Re: How close can you get to a Neutron star (Pulsar?) and not cook

"Erik Max Francis" <max@xxxxxxxxxxx> wrote in message
news:z_2dnQWvxanMEp3bnZ2dnUVZ_riknZ2d@xxxxxxxxxxxxxxxx
nunya@xxxxxxx wrote:

On Mar 20, 9:37 am, chornedsnork...@xxxxxxxxxxxx wrote:
What is NS-strength magnetic field?

10^7 to 10^14 Gauss. "Magnetars" are thought to slightly exceed
10^16 Gauss.

The neutron star magnetic field is strong at the order of magnitude of
10 km from the source of the said field.

Insanely strong; on the surface it pulls the predominantly iron
crust up unto fibers a tenth of a millimeter or so tall against the
NS's (not quite equally insanely strong) 10^11 or so gravities
(according to Robert L. Forward who did the math to get that sort of
detail for his _Dragon's Egg_ books).

Something to keep in mind through this discussion of magnetic fields is
that the units we're using here -- SI tesla, or c.g.s gauss -- are
measurements of *magnetic flux density*. Non-rigorously, this is the
number of magnetic field lines passing through a unit area. Needless to
say, this depends strongly on your distance from the source of the
magnetic field. These figures of up to 10^14 G ~ 10^10 T for neutron
stars is a measure of the magnetic flux density _at the surface of the
neutron star_.

It would be like saying, "The brightness of the Sun is 6 x 10^7 W/m^2."
That figure is correct -- for the surface of the Sun. But its
luminous intensity (W/m^2) depends on how far you area from it. What's
really important in determining how bright the Sun is intrinsically is
its luminosity, which we of course measure in watts, W, and for the sun
is about 4 x 10^26 W.

The analogous figure for a dipole magnet would be the *magnetic dipole
moment*, which has SI units of T m^3 ~ Wb m. To compute the magnetic
flux density Phi at a distance r from a dipole with dipole moment P,
you'd use

Phi = P/r^3,

Depends on the angle of the vector to the point where you measure the field
with the dipole as well.
I suppose that can be ignored for a BOTE approximation, but I wonder where
on the neutron star these field strengths are supposed to be measured.

(The power of three is because dipole field strength varies as 1/r^3,
not 1/r^2.) According to Planetary Fact Sheets [1], for instance,
Jupiter's dipole moment (with R_j = 71 398 km) is (4.28 G) R_j^3 = 1.56
x 10^20 Wb m. Note that writing it this way -- (4.28 G) R_j^3 -- just
means that the magnetic flux density at Jupiter's cloud tops is 4.28 G.

So a neutron star with a radius of 10 km and a surface magnetic flux
density of 10^10 T has a magnetic dipole moment of ~ 10^10 T (10 km)^3
is about 10^22 Wb m, on the order of a hundred times that of Jupiter's.
A magnetar would have have on the order of a hundred times more on top
of that. The Sun's surface magnetic flux density is about 5 mT -- a
hundred times that on the Earth's surface -- so its dipole moment is
~10^24 Wb m. That means that the dipole moment of the Sun is about the
same as that of a magnetar! (This shouldn't be all that shocking; the
magnetic field from neutron star arises in part from the core of its
collapsing progenitor.)

Hm. Interesting. I hadn't gotten around to comparing field strengths with
solar-system objects yet. Puts things in perspective.
The values I find on Googling for the solar magnetic field strength,
however, give me a value of ~1.6x10^23 Wb*m for the sun's dipole moment,
though. I attribute the difference to variability over the solar cycle.

Any terrestrial planet of appreciable size orbits at least a million
km from the neutron star.

We've gotten to Jinxians; deformed egg-shaped super-ex-Jovians
orbiting just outside the Roche limit.

So at ~1 000 000 km from a typical neutron star, the magnetic flux
density would be ~10^-5 T. That's on the order of the magnetic flux
density of the Earth at its surface (30-60 uT). That's a pretty big
whopping field for something that's 1 Gm away, but it's not
ripping-planets-apart strong.

A BOTE calculation of the Roche limit for a fluid body of density similar to
Earth around an average-size neutron star gives me a value of just under
1,000,000km (959,338 is the actual number I got, but that sort of accuracy
is completely unwarranted here). So that actually looks like a good
approximation.
Incidentally, a planet orbiting that close would be rather warm, unless it's
a very old neutron star. PSR 1257+12a orbits at .19AU (a little more than 28
times further out) and has an estimated mean surface temperature of 266K.

A field that is not too planet-destroyingly strong is very good for
imaginings of native life-forms.
But I'm thinking magnetic heating may only be an issue for very close
planets around really old neutron stars that have had time to cool off such
that magnetic heating becomes more important than regular radiant heating,
or planets around really freakin' powerful magnetars. Oh well.
The magnetic field from the pulsar at PSR 1257+12a is probably completely
negligible, then, unless it gets some significant boosts from trapped
interplanetary plasma. Might help by an order of magnitude or so.
But say you've got a planet in an orbit where the NS's field strength is of
the same order of magnitude as Earth's, around a NS that's cooled enough for
the planet to be comfortable- the rapid switching of an Earth-strength field
still out to be able to provide biologically useful energy, no? Hm. I have
some calculating to do.

In short, I think the strength of the magnetic fields of neutron stars,
at least in the context we're talking about here, has been overrated.
They have huge magnetic dipole moments for their size, so it's not
surprising that the magnetic fields at their surfaces are ridiculously
high.

All assuming, of course, I haven't made some gross errors, which given
my history of the last few days, probably isn't too safe a bet.

I don't think you have. But I suppose I could be wrong too.

-l.
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