Photon Bubble Research Articles

Dynamics of neutron star accretion columns in split-monopole magnetic fields

ABSTRACT We perform 2D axisymmetric radiative relativistic MHD simulations of radiation pressure supported neutron star accretion columns in split-monopole magnetic fields. The accretion columns exhibit quasi-periodic oscillations, which manifest in the luminosity power spectrum as 2–10 kHz peaks, together with broader extensions to somewhat higher frequencies. The peak frequency decreases for wider columns or higher mass accretion rates. In contrast to the case of shorter columns in uniform magnetic fields, pdV work contributes substantially to maintaining the radiation pressure inside the column against sideways radiative cooling. This is in part due to the compression associated with accretion along the converging magnetic field lines towards the stellar surface. Propagating entropy waves which are associated with the slow-diffusion photon bubble instability form in all our simulations. Radial advection of radiation from the oscillation itself as well as the entropy waves is also important in maintaining radiation pressure inside the column. The time-averaged profile of our fiducial simulation accretion is approximately consistent with the classical 1D stationary model provided one incorporates the correct column shape. We also quantify the porosity in all our accretion column simulations so that this may also in principle be used to improve 1D models.

Radiative relativistic magnetohydrodynamic simulations of neutron star column accretion in Cartesian geometry

ABSTRACT High luminosity accretion on to a strongly magnetized neutron star results in a radiation pressure dominated, magnetically confined accretion column. We investigate the dynamics of these columns using 2D radiative relativistic magnetohydrodynamic simulations, restricting consideration to modest accretion rates where the height of the column is low enough that Cartesian geometry can be employed. The column structure is dynamically maintained through high-frequency oscillations of the accretion shock at ≃ 10–25 kHz. These oscillations arise because it is necessary to redistribute the power released at the accretion shock through bulk vertical motions, both to balance the cooling and to provide vertical pressure support against gravity. Sideways cooling always dominates the loss of internal energy. In addition to the vertical oscillations, photon bubbles form in our simulations and add additional spatial complexity to the column structure. They are not themselves responsible for the oscillations, and they do not appear to affect the oscillation period. However, they enhance the vertical transport of radiation and increase the oscillation amplitude in luminosity. The time-averaged column structure in our simulations resembles the trends in standard 1D stationary models, the main difference being that the time-averaged height of the shock front is lower because of the higher cooling efficiency of the 2D column shape.

Quasi-Static and Dynamic Photon Bubbles in Cold Atom Clouds

Turbulent radiation flow is ubiquitous in many physical systems where light–matter interaction becomes relevant. Photon bubble instabilities, in particular, have been identified as a possible source of turbulent radiation transport in astrophysical objects such as massive stars and black hole accretion disks. Here, we report on the experimental observation of a photon bubble instability in cold atomic gases, in the presence of multiple scattering of light. Two different regimes are identified, namely, the growth and formation of quasi-static structures of depleted atom density and increased photon number, akin to photon bubbles in astrophysical objects, and the destabilisation of these structures in a second regime of photon bubble turbulence. A two-fluid theory is developed to model the coupled atom–photon gas and to describe both the saturation of the instability in the regime of quasi-static bubbles and the low-frequency turbulent phase associated with the growth and collapse of photon bubbles inside the atomic sample. We also employ statistical dimensionality reduction techniques to describe the low-dimensional nature of the turbulent regime. The experimental results reported here, along with the theoretical model we have developed, may shed light on analogue photon bubble instabilities in astrophysical scenarios. Our findings are consistent with recent analyses based on spatially resolved pump–probe measurements.

Radiative MHD simulations of photon bubbles in radiation-supported magnetized atmospheres of neutron stars with isotropic Thomson scattering

ABSTRACT A major uncertainty in the structure and dynamics of magnetized, radiation pressure dominated neutron star accretion columns in X-ray pulsars and pulsating ultraluminous X-ray sources is that they are thought to be subject to the photon bubble instability. We present the results of two-dimensional radiation relativistic magnetohydrodynamic simulations of a non-accreting, static atmosphere to study the development of this instability assuming isotropic Thomson scattering in the slow diffusion regime that is relevant to neutron star accretion columns. Photon bubbles generally grow faster towards shorter wavelengths, until a maximum growth rate is achieved at the radiation viscosity length-scale, which is generally quite small and requires high numerical resolution to simulate. We confirm the consistency between our simulation results and linear theory in detail, and show that the non-linear evolution inevitably leads to collapse of the atmosphere with the higher resolution simulation collapsing faster due to the presence of shorter length-scale non-linear structures. At least in static atmospheres with horizontally periodic boundary conditions, this resolution dependence may make simulations of the non-linear dynamics of photon bubble instability in neutron star accretion columns challenging. It remains to be seen whether these difficulties will persist upon inclusion of an accretion flow through the top and magnetically confined horizontal boundaries through which photons can escape. Our results here provide a foundation for such future work.

Photon bubble turbulence in cold atom gases

Turbulent radiation flow is commonplace in systems with strong, incoherent, light-matter interactions. In astrophysical contexts, photon bubble turbulence is considered a key mechanism behind enhanced radiation transport, and its importance has been widely asserted for a variety of high energy objects such as accretion disks and massive stars. Here, we show that analogous conditions to those of dense astrophysical objects can be obtained in large clouds of cold atoms, prepared in a laser-cooling experiment, driven close to a sharp electronic resonance. By accessing the spatially-resolved atom density, we are able to identify a photon bubble instability and the resulting regime of photon bubble turbulence. We also develop a theoretical model describing the coupled dynamics of both photon and atom gases, which accurately describes the statistical properties of the turbulent regime. This study thus opens the possibility of simulating radiation-dominated astrophysical systems in cold atom experiments.

Photon Bubbles in a Self-gravitating Dust Gas: Collective Dust Interactions

Abstract We consider broadband radiation interacting with a gas of self-gravitating dust grains. We show that photon-bubble formation can occur, due to a modified Jeans instability, which will imply the formation of two different kinds of dust density perturbations. This could be useful for understanding the B-mode signal observed in the CMB polarization survey, and other astrophysical processes, such as the formation of protoplanets and voids in dust clouds.

PATCHY ACCRETION DISKS IN ULTRA-LUMINOUS X-RAY SOURCES

The X-ray spectra of the most extreme ultra-luminous X-ray sources -- those with L > 1 E+40 erg/s -- remain something of a mystery. Spectral roll-over in the 5-10 keV band was originally detected in in the deepest XMM-Newton observations of the brightest sources; this is confirmed in subsequent NuSTAR spectra. This emission can be modeled via Comptonization, but with low electron temperatures (kT_e ~ 2 keV) and high optical depths (tau ~ 10) that pose numerous difficulties. Moreover, evidence of cooler thermal emission that can be fit with thin disk models persists, even in fits to joint XMM-Newton and NuSTAR observations. Using NGC 1313 X-1 as a test case, we show that a patchy disk with a multiple temperature profile may provide an excellent description of such spectra. In principle, a number of patches within a cool disk might emit over a range of temperatures, but the data only require a two-temperature profile plus standard Comptonization, or three distinct blackbody components. A mechanism such as the photon bubble instability may naturally give rise to a patchy disk profile, and could give rise to super-Eddington luminosities. It is possible, then, that a patchy disk (rather than a disk with a standard single-temperature profile) might be a hallmark of accretion disks close to or above the Eddington limit. We discuss further tests of this picture, and potential implications for sources such as narrow-line Seyfert-1 galaxies (NLSy1s) and other low-mass active galactic nuclei (AGN).

Clumpy Outflows from Supercritical Accretion Flow

Abstract A significant amount of matter in supercritical (or super-Eddington) accretion flow is blown away by radiation force, thus forming outflows; however, the properties of such radiation-driven outflows have been poorly understood. We have performed global two-dimensional radiaion-magnetohydrodynamic simulations of supercritical accretion flow onto a black hole with 10 or 10$^{8} M_{\odot}$ in a large simulation box of 514 $r_{\rm S} \times 514 r_{\rm S}$ (with $r_{\rm S}$ being the Schwarzschild radius). We confirm that uncollimated outflows with velocities of 10 percent of the speed of light emerge from the innermost part of the accretion flow at a wide angle of 10$^{\circ}$ –50$^{\circ}$ from the disk rotation axis. Importantly, the outflows exhibit clumpy structures above heights of $\sim 250 r_{\rm S}$. The typical size of the clumps is $\sim 10 r_{\rm S}$, which corresponds to one optical depth, and their shapes are slightly elongated along the outflow direction. Since clumps start to form in the layer above which the (upward) radiation is superior in force to the (downward) gravity, the Rayleigh–Taylor instability seems to be a primary cause. In addition, a radiation-hydrodynamic instability, which arises when radiation funnels through a radiation-pressure-supported atmosphere, may also help to form clumps of one optical depth. A magnetic photon bubble instability does not seem to be essential, since a similar clumpy outflow structure is obtained in nonmagnetic radiation-hydrodynamic simulations. Since the spatial covering factor of the clumps is estimated to be $\sim$ 0.3, and since they are marginally optically thick, they will explain at least some of the rapid light variations of active galactic nuclei. We further discuss a possibility of producing broad-line region clouds by the clumpy outflow.

NONLINEAR EVOLUTION OF THE RADIATION-DRIVEN MAGNETO-ACOUSTIC INSTABILITY

We examine the nonlinear development of unstable magnetosonic waves driven by a background radiative flux -- the Radiation-Driven Magneto-Acoustic Instability (RMI, a.k.a. the "photon bubble" instability). The RMI may serve as a persistent source of density, radiative flux, and magnetic field fluctuations in stably-stratified, optically-thick media. The conditions for instability are present in a variety of astrophysical environments, and do not require the radiation pressure to dominate or the magnetic field to be strong. Here we numerically study the saturation properties of the RMI, covering three orders of magnitude in the relative strength of radiation, magnetic field, and gas energies. Two-dimensional, time-dependent radiation-MHD simulations of local, stably-stratified domains are conducted with Zeus-MP in the optically-thick, highly-conducting limit. Our results confirm the theoretical expectations of Blaes and Socrates (2003) in that the RMI operates even in gas pressure-dominated environments that are weakly magnetized. The saturation amplitude is a monotonically increasing function of the ratio of radiation to gas pressure. Keeping this ratio constant, we find that the saturation amplitude peaks when the magnetic pressure is comparable to the radiation pressure. We discuss the implications of our results for the dynamics of magnetized stellar envelopes, where the RMI should act as a source of sub-photospheric perturbations.

A GODUNOV METHOD FOR MULTIDIMENSIONAL RADIATION MAGNETOHYDRODYNAMICS BASED ON A VARIABLE EDDINGTON TENSOR

We describe a numerical algorithm to integrate the equations of radiation magnetohydrodynamics in multidimensions using Godunov methods. This algorithm solves the radiation moment equations in the mixed frame, without invoking any diffusion-like approximations. The moment equations are closed using a variable Eddington tensor whose components are calculated from a formal solution of the transfer equation at a large number of angles using the method of short characteristics. We use a comprehensive test suite to verify the algorithm, including convergence tests of radiation-modified linear acoustic and magnetosonic waves, the structure of radiation modified shocks, and two-dimensional tests of photon bubble instability and the ablation of dense clouds by an intense radiation field. These tests cover a very wide range of regimes, including both optically thick and thin flows, and ratios of the radiation to gas pressure of at least 10^{-4} to 10^{4}. Across most of the parameter space, we find the method is accurate. However, the tests also reveal there are regimes where the method needs improvement, for example when both the radiation pressure and absorption opacity are very large. We suggest modifications to the algorithm that will improve accuracy in this case. We discuss the advantages of this method over those based on flux-limited diffusion. In particular, we find the method is not only substantially more accurate, but often no more expensive than the diffusion approximation for our intended applications.

Photon Bubbles in Ultracold Matter

We show that static and oscillating photon bubbles can be excited by diffused light in the laser cooled matter confined in a magneto-optical trap. The bubble instability is due to the coupling between the radiation field and the mean field oscillations of the ultracold gas, and it can provide a source for low frequency turbulence. We consider a diffusion-dominated regime, which can be described by a radiation transport equation, coupled with the mean field equations for the cold atom gas. A perturbative analysis shows the occurrence of two different regimes with either oscillating or purely growing bubbles. This work could also be useful to understand similar processes in astrophysics.

LOCAL RADIATION MAGNETOHYDRODYNAMIC INSTABILITIES IN MAGNETICALLY STRATIFIED MEDIA

We study local radiation magnetohydrodynamic instabilities in static, optically thick, vertically stratified media with constant flux mean opacity. We include the effects of vertical gradients in a horizontal background magnetic field. Assuming rapid radiative diffusion, we use the zero gas pressure limit as an entry point for investigating the coupling between the photon bubble instability and the Parker instability. Apart from factors that depend on wavenumber orientation, the Parker instability exists for wavelengths longer than a characteristic wavelength lambda_{tran}, while photon bubbles exist for wavelengths shorter than lambda_{tran}. The growth rate in the Parker regime is independent of the orientation of the horizontal component of the wavenumber when radiative diffusion is rapid, but the range of Parker-like wavenumbers is extended if there exists strong horizontal shear between field lines (i.e. horizontal wavenumber perpendicular to the magnetic field). Finite gas pressure introduces an additional short wavelength limit to the Parker-like behavior, and also limits the growth rate of the photon bubble instability to a constant value at short wavelengths. We also consider the effects of differential rotation with accretion disk applications in mind. Our results may explain why photon bubbles have not yet been observed in recent stratified shearing box accretion disk simulations. Photon bubbles may physically exist in simulations with high radiation to gas pressure ratios, but higher spatial resolution will be needed to resolve the asymptotically growing unstable wavelengths.

Observation of a Cooperative Radiation Force in the Presence of Disorder

Cooperative scattering of light by an extended object such as an atomic ensemble or a dielectric sphere is fundamentally different from scattering from many pointlike scatterers such as single atoms. Homogeneous distributions tend to scatter cooperatively, whereas fluctuations of the density distribution increase the disorder and suppress cooperativity. In an atomic cloud, the amount of disorder can be tuned via the optical thickness, and its role can be studied via the radiation force exerted by the light on the atomic cloud. Monitoring cold (87)Rb atoms released from a magneto-optical trap, we present the first experimental signatures of radiation force reduction due to cooperative scattering. The results are in agreement with an analytical expression interpolating between the disorder and the cooperativity-dominated regimes.

X‐Ray Spectral Signatures of the Photon Bubble Model for Ultraluminous X‐Ray Sources

The nature of ultraluminous X-ray sources in nearby galaxies is one of the major open questions in modern X-ray astrophysics. One possible explanation for these objects is an inhomogeneous, radiation dominated accretion disk around a $\sim 10 M_{\odot}$ black hole -- the so-called ``photon bubble'' model. While previous studies of this model have focused primarily on its radiation-hydrodynamics aspects, in this paper, we provide an analysis of its X-ray spectral (continuum and possible edge and line) characteristics. Compton reflection between high and low density regions in the disk may provide the key to distinguishing this model from others, such as accretion onto an intermediate mass black hole. We couple a Monte Carlo/Fokker-Planck radiation transport code with the XSTAR code for reflection to simulate the photon spectra produced in a photon bubble model for ULXs. We find that reflection components tend to be very weak and in most cases not observable, and make predictions for the shape of the high-energy Comptonizing spectra. In many cases the Comptonization dominates the spectra even down to $\sim$ a few keV. In one simulation, a $\sim 9 \kev$ feature was found, which may be considered a signature of photon bubbles in ULXs; furthermore, we make predictions of high energy power-laws which may be observed by future instruments.

Photon Bubbles and Ion Acceleration in a Plasma Dominated by the Radiation Pressure of an Electromagnetic Pulse

The stability of a thin plasma foil accelerated by the radiation pressure of a high intensity electromagnetic (e.m.) pulse is investigated analytically and with particle in cell numerical simulations. It is shown that the onset of a Rayleigh-Taylor-like instability can lead to transverse bunching of the foil and to broadening of the energy spectrum of fast ions. The use of a properly tailored e.m. pulse with a sharp intensity rise can stabilize the foil acceleration.

Surface Structure in an Accretion Disk Annulus with Comparable Radiation and Gas Pressure

We have employed a 3-d energy-conserving radiation MHD code to simulate the vertical structure and thermodynamics of a shearing box whose parameters were chosen so that the radiation and gas pressures would be comparable. The upper layers of this disk segment are magnetically-dominated, creating conditions appropriate for both photon bubble and Parker instabilities. We find little evidence for photon bubbles, even though the simulation has enough spatial resolution to see them and their predicted growth rates are high. On the other hand, there is strong evidence for Parker instabilities, and they appear to dominate the evolution of the magnetically supported surface layers. The disk photosphere is complex, with large density inhomogeneities at both the scattering and effective (thermalization) photospheres of the evolving horizontally-averaged structure. Both the dominant magnetic support and the inhomogeneities are likely to have strong effects on the spectrum and polarization of thermal photons emerging from the disk atmosphere. The inhomogeneities are also large enough to affect models of reflection spectra from the atmospheres of accretion disks.

Coulomb Bubbles: Overstable Driving of Magnetoacoustic Waves Due to the Rapid and Anisotropic Diffusion of Energy

We perform a linear magnetohydrodynamic perturbation analysis for a stratified magnetized envelope where the diffusion of heat is mediated by charged particles that are confined to flow along magnetic field lines. We identify an instability, the "Coulomb bubble instability," which may be thought of as standard magnetosonic fast and slow waves, driven by the rapid diffusion of heat along the direction of the magnetic field. We calculate the growth rate and stability criteria for the Coulomb bubble instability for various choices of equilibrium conditions. The Coulomb bubble instability is intimately related to the photon bubble instability. The bulk thermodynamic properties of both instability mechanisms are quite similar in that they require the timescale for heat to diffuse across a wavelength to be shorter than the corresponding wave crossing time. Furthermore, overstability occurs only as long as the driving resulting from the presence of the background heat flux can overcome diffusive Silk damping. However, the geometric and therefore mechanical properties of the Coulomb bubble instability are the complete mirror opposite of the photon bubble instability. The Coulomb bubble instability is most strongly driven for weakly magnetized atmospheres that are strongly convectively stable. We briefly discuss a possible application of astrophysical interest: diffusion of interstellar cosmic rays in the hot T ∼ 106 K Galactic corona. We show that for commonly accepted values of the cosmic-ray and gas pressure as well as its overall characteristic dimensions, the Galactic corona is in a marginal state of stability with respect to a cosmic-ray Coulomb bubble instability. The implication being that a cosmic-ray Coulomb bubble instability plays a role in regulating both the pressure and transport properties of interstellar cosmic rays, while serving as a source of acoustic power above the Galactic disk.

Photon Bubbles in the Circumstellar Envelopes of Young Massive Stars

We show that the optically-thick dusty envelopes surrounding young high-mass stars are subject to the photon bubble instability. The infrared radiation passing through the envelope amplifies magnetosonic disturbances, with growth rates in our local numerical radiation MHD calculations that are consistent with a linear analysis. Modes with wavelengths comparable to the gas pressure scale height grow by more than two orders of magnitude in a thousand years, reaching non-linear amplitudes within the envelope lifetime. If the magnetic pressure in the envelope exceeds the gas pressure, the instability develops into trains of propagating shocks. Radiation escapes readily through the low-density material between the shocks, enabling accretion to continue despite the Eddington limit imposed by the dust opacity. The supersonic motions arising from the photon bubble instability can help explain the large velocity dispersions of hot molecular cores, while conditions in the shocked gas are suitable for maser emission. We conclude that the photon bubble instability may play a key role in the formation of massive stars.

Spectral Features of Photon Bubble Models of Ultraluminous X-ray Sources

The nature of Ultraluminous X-ray Sources — Xray sources which exceed the Eddington luminosity for a ∼ 10M ⊙ black hole — remains a mystery. One possible explanation is an inhomogeneous accretion disk around a solar mass black hole where photon transport through radiation-pressure dominated “photon bubbles” can lead to super- Eddington accretion. While previous studies of this model have focused primarily on its radiation-hydrodynamics aspects, here we explore some observational implications of such a model with a Monte Carlo-Fokker Planck radiation transport code.

Source mergers and bubble growth during reionization

The recently introduced models of reionization bubbles based on extended Press-Schechter theory (Furlanetto, Zaldarriaga & Hernquist 2004) are generalized to include mergers of ionization sources. Sources with a recent major merger are taken to have enhanced photon production due to star formation, and accretion onto a central black hole if a black hole is present. This produces a scatter in the number of ionized photons corresponding to a halo of a given mass and a change in photon production over time for any given halo mass. Photon production histories, bubble distributions, and ionization histories are computed for several different parameter and recombination assumptions; the resulting distributions interpolate between previously calculated limiting cases.