Friday, 10 February 2012

Mapping Growth and Gravity with Robust Redshift Space Distortions

A quick post this evening, as I have been at a workshop for the SAMI instrument, and am off to Santa Barbara for the First Galaxies and Faint Dwarfs: First Galaxies and Faint Dwarfs conference next week, but a couple of things to post. The first is a paper by my ex-phd student, Juliana Kwan, who is now a postdoc in the US at the Argonne National Laboratory.

The paper is quite complex, and focuses on redshift space distortions. This can be difficult to understand, but here goes. We've mentioned a couple of times that matter in the Universe is arranged on a cosmic web, with clusters, clumps, filaments and voids. In fact, it looks something like this:
Our Milky Way galaxy is just a little dot in there. But the detail of the way the mass is distributed is a probe of our Universe, as its present structure carries the imprint of the forces that created it, including the make up of the Universe, the cosmic evolution, and even the nature of gravity itself.

What do we see when we look out into the Universe? Well, we can measure the position to a galaxy on the sky very accurately, but distance is not. But we can easily measure the redshift, or the amount features in the spectrum are moving to longer wavelength, and use our cosmology to turn this into a distance using the famous Hubble law.

However, there is a problem. The redshift we see is a mixture of two parts, one due to the cosmic expansion (the Hubble law bit) and one due to the `peculiar velocity, or how much the galaxy is whizzing about. By comparing to the Microwave Background, we know that our Milky Way is moving with a speed of about 500 km/s.

As we measure redshifts, not distances, these peculiar velocities distort the distances we calculate via the Hubble law. So, this happens
The blue on the right is the actual positions of galaxies in the cosmic web (in a simulation of the Universe). The green on the left show the effects of peculiar velocity, and things are stretched and squished from the space position.

In fact, clusters of galaxies, where velocities are typically several thousands of km/s, get stretched out into what are known as Fingers of God - although what they have to do with the Higgs boson, I don't know (and no, that's not a serious statement). Here's a real set of observations;
Now, the details of these Redshift Space Distortions allow us learn even more information about the Universe, but it is very hard to untangle. What Juliana's paper does is to look at the possible ways that can be used to extract science, and shows what needs to be done if you want to get "robust" measures. I'll write more on on what robust means later, but for now, I'll finish by saying "Well done Juliana!"

Mapping Growth and Gravity with Robust Redshift Space Distortions

 Juliana Kwan, Geraint F. Lewis, Eric V. Linder
Redshift space distortions caused by galaxy peculiar velocities provide a window onto the growth rate of large scale structure and a method for testing general relativity. We investigate through a comparison of N-body simulations to various extensions of perturbation theory beyond the linear regime, the robustness of cosmological parameter extraction, including the gravitational growth index, \gamma. We find that the Kaiser formula and some perturbation theory approaches bias the growth rate by 1-sigma or more relative to the fiducial at scales as large as k > 0.07 h/Mpc. This bias propagates to estimates of the gravitational growth index as well as \Omega_m and the equation of state parameter and presents a significant challenge to modelling redshift space distortions. We also determine an accurate fitting function for a combination of line of sight damping and higher order angular dependence that allows robust modelling of the redshift space power spectrum to substantially higher k.

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