# baryon acoustic oscillation

I have one question about baryon acoustic oscillation.

I understand why we should have the baryon-photon fluid sound wave before recombination: Suppose we have a spherical overdense region. This region attracts matter gravitationally, however the pressure gradient of photon counteracts this attraction that is the seed of baryon acoustic oscillation. Since then, baryon-photon fluid moves outward with the speed of sound.

I don't understand the last statement. Maybe, I am confused with a silly thing, but as far as I understand, transmission media don't move toward the direction of wave. Media(baryon-photon fluid in this case) just oscillate. In this sense, I would say that baryon-photon fluid should just oscillate, but it really moves outward.

What am I missing? I tried to make an analogy with actual sound wave in air, which was not quite helpful.

Thank you so much.

• "This region attracts matter gravitationally..." I think dark matter also plays a role in attracting ordinary matter gravitationally, and therefore, was crucial in setting up the BAO. Maybe the experts can enlighten. @john – SRS Mar 9 '18 at 14:01

Maybe your confusion comes from thinking that oscillations must be perpendicular to the direction of propagation, but it doesn't.

The fluid does oscillate, just as a sound wave in air oscillates. Hence the name baryonic acoustic oscillations (BAOs). Particles are compressed, and this compression moves away with the speed of sound (which is something like half the speed of light), but if you consider a single particle, it only moves back and forth in the direction of the sound wave.

I suppose you do know the difference, but for future readers, here are two animations (burrowed from here) showing the two types of waves. First the longitudal wave, of which BAOs are an example:

And next the transversal wave, of which light and ripples in a pond are examples:

• First of all, thank you for your answer. I think I understood BAO is longitudinal wave. What BAO tells us that original overdense region induces baryon-photon fluid sound wave and because of this baryon-photon fluid moves outward. See the contents and animation at astro.ucla.edu/~wright/BAO-cosmology.html. Your animation has a few of crests, whereas the animation at the above website has only one and moves outward. Where does this difference come from? – john Jul 31 '15 at 14:36
• @john: My animation is just a general wave 1D, not particularly a BAO. The one you link to is a 2D animation. In reality, the waves propagate in all three dimensions. In addition, the waves in my animation are continiously stimulated (as from a vibrating guitar string), whereas yours is a single wave (sort of like the shock wave from an explosion). The BAOs were more or less continuously supported, until decoupling when the photons diffused away, "freezing" the waves. I think the Wiki article explains it well. – pela Aug 1 '15 at 21:08
• I think my animation describes BAO before decoupling, because it won't move after decoupling as you said(the last moment of mine). Is it what you wanted to say? (You said that The BAOs were more or less continuously supported, until decoupling, which I think is wrong to explain my animation) @pela – john Aug 2 '15 at 3:18
• @john: Okay, "continuously supported" was bad phrasing, but when a disturbance travels outward, the fluid elements push other fluid elements outward, which continue the disturbance. I'm a bit outside my zone of comfort here, but once the pressure has fallen in the central overdensity and the sound wave has left, my understanding is that the fluid will fall back, build up new pressure, be pushed out again, and so on until decoupling. – pela Aug 2 '15 at 20:33
• Yes. That was my understanding too. But, all references and animations imply that BAO should be a single wave, and we have only one characteristic scale, which is sound horizon. If you and I are correct, we have to have many scales that are the wavelength of BAO multiplied by integers. @pela – john Aug 3 '15 at 4:02