Spontaneously broken symmetry restoration of quantum fields in the vicinity of neutral and electrically charged black holes

We consider the restoration of a spontaneously broken symmetry of an interacting quantum scalar field around neutral, i.e., Schwarzschild, and electrically charged, i.e., Reissner-Nordstr\"om, black holes in four dimensions. This is done through a semiclassical self-consistent procedure, by solving the system of non-linear coupled equations describing the dynamics of the background field and the vacuum polarization. The black hole at its own horizon generates an indefinitely high temperature which decreases to the Hawking temperature at infinity. Due to the high temperature in its vicinity, there forms a bubble around the black hole in which the scalar field can only assume a value equal to zero, a minimum of energy. Thus, in this region the symmetry of the energy and the field is preserved. At the bubble radius, there is a phase transition in the value of the scalar field due to a spontaneous symmetry breaking mechanism. Indeed, outside the bubble radius the temperature is low enough such that the scalar field settles with a nonzero value in a new energy minimum, indicating a breaking of the symmetry in this outer region. Conversely, there is symmetry restoration from the outer region to the inner bubble close to the horizon. Specific properties that emerge from different black hole electric charges are also noteworthy. It is found that colder black holes, i.e., more charged ones, have a smaller bubble length of restored symmetry. In the extremal case the bubble has zero length, i.e., there is no bubble. Additionally, for colder black holes, it becomes harder to excite the quantum field modes, so the vacuum polarization has smaller values. In the extremal case, the black hole temperature is zero and the vacuum polarization is never excited.Comment: 16 pages, 4 figure

Discovery of Extended Main Sequence Turn-offs in Four Young Massive Clusters in the Magellanic Clouds

An increasing number of young massive clusters (YMCs) in the Magellanic Clouds have been found to exhibit bimodal or extended main sequences (MSs) in their color--magnitude diagrams (CMDs). These features are usually interpreted in terms of a coeval stellar population with different stellar rotational rates, where the blue and red MS stars are populated by non- (or slowly) and rapidly rotating stellar populations, respectively. However, some studies have shown that an age spread of several million years is required to reproduce the observed wide turn-off regions in some YMCs. Here we present the ultraviolet--visual CMDs of four Large and Small Magellanic Cloud YMCs, NGC 330, NGC 1805, NGC 1818, and NGC 2164, based on high-precision Hubble Space Telescope photometry. We show that they all exhibit extended main-sequence turn-offs (MSTOs). The importance of age spreads and stellar rotation in reproducing the observations is investigated. The observed extended MSTOs cannot be explained by stellar rotation alone. Adopting an age spread of 35--50 Myr can alleviate this difficulty. We conclude that stars in these clusters are characterized by ranges in both their ages and rotation properties, but the origin of the age spread in these clusters remains unknown.Comment: 14 pages, 9 figures, ApJ accepte

The radial distributions of the two main-sequence components in the young massive star cluster NGC 1856

The recent discovery of double main sequences in the young, massive star cluster NGC 1856 has caught significant attention. The observations can be explained by invoking two stellar generations with different ages and metallicities or by a single generation of stars composed of two populations characterized by different rotation rates. We analyzed the number ratios of stars belonging to both main-sequence components in NGC 1856 as a function of radius. We found that their number ratios remain approximately unchanged from the cluster's central region to its periphery, indicating that both components are homogeneously distributed in space. Through a comparison of the loci of the best-fitting isochrones with the ridge lines of both stellar components, we found that both multiple stellar populations and rapid stellar rotation can potentially explain the observed main-sequence bifurcation in NGC 1856. However, if NGC1856 were a young representative of the old globular clusters, then the multiple stellar populations model would not be able to explain the observed homogeneity in the spatial distributions of these two components, since all relevant scenarios would predict that the second stellar generation should be formed in a more compact configuration than that of the first stellar generation, while NGC 1856 is too young for both stellar generations to have been fully mixed dynamically. We speculate that the rapid stellar rotation scenario would be the favored explanation of the observed multiple stellar sequences in NGC 1856.Comment: 11 pages, 6 figures, ApJ accepte

New insights into the formation of the blue main sequence in NGC 1850

Recent discoveries of bimodal main sequences (MSs) associated with young clusters (with ages $\lesssim 1$ Gyr) in the Magellanic Clouds have drawn a lot of attention. One of the prevailing formation scenarios attributes these split MSs to a bimodal distribution in stellar rotation rates, with most stars belonging to a rapidly rotating population. In this scenario, only a small fraction of stars populating a secondary blue sequence are slowly or non-rotating stars. Here, we focus on the blue MS in the young cluster NGC 1850. We compare the cumulative number fraction of the observed blue-MS stars to that of the high-mass-ratio binary systems at different radii. The cumulative distributions of both populations exhibit a clear anti-correlation, characterized by a highly significant Pearson coefficient of $-0.97$. Our observations are consistent with the possibility that blue-MS stars are low-mass-ratio binaries, and therefore their dynamical disruption is still ongoing. High-mass-ratio binaries, on the other hand, are more centrally concentrated.Comment: 8 pages, 6 figures, accepted to Ap

Stars caught in the braking stage in young Magellanic Clouds clusters

The color-magnitude diagrams of many Magellanic Cloud clusters (with ages up to 2 billion years) display extended turnoff regions where the stars leave the main sequence, suggesting the presence of multiple stellar populations with ages which may differ even by hundreds million years (Mackey et al. 2008, Milone et al. 2009, Girardi et al. 2011). A strongly debated question is whether such an extended turnoff is instead due to populations with different stellar rotations (Girardi et al. 2011, Goudfrooij et al. 2011, Rubele et al. 2013, Li et al. 2014). The recent discovery of a `split' main sequence in some younger clusters (about 80--400Myr) added another piece to this puzzle. The blue (red) side of the main sequence is consistent with slowly (rapidly) rotating stellar models (D'Antona et al. 2015, Milone et al. 2016, Correnti et al. 2017, Milone et al 2016), but a complete theoretical characterization of the observed color-magnitude diagram appeared to require also an age spread (Correnti et al. 2017). We show here that, in three clusters so far analyzed, if the blue main sequence stars are interpreted with models that have been always slowly rotating, they must be about 30% younger than the rest of the cluster. If they are instead interpreted as stars initially rapidly rotating, but that have later slowed down, the age difference disappears, and "braking" also helps to explain the apparent age differences of the extended turnoff. The age spreads in Magellanic Cloud clusters are a manifestation of rotational stellar evolution. Observational tests are suggested.Comment: Accepted for publication and in state of Advance Online Publication (from 24 July 2017) on Nature Astronom

Atmospheric Parameters and Metallicities for 2191 stars in the Globular Cluster M4

We report new metallicities for stars of Galactic globular cluster M4 using the largest number of stars ever observed at high spectral resolution in any cluster. We analyzed 7250 spectra for 2771 cluster stars gathered with the VLT FLAMES+GIRAFFE spectrograph at VLT. These medium resolution spectra cover by a small wavelength range, and often have very low signal-to-noise ratios. We attacked this dataset by reconsidering the whole method of abundance analysis of large stellar samples from beginning to end. We developed a new algorithm that automatically determines the atmospheric parameters of a star. Nearly all data preparation steps for spectroscopic analyses are processed on the syntheses, not the observed spectra. For 322 Red Giant Branch stars with $V \leq 14.7$ we obtain a nearly constant metallicity, $= -1.07$ ($\sigma$ = 0.02). No difference in the metallicity at the level of $0.01 ~\textrm{dex}$ is observed between the two RGB sequences identified by \cite{Monelli:2013us}. For 1869 Subgiant and Main Sequence Stars $V > 14.7$ we obtain $= -1.16$ ($\sigma$ = 0.09) after fixing the microturbulent velocity. These values are consistent with previous studies that have performed detailed analyses of brighter RGB stars at higher spectroscopic resolution and wavelength coverage. It is not clear if the small mean metallicity difference between brighter and fainter M4 members is real or is the result of the low signal-to-noise characteristics of the fainter stars. The strength of our approach is shown by recovering a metallicity close to a single value for more than two thousand stars, using a dataset that is non-optimal for atmospheric analyses. This technique is particularly suitable for noisy data taken in difficult observing conditions.Comment: 17 pages, 20 figures, 3 tables. Accepted for publication in The Astronomical Journa

First evidence of multiple populations along the AGB from Str\"omgren photometry

Spectroscopic studies have demonstrated that nearly all Galactic globular clusters (GCs) harbour multiple stellar populations with different chemical compositions. Moreover, colour-magnitude diagrams based exclusively on Str\"omgrem photometry have allowed us to identify and characterise multiple populations along the RGB of a large number of clusters. In this paper we show for the first time that Str\"omgren photometry is also very effcient at identifying multiple populations along the AGB, and demonstrate that the AGB of M3, M92, NGC362, NGC1851, and NGC6752 are not consistent with a single stellar population. We also provide a catalogue of RGB and AGB stars photometrically identified in these clusters for further spectroscopic follow-up studies.We combined photometry and elemental abundances from the literature for RGB and AGB stars in NGC6752 where the presence of multiple populations along the AGB has been widely debated. We find that, while the MS, SGB, and RGB host three stellar populations with different helium and light element abundances, only two populations of AGB stars are present in the cluster. These results are consistent with standard evolutionary theory.Comment: 9 pages, 3 figures, 1 table in the main article, 3 tables in the appendix of which 2 tables containing coordinates and photometry of photometrically identified RGB and AGB star

Experimental verification of the interpolation method on a real damaged bridge

The identification of damage in a bridge from changes in its vibrational behavior is an inverse problem of important practical value. Significant advances have been obtained on this topic in the last two-three decades, both from the theoretical and applied point of view. One of the main problems when dealing with the assessment of vibration based damage identification methods is the lack of experimental data recorded on real damaged structures. Due to this, a large number of damage identification algorithms are tested using data simulated by numerical models. The availability of data recorded on a damaged bridge before its demolition gave the authors the uncommon chance to verify the sensitivity and reliability of the IDDM basing on data recorded on a real structure. Specifically data recorded on a reinforced concrete single-span supported bridge in the Municipality of Dogna (Friuli, Italy) were used to apply the damage localization algorithm. Harmonically forced tests were conducted after imposing artificial, increasing levels of localized damage. In this paper the sensitivity of the method is discussed with respect to the number of instrumented locations and to the severity of the damage scenarios considere

Multiple stellar populations in Galactic globular clusters: observational evidence

An increasing number of both photometric and spectroscopic observations over the last years have shown the existence of distinct sub-populations in many Galactic globular clusters and shattered the paradigm of globulars hosting single, simple stellar populations. These multiple populations manifest themselves in a split of different evolutionary sequences in the cluster color-magnitude diagrams and in star-to-star abundance variations. In this paper we will summarize the observational scenario.Comment: 6 pages, 3 figures, Proceedings SF2A 201