Binary stars in a supernova explosion.

[dougettinger]

What is the current hypothesis for explaining what happens when one star of a binary or tertiary family becomes a supernova? Does the non-exploding star(s) maintain an orbit around the supernova remnant, or are they expelled along with the ejected matter, or do they disintegrate and diffuse into the ejected matter? And is there any observational data to back-up any part of the hypothesis? such as a neutron-normal star or black hole-normal star binary combination??

[Wayne]

Sure: The first stellar black hole ever discovered, Cygnus X-1 is a young blue star in orbit around a black hole. If you want to go hardcore into it, PSR J0737-3039 is a binary pulsar system, with two pulsars in mutual orbit. A similar system (a pulsar around a neutron star), PSR B1913+16, was used to confirm the presence of gravity waves, as the orbit decays exactly as predicted by General Relativity.

During the supernova event the orbit changes, of course, as the supernova blows a whole lot of mass out into space (unless it just collapses into a black hole, in which case much less mass is lost). With a loss of mass, the angular momentum of the non-exploding body is of course conserved (as orbital energy) and so the orbit becomes wider.

[dougettinger]

Thank you, Wayne. I think what I am hearing is that the orbit of the non-exploding star is changed, but nevertheless, preserved. Do any calculations exist that predict that a star the size of our Sun would not be disintegrated or be ejected from the gravity field of the remnant of its sibling exploding star? Most binaries that are studied are within 1.5 to 60 star radii of each other. It is hard to conceive that the power of the supernova does not oblibirate its neighboring sibling.

[Wayne]

"Obliteration" is a lot more difficult than you might think.

You basically need to take every atom with in it and give them enough energy to defeat gravity and reach infinity: Gravitational binding energy. This can be estimated without scary mathematics by assuming an object is a uniformly dense sphere. Obviously not correct, but it's in the right order of magnitude for a solid body and within a few orders of magnitude for stars. The equation is:

U = (3GM^2)/5r
Where:
U = gravitational binding energy
G = Gravitational constant
M = Mass
r = radius

For one solar mass with one solar diameter (2E30 kg and 7E8 km) and a value for G of 6.7E-11 we work out that U is equal to 2.3E41 joules. (Text gives it as 1.2E44, stars are not good examples to use for the simplified equation, but planets are)

Okay, so how much energy does a supernova have? We measure that in ergs, it's a more convenient unit, but ergs is easily convertable to joules. 1E54 ergs, a typical supernova, is 1E48 joules.

So if the Sun were close enough to a supernova, it would, by our first-order estimations, have a chance of being entirely disrupted. It would need to absorb one ten thousandth of the supernova's output. The inverse square law (feel free to go calculate it) ensures the Sun would have to be ungodly close to the supernova to have a chance of absorbing that much energy.

[dougettinger]

"Obliteration" is a lot more difficult than you might think.

You basically need to take every atom with in it and give them enough energy to defeat gravity and reach infinity: Gravitational binding energy. This can be estimated without scary mathematics by assuming an object is a uniformly dense sphere. Obviously not correct, but it's in the right order of magnitude for a solid body and within a few orders of magnitude for stars. The equation is:

U = (3GM^2)/5r
Where:
U = gravitational binding energy
G = Gravitational constant
M = Mass
r = radius

For one solar mass with one solar diameter (2E30 kg and 7E8 km) and a value for G of 6.7E-11 we work out that U is equal to 2.3E41 joules. (Text gives it as 1.2E44, stars are not good examples to use for the simplified equation, but planets are)

Okay, so how much energy does a supernova have? We measure that in ergs, it's a more convenient unit, but ergs is easily convertable to joules. 1E54 ergs, a typical supernova, is 1E48 joules.

So if the Sun were close enough to a supernova, it would, by our first-order estimations, have a chance of being entirely disrupted. It would need to absorb one ten thousandth of the supernova's output. The inverse square law (feel free to go calculate it) ensures the Sun would have to be ungodly close to the supernova to have a chance of absorbing that much energy.

Wayne, thank you for illuminaing me about using the gravitational binding energy and inverse-square law to help resolve my question.

I am still pondering what happens to a neighboring binary in a supernova explosion. For talking purposes assume the non-exploding star is like the Sun and 60 Sun radii apart from the supernova star. What possible calculations and/or logic could be used to estimate whether the subject star increased or decreased in size (mass)? And what kinetic energy could be determined that is added to the star to increase its potential energy or orbital distance?

[Wayne]

For talking purposes assume the non-exploding star is like the Sun and 60 Sun radii apart from the supernova star.

That's difficult since a star like the Sun can never explode.

What possible calculations and/or logic could be used to estimate whether the subject star increased or decreased in size (mass)?

The non-exploding star won't really be affected much. It'll absorb some of the ejecta for sure, but that shouldn't be a whole lot. Most mass transfer is done before supernova, when the hugely distended red supergiant overflows its Hill sphere.

And what kinetic energy could be determined that is added to the star to increase its potential energy or orbital distance?

You're misunderstanding orbital dynamics. No energy is added, but the orbit becomes wider. This is because the 'potential energy' of the star has to stay the same. As there is now less mass pulling the orbiting star, the proper gravitational potential is further away.

The equation is F = GMm/r^2. As you can see, to reduce either of the masses has to reduce F and thereby increase r to maintain the same energy, or energy has to be gained or lost. As there is no mechanism for gaining or losing the energy, we're stuck with force and radius.

[dougettinger]

For talking purposes assume the non-exploding star is like the Sun and 60 Sun radii apart from the supernova star.

That's difficult since a star like the Sun can never explode.

For talking purposes I meant that the Sun is the non-exploding Star and is 60 solar radii away from the exploding star.

What possible calculations and/or logic could be used to estimate whether the subject star increased or decreased in size (mass)?

The non-exploding star won't really be affected much. It'll absorb some of the ejecta for sure, but that shouldn't be a whole lot. Most mass transfer is done before supernova, when the hugely distended red supergiant overflows its Hill sphere.

I am primarily interested in the ejecta from the Supernova that lands or is captured by the neighboring star. Is the ejecta that is captured mostly what is equal to the projected face of the neighboring star times the depth of ejected material ? Also, if I remember correctly, not all supernonae such as blue giants are preceded by the red giant phase similar to SN 1987A. The previous reply does lead to two more questions. What is a "Hill sphere"? For those close binary stars that are subjected to a distended supergiant phase what mass increase (2x, 0.5 x, ?) might be expected?

And what kinetic energy could be determined that is added to the star to increase its potential energy or orbital distance?

You're misunderstanding orbital dynamics. No energy is added, but the orbit becomes wider. This is because the 'potential energy' of the star has to stay the same. As there is now less mass pulling the orbiting star, the proper gravitational potential is further away.

The equation is F = GMm/r^2. As you can see, to reduce either of the masses has to reduce F and thereby increase r to maintain the same energy, or energy has to be gained or lost. As there is no mechanism for gaining or losing the energy, we're stuck with force and radius.

I understand how the law of gravity equation works. My question was poorly constructed. Does the blast energy and only the blast energy add any significant kinetic energy to the star adjacent to supernova in a binary star system? And how could it be estimated?

[Wayne]

No, it doesn't.