Discussion on the method

Several assumptions and simplifications were made at different levels to make the implementation of this Vmax computation possible. In this section, we detail the possible sources of error and in-

LAEs sorted by increasing Vmax 5 values

Volume ratio per LAE

Vmax 1 / Vmax 5 (15points) Vmax 2 / Vmax 5 (50points) Vmax 3 / Vmax 5 (100points) Vmax 4 / Vmax 5 (300points) Vmax 5 / Vmax 5 (1000points) 5% variations

Figure 4.16: Ratio of Vmax values computed from various series of tests using a different number

of points to resample the S/N curves. Test 5 having the higher resampling density is used as a reference. The Vmax ratios are computed for individual LAEs, and the LAEs are sorted from left

to right by increasing order of Vmax values, as computed during test 5.

the resulting LFs. The assumptions made are numerous and only the main ones are listed here by order of appearance in this chapter.

Noise in the bright pixel measurements. One of the first source of error is that we may include some noise when we retrieve the pixel values of the individual bright pixel profiles. As only the brightest pixel of Bp is used to compute the individual S/N curves, the inclusion of noise in this aspect of the method is minimal. And for the computation of the 2D masks most of the random noise is removed as a median profile computed from all the individual profiles is used. Therefore in average this should have only a minimal impact on the volume computation, and does not bias the results of the Vmax computation.

General bright pixel profiles. The use of Bpg instead of individual source profiles for the

creation of the masks and was already partly discussed in Sect. 4.4.2. For sources with extended profiles the use of Bpg leads to an overestimation of Vmax and for compact sources, it leads to an

underestimation of Vmax. However, in average this should not bias the distribution of Vmax values

as Bpg is still representative of the distribution of spatial profiles in the LAE sample. For the

sources for which Vmaxwas overestimated, the value can be somehow corrected by the computation

of the completeness correction since the simulations are done on masked layers (see completeness computation in Sect. 5.3.1 for which we use the real spectral and spatial source profile, and the discussion in Sect. 5.3.3). Indeed, if the volume is overestimated, the covering fraction of the mask used for the completeness simulations is also underestimated. This leads to a higher noise level in the layer used for the simulation and therefore a lower completeness for this source that tend to compensates the overestimated Vmax.

Furthermore, when using generalized profiles, part of the information about spatial profiles of LAEs is lost when creating the masks. However, this information remains stored within the indi- vidual Bp profiles used for the computation of the S/N curves and for picking the correct 2D mask.

In that sense, the final 3D mask still accounts for the surface brightness of individual LAEs.

Median RMS maps. The use of the median RMS images does not impact the Vmaxcomputation

in any significant way when it is performed through the entire spectral axis of the cubes, that is to say when Vmax is computed for 2.9 < z < 6.7. However, for reduced redshift intervals, the use

of a median RMS image may have an impact on the result. This computation is needed when the LAE population is split in redshift bins to investigate the evolution of the shape of the LF with redshift (see Sect. 5.4). For example, when computing Vmax for 5.0 < z < 6.7, the volume is only

computed from the layers of the cubes that corresponds to the wavelength of the Lyα emission in this redshift range, whereas the median RMS is computed from the full cube. In that situation, the median RMS image is not as representative of the individual RMS images in that spectral range. The possible effects of this is difficult to assess, since it would require to do the volume computation using different median RMS images for the different redshift bins used to compute the LFs. As seen on Fig. 4.11, the use of a single median RMS image doesn’t not seem to be a far-fetched approximation.

Simpler SExtractor criterion. When actually producing the 2D masks, we use a simpler cri- terion to mock the SExtractor detections. It is hard to know whether this impacts the covering fraction of the masks and if this has any effects on the resulting Vmax computation. There are no

obvious reasons that would lead to think that the use of this simpler criterion is biasing the volumes towards higher or lower values.

Limit magnification. In the definition of the limiting magnification in Eq. 4.6 and Eq. 4.7 we only define one average value per source per cube, when strictly speaking there should be one per source for each layer of each cube. The difficulty here again is the computation time and the difficulty to find a simple criterion that would be coherent with the Muselet detection process without having to do complex and lengthy simulations. As already specified in Sect. 4.5, only a few LAEs (the highly magnified ones) have their Vmax values completely dominated by the effects

of the limiting magnification. For these sources, a small difference in µlim would not significantly

impact Vmax since around the highly magnified area, the magnification gradient is strong. On the

opposite, for the LAE in the intermediate/lower magnification regime, a small change in µlim has

a greater impact on the volume computation because of the much smaller magnification gradient in the low magnification areas (see Fig. 3.5 and Fig. 3.6). For all these reasons, and lacking better options, the criteria used to compute these limit magnifications are intentionally conservative to not artificially over-estimate the steepness of the faint-end slope of the LF.

We have not identified any obvious bias or systematic effects that would have a major impact on the Vmax computation and therefore on the determination of the LF. The following chapter

5

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Determination of the Luminosity

Function of LAEs at 3 . z . 7

Contents

5.1 Lyα flux computation and final selection of lensed sources . . . 88