Astronomical image analysis begins with object detection which, in practice, involves dividing image pixels into ‘object’ and ‘sky’ categories. The information about how the pixels are split can then be saved in the form of a binary image containing a map of pixels assigned to the object with intensities equal to 1, and those comprising the sky, equal to 0. Throughout the text, I will refer to such a map as the ‘detection mask’.
2.2.1
Binary detection mask
To create the binary detection mask I employed an 8-connected structure detection algorithm, with 8-connected neighbours defined as all pixels touching one of the edges or corners of the central pixel (SDSS position pixel, Section 2.1.1). The algorithm searches for such neighbour- ing pixels with intensities above a threshold level defined as a function of the background sky level and its standard deviation. It is specifically designed to identify faint features in the out- skirts of galaxies. To enhance the detectability of such features without significantly lowering the detection threshold and potentially dropping to the noise level, each image is effectively passed through a 3×3 running average (mean) filter prior to the detection process. This reduces the noise in the images by not only amplifying the signal from the regions with low surface-brightness but also diminishing the pixellation effect in those regions where individ- ual pixels are too faint to be detected. Then, starting from the central pixel as given by the SDSS position, the binary detection mask is built by accepting all pixels that are 8-connected to previously accepted pixels and have intensities above the chosen threshold. After some ex- perimentation, I found the optimal threshold for a robust detection of faint tidal features is 1 standard deviation above the sky background level. For the SDSSr-band images of the SB/PSB sample, this corresponds to a mean limiting surface brightness of 24.7 mag/arcsec2. In Figure 2.1, I present examples of detection masks computed for SB/PSB galaxies with different levels
2.2. Extraction of sources
of morphological disturbance, as classified by visual inspection of the SDSSr-band images (the exact criteria of the visual classification are explained in detail in Section 4.2.1. In the case of an ongoing merger, with double nuclei joined by a bridge (see e.g. objects MORPH2, MORPH8, MORPH9, MORPH11 in Figure 3.1), the detection mask will include both components of the merging system.
Figure 2.1: Binary detection masks for selected galaxies in the evolutionary (post-)starburst sample
(Section 4.1), and comparison of the different definitions of radii. The horizontal panels show: top- the false colour SDSS images;middle- the SDSSr-band images with marked aperture sizes defined by the Petrosian radius, 2rp (red), and the radius introduced in Section 2.2.3,rma x(black);bottom- the
corresponding binary detection masks (Section 2.2.1).
Contamination by nearby sources
A common complication in astronomical image analysis is signal contamination due to pres- ence of nearby luminous sources. The light from the galaxy of interest may be contaminated by that from other objects, including either neighbouring galaxies or galaxies/stars that, although physically distant, happen to appear in the field of the imaging camera.
The usual solution to minimise the effects of contamination is to mask out the nearby sources before the analysis. Manually, this can be done to a high precision; however, in an au- tomated analysis, there is a risk of masking out parts of the galaxy of interest itself, particularly when the contaminating sources overlap the galaxy. Therefore, for the purpose of this project,
I limited this step of image preparation to masking out only those sources that are found out- side of the detection mask, to ensure that the galaxy itself is not affected. In future work, I intend to extend this process further to account for sources overlapping with the galaxy. At this stage, visual inspection is required and any images with significant contamination from overlapping sources (e.g. very bright stars) need to be discarded before the analysis.
2.2.2
Defining the ‘galaxy centre’
For initial identification of galaxies in the images, I used the position coordinates derived by the SDSS pipeline. However, to ensure that the morphological and structural parameters were measured robustly so that a meaningful way of comparison between the galaxies of different types could be facilitated, I employed the following definitions of the centroids:
• Maximum-intensity centroid, OI ma x - the position corresponding to the highest intensity
pixel within the boundaries defined by the detection mask. This definition was used during the computation of the surface-brightness profiles (Section 2.3.1), the central concentration index (C, Section 2.4.2) and the clumpiness parameter (S, Section 2.4.5). • Minimum-asymmetry centroid, OAmin- the position yielding the minimum value of rota- tional asymmetry (A, Section 2.4.3). To find the centroid, the values ofAare calculated for a 180o image rotation about every position within a boundary defined by highest- intensity pixels accounting for 30% of the total flux from the galaxy (here, the total flux is given by the summation of all pixels included in the detection mask). This centroid was used for computation of all parameters pertaining to the rotational asymmetry of the galaxy images (Section 2.4.3, 2.4.4, 2.5).
• Minimum-moment centroid, OM min - the position yielding the minimum value of the second-order moment of the galaxy total flux. Again, the moments are computed for the highest-intensity pixels comprising 30% of the total flux (measured within the bound- aries defined by the detection mask). This definition of the centre was used for the computation of theM20parameter (Section 2.4.7).
2.2.3
Defining the ‘galaxy radius’
Defining the radius of an extended light source, such as a galaxy, can be challenging due to lack of clear boundaries between the object and the sky. In 1976, Petrosian introduced
2.2. Extraction of sources
a definition of a galaxy radius determined by the shape of its azimuthally averaged surface- brightness profile (Petrosian, 1976). A modified version of Petrosian’s definition was adopted in the SDSS photometric analysis pipeline (Blanton et al., 2001; Yasuda et al., 2001), where it is computed by considering the Petrosian ratio (Rp(rp), the ratio of the local surface brightness
in an annulus at radius,r, to the mean surface brightness withinr):
RP(r) = R1.25r 0.8r 2πr0I(r0)d r0/[π(1.25 2 −0.82)r2] Rr 0 2πr0I(r0)d r0/(πr2) (2.2)
The Petrosian radius, rp, is the radius at which the Petrosian ratio equals 0.2. As shown by Blanton et al. (2001), in the case of normal galaxies, the aperture at 2rp is optimal for recov-
ering the majority of the galaxy’s flux (80% for early-type and 100% for late-type galaxies) without including a considerable amount of noise. Unfortunately, moving away from normal galaxies with reasonably smooth surface-brightness profiles can introduce complications. As discussed by Blanton et al. (2001), a galaxy with a complex substructure could have no or more than onerp, and in the case of a galaxy with a very bright stellar nucleus, rp could be determined solely by the innermost region.
In my study, I used a radius defined by the detection mask,rma x, as the distance between
the centre (defined as the maximum intensity pixel,OI ma x, see Section 2.2.2) and the most distant pixel from that centre. I found this definition of galaxy radius more suitable for the purpose of this work, over the commonly used Petrosian radius,rp(Petrosian, 1976; Blanton et al., 2001; Yasuda et al., 2001), in the case of galaxies with significant morphological dis- turbance. In the second row of Figure 2.1 apertures at the new radii (black) are compared to those at twice the Petrosian radii (red). The latter value is typically used to recover the majority of flux for galaxies with regular morphologies (Blanton et al., 2001). The radii are similar for morphologically undisturbed galaxies but in the presence of significant morpholog- ical disturbance,rma x includes the extended faint structures in the outskirts of galaxies, which can be excluded by 2rp.
With the information about the galaxy radii, the code can revise the initial estimate of the sky background level. The procedure described in Section 2.1.2 is repeated, but this time with the final value being computed within an annulus defined by the following radii: rin=
rma x+1[pi x]androut=2rma x. This final estimate of the sky background level was subtracted from the images prior to the measurement of the morphological parameters (although it differs
from the original one by no more than 3 digital counts per pixel, there is a drop in the standard deviation by as much as 50%).