Near-Infrared Extinction in The Coalsack Globule 2

We have conducted J, H, and Ks imaging observations for the Coalsack Globule 2 with the SIRIUS infrared camera on the IRSF 1.4 m telescope at SAAO, and determined the color excess ratio, E(J-H)/E(H-Ks). The ratio is determined in the same photometric system as our previous study for the rho Oph and Cha clouds without any color transformation; this enables us to directly compare the near-infrared extinction laws among these regions. The current ratio E(J-H)/E(H-Ks) = 1.91 +- 0.01 for the extinction range 0.5 < E(J-H) <1.8 is significantly larger than the ratios for the rho Oph and Cha clouds (E(J-H)/E(H-Ks) = 1.60-1.69). This ratio corresponds to a large negative index alpha = 2.34 +- 0.01 when the wavelength dependence of extinction is approximated by a power law which might indicate little growth of dust grains, or larger abundance of dielectric non-absorbing components such as silicates, or both in this cloud. We also confirm that the color excess ratio for the Coalsack Globule 2 has a trend of increasing with decreasing optical depth, which is the same trend as the rho Oph and Cha clouds have.Comment: 13 pages, 5 figures, and 2 tables, Ap

Time-Resolved Near-Infrared Photometry of Extreme Kuiper Belt Object Haumea

We present time-resolved near-infrared (J and H) photometry of the extreme Kuiper belt object (136108) Haumea (formerly 2003 EL61) taken to further investigate rotational variability of this object. The new data show that the near-infrared peak-to-peak photometric range is similar to the value at visible wavelengths, \Delta m_R = 0.30+/-0.02 mag. Detailed analysis of the new and previous data reveals subtle visible/near-infrared color variations across the surface of Haumea. The color variations are spatially correlated with a previously identified surface region, redder in B-R and darker than the mean surface. Our photometry indicates that the J-H colors of Haumea (J-H=-0.057+/-0.016 mag) and its brightest satellite Hi'iaka (J-H=-0.399+/-0.034 mag) are significantly (>9 sigma) different. The satellite Hi'iaka is unusually blue in J-H, consistent with strong 1.5 micron water-ice absorption. The phase coefficient of Haumea in the J-band is found to increase monotonically with wavelength in the range 0.4<lambda<1.3. We compare our findings with other Solar system objects and discuss implications regarding the surface of Haumea.Comment: 10 pages, 10 figures, 6 tables. Accepted for publication in The Astronomical Journal (2008 November 28

The baker's map with a convex hole

We consider the baker's map $B$ on the unit square $X$ and an open convex set $H\subset X$ which we regard as a hole. The survivor set $\mathcal J(H)$ is defined as the set of all points in $X$ whose $B$-trajectories are disjoint from $H$. The main purpose of this paper is to study holes $H$ for which $\dim_H \mathcal J(H)=0$ (dimension traps) as well as those for which any periodic trajectory of $B$ intersects $\overline H$ (cycle traps). We show that any $H$ which lies in the interior of $X$ is not a dimension trap. This means that, unlike the doubling map and other one-dimensional examples, we can have $\dim_H \mathcal J(H)>0$ for $H$ whose Lebesgue measure is arbitrarily close to one. Also, we describe holes which are dimension or cycle traps, critical in the sense that if we consider a strictly convex subset, then the corresponding property in question no longer holds. We also determine $\delta>0$ such that $\dim_H \mathcal J(H)>0$ for all convex $H$ whose Lebesgue measure is less than $\delta$. This paper may be seen as a first extension of our work begun in [3, 4, 6, 7, 13] to higher dimensions.Comment: 31 pages, 10 figure