In this paper, we look to analyse the spiral features of grand-design, multiarmed, and flocculent spiral galaxies using deep optical imaging from DESI Legacy Imaging Surveys. We explore the resulting distributions of various characteristics of spiral structure beyond the optical radius, such as the distributions of azimuthal angle, the extent of spiral arms, and of the spiral arm widths for the aforementioned galaxy classes. We also compare the measured properties for isolated galaxies and galaxies in groups and clusters. We find that, on average, compared to multiarmed and flocculent spiral galaxies, the spiral arms of grand-design galaxies exhibit slightly larger azimuthal angles, greater extent, and larger widths in the periphery of the galaxy. Furthermore, on average, isolated galaxies tend to have slightly smaller widths of outer spiral arms compared to galaxies in tight environments, which is likely related to the tidally induced mechanism for generating wider outer spiral arms. We also report that breaks of the disc surface brightness profiles are often related to the truncation of spiral arms in galaxies.

Polar-ring galaxies are photometrically and kinematically decoupled systems that are highly inclined to the major axis of the host. These galaxies have been explored since the 1970s, but the rarity of these systems has made such systematic studies difficult. However, over 250 good candidates have been identified. In this work, we examine a sample of over 18 000 galaxies from the Sloan Digital Sky Survey (SDSS) Stripe 82 for the presence of galaxies with polar structures. Using deep SDSS Stripe 82, DESI Legacy Imaging Surveys, and Hyper Suprime-Cam Subaru Strategic Program, we selected 53 good candidate galaxies with photometrically decoupled polar rings, 9 galaxies with polar halos, 6 galaxies with polar bulges, and 34 possibly forming polar-ring galaxies, versus 13 polar-ring candidates previously selected in Stripe 82. Our results suggest that the occurrence rate of galaxies with polar structures may be significantly underestimated, as revealed by the deep observations, and may amount to 1-3% of non-dwarf galaxies.

Spiral structure can contribute significantly to a galaxy’s luminosity. However, only rarely are proper photometric models of spiral arms used in decompositions. As we show in the previous work, including the spirals as a separate component in a photometric model of a galaxy would both allow to obtain their structural parameters, and reduce the systematic errors in estimating the parameters of other components. Doing so in different wavebands, one can explore how their properties vary with the wavelength. In this paper, second in this series, we perform decomposition of M 51 in 17 bands, from the far UV to far IR, using imaging from the DustPedia project. We use the same 2D photometric model of spiral structure where each arm is modelled independently. The complex and asymmetric spiral structure in M 51 is reproduced relatively well with our model. We analyze the differences between models with and without spiral arms, and investigate how the fit parameters change with wavelength. In particular, we find that the spiral arms demonstrate the largest width in the optical, whereas their contribution to the galaxy luminosity is most significant in the UV. The disk central intensity drops by a factor of 1.25–3 and its exponential scale changes by 5–10\\% when spiral arms are included, depending on wavelength. Taking into account the full light distribution across the arms, we do not observe the signs of a long-lived density wave in the spiral pattern of M 51 as a whole.

Spiral structure can occupy a significant part of the galaxy, but properly accounting for it in photometric decomposition is rarely done. This may lead to significant errors in the parameters determined. To estimate how exactly neglecting the presence of spiral arms affects the estimation of galaxy decomposition parameters, we perform fitting of 29 galaxies considering spiral arms as a separate component. In this study, we utilize 3.6 μm-band images from the S4G survey and use a new 2D photometric model where each spiral arm is modelled independently. In our model, the light distribution both along and across the arm and its overall shape can be varied significantly. We analyse the differences between models with and without spiral arms, and show that neglecting spiral arms in decomposition causes errors in estimating the parameters of the disc, the bulge, and the bar. We retrieve different parameters of the spiral arms themselves, including their pitch angles, widths, and spiral-to-total luminosity ratio, and examine various relations between them and other galaxy parameters. In particular, we find that the spiral-to-total ratio is higher for galaxies with more luminous discs and with higher bulge-to-total ratios. We report that the pitch angle of spiral arms decreases with increasing bulge or bar fraction. We measure the width of the spiral arms to be 53 per cent of the disc scale length, on average. We examine the contribution of the spiral arms to the azimuthally averaged brightness profile and find that spiral arms produce a ‘bump’ on this profile with a typical height of 0.3–0.7 mag.

Aims. The origin and maintenance of spiral structure in galaxies, the correlation between different types of spiral structure and several proposed mechanisms for their generation, and the evolution of spiral arms of galaxies with time are questions that are still controversial. In this note we study the spiral structure in a sample of distant galaxies in order to infer the evolution of spiral arm characteristics with redshift.

Methods. We considered a sample of 171 face-on spiral galaxies in the Hubble Space Telescope COSMOS (The Cosmic Evolution Survey) field. The galaxies are distributed up to z approximate to 1 with a mean value of 0.44. For all galaxies, we determined the pitch angles of the spiral arms and analysed their dependence on redshift; a total of 359 arms were measured.

Results. Analyses of our measurements combined with the literature data suggest a possible evolution of the pitch angles of spiral galaxies: by the modern epoch the spiral pattern, on average, becomes more tightly wound. This may be a consequence of the general evolution of the structure of galaxies as galaxies become more massive over time and their bulges grow. In addition, the distribution of the cotangent of pitch angle of galaxies indicates the possibility that the dominant mechanism of spiral pattern generation changes over time.

The approximation of real non-spherical scatterers by spheroids is used in various applications. It often requires fast massive calculations of the optical properties of spheroids. The most powerful approach to that is known to be a field expansion in terms of spheroidal wave functions, in particular, in the way suggested by Farafonov over 30 years ago. We improve the main shortcomings of such an approach. Our solution is formulated in terms of normalised spheroidal functions, and firstly for their definition given by Meixner & Schafke, which is computationally favourable and is required by the unique subroutines recently created to compute these functions. By means of T-matrix transformations we solve a long-standing major problem of Farafonov's version, namely the accuracy and time losses for one kind (TE mode) of the incident wave polarisation. Apart from this and other improvements of this solution, for the first time we relate its single particle spheroidal T-matrix to the standard spherical one which is widely employed for particle ensembles. The constructed algorithm has been extensively numerically tested. It is found to be very accurate for dielectric spheroids with the aspect ratio a/b reaching 100 and the diffraction (size) parameter xa = 2za/angstrom as large as 300, where a and b are the major and minor semi-axes, respectively, angstrom is the wavelength. The algorithm is supplied with a program interface to the free package CosTuuM to perform parallel computations of various optical properties for ensembles of spheroids with different distributions over orientation (alignment) and shape.