Direct Measurement of the Hubble Constant
The concordance cosmological model assumes a flat CDM universe composed of baryons, cold dark matter, and a mysterious Dark Energy (DE) that accelerates the expansion of the universe (Spergel et al. 2003). The location of the first peak in the angular power spectrum of the cosmic microwave background radiation (CMBR) determines the absolute (that is, independent of the Hubble constant Ho) angular-size distance to the surface of last scattering. This distance depends on the amount of DE, the geometry of the universe, and the current expansion rate Ho. Spergel et al. (2006) stress that the 3-year WMAP data are consistent with a wide range of Ho, so an external measurement of Ho is needed to justify the flatness assumption and tell us whether DE is (1) the cosmological constant of general relativity or (2) a variable quintessence (cf. Wetterick 1988, Ratra Peebles 1988). In his analysis of DE probes, Wayne Hu (2005) concluded that the most important single complement to CMBR data is a precise (3%) measurement of Ho.
What is the value of Ho. The current best value of Ho = 72 +- 7 km/s/Mpc from the HST Key Project (Freedman et al. 2001) is based on indirect distance measurements to extragalactic Cepheid variables treated as standard candles, so its 10% uncertainty is dominated by systematic errors that cannot be reduced by observations of more galaxies. So independent measurements of Ho are extremely important.
VLBA observations of the H2O megamaser in the nearby (D = 7.2 +- 0.5Mpc) Seyfert 2 galaxy NGC 4258 have been used to determine its distance geometrically, bypassing the problems of standard candles (Herrnstein et al. 1999). The H2O masers arise in a thin edge-on molecular annulus at galactocentric radii R from 0.14 to 0.28 pc. Lines near the systemic velocity come from the near side of the disk, and satellite lines with relative velocities V of 1100 km/s come from gas at both tangent points. The satellite lines have a Keplerian rotation curve implying a central mass of 39 million Msun. The recession velocities of individual near-systemic features are increasing by 9 km/s/yr (Haschick, Baan Peng 1994; Greenhill et al. 1995a) and measure the centripetal acceleration a = V 2/R of clouds moving across our line of sight to the nucleus (Watson Wallin 1994; Haschick, Baan, Peng 1994; Greenhill et al. 1995a,b).
Conceptually, the distance D to NGC 4258 can be determined geometrically in two independent ways: (1) by dividing the radius R = V 2/a of the annulus by the angular radius from a VLBI image or (2) dividing the velocity V by the proper motion d/dt of masers on the near side of disk (see Herrnstein et al. 1999 for a full explanation). NGC 4258 is too close to constrain Ho directly (although it can be used to anchor the zero-point of the Cepheid P-L relation). However, faint H2O masers in galaxies well into the Hubble flow at D between 50 and 200 Mpc are now being discovered (e.g. Braatz et al. 2004; Braatz Gugliucci 2006; Kondratko et al. 2006) and 150 are now known.
We are conducting an NRAO Key Science Project to measure Ho with 3% uncertainty. Since H2O maser distances are not dominated by systematic errors, the uncertainty in Ho determined from observations of N galaxies should fall nearly as sqrt(N), so we ultimately need to measure 10%-accurate distances for about 10 galaxies in the Hubble flow (cf. Greenhill 2004). VLBI data has been and will be taken on several such megamaser galaxies and could be analyzed by a graduate student for either a qualifying exam or a thesis project.
Links related to this project