[Paper Review] Hydrodynamical interaction between an accretion flow and a stellar wind

S. Mendoza, J. Cantó+1 more|Redalyc (Universidad Autónoma del Estado de México)|Jan 21, 2004

Astrophysics and Star Formation Studies3 citations

TL;DR

This paper presents a simplified hydrodynamical model for the interaction between a rotating accretion flow and a stellar wind, using ram pressure balance to predict shock evolution and radio continuum emission. The key contribution is a predictive framework for generating radio maps of the wind-accretion shock interface, with flux scaling as $ S_\nu \propto \dot{M}_w v_w^{1.68} $ at late times, valid for $ \lambda > 1/2 $ and $ \tau_\nu \ll 1 $.

ABSTRACT

Molecular clouds in the interstellar medium suffer gravitational instabilities that lead to the formation of one or multiple stars. A recently formed star inside a cold cloud communicates its gravitational force to the surrounding environment and soon an accretion flow falling into the star develops. After their formation, all stars soon eject a wind of gas that interacts with the external accretion flow. This interaction produces a shock wave that evolves with time. The work presented in this article formulates a simple prescription for the evolution of this interaction. With the aid of this model we construct a few radio continuum maps of the source.

Motivation & Objective

• To develop a tractable hydrodynamical model for the interaction between a rotating accretion flow and a stellar wind in young stellar objects.
• To predict observable radio continuum emission from the shock interface formed by wind-accretion interaction.
• To establish a thin-shell approximation valid under specific ram pressure balance conditions.
• To generate synthetic radio continuum maps for comparison with observations.
• To quantify the time evolution of the shock structure and emission flux using simplified force-balance dynamics.

Proposed method

• Uses ram pressure balance between stellar wind ($ \dot{M}_w v_w $) and accretion flow ($ \dot{M} v_k $) to define a dimensionless parameter $ \lambda $, where $ v_k $ is Keplerian velocity at $ r_d $.
• Applies Ulrich’s accretion model with cylindrical symmetry, assuming small angular momentum and polytropic equation of state $ p/p_\infty = (\rho/\rho_\infty)^\kappa $.
• Derives shock surface shape via force balance, assuming the shock is thin and evolves with time, with $ \lambda \gg 1 $ leading to unbounded expansion.
• Calculates optical depth $ \tau_\nu $ using the Curiel et al. (1989) formula for thermal free-free emission: $ \tau_\nu \propto n v_s^{1.68} T^{-0.55} \nu^{-2.1} $.
• Computes brightness temperature $ T_B = T \tau_\nu $ under the thin-layer approximation ($ \tau_\nu \ll 1 $), enabling brightness temperature isocontours.
• Integrates over projected solid angle using spherical coordinates to compute flux density $ S_\nu \propto \int \tau_\nu \, \mathrm{d}a / D^2 $, yielding observable maps.

Experimental results

Research questions

• RQ1 How does the shock surface evolve in time when a stellar wind interacts with a rotating, low-angular-momentum accretion flow?
• RQ2 Under what conditions does the interaction reach a steady state, and when does the shock expand to infinity?
• RQ3 What is the observable radio continuum emission signature of the wind-accretion shock interface?
• RQ4 How do the flux density and brightness temperature vary with time and physical parameters such as wind mass-loss rate and velocity?
• RQ5 What is the validity range of the thin-shell approximation for the shocked layer?

Key findings

• The shock surface expands to infinity when $ \lambda \gg 1 $, invalidating the thin-shell approximation; for $ \lambda < 1/2 $, a steady-state configuration is possible.
• For $ \lambda > 1/2 $, the emission flux asymptotes to a constant value at late times: $ S_\nu \approx 3.37 \, \text{mJy} \times (\dot{M}_w / 10^{-7} \, M_\odot \text{yr}^{-1}) (v_w / 300 \, \text{km s}^{-1})^{1.68} (T / 10^4 \, \text{K})^2 (\nu / 5 \, \text{GHz})^{-0.1} (D / 150 \, \text{pc})^{-2} $.
• The optical depth $ \tau_\nu \ll 1 $, validating the use of $ T_B = T \tau_\nu $ for brightness temperature calculations.
• Radio continuum maps of the shock surface are generated via projection of $ T_B $ isocontours on the plane of the sky, with structure dependent on $ \lambda $.
• The flux evolution is time-dependent and reaches a steady state only for $ \lambda < 1/2 $, with a characteristic timescale tied to $ \lambda $.
• The model predicts observable flux levels in the mJy range for typical young stellar object parameters, making it relevant for mm/sub-mm and cm-wave observations.