The Microlensing and Halo Models of the Galaxy

We investigated the dependence of the optical depth $\tau$ of the microlensing events on model parameters of the Galactic halo. We only consider Galactic mass models in which the rotation curve inside the Sun is compatible with the observation and LMC is bound to the Galaxy. It is found that $\tau$ varies up to a factor 2.5 from the standard spherical and flat rotation halo model. This implies that only the most centrally concentrated halo model can be consistent with the observation if the halo consists of only MACHOs. We also calculate the power $x$ of IMF of MACHO consistent with Tyson's CCD survey as well as Bahcall \etal's observation by {\em HST}. It is found that $x$ is greater than 5.Comment: 17 pages (including 8 figures), uuencoded gz-compressed postscrip

The Minimum Total Mass of MACHOs and Halo Models of the Galaxy

If the density distribution \rho (r) of MACHOs is spherically symmetric with respect to the Galactic center, it is shown that the minimal total mass M_{min}^{{ MACHO}} of the MACHOs is 1.7\times 10^{10}\sol \tau_{-6.7}^{{ LMC}} where \tau_{-6.7}^{{ LMC}} is the optical depth (\tau^{{ LMC}}) toward the Large Magellanic Cloud (LMC) in the unit of 2\times 10^{-7}. If \rho (r) is a decreasing function of r, it is proved that M_{min}^{{ MACHO}} is 5.6\times 10^{10}\sol \tau_{-6.7}^{{ LMC}}. Several spherical and axially symmetric halo models of the Galaxy with a few free parameters are also considered. It is found that M_{min}^{{ MACHO}} ranges from 5.6\times 10^{10}\sol \tau_{-6.7}^{{ LMC}} to \sim 3 \times 10^{11}\sol \tau_{-6.7}^{{ LMC}}. For general case, the minimal column density \Sigma_{min}^{{ MACHO}} of MACHOs is obtained as \Sigma_{min}^{{ MACHO}} =25 \sol { pc}^{-2}\tau_{-6.7}^{{ LMC}}. If the clump of MACHOs exist only halfway between LMC and the sun, M_{min}^{{ MACHO}} is 1.5\times 10^9\sol. This shows that the total mass of MACHOs is smaller than 5 \times 10^{10}\sol , i.e. \sim 10\% of the mass of the halo inside LMC, either if the density distribution of MACHOs is unusual or \tau^{{ LMC}}\ll 2\times 10^{-7}.Comment: 5 pages, 5 Encapsulated PostScript figures, Latex, Accepted for publication in Apj. Letter

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

Astrometry of Star Forming Region IRAS 05137+3919 in the far outer Galaxy

We present the results of astrometric observations with VERA toward the H2O maser sources in IRAS 05137+3919, which is thought to be located in the far outer Galaxy. We have derived the parallax of \pi = 0.086 +/- 0.027 mas, which corresponds to the source distance of D=11.6+5.3-2.8 kpc. Although the parallax measurement is only 3-sigma level and thus the distance uncertainty is considerably large, we can strongly constrain the minimum distance to this source, locating the source at the distance from the Sun greater than 8.3 kpc (or 16.7 kpc from the Galaxy's center) at 90% confidence level. Our results provide an astrometric confirmation that this source is located in the far outer Galaxy beyond 15 kpc from the Galaxy center, indicating that IRAS 05137+3919 is one of the most distant star-forming regions from the Galaxy center.Comment: 7 pages, 2 figures, to appear in PASJ vol 63. No1 (VERA special issue

Astrometry of H2_2O masers in the massive star--forming region IRAS 06061+2151 with VERA

We measured the trigonometric annual parallax of H$_2$O maser source associated with the massive star-forming regions IRAS 06061+2151 with VERA. The annual parallax of $0.496\pm0.031$ mas corresponding to a distance of $2.02^{+0.13}_{-0.12}$ kpc was obtained by 10 epochs of observations from 2007 October to 2009 September. This distance was obtained with a higher accuracy than the photometric distance previously measured, and places IRAS 06061+2151 in the Perseus spiral arm. We found that IRAS 06061+2151 also has a peculiar motion of larger than 15 km s$^{-1}$ counter to the Galactic rotation. That is similar to five sources in the Perseus spiral arm, whose parallaxes and proper motions have already been measured with higher accuracy. Moreover, these sources move at on average 27 km s$^{-1}$ toward the Galactic center and counter to the Galactic rotation.Comment: 8 pages, 4 figures, accepted to PAS

Astrometry of Water Maser Sources in Nearby Molecular Clouds with VERA - II. SVS 13 in NGC 1333

We report on the results of multi-epoch VLBI observations with VERA (VLBI Exploration of Radio Astrometry) of the 22 GHz H2O masers associated with the young stellar object SVS 13 in the NGC 1333 region. We have carried out phase-referencing VLBI astrometry and measured an annual parallax of the maser features in SVS 13 of 4.25+/-0.32 mas, corresponding to the distance of 235+/-18 pc from the Sun. Our result is consistent with a photometric distance of 220 pc previously reported. Even though the maser features were detectable only for 6 months, the present results provide the distance to NGC 1333 with much higher accuracy than photometric methods. The absolute positions and proper motions have been derived, revealing that the H2O masers with the LSR (local standard of rest) velocities of 7-8 km s-1 are most likely associated with VLA4A, which is a radio counterpart of SVS 13. The origin of the observed proper motions of the maser features are currently difficult to attribute to either the jet or the rotating circumstellar disk associated with VLA4A, which should be investigated through future high-resolution astrometric observations of VLA4A and other radio sources in NGC 1333.Comment: 9 pages, 5 figures. PASJ, in press (2008, Vol. 60, No. 1

Astrometry of Galactic Star Forming Region Sharpless 269 with VERA : Parallax Measurements and Constraint on Outer Rotation Curve

We have performed high-precision astrometry of H2O maser sources in Galactic star forming region Sharpless 269 (S269) with VERA. We have successfully detected a trigonometric parallax of 189+/-8 micro-arcsec, corresponding to the source distance of 5.28 +0.24/-0.22 kpc. This is the smallest parallax ever measured, and the first one detected beyond 5 kpc. The source distance as well as proper motions are used to constrain the outer rotation curve of the Galaxy, demonstrating that the difference of rotation velocities at the Sun and at S269 (which is 13.1 kpc away from the Galaxy's center) is less than 3%. This gives the strongest constraint on the flatness of the outer rotation curve and provides a direct confirmation on the existence of large amount of dark matter in the Galaxy's outer disk.Comment: 7 pages and 4 figures, Accepted by PASJ (Vol. 59, No. 5, October 25, 2007 issue

Distance to Orion KL Measured with VERA

We present the initial results of multi-epoch VLBI observations of the 22 GHz H2O masers in the Orion KL region with VERA (VLBI Exploration of Radio Astrometry). With the VERA dual-beam receiving system, we have carried out phase-referencing VLBI astrometry and successfully detected an annual parallax of Orion KL to be 2.29+/-0.10 mas, corresponding to the distance of 437+/-19 pc from the Sun. The distance to Orion KL is determined for the first time with the annual parallax method in these observations. Although this value is consistent with that of the previously reported, 480+/-80 pc, which is estimated from the statistical parallax method using proper motions and radial velocities of the H2O maser features, our new results provide the much more accurate value with an uncertainty of only 4%. In addition to the annual parallax, we have detected an absolute proper motion of the maser feature, suggesting an outflow motion powered by the radio source I along with the systematic motion of source I itself.Comment: 7 pages, 3 figures. PASJ, in press (Vol. 59, No. 5, October 25, 2007 issue

Absolute Proper Motions of H2O Masers Away from the Galactic Plane Measured with VERA in the "Superbubble" Region NGC 281

We report on absolute proper-motion measurements of an H2O maser source in the NGC 281 West molecular cloud, which is located ~320 pc above the Galactic plane and is associated with an HI loop extending from the Galactic plane. We have conducted multi-epoch phase-referencing observations of the maser source with VERA (VLBI Exploration of Radio Astrometry) over a monitoring period of 6 months since May 2006. We find that the H2O maser features in NGC 281 West are systematically moving toward the southwest and further away from the Galactic plane with a vertical velocity of ~20-30 km/s at its estimated distance of 2.2-3.5 kpc. Our new results provide the most direct evidence that the gas in the NGC 281 region on the HI loop was blown out from the Galactic plane, most likely in a superbubble driven by multiple or sequential supernova explosions in the Galactic plane.Comment: 10 pages, 5 figures, PASJ in press (Vol. 59, No. 4; August 25, 2007 issue