, U. hopp 5,6 , C. Haumea-one of the four known trans-Neptunian dwarf planetsis a very elongated and rapidly rotating body 1-3 . In contrast to other dwarf planets [4][5][6] , its size, shape, albedo and density are not well constrained. The Centaur Chariklo was the first body other than a giant planet known to have a ring system 7 , and the Centaur Chiron was later found to possess something similar to Chariklo's rings 8,9 . Here we report observations from multiple Earth-based observatories of Haumea passing in front of a distant star (a multichord stellar occultation). Secondary events observed around the main body of Haumea are consistent with the presence of a ring with an opacity of 0.5, width of 70 kilometres and radius of about 2,287 kilometres. The ring is coplanar with both Haumea's equator and the orbit of its satellite Hi'iaka. The radius of the ring places it close to the 3:1 mean-motion resonance with Haumea's spin period-that is, Haumea rotates three times on its axis in the time that a ring particle completes one revolution. The occultation by the main body provides an instantaneous elliptical projected shape with axes of about 1,704 kilometres and 1,138 kilometres. Combined with rotational light curves, the occultation constrains the three-dimensional orientation of Haumea and its triaxial shape, which is inconsistent with a homogeneous body in hydrostatic equilibrium. Haumea's largest axis is at least 2,322 kilometres, larger than previously thought, implying an upper limit for its density of 1,885 kilograms per cubic metre and a geometric albedo of 0.51, both smaller than previous estimates 1, 10,11 . In addition, this estimate of the density of Haumea is closer to that of Pluto than are previous estimates, in line with expectations. No global nitrogen-or methane-dominated atmosphere was detected.Within our programme of physical characterization of trans-Neptunian objects (TNOs), we predicted an occultation of the star URAT1 533− 182543 by the dwarf planet (136108) Haumea and arranged observations as explained in Methods. Positive occultation detections were obtained on 2017 January 21, from twelve telescopes at ten different observatories. The instruments and the main features of each station are listed in Table 1.As detailed in Methods (see also Fig. 1), the light curves (the normalized flux from the star plus Haumea versus time) show deep 1 2

Spectropolarimetry enables us to measure the geometry and chemical structure of the ejecta in supernova explosions, which is fundamental for the understanding of their explosion mechanism(s) and progenitor systems. We collected archival data of 35 Type Ia Supernovae (SNe Ia), observed with FORS on the Very Large Telescope at 127 epochs in total. We examined the polarization of the Si ii λ6355Å line (p Si ii ) as a function of time which is seen to peak at a range of various polarization degrees and epochs relative to maximum brightness. We reproduced the ∆m 15 -p Si ii relationship identified in a previous study, and show that subluminous and transitional objects display polarization values below the ∆m 15 -p Si ii relationship for normal SNe Ia. We found a statistically significant linear relationship between the polarization of the Si ii λ6355Å line before maximum brightness and the Si ii line velocity and suggest that this, along with the ∆m 15 -p Si ii relationship, may be explained in the context of a delayed-detonation model. In contrast, we compared our observations to numerical predictions in the ∆m 15 -v Si ii plane and found a dichotomy in the polarization properties between Chandrasekhar and sub-Chandrasekhar mass explosions, which supports the possibility of two distinct explosion mechanisms. A subsample of SNe display evolution of loops in the q-u plane that suggests a more complex Si structure with depth. This insight, which could not be gleaned from total flux spectra, presents a new constraint on explosion models. Finally, we compared our statistical sample of the Si ii polarization to quantitative predictions of the polarization levels for the double-detonation, delayed-detonation, and violent-merger models.

We reduced ESO's archival linear spectropolarimetry data (4000-9000Å) of 6 highly polarized and 8 unpolarized standard stars observed between 2010 and 2016, for a total of 70 epochs, with the FOcal Reducer and low dispersion Spectrograph (FORS2) mounted at the Very Large Telescope. We provide very accurate standard stars polarization measurements as a function of wavelength, and test the performance of the spectropolarimetric mode (PMOS) of FORS2. We used the unpolarized stars to test the time stability of the PMOS mode, and found a small ( 0.1%), but statistically significant, on-axis instrumental polarization wavelength dependency, possibly caused by the tilted surfaces of the dispersive element. The polarization degree and angle are found to be stable at the level of 0.1% and 0.2 degrees, respectively. We derived the polarization wavelength dependence of the polarized standard stars and found that, in general, the results are consistent with those reported in the literature, e.g. Fossati et al. (2007) who performed a similar analysis using FORS1 data. The recalibrated data provide a very accurate set of standards that can be very reliably used for technical and scientific purposes. The analysis of the Serkowski parameters revealed a systematic deviation from the width parameter K reported by Whittet et al. (1992). This is most likely explained by incorrect effective wavelengths adopted in that study for the R and I bands.

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