Biconical Outflow Model: Geometry & Kinematics

• Biconical outflow model is a framework that interprets directed mass flows in AGNs and starbursts as two oppositely-directed ionization cones emerging from a central engine.
• It employs detailed kinematic and 3D geometric modeling to reconcile observed projection effects, intrinsic half-opening angles, and variable velocity profiles.
• The model refines AGN unification scenarios by illustrating how interactions with host galaxy disks affect apparent outflow signatures and feedback estimates.

The biconical outflow model is a foundational framework for interpreting observations of energetic, directed mass flows in diverse astrophysical environments, including active galactic nuclei (AGNs), nuclear starbursts, and outflowing regions in both local and high-redshift galaxies. The model posits that outflows, whether composed of ionized, neutral, molecular, or dusty gas, are organized into two oppositely directed cones (“bicone”) emerging from a central engine—typically an accreting black hole or intense star-forming region—often aligned along the rotation axis and interacting with host galaxy disks and ambient environments. The bicone geometry underpins the interpretation of kinematic, morphological, spectroscopic, and polarimetric signatures of multiphase outflows across multiple observational domains, as exemplified in detailed studies of Seyfert galaxies such as Markarian 573 (Fischer et al., 2010).

1. Geometrical Framework and Disk Interactions

The biconical outflow model assumes that energetic radiation or wind from a compact nucleus escapes along two symmetric cones sharing a common apex. In Markarian 573, kinematic modeling constrained by HST WFPC2 imaging and STIS spectroscopy shows the apparent half-opening angle of the outflow to be ∼34°, while the true (deprojected) half-opening angle is almost 53°. This discrepancy arises due to the intersection and projection of the bicone with the galaxy’s inner dust/gas disk, inclined at about 30° to the plane of the sky with a major axis position angle near 103°. The orientation of the bicone (position angle near −36°, inclination 30°) ensures that a sector of the disk, including spiral arm segments, is illuminated by the AGN. This not only produces arcuate and spiral emission features in the extended narrow-line region (ENLR) but also causes significant projection effects that modulate the observed opening angle. The illuminated disk fragments can display their own kinematic signatures due to both rotational motion and acceleration at the bicone–disk interface.

2. Kinematic and Geometric Modeling Techniques

Detailed dynamical modeling of the outflow employs multi-parameter kinematic simulations. For Mrk 573, a seven-parameter kinematics code simulates the observed radial velocities along fixed slit positions, adjusting factors such as bicone height (zₘₐₓ), outer and inner opening angles (θₒₘₐₓ, θₘᵢₙ), position angle, maximum outflow velocity (Uₘₐₓ), turnover radius (rₜ) marking the point where acceleration transitions to deceleration, and axis inclination. The kinematic model is further refined by constructing a 3D geometric realization of the system, overlaying the best-fit bicone parameters on a disk of observed inclination and position angle.

A characteristic outflow velocity profile adopted in this context is the piecewise law:

$$v(r) = \begin{cases} U_{max} \cdot \frac{r}{r_t} & \text{if } r \leq r_t \ U_{max} \cdot \frac{z_{max} - r}{z_{max} - r_t} & \text{if } r > r_t \end{cases}$$

This simple prescription reproduces the rapid rise of velocity near the nucleus and the subsequent decrease at larger radii, matching observed kinematic gradients.

3. Observational Diagnostics

High-resolution imaging (WFPC2 F606W structure maps) reveals the morphology of the ionized gas, with emission regions tracing bright arcs and spirals and dust lanes as absorption features. Long-slit STIS spectra using both medium (G750M, e.g., Hα) and low (G430L, e.g., [O III]) dispersion gratings resolve the spatially dependent velocity fields, line widths, and flux distributions. In the inner ∼1″, double-peaked (blue- and redshifted) high-velocity components indicate the presence of hollow, limb-brightened bicones, while a more gradual, linear velocity increase is observed at larger radii, possibly attributable to rotation or secondary acceleration processes in the disk-intersected regions.

Figures in the original work explicitly demonstrate:

• The spatial alignment of emission arcs with dust lanes (Figure 1),
• The velocity and flux profiles along the STIS slit (Figure 2),
• The agreement between the best-fit kinematic model and observed radial velocities (Figure 3),
• The 3D geometry of bicone, disk, and orientation relative to Earth (Figure 4),
• The model’s spatial overlay on observed emission features (Figure 5).

4. Broader Implications for Seyfert Galaxies and AGN Unification

The demonstration that the true bicone opening angle (∼53°) in Mrk 573 is considerably larger than the apparent angle profoundly affects interpretations in Seyfert galaxy demographics and AGN unification scenarios. If similar disk–bicone intersection effects operate in other systems (e.g., NGC 1068, NGC 4151), apparent opening angles derived from direct imaging or 2D projections might significantly underestimate the intrinsic scale of nuclear ionization cones. This has ramifications for population-based estimates of obscured/unobscured AGN fractions, potentially necessitating additional obscuration mechanisms beyond a simple toroidal geometry to account for the observed high fraction of Type 2 Seyferts versus Type 1s. Consequently, the misclassification or underestimation of true bicone sizes could skew theoretical models of AGN feedback and galaxy evolution.

5. Model Visualization and Interpretation

Key visualizations include:

• Structure maps that clarify the spatial relationships between the bicone, disk, and emission/absorption features,
• Radial velocity and line dispersion plots capturing the kinematic complexity across the NLR,
• 3D projections illustrating the intersection and inclination of disk and bicone,
• Superpositions of model edges on real data with tolerances as fine as ≲5°, thereby grounding theoretical models in direct observational geometry.

A comparative summary of model and observations:

Parameter	Apparent Value	True (Modeled) Value
Half-opening angle	~34°	~53°
Bicone axis PA	From slit, ~–36°	Consistent with model
Disk inclination	~30°	Observed

The precise reconciliation of observations and model parameters underscores the importance of full 3D reconstructions in interpreting outflow geometry.

6. Synthesis and Future Directions

The biconical outflow model, as realized in Mrk 573, illustrates the critical interplay among nuclear activity, anisotropic illumination, host galaxy structure, and projection effects. Kinematic and geometric modeling anchored by high-resolution imaging and spectroscopy allow for the derivation of intrinsic outflow properties (velocities, geometry, spatial distribution), which differ substantially from naive projections. These insights should be directly extrapolated to analyses of other AGNs where ionization cone–disk interactions and projection effects confound the interpretation of outflow energetics and feedback. The generic methodology—integrating parametrized velocity laws, geometric intersection modeling, and direct observational mapping—provides a template for robustly inferring intrinsic properties of biconical AGN and galactic outflows.

Further systematic application of this approach, with careful attention to inclination, host structure, and multiphase gas signatures, is mandatory for refining AGN unification scenarios and feedback models. The inclusion of multiwavelength diagnostics (X-ray, IR, mm), improved spatial resolution, and integral field spectroscopy will enhance the fidelity of 3D outflow reconstructions in both local and high-redshift systems.