Ramesh Narayan

San Diego State University, San Diego, California, United States

Are you Ramesh Narayan?

Claim your profile

Publications (277)1390.03 Total impact

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Using the Very Long Baseline Array, we have measured a trigonometric parallax for the micro quasar GRS 1915+105, which contains a black hole and a K-giant companion. This yields a direct distance estimate of 8.6 (+2.0,-1.6) kpc and a revised estimate for the mass of the black hole of 12.4 (+2.0,-1.8) Msun. GRS 1915+105 is at about the same distance as some HII regions and water masers associated with high-mass star formation in the Sagittarius spiral arm of the Galaxy. The absolute proper motion of GRS 1915+105 is -3.19 +/- 0.03 mas/y and -6.24 +/- 0.05 mas/y toward the east and north, respectively, which corresponds to a modest peculiar speed of 22 +/-24 km/s at the parallax distance, suggesting that the binary did not receive a large velocity kick when the black hole formed. On one observational epoch, GRS 1915+105 displayed superluminal motion along the direction of its approaching jet. Considering previous observations of jet motions, the jet in GRS 1915+105 can be modeled with a jet inclination to the line of sight of 60 +/- 5 deg and a variable flow speed between 0.65c and 0.81c, which possibly indicates deceleration of the jet at distances from the black hole >2000 AU. Finally, using our measurements of distance and estimates of black hole mass and inclination, we provisionally confirm our earlier result that the black hole is spinning very rapidly.
  • [Show abstract] [Hide abstract]
    ABSTRACT: We present a sub-grid model that emulates the magnetic dynamo operating in magnetized accretion disks. We have implemented this model in the general relativisic radiation magnetohydrodynamic (GRRMHD) code \koral, using results from local shearing sheet simulations of the magnetorotational instability to fix the parameters of the dynamo. With the inclusion of this dynamo, we are able to run 2D axisymmetric GRRMHD simulations of accretion disks for arbitrarily long times. The simulated disks exhibit sustained turbulence, with the poloidal and toroidal magnetic field components driven towards a state similar to that seen in 3D studies. Using this dynamo code, we present a set of long-duration global simulations of super-Eddington, optically-thick disks around non-spinning and spinning black holes. Super-Eddington disks around non-rotating black holes exhibit a surprisingly large efficiency, $\eta\approx0.04$, independent of the accretion rate, where we measure efficiency in terms of the total energy output, both radiation and mechanical, flowing out to infinity. Super-Eddington disks around spinning black holes are even more efficient, and appear to extract black hole rotational energy through a process similar to the Blandford-Znajek mechanism. All the simulated models are characterized by highly super-Eddington radiative fluxes collimated along the rotation axis. We also present a set of simulations that were designed to have Eddington or slightly sub-Eddington accretion rates ($\dot{M} \lesssim 2\dot M_{\rm Edd}$). None of these models reached a steady state. Instead, the disks collapsed as a result of runaway cooling, presumably because of a thermal instability.
  • Xinyi Guo, Lorenzo Sironi, Ramesh Narayan
    [Show abstract] [Hide abstract]
    ABSTRACT: Electron acceleration to non-thermal energies in low Mach number (M<5) shocks is revealed by radio and X-ray observations of galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Diffusive shock acceleration, also known as first-order Fermi acceleration, cannot be directly invoked to explain the acceleration of electrons. Rather, an additional mechanism is required to pre-accelerate the electrons from thermal to supra-thermal energies, so they can then participate in the Fermi process. In this work, we use two- and three-dimensional particle-in-cell plasma simulations to study electron acceleration in low Mach number shocks. We focus on the particle energy spectra and the acceleration mechanism in a reference run with M=3. We find that about 15 percent of the electrons can be efficiently accelerated, forming a non-thermal power-law tail in the energy spectrum with a slope of p~2.4. Initially, thermal electrons are energized at the shock front via shock drift acceleration. The accelerated electrons are then reflected back upstream, where their interaction with the incoming flow generates magnetic waves. In turn, the waves scatter the electrons propagating upstream back toward the shock, for further energization via shock drift acceleration. In summary, the self-generated waves allow for repeated cycles of shock drift acceleration, similarly to a sustained Fermi-like process. This mechanism offers a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.
  • Pankaj S. Joshi, Ramesh Narayan
    [Show abstract] [Hide abstract]
    ABSTRACT: One of the most spectacular predictions of the general theory of relativity is the black hole, an object that plays a central role in modern physics [1,2,3] and astrophysics [4,5]. Black holes are, however, plagued by fundamental paradoxes that remain unresolved to this day. First, the black hole event horizon is teleological in nature [6], which means that we need to know the entire future space-time of the universe to determine the current location of the horizon. This is essentially impossible. Second, any information carried by infalling matter is lost once the material falls through the event horizon. Even though the black hole may later evaporate by emitting Hawking radiation [7], the lost information does not reappear, which has the rather serious and disturbing consequence that quantum unitarity is violated [8]. Here we propose that the above paradoxes are restricted to a particular idealized model of collapse first studied in the 1930s [9, 10] in which the event horizon, which defines the boundary of the black hole, forms initially, and the singularity in the interior of the black hole forms at a later time. In contrast, gravitational collapse from more reasonable and/or physically more realistic initial conditions often leads to models in which the event horizon and the singularity form simultaneously. We show that this apparently simple modification mitigates the causality and teleological paradoxes and at the same time lends support to two recently proposed solutions to the information paradox, namely, the "firewall" [11] and "classical chaos" [12].
  • David Abarca, A. Sadowski, R. Narayan
    [Show abstract] [Hide abstract]
    ABSTRACT: Recent observations have shown a 3 Earth Mass cloud of ionized gas en route towards Sgr A*, the black hole at the center of the Galaxy. In the event that G2 or a similar cloud deposits some of its mass in the accretion disk around Sgr A*, we expect this mass to accrete onto the black hole over the course of several years, with observable consequences. We have investigated the process by which excess mass is propagated through a radiatively inefficient accretion flow. We attempt to derive a prescription for the accretion timescale as a function of the initial conditions of the excess mass. We also attempt to predict the fraction of the deposited mass that is accreted and the fraction that is lost to an outflow, as well as the change in the radio luminosity of Sgr A* as a function of time. To derive these estimates, we adopt a toy model in which gas from the cloud is placed in a torus on top of a previously run numerical MHD simulation of a radiatively inefficient accretion disk, and then continue the simulation to monitor the fate of the torus gas. For various scenarios, we track the accretion rate and surface density of the excess matter.
  • Source
    Ramesh Narayan, Jeffrey E. McClintock
    [Show abstract] [Hide abstract]
    ABSTRACT: Astronomers have discovered two populations of black holes: (i) stellar-mass black holes with masses in the range 5 to 30 solar masses, millions of which are present in each galaxy in the universe, and (ii) supermassive black holes with masses in the range $10^6$ to $10^{10}$ solar masses, one each in the nucleus of every galaxy. There is strong circumstantial evidence that all these objects are true black holes with event horizons. The measured masses of supermassive black hole are strongly correlated with properties of their host galaxies, suggesting that these black holes, although extremely small in size, have a strong influence on the formation and evolution of entire galaxies. Spin parameters have recently been measured for a handful of black holes. Based on the data, there is an indication that the kinetic power of at least one class of relativistic jet ejected from accreting black holes may be correlated with black hole spin. If verified, it would suggest that these jets are powered by a generalized Penrose process mediated by magnetic fields.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Black hole (BH) accretion flows and jets are dynamic hot relativistic magnetized plasma flows whose radiative opacity can significantly affect flow structure and behavior. We describe a numerical scheme, tests, and an astrophysically relevant application using the M1 radiation closure within a new three-dimensional (3D) general relativistic (GR) radiation (R) magnetohydrodynamics (MHD) massively parallel code called HARMRAD. Our 3D GRRMHD simulation of super-Eddington accretion (about $20$ times Eddington) onto a rapidly rotating BH (dimensionless spin $j=0.9375$) shows sustained non-axisymmemtric disk turbulence, a persistent electromagnetic jet driven by the Blandford-Znajek effect, and a total radiative output consistently near the Eddington rate. The total accretion efficiency is of order $20\%$, the large-scale electromagnetic jet efficiency is of order $10\%$, and the total radiative efficiency that reaches large distances remains low at only order $1\%$. However, the radiation jet and the electromagnetic jet both emerge from a geometrically beamed polar region, with super-Eddington isotropic equivalent luminosities. Such simulations with HARMRAD can enlighten the role of BH spin vs.\ disks in launching jets, help determine the origin of spectral and temporal states in x-ray binaries, help understand how tidal disruption events (TDEs) work, provide an accurate horizon-scale flow structure for M87 and other active galactic nuclei (AGN), and isolate whether AGN feedback is driven by radiation or by an electromagnetic, thermal, or kinetic wind/jet. For example, the low radiative efficiency and weak BH spin-down rate from our simulation suggest that BH growth over cosmological times to billions of solar masses by redshifts of $z\sim 6-8$ is achievable even with rapidly rotating BHs and ten solar mass BH seeds.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Black hole binaries exhibit a wide range of variability phenomena, from large-scale state changes to broadband noise and quasi-periodic oscillations, but the physical nature of much of this variability is poorly understood. We examine the variability properties of three GRMHD simulations of thin accretion disks around black holes of varying spin, producing light curves and power spectra as would be seen by observers. We find that the simulated power spectra show a broad feature at high frequency, which increases in amplitude with the inclination of the observer. We show that this high-frequency feature is a product of the Doppler effect and that its location is a function of the mass and spin of the black hole. This Doppler feature demonstrates that power spectral properties of the accretion disk can be tied to, and potentially used to determine, physical properties of the black hole.
    12/2013; 785(2).
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A new general relativistic radiation magnetohydrodynamical code KORAL, is described, which employs the M1 scheme to close the radiation moment equations. The code has been successfully verified against a number of tests. Axisymmetric simulations of super-critical magnetized accretion on a non-rotating black hole (a=0.0) and a spinning black hole (a=0.9) are presented. The accretion rates in the two models are \dot M = 100-200 \dot M_Edd. These first general relativistic simulations of super-critical black hole accretion are potentially relevant to tidal disruption events and hyper-accreting supermassive black holes in the early universe. Both simulated models are optically and geometrically thick, and have funnels through which energy escapes in the form of relativistic gas, Poynting flux and radiative flux. The jet is significantly more powerful in the a=0.9 run. The net energy outflow rate in the two runs correspond to efficiencies of 5% (a=0) and 33% (a=0.9), as measured with respect to the mass accretion rate at the black hole. These efficiencies agree well with those measured in previous simulations of non-radiative geometrically thick disks. Furthermore, in the a=0.9 run, the outflow power appears to originate in the spinning black hole, suggesting that the associated physics is again similar in non-radiative and super-critical accretion flows. While the two simulations are efficient in terms of total energy outflow, both runs are radiatively inefficient. Their luminosities are only \sim 1-10 L_Edd, which corresponds to a radiative efficiency \sim 0.1%. Interestingly, most of the radiative luminosity emerges through the funnels, which subtend a very small solid angle. Therefore, measured in terms of a local radiative flux, the emitted radiation is highly super-Eddington.
    11/2013; 439(1).
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In the case involving particles the necessary and sufficient condition for the Penrose process to extract energy from a rotating black hole is absorption of particles with negative energies and angular momenta. No torque at the black hole horizon occurs. In this article we consider the case of arbitrary fields or matter described by an unspecified, general energy-momentum tensor and show that the necessary and sufficient condition for extraction of black-hole's rotational energy is analogous to that in mechanical Penrose process: absorption of negative energy and negative angular momentum. We also show that a necessary condition for the Penrose process to occur is for the Noether current (the conserved energy-momentum density vector) to be spacelike or past-directed (timelike or null) on some part of the horizon. In the particle case our general criterion for the occurrence of a Penrose process reproduces the standard result. In the case of relativistic jet-producing "magnetically arrested disks" we show that the negative energy and angular momentum absorption condition is obeyed when the Blandford-Znajek mechanism is at work and hence the high energy extraction efficiency up to $\sim 300%$ found in recent numerical simulations of such accretion flows results from tapping of the black hole's rotational energy through the Penrose process. We show how black-hole rotational energy extraction works in this case by describing the Penrose process in terms of the Noether current.
    10/2013; 89(2).
  • Source
    Robert F. Penna, Akshay Kulkarni, Ramesh Narayan
    [Show abstract] [Hide abstract]
    ABSTRACT: General relativistic magnetohydrodynamic (GRMHD) simulations are providing influential models for black hole spin measurements, gamma ray bursts, and supermassive black hole feedback. Many of these simulations use the same initial condition: a rotating torus of fluid in hydrostatic equilibrium. A persistent concern is that simulation results sometimes depend on arbitrary features of the initial torus. For example, the Bernoulli parameter (which is related to outflows), appears to be controlled by the Bernoulli parameter of the initial torus. In this paper, we give a new equilibrium torus solution and describe two applications for the future. First, it can be used as a more physical initial condition for GRMHD simulations than earlier torus solutions. Second, it can be used in conjunction with earlier torus solutions to isolate the simulation results that depend on initial conditions. We assume axisymmetry, an ideal gas equation of state, constant entropy, and ignore self-gravity. We fix an angular momentum distribution and solve the relativistic Euler equations in the Kerr metric. The Bernoulli parameter, rotation rate, and geometrical thickness of the torus can be adjusted independently. Our torus tends to be more bound and have a larger radial extent than earlier torus solutions. While this paper was in preparation, several GRMHD simulations appeared based on our equilibrium torus. We believe it will continue to provide a more realistic starting point for future simulations.
    Astronomy and Astrophysics 09/2013; · 5.08 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In Gou et al. (2011), we reported that the black hole primary in the X-ray binary Cygnus X-1 is a near-extreme Kerr black hole with a spin parameter a*>0.95(3{\sigma}). We confirm this result while setting a new and more stringent limit: a*>0.983 at the 3{\sigma}(99.7%) level of confidence. The earlier work, which was based on an analysis of all three useful spectra that were then available, was possibly biased by the presence in these spectra of a relatively strong Compton power-law component: The fraction of the thermal seed photons scattered into the power law was f_s=23-31%, while the upper limit for reliable application of the continuum-fitting method is f_s<25%. We have subsequently obtained six additional spectra of Cygnus X-1 suitable for the measurement of spin. Five of these spectra are of high quality with f_s in the range 10% to 19%, a regime where the continuum-fitting method has been shown to deliver very reliable results. Individually, the six spectra give lower limits on the spin parameter that range from a*>0.95 to a*>0.98, allowing us to conservatively conclude that the spin of the black hole is a*>0.983 (3{\sigma}).
    The Astrophysical Journal 08/2013; 790(1). · 6.73 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Recently it has been observed that the scaling of jet power with black hole spin in galactic X-ray binaries is consistent with the predictions of the Blandford-Znajek (BZ) jet model. These observations motivate us to revisit the BZ model using general relativistic magnetohydrodynamic simulations of magnetized jets from accreting (h/r ~ 0.3), spinning (0 < a_* < 0.98) black holes. We have three main results. First, we quantify the discrepancies between the BZ jet power and our simulations: assuming maximum efficiency and uniform fields on the horizon leads to a ~10% overestimate of jet power, while ignoring the accretion disk leads to a further ~50% overestimate. Simply reducing the standard BZ jet power prediction by 60% gives a good fit to our simulation data. Our second result is to show that the membrane formulation of the BZ model correctly describes the physics underlying simulated jets: torques, dissipation, and electromagnetic fields on the horizon. This provides intuitive yet rigorous pictures for the black hole energy extraction process. Third, we compute the effective resistance of the load region and show that the load and the black hole achieve near perfect impedance matching. Taken together, these results increase our confidence in the BZ model as the correct description of jets observed from astrophysical black holes.
    Monthly Notices of the Royal Astronomical Society 07/2013; 436(4). · 5.52 Impact Factor
  • Source
    A. Sadowski, R. Narayan, R. Penna, Y. Zhu
    [Show abstract] [Hide abstract]
    ABSTRACT: A set of long-duration general relativistic magnetohydrodynamic simulations of radiatively inefficient accretion discs around rotating black holes are presented, and are used to estimate the energy, mass and momentum outflow rates from such systems. Outflows occur via two fairly distinct modes: a relativistic jet and a sub-relativistic wind. The jet power depends strongly on the black hole spin and on the magnetic flux at the horizon. Unless these are very small, the energy output in the jet dominates over that in the wind. In the limit of a rapidly spinning black hole accreting in the magnetically arrested limit, when the magnetic flux at the black hole is maximum, the jet power exceeds the total rate of accretion of rest mass energy. However, because of strong collimation, the jet probably does not have a significant effect on its surrounding. In the case of an accreting supermassive black hole, external feedback via a jet is likely important only on the largest galaxy cluster scales. The power in the wind is more modest and shows a weaker dependence on the black spin and magnetic flux. Nevertheless, because the wind subtends a large solid angle, it is expected to provide efficient feedback on a wide range of scales inside the host galaxy. Using the simulation results as a guide, empirical formulae are obtained for the energy outflow rates in the jet and the wind, and also for the respective momentum outflow rates. The mass outflow rates are more uncertain, especially in the case of the wind.
    Monthly Notices of the Royal Astronomical Society 07/2013; · 5.52 Impact Factor
  • Source
    Yucong Zhu, Ramesh Narayan
    [Show abstract] [Hide abstract]
    ABSTRACT: The standard thin accretion disc model predicts that discs around stellar mass black holes become radiation pressure dominated and thermally unstable once their luminosity exceeds L>0.02 L_Edd. Observationally, discs in the high/soft state of X-ray binaries show little variability in the range 0.01 L_Edd < L < 0.5 L_Edd, implying that these discs in nature are in fact quite stable. In an attempt to reconcile this conflict, we investigate one-zone disc models including turbulent and convective modes of vertical energy transport. We find both mixing mechanisms to have a stabilizing effect, leading to an increase in the L threshold up to which the disc is thermally stable. In the case of stellar mass black hole systems, convection alone leads to only a minor increase in this threshold, up to ~5 per cent of Eddington. However turbulent mixing has a much greater effect -- the threshold rises up to ~20 per cent Eddington under reasonable assumptions. In optimistic models with superefficient turbulent mixing, we even find solutions that are completely thermally stable for all accretion rates. Similar results are obtained for supermassive black holes, except that all critical accretion rates are a factor ~10 lower in Eddington ratio.
    Monthly Notices of the Royal Astronomical Society 06/2013; 434(3). · 5.52 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We show that, in principle, a slowly evolving gravitationally collapsing perfect fluid cloud can asymptotically settle to a static spherically symmetric equilibrium configuration with a naked singularity at the center. We consider one such asymptotic final configuration with a finite outer radius, and construct a toy model in which it is matched to a Schwarzschild exterior geometry. We examine the properties of circular orbits in this model. We then investigate observational signatures of a thermal accretion disk in this spacetime, comparing them with the signatures expected for a disk around a black hole of the same mass. Several notable differences emerge. A disk around the naked singularity is much more luminous than one around an equivalent black hole. Also, the disk around the naked singularity has a spectrum with a high frequency power law segment that carries a major fraction of the total luminosity. Thus, at least some naked singularities can, in principle, be distinguished observationally from black holes of the same mass. We discuss possible implications of these results.
    Classical and Quantum Gravity 04/2013; · 3.56 Impact Factor
  • Source
    A. Sadowski, R. Narayan, L. Sironi, F. Ozel
    [Show abstract] [Hide abstract]
    ABSTRACT: We perform detailed magnetohydrodynamic simulations of the gas cloud G2 interacting with the accretion flow around the Galactic Center black hole Sgr A*. We take as our initial conditions a steady-state, converged solution of the accretion flow obtained earlier using the general-relativistic magnetohydrodynamic code HARM. Using the observed parameters for the cloud's orbit, we compute the interaction of the cloud with the ambient gas and identify the shock structure that forms ahead of the cloud. We show that for many configurations, the cloud front crosses orbit pericenter 7 to 9 months earlier than the center-of-mass.
    Monthly Notices of the Royal Astronomical Society 03/2013; 433(3). · 5.52 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The spins of ten stellar black holes have been measured using the continuum-fitting method. These black holes are located in two distinct classes of X-ray binary systems, one that is persistently X-ray bright and another that is transient. Both the persistent and transient black holes remain for long periods in a state where their spectra are dominated by a thermal accretion disk component. The spin of a black hole of known mass and distance can be measured by fitting this thermal continuum spectrum to the thin-disk model of Novikov and Thorne; the key fit parameter is the radius of the inner edge of the black hole's accretion disk. Strong observational and theoretical evidence links the inner-disk radius to the radius of the innermost stable circular orbit, which is trivially related to the dimensionless spin parameter a_* of the black hole (|a_*| < 1). The ten spins that have so far been measured by this continuum-fitting method range widely from a_* \approx 0 to a_* > 0.95. The robustness of the method is demonstrated by the dozens or hundreds of independent and consistent measurements of spin that have been obtained for several black holes, and through careful consideration of many sources of systematic error. Among the results discussed is a dichotomy between the transient and persistent black holes; the latter have higher spins and larger masses. Also discussed is recently discovered evidence in the transient sources for a correlation between the power of ballistic jets and black hole spin.
    Space Science Reviews 03/2013; · 5.52 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: It has for long been an article of faith among astrophysicists that black hole spin energy is responsible for powering the relativistic jets seen in accreting black holes. Two recent advances have strengthened the case. First, numerical general relativistic magnetohydrodynamic simulations of accreting spinning black holes show that relativistic jets form spontaneously. In at least some cases, there is unambiguous evidence that much of the jet energy comes from the black hole, not the disk. Second, spin parameters of a number of accreting stellar-mass black holes have been measured. For ballistic jets from these systems, it is found that the radio luminosity of the jet correlates with the spin of the black hole. This suggests a causal relationship between black hole spin and jet power, presumably due to a generalized Penrose process.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We calculate radio light curves produced by the bow shock that is likely to form in front of the G2 cloud when it penetrates the accretion disk of Sgr A*. The shock acceleration of the radio-emitting electrons is captured self-consistently by means of first-principles particle-in-cell simulations. We show that the radio luminosity is expected to reach maximum in early 2013, roughly a month after the bow shock crosses the orbit pericenter. We estimate the peak radio flux at 1.4GHz to be 1.4 - 22Jy depending on the assumed orbit orientation and parameters. We show that the most promising frequencies for radio observations are in the 0.1<\nu<1GHz range, for which the bow shock emission will be much stronger than the intrinsic radio flux for all the models considered.
    Monthly Notices of the Royal Astronomical Society 01/2013; 432(1). · 5.52 Impact Factor

Publication Stats

11k Citations
1,390.03 Total Impact Points


  • 2013
    • San Diego State University
      • Department of Astronomy
      San Diego, California, United States
  • 1992–2013
    • Harvard-Smithsonian Center for Astrophysics
      • • Institute for Theory and Computation
      • • Smithsonian Astrophysical Observatory
      Cambridge, Massachusetts, United States
  • 2010
    • Stanford University
      • Kavli Institute for Particle Physics and Cosmology (KIPAC)
      Stanford, CA, United States
  • 1996–2010
    • Harvard University
      • Department of Astronomy
      Cambridge, Massachusetts, United States
  • 2002
    • Princeton University
      • Department of Astrophysical Sciences
      Princeton, New Jersey, United States
  • 2001
    • University of Rochester
      • Laboratory for Laser Energetics (LLE)
      Rochester, New York, United States
  • 2000
    • University of Toronto
      • Canadian Institute for Theoretical Astrophysics
      Toronto, Ontario, Canada
    • Chalmers University of Technology
      Goeteborg, Västra Götaland, Sweden
  • 1999
    • Kurchatov Institute
      Moskva, Moscow, Russia
  • 1991
    • Tel Aviv University
      • Department of Physics and Astronomy
      Tell Afif, Tel Aviv, Israel
  • 1986–1989
    • California Institute of Technology
      • Jet Propulsion Laboratory
      Pasadena, California, United States
  • 1981–1985
    • Raman Research Institute
      Bengalūru, Karnātaka, India