Fairly straightforward question. Imagine a gas giant planet, like the size of Jupiter, in orbit around a massive star. The star goes supernova.
What happens to the planet? Is the energy of the supernova enough to strip away the atmosphere, leaving just the rocky core behind? Is there a way for the planet to remain in orbit around the resulting white dwarf?
Simulations of the dynamics of planets close to massive stars during a supernova (Veras et al. 2011) indicate that a planet in a reasonably tight orbit ($\sim2\text{ AU}$) around all but the lowest-mass supernova progenitors is almost certainly going to be ejected from the system. The cases where a planet does survive place it near periapsis, almost as far from the star as it can be. As many giant planets are hot Jupiters and thus reside only a fraction of an AU from their parent stars, the percentage of these planets that are not ejected from the system is extremely tiny. The survival rate for a planet in an orbit like Jupiter's are certainly better, but still quite slim.
Additionally, many supergiants undergo periods of extreme mass loss ("superwinds") in the stages of their lives immediately preceding a supernova. This mass loss plays a significant role in the evolution of the star and the evolution of the orbits of any planets bound to it. In fact, Veras et al. argue that it could lead to the ejection of small bodies orbiting the star even before the supernova itself occurs.
Of course, a large fraction (although not all!) of the planet's material will be stripped away by the ejecta. I haven't been able to find many good treatments modeling mass loss by the planet, but Vila et al 1980 (not the clearest or most detailed paper, I know) put together a couple grids of models of various planet masses and semi-major axes. It looks like a 1-2 Jupiter-mass planet at a couple AU around a 4-8 solar mass star could lose about 30% of its material. In addition to being flung out of the system, your planet is going to get a lot of its mass ablated away and ejected.
As a side note: The remnant of a star that undergoes a supernova will be a neutron or a black hole, not a white dwarf. The planet will remain in orbit around it (assuming the scenario where it orbits far enough away to not be fully destroyed) but will actually have its orbit expand, as the remnant will be several times less massive than the original star and angular momentum must be conserved. This expansion could be on the order of several times the original orbit's semi-major axis.
Quoting Randall Munroe:
[the] rule of thumb for estimating supernova-related numbers: However big you think supernovae are, they're bigger than that.
Here's a question to give you a sense of scale: Which of the following would be brighter, in terms of the amount of energy delivered to your retina:
- A supernova, seen from as far away as the Sun is from the Earth, or
- The detonation of a hydrogen bomb pressed against your eyeball?
Applying the physicist rule of thumb suggests that the supernova is brighter. And indeed, it is ... by nine orders of magnitude.
Based on the above, my guess is that the gas giant will be stripped naked of all its gases and maybe even part if not all of its rocky core will sublimate under the astonishing large radiative flux which will shower it.
Then, whatever remains will be probably moving too fast to be gravitationally bound to the remaining dwarf, and would probably fly away into space, or at least on a different orbit.
From "Rescue Party" by Arthur C. Clarke...
"He increased the magnification until only the center portion of the nova was visible. Close to its heart were two minute condensations, one on either side of the nucleus. 'Those are the two giant planets of the system. They have still managed to retain their existence—after a fashion. And they were several hundred million miles from the sun. The nova is still expanding—but it's already twice the size of the Solar System.'"
Yes, this is science fiction from 1946, but it actually seems to be pretty accurate.
A more scientific analysis
It has often been claimed that a supernova can radiate as much energy as the Sun will in its entire lifetime.
10 billion years * 365 days * 86400 seconds * 3.8 * 10^26 J/s = roughly 10^43 Joules of energy.
Now, to find the binding energy of the gas giant(to see if it even survives the explosion)
E = 3GM^2/5R. Let's use Jupiter as an example.
(3 * (6.67 * 10^-11) * (10^54 kg))/(5 *(6.6854 * 10^7 m)) = 10^35 J.
The gravitational binding energy of Jupiter is eight orders of magnitude less than the total amount released by the supernova.
"But Jupiter's orbit is 2.444 billion kilometers in circumference!" says the annoying man in the back row. "Surely all of that energy cannot be distributed in a cone directly at it!"
sqrt(6.6854 x 10^5 km Jupiter radius/7.606 * 10^18 kilometers orbital "surface area") = ~8.7 * 10^-13. Multiply by 10^43. Yep, Jupiter is toast. Within an order of magnitude of the necessary gravitational binding energy, but most of the upper atmosphere will boil off. The most you can probably hope for is a rapidly expanding plasma cloud. At that point, it doesn't really matter whether it still orbits the white dwarf or not, you at most will only have an Earth-mass barren rock anyway.
TL;DR: Your gas giant is toast unless it is very far from the host star. Hope you weren't using it for a fusion candle.
