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Shapes of Dark Matter Halos and Disk Galaxy Kinematics

This presentation explores the structure and shape of dark matter halos and its impact on the kinematics of disk galaxies. It discusses the triaxial nature of CDM halos, their density potential, isopotential shapes, and their implications for disk rotation curves. It also examines the role of non-axisymmetric potentials on disk kinematics and presents a case study on NGC 2976. The presentation concludes with future research possibilities and improvements in modeling techniques.

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Shapes of Dark Matter Halos and Disk Galaxy Kinematics

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  1. Shapes of Dark Matter Halos andDisk Galaxy Kinematics Eric Hayashi MPA Garching

  2. Introduction • Over the past 20+ years, numerical simulations have been an invaluable tool for investigating the detailed predictions of CDM cosmological models • In particular, the structure of CDM halos (at least in the absence of baryons) is now a firm prediction (although a theoretical understanding of the simulation results remains elusive) • In spite of orders of magnitude improvement in numerical resolution, some of the main results remain unchanged since the “early days” of dark matter halo simulations

  3. Dark Halo Structure: Then and Now Navarro, Frenk & White (NFW, 1996) Navarro, Hayashi et al (2004) • CDM halos are ‘cuspy’ - the density increases towards the centre of the halo • NFW profile remains a reasonably good fit, although in simulated halos the slope of the density profile actually becomes shallower as r0

  4. Dark Matter Halo Shape Density Potential • CDM halos are triaxial - typical axis ratios of mass distribution are c/a~0.5, b/a~0.6 • Shape of halo isopotential surfaces are more spherical, but deviations from symmetry could still have significant effects on dynamical tracers of halo potential

  5. 2D Isopotential Shape • Calculate potential in the plane perpendicular to angular momentum of simulated halo (plane of disk galaxy) and fit ellipses to isopotential contours • In most halos, the ellipticity increases toward the centre • This can significantly affect the kinematics of a disk as we will see later

  6. 3D Isopotential Shape • Fit ellipsoid to isopotential contours on three orthogonal planes intersecting at the halo centre (Springel et al 2003) • Axis ratios tend to decrease towards the centre of the halo • Possible implications for constraints on shape of Milky Way halo based on simulations of Sagittarius tidal stream (e.g., Ibata et al 2001, Helmi et al 2004)

  7. Triaxial Halos and Disk Rotation Curves • If galactic disks are in circular motion, observed disk rotation velocities are directly proportional to the circular velocity of the halo, Vc = (GM/R)0.5 • Under this assumption, Hayashi et al (2004) find that ~1/3 of LSB galaxy rotation curves are inconsistent with cuspy halo profiles • How does the shape of CDM halos affect the interpretation of disk rotation curves? Hayashi et al (2004)

  8. Disks in Non-axisymmetric Potentials • Use solutions for closed loop orbits in non-axisymmetric potentials (Gerhard & Vietri 1986) to investigate kinematics of disks in triaxial halo potentials • Orbits are elongated perpendicular to elongation of halo potential • Viewing angle fa defined relative • to minor axis of disk orbits • We construct a disk model from closed • orbit solutions and simulate long-slit • observations of the model FDM Rorbit a

  9. Triaxial Halo, a=30o Triaxial Halo, a=0o Spherical Halo Disk Kinematics in Triaxial Halos • When velocities near the major axis of the closed loop orbits are sampled, the rotation curve looks “solid-body,” mimicking the presence of a constant-density core • For other viewing angles, the rotation curve is steeper and may resemble the circular velocity of the unperturbed NFW potential. Hayashi & Navarro (2006)

  10. Ellipticity of Potential • Ellipticity in halo potential must increase toward the centre to produce solid-body rotation curves • Similar trend (with similar magnitude of ellipticity) is seen in isopotential contours of simulated halos • Simulated halos have the proper variation in shape with radius to account for noncircular orbits

  11. Case Study: NGC 2976 • Rotation curves provide limited information about the kinematics - observations of 2D velocity fields are now possible • Based on tilted ring modelling of 2D velocity field data, Simon et al (2004) conclude that NGC 2976 does not contain a cuspy dark matter halo • Tilted ring modeling may not be able to account for the presence of realistic non-circular motions Simon et al (2004)

  12. 2D Velocity Fields • Lines of constant speed are asymmetric, and show characteristic “kinks” • Iso-velocity contours are (anti)symmetric in diagonally opposite quadrants, but differ in adjacent ones • Velocity field of NGC 2976 is also quite asymmetric, and exhibits similar “kinks” Data courtesy J. Simon

  13. Conclusions • Triaxiality of CDM halos increases towards the centre • This is exactly the shape required to mask the presence of a cusp as inferred by rotation curves • One can use 2D velocity fields distinguish between the kinematics of a disk in a spherical halo with a core and a disk in a cuspy triaxial halo • Future work involves detailed comparison with 2D velocity field observations, possible improvement on tilted ring modeling techniques

  14. End Presentation

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