Final Instalment – Results

We split our LAEs into Active Galactic Nuclei (AGN) sources and star forming only sources. The scale-length of the LAEs in this case are measured in the same way as when measuring the stack of all LAEs at each redshift slice. We only have AGN sources that we can measure the halo for at low redshifts. Other redshift slices either contain no AGNs in the catalogue or we are unable to measure the halo for these. 

We measure the scale-lengths using the two different methods mentioned in the previous instalment. One is to perform the fit to the surface brightness profiles from the radius corresponding to 96% of the PSF in that filter to a radius of 5 arc-seconds and then secondly, is to perform our fit to the PSF subtracted surface brightness profile measurements across the whole radius range of detections. 

Figure 1 – Redshift evolution of the scale-lengths measured from the AGN only stacks (circle marker) and star forming only stacks (star marker) separately. The scale-lengths are shown measured from the two different approaches of fitting to the halo only (green) and from 96\% of the PSF (blue) with the median values plotted with dashed lines for AGN and dotted lines for star forming. AGN only points are shifted by 0.1 in redshift in order to make the points more visible.

The scale-lengths produced by the fit from 96% of the PSF are on average lower than those given by the fit to the halo only (PSF subtracted profile). We trust the PSF subtracted measurements over the others, as we can be sure these are not measuring the size and extension of the central bright regions of the galaxies and is only probing the halo. However, for the AGN only sources there are only two measurements of scale-length at z ~ 3 and z ~ 3.33, the PSF subtracted method, as the rest of the redshifts are unable to perform a fit due to not enough detections. This is due to the errors on the PSF subtracted measurements being a combination of the PSF errors and the SB profile measurement errors. 

The two methods are also in disagreement over whether the AGN or star forming sources produce LAEs with larger scale-lengths. The halo only (PSF subtracted) suggest that the star forming sources are on average producing greater scale-lengths than the AGN sources since the median is higher, however it is not a significant different. The fit from 96% of the PSF suggests the opposite, that the AGN driven LAEs produce greater scale-lengths than star forming driven LAEs, since the median in this case is higher. Again, the difference is not significant suggesting that in fact AGN and star-forming driven LAEs produce similar scale-lengths for the LAH. 

Figure 2 – Scale-lengths over redshfit for the AGN only stacks and sub-stacks of radio (square) and X-ray AGN (triangle). The median of Wisotzki et al (2018) results with MUSE are included in the plot for reference, dashed line. All AGN points are plotted at the median redshift, radio AGN are displaced by 0.5 in redshift and X-ray AGN by -0.5 in redshift, in order to aid visualisation of the points.

Next, we used new stacks that divided the AGN category further into radio AGN and X-ray AGN. The AGN and sub stacks of radio and X-ray only are plotted in Figure 2, with the scale-lengths determined from the two different fitting methods. The point at z=2.5 seems to suggest that X-Ray AGN produce greater scale-lengths than the radio sources, however the error bars on this point are considerably larger than any other. We cannot draw conclusions from the small subset of measurements we have, as to whether there is a difference in the haloes produced by the two different types of AGN. 

The next step to be able to do this would be to combine our stacks of LAEs across all redshifts to improve the data and the number of AGNs in a stack and thus improve the measurement of the scale-length for this stack. This way we would be able to see if overall the scale-lengths differ between the two samples of AGN. We are able to do this since we observe that there appears to be no evolution in the scale-length over redshift in the range that we investigate. In order to stack across redshift, we must first PSF match the images. The data taken in one filter is of different quality of that in the next filter due to different atmospheric seeing and the different effects this has on observations in different filters. We can worsen our images such that they all have the same PSF – the PSF of the ‘worst’ image. Then we will have more LAEs for the radio and X-ray stacks making the stacks more reliable and the possibility of measuring an accurate scale-length more likely. We can then compare the two measurements to see if the radio or X-ray AGN are, on average, producing different size LAHs. My supervisor, David Sobral, will carry out this work to further investigate the LAE stacks. 

Figure 3 – Scale-length vs luminosity, with the scale-lengths measured from the PSF subtracted surface brightness profile for the luminosity constrained stacks over the entire redshift sample.

Using new sub stacks we also investigated if the luminosity of the LAE correlates with its scale-length. The LAEs at each redshift were split into four luminosity bins; log10(LLya) = 42.5 – 42.8, 42.8 – 43.0, 43.0 – 43.3 and >43.3. Stacks were created for each luminosity bin for each redshift and the best fit scale-lengths derived from fitting an exponential profile to the measured SB profiles of each stack, as was done previously for the other stacks. Figure 3 shows the results of these luminosity sub stacks and it can be noted that no clear trend is obvious for each redshift or overall and it is suggestive that all luminosity LAEs produce the same size LAHs. 

Figure 4 – The redshift evolution of scale-lengths for this work and past literature. The three different approaches for fitting to the surface brightness profile to measure the scale-lengths are shown on the plot with the medians plotted with a dashed line in the corresponding colour.

Figure 4 shows the final results plot of the scale-length evolution over redshift as presented in the last instalment. I have included it again in this blog post as it presents all of my final results plots. The Wisotzki 2018 measurements were taken with MUSE and are the best measurements of the Lyman alpha haloes to date. The median of these values is in agreement with our results from fitting to the halo only. This sample of LAEs does not overlap with the SC4K sample at all and measures very different LAEs. The SC4K catalogue spans a large area of the sky where as Wisotzki image a small area of sky, going really deep and detect faint LAEs, which we do not have in our work. However, the fact that the results match up so well suggests that the scale-length is definitely invariant of luminosity of the LAE and that all LAEs are producing similar size LAHs. 

Figure 5 – Surface brightness profile for the narrow band LAE stacks with the PSF plotted in black and any respective fits that were successful in deriving a scale-length. The SB was measured using anuuli photometry.

Figures 5 and 6 present the surface brightness profiles for the narrow and medium bands respectively constructed in this study in order to measure the halo of the LAEs. The SB profiles were measured using annuli photometry starting from r=0.05 to 10.05 arc seconds in steps of 0.25 arc seconds. A measurement was only considered a detection if the S/N was greater than 3 and this is shown as a star marker in the plots, any non detections were re-set to 3 times the noise and presented as an upper limit using a triangle. The black edge measurements are of the SB profile measured from the image stacks and the coloured edge points are of the PSF subtracted SB profile results. The error on these points are a combination of the SB profile and PSF error such that some detections in the SB profile became non detections in the subtracted profile as the noise had changed such that the measurement was no longer above the S/N cut. Again the non-detections were reset to 3 times the error and presented as an upper limit. The SB profile and PSF subtracted profile measurements were then fit with an exponential profile, to determine the scale-length, if there were at least 3 consecutive detections.

Figure 6 – Surface brightness profile for the medium band LAE stacks with the PSF plotted in black and any respective fits that were successful in deriving a scale-length. The SB was measured using anuuli photometry.

In the first instalment, I mentioned about how studying the evolution of LAHs across redshift can help to constrain the time in which the epoch of reionisation occurred, as the size of the halo should increase during this epoch. However, our data is not deep enough to be able to detect LAHs at the redshifts required (z~ 6 and above) to aid the understanding of this epoch, but the methods could be in future applied to deeper, higher redshift data to aid this investigation.

The work I have completed this summer has led to me being able to write a scientific paper, with David, to present our methods and findings. I am really proud of the work I have managed to complete this summer, none of which would have been possible without the funding I received from the Ogden Trust. I am extremely grateful to have been given this wonderful opportunity, and for all the support I have received from David, not only this summer but throughout my time at University. I am extremely grateful for all of the support and guidance I have received from my supervisor and also the other XGAL interns. Although we were all working on our own individual projects this summer, there has been a real sense of team spirit in the astro lab, and I have really enjoyed being a part of this and getting to know such great people!

Emma

The Third Instalment – Weeks 4-5

In order to convince myself that I am measuring the halo of the LAEs, I spent this week looking into measuring and understanding the point spread function (PSF). The PSF is a consequence of observation and is due to the atmospheric seeing on the night of observations. Different filters are affected differently by the conditions, higher redshift sources will have a lower PSF as a result of observing in redder wavelengths. It is a quantitative measure of how extended a point source will be in an image and since a star is a point source, it should appear so in an image under perfect conditions. However, it will never appear entirely point like in observational images, any extension seen in a star’s appearance is not real and is entirely due to these conditions of observation and can be quantified by the PSF of the image. Thus, when we are wanting to measure the extension of the Lyman alpha emission from our LAEs, the halo, we can only measure this beyond the PSF. The LAH is already extended by this amount due to observation. We can measure the effects of the PSF and subtract this from our surface brightness (SB) measurements of the LAH. It is also important to know the extent of the PSF as we can only begin to fit our exponential profile to the LAH at radii exceeding this. 

Table 1: showing the radii at which the PSF diminishes by 50%, 68% and 96%.

We measured the PSF per redshift using the stars in the corresponding filter images of the COSMOS field. The PSF was measured by performing annuli photometry on the stars and constructing a SB profile from these measurements, over the same range of radii and by measuring at the same intervals as the SB profiles for the LAEs. The SB profile of the stars were then normalised to start from 1 and all the stars in the catalogue median combined. This gave us a PSF for this redshift, and the same was repeated for each filter. I then plotted the PSF onto the SB profiles of the LAEs by normalising this to the maximum of the SB profile, in order to see visually the similarities and differences between the PSF and the SB profile of the LAEs.

By finding the point where the PSF diminishes, I determined a radius to start my exponential fit, for determining the scale length of the LAEs. We only want to be measuring beyond the PSF. I started by looking at the radius that corresponds to 50% of the flux, then 68% and then finally 96%, which corresponds to plus or minus 3 sigma. Since the SB profiles are normalised, the radius that corresponds to say 68% of the flux, is just the radius where the SB drops to a value of 0.32. These radii were determined for each filter from the corresponding PSF and for the three different flux cuts, see Table 1 and Figure 1.

Figure 1 – Example of the PSF in one of the bands, with the 50% flux value labelled in green, the 68% flux in red and the 96% in blue. The nearest value is calculated and then the corresponding radius given. Note the PSF has an exponential form as expected and also diminishes to the minimum level at a radius of less than 2 arc-seconds.

What we find is useful as it allows us to be able to make our exponential fits to the SB profile starting from a radius of less than 2 arc-seconds. Other studies, e.g. Momose et al 2014, start there fit from 2” but when we do this, at most of the redshifts, we are unable to measure a scale length as there are not enough detections to be able to make the fit. Our data is not deep enough. Therefore, being able to fit from lower radii is very useful and using the PSF we are quantitatively able to demonstrate why we are able to do this.

We then re-plot our SB profile with the PSF subtracted where the errors on this are now the errors on the PSF plus the SB profile errors originally.

Figure 2 – Surface Brightness profile for LAE stack in IA427. Note that errors on the PSF are very larger such that are no PSF subtracted detections due to the signal to noise cut of 3.
Figure 3 – Surface Brightness profile for NB816. Here there are no detections and we are unable to measure the halo at this redshift, the LAEs are more compact. Also note the difference in PSF between this profile and for IA427 (Figure 2) and how the PSF lies above the SB profile in this case so we are only able to measure the central regions.

Since all the stars SB measurements are median combined per radii, we calculated the errors on the PSF using the 16thand 68thpercentiles of the variation of the measurement from the median, per radii, as the down and up error respectively. We noticed that these errors were growing large towards the tail of the PSF, see Figure 2, and for some bands the PSF lies above the SB profile, see Figure 3. So, we decided to visually check the stars in the catalogue to make sure we were measuring the PSF correctly. The catalogue contains over 300 stars which we investigate in each of the 14 filters. Using DS9 imaging software we are able to view the images of these stars and easily inspect them. We remove double stars, stars that are too faint and also stars that are saturated, see Figure 4 for examples of these. Once we removed the flagged stars that may be affecting our PSF measurements, we end up having a catalogue of 196 stars to use. As well as measuring the SB for each individual star and then median combining these into a PSF, we decided to also stack the 196 stars images in 2D. Then from this measure the SB profile as the PSF. This way is more stable and the errors on the PSF are quantified by measuring the noise in the background of the stacked image, as opposed to using the percentiles of the spread of the individual stacks. It also means we are being consistent in the way we measure our PSF from the images of stars and the SB profile from the stacked images of LAEs. We find that the two methods are consistent in the PSF they produce, although we minimise the errors significantly with the 2D stack. This is what we use going forward with our measurements.

Figure 4 – Examples of stars in the catalogue that we use for measuring the PSF. The top panel shows stars that we expect to see and that remain in the catalogue. The second panel shows a binary or double star, which is not useful for measuring the PSF and will increase the errors in the tail of the distribution. The third panel is an example of a star that is too faint and so that is flagged and removed from the catalogue. Finally, the fourth panel is a star that is saturated. This is also flagged and removed from the catalogue.

A check we can do is to fit the PSF profiles with the exponential profiles like we do with the LAEs. Stars have no Lyman alpha halo and so this fit is not physical but it is useful to see that it produces the same results as a fit to the LAEs over the central regions, r=0-2”. The two are plotted together in Figure 5 such that the similarities can be highlighted. It is reassuring to see that the PSF includes the central regions of the galaxy and thus by investigating at our SB profiles past the PSF we are indeed measuring the halo, and not the light from stars in the galaxy.

Figure 5 – This plot shows the scale-lengths determined from the central fit to both the LAE stacks and also the star stacks, across redshift. This shows that the PSF is on the scale of the central 2″ of the galaxies and that the central fit is telling us only about the PSF and not about the halo region of the galaxies.

My next task was to then fit the exponential profile to the PSF subtracted SB profile detections, like has been done with the SB profile previously over a set radius range. The difference now was that I could fit across the whole range of radii in which there were detections as the central regions have been removed by subtracting the PSF. We thus are able to fit from lower radii now and get a better fit to the halo and a better estimate for our scale lengths. 

Figure 6 – SB profile for the IA527 stack with the stars stacked in 2D in the same filter to obtain the PSF. The SB profile has been fit from 2″ and from 96% of the PSF. The PSF subtracted SB profile has also been fit, across the entire radius range of the detections. Note the differences between the different fits and what they seem to say about the halo.

My results seem to suggest no redshift evolution of LAE scale-lengths over redshift. The PSF subtracted measurements appear to show a small decrease with redshift but it is not significant. We notice that the different approaches to fitting the SB profile and determining the scale-length produce different results. 

Figure 7 – The scale-length evolution of LAEs over redshift. The studies, previously mentioned in other instalments, for comparison are included and we can see they probe the same scales. The results of the three different approaches to fitting are shown and the medians plotted as dashed lines in the corresponding colour. Looking at my results, the fit from 2″ and the fit to the PSF subtracted profile are consistent with one another, where as the fit from 96% of the PSF seems to suggest LAHs of a smaller size.

The median scale length for each fit is shown by the dashed lines in the corresponding colours in Figure 7. The fit from 2” gives a value of 6.1645, the fit from 96% of the PSF gives a much lower value of 3.8067 and the fit to the PSF subtracted SB profile gives a value of 6.3981, which is in agreement with the first. The fit from 2” can only be applied to the data for two of the redshift slices and so the median that results from this data is not necessarily the most reliable. The scale-length derived from the fit to the PSF subtracted SB profile, is trusted the most as this method is more robust and we can be sure we are measuring the halo only and no components of the bright central regions. 

It can be seen in the SB profile for IA527, z =3.33, in Figure 6, why the three fits produce different values and that the PSF subtracted (halo only) and fit from 2” are in more of an agreement with each other than the fit from 96% of the PSF. 

The Second Instalment – Week 3

In the First Instalment – Weeks 1-2 I had finished my week having got to grips with understanding the physics behind Lyman alpha haloes (LAHs), the sample and data I am investigating and also the significance of surface brightness (SB) profiles. The scripts have been developed in order to measure these SB profiles from the stacked images of various groupings of LAEs. 

I have settled on using a dr of 0.25 for my SB plots, such that a measurement of surface brightness is taken every 0.25 arc-seconds for annuli of this size. 

The SC4K catalogue uses 12 medium band filters, 4 narrow bands and 7 broadband filters to image the LAEs across a range of redshifts. The SB profiles will be measured and plotted for the 12 medium bands and 2 of the narrow bands such that there are 14 filters altogether. Since the LAEs in the SC4K catalogue stacks I am using are across 14 different filters, this corresponds to 14 different redshift slices ranging from z~2 to 6. 

This way, we are able to study not only the LAEs at a specific redshift, but also compare between redshifts and see if there is any evolution in the size of these LAHs, where the size is parametrised by reff, the scale-length.

This way, we are able to study not only the LAEs at a specific redshift, but also compare between redshifts and see if there is any evolution in the size of these LAHs, where the size is parametrised by the scale-length, r. 

One important aspect to look into is if the luminosity of a LAE correlates with its scale length, see Figure 1.

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Figure 1 – – The median Lyman alpha luminosity of each stack plotted against the measured scale-length from this stack. The measurements are shown for each of the four exponential fits performed, where the only difference is the radius range in which the fit is performed such that it either measures the central regions or the LAH.
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Figure 2 – The same as Figure 1 on a different scale and where the y errors correspond to the error in the determining the scale length from the exponential fit and the x ‘errors’ are shown to illustrate the range of LAE luminosities included in each stack.

There are stacks of LAEs for each redshift slice containing all the LAEs in that image using the SC4K catalogue. The median combined stacked LAE, that represents this sample of galaxies, has a luminosity equal to the median of all the luminosities of the LAEs in that stack. This is the luminosity I used to investigate a correlation with scale-length. 

The ‘x errors’ on these plots correspond to the minimum and maximum luminosity galaxy in the stack, such they span the entire luminosity range of the data. Each point in Figures 2 is a different stack, with its median luminosity plotted on the x axis and the measured scale-length on the y axis. The scale-length is measured by an exponential fit to the SB profile of the stack measured using annuli photometry discussed in the previous instalment. 

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Figure 3 – Median luminosity of each stack against the scale-length determined from the exponential fit to the SB measurements across a radius range of 1.5 – 5 arc-seconds in order to probe the size of the LAH. The colour bar shows the redshift of the stack.

Since all the stacks span a similar luminosity range and all the exponential fit measured scale-lengths are included in the same plot, see Figure 2, it is a very over-crowded and not very useful plot. Instead the same figure was created for each fit individually with the median luminosity and the range in luminosity, as well as being colour coded according to the redshift corresponding to each stack. These are much easier to read and interpret and an example of one these for the fit of 1.5 to 5 arc-seconds is shown here, Figure 2. It is important, when the best fit is decided using the point spread function (PSF), to re-make these plots for that fit. We already know we want to finish our fit at a radius of 5 arc-seconds, which corresponds to 40kpc at z=3, as beyond this the LAH is non-longer able to be detected above the noise. The issue is choosing the starting radius for the fit, which the PSF is needed for as discussed previously. This work will be completed next week and uploaded in the next instalment of the blog!  

It can also be useful to, instead of using the stacks for all the LAEs at a specific redshift, to use the already luminosity constrained stacks. So, for each filter, and hence redshift, the LAEs above a threshold (threshold luminosity of 43.0 ergs-1) have been stacked to produce a bright LAE stack, and then also those below the threshold to produce a faint LAE stack. Using these two stacks separately and measuring the SB profile, and hence the scale-length, is more useful for seeing any correlation between scale-length and luminosity over different redshifts.

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Figure 4 – The same as Figure 3 but for the stacks of only the bright LAEs, above a luminosity of 43.0 ergs-1.
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Figure 5 – The same as Figure 3 but for the stacks of only the faint LAEs, below a luminosity of 43.0 ergs-1.

The plots however, don’t appear to show any form of relationship between the luminosity and the scale-length of either the bright, faint or full sample of LAE’s; Figures 3, 4 and 5 respectively.  All of the Figures are plotted with a log scale in the y axis in order to see any small deviations or differences in scale-length more clearly. 

I mentioned that it would be possible, using the stacks in the different filters, to see if there is any evolution in the size of LAHs across redshift, and hence across cosmic time, instead of just looking at the size of LAHs on the whole.

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Figure 6 – Evolution of scale-length over redshift for stacks of all sources in each filter. The four different exponential fit ranges are included to highlight the differences between each.

Firstly, I investigated how the LAH’s scale-length (size) changes over redshift for all LAEs in the SC4K catalogue, such that each point in Figure 6, per fit, corresponds to a stack of all the sources at that redshift (those imaged in that corresponding filter). The scale-lengths are measured again for the different stacks using the four different exponential fits, where the difference is just the starting and finishing radii for the fit. All of these are plotted to highlight any differences or similarities between the different fits of scale-length across redshift. The black points, the fit from 0 to 2 arc-seconds is just telling us about the central light of the galaxy and not the LAH and so is not indicating the size of the LAH like the other fits are being used for.

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Figure 7 – Evolution of scale-length over redshift for stacks of the bright sources, above the threshold luminosity, in each filter.

We also look at the evolution of scale-length over redshift for the bright sources only for each filter, so measuring from the stack of the bright LAEs, which is a stack of the those with luminosities above the threshold luminosity of 43.0 ergs-1. This is because at high redshift we are unable to pick up fainter sources due to selection biases when observing. Therefore, looking at only the bright sources, which can be observed across all redshifts, we reduce this selection bias and are able to see if there is any evolution of the size of these bright sources across redshift and time, see Figure 7. 

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Figure 8 – Evolution of scale-length over redshift for AGN LAEs vs star forming LAEs.

Using the stacks of LAEs with AGN and those with no AGN, we can also investigate the difference in scale-length between AGN driven and star forming LAEs. Since, AGN and also forming O and B stars are the main producers of Lyman-alpha photons in galaxies, it can be important to separate the two and see if there are any differences between the LAHs produced by each and investigate any effects due to different mechanisms or whether the two mechanisms produce similar scale LAHs. It can also be important to separate the two in order to see if there are evolutions in scale-length over time for one mechanism of Lyman-alpha production and not the other. Do the two mechanisms produce the same type and scale of LAH? And if so, is this true for across all redshifts and time? Or are they producing similar LAHs originally but over time differences appear between the two? 

From Figure 8 we can see that the AGN powered LAHs are a lot larger in size than those produced by star formation only. It is difficult to see any evolution in the AGN powered LAHs sizes over redshift as our sample contains no LAEs containing AGN at the higher redshift and so we can only compare within a small redshift range. It is also important to note that the sample of AGN LAEs is also a lot smaller than the star forming LAEs. More data is needed to be able to see if there is an evolution of AGN powered LAHs sizes across time. However, our results do suggest that for the star forming produced LAHs, there is no redshift evolution over time. We also see that there is a clear difference in the size of LAHs produced by the two mechanisms. 

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Figure 9 – Scale-length over redshift for this work using exponential fits to measure the size of the LAH only for the LAEs. Other work is included to highlight similarities between our results and previous studies.

Finally, I compare the two different exponential fits to our data, specifically to the outer regions of the LAEs, with past literature. The two exponential fits to the SB profiles that start at 1.5 and 2 arc-seconds, are probing the LAH, and so can be compared to previous literature that also look into the haloes. Various studies are shown alongside our results in Figure 9. Firstly, Wisotzki et al 2015, presents the Lyα emission around individual star-forming galaxies at redshifts = 3–6 using an ultradeep exposure of the Hubble Deep Field South obtained with Multi Unit Spectroscopic Explorer (MUSE) on the ESO-VLT.

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The Very Larger Telescope (VLT) – ESO. Image credit: https://www.eso.org/public/images/eso0137k/

In a follow up, Wisotzki et al 2018, MUSE data of 270 Lyα emitting galaxies at 3 < z < 6 were used, fitting circular Sersic models, to describe the Lyα haloes, rather than the exponential profile we use. Regardless of the different fitting methods, the results from this study appear to match up almost perfectly with our results, for an exponential fit from 1.5 arc seconds.

Next we compare with Momose et al 2014, that uses composite Subaru narrowband images to measure the scale lengths from the exponential profile fitted to the LAHs detected in the  z = 2.2 − 6.6 LAE samples. This study obtains scale lengths of ≃ 5 − 10 kpc at z = 2.2 − 5.7, and finds no evolution of scale lengths in this redshift range. The LAEs we observed also comes from using data collected with the Subaru telescope. Also, the LAHs were analysed in a similar way to to our work, over a similar redshift range, and also using exponential fits to the SB profiles. This makes comparisons really useful and our results, with the exponential fit starting from 1.5 arc seconds specifically, also appears to show no evolution in the scale-length over redshift, within the errors of our measurements.

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Subaru telescope – the 8.2-meter telescope of the National Astronomical Observatory of Japan. Image credit: https://www.nao.ac.jp/en/research/telescope/subaru.html

Finally we also compare with Leclercq et al 2017, which investigates lower luminosity sources, but spans a similar redshift range. Although the scale-lengths found in this study are, on average, lower than those in our work and other studies, probably due to their sample consisting of continuum-faint (−15 ≥ MUV ≥ −22) LAEs, they do however appear to show the same with regards to the evolution of scale-length over redshift.

Next week I plan to investigate and measure the point spread function (PSF) for the data I am using. Using this we can then determine a more accurate starting radius for our exponential fits and also convince ourselves that what we are measuring in our SB profiles is actually the LAH, and the emission is not simply coming from the central stars of the galaxy.

Emma Dodd

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