The Shortest-Known–Period Star Orbiting Our Galaxy’s Supermassive Black Hole

Abstract

The nucleation process is crucial to many phase transitions, but its kinetics are difficult to predict and measure. We superheated and melted the interior of thermal-sensitive colloidal crystals and investigated by means of video microscopy the homogeneous melting at single-particle resolution. The observed nucleation precursor was local particle-exchange loops surrounded by particles with large displacement amplitudes rather than any defects. The critical size, incubation time, and shape and size evolutions of the nucleus were measured. They deviate from the classical nucleation theory under strong superheating, mainly because of the coalescence of nuclei. The superheat limit agrees with the measured Born and Lindemann instabilities. C rystal melting is of considerable fundamental and practical importance to science and technology. Yet, our understanding of it is still rather incomplete. Thermodynamics reveals to us the equilibrium phases, but the kinetics of phase transitions have proved difficult to predict (1-3). Crystals melt heterogeneously from surfaces or grain boundaries once they are heated to the melting point (3, 4). By suppressing surface melting (5-8), a single crystal can be superheated to temperatures above its melting point. This metastable state will eventually melt from the interior without any preferential sites. In such homogeneous melting, small liquid nuclei form spontaneously by thermal fluctuations. A spherical nucleus has the free energy (9) DG ¼ 4pr 2 g − 4 3 pr 3 nDm þ E strain ð1Þ where r is the radius, g is the surface tension, n is the number density of the nucleus, ∆m (>0) is the chemical potential difference between the super-heated crystal and liquid, E strain ¼ 4 3 pr 3 nDD is the misfit strain energy in the crystal caused by the volume change of the nucleus, and ∆D is the mean strain energy per particle from continuum elasticity and is not expected to depend on r. E strain is zero when the parent phase is fluid but is finite when the parent phase is solid (10). To minimize ∆G, small liquid nuclei tend to recrystallize rather than grow unless their size exceeds a critical value r* = 2g/[(∆m − ∆)n] corresponding to the barrier height of ∆G. The small length and time scales of the nu-cleation process preclude observation at the single-particle level in molecular systems. In contrast, micrometer-sized colloidal particles can serve as good model systems for phase transition studies because their thermal motions can be directly visualized and measured with video microscopy (11, 12). Crystallization (13), sublimation (14), and heterogeneous melting in polycrystals (4, 15) have been studied in colloids. We used thermal-sensitive N-isopropylacrylamide (NIPA) microgel colloidal spheres (4), whose effective diameter s linearly changes from 0.76 mm at 26.4°C to 0.67 mm at 30.6°C (10). The effective diameter is defined so that the melting volume fraction f m = 54.5%, which is the same as that of the hard spheres. By this definition, the measured freezing point f f = 49%, which is close to ...

An Improved Distance and Mass Estimate for SGR A* From a Multistar Orbit Analysis

“…The goal of this orbital period criteria is to select a star that would give the most information about the central gravitational potential once new speckle holography detections are included in its orbital fit. There are two stars not consistently directly detected in the speckle holography images that meet this constraint: S0-38 (P = 19 yr) and S0-102 (P = 11.5 yr; Meyer et al 2012). We chose to apply the new methodology to S0-38 for the following reasons.…”

“…For each epoch, both a final image and three subset images of similar quality are constructed. An early version of our analysis of these data was reported in our recent work on S0-102 (Meyer et al 2012). A subset of the epochs presented in that early analysis used a preliminary version of the algorithm described in Schödel et al (2013), with a smaller field of view and a different treatment of the PSF reference sources.…”

“…In the running of StarFinder to detect sources in both the main and subset images, we choose to set the correlation threshold to 0.8 instead of the value of 0.7 used in Meyer et al (2012). This more conservative correlation threshold value is chosen to minimize the number of fake sources detected in this preliminary analysis of the images.…”

“…Right: final joint probability distribution of M bh and R o as derived by the simultaneous fit of S0-2 and S0-38. et al 2012) and (4.30±0.36)×10 6 M e (Genzel et al 2010) for the mass of the BH and 7.7±0.4 kpc (Meyer et al 2012) and 8.2±0.34kpc (Gillessen et al 2013)for R o . The uncertainties derived from the orbital fit of S0-2 alone are slightly smaller than the uncertainties of these previous measurements due to the increased orbital phase coverage of this star, but the primary improvement in this work is the added information from the orbit of S0-38.…”

“…As a pilot study for this new methodology, we apply this technique to S0-38, one of the three stars at the Galactic center with an orbital period of less than 20 yr(in addition to S0-2 and S0-102; see Meyer et al 2012), with the ultimate goal of using this star as an additional constraint on the BH mass and R o . At a magnitude of K=17.0, S0-38 is consistently detected in our deep AO data taken from 2005 to 2013, but it has not previously been detected in our speckle imaging data taken from 1995 to 2005.…”