Star Matter Gate Blast Radius

Question

In an act of magical warfare, a wizard opens a gateway leading to the center of the Sun. Matter can pass through the gate freely in either direction. The gate does not last very long -- the wizard dies immediately and the gate vanishes shortly after that.

The gate is 20ft in diameter and is positioned a few hundred feet off the ground.

How fast does matter and energy pour through the opening? How long does the gate need to remain open in order to kill everything in a 10-mile radius? How long does the gate need to remain open in order to destroy the biosphere?

I am hoping the answer will contain math -- for example, X amount of energy will pour through per second, after Y microseconds this will be the equivalent of a large nuclear weapon which might kill everything in a 10-mile radius, after Z microseconds this will be the equivalent of the dinosaur-killing asteroid.

Answer 1

I'd like to take Lio's numbers and spin them a different way. His research found:

[The sun] has a density of 150 g/cm³ (150 times the density of liquid water) at the center, and a temperature of 15 million degrees Celsius. The core is made of hot, dense gas in the plasmic state (ions and electrons), at a pressure estimated at 265 billion bar (3.84 trillion psi or 26.5 petapascals (PPa)) at the center. Due to fusion, the composition of the solar plasma drops from 68-70% hydrogen by mass at the outer core, to 33% hydrogen at the core/Sun center.

Two things are going to come through this portal:

• EM radiation
• Hot matter

EM radiation is going to consist of photons passing through the portal while it is open, while hot matter is matter which will pass through first and then transfer its heat to the environment once it's on this side.

The key question is going to be how much energy gets to the Earth, so we can focus entirely on that.

One thing which is not explicitly specified in the question is how the expansion of the matter occurs. As the high pressure plasma from the sun spews through the stargate, it is going to pick up velocity and it is going to drop in pressure. The balance of these will affect the flux of matter. If the stargate acts like a giant nozzle, then all of the pressure will be converted to forward velocity, and the exit of the stargate will not result in a sudden decrease in pressure. If this is the case, we will see the entire raw temperature of the sun on both sides of the gate. On the other hand, if it acts more like a hole in a pressure cylinder, there will be less time to accelerate the matter. Less matter will pour through per second, and the matter that does pour through will undergo rapid expansion and cooling. In this case, the temperature differential across the gate will be larger, and infra-red radiation passing through will matter.

Fortunately, there is a reasonable guess as to what will happen: choked flow. Under choked flow conditions, the exit velocity of the material is the speed of sound at the outside pressure. This is a natural limit if you aren't paying attention to what you're doing with a nozzle, so its reasonable to guess that our wizard, failing to specify the conditions of the gate, will run into this limit. This limit is quite slow compared to the speeds that could be achieved with a better nozzle shape, but it does mean that calculating the EM radiation will be difficult because there will be a sudden drop in pressure. I'll ignore EM radiation from here on out (the matter itself is damaging enough).

The speed of sound is roughly 340m/s. Your 20ft diameter gate has an area of about 30m^2. This means we will have a volumetric flow of plasma around 10,200 m^3/s. At the specified density, that's 1530000000kg/s of matter streaming through the gate!

That's a lot of matter. This is going to get hot quite quickly!. The center of the sun is mostly helium. To keep the numbers simple I'll just pretend it's all helium. Helium has a heat capacity of 5.19 kJ/kg-K. Since the sun is roughly 15 million degrees K hotter than the earth, each kilogram of helium will carry 77,400,000 kJ of energy. Multiplying this by our mass flow rate we get a total energy flux coming through the gate of: 118,422,000,000,000,000 kJ/s. That's 118 EJ/s, or 118PJ/ms, if I do some conversions.

I do those conversions to make it easier to reference Order of Magnitude (Energy), one of the more fun pages on Wikipedia. They list:

• 210PJ - Energy released in the detonation of Tsar Bomba, the largest nuclear weapon ever detonated.

So right off the bat, we can see the thresholds. In the first millisecond or two that the gate is left open, the damage will be as mighty as the strongest nuclear bomb ever tested. Your 10 mile damage marker would have been more in line with what Fat Man did to Nagasaki in WWII. Fat Man was a mere 21kT, cmpared to Tsar Bomba's 50Mt, so your 10 mile line is broken in the first microseconds that the gate is left open!

As for ecosystems, it's not clear how resilient ecosystems are. However, it is worth pointing out that in the first hundred seconds, this gate would pump out more energy than strikes the earth from the sun in a single day. I would not want this gate open for any measurable periods of time!

Answer 2

Your blast radius encompasses more than the size of earth, plus you evaporate all rock in said planet:

Firstly lets have a look at the centre of the sun - the stuff you want to pour out on your unsuspecting enemies (and quite possibly everyone else). This link (emphasis by me) says:

It has a density of 150 g/cm³ (150 times the density of liquid water) at the center, and a temperature of 15 million degrees Celsius. The core is made of hot, dense gas in the plasmic state (ions and electrons), at a pressure estimated at 265 billion bar (3.84 trillion psi or 26.5 petapascals (PPa)) at the center. Due to fusion, the composition of the solar plasma drops from 68-70% hydrogen by mass at the outer core, to 33% hydrogen at the core/Sun center.

So lets compare that to your standard day on earth:

• Average air pressure of 1.01325 bars.
• Average temperature $16^{o}C$
• Air density $0.0012gcm^{-3}$.

The main driving force here is the difference in pressure being about 265 billion bar higher so the stuff at the center of the sun will flood through and quickly increase the temperature of the surrounding area to $\approx 15 million ^{o}C$ (not quite ideal conditions to support life). After 6 seconds, at this temperature difference we can expect to have boiled off the ground. The rate at which this will happen is given by:

$$ \frac{dT}{dt} = k (T_{s}-T_{e}) $$ Where $T_{s}$ is the temperature of the sun $T_{e}$ is the temperature of earth and k is some proportionality constant (depending mostly on the make up of gasses). Since this isn't hard science I won't go much further into this than to say that we can assume, at these temperatures and pressures that your particles are travelling around the speed of light so if we look at a basic radius calculation of $r= c t$ where r is the radius, c is the speed of light and t is our 6 seconds, we get a radius of $18\times 10^{8}m$, for a sense of scale Earth's radius is $6.4\times 10^{6}m$. Now perhaps some argument can be made for the boiled off rock delaying this rate of travel but you have to reduce it by a couple of orders of magnitude just to make it that you're only just about evaporating earth...you would need to have it open for much less than six seconds to even have a chance of keeping your planet in tact let alone anyone left alive.

Edit: Okay, you changed it from 6 seconds, however the whole idea is still going to wipe out all life unless you put the portal somewhere other than the center of the sun (the surface is around 6000 degrees rather than the ridiculous 15 million). Whatever you do you'll have to deal with the hydrogen gas which will come through hot enough to ignite and, with some tiny margin where you could possibly survive, you will burn off all the oxygen on your planet.

I know you want it to work though, so picking somewhere hot but much less dense (like the surface) is your best chance of keeping a planet intact.

Answer 3

Well. A fun question.

Lets ignore the physics of how the gate was created and just assume that there's a nice little hole in the centre of the sun where matter (and forces) go in on one side and comes out the other on Earth. This is where specifics about the operation of the portal matter.

Firstly: if you're not careful gravity is going to be fun. You've just opened a portal with half the mass of the sun on one side of it. If we say that the portal only lets forces through from the 'open' side (like a Stargate) then that's a whole lotta mass in a not very large area. Depending on the orientation of the portal you could be exposing the other side of the Earth to over 33000 g (this is a very naive calculation and assumes the portal just became a 20 foot wide ball with half the mass of the sun, but only if you're on the right side of it). Just for reference: The surface of Jupiter is dealing with 26 g.

If we assume the portal is barely open long enough for any plasma to get pushed through (See Leo Elbammalf's answer for more on that) then you still have issues: Namely that gravity propagates at the speed of light, passes through everything and doesn't discriminate between forms of matter. No matter how briefly the portal is open you just transmitted a shockwave of unimaginable magnitude not only through the crust of the planet (neatly cracking it like an egg hit by a nail) but also through the rest of the solar system, briefly creating a second gravitational body capable of knocking pretty much everything out of orbit including (and this is why we all hate instantaneous portal technology) the sun itself, which eight minutes later would find itself momentarily trying to orbit half of itself.

And that's not even all the fun! You've just blocked gravitational forces acting on half the sun, momentarily throwing the delicate balance of radiation pressure <-> gravity way, waaaay off. It might not seem like much time to you, but the energies involved here are mind boggling and very finely balanced. I don't even want to think what such a shock would do to the sun, but you can bet it wouldn't be pretty in the slightest. While the sun would probably survive there would (at the least) be a huge uptick in solar activity (you might even cause a small nova) scouring the Earth clean of all life.

Of course: If your portal doesn't transmit gravitational effects until you're already in it (a'la Portal) or transmits forces from all sides (a spherical portal of some form) then opening it in the middle of the sun won't have any meaningful gravitational impact. It will oddly be in a place where all the forces cancel out.

So: The specifics of your portal might matter more than you think. On the one hand You kill the Earth with superheated plasma, on the other you kill pretty much the whole solar system...

Answer 4

Due to scale, the vast majority of initial energy released will be "black-body" radiation. This will be released at close to the speed of light in a hemisphere shape. The angle of the gate relative to the surface of the earth is obviously important if enough energy is released.

The effect depends on the amount of energy required to destroy your gate-structure/mage. As soon as that much energy is released "into" the gate-structure/mage itself then the gate will (presumably) be instantly destroyed. Then you need to know what percentage of the released energy is intercepted and absorbed by the gate-structure/mage. The rest is what effects the surrounding area.

If your gate-structure/mage blocks $1\%$ of the radiation and requires $n$ joules to destroy then the gate will release $n\times 99$ joules before closing.

If the physical gate doesn't have a structure as such and it only shuts down when the Mage is "incapacitated" then just calculate as if the mage was the "structure". How many joules does it take to vaporise your mage? Note that it may also depend on how close the mage is to the gate. Light travels about $30cm$ in $1 nanosecond$. It may also depend on exactly what part of the mages body needs to be destroyed to close the portal. Hippocampus? The entire brain?

Based on Mrkvička's "Stefan–Boltzmann law" calculation above the joules of energy from black body radiation works out to the equivalent of about $2,002,582,949$ 1 megaton nuclear bombs per second. Or about 2 every nano second.

Note that it is entirely likely the gate will be destroyed before there is time for any matter to push through, regardless of the pressure. Matter is just too slow compared to electromagnetic radiation.

This wikipedia page gives lots of examples of orders of magnitude for energy.

Answer 5

Opening such a portal for even a fraction of a second would be like setting off a large hydrogen bomb.

The effect of an atomic bomb's detonation is to release a lot of energy (although not very much compared with the activity within a star's core). The bomb's initial radiation is blocked after the first fraction of a second because the air around the bomb becomes too hot and becomes opaque. After a fraction of a second, the sphere of air itself begins to glow intensely via black body radiation because it is now at several million degrees. This sphere expands rapidly because it's at extremely high pressure because of the heat. This expanding sphere becomes the blast wave. Objects in the path of the blast wave get turned into shrapnel. If the ground gets hit by the blast wave while it's still superhot, you get a lot of radioactive dust as well.

A mass of solar core material suddenly deposited into the air 100ft above the ground would behave very similarly- the main immediate effect on the surroundings would be to ionize and superheat the air around it and create a massive blast wave. Any wizard standing near (ie, within several miles of) such an event would be quickly killed unless they were standing behind cover (ie hiding in a trench or behind a mountain). At an elevation of 100ft, it would probably throw up a lot of radioactive dust since that's a very low altitude for even a kiloton class weapon- essentially you're getting the effects of a high yield groundburst.

And that's only the effect of keeping the portal open for a fraction of a second. Assuming no gravitational effects coming through the portal (as in Stargate SG-1), the jet of solar material would come through very rapidly (like a giant firehose of superheated plasma, producing similar atomic bomb effects down the entire length of the stream) and continue to produce unpleasant effects in an increasingly great radius. Keep in mind that a lot of the effects would actually be dissipated upwards out of the atmosphere, kind of like an enormous solar flare made from burning atmosphere and solar mass. For the most part, I suspect the stream of plasma would have sufficient velocity and mass that it would probably proceed in whatever direction the portal remained pointing, resulting in a stream of burning hydrogen and helium spraying out into space. I think you can mostly ignore the effects of gravity on the stream of solar mass if you chose to leave the portal open.

It would probably constitute an extreme hazard for thousands of miles and would considerably increase the heat of the atmosphere over time, but I suspect most of the energy of the phenomenon would end up dissipated into space around the planet. If the portal was pointed downwards, this analysis would not apply. In this case, my prediction is lava. Lots of lava.