Detecting Galactic MACHOs with VERA through Astrometric Microlensing of Distant Radio Sources

In this paper we investigate the properties of astrometric microlensing of distant radio sources (QSOs and radio galaxies) due to MACHOs, and discuss their implications for VERA (VLBI Exploration of Radio Astrometry). First we show that in case of astrometric microlensing of distant sources, the event duration is only a function of the lens mass and tangential velocity, but independent of the lens distance, in contrast to the well-known three-fold degeneracy for photometric microlensing. Moreover, the lens mass $M$ is scaled by the tangential velocity $v_\perp$ as $M\propto v_\perp$, rather than $M\propto v_\perp^2$ which is the case for photometric microlensing. Thus, in astrometric microlensing the dependence of the lens mass on the unknown parameter $v_\perp$ is weaker, indicating that the duration of astrometric microlensing event is a better quantity to study the mass of lensing objects than that of photometric microlensing. We also calculate the optical depth and event rate, and show that within 20$^\circ$ of the galactic center a typical event rate for 10 $\mu$as-level shift is larger than $2.5 \times 10^{-4}$ event per year, assuming that a quarter of the halo is made up with MACHOs. This indicates that if one monitors a few hundred sources for $\sim$20 years, such an astrometric microlensing event is detectable. Since a typical event duration is found to be fairly long (5 to 15 years), the frequency of the monitoring observation can be relatively low, i.e., once per six months, which is rather reasonable for practical observations. We discuss practical strategy for observing astrometric microlensing with VERA, and argue that an astrometric microlensing event due to MACHOs can be detected by VERA within a few decades.Comment: 10 pages, 6 figures included, accepted for publication in PAS

Mass of the Galaxy Inferred from Outer Rotation Curve

Using an outer rotation curve of the Galaxy, we explore the galactic constants and the mass of the Galaxy. We show that \Theta_0 of 200 km/s is more favorable than the IAU standard value of 220 km/s, and also show that if \Theta_0 is smaller than 207 km/s the rotation curve beyond 2R_0 is declining in Keplerian fashion. In the case of \Theta_0= 200 km/s and R_0= 7.6 kpc, the total mass and the extent of the Galaxy inferred from the rotation curve are 2.0+/-0.3x 10^{11} M_\odot and 15 kpc, respectively. These results may significantly change the previous view of the Galaxy, that its outer region is dominated by a massive dark halo extending out to several tens of kpc.Comment: Latex, 4 pages and 3 figures, to appear in PASJ Letter Vol.48 No.

Nuclear Rotation Curves of Galaxies in the CO Line Emission

We have obtained high-resolution position-velocity (PV) diagrams along the major axes of the central regions of nearby galaxies in the CO-line emission using the Nobeyama 45-m telescope and the Millimeter Array. Nuclear rotation curves for 14 galaxies have been derived based on the PV diagrams using the envelope-tracing method. The nuclear rotation curves for most of the galaxies show a steep rise within a few hundred pc, which indicates a high-density concentration of mass. Keywords: Galaxies: general - Galaxies: structure - ISM: molecular lineComment: To appear in AJ, Plain TeX, Figures on reques

On the Keplerian Rotation Curves of Galaxies

We propose a criterion for examining whether or not the uncertainty of the outer rotation curves is sufficiently small to distinguish a Keplerian rotation curve from flat ones. We have applied this criterion to both Keplerian and non-Keplerian rotation curves so far obtained, and investigated their relative fraction. We also studied the minimum extent of the dark halos indicated by non-Keplerian rotation curves using the criterion. We have found that one cannot rule out the possibility that a significant fraction of rotation curves become Keplerian within 10-times the disk scale length. If the Keplerian rotation curves so far observed trace the mass truncation, several galaxies may have rather small halos, the extent of which is not larger than twice that of the optical disk.Comment: Latex, 6 pages and 3 figures, to appear in PASJ Vol.49 No.

Declining Rotation Curve and Brown Dwarf MACHOs

If the Galactic rotation speed at the Solar circle is $\sim 200$ km s$^{-1}$ or smaller, which is supported by several recent studies, the rotation curve of the Galaxy could be declining in the outermost region. Motivated by this, we investigate the effect of such declining rotation curve on the estimate of the MACHO mass and the fractional contribution of the MACHOs to the Galactic dark halo. Using Hernquist and Plummer halo models instead of the standard halo model, we find that the MACHO mass could be significantly smaller than that for the standard halo case. In particular, there exists a certain set of halo parameters for which the MACHO mass is 0.1$M_\odot$ or less and at the same time the MACHO contribution to the total mass of the halo is almost 100 %. This result indicates that a halo which consists solely of brown dwarfs can be consistent with both of the observed microlensing properties and the constraints from the rotation curve, provided the outer rotation curve is indeed declining.Comment: 8 pages and 4 figures, accepted for publication in ApJ Letter