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We study temporal variability of radiation driven winds using one dimensional, time dependent simulations and an extension of the classic theory of line driven winds developed by Castor Abbott and Klein. We drive the wind with a sinusoidally varying radiation field and find that after a relaxation time, determined by the propagation time for waves to move out of the acceleration zone of the wind, the solution settles into a periodic state. Winds driven at frequencies much higher than the dynamical frequency behave like stationary winds with time averaged radiation flux whereas winds driven at much lower frequencies oscillate between the high and low flux stationary states. Most interestingly, we find a resonance frequency near the dynamical frequency which results in velocity being enhanced or suppressed by a factor comparable to the amplitude of the flux variation. Whether the velocity is enhanced or suppressed depends on the relative phase between the radiation and the dynamical variables. These results suggest that a time-varying radiation source can induce density and velocity perturbations in the acceleration zones of line driven winds.
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Ultra Fast Outflows (UFOs) are an established feature in X-ray spectra of AGNs. According to the standard picture, they are launched at accretion disc scales with relativistic velocities, up to 0.3-0.4 c. Their high kinetic power is enough to induce an efficient feedback on galactic-scale, possibly contributing to the co-evolution between the central supermassive black hole (SMBH) and the host galaxy. It is therefore of paramount importance to fully understand the UFO physics, in particular the forces driving their acceleration and the relation with the accretion flow they originate from. In this paper we investigate the impact of special relativity effects on the radiative pressure exerted onto the outflow. The radiation received by the wind decreases for increasing outflow velocity v, implying that the standard Eddington limit argument has to be corrected according to v. Due to the limited ability of the radiation to counteract the SMBH gravity, we expect to find lower typical velocities with respect to the non-relativistic scenario. We integrate the relativistic-corrected outflow equation of motion for a realistic set of starting conditions. We concentrate on UFO typical values of ionisation, column density and launching radius. We explore a one-dimensional, spherical geometry and a 3D setting with a rotating thin accretion disc. We find that the inclusion of relativistic effects leads to sizeable differences in the wind dynamics and that v is reduced up to 50% with respect to the non-relativistic treatment. We compare our results with a sample of UFO from the literature, and we find that the relativistic-corrected velocities are systematically lower than the reported ones, indicating the need for an additional mechanism, such as magnetic driving, to explain the highest velocity components. These conclusions, derived for AGN winds, have a general applicability.
Recent observation of some luminous transient sources with low color temperatures suggests that the emission is dominated by optically thick winds driven by super-Eddington accretion. We present a general analytical theory of the dynamics of radiation pressure-driven, optically thick winds. Unlike the classical adiabatic stellar wind solution whose dynamics are solely determined by the sonic radius, here the loss of the radiation pressure due to photon diffusion also plays an important role. We identify two high mass loss rate regimes ($dot{M} > L_{rm Edd,}/c^2$). In the large total luminosity regime the solution resembles an adiabatic wind solution. Both the radiative luminosity, $L$, and the kinetic luminosity, $L_k$, are super-Eddington with $L < L_k$ and $L propto L_k^{1/3}$. In the lower total luminosity regime most of the energy is carried out by the radiation with $L_k < L approx L_{rm Edd,}$. In a third, low mass loss regime ($dot{M} < L_{rm Edd,}/c^2$), the wind becomes optically thin early on and, unless gas pressure is important at this stage, the solution is very different from the adiabatic one. The results are independent from the energy generation mechanism at the foot of the wind, therefore they are applicable to a wide range of mass ejection systems, from black hole accretion, to planetary nebulae, and to classical novae.
We study line driven winds for models with different radial intensity profiles: standard Shakura-Sunyaev radiating thin discs, uniform intensity discs and truncated discs where driving radiation is cutoff at some radius. We find that global outflow properties depend primarily on the total system luminosity but truncated discs can launch outflows with $sim 2$ times higher mass flux and $sim 50%$ faster outflow velocity than non-truncated discs with the same total radiation flux. Streamlines interior to the truncation radius are largely unaffected and carry the same momentum flux as non-truncated models whereas those far outside the truncation radius effectively carry no outflow because the local radiation force is too weak to lift matter vertically away from the disc. Near the truncation radius the flow becomes more radial, due to the loss of pressure/radiation support from gas/radiation at larger radii. These models suggest that line driven outflows are sensitive to the geometry of the radiation field driving them, motivating the need for self-consistent disc/wind models.
We study the 2-D, time-dependent hydrodynamics of radiation-driven winds from accretion disks in which the radiation force is mediated by spectral lines. If the dominant contribution to the total radiation field comes from the disk, then we find the outflow is intrinsically unsteady and characterised by large amplitude velocity and density changes. Both infall and outflow can occur in different regions of the wind at the same time. On the other hand, if the total luminosity of the system is dominated by the central star, then the outflow is steady. In either case, we find the 2-D structure of the wind consists of a dense, slow outflow, typically confined to angles within about 45$^o$ of the equatorial plane, that is bounded on the polar side by a high -velocity, lower density stream. The flow geometry is controlled largely by the geometry of the radiation field. Global properties e.g., the total mass loss rate and terminal velocity depend more on the system luminosity and are insensitive to geometry. Matter is fed into the fast wind from within a few stellar radii of the central star. Our solutions agree qualitatively with the kinematics of outflows in CV systems inferred from spectroscopic observations. We predict that low luminosity systems may display unsteady behavior in wind-formed spectral lines. Our study also has application to winds from active galactic nuclei and from high mass YSOs.
The escape of cosmic rays from the Galaxy leads to a gradient in the cosmic ray pressure that acts as a force on the background plasma, in the direction opposite to the gravitational pull. If this force is large enough to win against gravity, a wind can be launched that removes gas from the Galaxy, thereby regulating several physical processes, including star formation. The dynamics of these cosmic ray driven winds is intrinsically non-linear in that the spectrum of cosmic rays determines the characteristics of the wind (velocity, pressure, magnetic field) and in turn the wind dynamics affects the cosmic ray spectrum. Moreover, the gradient of the cosmic ray distribution function causes excitation of Alfven waves, that in turn determine the scattering properties of cosmic rays, namely their diffusive transport. These effects all feed into each other so that what we see at the Earth is the result of these non-linear effects. Here we investigate the launch and evolution of such winds, and we determine the implications for the spectrum of cosmic rays by solving together the hydrodynamical equations for the wind and the transport equation for cosmic rays under the action of self-generated diffusion and advection with the wind and the self-excited Alfven waves.
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