held by the largest known star, discovered by Lalande in 1801,
Canis Majoris (3500 K).
The lowest possible temperature of such dying red supergiants
is believed to be around 3000 K.
(2007-09-27) Rigel and Blue Giants
Rigel is the brightest star in Orion, located at the "left foot" of
that winter constellation
(itself readily identified by the prominent three-star alignment
known as "Orion's belt").
Rigel is the dominant component of a system which also
includes a distant binary blue star (at right in the above
Rigel is a pulsating blue supergiant at a distance of
about 800 light-years.
Its diameter is roughly 70 times that of the Sun.
The Helix Nebula - NGC 7293 (HST, 2004)
Aftermaths of stellar explosions.
The Helix Nebula pictured at left is the closest
example of a planetary nebula (it's about 400 light-years away).
Its apparent size is almost as large as that of the Moon.
Such celestial objects are called planetary because, unlike
stars, they feature a sizeable roundish shape resembling that of planets.
(2007-09-27) Sirius B & White Dwarfs
Cinders of former typical stars (like our Sun).
Sirius, the brightest star in the sky,
is actually a binary star with a faint component
called the Companion of Sirius
(Sirius-B). It was the first white dwarf
ever discovered. It's still the closest known one.
Well before it could be observed directly, that faint star betrayed
its presence by the gravitational pull it exerts on Sirius-A.
indicate that Sirius-A is twice as massive as the Sun
whereas Sirius-B has about the same mass as the Sun
(although it probably started out as a "live" star weighing 5 times that much).
They orbit around each other in about 50 years.
(2007-09-27) Pulsars & Neutron Stars
The fate of a dying star which is too massive to settle as a white dwarf.
The first pulsar was discovered in July 1967
by Dame Jocelyn Bell Burnell (1943-)
when she was a post-graduate srudent. For their subsequent joint work,
her advisor, Antony Hewish,
would share with Martin Ryle
the 1974 Nobel Prize in physics.
Sir Fred Hoyle (1915-2001) argued that Jocelyn
Bell was unjustly deprived of a share ot that award, which remains known as the No-Bell prize.
It was the first Nobel prize ever awarded for work in astronomy
had been instrumental in making astrophysicists eligible for the Nobel prize in physics).
The name pulsar (short for "pulsating radio star")
was proposed to Bell & Hewish, early on, by Tony Michaelis
who was science correspondent of the
from 1963 to 1973.
Characteristics of a Typical Pulsar :
Mass of about 4 1031 kg (between 1.4 and 3.2 solar masses).
The Crab Nebula was first discovered in 1731,
by John Bevis.
In 1758, Charles Messier
rediscovered it during his hunt for the return of Halley's comet, predicted by
Messier's famous catalog was originally a list of objects that could be mistaken for comets.
The Crab Nebula (M1) became the first of those.
(The name "Crab Nebula" was coined in 1844 by the Earl of Rosse.)
The association of the Crab Nebula with SN 1054 was first suggested
by the astronomical and historical work of
Jean-Baptiste Biot (1774-1862; X1794)
and his only son
Edouard in 1843.
In 1921, Carl Otto Lampland
observed changes in the structure of the nebula at a rate consistent with the hypothesis.
A definite conjecture was formulated in 1939.
The final identification of the Crab Nebula as the remnant of SN 1054 was made
in 1942 by Jan Oort.
The pulsar at the center of the Crab Nebula was formally discovered in 1968.
The period of this "young" pulsar (33.5 ms) is increasing at a
steady rate of about 38 ns / day.
The corresponding period
of 29.85 Hz can be perceived by gifted individuals as stroboscopic
flashes of light
(rapid eye motion may leave the impression of dotted lines).
According to Jocelyn Bell, an anonymous woman, who was a trained pilot, made
such an observation in the late 1950's using the
University of Chicago's telescope (then open to the public).
She reported that to the astronomer Elliot Moore, who dismissed her observation
as mere scintillation, againt the woman's strong protestations...
Arguably, this incident may have been the first observation of a pulsar, more than 17 years before
they were officially discovered !