[Paper Review] The Intrinsic Ellipticity of Spiral Disks

David R. Andersen, Matthew A. Bershady|arXiv (Cornell University)|Jan 24, 2002

Galaxies: Formation, Evolution, Phenomena3 citations

TL;DR

This study measures the intrinsic ellipticities of 28 face-on spiral disks using combined Hα velocity fields and R/I-band imaging to compare kinematic and photometric inclinations and position angles, revealing a log-normal distribution with a mean ellipticity of ε̄ = 0.06. The method resolves the degeneracy between ellipticity and orientation, enabling precise Tully-Fisher relation calibration with only 0.44 mag scatter, and shows disk ellipticity contributes significantly to TF scatter, constraining halo and disk mass-to-light variations.

ABSTRACT

We have measured the distribution of intrinsic ellipticities for a sample of 28 relatively face-on spiral disks. We combine H-alpha velocity fields and R and I-band images to determine differences between kinematic and photometric inclination and position angles, from which we estimate intrinsic ellipticities of galaxy disks. Our findings suggest disks have a log-normal distribution of ellipticities (mean epsilon =0.06) and span a range from epsilon= 0 (circular) to epsilon=0.2. We are also able to construct a tight Tully-Fisher relation for our face-on sample. We use this to assess the contribution of disk ellipticity on the observed Tully-Fisher scatter.

Motivation & Objective

• To determine the intrinsic ellipticity distribution of spiral disks using a method that breaks the degeneracy between ellipticity and orientation.
• To assess the contribution of disk ellipticity to scatter in the Tully-Fisher relation.
• To calibrate the Tully-Fisher relation using nearly face-on galaxies with minimal internal absorption and high kinematic precision.
• To evaluate whether disk ellipticity influences the observed scatter in the Tully-Fisher relation, thereby constraining other astrophysical sources of scatter.
• To estimate the ellipticity of dark matter halos by modeling the ellipticity of disk components.

Proposed method

• Used Hα velocity fields from DensePak integral field spectroscopy on the WIYN 3.5m telescope to derive kinematic inclinations and position angles.
• Acquired R and I-band imaging from multiple telescopes to measure photometric axis ratios and position angles, avoiding distortions from warps and spiral structure.
• Applied a monolithic, inclined, differentially rotating disk model with a hyperbolic tangent rotation curve to fit velocity fields, using all azimuthal data including θ > 45°, unlike tilted-ring models.
• Compared kinematic and photometric inclination and position angle differences to isolate intrinsic disk ellipticity, assuming deviations arise solely from ellipticity.
• Fitted the ellipticity distribution using a log-normal model, with parameters derived from maximum-likelihood estimation on ln(εD).
• Constructed a Tully-Fisher relation using 24 nearly face-on galaxies with reliable photometry and corrected for color, comparing residuals to Courteau (1997) and assessing scatter contributions.

Experimental results

Research questions

• RQ1 What is the intrinsic distribution of ellipticities in face-on spiral disks, and is it well-described by a log-normal distribution?
• RQ2 To what extent does disk ellipticity contribute to the scatter in the Tully-Fisher relation?
• RQ3 Can the kinematic inclinations derived from monolithic velocity-field modeling be used to construct a precise Tully-Fisher relation for face-on galaxies?
• RQ4 How does the ellipticity of spiral disks relate to the ellipticity of their underlying dark matter halos?
• RQ5 What fraction of Tully-Fisher scatter is attributable to disk ellipticity, and what does this imply about other sources of scatter?

Key findings

• The intrinsic ellipticity distribution of spiral disks is well-fit by a log-normal distribution with a mean of ε̄D = 0.060 and a standard deviation of 0.064 on the natural log scale.
• The mean kinematic ellipticity of the sample is ε̄D = 0.076, with a range from ε = 0 (circular) to ε = 0.2.
• The halo ellipticity is estimated to be ε̄Φ = 0.054, consistent with previous studies, assuming a non-rotating, constant-ellipticity halo potential.
• The Tully-Fisher relation for the nearly face-on sample exhibits only 0.44 magnitudes of scatter, comparable to the 0.46 mag scatter in Courteau’s (1997) higher-inclination sample.
• Excluding galaxies with strong kinematic asymmetries reduces the TF scatter to 0.36 mag, indicating that kinematic irregularities are a major source of scatter.
• A statistically significant correlation is found between disk ellipticity and Tully-Fisher scatter, implying that ellipticity contributes meaningfully to the observed scatter and helps constrain other sources such as mass-to-light ratio variations.