Physical Sciences and Mathematics Commons^™

Information Horizon Of Solar Active Regions, Jay R. Johnson, Simon Wing, Carson O'Ffill, Bishwa Neupane

Faculty Publications

Information theory is used to characterize the solar active region periodicities and memories from the Carrington map images 1974–2021. The active regions typically evolve and move from one map to the next. In order to track these active region structures in sequences of images, an innovative method based on information theory is developed. Image entropy provides a measure of the organization of structures in the images. The entropy can also be used as a filter to identify structures and partition the active regions, which are then registered for each image. The partitions are used to compute the mutual information and …

Off-Shell Effects In Bound Nucleons And Parton Distributions From 1H, 2H, 3H, And 3He Data, S. I. Alekhin, S. A. Kulagin, Roberto Petti

Faculty Publications

We report the results of a new global QCD analysis including deep-inelastic scattering data off ¹H, ²H, ³H, and ³He targets. Nuclear corrections are treated in terms of a nuclear convolution approach with off-shell bound nucleons. The off-shell (OS) corrections responsible for the modification of the structure functions (SFs) of bound nucleons are constrained in a global fit along with the proton parton distribution functions (PDFs) and the higher-twist (HT) terms. We investigate the proton-neutron difference for the OS correction and discuss our predictions for the SF ratio F ⁿ ₂ / F ^p ₂ and …

Measurement Of The Double-Differential Muon-Neutrino Charged-Current Inclusive Cross Section In The Nova Near Detector, M. A. Acero, P. Adamson, L. Aliaga, N. Anfimov, A. Antoshkin, E. Arrieta-Diaz, L. Asquith, A. Aurisano, A. Back, M. Baird, N. Balashov, P. Baldi, B. A. Bambah, S. Bashar, K. Bays, B. Behera, R. Bernstein, V. Bhatnagar, D. Bhattarai, B. Bhuyan, Roberto Petti, Et. Al.

Faculty Publications

We report cross-section measurements of the final-state muon kinematics for ν_μ charged-current interactions in the NOvA near detector using an accumulated 8.09×10²⁰ protons on target in the NuMI beam. We present the results as a double-differential cross section in the observed outgoing muon energy and angle, as well as single-differential cross sections in the derived neutrino energy, E_ν, and square of the four-momentum transfer, Q². We compare the results to inclusive cross-section predictions from various neutrino event generators via χ² calculations using a covariance matrix that accounts for bin-to-bin correlations of systematic uncertainties. …

Evolution Of Coronal Magnetic Field Parameters During X5.4 Solar Flare, Seth H. Garland, Benjamin F. Akers, Vasyl B. Yurchyshyn, Robert D. Loper, Daniel J. Emmons

Faculty Publications

The coronal magnetic field over NOAA Active Region 11,429 during a X5.4 solar flare on 7 March 2012 is modeled using optimization based Non-Linear Force-Free Field extrapolation. Specifically, 3D magnetic fields were modeled for 11 timesteps using the 12-min cadence Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager photospheric vector magnetic field data, spanning a time period of 1 hour before through 1 hour after the start of the flare. Using the modeled coronal magnetic field data, seven different magnetic field parameters were calculated for 3 separate regions: areas with surface |Bz| ≥ 300 G, areas of flare brightening seen …

How Noise Thresholds Affect The Information Content Of Stellar Flare Sequences, Elmer C. Rivera, Jay R. Johnson, Jonathan Homan, Simon Wing

Faculty Publications

Systems that exhibit discrete dynamics can be well described and reconstructed by considering the set of time intervals between the discrete events of the system. The Kepler satellite has cataloged light curves for many Sun-like stars, and these light curves show strong bursts in intensity that are associated with stellar flares. The waiting time between these flares describes the fundamental dynamics of the stars and is driven by physical processes, such as flux emergence. While it is rather straightforward to identify large flares, the identification of weaker flares can be challenging because of the presence of noise. A common practice …

Measurement Of The VE- Nucleus Charged-Current Double-Differential Cross Section At 〈EV⟩ = 2.4 Gev Using Nova, M. A. Acero, P. Adamson, L. Aliaga, N. Anfimov, A. Antoshkin, E. Arrieta-Diaz, L. Asquith, A. Aurisano, A. Back, M. Biard, N. Balashov, P. Baldi, B. A. Bambah, S. Bashar, K. Bays, R. Bernstein, V. Bhatnagar, D. Bhattarai, B. Bhuyan, J. Bian, Roberto Petti, Et. Al.

Faculty Publications

The inclusive electron neutrino charged-current cross section is measured in the NOvA near detector using 8.02×10²⁰ protons-on-target in the NuMI beam. The sample of GeV electron neutrino interactions is the largest analyzed to date and is limited by ≃17% systematic rather than the ≃7.4% statistical uncertainties. The double-differential cross section in final-state electron energy and angle is presented for the first time, together with the single-differential dependence on Q² (squared four-momentum transfer) and energy, in the range 1  GeV≤E_νGENIE, GiBUU, NEUT, and NuWro neutrino event generators. The data do not strongly favor a model over the …

All-Sky Search For Short Gravitational-Wave Bursts In The Third Advanced Ligo And Advanced Virgo Run, Ligo Scientific Collaboration, Virgo Collaboration, Kagra Collaboration, Tiffany Z. Summerscales

Faculty Publications

After the detection of gravitational waves from compact binary coalescences, the search for transient gravitational-wave signals with less well-defined waveforms for which matched filtering is not well suited is one of the frontiers for gravitational-wave astronomy. Broadly classified into “short” ≲1  s and “long” ≳1  s duration signals, these signals are expected from a variety of astrophysical processes, including non-axisymmetric deformations in magnetars or eccentric binary black hole coalescences. In this work, we present a search for long-duration gravitational-wave transients from Advanced LIGO and Advanced Virgo’s third observing run from April 2019 to March 2020. For this search, we use …

Probing Free Nucleons With (Anti)Neutrinos, Roberto Petti

Faculty Publications

We discuss a method to study free protons and neutrons using ν(⊽)-hydrogen (H) Charged Current (CC) inelastic interactions, together with various precision tests of the isospin (charge) symmetry using ν and ⊽ CC interactions on both H and nuclear targets. Probing free nucleons with (anti)neutrinos provides information about their partonic structure, as well as a crucial input for the modeling of ν(⊽)-nucleus (A) interactions. Such measurements concurrently represent a valuable tool to address the main limitations of accelerator-based neutrino scattering experiments on nuclear targets, originating from the combined effect of the unknown (anti)neutrino energy and of the …

Separation Of Track- And Shower-Like Energy Deposits In Protodune-Sp Using A Convolutional Neural Network, A. Abed Abud, B. Abi, R, Acciarri, M. A. Acero, M. R. Adames, G. Adamov, M. Adamowski, D. Adams, M. Adinolfi, A. Aduszkiewicz, M. Andreotti, M. Andrews, F. Andrianala, S. Andringa, N. Anfimov, A. Ankowski, M. Antoniassi, M. Antonova, A. Antoshkin, S. Antusch, Roberto Petti, Et. Al.

Faculty Publications

Liquid argon time projection chamber detector technology provides high spatial and calorimetric resolutions on the charged particles traversing liquid argon. As a result, the technology has been used in a number of recent neutrino experiments, and is the technology of choice for the Deep Underground Neutrino Experiment (DUNE). In order to perform high precision measurements of neutrinos in the detector, final state particles need to be effectively identified, and their energy accurately reconstructed. This article proposes an algorithm based on a convolutional neural network to perform the classification of energy deposits and reconstructed particles as track-like or arising from electromagetic …

Tau Neutrinos In The Next Decade: From Gev To Eev, Roshan Mammen Abraham, Jamie Alvarez-Muñiz, Carlos A. Argüelles, Akitaka Ariga, Tomoko Ariga, Adam Aurisano, Dario Autiero, Mary Bishai, Nilay Bostan, Mauricio Bustamante, Austin Cummings, Valentin Decoene, André De Gouvêa, Giovanni De Lellis, Albert De Roeck, Peter B. Denton, Antonia Di Crescenzo, Milind V. Diwan, Yasaman Farzan, Anatoli Fedynitch, Jonathan L. Feng, Laura J. Fields, Alfonso Garcia, Maria Vittoria Garzelli, Julia Gehrlein, Christian Glaser, Katarzyna Grzelak, Steffen Hallmann, Jeremy Hewes, D Indumathi, Ahmed Ismail, Sudip Jana, Yu Seon Jeong, Kevin J. Kelly, Spencer R. Klein, Felix Kling, Thomas Kosc, Umut Kose, D Jason Koskinen, John Krizmanic, Jeff Lazar, Yichen Li, Ivan Martinez-Soler, Irina Mocioiu, Jiwoo Nam, Valentin Niess, Nepomuk Otte, Sameer Patel, Roberto Petti, Et. Al.

Faculty Publications

Tau neutrinos are the least studied particle in the standard model. This whitepaper discusses the current and expected upcoming status of tau neutrino physics with attention to the broad experimental and theoretical landscape spanning long-baseline, beam-dump, collider, and astrophysical experiments. This whitepaper was prepared as a part of the NuTau2021 Workshop.

Clustering Behavior In Solar Flare Dynamics, Elmer C. Rivera, Jay R. Johnson, Jonathan Homan, Simon Wing

Faculty Publications

The solar magnetic activity cycle provides energy input that is released in intense bursts of radiation known as solar flares. As such, the dynamics of the activity cycle is embedded in the sequence of times between the flare events. Recent analysis shows that solar flares exhibit memory on different timescales. These previous studies showed that the time ordering of flare events is not random, but rather there is dependence between successive flares. In the present work, the clustering of flares is demonstrated through a straightforward nonparametric method where the cumulative distribution function of successive flares is compared with the cumulative …

The Roles Of Flux Tube Entropy And Effective Gravity In The Inward Plasma Transport At Saturn, S. Wing, M. F. Thomsen, J. R. Johnson, D. G. Mitchell, R. C. Allen, X. Ma, P. A. Delamere

Faculty Publications

The inward plasma transport at the Saturnian magnetosphere is examined using the flux tube interchange stability formalism developed by Southwood & Kivelson. Seven events are selected. Three cases are considered: (1) the injected flux tube and ambient plasmas are nonisotropic, (2) the injected flux tube and ambient plasmas are isotropic, and (3) the injected flux tube plasma is isotropic, but the ambient plasma is nonisotropic. Case 1 may be relevant for fresh injections, while case 3 may be relevant for old injections. For cases 1 and 2, all but one event have negative stability conditions, suggesting that the flux tube …

Improved Measurement Of Neutrino Oscillation Parameters By The Nova Experiment, M. A. Acero, P. Adamson, L. Aliaga, N. Anfimov, A. Antoshkin, E. Arrieta-Diaz, L. Asquith, A. Aurisano, A. Back, C. Backhouse, M. Baird, N. Balashov, P. Baldi, B. A. Bambah, S. Bashar, K. Bays, R. Bernstein, V. Bhatnagar, D. Bhattarai, B. Bhuyan, Roberto Petti, Et. Al.

Faculty Publications

We present new ν_μ → ν_e, ν_μ → ν_μ, ⊽ _μ →⊽ _e, and ⊽ _μ → ⊽ _μ oscillation measurements by the NOvA experiment, with a 50% increase in neutrino-mode beam exposure over the previously reported results. The additional data, combined with previously published neutrino and antineutrino data, are all analyzed using improved techniques and simulations. A joint fit to the ν_e, ν_μ, ⊽ _e, and ⊽ _μ candidate samples within the 3-flavor neutrino oscillation framework continues to yield a best-fit point in the normal mass …

Scintillation Light Detection In The 6-M Drift-Length Protodune Dual Phase Liquid Argon Tpc, A. Abed, B. Abi, R. Acciarri, M. A. Acero, M. R. Adames, G. Adamov, M. Adamowski, D. Adams, M. Adinolfi, A. Aduszkiewicz, J. Aguilar, Z. Ahmad, J. Ahmed, B. Aimard, B. Ali-Mohammadzadeh, T. Alion, K. Allison, S. Alonso Monsalve, M. Alrashed, C. Alt, Roberto Petti, Et. Al.

Faculty Publications

DUNE is a dual-site experiment for long-baseline neutrino oscillation studies, neutrino astrophysics and nucleon decay searches. ProtoDUNE Dual Phase (DP) is a 6×6×6 m³ liquid argon time-projection-chamber (LArTPC) that recorded cosmic-muon data at the CERN Neutrino Platform in 2019–2020 as a prototype of the DUNE Far Detector. Charged particles propagating through the LArTPC produce ionization and scintillation light. The scintillation light signal in these detectors can provide the trigger for non-beam events. In addition, it adds precise timing capabilities and improves the calorimetry measurements. In ProtoDUNE-DP, scintillation and electroluminescence light produced by cosmic muons in the LArTPC is collected …

Search For Multimessenger Signals In Nova Coincident With Ligo/Virgo Detections, M. A. Acero, P. Adamson, L. Aliaga, T. Alion, V. Alakhberdian, N. Anfimov, A. Antoshkin, L. Asquith, A. Aurisano, A. Back, C. Backhouse, M. Biard, N. Balashov, P. Baldi, B. A. Bambah, S. Bashar, K. Bays, S. Bending, R. Bernstein, V. Bhatnagar, Roberto Petti, Et. Al.

Faculty Publications

Using the NOvA neutrino detectors, a broad search has been performed for any signal coincident with 28 gravitational wave events detected by the LIGO/Virgo Collaboration between September 2015 and July 2019. For all of these events, NOvA is sensitive to possible arrival of neutrinos and cosmic rays of GeV and higher energies. For five (seven) events in the NOvA Far (Near) Detector, timely public alerts from the LIGO/Virgo Collaboration allowed recording of MeV-scale events. No signal candidates were found.

All-Sky Search For Gravitational Wave Emission From Scalar Boson Clouds Around Spinning Black Holes In Ligo O3 Data, Ligo Scientific Collaboration, Virgo Collaboration, Kagra Collaboration, Tiffany Z. Summerscales

Faculty Publications

This paper describes the first all-sky search for long-duration, quasimonochromatic gravitational-wave signals emitted by ultralight scalar boson clouds around spinning black holes using data from the third observing run of Advanced LIGO. We analyze the frequency range from 20 to 610 Hz, over a small frequency derivative range around zero, and use multiple frequency resolutions to be robust towards possible signal frequency wanderings. Outliers from this search are followed up using two different methods, one more suitable for nearly monochromatic signals, and the other more robust towards frequency fluctuations. We do not find any evidence for such signals and set …

Search Of The Early O3 Ligo Data For Continuous Gravitational Waves From The Cassiopeia A And Vela Jr. Supernova Remnants, Ligo Scientific Collaboration, Virgo Collaboration, Tiffany Z. Summerscales

Faculty Publications

We present directed searches for continuous gravitational waves from the neutron stars in the Cassiopeia A (Cas A) and Vela Jr. supernova remnants. We carry out the searches in the LIGO detector data from the first six months of the third Advanced LIGO and Virgo observing run using the weave semicoherent method, which sums matched-filter detection-statistic values over many time segments spanning the observation period. No gravitational wave signal is detected in the search band of 20–976 Hz for assumed source ages greater than 300 years for Cas A and greater than 700 years for Vela Jr. Estimates from simulated …

Search For Gravitational Waves Associated With Gamma-Ray Bursts Detected By Fermi And Swift During The Ligo–Virgo Run O3b, Ligo Scientific Collaboration, Virgo Collaboration, Kagra Collaboration, Tiffany Z. Summerscales

Faculty Publications

We search for gravitational-wave signals associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (2019 November 1 15:00 UTC–2020 March 27 17:00 UTC). We conduct two independent searches: a generic gravitational-wave transients search to analyze 86 GRBs and an analysis to target binary mergers with at least one neutron star as short GRB progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these GRBs. A weighted binomial test of the combined results finds no evidence …

Untangling The Solar Wind And Magnetospheric Drivers Of The Radiation Belt Electrons, Simon Wing, Jay R. Johnson, Drew L. Turner, Aleksandr Y. Ukhorskiy, Alexander J. Boyd

Faculty Publications

Plain Language Summary

Many solar wind parameters correlate with one another, which complicates the causal-effect studies of solar wind driving of the magnetosphere. We use conditional mutual information, which is part of information theory, to untangle and isolate the effect of individual solar wind and magnetospheric drivers of the radiation belt electrons. For example, the solar wind density negatively correlates with electron phase space density (PSD) (average energy ∼1.6 MeV) with the response time lag of 15 hr. This has been attributed to the electron loss process such as magnetopause shadowing. The time lag suggests the time scale for this …

Possible Studies On Generalized Parton Distributions And Gravitational Form Factors In Neutrino Reactions, Shunzo Kumano, Roberto Petti

Faculty Publications

Spacelike and timelike generalized parton distributions (GPDs) have been investigated in charged-lepton scattering and electron-positron collisions via deeply virtual Compton scattering and two-photon processes, respectively. Furthermore, we expect that hadron-accelerator-facility measurements will be performed in future. The GPDs will play a crucial role in clarifying the origins of hadron spins and masses in terms of quarks and gluons. It is also possible to probe internal pressure within hadrons for understanding their stability. Gravitational form factors of hadrons used to be considered as a purely academic subject because gravitational interactions are too weak to be measured in microscopic systems. However, due …

Constraints On Dark Photon Dark Matter Using Data From Ligo’S And Virgo’S Third Observing Run, Ligo Scientific Collaboration, Virgo Collaboration, Kagra Collaboration, Tiffany Z. Summerscales

Faculty Publications

We present a search for dark photon dark matter that could couple to gravitational-wave interferometers using data from Advanced LIGO and Virgo’s third observing run. To perform this analysis, we use two methods, one based on cross-correlation of the strain channels in the two nearly aligned LIGO detectors, and one that looks for excess power in the strain channels of the LIGO and Virgo detectors. The excess power method optimizes the Fourier transform coherence time as a function of frequency, to account for the expected signal width due to Doppler modulations. We do not find any evidence of dark photon …

A Multiparameter Degeneracy In Microlensing Events With Extreme Finite Source Effects, Samson A. Johnson, Matthew T. Penny, B. Scott Gaudi

Faculty Publications

For microlenses with sufficiently low mass, the angular radius of the source star can be much larger than the angular Einstein ring radius of the lens. For such extreme finite source effect (EFSE) events, finite source effects dominate throughout the duration of the event. Here, we demonstrate and explore a continuous degeneracy between multiple parameters of such EFSE events. The first component in the degeneracy arises from the fact that the directly observable peak change of the flux depends on both the ratio of the angular source radius to the angular Einstein ring radius and the fraction of the baseline …

Gaia Gral: Gaia Dr2 Gravitational Lens Systems. Vii. Xmm-Newton Observations Of Lensed Quasars, Thomas Connor, Daniel Stern, Alberto Krone-Martins, S. G. Djorgovski, Matthew J. Graham

Faculty Publications

We present XMM-Newton X-ray observations of nine confirmed lensed quasars at 1 less than or similar to z less than or similar to 3 identified by the Gaia Gravitational Lens program. Eight systems are strongly detected, with 0.3-8.0 keV fluxes F (0.3-8.0) greater than or similar to 5 x10(-14) erg cm(-2) s(-1). Modeling the X-ray spectra with an absorbed power law, we derive power-law photon indices and 2-10 keV luminosities for the eight detected quasars. In addition to presenting sample properties for larger quasar population studies and for use in planning for future caustic-crossing events, we also identify three quasars …

Measurement Of The Nucleon F N2 / F P2 Tructure Function Ratio By The Jefferson Lab Marathon Tritium/Helium-3 Deep Inelastic Scattering Experiment, D. Abrams, H. Albataineh, B. S. Aljawrneh, S. Alsalmi, D. Androic, K. Aniol, W. Armstrong, J. Arrington, H. Atac, T. Averett, C. Ayerbe Gayoso, X. Bai, J. Bane, S. Barcus, A. Beck, V. Bellini, H. Bhatt, D. Bhetuwal, D. Biswas, D. Blyth, Roberto Petti, Et. Al.

Faculty Publications

The ratio of the nucleon F₂ structure functions, F ⁿ₂ / F ^p₂ is determined by the MARATHON experiment from measurements of deep inelastic scattering of electrons from ³H and ³He nuclei. The experiment was performed in the Hall A Facility of Jefferson Lab using two high-resolution spectrometers for electron detection, and a cryogenic target system which included a low-activity tritium cell. The data analysis used a novel technique exploiting the mirror symmetry of the two nuclei, which essentially eliminates many theoretical uncertainties in the extraction of the ratio. The results, which cover the Bjorken …

Search Full Text Options Here 2 Of 4 Kmt-2021-Blg-0912lb: A Microlensing Super Earth Around A K-Type Star, Cheongho Han, Ian A. Bond, Jennifer C. Yee, Weicheng Zang, Michael D. Albrow

Faculty Publications

Aims. The light curve of the microlensing event KMT-2021-BLG-0912 exhibits a very short anomaly relative to a single-lens single-source form. We investigate the light curve for the purpose of identifying the origin of the anomaly.

Methods. We model the light curve under various interpretations. From this, we find four solutions, in which three solutions are found under the assumption that the lens is composed of two masses (2L1S models), and the other solution is found under the assumption that the source is comprised of binary stars (1L2S model). The 1L2S model is ruled out based on the contradiction that the …

Search For Continuous Gravitational Waves From 20 Accreting Millisecond X-Ray Pulsars In O3 Ligo Data, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams

Faculty Publications

Results are presented of searches for continuous gravitational waves from 20 accreting millisecond x-ray pulsars with accurately measured spin frequencies and orbital parameters, using data from the third observing run of the Advanced LIGO and Advanced Virgo detectors. The search algorithm uses a hidden Markov model, where the transition probabilities allow the frequency to wander according to an unbiased random walk, while the J-statistic maximum-likelihood matched filter tracks the binary orbital phase. Three narrow subbands are searched for each target, centered on harmonics of the measured spin frequency. The search yields 16 candidates, consistent with a false alarm probability of …

Search For Continuous Gravitational Waves From 20 Accreting Millisecond X-Ray Pulsars In O3 Ligo Data, Ligo Scientific Collaboration, Virgo Collaboration, Kagra Collaboration, Tiffany Z. Summerscales

Faculty Publications

Results are presented of searches for continuous gravitational waves from 20 accreting millisecond x-ray pulsars with accurately measured spin frequencies and orbital parameters, using data from the third observing run of the Advanced LIGO and Advanced Virgo detectors. The search algorithm uses a hidden Markov model, where the transition probabilities allow the frequency to wander according to an unbiased random walk, while the J-statistic maximum-likelihood matched filter tracks the binary orbital phase. Three narrow subbands are searched for each target, centered on harmonics of the measured spin frequency. The search yields 16 candidates, consistent with a false alarm probability of …

Coupling Between Alfvén Wave And Kelvin–Helmholtz Waves In The Low Latitude Boundary Layer, Eun-Hwa Kim, Jay R. Johnson

Faculty Publications

The Kelvin–Helmholtz (KH) instability of magnetohydrodynamic surface waves at the low latitude boundary layer is examined using both an eigenfrequency analysis and a time-dependent wave simulation. The analysis includes the effects of sheared flow and Alfvén velocity gradient. When the magnetosheath flows are perpendicular to the ambient magnetic field direction, unstable KH waves that propagate obliquely to the sheared flow direction occur at the sheared flow surface when the Alfvén Mach number is higher than an instability threshold. Including a shear transition layer between the magnetosphere and magnetosheath leads to secondary KH waves (driven by the sheared flow) that are …

Towards A Quantum Notion Of Covariance In Spherically Symmetric Loop Quantum Gravity, Rodolfo Gambini, Javier Olmedo, Jorge Pullin

Faculty Publications

The covariance of loop quantum gravity studies of spherically symmetric space-times has recently been questioned. This is a reasonable worry, given that they are formulated in terms of slicing-dependent variables. We show explicitly that the resulting space-times, obtained from Dirac observables of the quantum theory, are covariant in the usual sense of the way-they preserve the quantum line element-for any gauge that is stationary (in the exterior, if there is a horizon). The construction depends crucially on the details of the Abelianized quantization considered, the satisfaction of the quantum constraints, and the recovery of standard general relativity in the classical …

Towards A Quantum Notion Of Covariance In Spherically Symmetric Loop Quantum Gravity, Rodolfo Gambini, Javier Olmedo, Jorge Pullin

Faculty Publications

The covariance of loop quantum gravity studies of spherically symmetric space-times has recently been questioned. This is a reasonable worry, given that they are formulated in terms of slicing-dependent variables. We show explicitly that the resulting space-times, obtained from Dirac observables of the quantum theory, are covariant in the usual sense of the way-they preserve the quantum line element-for any gauge that is stationary (in the exterior, if there is a horizon). The construction depends crucially on the details of the Abelianized quantization considered, the satisfaction of the quantum constraints, and the recovery of standard general relativity in the classical …