Richard Klein - Academia.edu (original) (raw)
Papers by Richard Klein
arXiv (Cornell University), Sep 7, 1999
We report the discovery of kHz fluctuations, including quasi-periodic oscillations (QPO) at ∼ 330... more We report the discovery of kHz fluctuations, including quasi-periodic oscillations (QPO) at ∼ 330 Hz (260−407 Hz) and ∼ 760 Hz (671−849 Hz) and a broadband kHz continuum in the power density spectrum of the high mass X-ray binary pulsar Centaurus X-3 (Jernigan, Klein and Arons 1999). These observations of Cen X-3 were carried out with the Rossi X-ray Timing Explorer (RXTE). The fluctuation spectrum is flat from mHz to a few Hz, then steepens to f −2 behavior between a few Hz and ∼ 100 Hz. Above a hundred Hz, corrections for the observations of Cen X-3, we have also demonstrated that the black hole Cyg X-1 shows clear evidence of variability up to a frequency of ∼ 280 Hz. Also observations of GX 17+2 were used to validate the procedure for deadtime corrections. This analysis of GX 17+2 clearly indicates the presence of a kHz QPO and the absence of any significant simultaneous kHz continuum.
Ambipolar diffusion (AD) is believed to be a crucial process for redistributing magnetic flux in ... more Ambipolar diffusion (AD) is believed to be a crucial process for redistributing magnetic flux in the dense molecular gas that occurs in regions of star formation. We carry out numerical simulations of this process in regions of low ionization using the heavy ion approximation. The simulations are for regions of strong field (plasma β = 0.1) and mildly supersonic turbulence (M = 3, corresponding to an Alfvén mach number of 0.67). The velocity power spectrum of the neutral gas changes from an Iroshnikov-Kraichnan spectrum in the case of ideal MHD to a Burgers spectrum in the case of a shock-dominated hydrodynamic system. The magnetic power spectrum shows a similar behavior. We use a 1D radiative transfer code to post-process our simulation results; the simulated emission from the CS J = 2−1 and H13CO+ J = 1−0 lines shows that the effects of AD are observable in principle. Linewidths of ions are observed to be less than those of neutrals, and we confirm previous suggestions that this ...
We compute the molecular line emission of massive protostellar disks by solving the equation of r... more We compute the molecular line emission of massive protostellar disks by solving the equation of radiative transfer through the cores and disks produced by the recent radiation-hydrodynamic simulations of Krumholz, Klein, & McKee. We find that in several representative lines the disks show brightness temperatures of hundreds of Kelvin over velocity channels ∼ 10 km s −1 wide, extending over regions hundreds of AU in size. We process the computed intensities to model the performance of next-generation radio and submillimeter telescopes. Our calculations show that observations using facilities such as the EVLA and ALMA should be able to detect massive protostellar disks and measure their rotation curves, at least in the nearest massive star-forming regions. They should also detect significant sub-structure and non-axisymmetry in the disks, and in some cases may be able to detect star-disk velocity offsets of a few km s −1, both of which are the result of strong gravitational instabilit...
Performing a stable, long duration simulation of driven MHD turbulence with a high thermal Mach n... more Performing a stable, long duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing positivity of the density and pressure. We have implemented a robust combination of reconstruction schemes, Riemann solvers, limiters, and Constrained Transport EMF averaging schemes that can meet this challenge, and using this strategy, we have developed a new Adaptive Mesh Refinement (AMR) MHD module of the ORION2 code. We investigate the effects of AMR on several statistical properties of a turbulent ideal MHD system with a thermal Mach number of 10 and a plasma β 0 of 0.1 as initial conditions; our code is shown to be stable for simulations with higher Mach numbers (M rms = 17.3) and smaller plasma beta (β 0 = 0.0067) as well. Our results show that the quality of the turbulence simulation is generally related to the volume-averaged refinement. Our AMR simulations show that the turbulent dissipation coefficient for supersonic MHD turbulence is about 0.5, in agreement with unigrid simulations.
Journal of Open Source Software, 2021
The formation of stars and stellar clusters remains a grand challenge problem in astrophysics tha... more The formation of stars and stellar clusters remains a grand challenge problem in astrophysics that has important implications for the evolution of the interstellar medium as well as shaping the evolution of galaxies. The computational challenges are formidable and involve a coupling of highly non-linear physical processes such as hydrodynamics, self-gravity, magnetic fields, radiation transfer, supersonic turbulence, ionization, protostellar outflows, stellar winds and chemistry that have both disparate timescales as well as operate over many decades of physical length scale. These processes can regulate the feedback from nascent protostars onto the surrounding turbulent gas clouds that are the embryos of new star formation, and as a result, the feedback itself can influence the gaseous reservoir feeding newly formed protostars which in turn influence the star formation process.
We analyze the equations of radiation hydrodynamics under the approximations of flux-limited diff... more We analyze the equations of radiation hydrodynamics under the approximations of flux-limited diffusion and a thermal radiation field, and derive the minimal set of evolution equations that includes all terms that are of leading order in any regime of non-relativistic radiation hydrodynamics. Our equations are accurate to first order in v/c in the static diffusion regime. We give the equations in a conservation law form well-suited to implementation in numerical algorithms. Our work improves on previous zeroth order derivations of the equations by retaining differences between laboratory frame and comoving frame quantities, which are neglected at zeroth order. We compare our equations to the zeroth order equations, and show that in certain regimes the zeroth order equations omit terms that are formally of leading order. We discuss the circumstances under which this will produce significant errors. For systems in the static diffusion regime, our analysis of the equations suggests an a...
Proceedings of the International Astronomical Union, 2015
Numerical simulations of star formation faces challenges including the huge spatial dynamic range... more Numerical simulations of star formation faces challenges including the huge spatial dynamic range and the presence of multiply coupled highly non-linear physics, such as magnetic field, supersonic turbulence, gravitation, radiation and protostellar outflow feedback. We present in this symposium our latest high resolution adaptive mesh refinement numerical simulations of the formation of filamentary dark molecular clouds from 4.55 pc size scale down to the formation of a protostellar cluster with maximum resolution at 28 AU. The physical properties of the long braided filamentary dark cloud formed in the simulation, the magnetic field properties of the cloud clumps, and the protostellar mass function in the simulations match well with the latest observations.
Monthly Notices of the Royal Astronomical Society, 2019
We perform ideal magnetohydrodynamics high-resolution adaptive mesh refinement simulations with d... more We perform ideal magnetohydrodynamics high-resolution adaptive mesh refinement simulations with driven turbulence and self-gravity and find that long filamentary molecular clouds are formed at the converging locations of large-scale turbulence flows and the filaments are bounded by gravity. The magnetic field helps shape and reinforce the long filamentary structures. The main filamentary cloud has a length of ∼4.4 pc. Instead of a monolithic cylindrical structure, the main cloud is shown to be a collection of fibre/web-like substructures similar to filamentary clouds such as L1495. Unless the line-of-sight is close to the mean field direction, the large-scale magnetic field and striations in the simulation are found roughly perpendicular to the long axis of the main cloud, similar to L1495. This provides strong support for a large-scale moderately strong magnetic field surrounding L1495. We find that the projection effect from observations can lead to incorrect interpretations of th...
Proceedings of the International Astronomical Union, 2010
Ambipolar diffusion (AD) is a key process in molecular clouds (MCs). Non-ideal MHD turbulence sim... more Ambipolar diffusion (AD) is a key process in molecular clouds (MCs). Non-ideal MHD turbulence simulations are technically very challenging because of the large Alfvén speed of ions in weakly ionized clouds. Using the Heavy-Ion Approximation method (Li, McKee & Klein 2006), we have carried out two-fluid simulations of AD in isothermal, turbulent boxes at a resolution of 5123, to investigate the effect of AD on the weakly ionized turbulence in MCs. Our simulation results show that the neutral gas component of the two-fluid system gradually transforms from an ideal MHD turbulence system to near a pure hydrodynamic turbulence system within the standard AD regime, in which the neutrals and ions are coupled over a flow time. The change of the turbulent state has a profound effect on the weakly ionized MCs.
Monthly Notices of the Royal Astronomical Society, 2015
The most accurate measurements of magnetic fields in star-forming gas are based on the Zeeman obs... more The most accurate measurements of magnetic fields in star-forming gas are based on the Zeeman observations analysed by Crutcher et al. We show that their finding that the 3D magnetic field scales approximately as density 0.65 can also be obtained from analysis of the observed line-of-sight fields. We present two large-scale adaptive-mesh-refinement magnetohydrodynamic simulations of several thousand M of turbulent, isothermal, self-gravitating gas, one with a strong initial magnetic field (Alfvén Mach number M A,0 = 1) and one with a weak initial field (M A,0 = 10). We construct samples of the 100 most massive clumps in each simulation and show that they exhibit a power-law relation between field strength and density (n H) in excellent agreement with the observed one. Our results imply that the average field in molecular clumps in the interstellar medium (ISM) is B tot (n H) ≈ 42n 0.65 H, 4 μG. Furthermore, the median value of the ratio of the line-of-sight field to density 0.65 in the simulations is within a factor of about (1.3, 1.7) of the observed value for the strong-and weak-field cases, respectively. The median value of the mass-to-flux ratio, normalized to the critical value, is 70 per cent of the line-of-sight value. This is larger than the 50 per cent usually cited for spherical clouds because the actual mass-to-flux ratio depends on the volume-weighted field, whereas the observed one depends on the mass-weighted field. Our results indicate that the typical molecular clump in the ISM is significantly supercritical (∼ factor of 3). The results of our strong-field model are in very good quantitative agreement with the observations of Li et al., which show a strong correlation in field orientation between small and large scales. Because there is a negligible correlation in the weak-field model, we conclude that molecular clouds form from strongly magnetized (although magnetically supercritical) gas, in agreement with the conclusion of Li et al.
Proceedings of the International Astronomical Union, 2005
The Astrophysical Journal, 2004
The Astrophysical Journal, 2012
The Astrophysical Journal, 2011
The Astrophysical Journal, 2009
We study rapidly accreting, gravitationally unstable disks with a series of global, three dimensi... more We study rapidly accreting, gravitationally unstable disks with a series of global, three dimensional, numerical experiments using the code ORION. In this paper we conduct a numerical parameter study focused on protostellar disks, and show that one can predict disk behavior and the multiplicity of the accreting star system as a function of two dimensionless parameters which compare the disk's accretion rate to its sound speed and orbital period. Although gravitational instabilities become strong, we find that fragmentation into binary or multiple systems occurs only when material falls in several times more rapidly than the canonical isothermal limit. The disk-to-star accretion rate is proportional to the infall rate, and governed by gravitational torques generated by low-m spiral modes. We also confirm the existence of a maximum stable disk mass: disks that exceed ∼ 50% of the total system mass are subject to fragmentation and the subsequent formation of binary companions.
The Astrophysical Journal, 2005
The Astrophysical Journal, 2004
The Astrophysical Journal, 2007
The Astrophysical Journal, 2000
The Astrophysical Journal, 2006
arXiv (Cornell University), Sep 7, 1999
We report the discovery of kHz fluctuations, including quasi-periodic oscillations (QPO) at ∼ 330... more We report the discovery of kHz fluctuations, including quasi-periodic oscillations (QPO) at ∼ 330 Hz (260−407 Hz) and ∼ 760 Hz (671−849 Hz) and a broadband kHz continuum in the power density spectrum of the high mass X-ray binary pulsar Centaurus X-3 (Jernigan, Klein and Arons 1999). These observations of Cen X-3 were carried out with the Rossi X-ray Timing Explorer (RXTE). The fluctuation spectrum is flat from mHz to a few Hz, then steepens to f −2 behavior between a few Hz and ∼ 100 Hz. Above a hundred Hz, corrections for the observations of Cen X-3, we have also demonstrated that the black hole Cyg X-1 shows clear evidence of variability up to a frequency of ∼ 280 Hz. Also observations of GX 17+2 were used to validate the procedure for deadtime corrections. This analysis of GX 17+2 clearly indicates the presence of a kHz QPO and the absence of any significant simultaneous kHz continuum.
Ambipolar diffusion (AD) is believed to be a crucial process for redistributing magnetic flux in ... more Ambipolar diffusion (AD) is believed to be a crucial process for redistributing magnetic flux in the dense molecular gas that occurs in regions of star formation. We carry out numerical simulations of this process in regions of low ionization using the heavy ion approximation. The simulations are for regions of strong field (plasma β = 0.1) and mildly supersonic turbulence (M = 3, corresponding to an Alfvén mach number of 0.67). The velocity power spectrum of the neutral gas changes from an Iroshnikov-Kraichnan spectrum in the case of ideal MHD to a Burgers spectrum in the case of a shock-dominated hydrodynamic system. The magnetic power spectrum shows a similar behavior. We use a 1D radiative transfer code to post-process our simulation results; the simulated emission from the CS J = 2−1 and H13CO+ J = 1−0 lines shows that the effects of AD are observable in principle. Linewidths of ions are observed to be less than those of neutrals, and we confirm previous suggestions that this ...
We compute the molecular line emission of massive protostellar disks by solving the equation of r... more We compute the molecular line emission of massive protostellar disks by solving the equation of radiative transfer through the cores and disks produced by the recent radiation-hydrodynamic simulations of Krumholz, Klein, & McKee. We find that in several representative lines the disks show brightness temperatures of hundreds of Kelvin over velocity channels ∼ 10 km s −1 wide, extending over regions hundreds of AU in size. We process the computed intensities to model the performance of next-generation radio and submillimeter telescopes. Our calculations show that observations using facilities such as the EVLA and ALMA should be able to detect massive protostellar disks and measure their rotation curves, at least in the nearest massive star-forming regions. They should also detect significant sub-structure and non-axisymmetry in the disks, and in some cases may be able to detect star-disk velocity offsets of a few km s −1, both of which are the result of strong gravitational instabilit...
Performing a stable, long duration simulation of driven MHD turbulence with a high thermal Mach n... more Performing a stable, long duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing positivity of the density and pressure. We have implemented a robust combination of reconstruction schemes, Riemann solvers, limiters, and Constrained Transport EMF averaging schemes that can meet this challenge, and using this strategy, we have developed a new Adaptive Mesh Refinement (AMR) MHD module of the ORION2 code. We investigate the effects of AMR on several statistical properties of a turbulent ideal MHD system with a thermal Mach number of 10 and a plasma β 0 of 0.1 as initial conditions; our code is shown to be stable for simulations with higher Mach numbers (M rms = 17.3) and smaller plasma beta (β 0 = 0.0067) as well. Our results show that the quality of the turbulence simulation is generally related to the volume-averaged refinement. Our AMR simulations show that the turbulent dissipation coefficient for supersonic MHD turbulence is about 0.5, in agreement with unigrid simulations.
Journal of Open Source Software, 2021
The formation of stars and stellar clusters remains a grand challenge problem in astrophysics tha... more The formation of stars and stellar clusters remains a grand challenge problem in astrophysics that has important implications for the evolution of the interstellar medium as well as shaping the evolution of galaxies. The computational challenges are formidable and involve a coupling of highly non-linear physical processes such as hydrodynamics, self-gravity, magnetic fields, radiation transfer, supersonic turbulence, ionization, protostellar outflows, stellar winds and chemistry that have both disparate timescales as well as operate over many decades of physical length scale. These processes can regulate the feedback from nascent protostars onto the surrounding turbulent gas clouds that are the embryos of new star formation, and as a result, the feedback itself can influence the gaseous reservoir feeding newly formed protostars which in turn influence the star formation process.
We analyze the equations of radiation hydrodynamics under the approximations of flux-limited diff... more We analyze the equations of radiation hydrodynamics under the approximations of flux-limited diffusion and a thermal radiation field, and derive the minimal set of evolution equations that includes all terms that are of leading order in any regime of non-relativistic radiation hydrodynamics. Our equations are accurate to first order in v/c in the static diffusion regime. We give the equations in a conservation law form well-suited to implementation in numerical algorithms. Our work improves on previous zeroth order derivations of the equations by retaining differences between laboratory frame and comoving frame quantities, which are neglected at zeroth order. We compare our equations to the zeroth order equations, and show that in certain regimes the zeroth order equations omit terms that are formally of leading order. We discuss the circumstances under which this will produce significant errors. For systems in the static diffusion regime, our analysis of the equations suggests an a...
Proceedings of the International Astronomical Union, 2015
Numerical simulations of star formation faces challenges including the huge spatial dynamic range... more Numerical simulations of star formation faces challenges including the huge spatial dynamic range and the presence of multiply coupled highly non-linear physics, such as magnetic field, supersonic turbulence, gravitation, radiation and protostellar outflow feedback. We present in this symposium our latest high resolution adaptive mesh refinement numerical simulations of the formation of filamentary dark molecular clouds from 4.55 pc size scale down to the formation of a protostellar cluster with maximum resolution at 28 AU. The physical properties of the long braided filamentary dark cloud formed in the simulation, the magnetic field properties of the cloud clumps, and the protostellar mass function in the simulations match well with the latest observations.
Monthly Notices of the Royal Astronomical Society, 2019
We perform ideal magnetohydrodynamics high-resolution adaptive mesh refinement simulations with d... more We perform ideal magnetohydrodynamics high-resolution adaptive mesh refinement simulations with driven turbulence and self-gravity and find that long filamentary molecular clouds are formed at the converging locations of large-scale turbulence flows and the filaments are bounded by gravity. The magnetic field helps shape and reinforce the long filamentary structures. The main filamentary cloud has a length of ∼4.4 pc. Instead of a monolithic cylindrical structure, the main cloud is shown to be a collection of fibre/web-like substructures similar to filamentary clouds such as L1495. Unless the line-of-sight is close to the mean field direction, the large-scale magnetic field and striations in the simulation are found roughly perpendicular to the long axis of the main cloud, similar to L1495. This provides strong support for a large-scale moderately strong magnetic field surrounding L1495. We find that the projection effect from observations can lead to incorrect interpretations of th...
Proceedings of the International Astronomical Union, 2010
Ambipolar diffusion (AD) is a key process in molecular clouds (MCs). Non-ideal MHD turbulence sim... more Ambipolar diffusion (AD) is a key process in molecular clouds (MCs). Non-ideal MHD turbulence simulations are technically very challenging because of the large Alfvén speed of ions in weakly ionized clouds. Using the Heavy-Ion Approximation method (Li, McKee & Klein 2006), we have carried out two-fluid simulations of AD in isothermal, turbulent boxes at a resolution of 5123, to investigate the effect of AD on the weakly ionized turbulence in MCs. Our simulation results show that the neutral gas component of the two-fluid system gradually transforms from an ideal MHD turbulence system to near a pure hydrodynamic turbulence system within the standard AD regime, in which the neutrals and ions are coupled over a flow time. The change of the turbulent state has a profound effect on the weakly ionized MCs.
Monthly Notices of the Royal Astronomical Society, 2015
The most accurate measurements of magnetic fields in star-forming gas are based on the Zeeman obs... more The most accurate measurements of magnetic fields in star-forming gas are based on the Zeeman observations analysed by Crutcher et al. We show that their finding that the 3D magnetic field scales approximately as density 0.65 can also be obtained from analysis of the observed line-of-sight fields. We present two large-scale adaptive-mesh-refinement magnetohydrodynamic simulations of several thousand M of turbulent, isothermal, self-gravitating gas, one with a strong initial magnetic field (Alfvén Mach number M A,0 = 1) and one with a weak initial field (M A,0 = 10). We construct samples of the 100 most massive clumps in each simulation and show that they exhibit a power-law relation between field strength and density (n H) in excellent agreement with the observed one. Our results imply that the average field in molecular clumps in the interstellar medium (ISM) is B tot (n H) ≈ 42n 0.65 H, 4 μG. Furthermore, the median value of the ratio of the line-of-sight field to density 0.65 in the simulations is within a factor of about (1.3, 1.7) of the observed value for the strong-and weak-field cases, respectively. The median value of the mass-to-flux ratio, normalized to the critical value, is 70 per cent of the line-of-sight value. This is larger than the 50 per cent usually cited for spherical clouds because the actual mass-to-flux ratio depends on the volume-weighted field, whereas the observed one depends on the mass-weighted field. Our results indicate that the typical molecular clump in the ISM is significantly supercritical (∼ factor of 3). The results of our strong-field model are in very good quantitative agreement with the observations of Li et al., which show a strong correlation in field orientation between small and large scales. Because there is a negligible correlation in the weak-field model, we conclude that molecular clouds form from strongly magnetized (although magnetically supercritical) gas, in agreement with the conclusion of Li et al.
Proceedings of the International Astronomical Union, 2005
The Astrophysical Journal, 2004
The Astrophysical Journal, 2012
The Astrophysical Journal, 2011
The Astrophysical Journal, 2009
We study rapidly accreting, gravitationally unstable disks with a series of global, three dimensi... more We study rapidly accreting, gravitationally unstable disks with a series of global, three dimensional, numerical experiments using the code ORION. In this paper we conduct a numerical parameter study focused on protostellar disks, and show that one can predict disk behavior and the multiplicity of the accreting star system as a function of two dimensionless parameters which compare the disk's accretion rate to its sound speed and orbital period. Although gravitational instabilities become strong, we find that fragmentation into binary or multiple systems occurs only when material falls in several times more rapidly than the canonical isothermal limit. The disk-to-star accretion rate is proportional to the infall rate, and governed by gravitational torques generated by low-m spiral modes. We also confirm the existence of a maximum stable disk mass: disks that exceed ∼ 50% of the total system mass are subject to fragmentation and the subsequent formation of binary companions.
The Astrophysical Journal, 2005
The Astrophysical Journal, 2004
The Astrophysical Journal, 2007
The Astrophysical Journal, 2000
The Astrophysical Journal, 2006