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We present new analytical solutions for the evolution of protoplanetary discs (PPDs) where magnetohydrodynamic (MHD) wind-driven processes dominate. Our study uses a 1D model which incorporates equations detailing angular momentum extraction by MHD winds and mass-loss rates. Our solutions demonstrate that the disc retains its initial state during the early phases; however, it rapidly evolves towards a self-similar state in the later stages of disc evolution. The total disc mass undergoes a continuous decline over time, with a particularly rapid reduction occurring beyond a certain critical time threshold. This gradual decrease in mass is influenced by the wind parameters and the initial surface density of the disc. In the MHD wind-dominated regime, we show that the disc's lifespan correlates positively with the magnetic lever arm up to a certain threshold, irrespective of the initial disc size. PPDs with a larger magnetic lever arm are found to maintain significantly higher total disc mass over extended periods compared to their counterparts. The mass ejection-to-accretion ratio increases in efficient wind scenarios and is further amplified by a steeper initial surface density profile. Our analysis also reveals varied evolutionary trajectories in the plane of accretion rate and total disc mass, influenced by magnetic parameters and initial disc size. In scenarios with efficient MHD winds, discs with bigger sizes have extended operation time for mechanisms governing planet formation., Comment: 10 pages, 8 figures, Accepted for publication in MNRAS

Recent numerical simulations of magnetized accretion discs show that the radial-azimuthal component of the stress tensor due to the magnetorotational instability (MRI) is well represented by a power-law function of the gas pressure rather than a linear relation which has been used in most of the accretion disc studies. The exponent of this power-law function which depends on the net flux of the imposed magnetic field is reported in the range between zero and unity. However, the physical consequences of this power-law stress-pressure relation within the framework of the standard disc model have not been explored so far. In this study, the structure of an accretion disc with a power-law stress-pressure relation is studied using analytical solutions in the steady-state and time-dependent cases. The derived solutions are applicable to different accreting systems, and as an illustrative example, we explore structure of protoplanetary discs using these solutions. We show that the slopes of the radial surface density and temperature distributions become steeper with decreasing the stress exponent. However, if the disc opacity is dominated by icy grains and value of the stress exponent is less than about $0.5$, the surface density and temperature profiles become so steep that make them unreliable. We also obtain analytical solutions for the protoplanetary discs which are irradiated by the host star. Using these solutions, we find that the effect of the irradiation becomes more significant with decreasing the stress exponent., Comment: Accepted for publication in MNRAS

We present an analytical model to investigate the production of pebbles and their radial transport through a protoplanetary disk (PPD) with magnetically driven winds. While most of the previous analytical studies in this context assume that the radial turbulent coefficient is equal to the vertical dust diffusion coefficient, in the light of the results of recent numerical simulations, we relax this assumption by adopting effective parametrisations of the turbulent coefficients involved in terms of the strength of the magnetic fields driving the wind. Theoretical studies have already pointed out that even in the absence of winds, these coefficients are not necessarily equal, though its consequences regarding pebble production have not been explored. In this paper, we investigate the evolution of the pebble production line, the radial mass flux of the pebbles and their corresponding surface density as a function of the plasma parameter at the disk midplane. Our analysis explicitly demonstrates that the presence of magnetically-driven winds in a PPD leads to considerable reduction of the rate and duration of the pebble delivery. We show that when the wind is strong, the core growth in mass due to the pebble accretion is so slow that it is unlikely that a core could reach a pebble isolation mass during a PPD lifetime. When the mass of a core reaches this critical value, pebble accretion is halted due to core-driven perturbations in the gas. With decreasing wind strength, however, pebble accretion may, in a shorter time, increase the mass of a core to the pebble isolation mass., Comment: 15 pages, accepted for publication in ApJ

We present a new set of analytical solutions to model the steady state structure of a protoplanetary disc with a magnetically-driven wind. Our model implements a parametrization of the stresses involved and the wind launching mechanism in terms of the plasma parameter at the disc midplane, as suggested by the results of recent, local MHD simulations. When wind mass-loss is accounted for, we find that its rate significantly reduces the disc surface density, particularly in the inner disc region. We also find that models that include wind mass-loss lead to thinner dust layers. As an astrophysical application of our models, we address the case of HL Tau, whose disc exhibits a high accretion rate and efficient dust settling at its midplane. These two observational features are not easy to reconcile with conventional accretion disc theory, where the level of turbulence needed to explain the high accretion rate would prevent a thin dust layer. Our disc model that incorporates both mass-loss and angular momentum removal by a wind is able to account for HL Tau observational constraints concerning its high accretion rate and dust layer thinness., Comment: Accepted for publication in MNRAS, 13 pages, 8 figures

Recent numerical simulations of magnetized accretion discs show that the radial-azimuthal component of the stress tensor due to the magnetorotational instability (MRI) is well represented by a power-law function of the gas pressure rather than a linear relation which has been used in most of the accretion disc studies. The exponent of this power-law function which depends on the net flux of the imposed magnetic field is reported in the range between zero and unity. However, the physical consequences of this power-law stress-pressure relation within the framework of the standard disc model have not been explored so far. In this study, the structure of an accretion disc with a power-law stress-pressure relation is studied using analytical solutions in the steady-state and time-dependent cases. The derived solutions are applicable to different accreting systems, and as an illustrative example, we explore structure of protoplanetary discs using these solutions. We show that the slopes of the radial surface density and temperature distributions become steeper with decreasing the stress exponent. However, if the disc opacity is dominated by icy grains and value of the stress exponent is less than about $0.5$, the surface density and temperature profiles become so steep that make them unreliable. We also obtain analytical solutions for the protoplanetary discs which are irradiated by the host star. Using these solutions, we find that the effect of the irradiation becomes more significant with decreasing the stress exponent., Comment: Accepted for publication in MNRAS

We present an analytical model to investigate the production of pebbles and their radial transport through a protoplanetary disk (PPD) with magnetically driven winds. While most of the previous analytical studies in this context assume that the radial turbulent coefficient is equal to the vertical dust diffusion coefficient, in the light of the results of recent numerical simulations, we relax this assumption by adopting effective parametrisations of the turbulent coefficients involved in terms of the strength of the magnetic fields driving the wind. Theoretical studies have already pointed out that even in the absence of winds, these coefficients are not necessarily equal, though its consequences regarding pebble production have not been explored. In this paper, we investigate the evolution of the pebble production line, the radial mass flux of the pebbles and their corresponding surface density as a function of the plasma parameter at the disk midplane. Our analysis explicitly demonstrates that the presence of magnetically-driven winds in a PPD leads to considerable reduction of the rate and duration of the pebble delivery. We show that when the wind is strong, the core growth in mass due to the pebble accretion is so slow that it is unlikely that a core could reach a pebble isolation mass during a PPD lifetime. When the mass of a core reaches this critical value, pebble accretion is halted due to core-driven perturbations in the gas. With decreasing wind strength, however, pebble accretion may, in a shorter time, increase the mass of a core to the pebble isolation mass., Comment: 15 pages, accepted for publication in ApJ

We present a new set of analytical solutions to model the steady state structure of a protoplanetary disc with a magnetically-driven wind. Our model implements a parametrization of the stresses involved and the wind launching mechanism in terms of the plasma parameter at the disc midplane, as suggested by the results of recent, local MHD simulations. When wind mass-loss is accounted for, we find that its rate significantly reduces the disc surface density, particularly in the inner disc region. We also find that models that include wind mass-loss lead to thinner dust layers. As an astrophysical application of our models, we address the case of HL Tau, whose disc exhibits a high accretion rate and efficient dust settling at its midplane. These two observational features are not easy to reconcile with conventional accretion disc theory, where the level of turbulence needed to explain the high accretion rate would prevent a thin dust layer. Our disc model that incorporates both mass-loss and angular momentum removal by a wind is able to account for HL Tau observational constraints concerning its high accretion rate and dust layer thinness., Comment: Accepted for publication in MNRAS, 13 pages, 8 figures

We obtain a new set of analytical solutions for the evolution of a self-gravitating accretion disc by holding the Toomre parameter close to its threshold, and obtaining the stress parameter from the cooling rate. In agreement with the previous numerical solutions, furthermore, the accretion rate is assumed to be independent of the disc radius. Extreme situations where the entire disc is either optically thick or optically thin are studied independently and the obtained solutions can be used for exploring the early or the final phases of a protoplanetary disc evolution. Our solutions exhibit decay of the accretion rate as a power-law function of the age of the system with the exponent -0.75 and -1.04 for optically thick and thin cases, respectively. Our calculations permit us to explore evolution of the snow line analytically. Location of the snow line in the optically thick regime evolves as a power-law function of time with the exponent -0.16, however, when the disc is optically thin, location of the snow line as a function of time with the exponent -0.7 has a stronger dependence on time. It means that in an optically thin disc inward migration of the snow line is faster than an optically thick disc., Comment: 9 pages, accepted for publication in ApJ

We obtain a new set of analytical solutions for the evolution of a self-gravitating accretion disc by holding the Toomre parameter close to its threshold, and obtaining the stress parameter from the cooling rate. In agreement with the previous numerical solutions, furthermore, the accretion rate is assumed to be independent of the disc radius. Extreme situations where the entire disc is either optically thick or optically thin are studied independently and the obtained solutions can be used for exploring the early or the final phases of a protoplanetary disc evolution. Our solutions exhibit decay of the accretion rate as a power-law function of the age of the system with the exponent -0.75 and -1.04 for optically thick and thin cases, respectively. Our calculations permit us to explore evolution of the snow line analytically. Location of the snow line in the optically thick regime evolves as a power-law function of time with the exponent -0.16, however, when the disc is optically thin, location of the snow line as a function of time with the exponent -0.7 has a stronger dependence on time. It means that in an optically thin disc inward migration of the snow line is faster than an optically thick disc., Comment: 9 pages, accepted for publication in ApJ

Self-gravitating accretion discs in a gravitoturbulent state, including radiation and gas pressures, are studied using a set of new analytical solutions. While the Toomre parameter of the disc remains close to its critical value for the onset of gravitational instability, the dimensionless stress parameter is uniquely determined from the thermal energy reservoir of the disc and its cooling rate. Our solutions are applicable to the accretion discs with dynamically important radiation pressure like in the quasars discs. We show that physical quantities of a gravitoturbulent disc in the presence of radiation are significantly modified compared to solutions with only gas pressure. We show that the dimensionless stress parameter is an increasing function of the radial distance so that its steepness strongly depends on the accretion rate. In a disc without radiation its slope is 4.5, however, we show that in the presence of radiation, it varies between 2 and 4.5 depending on the accretion rate and the central mass. As for the surface density, we find a shallower profile with an exponent -2 in a disc with sub-Eddington accretion rate compared to a similar disc, but without radiation, where its surface density slope is -3 independent of the accretion rate. We then investigate gravitational stability of the disc when the stress parameter reaches to its critical value. In order to self-consistently determine the fragmentation boundary, however, it is shown that the critical value of the stress parameter is a power-law function of the ratio of gas pressure and the total pressure and its exponent is around 1.7. We also estimate the maximum mass of the central black hole using our analytical solutions., Comment: Accepted for publication in MNRAS

We investigate orbital motion of cold clouds in the broad line region of active galactic nuclei subject to the gravity of a black hole and a force due to a nonisotropic central source and a drag force proportional to the velocity square. The intercloud is described using the standard solutions for the advection-dominated accretion flows. Orbit of a cloud decays because of the drag force, but the typical time scale of falling of clouds onto the central black hole is shorter comparing to the linear drag case. This time scale is calculated when a cloud is moving through a static or rotating intercloud. We show that when the drag force is a quadratic function of the velocity, irrespective of the initial conditions and other input parameters, clouds will generally fall onto the central region much faster than the age of whole system and since cold clouds present in most of the broad line regions, we suggest that mechanisms for continuous creation of the clouds must operate in these systems., Comment: Accepted for publication in ApJ

Self-gravitating accretion discs in a gravitoturbulent state, including radiation and gas pressures, are studied using a set of new analytical solutions. While the Toomre parameter of the disc remains close to its critical value for the onset of gravitational instability, the dimensionless stress parameter is uniquely determined from the thermal energy reservoir of the disc and its cooling rate. Our solutions are applicable to the accretion discs with dynamically important radiation pressure like in the quasars discs. We show that physical quantities of a gravitoturbulent disc in the presence of radiation are significantly modified compared to solutions with only gas pressure. We show that the dimensionless stress parameter is an increasing function of the radial distance so that its steepness strongly depends on the accretion rate. In a disc without radiation its slope is 4.5, however, we show that in the presence of radiation, it varies between 2 and 4.5 depending on the accretion rate and the central mass. As for the surface density, we find a shallower profile with an exponent -2 in a disc with sub-Eddington accretion rate compared to a similar disc, but without radiation, where its surface density slope is -3 independent of the accretion rate. We then investigate gravitational stability of the disc when the stress parameter reaches to its critical value. In order to self-consistently determine the fragmentation boundary, however, it is shown that the critical value of the stress parameter is a power-law function of the ratio of gas pressure and the total pressure and its exponent is around 1.7. We also estimate the maximum mass of the central black hole using our analytical solutions., Comment: Accepted for publication in MNRAS

We investigate orbital motion of cold clouds in the broad line region of active galactic nuclei subject to the gravity of a black hole and a force due to a nonisotropic central source and a drag force proportional to the velocity square. The intercloud is described using the standard solutions for the advection-dominated accretion flows. Orbit of a cloud decays because of the drag force, but the typical time scale of falling of clouds onto the central black hole is shorter comparing to the linear drag case. This time scale is calculated when a cloud is moving through a static or rotating intercloud. We show that when the drag force is a quadratic function of the velocity, irrespective of the initial conditions and other input parameters, clouds will generally fall onto the central region much faster than the age of whole system and since cold clouds present in most of the broad line regions, we suggest that mechanisms for continuous creation of the clouds must operate in these systems., Comment: Accepted for publication in ApJ

We investigate effects of a global magnetic field on the dynamics of an ensemble of clumps within a magnetized advection-dominated accretion flow by neglecting interactions between the clumps and then solving the collisionless Boltzman equation. In the strong-coupling limit, in which the averaged radial and the rotational velocities of the clumps follow the ADAF dynamics, the averaged radial velocity square of the clumps is calculated analytically for different magnetic field configurations. The value of the averaged radial velocity square of the clumps increases with increasing the strength of the radial or vertical components of the magnetic field. But a purely toroidal magnetic field geometry leads to a reduction of the value of the averaged radial velocity square of the clumps at the inner parts with increasing the strength of this component. Moreover, dynamics of the clumps strongly depends on the amount of the advected energy so that the value of the averaged radial velocity square of the clumps increases in the presence of a global magnetic field as the flow becomes more advective., Comment: Accepted for publication in RAA

We investigate effects of a global magnetic field on the dynamics of an ensemble of clumps within a magnetized advection-dominated accretion flow by neglecting interactions between the clumps and then solving the collisionless Boltzman equation. In the strong-coupling limit, in which the averaged radial and the rotational velocities of the clumps follow the ADAF dynamics, the averaged radial velocity square of the clumps is calculated analytically for different magnetic field configurations. The value of the averaged radial velocity square of the clumps increases with increasing the strength of the radial or vertical components of the magnetic field. But a purely toroidal magnetic field geometry leads to a reduction of the value of the averaged radial velocity square of the clumps at the inner parts with increasing the strength of this component. Moreover, dynamics of the clumps strongly depends on the amount of the advected energy so that the value of the averaged radial velocity square of the clumps increases in the presence of a global magnetic field as the flow becomes more advective., Comment: Accepted for publication in RAA

Position of the ice line in a circumbinary disc is determined using a simplified and illustrative model. Main sources of the heat in the energy balance of the disc, i.e. heating by the turbulence, irradiation by the components of the binary and the tidal heating are considered. Our goal is to clarify role of the tidal heating in the position of the ice line. When viscous heating and irradiation of the binary are considered, ice line lies interior to the inner radius of the disc in most of the binaries represented by our parameter survey. But tidal heating significantly extends position of the ice line to a larger radius, so that a smaller fraction of the circumbinaries' population may have ice lines interior to the inner radius of the disc., Comment: Accepted for publication in MNRAS

We investigate orbital motion of spherical, pressure-confined clouds in the broad-line region (BLR) of active galactic nuclei (AGN). The combined influence of gravity of the central object and the non-isotropic radiation of the central source are taking into account. While most of the previous studies assume that the pressure of the intercloud gaseous component is proportional to a power-law function of the radial coordinate, we generalize it to a case where the external pressure depends on both the radial distance and the latitudinal angle. Our prescribed pressure profile determines the radius and the column density of BLR clouds as a function of their location. We also discuss about stability of the orbits and a condition for the existence of bound orbits is obtained. We found that BLR clouds tend to populate the equatorial regions more than other parts simply because of the stability considerations. Although this finding is obtained for a particular pressure profile, we think, this result is valid as long as the pressure distribution of the intercloud medium decreases from the equator to the pole., Comment: Accepted for publication in MNRAS

Dynamics of clumps within a magnetized advection dominated accretion flow is investigated by solving the collisionless Boltzmann equation and considering the drag force due to the relative velocity between the clumps and the gas. Toroidal component of the magnetic field is assumed to be dominant. Dynamical properties of the hot gaseous component such as the radial and the rotational velocities are affected by the magnetic effects, and so, drag force varies depending on the strength of magnetic field and the velocity dispersion of the clumps is then modified significantly. We show that when magnetic pressure is less than the gas pressure, the root of the averaged radial velocity square of the clumps decreases at the inner parts of the hot flow and increases slightly at its outer edge., Comment: 6 pages, Accepted for publication in MNRAS

Position of the ice line in a circumbinary disc is determined using a simplified and illustrative model. Main sources of the heat in the energy balance of the disc, i.e. heating by the turbulence, irradiation by the components of the binary and the tidal heating are considered. Our goal is to clarify role of the tidal heating in the position of the ice line. When viscous heating and irradiation of the binary are considered, ice line lies interior to the inner radius of the disc in most of the binaries represented by our parameter survey. But tidal heating significantly extends position of the ice line to a larger radius, so that a smaller fraction of the circumbinaries' population may have ice lines interior to the inner radius of the disc., Comment: Accepted for publication in MNRAS

We investigate orbital motion of spherical, pressure-confined clouds in the broad-line region (BLR) of active galactic nuclei (AGN). The combined influence of gravity of the central object and the non-isotropic radiation of the central source are taking into account. While most of the previous studies assume that the pressure of the intercloud gaseous component is proportional to a power-law function of the radial coordinate, we generalize it to a case where the external pressure depends on both the radial distance and the latitudinal angle. Our prescribed pressure profile determines the radius and the column density of BLR clouds as a function of their location. We also discuss about stability of the orbits and a condition for the existence of bound orbits is obtained. We found that BLR clouds tend to populate the equatorial regions more than other parts simply because of the stability considerations. Although this finding is obtained for a particular pressure profile, we think, this result is valid as long as the pressure distribution of the intercloud medium decreases from the equator to the pole., Comment: Accepted for publication in MNRAS

Dynamics of clumps within a magnetized advection dominated accretion flow is investigated by solving the collisionless Boltzmann equation and considering the drag force due to the relative velocity between the clumps and the gas. Toroidal component of the magnetic field is assumed to be dominant. Dynamical properties of the hot gaseous component such as the radial and the rotational velocities are affected by the magnetic effects, and so, drag force varies depending on the strength of magnetic field and the velocity dispersion of the clumps is then modified significantly. We show that when magnetic pressure is less than the gas pressure, the root of the averaged radial velocity square of the clumps decreases at the inner parts of the hot flow and increases slightly at its outer edge., Comment: 6 pages, Accepted for publication in MNRAS

Steady-state advective accretion flows in the presence of thermal conduction are studied. All three components of velocity in a spherical coordinates are considered and the flow displays both inflowing and outflowing regions according to our similarity solutions. Thermal conductivity provides latitudinal energy transport and so, the flow rotates more slowly and becomes hotter with increasing thermal conductivity coefficient. We also show that opening angle of the outflow region decreases as thermal conduction becomes stronger., Comment: 6 pages, 4 figures, accepted for publication in MNRAS

Steady-state advective accretion flows in the presence of thermal conduction are studied. All three components of velocity in a spherical coordinates are considered and the flow displays both inflowing and outflowing regions according to our similarity solutions. Thermal conductivity provides latitudinal energy transport and so, the flow rotates more slowly and becomes hotter with increasing thermal conductivity coefficient. We also show that opening angle of the outflow region decreases as thermal conduction becomes stronger., Comment: 6 pages, 4 figures, accepted for publication in MNRAS

When a gravitating point mass moves subsonically through a magnetized and isothermal medium, the dynamical structure of the flow is studied far from the mass using a perturbation analysis. Analytical solutions for the first-order density and the velocity perturbations are presented. Validity of our solutions is restricted to the cases where the Alfven velocity in the ambient medium is less than the accretor's velocity. The density field is less dense because of the magnetic effects according to the solutions and the dynamical friction force becomes lower as the strength of the magnetic field increases., Comment: Accepted for publication in MNRAS

When a gravitating object moves across a given mass distribution, it creates an overdense wake behind it. Here, we performed an analytical study of the structure of the flow far from object when the flow is isentropic and the object moves subsonically within it. We show that the dynamical friction force is the main drag force on the object and by using a perturbation theory, we obtain the density, velocity and pressure of the perturbed flow far from the mass. We derive the expression of the dynamical friction force in an isentropic flow and show its dependence on the Mach number of the flow and on the adiabatic index. We find that the dynamical friction force becomes lower as the adiabatic index increases. We show analytically that the wakes are less dense in our isentropic case in comparison to the isothermal ones., Comment: Accepted for publication in Astrophysics and Space Science

When a gravitating point mass moves subsonically through a magnetized and isothermal medium, the dynamical structure of the flow is studied far from the mass using a perturbation analysis. Analytical solutions for the first-order density and the velocity perturbations are presented. Validity of our solutions is restricted to the cases where the Alfven velocity in the ambient medium is less than the accretor's velocity. The density field is less dense because of the magnetic effects according to the solutions and the dynamical friction force becomes lower as the strength of the magnetic field increases., Comment: Accepted for publication in MNRAS

When a gravitating object moves across a given mass distribution, it creates an overdense wake behind it. Here, we performed an analytical study of the structure of the flow far from object when the flow is isentropic and the object moves subsonically within it. We show that the dynamical friction force is the main drag force on the object and by using a perturbation theory, we obtain the density, velocity and pressure of the perturbed flow far from the mass. We derive the expression of the dynamical friction force in an isentropic flow and show its dependence on the Mach number of the flow and on the adiabatic index. We find that the dynamical friction force becomes lower as the adiabatic index increases. We show analytically that the wakes are less dense in our isentropic case in comparison to the isothermal ones., Comment: Accepted for publication in Astrophysics and Space Science

Gravitational stability of a disc consisting of the gaseous and the stellar components are studied in the linear regime when the gaseous component is turbulent. A phenomenological approach is adopted to describe the turbulence, in which not only the effective surface density but the velocity dispersion of the gaseous component are both scale-dependent as power-law functions of the wavenumber of the perturbations. Also, the stellar component which has gravitational interaction with the gas is considered as a fluid. We calculate growth rate of the perturbations and in the most of the studied cases, the stability of the disc highly depends on the existence of the stars and the exponents of the functions for describing the turbulence. Our analysis suggests that the conventional gas and star threshold is not adequate for analyzing stability of the two-component discs when turbulence is considered., Comment: 7 pages, Accepted for publication in MNRAS

We present a linear perturbation analysis of the magnetorotational instability in the presence of the cosmic rays. Dynamical effects of the cosmic rays are considered by a fluid description and the diffusion of cosmic rays is only along the magnetic field lines. We show an enhancement in the growth rate of the unstable mode because of the existence of cosmic rays. But as the diffusion of cosmic rays increases, we see that the growth rate decreases. Thus, cosmic rays have a destabilizing role in the magnetorotational instability of the accretion discs., Comment: Accepted for publication in Astrophysics & Space Science

Gravitational stability of a disc consisting of the gaseous and the stellar components are studied in the linear regime when the gaseous component is turbulent. A phenomenological approach is adopted to describe the turbulence, in which not only the effective surface density but the velocity dispersion of the gaseous component are both scale-dependent as power-law functions of the wavenumber of the perturbations. Also, the stellar component which has gravitational interaction with the gas is considered as a fluid. We calculate growth rate of the perturbations and in the most of the studied cases, the stability of the disc highly depends on the existence of the stars and the exponents of the functions for describing the turbulence. Our analysis suggests that the conventional gas and star threshold is not adequate for analyzing stability of the two-component discs when turbulence is considered., Comment: 7 pages, Accepted for publication in MNRAS

We present a linear perturbation analysis of the magnetorotational instability in the presence of the cosmic rays. Dynamical effects of the cosmic rays are considered by a fluid description and the diffusion of cosmic rays is only along the magnetic field lines. We show an enhancement in the growth rate of the unstable mode because of the existence of cosmic rays. But as the diffusion of cosmic rays increases, we see that the growth rate decreases. Thus, cosmic rays have a destabilizing role in the magnetorotational instability of the accretion discs., Comment: Accepted for publication in Astrophysics & Space Science

(abridged) We develop a model which describes the coevolution of the mass function of dense cores and of the IMF in a protocluster clump. In the model, cores injected in the clump evolve under the effect of gas accretion. Accretion onto the cores follows a time-dependent accretion rate that describes accretion in a turbulent medium. Once the accretion timescales of cores exceed their contraction timescales, they are turned into stars. We include the effect of feedback by the newly formed massive stars through their stellar winds. A fraction of the wind's energy is assumed to counter gravity and disperse the gas from the protocluster and as a consequence, quench further star formation. The latter effect sets the final IMF of the cluster. We apply our model to a clump that is expected to resemble the progenitor clump of the Orion Nebula Cluster (ONC). Our model is able to reproduce both the shape and normalization of the ONC's IMF and the mass function of dense cores in Orion. The complex features of the ONC's IMF,i.e., a shallow slope in the mass range ~0.3-2.5 Msol,a steeper slope in the mass range ~2.5-12 Msol, and a nearly flat tail at the high mass end are reproduced. The model predicts a 'rapid' star formation process with an age spread for the stars of 2.3 10^5 yr which is consistent with the fact that 80% of the ONC's stars have ages of <=0.3 Myr. The model predicts a primordial mass segregation with the most massive stars being born in the region between 2-4 times the core radius of the cluster. In parallel, the model also reproduces, simultaneously, the mass function of dense cores in Orion. We study the effects of varying the model parameters on the resulting IMF and show that the IMF of stellar clusters is expected to show significant variations, provided variations in the clumps and cores properties exist., Comment: accepted to MNRAS. 22 pages, 17 figures. 2 new sections added to better present the model parameters and compare to previous work. Some figures are now better presented. Main conclusions unchanged

(abridged) We develop a model which describes the coevolution of the mass function of dense cores and of the IMF in a protocluster clump. In the model, cores injected in the clump evolve under the effect of gas accretion. Accretion onto the cores follows a time-dependent accretion rate that describes accretion in a turbulent medium. Once the accretion timescales of cores exceed their contraction timescales, they are turned into stars. We include the effect of feedback by the newly formed massive stars through their stellar winds. A fraction of the wind's energy is assumed to counter gravity and disperse the gas from the protocluster and as a consequence, quench further star formation. The latter effect sets the final IMF of the cluster. We apply our model to a clump that is expected to resemble the progenitor clump of the Orion Nebula Cluster (ONC). Our model is able to reproduce both the shape and normalization of the ONC's IMF and the mass function of dense cores in Orion. The complex features of the ONC's IMF,i.e., a shallow slope in the mass range ~0.3-2.5 Msol,a steeper slope in the mass range ~2.5-12 Msol, and a nearly flat tail at the high mass end are reproduced. The model predicts a 'rapid' star formation process with an age spread for the stars of 2.3 10^5 yr which is consistent with the fact that 80% of the ONC's stars have ages of <=0.3 Myr. The model predicts a primordial mass segregation with the most massive stars being born in the region between 2-4 times the core radius of the cluster. In parallel, the model also reproduces, simultaneously, the mass function of dense cores in Orion. We study the effects of varying the model parameters on the resulting IMF and show that the IMF of stellar clusters is expected to show significant variations, provided variations in the clumps and cores properties exist., Comment: accepted to MNRAS. 22 pages, 17 figures. 2 new sections added to better present the model parameters and compare to previous work. Some figures are now better presented. Main conclusions unchanged

We study the effects of outflow/wind on the gravitational stability of accretion discs around supermassive black holes using a set of analytical steady-state solutions. Mass-loss rate by the outflow from the disc is assumed to be a power-law of the radial distance and the amount of the energy and the angular momentum which are carried away by the wind are parameterized phenomenologically. We show that the mass of the first clumps at the self-gravitating radius linearly decreases with the total mass-loss rate of the outflow. Except for the case of small viscosity and high accretion rate, generally, the self-gravitating radius increases as the amount of mass-loss by the outflow increases. Our solutions show that as more angular momentum is lost by the outflow, then reduction to the mass of the first clumps is more significant., Comment: Accepted for publication in Astrophysics & Space Science

The steady-state structure of a disc with a corona is analyzed when the vertical component of the gravitational force due to the self-gravity of the disc is considered. For the energy exchange between the disc and the corona, we assume a fraction f of the dissipated energy inside the accretion disc is transported to the corona via the magnetic tubes. Analytical solutions corresponding to a prescription for f (in which this parameter directly depends on the ratio of the gas pressure to the total pressure) or free f are presented and their physical properties are studied in detail. We show that the existence of the corona not only decreases the temperature of the disc, but also increases the surface density.The vertical component of the gravitational force due to the self-gravity of the disc decreases the self-gravitating radius and the mass of the fragments at this radius. However, as more energy is transported from the disc to the corona, the effect of the vertical component of the gravitational force due to the self-gravity of the disc on the self-gravitating radius becomes weaker, though the mass of the fragments is reduced irrespective of the amount of the energy exchange from the disc to the corona., Comment: Accepted by MNRAS

We study the steady-state structure of an accretion disc with a corona surrounding a central, rotating, magnetized star. We assume that the magneto-rotational instability is the dominant mechanism of angular momentum transport inside the disc and is responsible for producing magnetic tubes above the disc. In our model, a fraction of the dissipated energy inside the disc is transported to the corona via these magnetic tubes. This energy exchange from the disc to the corona which depends on the disc physical properties is modified because of the magnetic interaction between the stellar magnetic field and the accretion disc. According to our fully analytical solutions for such a system, the existence of a corona not only increases the surface density but reduces the temperature of the accretion disc. Also, the presence of a corona enhances the ratio of gas pressure to the total pressure. Our solutions show that when the strength of the magnetic field of the central neutron star is large or the star is rotating fast enough, profiles of the physical variables of the disc significantly modify due to the existence of a corona., Comment: Accepted for publication in Astrophysics & Space Science

We study the effects of outflow/wind on the gravitational stability of accretion discs around supermassive black holes using a set of analytical steady-state solutions. Mass-loss rate by the outflow from the disc is assumed to be a power-law of the radial distance and the amount of the energy and the angular momentum which are carried away by the wind are parameterized phenomenologically. We show that the mass of the first clumps at the self-gravitating radius linearly decreases with the total mass-loss rate of the outflow. Except for the case of small viscosity and high accretion rate, generally, the self-gravitating radius increases as the amount of mass-loss by the outflow increases. Our solutions show that as more angular momentum is lost by the outflow, then reduction to the mass of the first clumps is more significant., Comment: Accepted for publication in Astrophysics & Space Science

The steady-state structure of a disc with a corona is analyzed when the vertical component of the gravitational force due to the self-gravity of the disc is considered. For the energy exchange between the disc and the corona, we assume a fraction f of the dissipated energy inside the accretion disc is transported to the corona via the magnetic tubes. Analytical solutions corresponding to a prescription for f (in which this parameter directly depends on the ratio of the gas pressure to the total pressure) or free f are presented and their physical properties are studied in detail. We show that the existence of the corona not only decreases the temperature of the disc, but also increases the surface density.The vertical component of the gravitational force due to the self-gravity of the disc decreases the self-gravitating radius and the mass of the fragments at this radius. However, as more energy is transported from the disc to the corona, the effect of the vertical component of the gravitational force due to the self-gravity of the disc on the self-gravitating radius becomes weaker, though the mass of the fragments is reduced irrespective of the amount of the energy exchange from the disc to the corona., Comment: Accepted by MNRAS

We study the steady-state structure of an accretion disc with a corona surrounding a central, rotating, magnetized star. We assume that the magneto-rotational instability is the dominant mechanism of angular momentum transport inside the disc and is responsible for producing magnetic tubes above the disc. In our model, a fraction of the dissipated energy inside the disc is transported to the corona via these magnetic tubes. This energy exchange from the disc to the corona which depends on the disc physical properties is modified because of the magnetic interaction between the stellar magnetic field and the accretion disc. According to our fully analytical solutions for such a system, the existence of a corona not only increases the surface density but reduces the temperature of the accretion disc. Also, the presence of a corona enhances the ratio of gas pressure to the total pressure. Our solutions show that when the strength of the magnetic field of the central neutron star is large or the star is rotating fast enough, profiles of the physical variables of the disc significantly modify due to the existence of a corona., Comment: Accepted for publication in Astrophysics & Space Science

We study the dynamical structure of a self-gravitating disc with corona around a super-massive black hole. Assuming that the magneto-rotational-instability (MRI) responsible for generating the turbulent stresses inside the disc is also the source for a magnetically dominated corona, a fraction of the power released when the disc matter accretes is transported to and dissipated in the corona. This has major effect on the structure of the disc and its gravitational (in)stability according to our analytical and self-consistent solutions. We determine the radius where the disc crosses the inner radius of gravitational instability and forms the first stars. Not only the location of this radius which may extend to very large distances from the central black hole, but also the mass of the first stars highly depends on the input parameters, notably the viscous coefficient, mass of the central object and the accretion rate. For accretion discs around quasi-stellar objects (QSOs) and the Galactic center, we determine the self-gravitating radius and the mass of the first clumps. Comparing the cases with a corona and without a corona for typical discs around QSOs or the Galactic center, when the viscosity coefficient is around 0.3, we show that the self-gravitating radius decreases by a factor of approximately 2, but the mass of the fragments increases with more or less the same factor. Existence of a corona implies a more gravitationally unstable disc according to our results. The effect of a corona on the instability of the disc is more effective when the viscosity coefficient increases., Comment: accepted by MNRAS

We study the dynamical structure of a self-gravitating disc with corona around a super-massive black hole. Assuming that the magneto-rotational-instability (MRI) responsible for generating the turbulent stresses inside the disc is also the source for a magnetically dominated corona, a fraction of the power released when the disc matter accretes is transported to and dissipated in the corona. This has major effect on the structure of the disc and its gravitational (in)stability according to our analytical and self-consistent solutions. We determine the radius where the disc crosses the inner radius of gravitational instability and forms the first stars. Not only the location of this radius which may extend to very large distances from the central black hole, but also the mass of the first stars highly depends on the input parameters, notably the viscous coefficient, mass of the central object and the accretion rate. For accretion discs around quasi-stellar objects (QSOs) and the Galactic center, we determine the self-gravitating radius and the mass of the first clumps. Comparing the cases with a corona and without a corona for typical discs around QSOs or the Galactic center, when the viscosity coefficient is around 0.3, we show that the self-gravitating radius decreases by a factor of approximately 2, but the mass of the fragments increases with more or less the same factor. Existence of a corona implies a more gravitationally unstable disc according to our results. The effect of a corona on the instability of the disc is more effective when the viscosity coefficient increases., Comment: accepted by MNRAS

The steady-state structure of self-gravitating, magnetized accretion disks is studied using a set of self-similar solutions which are appropriate in the outer regions. The disk is assumed to be isothermal and the magnetic field outside of the disk is treated in a phenomenological way. However, the internal field is determined self-consistently. The behaviour of the solutions are investigated by changing the input parameters of the model, i.e. mass accretion rate, coefficients of viscosity and resistivity, and the magnetic field configuration., Comment: Accepted by ApJ

Thermal conduction has been suggested as a possible mechanism by which sufficient extra heating is provided in radiation-dominated accretion flows. We consider the extreme case in which the generated energy due to the viscosity and the energy transported by a saturated form of thermal conduction are balanced by the advection cooling. For the steady-state structure of such accretion flows a set of self-similar solution are presented. Based on these solutions while the radial and the rotational velocities are both sub-Keplerian, increasing the level of thermal conduction has the effects of decreasing the rotational velocity, but increasing the radial velocity. Conduction provides extra heating and the temperature of the gas increases with thermal conduction., Comment: submitted to ApJ

We investigate the effects of a large-scale magnetic field with open field lines on the steady-state structure of a radiation-dominated accretion disk, using self-similarity technique. The disk is supposed to be turbulent and possesses an effective viscosity and an effective magnetic diffusivity. We consider the extreme case in which the generated energy due to viscous and magnetic dissipation is balanced by the advection cooling. While the magnetic field outside of the disk is treated in a phenomenological way, the internal field is determined self-consistently. Magnetized and nonmagnetized solutions have the same radial dependence, irrespective of the values of the input parameters. Generally, our self-similar solutions are very sensitive to the viscosity or diffusivity coefficients. For example, the density and the rotation velocity increase when the viscosity coefficient decreases. The gas rotates with sub-Keplerian angular velocity with a factor less than unity which depends on the magnetic field configuration. Magnetic field significantly reduce disk thickness, however, tends to increase the radial velocity comparing to the nonmagnetic self-similar solutions., Comment: accepted by MNRAS

We investigate the effects of a large-scale magnetic field with open field lines on the steady-state structure of a radiation-dominated accretion disk, using self-similarity technique. The disk is supposed to be turbulent and possesses an effective viscosity and an effective magnetic diffusivity. We consider the extreme case in which the generated energy due to viscous and magnetic dissipation is balanced by the advection cooling. While the magnetic field outside of the disk is treated in a phenomenological way, the internal field is determined self-consistently. Magnetized and nonmagnetized solutions have the same radial dependence, irrespective of the values of the input parameters. Generally, our self-similar solutions are very sensitive to the viscosity or diffusivity coefficients. For example, the density and the rotation velocity increase when the viscosity coefficient decreases. The gas rotates with sub-Keplerian angular velocity with a factor less than unity which depends on the magnetic field configuration. Magnetic field significantly reduce disk thickness, however, tends to increase the radial velocity comparing to the nonmagnetic self-similar solutions., Comment: accepted by MNRAS

The steady-state structure of self-gravitating, magnetized accretion disks is studied using a set of self-similar solutions which are appropriate in the outer regions. The disk is assumed to be isothermal and the magnetic field outside of the disk is treated in a phenomenological way. However, the internal field is determined self-consistently. The behaviour of the solutions are investigated by changing the input parameters of the model, i.e. mass accretion rate, coefficients of viscosity and resistivity, and the magnetic field configuration., Comment: Accepted by ApJ

Thermal conduction has been suggested as a possible mechanism by which sufficient extra heating is provided in radiation-dominated accretion flows. We consider the extreme case in which the generated energy due to the viscosity and the energy transported by a saturated form of thermal conduction are balanced by the advection cooling. For the steady-state structure of such accretion flows a set of self-similar solution are presented. Based on these solutions while the radial and the rotational velocities are both sub-Keplerian, increasing the level of thermal conduction has the effects of decreasing the rotational velocity, but increasing the radial velocity. Conduction provides extra heating and the temperature of the gas increases with thermal conduction., Comment: submitted to ApJ