Vertical structure and dynamics of a galactic disk

In this paper we present detailed models of the vertical structure (temperature and density) of passive irradiated circumstellar disks around T Tauri and Herbig Ae/Be stars. In contrast to earlier work, we use full frequency- and angle-dependent radiative transfer instead of the usual moment equations. We nd that this improvement of the radiative transfer has a strong influence on the resulting vertical structure of the disk, with dierences in temperature as large as 70%. However, the spectral energy distribution (SED) is only mildly aected by this change. In fact, the SED compares reasonably well with that of improved versions of the Chiang & Goldreich (CG) model. This shows that the latter is a reasonable model for the SED, in spite of its simplicity. It also shows that from the SED alone, little can be learned about the vertical structure of a passive circumstellar disk. The molecular line emission from these disks is more sensitive to the vertical temperature and density structure, and we show as an example how the intensity and proles of various CO lines depend on the adopted disk model. The models presented in this paper can also serve as the basis of theoretical studies of e.g. dust coagulation and settling in disks.

Similar to their low-mass counterparts, h igh-mass young stellar objects (HMYSOs) exhibit episodic accretion bursts. Understanding the physical mechanisms behind these bursts is crucial for elucidating the early stages of massive star formation and the evolution of disks around high-mass protostars This study aims to investigate the role of thermal instability in triggering accretion outbursts by developing a two-dimensional hydrodynamical model that fully resolves the vertical structure of the inner disk. Our goal is to provide a more realistic depiction of axially symmetric disk dynamics during these events and to assess the observable signatures of such bursts. We performed simulations of the inner 10 astronomical units of a circumstellar disk surrounding a high-mass protostar. The model we used incorporates heating from viscous dissipation and radiative transport in both the radial and vertical directions. Unlike previous one-dimensional studies, our two-dimensional axially symmetric study resolves the time-dependent vertical disk structure, capturing the complex interplay between radial and vertical dynamics within the disk. Our simulations reveal that thermal instability leads to significant changes in the disk structure. In the inner regions, steep temperature gradients and vigorous convective motions develop at the onset of outbursts, with gas flows differing between the midplane and the upper disk layers rather than following a purely one-dimensional pattern . The energy released during the burst is distributed gradually throughout the disk, producing outbursts with durations of 15–30 years and peak mass accretion rates in the range of $2-3 Although these bursts are observable, they are insufficiently bright, and their rise times and overall profiles differ from some of the more rapid events seen in observations. Notably, our models also do not produce the weaker “reflares” that sometimes occur atop stronger outbursts in one-dimensional thermal instability calculations. Resolving the full vertical structure of the disk is essential for accurately modeling thermal instability outbursts in high-mass young stellar objects. While thermal instability significantly influences episodic accretion, our results suggest that it appears insufficient on its own to explain the full range of observed outburst phenomena in HMYSOs. Additional mechanisms seem to be required to fully explain the diversity of observed burst phenomena. Future studies incorporating further physical processes are needed to develop a comprehensive understanding of episodic accretion in massive star formation.

Radiation from accretion discs in cataclysmic variable stars (CVs) provides fundamental information about the properties of these close binary systems and about the physics of accretion in general. The detailed diagnostics of accretion disc structure can be achieved by including in its description all the relevant heating and cooling physical mechanism, in particular the convective energy transport that, although dominant at temperatures less than about 10 000 K, is usually not taken into account when calculating spectra of accretion discs. We constructed a radiative transfer code coupled with a code determining the disc's hydrostatic vertical structure. We have obtained for the first time model spectra of cold, convective accretion discs. As expected, these spectra are mostly flat in the optical wavelengths with no contribution from the UV, which in quiescence must be emitted by the white dwarf. The disc structures obtained with our radiative-transfer code compare well with the solutions of equations used to describe the dwarf-nova outburst cycle according to the thermal-viscous disc instability model thus allowing the two to be combined. Our code allows calculating the spectral evolution of dwarf nova stars through their whole outburst cycle, providing a new tool for testing models of accretion discs in cataclysmic variables. We show that convection plays an important role in determining the vertical disc structure and substantially affects emitted spectra when, as often the case, it is effective at optical depths tau ~ 1. The emergent spectrum is independent of the parameters of the convection model.(Abstract shortened)

The structure and stability of the inner regions of accretion disks surrounding neutron stars and black holes have been studied. Within the framework of the α viscosity prescription for optically thick disks, we assume the viscous stress scales with gas pressure only, and the α parameter, which is less than or equal to unity, is formulated as α0(h/r)n, where h is the local scale height and n and α0 are constants. We neglect advective energy transport associated with radial motions and construct the vertical disk structures by assuming a Keplerian rotation law and local hydrostatic and thermal equilibrium. The vertical structures have been calculated with and without convective energy transport, and it is found that convection is important especially for mass accretion rates greater than about 0.1 times the Eddington value, ṀEdd. Although convective efficiency is low, convection does help to stabilize the disk. The results show that the disk can be locally unstable and that for n≳0.75, an S‐shaped relation can exist between Ṁ and the column density, Σ, at a given radius. The upper stable branch exists because of the saturation of α and the disk can be stabilized by this saturation for Ṁ≲ṀEdd.

view Abstract Citations (28) References (29) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Galactic spiral shocks - Vertical structure, thermal phase effects, and self-gravity Tubbs, A. D. Abstract By use of two-dimensional, time-dependent, hydrodynamical calculations, the steady-state vertical gas structure of galactic shocks has been determined. A variety of energy densities of gas, magnetic field, and relativistic cosmic rays was assumed. The midplane shock structure is remarkably similar to that found in one-dimensional calculations, with no significant decrease in shock strength and no sudden vertical motion of the postshock gas. The shocks are straight and nearly perpendicular to the galactic plane for almost any realistic galactic parameters. Two-phase calculations, utilizing a time-dependent model of the heating and cooling of the interstellar medium, show no evidence for so-called accretion fronts. The clouds or high-density regions which form in these calculations are shown to form only in the midplane of the galaxy. Publication: The Astrophysical Journal Pub Date: August 1980 DOI: 10.1086/158174 Bibcode: 1980ApJ...239..882T Keywords: Density Wave Model; Gravitational Effects; Interstellar Gas; Shock Waves; Spiral Galaxies; Stellar Motions; Temperature Effects; Disk Galaxies; Galactic Structure; Gas Density; Gas Heating; Gas Temperature; Isothermal Processes; Vertical Distribution; Astrophysics full text sources ADS |

view Abstract Citations (164) References (48) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The vertical structure and stability of alpha model accretion disks. Cannizzo, J. K. ; Wheeler, J. C. Abstract In order to understand the physical processes that determine the time-dependent characteristics of accretion disks, a parameter investigation is conducted of the vertically explicit structure corresponding to steady state, alpha-model thin disk accretion for accreting objects of 1 solar mass. Attention is given to the role of convection in the vertical structure and the location of critical points representing the onset of thermal instability, as well as optically thin conditions. It is shown that the temperature in quiescence is likely to be low for most of the matter, and scaling laws are presented for the fundamental properties of the vertically explicit models from which the time scales for various idealized phenomena are derived. The ordering of three disk time scales obtained should allow discrimination among different models. Publication: The Astrophysical Journal Supplement Series Pub Date: July 1984 DOI: 10.1086/190959 Bibcode: 1984ApJS...55..367C Keywords: Accretion Disks; Binary Stars; Stellar Mass Accretion; Stellar Structure; Variable Stars; X Ray Sources; Convection; Dwarf Novae; Opacity; Radiative Transfer; Stellar Luminosity; Stellar Models; Thermal Instability; Astrophysics full text sources ADS | data products SIMBAD (7)

Constraining the vertical and radial structure of debris discs is crucial to understanding their formation, evolution, and dynamics. To measure both the radial and vertical structure, a disc must be sufficiently inclined. However, if a disc is too close to edge-on, deprojecting its emission becomes non-trivial. In this paper we show how Frankenstein, a non-parametric tool to extract the radial brightness profile of circumstellar discs, can be used to deproject their emission at any inclination as long as they are optically thin and axisymmetric. Furthermore, we extend Frankenstein to account for the vertical thickness of an optically thin disc (H(r)) and show how it can be constrained by sampling its posterior probability distribution and assuming a functional form (e.g. constant h = H/r), while fitting the radial profile non-parametrically. We use this new method to determine the radial and vertical structures of 16 highly inclined debris discs observed by ALMA. We find a wide range of vertical aspect ratios, h, ranging from 0.020 ± 0.002 (AU Mic) to 0.20 ± 0.03 (HD 110058), which are consistent with parametric models. We find a tentative correlation between h and the disc fractional width, as expected if wide discs were more stirred. Assuming discs are self-stirred, the thinnest discs would require the presence of at least 500-km-sized planetesimals. The thickest discs would likely require the presence of planets. We also recover previously inferred and new radial structures, including a potential gap in the radial distribution of HD 61005. Finally, our new extension of Frankenstein also allows constraining how h varies as a function of radius, which we test on 49 Ceti, finding that h is consistent with being constant.

We investigate the vertical structure of the outer layers of accretion discs in which the local viscous energy dissipation rate scales with the pressure as for standard Shakura‐Sunyaev discs. It has been pointed out by several authors that a thermal instability occurs in the outer layers of such discs when the gas pressure drops below a certain value. When the density becomes too low thermal equilibrium can no longer be maintained and the gas heats up, forming a hot corona or possibly a wind. To assess the importance of this effect we estimate the pressure and temperature at which this instability will occur, where the instability point lies with respect to the total vertical disc structure, and whether the instability is likely to be important for the disc as a whole. The main difference between our work and earlier estimates lies in a more detailed treatment of the heating and cooling processes and the inclusion of the effects of an external radiation field. By solving for the accretion disc vertical structure using the grey two-stream approximation instead of the usual diffusion approximation for the radiative transfer, we first show that the thermal structure of the optically thin outer layers is in first approximation independent of radiative transfer effects, and follows the thermal equilibrium curve for optically thin plasmas in the pressure‐temperature plane. We then calculate the thermal structure using the detailed photoionization code mappings, which includes much more accurate heating and cooling physics than the mean opacity used in the vertical structure calculations. This approach also allows a straightforward inclusion of the effects of an external radiation field from the centre of the accretion flow. We apply our method to cataclysmic variable (CV) and stellar mass black hole discs, and show that evaporation due to the thermal instability can be important under a variety of conditions. In the case of CVs, radiative heating by photons emanating from the boundary layer can increase the evaporation rate significantly over the non-irradiated case, but for steady-state CV discs the evaporation by the mechanism considered here is still not sufficient to evaporate the entire disc. It may become important however in non-steady discs in dwarf novae if the accretion-heated white dwarf plays a role in irradiating the disc after an outburst. In the case of black hole soft X-ray transients, the evaporation can have a significant effect on the structure of the outer regions of the disc, resulting in mass loss rates comparable to the local mass accretion rate through the disc for _

Recent isolated galactic simulations show that the morphology of galactic discs in modified gravity differs from that of the standard dark matter model. In this study, we focused on the vertical structure of galactic discs and compared the bending instability in the vertical direction for both paradigms. To achieve this, we utilized high-resolution N-body simulations to construct two models in a specific non-local gravity theory (NLG) and the standard dark matter model and compared their stability against the bending perturbations. Our numerical results demonstrate that the outer regions of the disc are more susceptible to the instability in NLG, whereas the disc embedded in the dark matter halo is more unstable in the central regions. We then interpret these results based on the dispersion relation of the bending waves. To do so, we presented an analytical study to derive the dispersion relation in NLG. Our numerical results align with the predictions of our analytical models. Consequently, we conclude that the analysis of bending instability in galactic discs offers an explanation for the distinct vertical structures observed in simulated galactic discs under these two theories. These findings represent a significant step towards distinguishing between the modified gravity and dark matter models.

view Abstract Citations (290) References (25) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Vertical Structure of Accretion Disks: A Simplified Analytical Model Hubeny, I. Abstract A simplified model of the vertical structure of accretion disks is derived. Analytical expressions for the temperature and density structure, which represent a generalization of the gray model long known in the theory of classical stellar atmospheres, are presented. The formalism naturally explains similarities and differences between the structure of a disk and a stellar atmosphere. In particular, the influence of viscous dissipation and external irradiation of the disk by the central star, as well as of the finite optical thickness of the disk, may be easily accounted for and explained by the present model. Publication: The Astrophysical Journal Pub Date: March 1990 DOI: 10.1086/168501 Bibcode: 1990ApJ...351..632H Keywords: Accretion Disks; Astronomical Models; Gray Gas; Stellar Atmospheres; Stellar Mass Accretion; Hydrostatics; Irradiation; Optical Thickness; Thermodynamic Equilibrium; Vertical Distribution; Viscous Damping; Astrophysics; RADIATIVE TRANSFER; STARS: ACCRETION; STARS: ATMOSPHERES full text sources ADS |

Radial structure of accretion discs around compact objects is often described using analytic approximations which are derived from averaging or integrating vertical structure equations. For non-solar chemical composition, partial ionization, or for supermassive black holes, this approach is not accurate. Additionally, radial extension of ‘analytically-described’ disc zones is not evident in many cases. We calculate vertical structure of accretion discs around compact objects, with and without external irradiation, with radiative and convective energy transport taken into account. For this, we introduce a new open Python code, allowing different equations of state and opacity laws, including tabular values. As a result, radial structure and stability ‘S-curves’ are calculated for specific disc parameters and chemical composition. In particular, based on more accurate power-law approximations for opacity in the disc, we supply new analytic formulas for the farthest regions of the hot disc around stellar-mass object. On calculating vertical structure of a self-irradiated disc, we calculate a self-consistent value of the irradiation parameter Cirr for stationary α-disc. We find that, for a fixed shape of the X-ray spectrum, Cirr depends weakly on the accretion rate but changes with radius, and the dependence is driven by the conditions in the photosphere and disc opening angle. The hot zone extent depends on the ratio between irradiating and intrinsic flux: corresponding relation for $T_{\rm irr,\, crit}$ is obtained.

view Abstract Citations (47) References (11) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Vertical Structure of T Tauri Accretion Disks. I. Heating by the Central Star Malbet, Fabien ; Bertout, Claude Abstract The paper presents the LTE formal solution for the vertical atmospheric temperature structure of an accretion disk illuminated by its central star. It is shown that there are two consequences of irradiation: (1) heating of the photospheric layers resulting in continuum radiation, and (2) heating of the optically thin layers resulting in a chromosphericlike temperature increase that may produce disk emission lines in these regions. These results are illustrated by computing the gray vertical temperature structure of a flat accretion disk. Because of the emergent intensity's anisotropy, the observed disk temperature distribution depends on the disk's view angle. Publication: The Astrophysical Journal Pub Date: December 1991 DOI: 10.1086/170839 Bibcode: 1991ApJ...383..814M Keywords: Accretion Disks; Radiative Transfer; Stellar Temperature; T Tauri Stars; Computational Astrophysics; Stellar Atmospheres; Stellar Luminosity; Astrophysics; RADIATIVE TRANSFER; STARS: ACCRETION; STARS: PRE--MAIN-SEQUENCE full text sources ADS | Related Materials (3) Part 2: 2001A&A...379..515M Part 3: 2003A&A...400..185L Part 4: 2004A&A...422..171L

The structure of protosolar accretion disk

The structure and stability of the inner regions of accretion disks surrounding neutron stars and black holes have been investigated. Within the framework of the alpha viscosity prescription for optically thick disks, we assume the viscous stress scales with gas pressure only, and the alpha parameter, which is less than or equal to unity, is formulated as alpha(sub 0)(h/r)(exp n), where h is the local scale height and n and alpha(sub 0) are constants. We neglect advective energy transport associated with radial motions and construct the vertical structure of the disks by assuming a Keplerian rotation law and local hydrostatic and thermal equilibrium. The vertical structures have been calculated with and without convective energy transport, and it has been demonstrated that convection is important especially for mass accretion rates, M-dot, greater than about 0.1 times the Eddington value, M-dot(sub Edd). Although the efficiency of convection is not high, convection significantly modifies the vertical structure of the disk (as compared with a purely radiative model) and leads to lower temperatures at a given M-dot. The results show that the disk can be locally unstable and that for n greater than or = 0.75, an S-shaped relation can exist between M-dot and the column density, sigma, at a given radius. While the lower stable branch (derivative of M-dot/derivative of sigma greater than 0) and middle unstable branch (derivative of M-dot/derivative of sigma less than 0) represent structures for which the gas and radiation pressure dominate respectively, the stable upper branch (derivative of M-dot/derivative of sigma greater than 0) is a consequence of the saturation of alpha. This saturation of alpha can occur for large alpha(sub 0) and at M-dot less than or = M-dot(sub Edd). The instability is found to occur at higher mass accretion rates for neutron stars than for black holes. In particular, the disk is locally unstable for M-dot greater than or = 0.5 M-dot(sub Edd) for neutron stars and for M-dot greater than or = M-dot(sub Edd) for black holes for a viscosity prescription characterized by n = 1 and alpha(sub 0) = 10.

We investigate the dynamics of the accretion disks of young stars with fossil large-scale magnetic field. The author’s magnetohydrodynamic (MHD) model of the accretion disks is generalized to take into account the dynamical influence of the magnetic field on gas rotation speed and vertical structure of the disks. With the help of the developed MHD model, the structure of an accretion disk of a solar mass T Tauri star is simulated for different accretion rates $$\dot {M}$$ and dust grain sizes $${{a}_{d}}$$ . The simulations of the radial structure of the disk show that the magnetic field in the disk is kinematic, and the electromagnetic force does not affect the rotation speed of the gas for typical values $$\dot {M} = {{10}^{{ - 8}}}$$ $${{M}_{ \odot }}$$ /yr and $${{a}_{d}} = 0.1$$ µm. In the case of large dust grains, $${{a}_{d}} \geqslant 1$$ mm, the magnetic field is frozen into the gas and a dynamically strong magnetic field is generated at radial distances from the star $$r \gtrsim 30$$ AU, the tensions of which slow down the rotation speed by $$ \lesssim {\kern 1pt} 1.5$$ % of the Keplerian velocity. This effect is comparable to the contribution of the radial gradient of gas pressure and can lead to the increase in the radial drift velocity of dust grains in the accretion disks. In the case of high accretion rate, $$\dot {M} \geqslant $$ 10–7 $${{M}_{ \odot }}$$ /yr, the magnetic field is also dynamically strong in the inner region of the disk, $$r < $$ 0.2 AU. The simulations of the vertical structure of the disk show that, depending on the conditions on the surface of the disk, the vertical gradient of magnetic pressure can lead to both decrease and increase in the characteristic thickness of the disk as compared to the hydrostatic one by 5–20%. The change in the thickness of the disk occurs outside the region of low ionization fraction and effective magnetic diffusion (“dead” zone), which extends from $$r = 0.3$$ to 20 AU.