Christopher Matzner - Academia.edu (original) (raw)
Papers by Christopher Matzner
The Astrophysical Journal, 1999
We examine the relation between presupernova stellar structure and the distribution of ejecta in ... more We examine the relation between presupernova stellar structure and the distribution of ejecta in core-collapse supernovae of types Ib, Ic and II, under the approximations of adiabatic, spherically symmetric flow. We develop a simple yet accurate analytical formula for the velocity of the initial forward shock that traverses the stellar envelope. For material that does not later experience a strong reverse shock, the entropy deposited by this forward shock persists into the final, freely-expanding state. We demonstrate that the final density distribution can be approximated with simple models for the final pressure distribution, in a way that matches the results of simulations. Our results indicate that the distribution of density and radiation pressure in a star's ejecta depends on whether the outer envelope is radiative or convective, and if convective, on the composition structure of the star.
The Astrophysical Journal, 2009
We evaluate the role of radiation pressure in the dynamics of H ii regions. We first determine un... more We evaluate the role of radiation pressure in the dynamics of H ii regions. We first determine under what conditions radiation pressure is significant in comparison to gas pressure and show that, while radiation pressure is generally unimportant for H ii regions driven by a handful of massive stars, it is dominant for the larger H ii regions produced by the massive star clusters found near the Galactic center and in starburst environments. We then provide a solution for the problem of how H ii regions expand when radiation pressure influences their behavior. Finally, we compare radiation-dominated H ii regions to other sources of stellar feedback, and argue that H ii regions are probably the primary mechanism for regulating the formation of massive star clusters.
The Astrophysical Journal, 2011
The Milky Way harbors giant H II regions which may be powered by star complexes more luminous tha... more The Milky Way harbors giant H II regions which may be powered by star complexes more luminous than any Galactic OB association known. Being across the disk of the Galaxy, however, these brightest associations are severely extinguished and confused. We present a search for one such association toward the most luminous H II region in the recent catalog by Murray and Rahman, which, at ∼9.7 kpc, has recombination rate of ∼ 7 × 10 51 sec −1 . Prior searches have identified only small scale clustering around the rim of this shell-like region, but the primary association has not previously been identified. We apply a near-infrared color selection and find an overdensity of point sources toward its southern central part. The colors and magnitudes of these excess sources are consistent with Oand early B-type stars at extinctions 0.96 < A K < 1.2, and they are sufficiently numerous (406 ± 102 after subtraction of field sources) to ionize the surrounding H II region, making this a candidate for the most luminous OB association in the Galaxy. We reject an alternate theory, in which the apparent excess is caused by localized extinction, as inconsistent with source demographics.
The Astrophysical Journal, 1997
We present an analytic calculation of the thermonuclear depletion of lithium in contracting, full... more We present an analytic calculation of the thermonuclear depletion of lithium in contracting, fully convective, pre-main sequence stars of mass M ∼ < 0.5M ⊙ . Previous numerical work relies on still-uncertain physics (atmospheric opacities and convection, in particular) to calculate the effective temperature as a unique function of stellar mass. We assume that the star's effective temperature, T eff , is fixed during Hayashi contraction and allow its actual value to be a free parameter constrained by observation. Using this approximation, we compute lithium burning analytically and explore the dependence of lithium depletion on T eff , M , and composition. Our calculations yield the radius, age, and luminosity of a pre-main sequence star as a function of lithium depletion. This allows for more direct comparisons to observations of lithium depleted stars. Our results agree with those numerical calculations that explicitly determine stellar structure during Hayashi contraction. In agreement with , we show that the absence of lithium in the Pleiades star HHJ 3 implies that it is older than 100 Myr. We also suggest a generalized method for dating galactic clusters younger than 100 Myr (i.e., those with contracting stars of M ∼ > 0.08M ⊙ ) and for constraining the masses of lithium depleted stars.
The Astrophysical Journal, 2001
Rossby waves (r-modes) have been suggested as a means to regulate the spin periods of young or ac... more Rossby waves (r-modes) have been suggested as a means to regulate the spin periods of young or accreting neutron stars, and also to produce observable gravitational wave radiation. R-modes involve primarily transverse, incompressive motions of the star's fluid core. However, neutron stars gain crusts early in their lives: therefore, r-modes also imply shear in the fluid beneath the crust. We examine the criterion for this shear layer to become turbulent, and derive the rate of dissipation in the turbulent regime. Unlike dissipation from a viscous boundary layer, turbulent energy loss is nonlinear in mode energy and can therefore cause the mode to saturate at amplitudes typically much less than unity. This energy loss also reappears as heat below the crust. We study the possibility of crust melting as well as its potential implications for the spin evolution of low-mass X-ray binaries. Lastly, we identify some universal features of the spin evolution that may have observational consequences.
The Astrophysical Journal, 1998
We present an analytic calculation of the thermonuclear depletion of the light elements lithium, ... more We present an analytic calculation of the thermonuclear depletion of the light elements lithium, beryllium, and boron in fully convective, low-mass stars. Under the presumption that the pre-main-sequence star is always fully mixed during contraction, we find that the burning of these rare light elements can be computed analytically, even when the star is degenerate. Using the effective temperature as a free parameter, we constrain the properties of low-mass stars from observational data, independently of the uncertainties associated with modeling their atmospheres and convection. Our results are in excellent agreement with the detailed calculations of D'Antona & and Chabrier, . Our analytic solution explains the dependence of the age at a given level of elemental depletion on the stellar effective temperature, nuclear cross sections, and chemical composition. These results are also useful as benchmarks to those constructing full stellar models. Most importantly, our results allow observers to translate lithium non-detections in young cluster members into a model-independent minimum age for that cluster. Using this procedure, we have found lower limits to the ages of the Pleiades (100 Myr) and Alpha Persei (60 Myr) clusters. Dating an open cluster using low-mass stars is also independent of techniques that fit upper main-sequence evolution. Comparison of these methods provides crucial information on the amount of convective overshooting (or rotationally induced mixing) that occurs during core hydrogen burning in the 5-10 M ⊙ stars typically at the main-sequence turnoff for these clusters. We also discuss beryllium depletion in pre-main-sequence stars. Recent experimental work on the low energy resonance in the 10 B(p, α) 7 Be reaction has greatly enhanced estimates of the destruction rate of 10 B, making it possible for stars with M ∼ > 0.1M ⊙ to deplete both 10 B and 11 B before reaching the main sequence. Moreover, there is an interesting range of masses, 0.085M ⊙ ∼ < M ∼ < 0.13M ⊙ , where boron depletion occurs on the main sequence in less than a Hubble time, providing a potential "clock" for dating low-mass stars.
The Astrophysical Journal, 2008
Most analytic work to date on protostellar disks has focused on those in isolation from their env... more Most analytic work to date on protostellar disks has focused on those in isolation from their environments. However, observations are now beginning to probe the earliest, most embedded phases of star formation, during which disks are rapidly accreting from their parent cores and cannot be modeled in isolation. We present a simple, one-zone model of protostellar accretion disks with high mass infall rates. Our model combines a self-consistent calculation of disk temperatures with an approximate treatment of angular momentum transport via two mechanisms. We use this model to survey the properties of protostellar disks across a wide range of stellar masses and evolutionary times, and make predictions for disks' masses, sizes, spiral structure, and fragmentation that will be directly testable by future large-scale surveys of deeply embedded disks. We define a dimensionless accretion-rotation parameter which, in conjunction with the disk's temperature, controls the disk evolution. We track the dominant mode of angular momentum transport, and demonstrate that for stars with final masses greater than roughly one solar mass, gravitational instabilities are the most important mechanism as most of the mass accumulates. We predict that binary formation through disk fission, fragmentation of the disk into small objects, and spiral arm strength all increase in importance to higher stellar masses.
The Astrophysical Journal, 2006
We present semi-analytic dynamical models for giant molecular clouds evolving under the influence... more We present semi-analytic dynamical models for giant molecular clouds evolving under the influence of HII regions launched by newborn star clusters. In contrast to previous work, we neither assume that clouds are in virial or energetic equilibrium, nor do we ignore the effects of star formation feedback. The clouds, which we treat as spherical, can expand and contract homologously. Photoionization drives mass ejection; the recoil of cloud material both stirs turbulent motions and leads to an effective confining pressure. The balance between these effects and the decay of turbulent motions through isothermal shocks determines clouds' dynamical and energetic evolution. We find that for realistic values of the rates of turbulent dissipation, photoevaporation, and energy injection by HII regions, the massive clouds where most molecular gas in the Galaxy resides live for a few crossing times, in good agreement with recent observational estimates that large clouds in local group galaxies survive roughly 20 − 30 Myr. During this time clouds remain close to equilibrium, with virial parameters of 1 − 3 and column densities near 10 22 H atoms cm −2 , also in agreement with observed cloud properties. Over their lives they convert 5 − 10% of their mass into stars, after which point most clouds are destroyed when a large HII region unbinds them. In contrast, small clouds like those found in the solar neighborhood only survive ∼ 1 crossing time before being destroyed.
The Astrophysical Journal, 2003
We present a scenario for non-radiative accretion onto the supermassive black hole at the galacti... more We present a scenario for non-radiative accretion onto the supermassive black hole at the galactic center. Conducting MHD simulations with 1400 3 grid zones that break the axial and reflection symmetries of earlier investigations and extend inward from the Bondi radius, we find a quasi-hydrostatic radial density profile ρ ∝ r −0.72 with superadiabatic gradient corresponding to an n ∼ 0.72 polytrope. Buoyancy generated by magnetic dissipation is resisted by the same fields so effectively that energy is advected inward: a state of magnetically-frustrated convection. This scenario is consistent with observational constraints on energetics andouter boundary conditions.
The Astrophysical Journal, 1999
We demonstrate that magnetically-collimated protostellar winds will sweep ambient material into t... more We demonstrate that magnetically-collimated protostellar winds will sweep ambient material into thin, radiative, momentum-conserving shells whose features reproduce those commonly observed in bipolar molecular outflows. We find the typical position-velocity and mass-velocity relations to occur in outflows in a wide variety of ambient density distributions, regardless of the time histories of their driving winds.
The Astrophysical Journal, 2010
We investigate how the removal of interstellar material by stellar feedback limits the efficiency... more We investigate how the removal of interstellar material by stellar feedback limits the efficiency of star formation in molecular clouds and how this determines the shape of the mass function of young star clusters. In particular, we derive relations between the power-law exponents of the mass functions of the clouds and clusters in the limiting regimes in which the feedback is energy-driven and momentum-driven, corresponding to minimum and maximum radiative losses, and likely to bracket all realistic cases. We find good agreement between the predicted and observed exponents, especially for momentum-driven feedback, provided the protoclusters have roughly constant mean surface density, as indicated by observations of the star-forming clumps within molecular clouds. We also consider a variety of specific feedback mechanisms, concluding that H ii regions inflated by radiation pressure predominate in massive protoclusters, a momentum-limited process when photons can escape after only a few interactions with dust grains. We show in this case that the star formation efficiency depends on the masses and sizes of the protoclusters only through their mean surface density, thus ensuring consistency between the observed exponents of the mass functions of the clouds and clusters. Our numerical estimate of this efficiency is also consistent with observations.
Spitzer observations of nearby galaxies have produced considerable insight into the question of w... more Spitzer observations of nearby galaxies have produced considerable insight into the question of where and when star formation occurs. By combining Spitzer maps of galactic disks, which probe embedded regions of star formation at high spatial resolution, with large-scale surveys of atomic and molecular gas, we have for the first time been able to determine the spatial and temporal distribution of star formation and its relation to the distributions of gas and old stars. To date, no comprehensive theoretical model has been capable of reproducing these observations in detail. Simulations indicate that large-scale gravitational instability plays a key role in determining where atomic gas condenses to form giant molecular clouds (GMCs), but they are limited by their inability to resolve the internal dynamics of these objects. Because the conversion of GMC gas into stars is an extremely inefficient and comparatively slow process, most likely as a result of stellar feedback, it is not poss...
Monthly Notices of the Royal Astronomical Society, 2008
We present solutions for the structure and evolution of bubbles created by slow stellar winds, du... more We present solutions for the structure and evolution of bubbles created by slow stellar winds, during their fully and partially radiative phases. Exact limiting forms are derived for the partially radiative case, and the transition between the two phases is analysed under the assumption of steady spherical flow. We compute the factor by which the bubble's radial momentum is amplified relative to that of the wind, and provide accurate formulae for its expansion across the fully-to-partially radiative transition. Our results will be useful in the study of protostellar outflow cocoons and bubbles driven by mass-loaded winds from star clusters.
The Astrophysical Journal, 1999
We examine the relation between presupernova stellar structure and the distribution of ejecta in ... more We examine the relation between presupernova stellar structure and the distribution of ejecta in core-collapse supernovae of types Ib, Ic and II, under the approximations of adiabatic, spherically symmetric flow. We develop a simple yet accurate analytical formula for the velocity of the initial forward shock that traverses the stellar envelope. For material that does not later experience a strong reverse shock, the entropy deposited by this forward shock persists into the final, freely-expanding state. We demonstrate that the final density distribution can be approximated with simple models for the final pressure distribution, in a way that matches the results of simulations. Our results indicate that the distribution of density and radiation pressure in a star's ejecta depends on whether the outer envelope is radiative or convective, and if convective, on the composition structure of the star.
The Astrophysical Journal, 2009
We evaluate the role of radiation pressure in the dynamics of H ii regions. We first determine un... more We evaluate the role of radiation pressure in the dynamics of H ii regions. We first determine under what conditions radiation pressure is significant in comparison to gas pressure and show that, while radiation pressure is generally unimportant for H ii regions driven by a handful of massive stars, it is dominant for the larger H ii regions produced by the massive star clusters found near the Galactic center and in starburst environments. We then provide a solution for the problem of how H ii regions expand when radiation pressure influences their behavior. Finally, we compare radiation-dominated H ii regions to other sources of stellar feedback, and argue that H ii regions are probably the primary mechanism for regulating the formation of massive star clusters.
The Astrophysical Journal, 2011
The Milky Way harbors giant H II regions which may be powered by star complexes more luminous tha... more The Milky Way harbors giant H II regions which may be powered by star complexes more luminous than any Galactic OB association known. Being across the disk of the Galaxy, however, these brightest associations are severely extinguished and confused. We present a search for one such association toward the most luminous H II region in the recent catalog by Murray and Rahman, which, at ∼9.7 kpc, has recombination rate of ∼ 7 × 10 51 sec −1 . Prior searches have identified only small scale clustering around the rim of this shell-like region, but the primary association has not previously been identified. We apply a near-infrared color selection and find an overdensity of point sources toward its southern central part. The colors and magnitudes of these excess sources are consistent with Oand early B-type stars at extinctions 0.96 < A K < 1.2, and they are sufficiently numerous (406 ± 102 after subtraction of field sources) to ionize the surrounding H II region, making this a candidate for the most luminous OB association in the Galaxy. We reject an alternate theory, in which the apparent excess is caused by localized extinction, as inconsistent with source demographics.
The Astrophysical Journal, 1997
We present an analytic calculation of the thermonuclear depletion of lithium in contracting, full... more We present an analytic calculation of the thermonuclear depletion of lithium in contracting, fully convective, pre-main sequence stars of mass M ∼ < 0.5M ⊙ . Previous numerical work relies on still-uncertain physics (atmospheric opacities and convection, in particular) to calculate the effective temperature as a unique function of stellar mass. We assume that the star's effective temperature, T eff , is fixed during Hayashi contraction and allow its actual value to be a free parameter constrained by observation. Using this approximation, we compute lithium burning analytically and explore the dependence of lithium depletion on T eff , M , and composition. Our calculations yield the radius, age, and luminosity of a pre-main sequence star as a function of lithium depletion. This allows for more direct comparisons to observations of lithium depleted stars. Our results agree with those numerical calculations that explicitly determine stellar structure during Hayashi contraction. In agreement with , we show that the absence of lithium in the Pleiades star HHJ 3 implies that it is older than 100 Myr. We also suggest a generalized method for dating galactic clusters younger than 100 Myr (i.e., those with contracting stars of M ∼ > 0.08M ⊙ ) and for constraining the masses of lithium depleted stars.
The Astrophysical Journal, 2001
Rossby waves (r-modes) have been suggested as a means to regulate the spin periods of young or ac... more Rossby waves (r-modes) have been suggested as a means to regulate the spin periods of young or accreting neutron stars, and also to produce observable gravitational wave radiation. R-modes involve primarily transverse, incompressive motions of the star's fluid core. However, neutron stars gain crusts early in their lives: therefore, r-modes also imply shear in the fluid beneath the crust. We examine the criterion for this shear layer to become turbulent, and derive the rate of dissipation in the turbulent regime. Unlike dissipation from a viscous boundary layer, turbulent energy loss is nonlinear in mode energy and can therefore cause the mode to saturate at amplitudes typically much less than unity. This energy loss also reappears as heat below the crust. We study the possibility of crust melting as well as its potential implications for the spin evolution of low-mass X-ray binaries. Lastly, we identify some universal features of the spin evolution that may have observational consequences.
The Astrophysical Journal, 1998
We present an analytic calculation of the thermonuclear depletion of the light elements lithium, ... more We present an analytic calculation of the thermonuclear depletion of the light elements lithium, beryllium, and boron in fully convective, low-mass stars. Under the presumption that the pre-main-sequence star is always fully mixed during contraction, we find that the burning of these rare light elements can be computed analytically, even when the star is degenerate. Using the effective temperature as a free parameter, we constrain the properties of low-mass stars from observational data, independently of the uncertainties associated with modeling their atmospheres and convection. Our results are in excellent agreement with the detailed calculations of D'Antona & and Chabrier, . Our analytic solution explains the dependence of the age at a given level of elemental depletion on the stellar effective temperature, nuclear cross sections, and chemical composition. These results are also useful as benchmarks to those constructing full stellar models. Most importantly, our results allow observers to translate lithium non-detections in young cluster members into a model-independent minimum age for that cluster. Using this procedure, we have found lower limits to the ages of the Pleiades (100 Myr) and Alpha Persei (60 Myr) clusters. Dating an open cluster using low-mass stars is also independent of techniques that fit upper main-sequence evolution. Comparison of these methods provides crucial information on the amount of convective overshooting (or rotationally induced mixing) that occurs during core hydrogen burning in the 5-10 M ⊙ stars typically at the main-sequence turnoff for these clusters. We also discuss beryllium depletion in pre-main-sequence stars. Recent experimental work on the low energy resonance in the 10 B(p, α) 7 Be reaction has greatly enhanced estimates of the destruction rate of 10 B, making it possible for stars with M ∼ > 0.1M ⊙ to deplete both 10 B and 11 B before reaching the main sequence. Moreover, there is an interesting range of masses, 0.085M ⊙ ∼ < M ∼ < 0.13M ⊙ , where boron depletion occurs on the main sequence in less than a Hubble time, providing a potential "clock" for dating low-mass stars.
The Astrophysical Journal, 2008
Most analytic work to date on protostellar disks has focused on those in isolation from their env... more Most analytic work to date on protostellar disks has focused on those in isolation from their environments. However, observations are now beginning to probe the earliest, most embedded phases of star formation, during which disks are rapidly accreting from their parent cores and cannot be modeled in isolation. We present a simple, one-zone model of protostellar accretion disks with high mass infall rates. Our model combines a self-consistent calculation of disk temperatures with an approximate treatment of angular momentum transport via two mechanisms. We use this model to survey the properties of protostellar disks across a wide range of stellar masses and evolutionary times, and make predictions for disks' masses, sizes, spiral structure, and fragmentation that will be directly testable by future large-scale surveys of deeply embedded disks. We define a dimensionless accretion-rotation parameter which, in conjunction with the disk's temperature, controls the disk evolution. We track the dominant mode of angular momentum transport, and demonstrate that for stars with final masses greater than roughly one solar mass, gravitational instabilities are the most important mechanism as most of the mass accumulates. We predict that binary formation through disk fission, fragmentation of the disk into small objects, and spiral arm strength all increase in importance to higher stellar masses.
The Astrophysical Journal, 2006
We present semi-analytic dynamical models for giant molecular clouds evolving under the influence... more We present semi-analytic dynamical models for giant molecular clouds evolving under the influence of HII regions launched by newborn star clusters. In contrast to previous work, we neither assume that clouds are in virial or energetic equilibrium, nor do we ignore the effects of star formation feedback. The clouds, which we treat as spherical, can expand and contract homologously. Photoionization drives mass ejection; the recoil of cloud material both stirs turbulent motions and leads to an effective confining pressure. The balance between these effects and the decay of turbulent motions through isothermal shocks determines clouds' dynamical and energetic evolution. We find that for realistic values of the rates of turbulent dissipation, photoevaporation, and energy injection by HII regions, the massive clouds where most molecular gas in the Galaxy resides live for a few crossing times, in good agreement with recent observational estimates that large clouds in local group galaxies survive roughly 20 − 30 Myr. During this time clouds remain close to equilibrium, with virial parameters of 1 − 3 and column densities near 10 22 H atoms cm −2 , also in agreement with observed cloud properties. Over their lives they convert 5 − 10% of their mass into stars, after which point most clouds are destroyed when a large HII region unbinds them. In contrast, small clouds like those found in the solar neighborhood only survive ∼ 1 crossing time before being destroyed.
The Astrophysical Journal, 2003
We present a scenario for non-radiative accretion onto the supermassive black hole at the galacti... more We present a scenario for non-radiative accretion onto the supermassive black hole at the galactic center. Conducting MHD simulations with 1400 3 grid zones that break the axial and reflection symmetries of earlier investigations and extend inward from the Bondi radius, we find a quasi-hydrostatic radial density profile ρ ∝ r −0.72 with superadiabatic gradient corresponding to an n ∼ 0.72 polytrope. Buoyancy generated by magnetic dissipation is resisted by the same fields so effectively that energy is advected inward: a state of magnetically-frustrated convection. This scenario is consistent with observational constraints on energetics andouter boundary conditions.
The Astrophysical Journal, 1999
We demonstrate that magnetically-collimated protostellar winds will sweep ambient material into t... more We demonstrate that magnetically-collimated protostellar winds will sweep ambient material into thin, radiative, momentum-conserving shells whose features reproduce those commonly observed in bipolar molecular outflows. We find the typical position-velocity and mass-velocity relations to occur in outflows in a wide variety of ambient density distributions, regardless of the time histories of their driving winds.
The Astrophysical Journal, 2010
We investigate how the removal of interstellar material by stellar feedback limits the efficiency... more We investigate how the removal of interstellar material by stellar feedback limits the efficiency of star formation in molecular clouds and how this determines the shape of the mass function of young star clusters. In particular, we derive relations between the power-law exponents of the mass functions of the clouds and clusters in the limiting regimes in which the feedback is energy-driven and momentum-driven, corresponding to minimum and maximum radiative losses, and likely to bracket all realistic cases. We find good agreement between the predicted and observed exponents, especially for momentum-driven feedback, provided the protoclusters have roughly constant mean surface density, as indicated by observations of the star-forming clumps within molecular clouds. We also consider a variety of specific feedback mechanisms, concluding that H ii regions inflated by radiation pressure predominate in massive protoclusters, a momentum-limited process when photons can escape after only a few interactions with dust grains. We show in this case that the star formation efficiency depends on the masses and sizes of the protoclusters only through their mean surface density, thus ensuring consistency between the observed exponents of the mass functions of the clouds and clusters. Our numerical estimate of this efficiency is also consistent with observations.
Spitzer observations of nearby galaxies have produced considerable insight into the question of w... more Spitzer observations of nearby galaxies have produced considerable insight into the question of where and when star formation occurs. By combining Spitzer maps of galactic disks, which probe embedded regions of star formation at high spatial resolution, with large-scale surveys of atomic and molecular gas, we have for the first time been able to determine the spatial and temporal distribution of star formation and its relation to the distributions of gas and old stars. To date, no comprehensive theoretical model has been capable of reproducing these observations in detail. Simulations indicate that large-scale gravitational instability plays a key role in determining where atomic gas condenses to form giant molecular clouds (GMCs), but they are limited by their inability to resolve the internal dynamics of these objects. Because the conversion of GMC gas into stars is an extremely inefficient and comparatively slow process, most likely as a result of stellar feedback, it is not poss...
Monthly Notices of the Royal Astronomical Society, 2008
We present solutions for the structure and evolution of bubbles created by slow stellar winds, du... more We present solutions for the structure and evolution of bubbles created by slow stellar winds, during their fully and partially radiative phases. Exact limiting forms are derived for the partially radiative case, and the transition between the two phases is analysed under the assumption of steady spherical flow. We compute the factor by which the bubble's radial momentum is amplified relative to that of the wind, and provide accurate formulae for its expansion across the fully-to-partially radiative transition. Our results will be useful in the study of protostellar outflow cocoons and bubbles driven by mass-loaded winds from star clusters.