This Wiki article claims that the surface of this pulsar, at it’s equator, is spinning at a quarter of the speed of light. That’s seems incredibly fast for ordinary matter to be to be moving, much less revolving around a very tight radius.
Is it just the incredible denseness that keeps it from flying apart? If it slowed down would it become a black hole?
Really interesting! My quick, back-of-the-envelope calcs using the Wikipedia-provided values give me:
vs
So… the gravity force is about 2000 times greater than needed to keep the star together. Of course, I’m not including anything fancy like relativity.
Yes. It’s useful to keep in mind that on the scale of planets and stars, tensile strength effectively doesn’t exist and objects can be treated as droplets of liquid for such questions as “why are they that shape” and “how do they hold together”.
Wow. Thanks.
Also, pretty much all of the numbers associated with pulsars are huge beyond human imagining. Like, in some pulsars, the magnetic field has a density ten thousand times as great as lead. Not the matter of the star; literally just the magnetic field.
I’ve been trying to understand that since you posted it. Even googling and reading up on it doesn’t really help much.
AI overview:
The magnetic field energy surrounding a neutron star—specifically a magnetar—possesses an energy density that is profoundly greater than the physical density of lead.
- Mass Density of Magnetar Magnetic Fields: The magnetic field of a magnetar can reach intensities of 1010Tesla (or higher), which results in an energy density (E/c2) more than 10,000 times greater than the physical density of lead.
- Physical Density of Lead: Lead has a density of approximately 11.34 g/cm³.
- Neutron Star Density: A teaspoon of neutron star material, regardless of its magnetic field, already weighs about 10 million tons.
- Magnetic vs. Material Density: The energy stored in the magnetic field of a magnetar is so high that it can deform atoms into thin cylinders and polarize the vacuum itself.
- Theoretical Comparison: This magnetic field energy density is so intense that it is suggested to be one of the only things in the universe (other than a black hole) that can store energy at a higher density than ordinary physical matter.
I’m trying to picture what that gravity field would look like? !s it still transparent (like gravity fields on earth) or is it more like a solid?
Correction, Magnetic field - not gravity field.
That is interesting. Some stars spin so rapidly that they become flattened (oblate), like M+Ms; Regulus and Achernar are examples.
Despite spinning much more rapidly than Achernar, a typical magnetar is hardly oblate at all
A nice animation here.
NASA SVS | Migrating Magnetar Hot Spot Animations.
Trapped particles and starquakes in this field would produce brilliant flashes of X-rays, so I really don’t think you’d want to get close enough to see the surface in any detail.
A quote from Wikipedia on Magnetars, the term for this subtype of pulsars.
As described in the February 2003 Scientific American cover story, remarkable things happen within a magnetic field of magnetar strength. “X-ray photons readily split in two or merge. The vacuum itself is polarized, becoming strongly birefringent, like a calcite crystal. Atoms are deformed into long cylinders thinner than the quantum-relativistic de Broglie wavelength of an electron.”
If even x-rays are being messed up, I doubt visible light would get through without being wildly distorted.
OK, you know how matter can be converted to energy? Well, it’s not really converted: Matter is always energy. We just don’t think of it as such, because it’s so much denser than most other forms of energy we encounter.
Most. But electromagnetic fields also contain energy. And the electromagnetic fields in a magnetar are so ludicrously strong, that they contain energy much denser than any sort of what we’d call “normal” matter.
That AI overview is wrong, though: Magnetic fields that strong cannot polarize the vacuum, because doing that would require producing magnetic monopoles, and magnetic monopoles are way too massive. An electric field of comparable magnitude probably would polarize the vacuum, but you only need electrons (much lighter) in order to do that.
The Scientific American quote used the term too, and googling it does seem like magnetic fields can polarize the vacuum.
Vacuum Polarization by a Magnetic Field and its Astrophysical Manifestations
A region with such a strong magnetic field wouldn’t fit into familiar material-like labels. It would rip standard matter into hot plasma instantly.
Electric and magnetic fields are interchangeable (within rules) by simply changing reference frames. To see the violence that even stationary matter would experience in such magnetic fields, consider the electron in an orbital of a hydrogen atom. A characteristic speed for that electron (for the purposes of a semi-classical estimation of effects) is around 106 m/s. In the reference frame of this electron, a magnetic field of 109 tesla would appear as an electric field of 1015 V/m, much higher than is needed to rip the atom apart.
Similar levels of violence can be seen through other considerations. For instance, the magnetic moments intrinsic to charged particles and to electrons in atomic orbitals are of the general size of one “Bohr magneton”. In the presence of this strong field, the magnetic energy experienced by the particle would be around 10 keV, or some ten thousand times higher than the binding energy of hydrogen.
The intrinsic connectedness of electric and magnetic fields (thus, the “electromagnetic” field) means that large electric and magnetic fields must both be able to influence the vacuum if either can. One vacuum effect from such strong magnetic fields is that radiation (say, an X-ray photon) will propagate differently depending on its polarization. This is observationally relevant since X-rays are a handy way to look at violent astrophysical objects.
On thinking about it, I think what’s referred to as “vacuum polarization” is not production of real particles, but influence on light via photon-photon scattering, which is a process that requires virtual electrons and higher-order interactions, and which therefore occurs to only a negligible degree at human-scale energies.
The language around this topic often includes casual flip-flopping between classical and quantum descriptions.
The magnetic (or electric) fields here are those from the classical Maxwell’s equations. Polarization is a property of continuous (classical) media or in this case the continuous vacuum. And while vacuum polarization only arises due to quantum effects, the classical language remains common when describing the effects for small enough deviations from the classical behavior. The intrinsically quantum corrections can indeed be cast as classical polarizations (or magnetizations), as changes to classical charges, or as modifications to Coulomb’s law, depending on the context at hand.
Since, in a physical medium, polarization arises when an external electric field induces (or aligns existing) dipoles in the medium, it’s an attractive analogy to think how “dipoles” might be “formed” in the quantum picture, but as is often the case with virtual particles, the analogies get sketchy pretty fast. It’s always just “loop corrections” or similar in the underlying calculations, and the virtual particles are doing their virtual particle thing within those calculations.
I am trying to understand this better. Can @Chronos provide any references? I am following the discussion in this thread and that helps, but I would like to see some more background.
Thanks
A magnetic (or electric) field contains energy. The energy per unit volume depends on the strength of the field. Specifically, the energy density is given by u = \frac{B^2}{2\mu_0} , where B is the strength of the magnetic field, and \mu_0 is a fundamental constant called the permeability of free space, which describes the strength of magnetic interactions. In SI units, magnetic field would be measured in teslas, energy per volume would be measured in joules per cubic meter, and \mu_0 = 4\pi\cdot10^{-7} Tm/A.
The pulsars with the strongest magnetic fields, called magnetars, can have fields as strong as 10^11 tesla. Plug that into our formula, there, and you’d get an energy density of about u_{mag} = 4\cdot10^{27} \frac{J}{m^3}.
Meanwhile, lead has a mass density of around 19000 kg/m^3. If we use Einstein’s famous equation to convert that to an energy density, we have u_{lead} = 19000\cdot(3\cdot10^8)^2 \frac{J}{m^3}, or 1.7*10^21 J/m^3.
So I guess I understated it before; it can be more like a factor of a million.
@Chronos, Thanks for your contributions to this thread. I have a better understanding - better, but still a lot of this is hard to wrap my head around.
As long as you are still participating… I’m trying to imagine how something this massive isn’t a black hole.
How much denser would PSR J1748−2446ad have to be before it became a black hole. Or am completely misunderstanding how that works?
For that specific pulsar, we’re not entirely sure, because we don’t actually know its precise mass nor radius, just estimates. On the other hand, there are some that we do have a better handle on, such as PSR J0952−0607 - Wikipedia . That one has a mass of about 2.35 times the mass of the Sun, and a radius of around 12 km.
For comparison, a black hole with that same mass would have a radius of 7 km. But that’s the radius for an object to have to be a black hole, not the radius for it to become one: If you take a non-black-hole object, and increase its mass and/or decrease its radius enough, and it’ll get to a point where it starts collapsing, with nothing that can stop it. We don’t know precisely where that point is, because we don’t have a good enough understanding of the strong nuclear interaction to calculate it, but PSR J0952-0607 is probably very close to that limit (in fact, its mere existence rules out a lot of neutron star models).
That is fascinating reading. This bit is interesting:
“The distance of PSR J0952−0607 from Earth is highly uncertain”
And it’s 5 billon years old - if I’m reading that right! Wow.