The First Instalment – Weeks 1-2

I spent the first few days of the internship looking at the stacks and the scripts I had been given. An example of one of the initial stacks can be seen in Figure 1.

Figure 1 – One of the initial median combined stacks of Lyman Alpha Emitters in the SC4K catalogue (Sobral et al 2018). 

I have been using a Python script to measure the surface brightness of the sources in the stacks. The image stacks are centred on the stacked LAE galaxy and so the script measures the flux with the aperture centred here. It then takes measurements of the flux from a specified starting radius and ending radius in steps of equal interval, dr, which can be varied. The flux is measured using an annulus, which measures the flux in a ring shape starting from the specified radius and spanning the interval, dr. This means the measurements aren’t dominated by the central brightest regions of each galaxy and we can begin to measure the Lyman alpha halo. The surface brightness could then be calculated from the flux measured divided by the area of the annulus and is given in units of ergs-1cm-2arcsec-2

We are measuring the scale length for the stacks of the sources in each filter. We are unable to produce an accurate stack of all the SC4K sources across the entire redshift range since the different filters have different PSFs (different atmospheric seeing when observing) and also a different arc-second to kpc scale. Therefore, if we want to stack outside of each individual filter, we are only able to stack over a small redshift range and will need to control the PSF by degrading the images with better PSF to have the same seeing as the worst such that they are of the same quality.

The errors on these SB measurements were quantified by measuring the noise variation from the 3D cube of non-emitters stacks as discussed in more detail in my introduction to this project, which can be found here. The stacks of non-emitters were produced with the same number of sources as the emitter stack and the same magnitude distribution. This stack was repeated for another set of random galaxies in the COSMOS field with the same properties and added to the data cube. The noise could then be measured per pixel by looking at the median of the variation from stack to stack along the cube for each pixel. Once the noise had been quantified, a signal to noise (S/N) cut had to be applied so that only sources with a S/N equal to or greater than the cut were considered as detections. We are only able to make the fit to points that we can trust and thus only the detections that satisfy the cut. I have been using a S/N cut of three for this work.  Since the central regions are the brightest, with the highest signal, then as the radius of the annuli increases we are beginning to probe the faint Lyman alpha halo, with a lower signal, and so there is a lower chance of detection as the signal is decreasing while the noise is assumed fairly constant across the image, and hence a lower S/N. This is why it is so important to stack the data and reduce the noise in these images whilst amplifying the signal, otherwise the halo cannot be measured as the signal from these fainter regions cannot be distinguished from the noise for individual images of the sources.  

The script was then used to fit an exponential profile to the SB measurements of the form, , where Cnis the normalisation factor and ris the best fit scale length. We restrict the radius range in which we want to fit to, r, such that we only fit to the data points that measure the halo region of the galaxy and not the bright central regions. We only attempt to fit to the points if there are at least three data points that are both above the S/N cut, and also satisfy the radius range of the fit. 

Decreasing the radius interval, dr, can mean there are more points within a specified radius interval, however, this does not necessarily increase the number of detections as it decreases the amount of flux in the annuli and thus the signal is lower and so less chance of the S/N satisfying the cut. 

Figure 2 – Plot to show the number of points in a SB measurement of that stack, that are above the S/N cut limit of three.

We observe the expected trends in our data such as more detections above the S/N cut at lower redshift since the catalogue contains many more sources at lower redshift due to detection bias when observing across large redshift ranges and also due to imaging at lower redshift being of better quality. Only the brightest sources are detected at high redshift, not simply because there are no lower luminosity sources at this time in the universe, but because detection limits the ability to confirm faint objects in this data. 

Figure 3 – Plot to demonstrate the number of points that fall between a specified radius range for fitting the data to the regions that represent the Lyman alpha halo. The fit is only possible if there are at least three points available and so it is much harder at higher redshifts.

We also observed that the number of points in fit four that are above the signal to noise cut, (S/N greater than or equal to 3), and that satisfy the radius range of this fit, decreases significantly with redshift due to the lack of measurements above the S/N for the high redshift sources. 

The script has been written such that it gives a negative value of -99 for the best fit scale length if it is unable to perform a fit to that data, we can then log the y axis to remove these values from our plot so we can see the structure in the positive y values, the successful fits, more clearly and so that we discount any failed detections. 

I spent some time changing the starting radius, final radius and dr to see how this changed the data and try to find the ideal values. I also changed the radii over which we apply the fit such that there is now a separate exponential fit to the inner central bright regions of the galaxy and then a second fit to the fainter halo which can be demonstrated by the different fits in Figure 7.

Figure 4 – Table to show the conversions from arc-second measurements to kpc for the different redshift slices.

It is ideal to fit from a scale length of two arc-seconds such that we neglect light from the stars and are also not affected by the point spread function (PSF). Any real extension seen will be picked up by detections, and illustrated in the surface brightness profile, beyond this radius. We chose to measure up to a radius of five arc-seconds, which corresponds to roughly 40kpc at a redshift 3. Measurements in arc-seconds correspond to different sizes in kpc at different redshifts, as arc-second measures different scales at different redshift. Figure 4 shows the arc-second to kpc conversion ratio for the different redshifts, (and hence filters), these were calculated using the online Cosmological Calculator (Wright 2006).

However, attempting to fit from 2 arc-seconds only proves difficult as there are not many detections above the S/N cut across the redshift range making it difficult to obtain a SB fit and hence a best fit scale length. I may need to reduce my S/N cut in order to obtain more detections at higher redshifts such that we can measure a scale-length for these sources. 

Momose et al 2014, fit from a radius of 2” to a radius of 40kpc, which corresponds to 5.1 arc-seconds at z=3. Our data is not as deep as the data used in this study and so this is why we are not getting enough measurements in this radius range. This study uses a S/N cut of three and so we are continuing to use this for now in order to make direct comparisons. 

I plotted some of the surface brightness profiles for different dr and grouping combinations for each filter in order to check that the fit is working as expected. An example of which is the stack for the bright only sources in the filter IA484 and the SB measurements along with the fit is presented in Figures 5 and 6. When plotting the SB profiles, I have plotted the points with S/N>3 with a different marker style to the other points such that we don’t totally discard them, and also to visually demonstrate that they have higher errors as can be seen in Figure 6 with the SB in a log scale.

Figure 5 – Surface Brightness measurements for the bright source stack in the IA484 filter, with the initial exponential fit overplayed in a dashed line with a dr of 0.25 and measuring from a radius of 0 arc-seconds to 10 arc-seconds.
Figure 6 – The same Surface Brightness measurements for the bright source stack in the IA484 filter and exponential fit but with the y values logged such that small deviations from the fit and errors on the measurements can be seen more clearly.

Some stacks SB measurements have detections at a radius of around 6.5 arc-seconds, but this is not real. Hence why I needed to plot the SB profiles to see this, it appears that there are many detections around smaller radii values and then no detections for a few values, then suddenly a detection at a larger radius. This suggests the detections at larger radii are from noise fluctuating or another nearby source.

I have learnt through plotting many different plots, that I don’t want to be using anything greater than dr=0.6 for the measurements as there are not enough points within the radius intervals to be able to make the cut and so the fit is unsuccessful. 

Figure 7 – SB measurements for all sources in the IA427 band stack along with the different fits starting from different radii to probe both the central region and the LAH. All fits end at a radius of 5 arc-seconds.

I have begun looking into the fits more clearly and will now be fitting the data from a radius of 0 to 2 arc-seconds to probe the central regions and then from 1, 1.5 and 2 arc-seconds to 5 arc-seconds to look at the LAH, whilst varying dr = 0.25, 0.4, 0.5, 0.6. I will then investigate these fits further to decided on which represents the data the best. I will also need to plot the SB profiles using the radius in kpc rather than arc-seconds for reasons discussed previously. I also plan to plot the PSF for each filter onto these SB plots, which will be measured by looking at how far a star is extended in the images as an extension here is due to the PSF as a star should be a perfect point source.

I have also started to look at the evolution of scale length over redshift for all sources, at each redshift slice, and also for all the different groupings, such as AGN only vs star forming only, to see if there is any difference between these two samples. I am also starting to investigate if there is any relation between the median Lyman alpha luminosity of the sources in the stack and the measured scale length of the stack.

This work and my findings will be put into my next blog post on here very soon!

Emma Dodd

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