Neutron star destruction question

OmegaGuy · Post by **OmegaGuy** » 2006-11-14 09:09pm

How would I calculate how much energy it would take to scatter the mass of a neutron star of about 1.5 solar masses and accelerate it in all directions at 99.999999999999999% lightspeed?

Post by **Surlethe** » 2006-11-14 09:16pm

0.99999999999999999c is so close to c itself that any actual calculations you do are going to get a rounding error, I think. If you want a Newtonian lower limit, you could try the method outlined on the Alderaan destruction page of the main site; I'm not sure how GTR is going to impact the energy figures, though.

Kuroneko · Post by **Kuroneko** » 2006-11-14 10:07pm

Well, if your stated speed is v = [1-1.00e-17], then 1-v² = 2.00e-17, so that γ = 2.24e8. Then, at M = 1.5M_☉, the kinetic energy is E = (γ-1)Mc² = 6.0e55J. As for GTR, the absolute minimal timeframe for delivering this amount of energy is about 110 minutes; anything less will be stopped by a horizon. Not that a device with power of even a couple of dozen orders of magnitude less than this is even remotely realistic, of course.

Edit: recalculated for 1.5M_☉ instead of 1.4M_☉as before.

OmegaGuy · Post by **OmegaGuy** » 2006-11-15 01:35am

Yes, it's part of my original writing contest where I constantly try to outdo myself with ever wankier things.

Admiral Valdemar · Post by **Admiral Valdemar** » 2006-11-15 05:27am

Kuroneko wrote:Well, if your stated speed is v = [1-1.00e-17], then 1-v² = 2.00e-17, so that γ = 2.24e8. Then, at M = 1.5M_☉, the kinetic energy is E = (γ-1)Mc² = 6.0e55J. As for GTR, the absolute minimal timeframe for delivering this amount of energy is about 110 minutes; anything less will be stopped by a horizon. Not that a device with power of even a couple of dozen orders of magnitude less than this is even remotely realistic, of course.

Edit: recalculated for 1.5M_☉ instead of 1.4M_☉as before.

Pfft, that's why this is obviously the work of a Type-III or IV civilisation. When you control galaxies, what's a little smashing of neutron stars?

Course, real men throw galaxies.

Kuroneko · Post by **Kuroneko** » 2006-11-15 06:27am

Admiral Valdemar wrote:Pfft, that's why this is obviously the work of a Type-III or IV civilisation. When you control galaxies, what's a little smashing of neutron stars? Course, real men throw galaxies.

You must be joking. To perform this feat in, say, a day requires about ten orders of magnitude more power as the output of entire Virgo supercluster. A "Type IV" civilization would be completely incapable of accomplishing this--even if the costs of energy transport are magically neglected and it concentrates all resources to this task, it would still take centuries. Extrapolating the Kardashev scale, one could argue for a "Type V" civilization, but given that the requisite power level is higher than that of the visible universe, it's very dubious if that is even physically meaningful. Power greater than ~1e52W has no physical meaning whatsoever.

Ariphaos · Post by **Ariphaos** » 2006-11-15 09:54am

Kuroneko wrote:Power greater than ~1e52W has no physical meaning whatsoever.

Doesn't this only apply to a single point source? Anything skirting that is going to be generating an event horizon anyway - a civilization wouldn't want to concentrate that kind of power overmuch...

Kuroneko · Post by **Kuroneko** » 2006-11-15 11:05am

Xeriar wrote:Doesn't this only apply to a single point source? Anything skirting that is going to be generating an event horizon anyway - a civilization wouldn't want to concentrate that kind of power overmuch...

No, actually the opposite--pointlike objects are the exception. It's the fact that material objects will have a certain minimum size that leads to this power limit. One can think of the energy output causing gravitational redshift on further energy output, thus decreasing its intensity. This makes it at least plausible that there is a finite upper bound; to get a feel what it might be, think of an device of energy mc² radiating all of it away. The maximum speed of this delivery is limited by the speed of light and the size of the object, but the size of the object should be no less than the Schwarzschild radius (R ~ Gm/c²), giving maximum power output of c^5/G, give or take an Oppenheimer factor; perhaps not top surprisingly, this is the Planck power, i.e., Planck energy per Planck time. Strictly speaking, this is a "bad" argument, but a more rigorous relativistic one is possible (which actually shows that the maximum power is a quarter of the Planck power).

Ariphaos · Post by **Ariphaos** » 2006-11-15 03:07pm

Kuroneko wrote:No, actually the opposite--pointlike objects are the exception. It's the fact that material objects will have a certain minimum size that leads to this power limit. One can think of the energy output causing gravitational redshift on further energy output, thus decreasing its intensity. This makes it at least plausible that there is a finite upper bound; to get a feel what it might be, think of an device of energy mc² radiating all of it away. The maximum speed of this delivery is limited by the speed of light and the size of the object, but the size of the object should be no less than the Schwarzschild radius (R ~ Gm/c²), giving maximum power output of c^5/G, give or take an Oppenheimer factor; perhaps not top surprisingly, this is the Planck power, i.e., Planck energy per Planck time. Strictly speaking, this is a "bad" argument, but a more rigorous relativistic one is possible (which actually shows that the maximum power is a quarter of the Planck power).

Except for point particles actually being an exception (O_o) I understood that (Planck energy is roughly two gigajoules et al...) -

What I meant was, couldn't you have multiple, separate sources less than Planck power output individually but more so in total? Eventually, neglecting the expansion of space, I can understand how a horizon is inevitable - but until then, couldn't you assign a sum and find it meaningfully greater than the limit (even if separation is spacelike and the amount of meaning is thus questionable)?

For the relativistic argument, is the lower limit a function of redshifting?

Admiral Valdemar · Post by **Admiral Valdemar** » 2006-11-15 06:36pm

Kuroneko wrote: You must be joking. To perform this feat in, say, a day requires about ten orders of magnitude more power as the output of entire Virgo supercluster. A "Type IV" civilization would be completely incapable of accomplishing this--even if the costs of energy transport are magically neglected and it concentrates all resources to this task, it would still take centuries. Extrapolating the Kardashev scale, one could argue for a "Type V" civilization, but given that the requisite power level is higher than that of the visible universe, it's very dubious if that is even physically meaningful. Power greater than ~1e52W has no physical meaning whatsoever.

Well, yeah, since throwing galaxies would be at least a Type-V or more, where you're controlling superclusters with ease (the species I've read at that level don't see centuries as being anything further ahead than next week to us, I mean, if you're engineering galaxies, you obviously have plenty of space to spare). Apart from the fact that this exercise is entirely stupid anyway, there's little point in talking about such an event below some godly like beings.

I think someone just held down the "9" key a few seconds too long. The energy needed to make a neutron star be a degenerate cluster bomb (if that's what this is) is far less than having each piece fly off at essentially c. You could prod a quasar into a planet and knacker it, letalone throwing these things around as one would water balloons.

Sriad · Post by **Sriad** » 2006-11-15 07:17pm

I don't know about Valdemar, but throwing water balloons at .99999999999999999C is a bit beyond me. Sounds like a job for at least a Class III civ.

Admiral Valdemar · Post by **Admiral Valdemar** » 2006-11-16 11:28am

Trust you to take my analogy wrong.

Yeah, throwing a water balloon at that speed is doable (destroying a planet by a kiddies toy?), but forcing a neutron star to go that speed and fragment in all directions is a tad ambitious. There's far better ways of doing damage. Just drag two dense stars together and cause them to produce a collapsar/hypernova GRB event and direct that where you want.

Kuroneko · Post by **Kuroneko** » 2006-11-16 05:38pm

Xeriar wrote:Except for point particles actually being an exception (O_o) I understood that

They're an exception in the sense that given pointlike massive objects, it is possible to surpass this limit, but pointlike massive particles exist only in the abstract.

Xeriar wrote:What I meant was, couldn't you have multiple, separate sources less than Planck power output individually but more so in total?

Sort of. The above argument doesn't care if it the 'device' is actually a collection of disparate smaller objects. What it does mean is that if there are two objects of combined power output of more than ~1e52W, then there must be a horizon that prevents any realistic (non-pointlike) observer from observing both of them at once.

Admiral Valdemar wrote:Well, yeah, since throwing galaxies would be at least a Type-V or more, where you're controlling superclusters with ease (the species I've read at that level don't see centuries as being anything further ahead than next week to us, ...). ... I think someone just held down the "9" key a few seconds too long.

Yes, including the author of whatever work of fiction has a "Type V" civilization.

wilfulton · Post by **wilfulton** » 2006-11-17 02:15am

Surlethe wrote: If you want a Newtonian lower limit, you could try the method outlined on the Alderaan destruction page of the main site; I'm not sure how GTR is going to impact the energy figures, though.

If you use the Alderaan destruction page, keep in mind that neutron stars are very small in terms of dimensions, only 16 to 20 km in diameter, so the UL will be a few orders of magnitude smaller than the LL, which calculates the bare minimum necessary to overcome gravitational binding energy. The UL is to blow the object apart at 5 diameters per second, like what we saw happen to Alderaan. Unfortunately, in the case of a neutron star, five diameters per second doesn't have a prayer of overcoming it's own gravity (a LL explosion would have to throw the star's matter outward at ~1/3 the speed of light, such an event would be VERY dramatic in its own right)

Plugging in a 20 km neutron star with a sufrace gravity of 2e11 g's (about what to expect, IIRC), yields a 2.939 e 30 kg object (~1.5 solar masses)
with a surface escape velocity of 198,100 km/s, okay, about 2/3 the speed of light. You need ~ 3.5e46 J to do the job. Going to the relativity calculator, and putting in 3e30 kg for the mass as 198,100,000 m/s (it's in meters) looks like I stand corrected, you need 9 e 46 J to do the trick.

Bare minimum. And if you're smart, you'd pass on front row seating to such an event

Admiral Valdemar · Post by **Admiral Valdemar** » 2006-11-17 12:27pm

Kuroneko wrote: Yes, including the author of whatever work of fiction has a "Type V" civilization.

That was really down to a species accidentally making terraforming like machines that acted as Von Neumann probes and went haywire too quickly before they could be stopped. After a couple billion years of running (no FTL because of causality problems e.g. Novikov self-consistency principle), they'd gotten to the point that they had converted every solar system in whole superclusters. It was an insanely long time, but it was akin to accidentally introducing GM bacteria into the world today in many ways.