On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes

2016

We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfven waves, and the tearing mode instability using the MHD code Aenus. By comparing the simu- lation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of tearing modes we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast-magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) syst…

A powerful hydrodynamic booster for relativistic jets

2006

Velocities close to the speed of light are a robust observational property of the jets observed in microquasars and AGNs, and are expected to be behind much of the phenomenology of GRBs. Yet, the mechanism boosting relativistic jets to such large Lorentz factors is still essentially unknown. Building on recent general-relativistic, multidimensional simulations of progenitors of short GRBs, we discuss a new effect in relativistic hydrodynamics which can act as an efficient booster in jets. This effect is purely hydrodynamical and occurs when large velocities tangential to a discontinuity are present in the flow, yielding Lorentz factors $\Gamma \sim 10^2-10^3$ or larger in flows with moderat…

On the dynamic efficiency of internal shocks in magnetized relativistic outflows

2009

We study the dynamic efficiency of conversion of kinetic-to-thermal/magnetic energy of internal shocks in relativistic magnetized outflows. We model internal shocks as being caused by collisions of shells of plasma with the same energy flux and a non-zero relative velocity. The contact surface, where the interaction between the shells takes place, can break up either into two oppositely moving shocks (in the frame where the contact surface is at rest), or into a reverse shock and a forward rarefaction. We find that for moderately magnetized shocks (magnetization $\sigma\simeq 0.1$), the dynamic efficiency in a single two-shell interaction can be as large as 40%. Thus, the dynamic efficiency…

An RMHD study of transition between prompt and afterglow GRB phases

2008

We study the afterglow phases of a GRB through relativistic magnetohydrodynamic simulations. The evolution of a relativistic shell propagating into a homogeneous external medium is followed. We focus on the effect of the magnetization of the ejecta on the initial phases of the ejecta-external medium interaction. In particular we are studying the condition for the existence of a reverse shock into the ejecta, the timescale for the transfer of the energy from the shell to the shocked medium and the resulting multiwavelength light curves. To this end, we have developed a novel scheme to include non-thermal processeses which is coupled to the relativistic magnetohydrodynamic code MRGENESIS in o…

Speeding up a few orders of magnitude the Jacobi method: high order Chebyshev-Jacobi over GPUs

2017

In this technical note we show how to reach a remarkable speed up when solving elliptic partial differential equations with finite differences thanks to the joint use of the Chebyshev-Jacobi method with high order discretizations and its parallel implementation over GPUs.

Dynamical efficiency of collisionless magnetized shocks in relativistic jets

2010

The so-called internal shock model aims to explain the light-curves and spectra produced by non-thermal processes originated in the flow of blazars and gamma-ray bursts. A long standing question is whether the tenuous collisionless shocks, driven inside a relativistic flow, are efficient enough to explain the amount of energy observed as compared with the expected kinetic power of the outflow. In this work we study the dynamic efficiency of conversion of kinetic-to- thermal/magnetic energy of internal shocks in relativistic magnetized outflows. We find that the collision between shells with a non-zero relative velocity can yield either two oppositely moving shocks (in the frame where the co…

Deceleration of arbitrarily magnetized GRB ejecta: the complete evolution

2008

(Abridged) We aim to quantitatively understand the dynamical effect and observational signatures of magnetization of the GRB ejecta on the onset of the afterglow. We perform ultrahigh-resolution one-dimensional relativistic MHD simulations of the interaction of a radially expanding, magnetized ejecta with the interstellar medium. The need of ultrahigh numerical resolution derives from the extreme jump conditions in the region of interaction between the ejecta and the circumburst medium. We study the evolution of an ultrarelativistic shell all the way to a the self-similar asymptotic phase. Our simulations show that the complete evolution can be characterized in terms of two parameters, name…

Angular Energy Distribution of Collapsar-Jets

2008

Collapsars are fast-spinning, massive stars, whose core collapse liberates an energy, that can be channeled in the form of ultrarelativistic jets. These jets transport the energy from the collapsed core to large distances, where it is dissipated in the form of long-duration gamma-ray bursts. In this paper we study the dynamics of ultrarelativistic jets produced in collapsars. Also we extrapolate our results to infer the angular energy distribution of the produced outflows in the afterglow phase. Our main focus is to look for global energetical properties which can be imprinted by the different structure of different progenitor stars. Thus, we employ a number of pre-supernova, stellar models…

Relativistic Magnetohydrodynamics: Renormalized eigenvectors and full wave decomposition Riemann solver

2010

We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as…

Termination of the MRI via parasitic instabilities in core-collapse supernovae: influence of numerical methods

2016

We study the influence of numerical methods and grid resolution on the termination of the magnetorotational instability (MRI) by means of parasitic instabilities in three-dimensional shearing-disc simulations reproducing typical conditions found in core-collapse supernovae. Whether or not the MRI is able to amplify weak magnetic fields in this context strongly depends, among other factors, on the amplitude at which its growth terminates. The qualitative results of our study do not depend on the numerical scheme. In all our models, MRI termination is caused by Kelvin-Helmholtz instabilities, consistent with theoretical predictions. Quantitatively, however, there are differences, but numerica…

The unusual γ-ray burst GRB 101225A from a helium star/neutron star merger at redshift 0.33

2011

Long Gamma-Ray Bursts (GRBs) are the most dramatic examples of massive stellar deaths, usually associated with supernovae. They release ultra-relativistic jets producing non-thermal emission through synchrotron radiation as they interact with the surrounding medium. Here we report observations of the peculiar GRB 101225A (the "Christmas burst"). Its gamma-ray emission was exceptionally long and followed by a bright X-ray transient with a hot thermal component and an unusual optical couuterpart. During the first 10 days, the optical emission evolved as an expanding, cooling blackbody after which an additional component, consistent with a faint supernova, emerged. We determine its distance to…

Computational general relativistic force-free electrodynamics

2020

General relativistic force-free electrodynamics is one possible plasma-limit employed to analyze energetic outflows in which strong magnetic fields are dominant over all inertial phenomena. The amazing images of black hole shadows from the galactic center and the M87 galaxy provide a first direct glimpse into the physics of accretion flows in the most extreme environments of the universe. The efficient extraction of energy in the form of collimated outflows or jets from a rotating BH is directly linked to the topology of the surrounding magnetic field. We aim at providing a tool to numerically model the dynamics of such fields in magnetospheres around compact objects, such as black holes an…

Characteristic structure of the resistive relativistic magnetohydrodynamic equations

2012

We present the analysis of the characteristic structure of the resistive (non-ideal) relativistic magnetohydrodynamics system of equations. This is a necessary step to develop high-resolution shock-capturing schemes that use the full characteristic information (Godunov-type methods), and it is convenient to establish proper boundary conditions.

Numerical study of broadband spectra caused by internal shocks in magnetized relativistic jets of blazars

2013

The internal-shocks scenario in relativistic jets has been used to explain the variability of blazars' outflow emission. Recent simulations have shown that the magnetic field alters the dynamics of these shocks producing a whole zoo of spectral energy density patterns. However, the role played by magnetization in such high-energy emission is still not entirely understood. With the aid of \emph{Fermi}'s second LAT AGN catalog, a comparison with observations in the $\gamma$-ray band was performed, in order to identify the effects of the magnetic field.

Computational general relativistic force-free electrodynamics

2021

Scientific codes are an indispensable link between theory and experiment; in (astro-)plasma physics, such numerical tools are one window into the universe's most extreme flows of energy. The discretization of Maxwell's equations - needed to make highly magnetized (astro)physical plasma amenable to its numerical modeling - introduces numerical diffusion. It acts as a source of dissipation independent of the system's physical constituents. Understanding the numerical diffusion of scientific codes is the key to classify their reliability. It gives specific limits in which the results of numerical experiments are physical. We aim at quantifying and characterizing the numerical diffusion propert…

Numerical simulations of the jetted tidal disruption event Swift J1644+57

2016

In this work we focus on the technical details of the numerical simulations of the non- thermal transient Swift J1644+57, whose emission is probably produced by a two-component jet powered by a tidal disruption event. In this context we provide details of the coupling between the relativistic hydrodynamic simulations and the radiative transfer code. First, we consider the technical demands of one-dimensional simulations of a fast relativistic jet, and show to what extent (for the same physical parameters of the model) do the computed light curves depend on the numerical parameters of the different codes employed. In the second part we explain the difficulties of computing light curves from …

Spectral evolution of superluminal components in parsec-scale jets

2008

27 pages, 18 figures, 1 table, 1 appendix.-- Pre-print archive.

Neutron star collapse and gravitational waves with a non-convex equation of state

2018

The thermodynamical properties of the equation of state (EoS) of high-density matter (above nuclear saturation density) and the possible existence of exotic states such as phase transitions from nuclear/hadronic matter into quark-gluon plasma, or the appearance of hyperons, may critically influence the stability and dynamics of compact relativistic stars. From a theoretical point of view, establishing the existence of those states requires the analysis of the `convexity' of the EoS. We show indications of the existence of regions in the dense-matter EoS where the thermodynamics may be non-convex as a result of a non-monotonic dependence of the sound speed with the rest-mass density. When th…

Effect of contact lenses on ocular biometric measurements based on swept-source optical coherence tomography

2019

ABSTRACT Purpose: To determine the reliability of swept- source optical coherence tomography in cases in which soft contact lenses cannot be removed when acquiring biometric measurements. Methods: Eight subjects were included and only one eye per participant was analyzed. Each eye was measured six times by swept-source optical coherence tomography with the IOLMaster 700 instrument (Carl Zeiss Meditec, Jena, Germany). Axial length, central corneal thickness, anterior chamber depth, lens thickness, and keratometric measurements were evaluated for the naked eye and while wearing soft contact lenses of three different powers (-1.5, -3.0, and +2.0 D). Results: There were statistically significan…

Numerical simulations of dynamics and emission from relativistic astrophysical jets

2013

Broadband emission from relativistic outflows (jets) of active galactic nuclei (AGN) and gamma-ray bursts (GRBs) contains valuable information about the nature of the jet itself, and about the central engine which launches it. Using special relativistic hydrodynamics and magnetohydronamics simulations we study the dynamics of the jet and its interaction with the surrounding medium. The observational signature of the simulated jets is computed using a radiative transfer code developed specifically for the purpose of computing multi-wavelength, time-dependent, non-thermal emission from astrophysical plasmas. We present results of a series of long-term projects devoted to understanding the dyn…

Afterglow light curves from magnetized GRB flows

2010

AbstractUsing the RMHD code MRGENESIS and the radiative transfer code SPEV we compute multiwavelength afterglow light curves of magnetized ejecta of gamma-ray bursts interacting with a uniform circumburst medium. We are interested in the emission from the reverse shock when ejecta magnetization varies from σ0 = 0 to σ0 = 1. For typical parameters of the ejecta, the emission from the reverse shock peaks for magnetization σ0 ~ 0.01 − 0.1, and is suppressed for higher σ0. We fit the early afterglow light curves of GRB 990123 and 090102 and discuss the possible magnetization of the outflows of these bursts. Finally we discuss the amount energy left in the magnetic field which is available for d…

A dust-enshrouded tidal disruption event with a resolved radio jet in a galaxy merger

2018

Tidal disruption events (TDEs) are transient flares produced when a star is ripped apart by the gravitational field of a supermassive black hole (SMBH). We have observed a transient source in the western nucleus of the merging galaxy pair Arp 299 that radiated >1.5 × 10 erg at infrared and radio wavelengths but was not luminous at optical or x-ray wavelengths. We interpret this as a TDE with much of its emission reradiated at infrared wavelengths by dust. Efficient reprocessing by dense gas and dust may explain the difference between theoretical predictions and observed luminosities of TDEs. The radio observations resolve an expanding and decelerating jet, probing the jet formation and evol…

On the equivalence between the Scheduled Relaxation Jacobi method and Richardson's non-stationary method

2017

The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations ($Au=b$) associated with elliptic problems. It inherits its robustness and accelerates its convergence rate computing a set of $P$ relaxation factors that result from a minimization problem. In a typical SRJ scheme, the former set of factors is employed in cycles of $M$ consecutive iterations until a prescribed tolerance is reached. We present the analytic form for the optimal set of relaxation factors for the case in which all of them are different, and find that the resulting algorithm is equivalent to a non-stationary generalized Richardson's method. …

THE MISSING LINK: MERGING NEUTRON STARS NATURALLY PRODUCE JET-LIKE STRUCTURES AND CAN POWER SHORT GAMMA-RAY BURSTS

2011

Short Gamma-Ray Bursts (SGRBs) are among the most luminous explosions in the universe, releasing in less than one second the energy emitted by our Galaxy over one year. Despite decades of observations, the nature of their "central-engine" remains unknown. Considering a binary of magnetized neutron stars and solving Einstein equations, we show that their merger results in a rapidly spinning black hole surrounded by a hot and highly magnetized torus. Lasting over 35 ms and much longer than previous simulations, our study reveals that magnetohydrodynamical instabilities amplify an initially turbulent magnetic field of ~ 10^{12} G to produce an ordered poloidal field of ~ 10^{15} G along the bl…

Instability of twisted magnetar magnetospheres

2019

We present three-dimensional force-free electrodynamics simulations of magnetar magnetospheres that demonstrate the instability of certain degenerate, high energy equilibrium solutions of the Grad-Shafranov equation. This result indicates the existence of an unstable branch of twisted magnetospheric solutions and allows to formulate an instability criterion. The rearrangement of magnetic field lines as a consequence of this instability triggers the dissipation of up to 30% of the magnetospheric energy on a thin layer above the magnetar surface. During this process, we predict an increase of the mechanical stresses onto the stellar crust, which can potentially result in a global mechanical f…

Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers

2010

Context. Global MHD simulations show Kelvin-Helmholtz (KH) instabilities at the contact surface of two merging neutron stars. That region has been identified as the site of efficient amplification of magnetic fields. However, these global simulations, due to numerical limitations, were unable to determine the saturation level of the field strength, and thus the possible back-reaction of the magnetic field onto the flow. Aims. We investigate the amplification of initially weak fields in KH unstable shear flows, and the back-reaction of the field onto the flow. Methods. We use a high-resolution ideal MHD code to perform 2D and 3D local simulations of shear flows. Results. In 2D, the magnetic …

Magnetorotational Instability in Core-Collapse Supernovae

2017

We discuss the relevance of the magnetorotational instability (MRI) in core-collapse supernovae (CCSNe). Our recent numerical studies show that in CCSNe, the MRI is terminated by parasitic instabilities of the Kelvin-Helmholtz type. To determine whether the MRI can amplify initially weak magnetic fields to dynamically relevant strengths in CCSNe, we performed three-dimensional simulations of a region close to the surface of a differentially rotating proto-neutron star in non-ideal magnetohydrodynamics with two different numerical codes. We find that under the conditions prevailing in proto-neutron stars, the MRI can amplify the magnetic field by (only) one order of magnitude. This severely …

Linear theory of the Rayleigh–Taylor instability at a discontinuous surface of a relativistic flow

2017

We address the linear stability of a discontinuous surface of a relativistic flow in the context of a jet that oscillates radially as it propagates. The restoring force of the oscillation is expected to drive a Rayleigh-Taylor instability (RTI) at the interface between the jet and its cocoon. We perform a linear analysis and numerical simulations of the growth of the RTI in the transverse plane to the jet flow with a uniform acceleration. In this system, an inertia force due to the uniform acceleration acts as the restoring force for the oscillation. We find that not only the difference in the inertia between the two fluids separated by the interface but also the pressure at the interface h…

Off-Axis Properties of Short Gamma-Ray Bursts

2005

Based on recent models of relativistic jet formation by thermal energy deposition around black hole-torus systems, the relation between the on- and off-axis appearance of short, hard gamma-ray bursts (GRBs) is discussed in terms of energetics, duration, average Lorentz factor, and probability of observation, assuming that the central engines are remnants of binary neutron star or neutron star-black hole mergers. As a consequence of the interaction with the torus matter at the jet basis and the subsequent expansion of the jets into an extremely low-density environment, the collimated ultrarelativistic outflows possess flat core profiles with only little variation of radially-averaged propert…

Numerical simulations of the internal shock model in magnetized relativistic jets of blazars

2015

The internal shocks scenario in relativistic jets is used to explain the variability of the blazar emission. Recent studies have shown that the magnetic field significantly alters the shell collision dynamics, producing a variety of spectral energy distributions and light-curves patterns. However, the role played by magnetization in such emission processes is still not entirely understood. In this work we numerically solve the magnetohydodynamic evolution of the magnetized shells collision, and determine the influence of the magnetization on the observed radiation. Our procedure consists in systematically varying the shell Lorentz factor, relative velocity, and viewing angle. The calculatio…

3D Relativistic Hydrodynamics

2007

We review the evolution of the numerical techniques applied in relativistic hydrodynamics since the sixties until today. We focus our attention on the state-of- the-art high-resolution shock-capturing methods and the astrophysical applications involving three-dimensional simulations.

EFFICIENCY OF INTERNAL SHOCKS IN MAGNETIZED RELATIVISTIC JETS

2011

We study the dynamic and radiative efficiency of conversion of kinetic-to-thermal/magnetic energy by internal shocks in relativistic magnetized outflows. A parameter study of a large number of collisions of cylindrical shells is performed. We explore how, while keeping the total flow luminosity constant, the variable fluid magnetization influences the efficiency and find that the interaction of shells in a mildly magnetized jet yields higher dynamic, but lower radiative efficiency than in a non-magnetized flow. A multi-wavelength radiative signature of different shell magnetization is computed assuming that relativistic particles are accelerated at internal shocks.

Jet stability and the generation of superluminal and stationary components

2001

We present a numerical simulation of the response of an expanding relativistic jet to the ejection of a superluminal component. The simulation has been performed with a relativistic time-dependent hydrodynamical code from which simulated radio maps are computed by integrating the transfer equations for synchrotron radiation. The interaction of the superluminal component with the underlying jet results in the formation of multiple conical shocks behind the main perturbation. These trailing components can be easily distinguished because they appear to be released from the primary superluminal component, instead of being ejected from the core. Their oblique nature should also result in distinc…

Search for Subsolar-Mass Ultracompact Binaries in Advanced LIGO's First Observing Run

2018

We present the first Advanced LIGO and Advanced Virgo search for ultracompact binary systems with component masses between 0.2 $M_\odot$ - 1.0 $M_\odot$ using data taken between September 12, 2015 and January 19, 2016. We find no viable gravitational wave candidates. Our null result constrains the coalescence rate of monochromatic (delta function) distributions of non-spinning (0.2 $M_\odot$, 0.2 $M_\odot$) ultracompact binaries to be less than $1.0 \times 10^6 \text{Gpc}^{-3} \text{yr}^{-1}$ and the coalescence rate of a similar distribution of (1.0 $M_\odot$, 1.0 $M_\odot$) ultracompact binaries to be less than $1.9 \times 10^4 \text{Gpc}^{-3} \text{yr}^{-1}$ (at 90 percent confidence). N…

SIMULATIONS OF DYNAMICS AND EMISSION FROM MAGNETIZED GRB AFTERGLOWS

2010

The role of magnetic fields in the GRB flow is still controversial. The afterglow emission, particularly the early phases, may provide a probe into the magnetization of the outflow. Using ultrahigh resolution relativistic MHD simulations, the interaction between radially expanding magnetized ejecta with the interstellar medium is studied. We explore the effect of the magnetic field strength of the ejecta on the afterglow structure, particularly regarding the presence and strength of a reverse shock. We compute synthetic afterglow light curves to quantify the effect of the magnetization of the flow on observed radiation.

Radiative signature of magnetic fields in internal shocks

2012

Common models of blazars and gamma-ray bursts assume that the plasma underlying the ob- served phenomenology is magnetized to some extent. Within this context, radiative signatures of dissipation of kinetic and conversion of magnetic energy in internal shocks of relativistic magnetized outflows are studied. We model internal shocks as being caused by collisions of homogeneous plasma shells. We compute the flow state after the shell interaction by solving Riemann problems at the contact surface between the colliding shells, and then compute the emission from the resulting shocks. Under the assumption of a constant flow luminosity we find that there is a clear difference between the models wh…

General Relativistic Simulations of the Collapsar Scenario

2013

We are exploring the viability of the collapsar model for long-soft gamma-ray bursts. For this we perform state-of-the-art general relativistic hydrodynamic simulations in a dynamically evolving space-time with the CoCoNuT code. We start from massive low metallicity stellar models evolved up to core gravitational instability, and then follow the subsequent evolution until the system collapses forming a compact remnant. A preliminary study of the collapse outcome is performed by varying the typical parameters of the scenario, such as the initial stellar mass, metallicity, and rotational profile of the stellar progenitor. 1D models (without rotation) have been used to test our newly developed…

Observational Effects of Anomalous Boundary Layers in Relativistic Jets

2008

Recent theoretical work has pointed out that the transition layer between a jet an the medium surrounding it may be more complex than previously thought. Under physically realizable conditions, the transverse profile of the Lorentz factor in the boundary layer can be non-monotonic, displaying the absolute maximum where the flow is faster than at the jet spine, followed by an steep fall off. Likewise, the rest-mass density, reaches an absolute minimum (coincident with the maximum in Lorentz factor) and then grows until it reaches the external medium value. Such a behavior is in contrast to the standard monotonic decline of the Lorentz factor (from a maximum value at the jet central spine) an…

Simulations of Jets from Active Galactic Nuclei and Gamma‐Ray Bursts

2012

GRAVITATIONAL WAVE SIGNATURES IN BLACK HOLE FORMING CORE COLLAPSE

2013

We present numerical simulations in general relativity of collapsing stellar cores. Our initial model consists of a low metallicity rapidly-rotating progenitor which is evolved in axisymmetry with the latest version of our general relativistic code CoCoNuT, which allows for black hole formation and includes the effects of a microphysical equation of state (LS220) and a neutrino leakage scheme to account for radiative losses. The motivation of our study is to analyze in detail the emission of gravitational waves in the collapsar scenario of long gamma-ray bursts. Our simulations show that the phase during which the proto-neutron star (PNS) survives before ultimately collapsing to a black hol…

On the convexity of relativistic ideal magnetohydrodynamics

2015

We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity con…

GW170817: Measurements of Neutron Star Radii and Equation of State

2018

On 17 August 2017, the LIGO and Virgo observatories made the first direct detection of gravitational waves from the coalescence of a neutron star binary system. The detection of this gravitational-wave signal, GW170817, offers a novel opportunity to directly probe the properties of matter at the extreme conditions found in the interior of these stars. The initial, minimal-assumption analysis of the LIGO and Virgo data placed constraints on the tidal effects of the coalescing bodies, which were then translated to constraints on neutron star radii. Here, we expand upon previous analyses by working under the hypothesis that both bodies were neutron stars that are described by the same equation…

Effect of contact lenses on ocular biometric measurements based on swept-source optical coherence tomography

2019

ABSTRACT Purpose: To determine the reliability of swept- source optical coherence tomography in cases in which soft contact lenses cannot be removed when acquiring biometric measurements. Methods: Eight subjects were included and only one eye per participant was analyzed. Each eye was measured six times by swept-source optical coherence tomography with the IOLMaster 700 instrument (Carl Zeiss Meditec, Jena, Germany). Axial length, central corneal thickness, anterior chamber depth, lens thickness, and keratometric measurements were evaluated for the naked eye and while wearing soft contact lenses of three different powers (-1.5, -3.0, and +2.0 D). Results: There were statistically significan…