We began this week by analysing the negative slices, using the same methodology as the week before. The intention of this was obtain a measure of to what extent the noise could have affected our detections in the positive mapping. The principle underpinning this technique is that any negative flux that exists within our slices is of nonphysical origin, and hence by calculating their significance in an aperture set to the size of the PSF (Point spread function) we can begin a statistical analysis of our data and begin computing a Luminosity Function for the region around CR7.

The above graph is a histogram of the signal to noise including all the apertures from our sample above 3σ. Clumps A, B and C of CR7 are highlighted in the lines. The positive apertures are given by the red lines, and the blue is from the negative map. Interesting to note, is that whilst at the lower end there appears to be an even number of bins with more positive than negative and vice versa, towards the higher end we observe an offset of positive over negative detections at the highest signal to noise. These are expected to correspond to real detections. Even more interestingly, our highest signal to noise source that we detected was in fact a negative, at 5.21σ. This has interesting implications into the nature of noise in the ALMA data to detect noise that is so significant. This is an interesting thing to observe, and we wonder if it is of the same origin as noise (from the CCD) in the rest of the cube or from something completely different to do with the observational apparatus.

What we want to achieve from this data, is to now compute a ‘CII Luminosity Function’ for the region surrounding CR7, and to compare this to theoretical models for this place and time in the Universe. A luminosity function relates the number density of galaxies to the luminosity they emit. This will allow us to observe whether this is an over dense region which holds implications on the nature of reionization in the Universe. One of the first steps in achieving this, is to calculate the volume of the region of the cube, so we can determine the number density of the galaxies in this region of space.

In order to calculate the volume of the ALMA data cube we started by looking at the redshift difference from the closest end of the cube to the far end of the cube. Using z=6.604 as the redshift at the centre of the cube we could calculate the redshift at each end by looking at the velocity offset. In one direction, the velocity offset was 957 km/s and the other -1289 km/s. Using Δz = Δv/c, where c is the speed of light, we calculated the redshift at each end of the cube. We could then use Ned Wright’s JavaScript Cosmological Calculator to find the co-moving volume at each redshift, with the difference between the two giving us a shell of volume within which the cube lies. In order to find the volume of the cube we then multiplied this shell by the area of one image slice over 4π (this is the fraction of the sky that the cube takes up). Each slice was found, from Gaia, to have an area of 51.2 arc seconds x 51.2 arc seconds. The total volume of our cube was calculated to be 12.33 mega-parsecs cubed.