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Context. The gravitational lens system SDSS J1004+4112 was the first known example of a quasar lensed by a galaxy cluster. The interest in this system has been renewed following the publication of r-band light curves spanning 14.5 years and the determination of the time delays between the four brightest quasar images. Aims. We constrained the quasar accretion disk size and the fraction of the lens mass in stars using the signature of microlensing in the quasar image light curves. Methods. We built the six possible histograms of microlensing magnitude differences between the four quasar images and compared them with simulated model histograms, using a $\chi^2$ test to infer the model parameters. Results. We infer a quasar disk half-light radius of $R_{1/2}=(0.70\pm0.04)\, R_E=(6.4\pm0.4) \sqrt{M/0.3M_{\odot}}$ light-days at 2407\r{A} in the rest frame and stellar mass fractions at the quasar image positions of $\alpha_A>0.059$, $\alpha_B=0.056^{+0.021}_{-0.027}$, $\alpha_C=0.030^{+0.031}_{-0.021}$, and $\alpha_D=0.072^{+0.034}_{-0.016}$. Conclusions. The inferred disk size is broadly compatible with most previous estimates, and the stellar mass fractions are within the expected ranges for galaxy clusters. In the region where image C lies, the stellar mass fraction is compatible with a stellar contribution from the brightest cluster galaxy, galaxy cluster members, and intracluster light, but the values at images B, D, and especially A are slightly larger, possibly suggesting the presence of extra stellar components., Comment: 7 pages, 6 figures, 2 tables, A&A in press

While elementary particles are the favored candidate for the elusive dark matter, primordial black holes (PBHs) have also been considered to fill that role. Gravitational microlensing is a very well-suited tool to detect and measure the abundance of compact objects in galaxies. Previous studies based on quasar microlensing exclude a significant presence of substellar to intermediate-mass BHs ($\lesssim 100\,\mathrm{M}_\odot$). However, these studies were based on a spatially uniform distribution of BHs while, according to current theories of PBHs formation, they are expected to appear in clusters. We study the impact of clustering in microlensing flux magnification finding that at large scales clusters act like giant pseudo-particles, strongly affecting the emission coming from the Broad Line Region, which can no longer be used to define the zero microlensing baseline. As an alternative, we set this baseline from the intrinsic magnification ratios of quasar images predicted by macro lens models and compare them with the observed flux ratios in emission lines, infrared (IR), and radio. The (magnitude) differences are the flux-ratio anomalies attributable to microlensing, which we estimate for 35 image pairs corresponding to 12 lens systems. A Bayesian analysis indicates that the observed anomalies are incompatible with the existence of a significant population of clustered PBHs. Furthermore, we find that more compact clusters exhibit a stronger microlensing impact. Consequently, we conclude that clustering makes the existence of a significant population of BHs in the substellar to intermediate mass range even more unlikely.

We introduce a novel method to derive rotation curves with light-day spatial resolution of the inner regions of lensed quasars. We aim to probe the kinematics of the inner part of the broad-line region (BLR) by resolving the microlensing response - a proxy for the size of the emitting region - in the wings of the broad emission lines (BELs). Specifically, we assess the strength of the microlensing effects in the wings of the high-ionization lines Si IV and C IV across various velocity bins in five gravitationally lensed quasars: SDSS J1001+5027, SDSS J1004+4112, HE 1104$-$1805, SDSS J1206+4332, and SDSS J1339+1310. Using Bayesian methods to estimate the dimensions of the corresponding emission regions and adopting a Keplerian model as our baseline, we examine the consistency of the hypothesis of disk-like rotation. Our results reveal a monotonic, smooth increase in microlensing magnification with velocity. The deduced velocity-size relationships inferred for the various quasars and emission lines closely conform to the Keplerian model of an inclined disk. This study provides the first direct evidence of Keplerian rotation in the innermost region of quasars across a range of radial distances spanning from $\sim$5 to 20 light-days.

We aim to unveil the structure of the continuum and broad-emission line (BEL) emitting regions in the gravitationally lensed quasar SDSS J1339+1310 by examining the distinct signatures of microlensing present in this system. Our study involves a comprehensive analysis of ten years (2009-2019) of photometric monitoring data and seven spectroscopic observations acquired between 2007 and 2017. This work focuses on the pronounced deformations in the BEL profiles between images A and B, alongside the chromatic changes in their adjacent continua and the striking microlensing variability observed in the $r$-band light curves. We employed a statistical model to quantify the distribution and impact of microlensing magnifications and utilized a Bayesian approach to estimate the dimensions of various emission regions within the quasar. The analysis of the $r$-band light curves reveals substantial microlensing variability in the rest-frame UV continuum, suggesting that image B is amplified relative to image A by a factor of up to six. This finding is corroborated by pronounced microlensing-induced distortions in all studied BEL profiles (Ly$\alpha$, Si IV, C IV, C III], and Mg II), especially a prominent magnification of image B's red wing. We estimated the average dimensions of the BLR to be notably smaller than usual: the region emitting the blue wings measures $R_{1/2} = 11.5 \pm 1.7$ light-days, while the red wings originate from a more compact area of $R_{1/2} = 2.9\pm0.6$ light-days. From the photometric monitoring data, we inferred that the region emitting the $r$-band is $R_{1/2} = 2.2\pm0.3$ light-days across. Furthermore, by assessing the gravitational redshift of the UV Fe III blend and combining it with the blend's microlensing-based size estimate, we calculated the central SMBH's mass to be $M_{BH} \sim2 \times 10^8 M_\odot$.

We propose and discuss a new experimental approach to measure the centroid shift induced by gravitational microlensing in the images of lensed quasars (astrometric microlensing). Our strategy is based on taking the photocenter of a region in the quasar large enough as to be insensitive to microlensing as reference to measure the centroid displacement of the continuum. In this way, single-epoch measurements of astrometric microlensing can be performed. Using numerical simulations, we show that, indeed, the centroid shift monotonically decreases as the size of the emitting region increases, and only for relatively large regions, like the broad line region (BLR), does the centroid shift become negligible. This opens interesting possibilities to study the stratification of the different emitters in the accretion disk and the BLR. We estimate the amplitude of the centroid shifts for 79 gravitationally lensed images and study more thoroughly the special cases Q2237+030 A, RXJ1131-1231 A, PG1115+080 A2 and SDSS J1004+4112 A. We propose to use spectro-astrometry to simultaneously obtain the photocenters of the continuum and of different emission line regions since, with the precision of forthcoming instruments, astrometric microlensing by $\sim 1 M_\odot$ mass microlenses may be detected in many quasar lensed images. When we consider more massive micro/millilenses, $M\gtrsim 10 M_\odot$, often proposed as the constituents of dark matter, the BLR becomes sensitive to microlensing and can no longer be used as a positional reference to measure centroid shifts. Differential microlensing between the images of a lensed quasar along several epochs should be used instead., Comment: 14 pages, 6 figures, 1 table. ApJ in press

Gravitational microlensing is a robust tool to detect and directly measure the abundance and mass of any kind of compact objects, either in our galaxy or in the extragalatic domain. On basis to generic, broadly applicable arguments, it is concluded that the observed microlensing magnifications are too small and the microlensing events less frequent than the expectations for a significant population of compact objects (other than normal stars). The detection of chromatic effects of microlensing, neither supports the presence of BHs. Detailed statistical studies of the observed microlensing magnifications and events frequency impose strict upper limits to the fraction of total mass of BHs ($\ltsim$ 1\%) from $10^{-7}M_\odot$ to indefinitely large masses. These results hold even when the BHs are distributed according to a mass spectrum or are forming clusters., Comment: 15 pages, 5 figures, To appear as Chapter 24 in the book "Primordial Black Holes", ed. Chris Byrnes, Gabriele Franciolini, Tomohiro Harada, Paolo Pani, Misao Sasaki; Springer (2024)

Precise lens modeling is a critical step in time delay studies of multiply imaged quasars, which are key for measuring some important cosmological parameters (specially $H_0$). However, lens models (in particular those semi-automatically generated) often show discrepancies with the observed flux-ratios between the different quasar images. These flux-ratio anomalies are usually explained through differential effects between images (mainly microlensing) that alter the intrinsic magnification ratios predicted by the models. To check this hypothesis, we collect direct measurements of microlensing to obtain the histogram of microlensing magnifications. We compare this histogram with recently published model flux-ratio anomalies and conclude that they cannot be statistically explained by microlensing. The average value of the model anomalies ($0.74\,$magnitudes) significantly exceeds the mean impact of microlensing ($0.33\,$magnitudes). Moreover, the histogram of model anomalies presents a significant tail with high anomalies ($|\Delta m| \ge 0.7$ magnitudes) which is completely unexpected from the statistics of microlensing observations. Microlensing simulations neither predict the high mean nor the fat tail of the histogram of model anomalies. We perform several statistical tests which exclude that microlensing can explain the observed flux-ratio anomalies (although Kolmogorov-Smirnov, which is less sensitive to the tail of the distributions, is not always conclusive). Thus, microlensing cannot statistically explain the bulk of flux-ratio anomalies, and models may explore different alternatives to try to reduce them. In particular, we propose to complement photometric observations with accurate flux ratios of the broad emission lines obtained from integral field spectroscopy to check and, ideally, constrain lens models.

Bismuth selenide, a benchmark topological insulator, grows in a trigonal structure at ambient conditions and exhibits a number of enticing properties related to the formation of Dirac surface states. Besides this polytype, a metastable orthorhombic modification with Pnma space group has been produced by electrodeposition and high-pressure high-temperature synthesis displaying upon Sb doping significant thermoelectric properties in the midtemperature range. However, very little experimental information is available on the fundamental properties of this polytype, such as, e.g., the electronic band gap and the lattice dynamics. We report here the temperature dependence of the Raman spectra of orthorhombic Bi2Se3 between 10 K and 300 K, which displays an anharmonic behavior of the optical phonons that can be modelled with a two-phonon decay channel. In order to analyze the data we performed ab initio calculations of the electronic bandstructure, the phonon frequencies at the center of the Brillouin zone, and the phonon dispersion relations along the main symmetry directions, examining the effect of spin-orbit coupling in both phonon and electronic energies. Lastly, we report here cathodoluminescence experiments at 83 K that set a lower limit to the electronic bandgap at 0.835 eV, pointing to an indirect nature, in agreement with our calculations. These results shed light to essential properties of orthorhombic Bi2Se3 for further understanding of the potential of this semiconductor for thermoelectrics and new applications., Comment: 10 figures

We exhibit closed hyperbolic surfaces of genus $10$ and $17$ such that the multiplicity of the first nonzero eigenvalue of their Laplacian is larger than the maximum conjectured by Yves Colin de Verdi\`ere in 1986. In order to determine these multiplicities, we apply the twisted Selberg trace formula to the representations induced by the isometry groups of these surfaces on corresponding triangle groups., Comment: 20 pages, 3 figures, 3 ancillary files

We aim to reveal the sizes of the continuum and broad emission line (BEL) emitting regions in the gravitationally lensed quasar SDSS J1004+4112 by analyzing the unique signatures of microlensing in this system. Through a comprehensive analysis of 20 spectroscopic observations acquired between 2003 and 2018, we studied the striking deformations of various BEL profiles and determined the sizes of their respective emitting regions. Our approach involves a detailed analysis of the magnitude differences in the BEL wings and their adjacent continua, and the implementation of a statistical model to quantify the distribution and impact of microlensing magnifications. To ensure a reliable baseline for no microlensing, we used the emission line cores as a reference. We then applied a Bayesian estimate to derive the size lower limits of the Ly$\alpha$, Si IV, C IV, C III], and Mg II emitting regions, as well as the sizes of the underlying continuum-emitting sources. We analyzed the outstanding microlensing-induced distortions in the line profiles of various BELs in the quasar image A, characterized by a prominent magnification of the blue part and a strong demagnification of the red part. From the statistics of microlensing magnifications and using Bayesian methods, we estimate the lower limit to the overall size of the regions emitting the BELs to be a few lt-days across, which is significantly smaller than in typically lensed quasars. The asymmetric deformations in the BELs indicate that the broad-line region is generally not spherically symmetric, and is likely confined to a plane and following the motions of the accretion disk. Additionally, the inferred continuum-emitting region sizes are larger than predictions based on standard thin-disk theory by a factor of $\sim$3.6 on average. The size-wavelength relation is consistent with that of a geometrically thin and optically thick accretion disk.

We use X-ray observations of quasar microlensing (sensitive to smaller compact objects than in the optical) to study the possible presence of a population of low mass black holes (from $\sim$ $10^{-3}M_{\odot}$ to $10^{-1}M_{\odot}$) in lens galaxies. We compare these observations with microlensing magnification simulations of a mixed population of stars and black holes (BHs) plus a smooth matter component. We estimate the individual mass fractions of both, stars and BHs, for three different BH masses in the range of substellar to planetary masses. Our Bayesian analysis indicates that the contribution of BHs is negligible in the substellar mass range but that a population of BHs of planetary mass (M $\lesssim$ $10^{-3}M_{\odot}$) could pass unnoticed to X-ray microlensing. We provide new upper limits to the contribution of BHs to the fraction of dark matter based on both, the quasar microlensing data in the X-ray band, and our previous estimates in the optical of intermediate-mass BHs with an additional upper limit at $M=3M_{\odot}$., Comment: 11 pages, 3 figures

Our aim is to examine the size, kinematics, and geometry of the broad-line region (BLR) in the double-lensed quasar Q 0957+561 by analyzing the impact of microlensing on various rest-frame ultraviolet broad-emission lines (BELs). We explore the influence of intrinsic variability and microlensing on the C IV, C III], and Mg II emission lines through multiple spectroscopic observations taken between April 1999 and January 2017. By utilizing the line cores as a reference for no microlensing and correcting for the long time delay between the images, we estimate the sizes of the regions emitting the broad-line wings using a Bayesian approach. Our study of the microlensing amplitudes between the lensed images of the quasar Q 0957+561 reveals differing sizes of the regions emitting the three prominent BELs C IV, C III], and Mg II. The strength of the differential microlensing indicates that the high-ionization line C IV arises from a compact inner region of the BLR with a half-light radius of $R_{1/2} \gtrsim 16.0$ lt-days, which represents a lower limit on the overall size of the BLR and is comparable to the size of the region emitting the r-band continuum in this system. A somewhat larger size of $R_{1/2}\gtrsim 44$ lt-days is obtained for the semi-forbidden line C III]. Microlensing has a weak impact on the lower-ionization line Mg II, which is emitted from a region with a half-light radius of $R_{1/2} \gtrsim 50$ lt-days. These findings suggest that the BEL regions may have distinct geometries and kinematics, with the more extended ones being spherically symmetric, and the most compact ones being nonspherical, with motions likely confined to a plane.

We estimate black hole masses (M$_{\rm BH}$) for 14 gravitationally lensed quasars using the Balmer lines along with estimates based on MgII and CIV emission lines for four and two of them, respectively. We compare with results obtained for other lensed quasars. We use spectroscopic data from the Large Binocular Telescope (LBT), Magellan and the Very Large Telescope (VLT) to measure the FWHM of the broad emission lines. Combined with the bolometric luminosity measured from the spectra energy distribution, we estimate M$_{\rm BH}$ including uncertainties from microlensing and variability. We obtain MBH using the single-epoch method from the H$\alpha$ and/or H$\beta$ broad emission lines for 14 lensed quasars, including the first estimates for QJ0158-4325, HE0512-3329 and WFI2026-4536. The masses are typical of non-lensed quasars of similar luminosity, and the implied Eddington ratios are typical. We have increased the sample of lenses with estimates of MBH by 60%., Comment: 16 pages. Submitted to A&A