The Connection between Galaxy Kinematics and HI Line Widths as Applied to the Distance Scale

This document is fairly old. For more current information, please see my dissertation.

The Tully-Fisher (TF) relation (Tully & Fisher 1977) describes the empirical connection between neutral hydrogen (HI) global line profile widths and the absolute magnitudes of spiral galaxies. TF relations have been used as a powerful tool to calculate distances to galaxies (Jacoby et al. 1992), and therefore play an important role toward solving fundamental problems in Astronomy, such as determination of the Hubble constant (Theureau et al. 1997; Strauss & Willick 1995).

The errors in corrected line-widths are the dominant source of error in the TF-relation (Jacoby et al. 1992; Bothun & Mould 1987). The main cause of errors in corrected line-profile widths arise from several factors, such as low signal-to-noise ratio of the profiles, lack of a standard definition of the line-profile widths and lack of a proper definition of inclination correction. For example:

• There have been many different methods to calculate the uncorrected HI line-profile width. For example, Giovanelli et al. (1997a) use W₅₀, the width at 50% of the peak intensity as their definition of HI line-profile width, whereas conventionally W₂₀ has been used in literature (e.g. Tully & Fisher (1977); Haynes et al. (1998)). Tully & Fouqué (1985) used a combination of W₂₀ and W₅₀ to calculate the HI line-profile width. Additionally, no comprehensive model has been done to date to compare the differences between these methods.
• A standard and reliable inclination correction method has yet to be found. The most commonly used definition is: cos²i = (q² - q₀²) / (1 - q₀²), with q₀ = 0.2, q = observed axes ratio, and i = inclination angle. However, Heidmann et al. (1971) suggest that q₀ depends upon the morphological type T of a galaxy. Fouqué et al. (1990) use a similar variable q₀, but their values are higher than the ones proposed by Heidmann et al. Giovanelli et al. (1997b) use q₀ = 0.13 or 0.2, and correct q for various effects, such as seeing.
• It is thought that the line profile width of a galaxy represents its maximum rotation velocity, V_max. But the connection between HI line-profile width and maximum rotation curve velocity might not be direct and linear. In particular, no in-depth models have been made to determine how reliably one can predict v_max from the line-profile width.
• More than 50% of the field galaxies show asymmetric line profiles (Richter & Sancisi 1994). The fraction is expected to be even higher for cluster galaxies. Asymmetric line profiles raise several questions on calibration of the TF relation, since calculating line-profile widths of such asymmetric profiles may not accurately estimate the maximum rotational velocity of these galaxies. Many mechanisms have been suggested for the asymmetry in the line profiles of HI galaxies (see for example Richter & Sancisi 1994): non-circular motions of the gas (Haynes et al. 1978; Schulman et al. 1996), warping and flaring of HI layer (Sancisi & Allen 1979; Bottema 1995), and pointing errors.
  For asymmetric line profiles, the determination of line-profile width is even more error-prone. It is not sure if one should take the maximum of the two peaks as the "peak" (w.r.t. which W₂₀/W₅₀ is measured), or if one should average the two peaks, or use a different scheme altogether. The method to determine line-profile width is important because it is known that the galaxies with low HI content show more asymmetric profiles (Kornreich et al. 2001).
• The line profile shapes themselves are varied. Some galaxies show very steep two-horned profiles, whereas others have shallow profiles with bumps and other peculiar features in them. For example, Matthews et al. (1998) show that early-type galaxies have smoother line profiles and late-type galaxies in general have a central "bump" in their line profiles. These anomalies may bias the line-width definition as a function of morphological type.

I am developing a detailed kinematic model of neutral hydrogen in galaxies to simulate real-world HI line profiles of galaxies. In addition to learning about calibration issues mentioned above, the program is being developed with the aim of gaining insight into various other factors that go into the TF relation. The model would be used to create HI line profiles of galaxies based upon the factors we know about the 3-dimensional galaxy velocity fields. For example, the model would incorporate velocity fields, rotation curve shapes, turbulences, density distibution, density waves, warps, high-velocity clouds, etc. Then, the model could be used to study the effect of these parameters on the line profiles of galaxies.

The model is being developed in Python. As of now, I have a basic 3-dimensional galaxy model ready, which can be used to create line-profiles of galaxies with different velocity distributions.

The data for the model (rotation curves, line profiles, etc.) comes from existing literature and observations of galaxies using the Green Bank Telescope and the Giant Meterwave Radio Telescope.

Future work involves extending this model to incorporate other parameters mentioned, and then fine-tuning the model so as to predict the line-profiles of various galaxies.

References

1. Bothun G. D., Mould J. R., 1987, ApJ, 313, 629
2. Bottema R., 1995, 295, 605
3. Fouqué P., Bottinelli L., Gouguenheim L., Paturel G., 1990, ApJ, 349, 1
4. Giovanelli R., Haynes M. P., Herter T., Vogt N. P., da Costa L. N., Freudling W., Salzer J. J., Wegner G., 1997a, 113, 53
5. Giovanelli R., Haynes M. P., Herter T., Vogt N. P., Wegner G., Salzer J. J., da Costa L. N., Freudling W., 1997b, 113, 22
6. Haynes M. P., Giovanelli R., Burkhead M. S., 1978, 83, 938
7. Haynes M. P., van Zee L., Hogg D. E., Roberts M. S., Maddalena R. J., 1998, 115, 62
8. Jacoby G. H., Branch D., Clardullo R., Davies R. L., Harris W. E., Pierce M. J., Pritchet C. J., Tonry J. L., Welch D. L., 1992, PASP, 104, 599
9. Kornreich D. A., Haynes M. P., Jore K. P., Lovelace R. V. E., 2001, 121, 1358
10. Matthews L. D., van Driel W., Gallagher J. S., 1998, 116, 1169
11. Richter O.-G., Sancisi R., 1994, 290, L9
12. Sancisi R., Allen R. J., 1979, 74, 73
13. Schulman E., Bregman J. N., Brinks E., Roberts M. S., 1996, 112, 960
14. Strauss M. A., Willick J. A., 1995, 261, 271
15. Theureau G., Hanski M., Ekholm T., Bottinelli L., Gouguenheim L., Paturel G., Teerikorpi P., 1997, 322, 730
16. Tully R. B., Fisher J. R., 1977, 54, 661
17. Tully R. B., Fouqué P., 1985, 58, 67