A Question about tiny tiny stars, and radiating heat

[Chrono_13]

A brilliant person once said “First get your facts strait, then proceed to distort them at will” or something like that.

My question, is what would happen if say… a sun of relative density to our own, but only the size of a golf ball, just appeared in say… downtown LA, and sustained at that size for one minute?

What kind of effect could we expect? Would everything nearby simply burst into flames and evaporate? What kind of range could we expect? What if it was a Magnetar? (planet would probably implode around it… Magnetar you scary…)

Thank you so much for your input in advance!

 

[Bankoletti]

If it was a "sun" with comparable relative density to our own, than there is no chance it would be a magnetar (which is a neutron star, a completely different beast with many orders of magnitude higher density than ordinary stars).

Under assumption nuclear fusion would be somehow sustained inside your golf ball, you wouldn't get much else than a very bright and hot lightbulb. :) Actually, speaking very broadly and generalized, this is something that fusion nuclear power plants are attempting to recreate for energy production.

 

[sophiecentaur]

Boy, what a good question! It made me think of the boxing quote: "A good big one will beat a good little one".
I read this quote " Despite its intense temperature, the peak power generating density of the core overall is similar to an active compost heap, and is lower than the power density produced by the metabolism of an adult human" in a Wiki page about the Sun. That was not intuitive! - but maybe I really should have know it.
Your golf ball piece of the Sun would be at high temperature because it is inside a massive 'compost heap' but it would cool down very rapidly (in the sort of time that the filament of a very big light bulb would cool down. The Fusion would instantly stop but, in any case, it would only represent something like 1W of Power. So I would say that it would be a bit of a non-event for most of the inhabitants of LA .
Re reading your question makes me suspect it could be part of a SciFi plot(?).

 

[Chrono_13]

Interesting! So because of its size I assume the problem is that there simply wouldn’t be nearly enough pressure to create much heat and would almost instantly die out? Basically safe to touch, the way you describe it. I understand a flash in the pan wouldn’t have much effect. But I did specify that this tiny star was sustained for one minute. So let’s assume that it does not degrade for that minute because it’s being sustained by an outside force.

My understanding is that the core of the sun is approximately 15 million degrees Celsius. So the question now becomes, what happens when a golf ball sized object that is 15 million degrees Celsius, and stays at that temperature for one minute. What then happens in its surroundings?

Also you are quite correct that this is going to be (probably) used in a bit of fictional writing I’m working on. I dislike the “Because magic” mentality many writers use to cop out from learning a little bit of science.



*Oh I’m rather aware of the HUGE differences between an average star and a magnetar. I was merely posing the additional question, “What would happen if you had a sudden golf ball magnetar” given its incredible density and magnetic field.

 

[sophiecentaur]

My understanding is that the core of the sun is approximately 15 million degrees Celsius. So the question now becomes, what happens when a golf ball sized object that is 15 million degrees Celsius, and stays at that temperature for one minute. What then happens in its surroundings?

I was trying to work out the amount of heat in the hot golf ball. Apparently, the Sun's density is only a bit higher than water, so the mass of the golf ball sized piece would be around 50g. The specific heat capacity of Hydrogen is in the same region as Water so the golf ball would, in classical terms, have
0.05X 4200 X 15 X 10⁶J of thermal energy, which comes to about 3MJ, which is about 1kWhr.
It would be good for someone else to check on this because it, yet again, is really not much - but more than the heat generated whilst it's sitting there for a minute. So your scenario would perhaps need to be reconsidered. The range of cooling would be governed by the Stefan Boltzman law which tells us that the rate of heat transfer is proportional to the fourth power of the temperature difference so the thing would 'cool down' to a reasonable temperature 'ever so quickly'. So that would produce a bit of a bang - but only 3MJ worth of bang. That's like 0.5kg of Nitroglycerine? (see this Wiki link) but I don't know how to work out whether the cooling down would really cause such a rapid shock wave. Any container could slow it down and tame it a bit - in the end, the total energy would still only be around 1kWhr, so it would keep the room warm for an hour, lol. (Having blinded everyone at the start and warmed up the walls a bit)
Your idea of "stays at that temperature for one minute" would require it to be in a highly insulating and refractory box or it will cool down super quick. This particular scenario is a hard one (calls for a deus ex machina here). Your golf ball of Hydrogen would expand as well, until it has all changed into the gas phase. But you could take care of that in your gizmo (vent the gas safely outside through a pipe and let it burn safely as in an oil rig or just rise up in the air and be lost). The pressure in your gizmo would need to be around 10¹¹ Atmospheres but that may not represent a vast amount of energy - not like the energy in the 1kg of air in a compressed air cylinder, cos there's only 50g of Hydrogen.
You could make it pretty dramatic but still keep to a reasonable level of Science. Basically, it's not easy and so, as long as you don't take the Mick too much, I can't imagine too many people being able to pick holes.
On the other hand, if your gizmo keeps the golf ball intact and insulated, there really isn't much energy to be had (back to the compost heap). So you need to decide what you want to happen in your story and then the golf ball would have to be handled appropriately. Many unknowns here.

 

[BenAS]

I was trying to work out the amount of heat in the hot golf ball. Apparently, the Sun's density is only a bit higher than water, so the mass of the golf ball sized piece would be around 50g. The specific heat capacity of Hydrogen is in the same region as Water so the golf ball would, in classical terms, have
0.05X 4200 X 15 X 10⁶J of thermal energy, which comes to about 3MJ, which is about 1kWhr.
It would be good for someone else to check on this because it, yet again, is really not much - but more than the heat generated whilst it's sitting there for a minute. So your scenario would perhaps need to be reconsidered. The range of cooling would be governed by the Stefan Boltzman law which tells us that the rate of heat transfer is proportional to the fourth power of the temperature difference so the thing would 'cool down' to a reasonable temperature 'ever so quickly'. So that would produce a bit of a bang - but only 3MJ worth of bang. That's like 0.5kg of Nitroglycerine? (see this Wiki link) but I don't know how to work out whether the cooling down would really cause such a rapid shock wave. Any container could slow it down and tame it a bit - in the end, the total energy would still only be around 1kWhr, so it would keep the room warm for an hour, lol. (Having blinded everyone at the start and warmed up the walls a bit)
Your idea of "stays at that temperature for one minute" would require it to be in a highly insulating and refractory box or it will cool down super quick. This particular scenario is a hard one (calls for a deus ex machina here). Your golf ball of Hydrogen would expand as well, until it has all changed into the gas phase. But you could take care of that in your gizmo (vent the gas safely outside through a pipe and let it burn safely as in an oil rig or just rise up in the air and be lost). The pressure in your gizmo would need to be around 10¹¹ Atmospheres but that may not represent a vast amount of energy - not like the energy in the 1kg of air in a compressed air cylinder, cos there's only 50g of Hydrogen.
You could make it pretty dramatic but still keep to a reasonable level of Science. Basically, it's not easy and so, as long as you don't take the Mick too much, I can't imagine too many people being able to pick holes.
On the other hand, if your gizmo keeps the golf ball intact and insulated, there really isn't much energy to be had (back to the compost heap). So you need to decide what you want to happen in your story and then the golf ball would have to be handled appropriately. Many unknowns here.

Wikipedia has the density of the core of the sun at 150 times the density of water. That would make a bit of a difference. 15kg if the golf ball sized piece was from the core.

 

[sophiecentaur]

Wikipedia has the density of the core of the sun at 150 times the density of water. That would make a bit of a difference. 15kg if the golf ball sized piece was from the core.

Whoops - I was using the average density. Could make a difference to some of those conclusions. I'm really not sure about the 'heat content'. Specific heat capacity could be a nonsense concept in those conditions.
But what happens to the golf ball afterwards? Has it been maintained in the same condition or is it permitted (by the gizmo) fly apart / cool down. The compost heap figure still applies, though. Fact is that nuclear fusion is a low probability event. It only happens under very extreme conditions. Also, what we do in a fusion reactor is to cheat by using deuterium, extracted from regular water by separating out the D₂0. The time taken for two protons to come together and end up with Deuterium is very very long. Stars have to start with your bog standard protons so they have a lower energy output per kg.
How has this golf ball been obtained?

 

[stefan r]

I was trying to work out the amount of heat in the hot golf ball. Apparently, the Sun's density is only a bit higher than water, so the mass of the golf ball sized piece would be around 50g. The specific heat capacity of Hydrogen is in the same region as Water so the golf ball would, in classical terms, have
0.05X 4200 X 15 X 10⁶J of thermal energy, which comes to about 3MJ, which is about 1kWhr.
It would be good for someone else to check on this because it, yet again, is really not much - but more than the heat generated whilst it's sitting there for a minute. So your scenario would perhaps need to be reconsidered. The range of cooling would be governed by the Stefan Boltzman law which tells us that the rate of heat transfer is proportional to the fourth power of the temperature difference so the thing would 'cool down' to a reasonable temperature 'ever so quickly'. So that would produce a bit of a bang - but only 3MJ worth of bang. That's like 0.5kg of Nitroglycerine? (see this Wiki link) but I don't know how to work out whether the cooling down would really cause such a rapid shock wave. Any container could slow it down and tame it a bit - in the end, the total energy would still only be around 1kWhr, so it would keep the room warm for an hour, lol. (Having blinded everyone at the start and warmed up the walls a bit)

I think the bang would come from pressure change. The expanding ball would cool down when it expands. 0.5 kg of nitroglycerine is not trivial. Hand grenades weigh much less and they are mostly steel or iron.

Chrono13,

If you want descriptions to use in fiction try one of these:
thermic lance cutting
thermite welding
plasma cutter

The compost heap comparison is the current fusion rate. It took a long time to get hot. When you say you "sustain/contain" the gulf ball does it radiate? You can hold up a gulf ball and use it to eclipse the sun. At that distance looking at a ball of photosphere gas would be about the same as looking at the sun. Likewise sunburns etc would be the same/simlar. You can use a magnifying glass to amp up the sun's radiation. If the lense has 3X magnification the area is 9X, same as moving 3X distance from your gulf ball.
Here is a video of random objects burned with a concentrated solar. He also has a link for how to build a big solar concentrator using a CRT TV screen. The atmosphere filters some parts of the solar spectrum but it will be similar. A ball at core temperatures will have much more blue and UV light and will be brighter.

Magnetars are like magnets. The Tesla rating is the magnetic strength on the surface of the magnet. Field strength decreases with square of distance, same as gravity. A neodymium magnet might have around 1.2T field. Here is a demo of dangerous things done with a 4 tesla magnet. Magnetars can have over 10¹⁰T. A 4X10⁹ T magnet would have the same effect on an object at 10³ radius. A 2 cm ball of magnetar would have similar effects at 10 meters as a neodium magnet at 1 cm. Not an expert in magnets but I suspect a 10⁹T gulf ball in the center of a football field would pull in the bleachers, goal posts, and rip out the irrigation and any iron drainage pipes.

edit, the "mills bomb" fragmentation grenade from WWI weighed 765 grams.

 

[sophiecentaur]

I think the bang would come from pressure change. The expanding ball would cool down when it expands. 0.5 kg of nitroglycerine is not trivial. Hand grenades weigh much less and they are mostly steel or iron.

Chrono13,

If you want descriptions to use in fiction try one of these:
thermic lance cutting
thermite welding
plasma cutter

The compost heap comparison is the current fusion rate. It took a long time to get hot. When you say you "sustain/contain" the gulf ball does it radiate? You can hold up a gulf ball and use it to eclipse the sun. At that distance looking at a ball of photosphere gas would be about the same as looking at the sun. Likewise sunburns etc would be the same/simlar. You can use a magnifying glass to amp up the sun's radiation. If the lense has 3X magnification the area is 9X, same as moving 3X distance from your gulf ball.
Here is a video of random objects burned with a concentrated solar. He also has a link for how to build a big solar concentrator using a CRT TV screen. The atmosphere filters some parts of the solar spectrum but it will be similar. A ball at core temperatures will have much more blue and UV light and will be brighter.

Magnetars are like magnets. The Tesla rating is the magnetic strength on the surface of the magnet. Field strength decreases with square of distance, same as gravity. A neodymium magnet might have around 1.2T field. Here is a demo of dangerous things done with a 4 tesla magnet. Magnetars can have over 10¹⁰T. A 4X10⁹ T magnet would have the same effect on an object at 10³ radius. A 2 cm ball of magnetar would have similar effects at 10 meters as a neodium magnet at 1 cm. Not an expert in magnets but I suspect a 10⁹T gulf ball in the center of a football field would pull in the bleachers, goal posts, and rip out the irrigation and any iron drainage pipes.

edit, the "mills bomb" fragmentation grenade from WWI weighed 765 grams.

Interesting points. I got drawn into this despite it being such a daft (strictly) idea. No offence to the OP 'cos it's all a bit of fun. The set-up scenario would have to be even wackier than the one minute on Earth situation. There is a serious side to this thread, though. It's a lesson in how to simplify a physical situation and what variables you can ignore but still get sense. Someone introduces another variable and your mental model just collapsed.
I don't reckon you could even talk in terms of any fusion taking place in such an isolated golfball mass. The critical mass for the fusion in the centre a star must be enormous - more than Jupiter. perhaps?

 

[stefan r]

Interesting points. I got drawn into this despite it being such a daft (strictly) idea. No offence to the OP 'cos it's all a bit of fun. The set-up scenario would have to be even wackier than the one minute on Earth situation. There is a serious side to this thread, though. It's a lesson in how to simplify a physical situation and what variables you can ignore but still get sense. Someone introduces another variable and your mental model just collapsed.
I don't reckon you could even talk in terms of any fusion taking place in such an isolated golfball mass. The critical mass for the fusion in the centre a star must be enormous - more than Jupiter. perhaps?

I thought it was temperature and pressure for fusion. I am not sure you can call it "critical mass" unless it is fission. Plutonium splits because it is hit by a neutron. One nuetron and one plutonium nucleus is adequate for fission. In a critical mass the neutrons created by one fission event are likely to split more than one additional nucleus.

This thread claims 6.7% solar mass for proton fusion [link to article]. solar mass is 1048 Jupiter mass. So 70 Jupiter mass has enough pressure to resist expanding when the core is at proton fusion temperatures.

edit, supercritical is more than one. Critical mass is equal, each fission event creates one more.

 

[sophiecentaur]

I am not sure you can call it "critical mass" unless it is fission.

You could well be right and I could probably have used a more correct term but, to sustain fusion, the conditions have to be maintained. It happens in the Sun because there is such a large region of fusion and the conditions are right. You need sufficient Deuterium to be produced as an input to the process and the probability is very low. That implies to me that a golf ball volume may just not be enough for the statistics to work and to get a positive yield of energy out. If you have enough available power to sustain the conditions 1 golf ball's worth of fusion then the golf ball would be irrelevant(?).

 

[stoomart]

My question, is what would happen if say… a sun of relative density to our own, but only the size of a golf ball, just appeared in say… downtown LA, and sustained at that size for one minute?

What kind of effect could we expect?

Given the sun's Schwarzschild radius is just under 2 miles, I don't believe an object of its mass and the size of a golf ball is possible (even for primordial black holes); but either way, I would expect this BH-like object to promptly destroy the Earth and its moon.

 

[sophiecentaur]

just appeared in say… downtown LA,

I have been ignoring this stipulation because it would have to be 'brought' there and 'sustained', rather than just 'appearing'. How could it just turn up without having traveled there, unaided? If it was comping from outer space, then it would take minutes/ hours to arrive, during which time it would have to start off much bigger and have been dissipating itself in some way on the journey. That would be pretty impressive and involve much more Energy than the little remaining golf ball. SO I had to assume that 'someone' put the golf ball there and went away. But I can't see how It would sustain itself for a minute.

Given the sun's Schwarzschild radius is just under 2 miles

I don't think the OP suggests anything about a black hole. The word "sun" precludes the black hole idea.
Sci Fi scenarios are a nightmare for Physicists

 

[stoomart]

I don't think the OP suggests anything about a black hole. The word "sun" precludes the black hole idea.
Sci Fi scenarios are a nightmare for Physicists

Agreed. I interpreted "relative density" to mean 'equivalent mass' given the rest of the context, in which case it wouldn't be a sun, but rather a BH.

I imagine such an object would get there through a worm hole or quantum tunelling from another part of a multiverse.