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Systematic studies have revealed hundreds of ultra-compact dwarf galaxies (UCDs) in the nearby Universe. With half-light radii $r_h$ of approximately 10-100 parsecs and stellar masses $M_*$ $\approx$ $10^6-10^8$ solar masses, UCDs are among the densest known stellar systems. Although similar in appearance to massive globular clusters, the detection of extended stellar envelopes, complex star formation histories, elevated mass-to-light ratio, and supermassive black holes suggest that some UCDs are remnant nuclear star clusters of tidally-stripped dwarf galaxies, or even ancient compact galaxies. However, only a few objects have been found in the transient stage of tidal stripping, and this assumed evolutionary path has never been fully traced by observations. Here we show that 106 galaxies in the Virgo cluster have morphologies that are intermediate between normal, nucleated dwarf galaxies and single-component UCDs, revealing a continuum that fully maps this morphological transition, and fills the `size gap' between star clusters and galaxies. Their spatial distribution and redder color are also consistent with stripped satellite galaxies on their first few pericentric passages around massive galaxies. The `ultra-diffuse' tidal features around several of these galaxies directly show how UCDs are forming through tidal stripping, and that this evolutionary path can include an early phase as a nucleated ultra-diffuse galaxy (UDG). These UCDs represent substantial visible fossil remnants of ancient dwarf galaxies in galaxy clusters, and more low-mass remnants probably remain to be found., Comment: Published in Nature. Accepted on September 15

We present Keck/DEIMOS spectroscopy of the first complete sample of ultra-diffuse galaxies (UDGs) in the Virgo cluster. We select all UDGs in Virgo that contain at least 10 globular cluster (GC) candidates and are more than $2.5\sigma$ outliers in scaling relations of size, surface brightness, and luminosity (a total of 10 UDGs). We use the radial velocity of their GC satellites to measure the velocity dispersion of each UDG. We find a mixed bag of galaxies: from one UDG that shows no signs of dark matter, to UDGs that follow the luminosity-dispersion relation of early-type galaxies, to the most extreme examples of heavily dark matter dominated galaxies that break well-known scaling relations such as the luminosity-dispersion or the U-shaped total mass-to-light ratio relations. This is indicative of a number of mechanisms at play forming these peculiar galaxies. Some of them may be the most extended version of dwarf galaxies, while others are so extreme that they seem to populate dark matter halos consistent with that of the Milky-Way or even larger. Even though Milky-Way stars and other GC interlopers contaminating our sample of GCs cannot be fully ruled-out, our assessment of this potential problem and simulations indicate that the probability is low and, if present, unlikely to be enough to explain the extreme dispersions measured. Further confirmation from stellar kinematics studies in these UDGs would be desirable. The lack of such extreme objects in any of the state-of-the-art simulations, opens an exciting avenue of new physics shaping these galaxies., Comment: 27 pages, 12 figures. Accepted for publication in ApJ

We present a study of ultra-diffuse galaxies (UDGs) in the Virgo Cluster based on deep imaging from the Next Generation Virgo Cluster Survey (NGVS). Applying a new definition for the UDG class based on galaxy scaling relations, we define samples of 44 and 26 UDGs using expansive and restrictive selection criteria, respectively. Our UDG sample includes objects that are significantly fainter than previously known UDGs: i.e., more than half are fainter than $\langle\mu\rangle_e \sim27.5$ mag arcsec$^{-2}$. The UDGs in Virgo's core region show some evidence for being structurally distinct from "normal" dwarf galaxies, but this separation disappears when considering the full sample of galaxies throughout the cluster. UDGs are more centrally concentrated in their spatial distribution than other Virgo galaxies of similar luminosity, while their morphologies demonstrate that at least some UDGs owe their diffuse nature to physical processes---such as tidal interactions or low-mass mergers---that are at play within the cluster environment. The globular cluster (GC) systems of Virgo UDGs have a wide range in specific frequency ($S_N$), with a higher mean $S_N$ than "normal" Virgo dwarfs, but a lower mean $S_N$ than Coma UDGs at fixed luminosity. Their GCs are predominantly blue, with a small contribution from red clusters in the more massive UDGs. The combined GC luminosity function is consistent with those observed in dwarf galaxies, showing no evidence of being anomalously luminous. The diversity in their morphologies and their GC properties suggests no single process has given rise to all objects within the UDG class. Based on the available evidence, we conclude that UDGs are simply those systems that occupy the extended tails of the galaxy size and surface brightness distributions., Comment: 31 pages, 16 figures, 4 tables, accepted for publication in ApJ

It has long been speculated that many starburst or compact dwarf galaxies are resulted from dwarf-dwarf galaxy merging, but unequivocal evidence for this possibility has rarely been reported in the literature. We present the first study of deep optical broadband images of a gas-dominated blue compact dwarf galaxy (BCD) VCC848 (Mstar=2e8Msun) which hosts extended stellar shells and thus is confirmed to be a dwarf-dwarf merger. VCC848 is located in the outskirts of the Virgo Cluster. By analyzing the stellar light distribution, we found that VCC848 is the result of a merging between two dwarf galaxies with a primary-to-secondary mass ratio < ~ 5 for the stellar components and < ~ 2 for the presumed dark matter halos. The secondary progenitor galaxy has been almost entirely disrupted. The age-mass distribution of photometrically selected star cluster candidates in VCC848 implies that the cluster formation rate (CFR, proportional to star formation rate) was enhanced by a factor of ~ 7 - 10 during the past 1 Gyr. The merging-induced enhancement of CFR peaked near the galactic center a few hundred Myr ago and has started declining in the last few tens of Myr. The current star formation activities, as traced by the youngest clusters, mainly occur at large galactocentric distances (> ~ 1 kpc). The fact that VCC848 is still (atomic) gas-dominated after the period of most violent collision suggests that gas-rich dwarf galaxy merging can result in BCD-like remnants with extended atomic gas distribution surrounding a blue compact center, in general agreement with previous numerical simulations., Comment: 10 pages, 5 figures, accepted by ApJL

A major challenge in Atomic Force Microscopy (AFM) is to reduce the scan duration while retaining the image quality. Conventionally, the scan rate is restricted to a sufficiently small value in order to ensure a desirable image quality as well as a safe tip-sample contact force. This usually results in a conservative scan rate for samples that have a large variation in aspect ratio and/or for scan patterns that have a varying linear velocity. In this paper, an adaptive scan scheme is proposed to alleviate this problem. A scan line-based performance metric balancing both imaging speed and accuracy is proposed, and the scan rate is adapted such that the metric is optimised online in the presence of aspect ratio and/or linear velocity variations. The online optimisation is achieved using an extremum-seeking (ES) approach, and a semi-global practical asymptotic stability (SGPAS) result is shown for the overall system. Finally, the proposed scheme is demonstrated via both simulation and experiment.