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E. Mediavilla

Publications and source records attributed to E. Mediavilla.

At least 19 recordsLinked to original sources

Accretion Disk Sizes and Temperature Profiles in Lensed Quasars: NIR Microlensing Challenges Thin Disk Theory

Microlensing and reverberation mapping measurements of quasar accretion disk sizes and temperature gradients disagree with thin disk theory predictions. Previous microlensing results rely on heterogeneous wavelength coverage -primarily UV broad emission lines (BELs) from small samples -probing the disk only out to a typical radius of $\lesssim$5 light days on average. We use microlensing estimates from an homogeneous sample of near-infrared (NIR) observations of lensed quasars (21 image-pairs from 7 lens systems) to extend disk size measurements out to 14 light days. This analysis leverages narrow emission lines (NELs), which provide a more reliable microlensing-free baseline than BEL cores. We derive Bayesian accretion disk size estimates that reproduce the observed microlensing magnifications, as simulated from magnification maps. NEL-based sizes yield a logarithmic slope of $p=0.68\pm0.23$, consistent with prior estimates corresponding to inner disk regions ($r \lesssim$5 light days). Using a new homogeneous NIR dataset that allows us to reach radial distances of up to 14 light days, we find that accretion disks in these previously unexplored regions are also larger and exhibit steeper temperature gradients than thin disk theory predicts. The increased precision allows us to reject the theoretical logarithmic slope $p=4/3$ at the 98\% confidence level. Any hypothesis invoking BLR contamination to explain this discrepancy must account for how such contamination modulates the underlying accretion disk such that the combination of both results in a power law with logarithmic slope $p=0.68\pm0.23$ across a broad wavelength baseline spanning from $\sim$X-Ray to $\sim 5000$\AA.

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Microlensing time-scales and flux magnification probabilities of a sample of 204 lensed quasars

Quasar microlensing is both a very useful tool in cosmology and astrophysics, and a source of uncertainty in some studies like the determination of the Hubble constant from lensed quasars. Microlensing probability and time-scales have been statistically studied using as a reference scale the Einstein ring crossing time of an isolated mass. Our goal is to extend the statistical analysis of microlensing to all currently known lensed quasars with available data, considering realistic optical depths and the gravitational effect of the lens galaxy. We take into account new observational results about quasar sizes and peculiar velocities of lens galaxies. We apply automatic lens modeling to the 204 systems available. For each image, we compute microlensing magnification maps and histograms. Using thin disk source sizes scaled to take into account recent measurements of accretion disk sizes, we find a mean source crossing time of $2.59\pm 0.07$ years. The mean Einstein radius crossing time is $ 11.29 \pm 0.05$ years. When a fraction of mass in microlenses $\alpha=0.2$ is adopted, we find a good matching between the modeled histogram of mean microlensing magnifications for the images in our sample and the experimental histogram of microlensing magnifications. From the modeling of microlensing magnification histograms, we estimate the average half-light radius of the quasar source, $R_{1/2}=5.4\pm 2.7$ light-days, and a lower limit to the mass fraction in microlenses, $\alpha\ge 0.15$. From the microlensing magnification maps, we find that a lensed quasar image has a mean probability of approximately 9% of being involved in a high-magnification event ($\Delta m \le -0.32$). We select a group of images with the largest probabilities and the smallest crossing times.

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Joining forces: 30 years of optical monitoring of the Einstein Cross

We present an extended optical monitoring of the quadruply-imaged gravitationally lensed quasar QSO 2237+0305, the Einstein Cross, including observations from different observatories in both hemispheres and using a new photometric technique. This technique uses a region far enough from the lens system to determine accurately the sky background level, and minimises contamination from the lensing galaxy by combining analytical and numerical modeling of its structure. The resulting light curves of the four quasar images describe variations across practically the entire optical spectrum and span about 9000 days in the $VRI$ bands. The multi-band microlensing variability is captured with an unprecedented level of detail, and a preliminary microlensing analysis reveals an almost linear scaling of source radius with wavelength, providing direct evidence for the wavelength-dependent structure of the region contributing to optical passband fluxes. Specifically, assuming a mean microlens mass $\langle M \rangle$ = 0.3 $\rm{M_{\odot}}$ and concentric Gaussian sources that move according to the velocity distribution peaks (speed and direction) reported in a previous microlensing analysis, we find that the half-light radius of the $g$-band source is 9.6 $\pm$ 2.7 lt-day and the size of the sources grows with wavelength with a power-law index of $\alpha$ = 0.94 $\pm$ 0.05. We conclude that these long-term light curves set stringent empirical constraints on models of quasar emission and microlensing physics.

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Microlensing analysis of 14.5-year light curves in SDSS J1004+4112: Quasar accretion disk size and intracluster stellar mass fraction

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 $χ^2$ 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 2407Å in the rest frame and stellar mass fractions at the quasar image positions of $α_A>0.059$, $α_B=0.056^{+0.021}_{-0.027}$, $α_C=0.030^{+0.031}_{-0.021}$, and $α_D=0.072^{+0.034}_{-0.016}$. 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.

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First Direct Evidence for Keplerian Rotation in Quasar Inner Broad Line Regions

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.

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Revealing the inner workings of the lensed quasar SDSS J1339+1310: Insights from microlensing analysis

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$α$, 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 $M_{BH} \sim2 \times 10^8 M_\odot$.

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Single-epoch and Differential Astrometric Microlensing of Quasars

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.

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Lensing Constraints on PBHs: Substellar to Intermediate Masses

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.

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Quasar Microlensing Statistics and Flux-Ratio Anomalies in Lens Models

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 ($|Δm| \ge 0.7$ 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.

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Probing the structure of the lensed quasar SDSS J1004+4112 through microlensing analysis of spectroscopic data

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$α$, 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.

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Constraints on the Abundance of PBHs from X-ray Quasar Microlensing Observations: Substellar to Planetary Mass Range

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 $M=3M_{\odot}$.

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Revealing the structure of the lensed quasar Q 0957+561 III. Constraints on the size of the broad-line region

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.

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Black Hole masses for 14 gravitational lensed quasars

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$α$ and/or H$β$ 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%.

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Fast Multipole Method for Gravitational Lensing. Application to High Magnification Quasar Microlensing

We introduce the use of the Fast Multipole Method (FMM) to speed up gravitational lensing ray tracing calculations. The method allows very fast calculation of ray deflections when a large number of deflectors, $N_*$, is involved, while keeping rigorous control on the errors. In particular, we apply this method, in combination with the Inverse Polygon Mapping technique (IPM), to quasar microlensing to generate microlensing magnification maps with very high workloads (high magnification, large size and/or high resolution) that require a very large number of deflectors. Using, FMM-IPM, the computation time can be reduced by a factor $\sim 10^5$ with respect to standard Inverse Ray Shooting, making the use of this algorithm on a personal computer comparable to the use of standard IRS on GPUs. We also provide a flexible web interface for easy calculation of microlensing magnification maps using FMM-IPM\footnote{http://gloton.ugr.es/microlensing/}. We exemplify the power of this new method by applying it to some challenging interesting astrophysical scenarios, including clustered primordial black holes, or extremely magnified stars close to the giant arcs of galaxy clusters. We also show the performance/use of FMM to calculate ray deflection for a halo resulting from cosmological simulations composed by a large number ($N\gtrsim 10^7$) of elements.

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A Mass Model for the Lensing Cluster SDSS J1004+4112: Constraints From the Third Time Delay

We have built a new model for the lens system SDSS J1004+4112 including the recently measured time delay of the fourth quasar image. This time delay has a strong influence on the inner mass distribution of the lensing cluster ($ρ\propto r^{-α}$) allowing us to determine $α=1.18^{+0.02(+0.11)}_{-0.03(-0.18)}$ at the 68% (95%) confidence level in agreement with hydrodynamical simulations of massive galaxy clusters. We find an offset between the brightest cluster galaxy (BCG) and the dark matter halo of $3.8^{+0.6(+1.4)}_{-0.7(-1.3)}$ kpc at 68% (95%) confidence which is compatible with other galaxy cluster measurements. As an observational challenge, the estimated time delay between the leading image C and the faint (I=24.7) fifth image E is roughly 8 yr.

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Abundance of LIGO/Virgo Black Holes from Microlensing Observations of Quasars with Reverberation Mapping Size Estimates

Assuming a population of Black Holes (BHs) with masses in the range inferred by LIGO/Virgo from BH mergers, we use quasar microlensing observations to estimate their abundances. We consider a mixed population of stars and BHs and the presence of a smooth dark matter component. We adopt reverberation mapping estimates of the quasar size. According to a Bayesian analysis of the measured microlensing magnifications, a population of BHs with masses $\sim$ 30$M_{\odot}$ constitutes less than 0.4 % of the total matter at 68 % confidence level (less than 0.9 % at 90 % confidence). We have explored the whole mass range of LIGO/Virgo BHs finding that this upper limit ranges from 0.5 % to 0.4 % at 68 % C.L. (from 1.1 % to 0.9 % at 90 % C.L.) when the BHs mass change from 10 to 60$M_{\odot}$. We estimate a 16 % contribution from the stars, in agreement with previous studies based on a single mass population that do not consider explicitly the presence of BHs. These results are consistent with the estimates of BH abundances from the statistics of LIGO/Virgo mergers and rule out that PBHs (or any type of compact objects), in this mass range constitute a significant fraction of the dark matter.

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Limiting the Abundance of LIGO/Virgo Black Holes with Microlensing Observations of Quasars of Finite Size

We present a simple but general argument that strongly limits the abundance of Primordial Black Holes (PBHs) (or other unknown population of compact objects) with masses similar to those determined by LIGO/Virgo from BH binary mergers. We show that quasar microlensing can be very sensitive to the mass of the lenses, and that it is able to distinguish between stars and BHs of high mass, when the finite size of the source is taken into account. A significant presence of massive BHs would produce frequent high flux magnifications (except for unrealistically large sources) which have been very rarely observed. On the contrary, a typical stellar population would induce flux magnifications consistent with the observations. This result excludes PBHs (or any type of compact object) in the mass range determined by LIGO/Virgo as the main dark matter constituents in the lens galaxies.

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First black hole mass estimation for the quadruple lensed system WGD2038-4008

The quadruple lensed system WGD2038-4008 was recently discovered with the help of new techniques and observations. Even though black hole mass has been estimated for lensed quasars, it has been calculated mostly for one broad emission line of one image, but the images could be affected by microlensing, affecting the results. We present black hole mass (MBH) estimations for images A and B using the three most prominent broad emission lines (H$α$, H$β$ and MgII) obtained in one single-epoch spectra. This is the first time the mass is estimated in a lensed quasar in two images, allowing us to disentangle the effects of microlensing. We used the X-shooter instrument mounted in VLT, to observe this system taking advantage of its wide spectral range. Using the flux ratio between the continuum and the core of the emission lines we analyzed if microlensing was present in the continuum source. We obtained MBH using the single-epoch method with the H$α$ and H$β$ emission lines from the monochromatic luminosity and the velocity width. The luminosity at 3000 Å was obtained using the Spectral Energy Distribution (SED) of image A while the luminosity at 5100 Å was estimated directly from the spectra. The average MBH between the images obtained was $\rm log_{10}$(M$_{BH}/M_{\odot}$) = 8.27 $\pm$ 1.05, 8.25 $\pm$ 0.32 and 8.59 $\pm$ 0.35 for MgII, H$β$ and H$α$ respectively. We find Eddington ratios similar to those measured in the literature for unlensed low-luminosity quasars. Microlensing of -0.16 $\pm$ 0.06 mag. in the continuum was found but the induced error in the MBH is minor compared to the one associated to the macromodel magnification. We also obtained the accretion disk size using the MBH for the three emission lines, obtaining an average value of $\rm log_{10}(r_{s}/cm)$ = 15.3 +/- 0.63, which is in agreement with theoretical estimates.

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