Diffusion of radial action in a galactic disc

Wozniak, H.

doi:10.1051/0004-6361/202038959

Cited by 4 publications

(2 citation statements)

References 30 publications

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“…The rotation frequency Ω p , also called the pattern speed, of morphological features such as bars or spiral arms is a crucial parameter in most dynamical studies of disk galaxies because it allows describing the local dynamics in a rotating frame where time dependence is reduced. Physical and numerical reality is more complicated, however, because most self-consistent galaxy models, even when they do not include a dissipative gas component, show that several flexible patterns with distinct speeds coexist (Sparke & Sellwood 1987;Wozniak 2015Wozniak , 2020Wu et al 2016Wu et al , 2018. This implies that the system is not strictly time-invariant at meso-and macroscales in any rotating frame.…”

Section: Introductionmentioning

confidence: 99%

Five methods for determining pattern speeds in galaxies

Pfenniger¹,

Saha²,

Wu³

2023

Preprint

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Context. After matter distribution and kinematics, the bar or spiral pattern speeds are the next fundamental parameters determining the dynamics of a galaxy. Aims. New or refined methods for determining instantaneous scalar and vector pattern speeds from a restricted domain are developed for applications in N-body simulations or in galaxies such as the Milky Way, for which the stellar coordinates become increasingly better known. Methods. The general feature used throughout follows from the fact that the time derivative of a function of the coordinates is linearly proportional to its rotation rate and its particle velocities. Knowing these therefore allows retrieving the instantaneous pattern speed vector by linear optimization. Similarly, if an invariant function depends on the position and velocities, then its instantaneous rotation vectors in space can be retrieved. Knowing the accelerations also allows determining the pattern rotation of velocity space. Results. The first three methods are based on the assumed rotational invariance of functions at each point in space or velocity space: 1) The 6D invariant function method, measuring the pattern speed vectors in space and velocity space, 2) the differential/regional 3D Tremaine-Weinberg method, evaluated over regions with a high signal-to-noise ratio, 3) the 3D Jacobi integral method, yielding the potential pattern speed. Extensions to derive the rotation center position, speed, and acceleration are introduced in the first and third methods. The last two methods are based on the assumed invariance of average functions of the particle coordinates: 4) The 2D and 3D moment of inertia methods by using the derivative of the singular value decomposition, 5) the 2D Fourier method (3D for m = 2 mode), giving the mode rotation speeds. Pattern speed accelerations are also derived in the fourth and fifth methods. Conclusions. Depending on the available data in specific problems, the different methods provide a choice of approaches.

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Section: Introductionmentioning

confidence: 99%

Five methods for determining pattern speeds in galaxies

Pfenniger¹,

Saha²,

Wu³

2023

Preprint

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“…Conventional models should be handled as an approximation only. Slow changes of the angular momentum Lz and radial action JR were derived from N body simulations by Wozniak (2020), although they derived slower diffusion of these values.…”

Section: Introductionmentioning

confidence: 99%

Non-equilibrium in the Solar Neighbourhood using dynamical modelling with Gaia DR2

Kipper,

Tenjes,

Tempel

et al. 2021

Preprint

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Matter distribution models of the Milky Way galaxy are usually stationary, although there are known to be wave-like perturbations in the disc at ∼ 10% level of the total density. Modelling of the overall acceleration field by allowing non-equilibrium is a complicated task. We must learn to distinguish whether density enhancements are persistent or not by their nature. In the present paper, we elaborate our orbital arc method to include the effects of massless perturbations and non-stationarities in the modelling. The method is tested by modelling of simulation data and shown to be valid. We apply the method to the Gaia DR 2 data within a region of ∼ 0.5 kpc from the Sun and confirm that acceleration field in the Solar Neighbourhood has a perturbed nature -the phase space density along the orbits of stars grow in the order of h 5% per Myr due to non-stationarity. This result is a temporally local value and can be used only within the timeframe of a few Myrs. An attempt to pinpoint the origin of the perturbation shows that the stars having larger absolute angular momentum are the main carriers of the local perturbation. As they are faster than the average thin disc star, they are either originating further away and are close in their pericentre or they are perturbed locally by a fast co-moving perturber, such as gas disc inhomogenities.

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Five methods for determining pattern speeds in galaxies

Pfenniger¹,

Saha²,

Wu³

2023

A&A

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Context. After matter distribution and kinematics, the bar or spiral pattern speeds are the next fundamental parameters determining the dynamics of a galaxy. Aims. New or refined methods for determining instantaneous scalar and vector pattern speeds from a restricted domain are developed for applications in N-body simulations or in galaxies such as the Milky Way, for which the stellar coordinates become increasingly better known. Methods. The general feature used throughout follows from the fact that the time derivative of a function of the coordinates is linearly proportional to its rotation rate and its particle velocities. Knowing these therefore allows retrieving the instantaneous pattern speed vector by linear optimization. Similarly, if an invariant function depends on the position and velocities, then its instantaneous rotation vectors in space can be retrieved. Knowing the accelerations also allows determining the pattern rotation of velocity space. Results. The first three methods are based on the assumed rotational invariance of functions at each point in space or velocity space: (1) the 6D invariant function method, measuring the pattern speed vectors in space and velocity space, (2) the differential/regional 3D Tremaine-Weinberg method, evaluated over regions with a high signal-to-noise ratio, (3) the 3D Jacobi integral method, yielding the potential pattern speed. Extensions to derive the rotation center position, speed, and acceleration are introduced in the first and third methods. The last two methods are based on the assumed invariance of average functions of the particle coordinates: (4) the 2D and 3D moment of inertia methods by using the derivative of the singular value decomposition, (5) the 2D Fourier method (3D for m = 2 mode), giving the mode rotation speeds. Pattern speed accelerations are also derived in the fourth and fifth methods. Conclusions. Depending on the available data in specific problems, the different methods provide a choice of approaches.

show abstract

Diffusion of radial action in a galactic disc

Cited by 4 publications

References 30 publications

Five methods for determining pattern speeds in galaxies

Five methods for determining pattern speeds in galaxies

Non-equilibrium in the Solar Neighbourhood using dynamical modelling with Gaia DR2

Five methods for determining pattern speeds in galaxies

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