An anti matter planet behaving like a star

Question

In your space journey your ship systems have spotted an unusual source of gamma rays: it's the size and the mass of a planet and it has a pulsating behaviour.

Further observations shows that you are observing a planet made of anti matter hosted in a cloud of normal matter (for clarity sake, I envision this cloud to be more or less like the solar wind/cosmic dust around our planet, a "galactic stream of cosmic dust"). When the matter falls on the planet it generates a burst of gamma rays which blows away other matter and then shuts off the source of the gamma rays, which in turn allows other matter to fall on the planet. This results in the pulsating behaviour of the emission.

Let's assume the planet has formed. Is such scenario realistic under our currently known physics laws?

Answer 1

The scenario you describe - accreting matter being expelled by radiation pressure - will occur if the object exceeds the Eddington luminosity, a limit derived from hydrostatic equilibrium based on the balance between gravity and radiation pressure. The Eddington luminosity $L_{\mathrm{Edd}}$ is proportional to the mass of the accreting object $M$. If we assume that the mass of the planet is, say, roughly that of Jupiter, we find a maximum luminosity of $L_{\mathrm{Edd}}\sim126L_{\odot}$ - pretty significant!

Let's make our model a little more detailed. Let's assume the planet is made of pure antihydrogen, and that the outer layers are completely neutral. (The validity of the latter assumption is a point of contention in my view; low surface temperatures lead to higher accretion rates and a temperature increase, while high surface temperatures lead to lower accretion rates and a temperature decrease). We can also assume that the planet is embedded in a cloud of neutral hydrogen. If the energy generation of the planet at high energies is only due to matter-antimatter annihilation, then the luminosity should be $L=2\epsilon\dot{M}c^2$, where the $\epsilon$ describes the fraction of energy radiated away, and the factor of two arises from the fact that part of the planet is annihilated, too. Let's be conservative and say $\epsilon=1$. We then find that if the planet is radiating at the Eddington luminosity, the mass accretion rate is $\dot{M}=L_{\mathrm{Edd}}/(2c^2)\approx6.5\times10^{13}\text{ g s}^{-1}$.

Is the planet likely to be accreting at this rate? Let's assume the gas cloud is part of a cool, high-density portion of the interstellar medium - say a number density of $n\sim10^4\text{ cm}^{-3}$ and $T\sim10^2\text{ K}$. Assuming the accretion is spherically symmetric and transonic, this leads to an accretion rate of $\dot{M}_t\approx1.8\times10^{13}\text{ g s}^{-1}$, which is sub-Eddington. This would produce $L=3.2L_{\odot}$, which is fairly significant! However, I would guess that the true accretion rate (and therefore the true luminosity) would be lower, as the high-energy emission would quickly ionize and heat up nearby atoms, which in turn would lower the accretion rate until an equilibrium is reached.

Therefore, it seems likely that the planet's luminosity would be decidedly sub-Eddington, and the accretion would proceed roughly in equilibrium. Rather than pulsations, there would likely be steady emission (relative to the dynamics suggested in the original question).

Some notes:

• If accretion proceeded at the rate given by the Eddington limit, the planet would be destroyed on a timescale $\tau\sim M_J/\dot{M}\sim10^9$ years. The true lifetime will be higher given that the accretion rate is inversely dependent on mass.
• I'm curious about the ionization balance surrounding the planet. I believe $T\sim10^4\text{ K}$ would be required for us to assume essentially full ionization, and I would be surprised if the equilibrium surface temperature ends up being that high. Presumably, it would be quite higher than the temperature of a typical giant planet! A luminosity of $L=3.2L_{\odot}$ actually produces surface temperatures of $T\sim10^4\text{ K}$.
• The photons created from matter-antimatter annihilation should have energies of about $938\text{ GeV}$. That's more than enough energy to ionize a hydrogen atom; at the Eddington limit, this object will emit $3.2\times10^{38}$ of them per second. If we naively apply the Strömgren sphere model of HII regions, we find that ionization-recombination equilibrium requires that the planet be surrounded by a region of ionized hydrogen about $\sim1000\text{ AU}$ in radius. As the accretion should be sub-Eddington, the actual radius will be correspondingly lower.

Answer 2

There was an answer, now deleted, regarding the energy resulted from the annihilation of a proton with a anti-proton and the comparison with the energy resulted from fusion. Too bad it was deleted, because there are conditions in which the answer was valid.

In the event of matter/anti-matter annihilation, the energy is likely to be emitted in any direction. And it's many orders of magnitude higher than the chemical bond energy. Which means a gamma emitted towards the planet is very likely to vaporize some anti-matter and eject it in space towards the cloud of matter above. Would this anti-matter be electrically charged (very likely at the level of energy we are speaking), the magnetic fields will deviate the ejected antimatter in areas where the cloud wasn't repulsed by the "initial" explosion.

With enough density of normal matter in the cloud, you may assist to a cascade effect causing a gamma storm engulfing the entire surface of the planet.

Which bring us to the important parameters which describe what happens on the anti-matter planet - the (absolute) density and the distribution thereof for the matter cloud.

• On one extreme - if is homogeneous and zero, nothing happens.
• On the other extreme - if it's homogeneous and dense enough, you may see a gamma storm which cause the entire planet to be evaporated and thrown into space as an ionized plasma of antimatter.

In between, various other scenarios - regular pulses being improbable, though not impossible - e.g. still happen if the "cloud" is instead a "galactic stream of cosmic dust - after repulsing a "wave" by a gamma burst, the stream renews the density of the cloud with other incoming matter.

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See also: Herbig-Haro objects - protostars for which the accretion disk falling into the forming stars ionizes and the created magnetic field ejects polar jets at "supersonic" speeds. Those jets collide with the surrounding nebula and produces EM emission in visible spectrum (recombination and bow shocks) without the corresponding (for a mature star) IR part of the spectrum.

How's the above relevant? Well, astrophysical magnetohydrodynamics is complex enough to allow a pulsating phenomenon (caused by the described configuration) to actually occur in the right conditions.
It is also conveniently complex enough to allow for quite a fair bit of plausible hand-waving; feel free to do it I don't think someone will jump to say: "No, that's impossible", especially after accepting the presence of an anti-matter planet.

To asses the safety of handwaving, a google search for "pulsating bow shock" brings in something like:

• this:

  ... The process is complicated by the existence of a whole class of pulsating shocks for which no macroscopic theory has been fully developed

• this:

  Approaching the shock the density of diffuse super-thermal ions increases about exponentially causing the interaction to readily become non-linear, causing the pulsation wave amplitude to grow and steepen during the downstream connection towards the shock ramp.

Answer 3

It would not pulse regularly. The emissions would sweep away the infalling matter, and it would stay off until it happened upon another cloud.

If the original cloud gradually closed back in from random motion, it would start very gradually with a few atoms at a time; these would renew the blown-away zone and prevent the cloud from re-collapsing around the body.

It would flicker, not pulse.

Answer 4

A cloud would not generate the pulsing behavior you describe.

For convenience, suppose earth is the anti-matter planet. A anti-matter burst over New York City would not have any effect over material due to impact the air over Melbourne because it would be shielded by the planet. If the explosions occur at average altitude of 100 km (the international definition of where space begins) the line of sight is restricted to a fairly small section of the planet -- considers the video taken from the ISS where you see only a small section of the plant even though it is much higher (about 400 km).

An infalling cloud of matter would be more less a continuous source of gamma world-wide. The propulsive force of gamma radiation is quite small, and most of the cloud would be essentially unaffected in terms of velocity as the force would be very distance-limited by the inverse square law.

Now, since you can assume a anti-matter planet, why not assume a different type of orbital cloud. Fill the heavens with large numbers of small chunks of matter ranging in size as needed to make suitable explosions when impacting the atmosphere. The resulting radiation profile will indeed be bursty and essentially random. I.e., there could be considerable gaps between events, or occasionally almost simultaneous.

An explosion of 1 kg of matter and 1 kg of antimatter is a pretty large explosion 43 million tons of TNT, 1 gram is still 43 kton a couple of times that of Hiroshima so your "cloud" would appear quite cloud-like at any significant distance. You just need to make your cloud thin enough that you do not get an excessive rate of infall.

Since much of the energy is carried away by neutrinos, the explosive effect of annihilation reactions is perhaps 50% of that for the equivalent atomic explosion. Still, you would detect the gamma and other EM radiation coming from these events at quite a distance which does fit with your scenario.