The First Definitive Binary Orbit Determined with the Hubble Space Telescope Fine Guidance Sensors: Wolf 1062 (Gliese 748)

The M dwarf binary, Wolf 1062 (Gliese 748), has been observed with the Hubble Space Telescope (HST) Fine Guidance Sensor 3 in the transfer function scan mode to determine the apparent orbit. This is the first orbit defined fully and exclusively with HST, and is the most accurate definitive orbit for any resolved, noneclipsing system. The orbital period is 2.4490 ± 0.0119 yr and the semimajor axis is 01470 ± 00007—both quantities are now known to better than 1%. Using the weighted mean of seven parallax measurements and these HST data, we find the system mass to be 0.543 ± 0.031 M⊙, where the error of 6% is due almost entirely to the parallax error. An estimated fractional mass from the infrared brightness ratio and infrared mass-luminosity relation yields a mass for the primary of 0.37 M⊙, and the secondary falls in the regime of very low mass stars, with a mass of only 0.17 M⊙

Adaptively Secure Garbling with Near Optimal Online Complexity

We construct an adaptively secure garbling scheme with an online communication complexity of $n+m+\mathsf{poly}(\log |C|, \sec)$ where $C: \{0,1\}^n \rightarrow \{0,1\}^{m}$ is the circuit being garbled, and $\sec$ is the security parameter. The security of our scheme can be based on (polynomial hardness of) the Computational Diffie-Hellman (CDH) assumption, or the Factoring assumption or the Learning with Errors assumption. This is nearly the best achievable in the standard model (i.e., without random oracles) as the online communication complexity must be larger than both $n$ and $m$. The online computational complexity of our scheme is $O(n+m)+\mathsf{poly}(\log |C|, \sec)$. Previously known standard model adaptively secure garbling schemes had asymptotically worse online cost or relied on exponentially hard computational assumptions

Astrometry with the Hubble Space Telescope: A Parallax of the Fundamental Distance Calibrator RR Lyrae

We present an absolute parallax and relative proper motion for the fundamental distance scale calibrator, RR Lyrae. We obtain these with astrometric data from FGS 3, a white-light interferometer on the Hubble Space Telescope. We find πabs = 3.82 ± 0.2 mas. Spectral classifications and VRIJHKT2M and DDO 51 photometry of the astrometric reference frame surrounding RR Lyr indicate that field extinction is low along this line of sight. We estimate AV = 0.07 ± 0.03 for these reference stars. The extinction suffered by RR Lyr becomes one of the dominant contributors to the uncertainty in its absolute magnitude. Adopting theaverage field absorption AV = 0.07 ± 0.03, we obtain M = 0.61. This provides a distance modulus for the Large Magellanic Cloud (LMC) of m - M = 18.38–18.53, with the average extinction-corrected magnitude of RR Lyrae variables in the LMC, V(RR), remaining a significant uncertainty. We compare this result with more than 80 other determinations of the distance modulus of the LMC