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The mass-size relation is a fundamental galaxy scaling law closely tied to galaxy formation and evolution. Using added-value products of the Calar Alto Void Integral-field Treasury surveY (CAVITY) and SDSS DR16 images, we examine the effect of large-scale environments on the stellar mass-size relation. We analyse the Petrosian R50 and R90 radii of approximately 140000 galaxies in voids, filaments, and clusters, with a mass range of $10^{8.5} - 10^{11} M_{\odot}$. We explore the relation in terms of galaxy morphology and star formation history, parametrised by T50, T70, and T90. We find that early-type void galaxies are, on average, 10-20% smaller than their counterparts in denser environments, regardless of their mass assembly history. Moreover, the mass-size relation for massive early-type void galaxies has a shallower slope compared to those in denser regions. In contrast, early-type galaxies in filaments, and clusters show a more uniform mass-size relation. Late-type cluster galaxies with stellar masses $log(M_{\star} / M_{\odot}) = 9 - 10.5$ are smaller and more concentrated than their counterparts in lower-density environments, such as filaments, and voids. We conclude that large-scale environments influence the mass-size relation. Early-type galaxies appear to grow most of their mass during the initial formation phase. Subsequent size growth in voids is less significant, likely due to slower evolution, reduced minor merger activity, fewer accretion events, or a combination. The flatter slope for massive void galaxies indicates a lower rate of minor accretion, a trend also observed in late-type void galaxies with $\approx 10^{10.5} M_{\odot}$, where minor mergers contribute to size growth. Conversely, late-type quenched cluster galaxies are smaller due to environmental interactions, with early infallers being most affected., Comment: 12 pages. Paper accepted for publication in A&A

Cosmic voids, distinguished by their low-density environment, provide a unique opportunity to explore the interplay between the cosmic environment and the processes of galaxy formation and evolution. Data on the molecular gas has been scarce so far. In this paper, we continue previous research done in the CO-CAVITY pilot project to study the molecular gas content and properties in void galaxies to search for possible differences compared to galaxies that inhabit denser structures. We observed at the IRAM 30 m telescope the CO(1-0) and CO(2-1) emission of 106 void galaxies selected from the CAVITY survey. Together with data from the literature, we obtained a sample of 200 void galaxies with CO data. We conducted a comprehensive comparison of the specific star formation rate (sSFR = SFR/M$_*$), the molecular gas fraction (MH$_2$/M$_*$), and the star formation efficiency (SFE = SFR/MH$_2$) between the void galaxies and a comparison sample of galaxies in filaments and walls, selected from the xCOLD GASS survey. We found no statistically significant difference between void galaxies and the comparison sample in the molecular gas fraction as a function of stellar mass for galaxies on the star-forming main sequence (SFMS). However, for void galaxies, the SFE was found to be constant across all stellar mass bins, while there is a decreasing trend with M$_*$ for the comparison sample. Finally, we found some indications for a smaller dynamical range in the molecular gas fraction as a function of distance to the SFMS in void galaxies. Overall, our analysis finds that the molecular gas properties of void galaxies are not very different from denser environments. The physical origin of the most significant difference that we found - a constant SFE as a function of stellar mass in void galaxies - is unclear and requires further investigation and higher-resolution data., Comment: 26 pages, 9 figures. Accepted for publication in A&A

We aim to investigate how the local environment influences the star formation history (SFH) of galaxies residing in various large-scale environments. We categorise a sample of 9384 galaxies into the three primary large scale structures (voids, walls \& filaments, and clusters) and further classify them based on their local environment (as either "singlets" or group members), through a search of companion galaxies within sky-projected distances $\Delta r_p < 0.45$ Mpc and velocity differences $\Delta v < 160$ $\text{km s}^{-1}$. Subsequently, we explore these subsamples through SFH data from previous works. Throughout the study, galaxies are divided into long-timescale SFH galaxies (LT-SFH), which assemble their mass steadily along cosmic time, and short-timescale SFH galaxies (ST-SFH), which form their stars early. We then compare characteristic mass assembly look-back times. The distributions of mass assembly look-back times in ST-SFH galaxies are statistically different for singlets and groups. These differences are only found in LT-SFH galaxies when studying these distributions in stellar mass bins. Our results indicate that the large-scale environment is related to a delay in mass assembly of up to $\sim$2 Gyr, while this delay is $<$1 Gyr in the case of local environment. The effect of both kinds of environment is more significant in less massive galaxies, and in LT-SFHs. Our results are consistent with galaxies in groups assembling their stellar mass earlier than singlets, especially in voids and lower mass galaxies. Local environment plays a relevant role in stellar mass assembly times, although we find that large-scale structures also cause a delay in mass assembly, more so in the case of cluster galaxies., Comment: 7 pages, 4 figures. Accepted for publication in A&A

We have learnt in the last decades that the majority of galaxies belong to high density regions interconnected in a sponge-like fashion. This large-scale structure is characterised by clusters, filaments, walls, where most galaxies concentrate, but also under-dense regions, called voids. The void regions and the galaxies within represent an ideal place for the study of galaxy formation and evolution as they are largely unaffected by the complex physical processes that transform galaxies in high-density environments. These void galaxies can hold the key as well to answer current challenges to the $\Lambda$CDM paradigm. The Calar Alto Void Integral-field Treasury surveY (CAVITY) is a Legacy project approved by the Calar Alto Observatory to obtain spatially resolved spectroscopic information of $\sim300$ void galaxies in the Local Universe (0.005 < z < 0.050) covering from -17.0 to -21.5 in $\rm r$ band absolute magnitude. It officially started in January 2021 and has been awarded 110 useful dark observing nights at the 3.5 m telescope using the PMAS spectrograph. Complementary follow-up projects including deep optical imaging, integrated, as well as resolved CO data, and integrated HI spectra, have joint the PMAS observations and naturally complete the scientific aim of characterising galaxies in cosmic voids. The extension data has been denominated CAVITY+. The data will be available to the whole community in different data releases, the first of which is planned for July 2024, and it will provide the community with PMAS data cubes for around 100 void galaxies through a user friendly, and well documented, database platform. We present here the survey, sample selection, data reduction, quality control schemes, science goals, and some examples of the scientific power of the CAVITY and CAVITY+ data., Comment: 19 pages, 11 figures. Accepted for publication in A&A - Replacement after A&A minor language edition