[Petrochemicals (OP)]

I was reading about jupiter and its size, apparently if it where much more massive it would be smaller in size due to its own gravity.

That got me thinking about the sun. Has the sun expanded past its own graviational force due to its sheer energy ? Or is it already the correct density for its own gravitational force.

Further more is its colour due to this expansion, so a relationship is formed between the different factors. The relationship being the equilibrium between heat generated and heat lost due to radiation, the size of the sun surface and the colour there of to facilitate this radiation, the energy within the sun and its possible associated expansion?

[chiralSPO]

Yes, the heat energy (generated from fusion) in the sun keeps it more expanded than it would be if it were cold, and also makes it glow.

[evan_au]

Has the sun expanded past its own gravitational force due to its sheer energy ?

The visible surface of the Sun is about 1 million km across.
Earth's orbit is about 300 million km across.

Earth's orbit is controlled by the Sun's gravitational field.

So no, the Sun has not expanded past the reach of its gravitational field.
See: https://en.wikipedia.org/wiki/Solar_wind

Of course, if you include the Solar Wind as the outer reaches of the Sun's atmosphere, this reaches well beyond Pluto, but it is still within reach of the Sun's gravity.

[Kryptid]

The color of the Sun is due to its temperature: https://en.wikipedia.org/wiki/Black-body_radiation#Explanation

[Petrochemicals (OP)]

Point being that the colur is the exact colour needed to emitt enough radiation from the surface area to keep the equilibrium between generation and emmision.

The expantion thing isnt like just the thermal expantion ratio, it is far greater as it 2ould have to expand along wqy to become less dense, over riding the gravitational conpression of its own mass. Would this explain why the sun is so hot, and so cool on the surface ?

[evan_au]

why the sun is so hot in the core, and so cool on the surface ?

Modeling the inside of the Sun assumes that the Sun is in thermal equilibrium, ie the energy produced in the core equals the energy radiated from the surface. This is not just guesswork.
- Neutrino detection tells us how much energy is produced by hydrogen fusion in the core of the Sun
- Satellite observations of the surface of the Sun tell us how much is radiated into space
- These two figures line up (or they did, after neutrino oscillation was discovered)

The change in temperature between the core and visible surface occurs in distinct layers, where the energy transfer is primarily by radiation, and other layers where the primary transfer is via convection.
- With convection, when hot gas rises towards the surface, the pressure drops and the temperature drops.
- With radiation, when the radius increases by 41%, the area is doubled, and the temperature required to radiate this energy drops.
https://en.wikipedia.org/wiki/Sun#Structure_and_energy_production

could have to expand along way to become less dense, over riding the gravitational compression of its own mass

There is a group of stars called Cepheid variables which show considerable variation in size (by 25%) and brightness over a period of days to months.

A change in transparency of ionised Helium causes the star to cyclically heat up, expand, become brighter, shrink and fade. This type of star is not in thermal equilibrium.
See: https://en.wikipedia.org/wiki/Cepheid_variable#Dynamics_of_the_pulsation

[Petrochemicals (OP)]

You understand this isnt my own thinking about the temperature inbalance, this is information and direction about the surface picked up elewhere

Theoretical models indicate that if Jupiter had much more mass than it does at present, it would shrink.[31] For small changes in mass, the radius would not change appreciably, and above about 500 M⊕ (1.6 Jupiter masses)[31] the interior would become so much more compressed under the increased pressure that its volume would decrease despite the increasing amount of matter. As a result, Jupiter is thought to have about as large a diameter as a planet of its composition and evolutionary history can achieve.[32] The process of further shrinkage with increasing mass would continue until appreciable stellar ignition was achieved, as in high-mass brown dwarfs having around 50 Jupiter masses.[33]

This is from wikis article on jupiter.

I do not doubt the equilibrium (surface area neutrios colour temperature) the problem with my reading of other peoples stances of the suns very cool  surface even compared to its corona, is why the sun isnt either alot bigger and cooler even its corona and steadily getting warmer as you go to the centre (ive just realised the wiki quote above makes an argument why not with a density 1.41 but a huge gravity), or smaller and brighter, after all isnit it something like 2m degrees just inside its surface, with space at 0  ? Even for a cool star it has a huge difference in temerature between the surface and the near interior, and you would expect more of a discharge, perhaps from a smaller area.

Lyou would expect a more smooth temperature transition was what people where getting at?

Is the temperature emmision kept low by an atmosphere that is somehow stopping emmision of radiation  at a higher rate, a bit like a green house effect.


Another wiki quote on the sun

The corona is the next layer of the Sun. The low corona, near the surface of the Sun, has a particle density around 1015 m−3 to 1016 m−3.[100][f] The average temperature of the corona and solar wind is about 1,000,000–2,000,000 K; however, in the hottest regions it is 8,000,000–20,000,000 K.[101] Although no complete theory yet exists to account for the temperature of the corona, at least some of its heat is known to be from magnetic reconnection.[101][103] The corona is the extended atmosphere of the Sun, which has a volume much larger than the volume enclosed by the Sun's photosphere. A flow of plasma outward from the Sun into interplanetary space is the solar wind.[103]

And an artivcle giving temperatures

https://www.space.com/17137-how-hot-is-the-sun.html

[evan_au]

isn't (the Sun) something like 2 million degrees just inside its surface, with space at 0?

The temperature of the Sun drops to around 2 million degrees at about 70% of the Sun's radius, or about 200,000km below the visible surface. I wouldn't call this "just" inside the surface.

Intergalactic space might have a temperature close to absolute zero (about -270C), but the surface of the Sun has a temperature around +5200C: hot enough to easily vaporize iron.

Because the outer atmosphere of the Sun is transparent to visible light, the surface of the Sun is kept cool at this temperature by radiating its energy into space as visible light (plus infra-red, ultraviolet, and some X-Rays).

Models of the internal temperature and pressure inside the Sun can be tested in great detail using "helioseismology". Just as  earthquake waves allow geologists to peer inside the Earth, helioseismology allows astronomers to peer inside the Sun. The velocity, frequency and diffraction pattern of waves passing through the Sun are impacted by the internal structure of the Sun.

See: https://en.wikipedia.org/wiki/Helioseismology

[Petrochemicals (OP)]

Just as  earthquake waves allow geologists to peer inside the Sun, helioseismology allows astronomers to peer inside the Sun. The velocity, frequency and diffraction pattern of waves passing through the Sun are impacted by the internal structure of the Sun.

Ha! a typo.

Thanks evan.

It still seems though the sun should be

A) smaller and denser due to its own gravity

B) brighter due to this increaced density

C) less energy stored within

If you take polaris, its only 5.4 times the mass of the sun, but is 34 times the radius, and 1 14000 th  the gravity of the sun at 5he surface. It seems that a great deal of stars energy is kept by the star because of this reaction to gravitational compression.

[evan_au]

If you take Polaris, its only 5.4 times the mass of the sun

I think you are referring to the mass-luminosity relationship for stars?

Typically, the luminosity (brightness) of a star is proportional to mass^3.5.
Polaris, with a mass 5.4 times that of the Sun, would be expected to have a luminosity around 5.4^3.5 = 366 times greater than the Sun.

The internal temperature is much higher than the Sun, so it balloons out to a much greater volume and much lower surface gravity. This enormous area is enough to radiate the enormous energy output, so it is now in thermal equilibrium (until the fuel starts to run out, when its behavior will change dramatically). 

The interesting result is that Polaris will be a relatively short-lived star, compared to the Sun.
- It has 5.4 times the mass of the Sun
- So it has 5.4 times as much fuel
- But it is burning the fuel 366 times faster
- So it will run out of fuel 67 times sooner than the Sun.
- If Earth were orbiting Polaris, the star would have gone supernova billions of years ago.

On the other hand, red dwarf stars, with mass much smaller than the SUn burn their fuel very slowly, and will still be glowing long after the Sun has turned into a dark cinder.

See more at: https://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation

[Petrochemicals (OP)]

Yep  but evan

Every star must reach its equilibriem colour, if not kaboom !

Luminosity and flux are different th8ngs. I do not boubt that lumens =fusion-neutr8nos. But for polaris, its gravitational potentoal is much more than  the sun yet it balloon, and releases much more energy, as yyou say the mass bright ness

5.4 times the mass do3s not equal 34 times radius , not 34 times squar3d 3/4  the volume. How on gravity ! does it fight th3 gravitational pull.

[evan_au]

How on gravity ! does it fight th3 gravitational pull.

The Sun fights gravity with temperature. An increase in temperature produces an increase in pressure.
Pressure can be considered an expansion force which fights the compressive force of gravity.

At present, the Sun is a Hydrogen-burning star. During this process, the core shrinks, gravitational compression increases in the core, and the rate of fusion slowly increases, over billions of years. This means that radius is slowly increasing, luminosity is slowly increasing, but the temperature and color remains roughly the same.
See graph at: https://en.wikipedia.org/wiki/Sun#Main_sequence

However, in about 5 billion years (age: around 10 billion), the Sun will have run out of Hydrogen in its core (although there will still be hydrogen farther out). The radius of the Sun will reach Earth's current orbit, and the luminosity will be thousands of times higher than present - but the surface temperature will be lower (a dull red color), and the surface gravity will be much lower. The surface gravity will be so low that the Sun will shed most of its outer shell, as a planetary nebula.

A complicated sequence of events happen as helium burns into carbon - surface temperature grows to around 6 times the current temperature (a blue-white color), but radius shrinks to 10 times the current value.
See: https://en.wikipedia.org/wiki/Sun#After_core_hydrogen_exhaustion

But for polaris

There are highly non-linear relationships between:
- fusion fuel, reaction rates, core temperature and pressure
- surface temperature, surface area, color, and luminosity. 
- mass, radius, surface gravity and core gravity.
- mass loss over time
- and all these parameters continually change over the Sun's lifetime.

So don't expect a simple relationship between the size, surface gravity and color of the Sun and another star - or even when comparing the Sun at two different ages (measuring age in billions of years).

[Bored chemist]

Every star must reach its equilibriem colour, if not kaboom !

The equilibrium for a star is death.

[Petrochemicals (OP)]

Every star must reach its equilibriem colour, if not kaboom !

The equilibrium for a star is death.

Elabourate


Also i found this thanks Evan too

https://en.m.wikipedia.org/wiki/Virial_theorem

[evan_au]

There are highly non-linear relationships

It is best to model the behavior of stars in computer simulations that take into account all these nuclear. electromagnetic, gravitational and pressure/volume effects.

The equilibrium for a star is death.

A star is changing throughout its life as it burns fuel and radiates energy. It is not in thermal equilibrium.

The only time it stops changing (reaches thermal equilibrium) is when:
- It has burnt all its fuel
- It has radiated all its energy
- The denser material has sunk to the bottom, and lighter materials on top
- All the radioactive elements in the core have decayed
- Its surface temperature has dropped to match the background radiation in its vicinity
- Its core temperature is the same as the surface temperature
- ie it is a dead star
See more at: https://en.wikipedia.org/wiki/Stellar_evolution#Stellar_remnants

Of course, some physicists think that the proton may not be stable on extremely long timescales, so maybe it hasn't quite reached thermal equilibrium, even then!

[Petrochemicals (OP)]

Well it only burns a third of its fuel, and apparently? the proton is not a thermal 3nergy carrier ?

If the star where not emmitting as much energy as it produced within it, or conversley emmitted more than it preduced it's gravitational potential would have to change according to that viriall theory, it is apparently very well known within astronomical circles to estimate masses and energies. That surely is an equilibrium

[evan_au]

Well it only burns a third of its fuel, and apparently?

That depends on how well the star's matter is mixed by convection.
The Sun only mixes the outer 30%, so a lot of hydrogen can be left-over without undergoing fusion.
However, smaller red dwarf stars are fully convective, so they can burn almost all their hydrogen fuel.

the proton is not a thermal 3nergy carrier ?

In the Sun, the temperature is so high that protons and electrons (and helium nuclei) are separated into a plasma.
All of these in one patch of plasma are at the same temperature, which means that they have the same average kinetic energy. Because electrons are lighter than protons, they have a much higher velocity for the same kinetic energy.

But all of the components of the plasma (including the protons) carry thermal energy and participate in carrying it by convection, radiation and conduction into adjacent patches of plasma.

If the star where not emmitting as much energy as it produced within it, or conversley emmitted more than it preduced it's gravitational potential would have to change

If we ignore stellar winds (which represent a slow loss of mass), then from a distance, the star would have a constant mass and a constant gravitational potential.

If you look more closely under the surface, you would see changes in temperature, pressure and size over time within a non-equilibrium star. But I don't see how it changes the gravitational potential. Do you mean the "surface gravity"?

according to that virial theory

This is used to represent the movement of passive objects that interact loosely with each other, like the molecules in a gas, or the stars in a galaxy, or galaxies in the universe. It is not applicable in a strongly-interacting environment like a star which is generating heat by nuclear fusion.
You need a different kind of computer model to calculate the future of a galaxy compared to the future of an individual star (although knowledge gained from one simulation might result in tweaks to the other kind of simulation).

it is apparently very well known within astronomical circles to estimate masses and energies. That surely is an equilibrium

Yes, it is well known how to simulate these systems.
A gas in a closed vessel (no energy in, no energy out) can rapidly approach thermal equilibrium.

The orbits of stars in a galaxy could also reach an equilibrium after several galaxy rotations (a billion years or so) - provided you prevented collisions with other galaxies (or near misses), mergers of supermassive black holes, and other disruptive events that represent an injection or loss of energy.

The matter inside a star only reaches an equilibrium state after fusion stops (this represents an injection of energy) and if you prevented it radiating energy into space (this represents a loss of energy). In stars that aren't inside a Dyson sphere, this only happens when the star's temperature has dropped to almost absolute zero, from the surface right down to the core.

[Petrochemicals (OP)]

Well virial theory states energy conta8ned is averagely half the gravitational potential so i was reading. That would how ever mean the sun released energy at the same rate it produced it.

Im not too sure about the gravity as on a star as you travel toward the centre the gravity increaces, but on earth the gravity lowers the further you get to the centre ? Maybe to do with the atmosphere of a planet equating to the less dense outer regions of the sun. That would equate to the gravity of the suns own mass being over ridden.

[evan_au]

on earth the (acceleration due to) gravity lowers the further you get to the centre ?

This would be true if the Earth had a uniform density.
However, the Earth has a nickel/iron core of extremely high density, surrounded by lower-density silicate rocks (mainly silicon+oxygen), all the way to the surface.

As you move towards the center, there is less rock between you and the center of the Earth
- But counterbalancing this, you are getting closer to the high-density metal core
- The inverse-square law makes this proximity effect stronger
- So overall, the acceleration due to gravity is expected to stay constant (or even increases slightly) until you reach the core. Then it decreases towards the center.

So the relationship between surface gravity and gravitation at the core is not a simple one, even on the Earth.

When the Sun becomes a red giant, the surface gravity will be almost zero (allowing the surface to drift away), while there is considerable gravitational acceleration at the edge of the Sun's core (which by then will consist primarily of helium, and will be far more dense than the Sun's current Hydrogen-rich core)..

virial theory states energy conta8ned is averagely half the gravitational potential so i was reading

Let's take another example where misapplication of the virial equations is likely to give the wrong answer: a closed container containing a mixture of 33% oxygen and 67% hydrogen (by volume), at room temperature. No energy can get in or out.

The virial equations can tell you the equilibrium velocity distribution of the hydrogen and oxygen molecules.

But if a random cosmic ray happens to split apart a couple of those hydrogen and oxygen molecules (making almost no change to the energy content of the container), the picture changes dramatically. Because those molecules will reform in a different configuration, as water, releasing considerable energy in an explosion, and totally changing the velocity distribution. This is because injecting (chemical) energy changes the balance of kinetic and gravitational energy inside the container.

The basic virial equations do not take this into account (nor do they take into account energy injected by hydrogen fusion in a star).