Highest Mass a Star Can Have

I notice that the heat generated by a star's nuclear fusion reactions
counteract the gravity of the star. Is there a mass limit to stars,
such that stars above this mass limit would collapse even though it is
still producing heat from nuclear fusion reactions?


Michael

In sci.physics
(Michael Ejercito) wrote:

I notice that the heat generated by a star's nuclear fusion reactions
counteract the gravity of the star. Is there a mass limit to stars,
such that stars above this mass limit would collapse even though it is
still producing heat from nuclear fusion reactions?

The greater mass the star, the shorter the life. As for an absolute limit,
I don't know but it certainly makes sense too me.

nightbat wrote

Bruce wrote:

In sci.physics
(Michael Ejercito) wrote:

I notice that the heat generated by a star's nuclear fusion reactions
counteract the gravity of the star. Is there a mass limit to stars,
such that stars above this mass limit would collapse even though it is
still producing heat from nuclear fusion reactions?

The greater mass the star, the shorter the life. As for an absolute limit,
I don't know but it certainly makes sense too me.

nightbat

For stellar mass upper limits in normal gravity fields see
Chandra. For the brave who dare venture into strong constricting gravity
fields, see nightbat's posts on the " Black Comet " singularity.


the nightbat

COMMENT:





I'm interested in a related question, which is how small
(not how

large) can a gas planet be.



We had a discussion about this in the forum last March, some
of which

I'll reprint. But it is made a bit more topical by a recent
finding of

a 2.5 Jupiter mass planet orbiting a dead neutron star in a
globular

cluster which is 12.5 billion years old, and therefore
thought to

represent completely first generation stars. Thus, planets
there would

have almost no "metalicity" (elements Li and heavier) since
they'd be

made of post big-bang gas only (carbon, silicon and oxygen
are "metals"

in this phrasology). Basically they'd be only H and He in
the standard

primordial ratio, and only traces of anything else.



Now our own solar system gas giants are mostly H and He, but
being 2nd

generation planets they are thought to have "metallic" cores
(maybe

including a lot of carbon, but, certainly also a lot of
silicate rock).

But nobody thinks that if the cores of our solar system's
gas giants

disappeared, that they'd fly apart, do they? So why is
everyone shocked

when somebody finds a first generation star with a
Jupiter-sized

planet?



But that seems to have been the reaction of professional
astronomers a

few weeks ago.



Last March I calculated how big and massive would an object

have to be, in order to have as much gravitational
self-energy as (say)

a diamond has from chemical self-energy. Objects bigger than
this would

be bound more tightly from gravity than chemistry ever could
bind them,

since a diamond's chemical energy per unit of mass is close
to maximal

for solids. (The negative bond chemical energy in hydrogen
gas is 2e8

kJ/kg but it's not fair to use it here, since this energy
only holds

the atoms together in pairs, and isn't available to hold a
collection

of atoms together, which the negative potential of
gravitational or

carbon bond energy is).



For silicate rock the chem self energy is about 1.5e7 J/kg.
Call this

E/M the target chem energy per mass, and symbolize it "U".



Gravitational E/M for uniform spheres = 3/5 * G M/R
(exercise left to

student)



Replacing M in the formula above with the density* volume =

4/3 * pi* rho R^3



Grav E/M = 3/5 * (G/R) * 4/3 * pi * rho * R^3



= 4/5 * pi * rho * G * R^2.



Set this equal to U and solve for R:



R^2 = 5U / (4pi*G*rho)



Plug in numbers: U is roughly 1.5 e7 J/kg for silicate rock,
and rho

for such rocks is about 3500 kg/m^3, and G is 6.67e-11,



This gives R of 5e6 meters, which is pretty close to the 6e6
m diameter

of our own little silicate ball, the Earth. Which means
that the Earth

has about the same chemical binding energy/kg as it does
gravitational

energy.



If we run the problem with a rho of 1000 kg/m^3 (pretty
close to gas

giants and our own sun, so probably not too far off a metal
poor

figure), R comes out 9.5e6 m, or a little larger than Earth,
but with a

mass only 3.5e24 kg, which is 60% of Earth's.



So, if a planet with typical gas giant density and less than
the mass

of the Earth can be gravitationally bound as tightly (per
gram) as a

small rocky planet, then surely a planet 2.5 times Jupiter's
mass (this

would be about 5e27 kg) would have a large enough binding
energy to

survive any of the conditions any of the planets survived in
our own

solar system?

Michael Ejercito wrote:

I notice that the heat generated by a star's nuclear fusion reactions
counteract the gravity of the star. Is there a mass limit to stars,
such that stars above this mass limit would collapse even though it is
still producing heat from nuclear fusion reactions?



The upper limit of about 80 solar masses for a star on the main
sequence is due to photon pressure. At very high luminosity, the
photons literally blow off outer layers of a more massive star.

Sam Wormley wrote:

Michael Ejercito wrote:

I notice that the heat generated by a star's nuclear fusion reactions
counteract the gravity of the star. Is there a mass limit to stars,
such that stars above this mass limit would collapse even though it is
still producing heat from nuclear fusion reactions?


The upper limit of about 80 solar masses for a star on the main
sequence is due to photon pressure. At very high luminosity, the
photons literally blow off outer layers of a more massive star.

80 solar masses may be too conservative

Ref: http://www.aas.org/publications/baas...s/S006010.html

Session 6 - HII Regions & Massive Star Formation.
Display session, Wednesday, January 07
Exhibit Hall,

[6.10] Star Formation in R136: A Cluster of O3 Stars Revealed by HST Spectroscopy.

P. Massey (KPNO/NOAO), D. Hunter (Lowell Obs.)

R136 is the extremely populous star cluster at the heart of the 30
Doradus nebula. We have obtained HST/FOS spectra of 65 of the brightest
blue stars to investigate the massive star population of this prototype
``super star cluster", probably what a very young globular cluster
would resemble. We find that over half the stars in our sample are of
spectral type O3, the hottest, most luminous and massive subclass. We
have identified more O3 stars in this remarkable cluster than were
previously known elsewhere. The age of R136 is very young, 1-2 Myr.
Despite the preponderance of so many high mass stars, we find that the
IMF is completely normal, with a Salpeter slope (\Gamma=-1.3\pm0.1)
extending from 2.8 \cal M_ødot to 100 \cal M_ødot. The most massive
stars are well above the highest mass tracks available (120 \cal
M_ødot), and a conservative estimate places the highest mass star at
\sim 150\cal M_ødot, making this the highest mass unevolved star yet
found. Comparing this to other clusters suggests that we have yet to
encounter any physical limit to how massive a star may form in nature,
that the only limit we see is a statistical one, depending upon the
richness (and age) of the cluster.

Sam Wormley wrote:

Sam Wormley wrote:

Michael Ejercito wrote:

I notice that the heat generated by a star's nuclear fusion reactions
counteract the gravity of the star. Is there a mass limit to stars,
such that stars above this mass limit would collapse even though it is
still producing heat from nuclear fusion reactions?


The upper limit of about 80 solar masses for a star on the main
sequence is due to photon pressure. At very high luminosity, the
photons literally blow off outer layers of a more massive star.

80 solar masses may be too conservative

Ref: http://www.aas.org/publications/baas...s/S006010.html


Astronomy Picture of the Day -- Massive Stars Of 30 Doradus
Ref: http://antwrp.gsfc.nasa.gov/apod/ap990930.html
http://antwrp.gsfc.nasa.gov/apod/ima.../30dor_hst.jpg

"Dr. Zarkov" wrote in message
...
"Sam Wormley" wrote in message
...
Michael Ejercito wrote:

I notice that the heat generated by a star's nuclear fusion reactions
counteract the gravity of the star. Is there a mass limit to stars,
such that stars above this mass limit would collapse even though it is
still producing heat from nuclear fusion reactions?



The upper limit of about 80 solar masses for a star on the main
sequence is due to photon pressure. At very high luminosity, the
photons literally blow off outer layers of a more massive star.


I'm not sure if this is the question the previous poster had in mind, but
I
thought what he was asking was if there is any upper limit to a collapsing
mass such that a star would never even form--where you would just get a
collapse to a black hole (like galactic centers?)

That was the answer given, but instead of turning into a black hole the star
does during the main sequence the exact opposite - it shedds mass off in
violent outbursts. The larger the star, the larger the outbursts.

Of course, eventually and relatively soon, that star will have consumed it's
energysource and due to the massive remaining mass it will become a black
hole (unless some unknown prevents it), and very likely the initial black
holes central in galaxies were formed like that. The original stellar massed
black hole gulped up remaining gas, eventually entire stars, ending up with
a mass of million and even billions that of the sun.

Simulations indicate that the initial stars in the universe were all
singular massive (30 Msun) stars just like this.

Clear Skies,
Magnus

PLANETS ORBIT THE SUN TO CONSERVE TOTAL ENERGY
THE FORCE OF GRAVITY IS AN ILLUSION

Gravitational effect is the result of an acceleration
of mass. Galileo demonstrated this. Newton assumed
that this was caused by a force of gravity between
all masses. Was this a correct assumption? Einstein
and many other scientists felt that there must be
more to gravitation than an attraction at a distance.
Action at a distance was considered to be impossible
in the absence of a transfer of energy at the speed
of light.

Hubble then showed that the distant Galaxies were
moving away from the earth and that the universe
was expanding in all directions. If this is true ,
What else must be true?

1. The potential energy of the rest of the universe
must be decreasing relative to the mass of the earth.

It has long been assumed that the first law of
thermodynamics, which says that the total energy of
the universe is a constant, was a fact of nature.
If this is true what then.

2. The kinetic energy of the universe must be
increasing at the same rate that the potential
energy is decreasing as the universe expands.

How is this possible? Masses must be accelerating,
because, kinetic energy change is the result of an
acceleration. But all orbital masses are
accelerating toward the center of the earth or
some other mass. Why would this occur otherwise?

3. Orbital motion could then be the result of the
expansion of the universe. The Gravitational
illusion could be the result.

Based on the first law of thermodynamics
The total mass energy of the universe is a constant.
(total kinetic (mass) energy plus total potential
energy is a constant).
m(2 pi L)^2 / t^2 + G (M-m)m / L = A constant.
m is any mass say that of the earth.

From this equation the equation
Delta m (2 pi L)^2 / t^2 = - Delta G (M-m)m/L
follows mathematically.
From this equation the equation
Delta m 4 pi^2 L /t^2 = Delta - G (M-m)m / L^2
or the modified Newton equation for gravity can
be derived,but only when L is the orbital distance.
The earth orbit is a result of an energy equilibrium,
( the absence of a change of total energy )
and not the result of a force of gravity between masses.
Force of gravity is the resulting illusion
assumed by Newton to be a force.

If a planet (say earth) moved away from the sun
its potential energy would decrease as L increased.
Its kinetic energy would decrease because it is
no longer accelerating toward the sun in orbital
motion. Total energy would have to decrease. A very
great change of total energy would have to take place.

POTENTIAL ENERGY = G(M-m)m/L
KINETIC ENERGY = m(2 pi L)^2/t^2
m(2 pi L)^2/t^2 + G(M-m)m/L = A constant = M
G= Gravitational constant; M = total energy
of the universe (or effective universe) ;
m = mass in question.
t = time ; L = radial distance.

No mechanism exists for this to occur rapidly.
So it could not happen. The magnitudes of kinetic
and potential energies of planets and moons
travelling in orbital motion are equal and any
increase or decrease of orbital distance L results
in an equal change in magnitude of both.This is
the only value of L where no change of total energy
will occur if the value of L changes. At any other
distance L, an increase of kinetic energy will be at a
different rate than potential energy desreases.
Orbital motion conserves total energy.
Force of gravity isn't needed to explain orbital
motion or any other motion at a distance.



GRAVITY MECHANICS AND
RESEARCH ON ASTRONOMICAL OCEAN TIDES
Copyright 1984 to 2002 Allen C. Goodrich

An examination of United States Coast and Geodetic
Survey Tidal Data, which was gathered by extensive
measurements over long periods of time,was compared
with astronomical data showing the phases of the
moon at corresponding times for many years. This
correlation of the two sets of data revealed a
very interesting fact, in a manner that had never
before been mentioned in the literature.
It is invariably and exactly
the lowest tide that exists directly under the
full and new moons at deep ocean ports.

This was a very interesting discovery because
current physics,based on the gravitational theory,
discussed in the following U.S.Gov. documents:
PREDICT THE OCEAN TIDES
http://co-ops.nos.noaa.gov/restles1.html
SEE PHASES OF THE MOON FROM EARTH
http://space.jpl.nasa.gov/
,would lead one to believe that,except for many
possible reasons, the highest tides tend to be
under the full and new moons. The dictionary and
encyclopedia as well as physics texts predict this
with pictures of the earth and oceans bulging on
the side facing the full moon. Of course it never
happens as the gravitational theory predicts,
and many reasons are given for the discrepancies.

CONCLUSION:
No discrepancies were found in the occurence of
exactly the lowest tide directly under the full
and new moons, at deep ocean ports.

SIGNIFICANCE:
One must admit that this is beyond
question one of the most important discoveries
of modern physics research. It indicates that a
change must be made in the theory of gravitation.
One can no longer assume that a force between
the moon and the water of the earth's oceans,
is causing the ocean tides. The force of
gravity must be an illusion caused by some other,
more basic, reason. What would this be?
If the total energy ( kinetic and potential ) of
the universe is assumed to be a constant,from this
fundamental equation, many interesting things follow.
If the rest of the universe is expanding ( potential
energy decreasing) relative to masses, the masses
must be shrinking ( increasing in kinetic energy )
(gravitation) relative to the rest of the universe.

THE FIRST LAW OF MOTION-(GOODRICH)

Copyright 1984 to 2002 ALLEN C. GOODRICH

A body (m) continues in a state of rest (equilibrium)
or motion in a straight or curved line (equilibrium)
as long as no change occurs in its total (kinetic and
potential) energy, relative to the rest of the
effective universe (M-m),

Delta mL^2/t^2 = - Delta K(M-m)m/L

equilibrium = no change in the total energy
relative to the rest of the effective universe (M-m).

^ = to the power of.
Orbital motion complies with this equation.
This equation is derived from the fundamental
equation of the universe which states that
the total energy of the universe is a constant.
The sum of kinetic and potential energies is a
constant.
mL^2/t^2 + K(M-m)m/L = A constant.

SEE
THE UNIVERSE- A GRAND UNIFIED THEORY OF MASS ENERGY
SPACE TIME FRAME MECHANICS-APPEARING IN NEWSLETTER
"SPECTRUM" OF THE BUFFALO ASTRONOMICAL ASSOCIATION
INC. NOV.1996 TO FEB.1997
See http://ourworld.cs.com/gravitymechan.../business.html
FUNDAMENTAL EQUATION OF THE UNIVERSE
http://ourworld.cs.com/gravitymechan...e/profile.html
TIDES AND GRAVITY MECHANICS
http://ourworld.cs.com/gravitymechan...ge/resume.html

A new theory of gravitation is given, which
predicted, stimulated the above research,and is
consistent with, the new findings.

Choosing a hobby that is in line with ones past
experience can be a satisfying and rewarding
undertaking.

"Magnus Nyborg" wrote in message ...
"Dr. Zarkov" wrote in message
...
"Sam Wormley" wrote in message
...
Michael Ejercito wrote:

I notice that the heat generated by a star's nuclear fusion reactions
counteract the gravity of the star. Is there a mass limit to stars,
such that stars above this mass limit would collapse even though it is
still producing heat from nuclear fusion reactions?



The upper limit of about 80 solar masses for a star on the main
sequence is due to photon pressure. At very high luminosity, the
photons literally blow off outer layers of a more massive star.


I'm not sure if this is the question the previous poster had in mind, but
I
thought what he was asking was if there is any upper limit to a collapsing
mass such that a star would never even form--where you would just get a
collapse to a black hole (like galactic centers?)

That was the answer given, but instead of turning into a black hole the star
does during the main sequence the exact opposite - it shedds mass off in
violent outbursts. The larger the star, the larger the outbursts.
Which would be true as long as the nuclear fusion reactions start
before the escape velocity exceeds that of the speed of light.
A black hole with a higher mass has a lower density than a black
hole with a smaller mass. Currently, astrophysicists believe that gas
must be compressed to enormous densities to form a star. A
sufficiently massive cloud could collapse into a black hole before the
nuclear fusion reactions begin.


Michael