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This may seem like a weird question, but something got me thinking about it just recently.

The Sun's core is composed of mainly hydrogen and helium, and is present in the form of a extremely hot supercrushed plasma. The Sun's core is mind-bogglingly dense, about 150,000 kg/m3 (about 15x denser than lead, 7x denser than uranium, 6x denser than osmium). The density can get extremely high at the center of stars. This leads me to think that the solar core, due to the immense amount of atoms packed together would behave like a extremely hard solid, as per my understanding, most dense metals (excluding gold) are extremely hard, like tungsten.

I decided to dig into it a bit on the Internet, but whatever information I got were merely about the pressure at the center of the Sun, and not about the hardness of the solar core. By hardness, I mean having stiffness/rigidity, an ability to retain a certain shape when subjected to anisotropic stress.

To clarify things a bit: Supposing we submerged an "indestructible" observer really deep into the Sun, just inside the solar core. Supposing we got the indestructible observer to throw a punch randomly inside the Sun, what would this observer feel? More specifically, would the observer perceive the solar core material as being extremely hard, like a solid, or would it act like an extremely viscous fluid?

TL;DR

Would the solar core be extremely stiff and hard? Or would it simply behave like a dense and viscous gas?

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    $\begingroup$ @DaddyKropotkin What I am trying to say is that whether the solar core behaves like a solid i.e. extremely hard and tough, or does it simply behave like a viscous liquid? $\endgroup$
    – Alastor
    Jan 8, 2023 at 17:07
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    $\begingroup$ Note that 150 tons/m^3 isn't that extreme. Platinum weighs 21 tons / m^3. Sure, it's much more, but a factor of eight isn't that much more $\endgroup$
    – JollyJoker
    Jan 9, 2023 at 8:14
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    $\begingroup$ There seems to be a lot of confusion in the answers about hardness versus incompressibility. Many of the answers say the core of the Sun is very hard to compress, but I think that's pretty orthogonal to what's being asked about here. If the core of the Sun is a fluid then I think this question is really about its viscosity.$$\,$$For example, the Earth's mantle is a fluid, but its viscosity is so high that if you would be able to interact with it directly on human time scales it would behave like a rock. I think the question is about whether the Sun's core is similar. $\endgroup$
    – N. Virgo
    Jan 9, 2023 at 10:59
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    $\begingroup$ @StephenG-HelpUkraine I think the last sentence how it would feel was more a figure of speech(or what to call it), not exactly practically possible either. I think if was more indirectly, like, "I can't obviously touch it but if I could,in theory (...)" :) it was that I meant $\endgroup$ Jan 9, 2023 at 19:01
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    $\begingroup$ I am voting to NOT close this question. In fact, this is a fabulous question. It leads you to imagine and define what exactly "hard" would mean, whether we can even define it in such extreme conditions, if not are there there any analogous properties, etc. Perhaps more of a Physics question than an Anstronomy question, nonetheless, it is a great question. $\endgroup$
    – KalEl
    Jan 10, 2023 at 9:14

6 Answers 6

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The solar core can be considered soft in a relative sense (compared to other materials at the same density), but hard and incompressible in an absolute sense. The material behaves almost exactly like a perfect gas but would be as viscous as ketchup.

The equation of state is that of a perfect monatomic gas and thus the pressure $P \propto \rho^{\alpha}$, with $\alpha \sim 4/3$ in the solar core, where heat transport is dominated by radiative diffusion. This is a "soft equation of state" - the material is highly compressible - it takes a small fractional increase in pressure to produce a compression. For most solids, $\alpha$ would be in double figures and they are approximately incompressible.

However, what you are asking about could be represented by the "bulk modulus" (Young's modulus and Shear modulus are not meaningfully defined for a fluid). This is roughly equal to the pressure of a gas and is a measure of how much force in an absolute sense is required to change the volume of something. At the centre of the Sun, this is $2\times 10^{16}$ Pa. This can be compared with the bulk modulus of diamond which is $4\times 10^{11}$ Pa. Thus in that sense, the solar core is much harder than a diamond to compress.

In terms of viscosity, the microscopic kinematic viscosity in the solar core is of order $10^{-4}$ m$^2$/s (Ruediger & Kitchatinov 1996) and hence a dynamic viscosity of 15 Pa s. For comparison, the kinematic viscosity of water at 293K is $10^{-6}$ m$^2$/s and the dynamic viscosity is $10^{-3}$ Pa s. Thus the solar interior fluid is 100-10000 times more viscous than water, depending on how viscosity is defined. Fluids of comparable viscosity would be honey or ketchup. The viscosity of solids (like rocks) meanwhile, is of order $\sim 10^{20}$ Pa s.

To understand why the Sun behaves like a perfect gas, one must compare the interaction energies between the particles with their kinetic energies. At a density of 150000 kg/m$^3$ the mean separation of protons and electrons is $\sim 2\times 10^{-11}$ m, with a mutual Coulomb energy of about 100 eV. The kinetic energy of the particles is $3k_BT/2$, and with temperature $T \sim 1.5\times 10^7$ K in the solar core, this is about 1000 eV. Thus the kinetic energies are much greater than the Coulombic binding energies and so the particles behave like a gas. To "freeze" into a solid you would need the binding energy to be about 100 times the kinetic energy, which would require much higher densities at that temperature.

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    $\begingroup$ Is this the right way to answer the question. The"bulk modulus" would distinguish between a gas and liquid, but at solar core temperatures and pressures, I doubt words like "gas" and "liquid" have any meaning. The distinguishing factor of a solid is its resistance to flow. Reading between the lines I think you are saying that there is very little resistance to flow, and the core of the sun is "fluid". Normal fluids have viscosities. I'm not sure if viscosity makes sense for the kind of supercritical plasma, but if it does, what would be the viscosity of the core? $\endgroup$
    – James K
    Jan 8, 2023 at 18:50
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    $\begingroup$ @JamesK the interior of the Sun is a perfect gas at the 1% perturbation level. $\endgroup$
    – ProfRob
    Jan 9, 2023 at 7:31
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    $\begingroup$ @ScienceAJ the conditions inside are not much affected from the fusion process. These 150 metric tons of matter in 1 cubic meter produce some 300 watts of heat. $\endgroup$
    – fraxinus
    Jan 9, 2023 at 13:46
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    $\begingroup$ As a comparison, the dynamic viscosity of honey is around 10 Pa s, so on the same ballpark as the interior of the Sun. $\endgroup$
    – nonDucor
    Jan 10, 2023 at 9:00
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    $\begingroup$ @nonDucor interesting - I'll add that. $\endgroup$
    – ProfRob
    Jan 10, 2023 at 10:09
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If one thinks about "hard" as solid, having stiffness/rigidity, an ability to retain a certain shape when subjected to anisotropic stress, then the answer is NO, it is not hard.

The solid state emerges from having directional interactions between the particles. The solid substances in our daily life are solid either because of specific ordering of their atoms (particles that have size and don't allow penetration of each other) or because of the directional covalent bonds, or a combination thereof.

This is where your wrong assumption starts:

the immense amount of atoms packed together

No atoms there, at all. Atoms require much quieter environment in order to form. 3 orders of magnitude lower temperature could be a good start. Lower density advisable as well, or else one gets an electron-degenerate matter.

What exist in the Sol's core is an extremely compressed and hot gas of free electrons and free atomic nuclei.

Reasonable models for solid degenerate matter do exist and some properties of astronomic objects containing degenerate matter (white dwarfs, neutron stars) are explained by partial crystalization.

The core of a main sequence star (e.g. Sun) is considered not degenerate. It is a simple plasma where particles only isotropically scatter against each other.

(It is simple in regard to not having some underlying structure like e.g. in metals where we have plasma behavior of the electron gas but we also have a crystal lattice)

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    $\begingroup$ a neutron star isn't that some extremely packed(compact)(heavy) object, ? if I remember correctly $\endgroup$ Jan 9, 2023 at 15:56
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It is not solid. But it is hard. Its Young's modulus is about $10^{16.5}\text{ Pa}$. It is thousands or millions of times more than the Young's modulus of any ordinary solid matter. For comparison, the largest Young's modulus is approximately $10^{12}\text{ Pa}$ for diamond.

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    $\begingroup$ Interesting, I couldn't find any information on it's hardness, viscosity or other similar properties. How is Young's modulus defined for a plasma, It's often said that young's modulus is not defined for a gas or liquid. How is it defined in the sun. Can you cite these values ? $\endgroup$
    – James K
    Jan 8, 2023 at 16:25
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    $\begingroup$ I agree that the Young's modulus is not used for gas. But if an ideal gas is compressed by a piston in a cylinder isothermally, then it will be felt as a solid body with an corresponding Young's modulus at small changes of piston position. This value is approximately equal to the gas pressure. The solar core presure is [nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html] $2.477 \times 10^{11}\text{ bar} \approx 10^{16.5}\text{ Pa}$ $\endgroup$
    – Imyaf
    Jan 8, 2023 at 17:45
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    $\begingroup$ But "gas pressure" is still fluid. I don't think this pressure value corresponds to "hardness" or "resistance to flow", which would be characteristics of a solid. Does this answer the question "is the sun's core a solid", because it seems to say "yes it is". I have doubts about that. $\endgroup$
    – James K
    Jan 8, 2023 at 18:53
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    $\begingroup$ @Imyaf saying that "it would be stiff it were contained" and "it is hard" are quite different assertions. Specifically, in the contexts of the behaviours the question asks about, this question has relatively little relevance. $\endgroup$
    – Will
    Jan 9, 2023 at 8:54
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    $\begingroup$ @William Martens Link is nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html without ] $\endgroup$
    – Imyaf
    Jan 9, 2023 at 15:59
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The Sun's core is mind-bogglingly dense, about 150,000 kg/m3 (about 15x denser than lead, 7x denser than uranium, 6x denser than osmium).

Such a high pressure would compress matter into a wigner crystal (but with nuclei against an electron background instead of the other way around). But the core of the sun is also mind-bogglingly hot. The thermal energy prevents this from happening.

By hardness, I mean having stiffness/rigidity, an ability to retain a certain shape when subjected to anisotropic stress.

No. The core of the sun is a gas and has a low viscosity. Ideal gas viscosity increases with the square root of temperature and doesn't depend on pressure, so a naïve ideal gas formula predicts a viscosity about 225 times more viscous than air. This is somewhere between water and cooking oil.

Supposing we got the indestructible observer to throw a punch randomly inside the Sun, what would this observer feel?

The trouble would be the density. Swimming would be hard, much worse than in mercury, and you could only swim or punch at the center. Each g of gravity gives you up to 140 gs of buoyant forces. And gravity rises to over a hundred gs (compared to "only" 27g at the surface) at the right distance from the center. Your unobtanium body would survive these extreme forces but fluid dynamics alone would dictate your posture.

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Perhaps the core of the Sun (a Yellow dwarf / G2V Main sequence star. ) would be behaving like a Non-newtonian fluid.

Since The Sun is at Hydrostatic equillbrium i.e the gravity is the same as the thermal pressure created from thermonuclear fusion exerted thus there has to be something against the force you apply otherwise it would go supernova i.e though there is a lot of pressure trying to implode the core there is the same amount of pressure trying to explode the core.

Thus if you apply more pressure less force then it would behave like a Plasma/Gas however if you apply more force less pressure then it would behave like a solid.

The Internal pressure is approximately $3.4 \times 10 ^ {11}$ atm (Note: Atm means Standard Atmosphere or the pressure above anything on Earth)

You can plot the force it applies against the compression using Maxwell–Boltzmann distribution

Yellow dwarfs like the Sun usually aren't at the Chandrashekar limit, which prevents the Yellow dwarfs from becoming a Neutron stars which are Supported by Degeneracy pressure given by the Pauli exclusion principle

Neutron stars crust would kind of behave like a solid (it would be the hardest material of the entire universe known as nuclear spegghati) because it is more compact and packed even though one of it's forms, the Quark stars is a Quark gluon plasma, a hotter state of plasma.

There are cation atoms in an plasma thus there are free electrons, That's why plasma conducts electricity

To sum up: At less force it would behave like a plasma but the more you apply force the more hard it would become.

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    $\begingroup$ "the gravity is the same as the fusion energy/thermal pressure exerted" - you cannot compare or equate three quantities that have different units/dimensions. The interiors of neutron stars are not solid. $\endgroup$
    – ProfRob
    Jan 15, 2023 at 18:15
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    $\begingroup$ Just a note: plasmas do have atoms, they are ionized gases, which means that there are free electrons, but those electrons are coming from the ionized atoms $\endgroup$
    – Justin T
    Jan 15, 2023 at 18:18
  • $\begingroup$ Thanks a lot, @JustinT. Corrected $\endgroup$
    – user47732
    Jan 16, 2023 at 5:34
  • $\begingroup$ Thanks a lot, @ProfRob. I have a question: Why wouldn't an Neutron stars crust or the interiors be solid? $\endgroup$
    – user47732
    Jan 16, 2023 at 5:42
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    $\begingroup$ Can I ask how old you are? $\endgroup$
    – Connor Garcia
    Feb 9, 2023 at 16:30
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Solid is one of the four states of matter which is uncompressible with atoms that are bound together. The sun's core is compressible and its atoms are completely unbound. Apply a bit of extra force or vacuum and the core will compress or expand.

Solids comprise the following: ionic solids, molecular solids, network covalent solids, metallic solids, and amorphous solids like glass, rubber, gel, plastics can't be compressed either.

There is thermal energy equivalent to about 2700 megawatt hours per kilo, and an atom bomb is about 3500 megawatt hours per kilo of plutonium, so your immutable object would have to apply a higher kinetic force in order to move it.

The atoms of the core are like a billiard table knocking at 100ds of kilometres per second. If you put a space-time based object in hot gas higher than 100,000'C like a human hand, the hand has vaporized in a millionth of a second, only confined by other atomic explosions, the atoms fly off in all directions, hydrogen protons at 610KMS in a vaguely brownian motion.

If you imagine a solid, i.e. salt crystal and compare the sun core matter, the expanding atomic force is far greater than the force of contact of a hammer hitting a diamond, perhaps by millions of times. The speed of nuclei of atoms changes relative to temperature... Most matter in the sun's core travel at an average of 610km/s and sometimes 1200km/s: enter image description here

To qualify the sun's core, you can say it's thermally caustic and amorphous and dissolves anything very fast so that atoms dissipate pretty fast, immutable hands could compress or expand the core physically if they have a force higher than an atomic explosion, a real hand would vaporize outwards into a cloud that expands at 1-2 kilometres per second according to vaguely brownian motion, there's also gamma rays, x-rays, UV, visible light, at higher quantities than the lasers used for slicing steel.

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  • $\begingroup$ Thanks for the info's. A kilo of the sun material contains ~2.7 Gigawatt-hours of stored thermal energy, A kilo of Plutonium 239 can give 23 GWh, and a bomb is 15% efficient so it's only 3.45 Gigawatt for the bomb versus 2.7 gigawatt for the sun. Vaguely the same range. $\endgroup$ Jan 15, 2023 at 17:55
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    $\begingroup$ No you are confusing energy and power. In fact you seem to be confusing force, pressure, power, velocity and energy in your answer. $\endgroup$
    – ProfRob
    Jan 15, 2023 at 18:11
  • $\begingroup$ You are changing the subject from the atomic bomb comparison. Why? That was in fact, correct, wasn't it. The maths is of the thermal energy content are quite accurate, and changing the subject vaguely to avoid aknowledgeing that is silly. The protons move at 610 KMS and the latent the latent energy of the material is 2-3 gigawatts per kilogramme, exactly the same as an atomic bomb. It's a fair newbie reply. Why risk me labelling 500 pasting all over the website? $\endgroup$ Jan 15, 2023 at 19:29

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