Efficient dynamic optimization of logic programs

A summary is given of the dynamic optimization approach to speed up learning for logic programs. The problem is to restructure a recursive program into an equivalent program whose expected performance is optimal for an unknown but fixed population of problem instances. We define the term 'optimal' relative to the source of input instances and sketch an algorithm that can come within a logarithmic factor of optimal with high probability. Finally, we show that finding high-utility unfolding operations (such as EBG) can be reduced to clause reordering

The Orbit of the Companion to HD 100453A: Binary-Driven Spiral Arms in a Protoplanetary Disk

HD 100453AB is a 10+/-2 Myr old binary whose protoplanetary disk was recently revealed to host a global two-armed spiral structure. Given the relatively small projected separation of the binary (1.05", or ~108 au), gravitational perturbations by the binary seemed to be a likely driving force behind the formation of the spiral arms. However, the orbit of these stars remained poorly understood, which prevented a proper treatment of the dynamical influence of the companion on the disk. We observed HD 100453AB between 2015-2017 utilizing extreme adaptive optics systems on the Very Large Telescope and Magellan Clay Telescope. We combined the astrometry from these observations with published data to constrain the parameters of the binary's orbit to a=1.06"+/-0.09", e=0.17+/-0.07, and i=32.5+/- 6.5 degrees. We utilized publicly available ALMA CO data to constrain the inclination of the disk to i~28 degrees, which is relatively co-planar with the orbit of the companion and consistent with previous estimates from scattered light images. Finally, we input these constraints into hydrodynamical and radiative transfer simulations to model the structural evolution of the disk. We find that the spiral structure and truncation of the circumprimary disk in HD 100453 are consistent with a companion-dirven origin. Furthermore, we find that the primary star's rotation, its outer disk, and the companion exhibit roughly the same direction of angular momentum, and thus the system likely formed from the same parent body of material.Comment: 28 pages, 11 figures, Accepted to Ap

The Multiplicity of M-Dwarfs in Young Moving Groups

We image 104 newly identified low-mass (mostly M-dwarf) pre-main sequence members of nearby young moving groups with Magellan Adaptive Optics (MagAO) and identify 27 binaries with instantaneous projected separation as small as 40 mas. 15 were previously unknown. The total number of multiple systems in this sample including spectroscopic and visual binaries from the literature is 36, giving a raw multiplicity rate of at least $35^{+5}_{-4}\%$ for this population. In the separation range of roughly 1 - 300 AU in which infrared AO imaging is most sensitive, the raw multiplicity rate is at least $24^{+5}_{-4}\%$ for binaries resolved by the MagAO infrared camera (Clio). The M-star sub-sample of 87 stars yields a raw multiplicity of at least $30^{+5}_{-4}\%$ over all separations, $21^{+5}_{-4}\%$ for secondary companions resolved by Clio from 1 to 300 AU ($23^{+5}_{-4}\%$ for all known binaries in this separation range). A combined analysis with binaries discovered by the Search for Associations Containing Young stars shows that multiplicity fraction as a function of mass and age over the range of 0.2 to 1.2 $M_\odot$ and 10 - 200 Myr appears to be linearly flat in both parameters and across YMGs. This suggests that multiplicity rates are largely set by 100 Myr without appreciable evolution thereafter. After bias corrections are applied, the multiplicity fraction of low-mass YMG members ($< 0.6 M_\odot$) is in excess of the field.Comment: 25 page

The TWA 3 Young Triple System: Orbits, Disks, Evolution

We have characterized the spectroscopic orbit of the TWA 3A binary and provide preliminary families of probable solutions for the TWA 3A visual orbit as well as for the wide TWA 3A--B orbit. TWA 3 is a hierarchical triple located at 34 pc in the $\sim$10 Myr old TW Hya association. The wide component separation is 1."55; the close pair was first identified as a possible binary almost 20 years ago. We initially identified the 35-day period orbital solution using high-resolution infrared spectroscopy which angularly resolved the A and B components. We then refined the preliminary orbit by combining the infrared data with a re-analysis of our high-resolution optical spectroscopy. The orbital period from the combined spectroscopic solution is $\sim$35 days, the eccentricity is $\sim$0.63, and the mass ratio is $\sim$0.84; although this high mass ratio would suggest that optical spectroscopy alone should be sufficient to identify the orbital solution, the presence of the tertiary B component likely introduced confusion in the blended optical spectra. Using millimeter imaging from the literature, we also estimate the inclinations of the stellar orbital planes with respect to the TWA 3A circumbinary disk inclination and find that all three planes are likely misaligned by at least $\sim$30 degrees. The TWA 3A spectroscopic binary components have spectral types of M4.0 and M4.5; TWA 3B is an M3. We speculate that the system formed as a triple, is bound, and that its properties were shaped by dynamical interactions between the inclined orbits and disk.Comment: Accepted to Ap

Magellan Adaptive Optics first-light observations of the exoplanet beta Pic b. II. 3-5 micron direct imaging with MagAO+Clio, and the empirical bolometric luminosity of a self-luminous giant planet

Young giant exoplanets are a unique laboratory for understanding cool, low-gravity atmospheres. A quintessential example is the massive extrasolar planet $\beta$ Pic b, which is 9 AU from and embedded in the debris disk of the young nearby A6V star $\beta$ Pictoris. We observed the system with first light of the Magellan Adaptive Optics (MagAO) system. In Paper I we presented the first CCD detection of this planet with MagAO+VisAO. Here we present four MagAO+Clio images of $\beta$ Pic b at 3.1 $\mu$m, 3.3 $\mu$m, $L^\prime$, and $M^\prime$, including the first observation in the fundamental CH$_4$ band. To remove systematic errors from the spectral energy distribution (SED), we re-calibrate the literature photometry and combine it with our own data, for a total of 22 independent measurements at 16 passbands from 0.99--4.8 $\mu$m. Atmosphere models demonstrate the planet is cloudy but are degenerate in effective temperature and radius. The measured SED now covers $>$80\% of the planet's energy, so we approach the bolometric luminosity empirically. We calculate the luminosity by extending the measured SED with a blackbody and integrating to find log($L_{bol}$/$L_{Sun}$) $= -3.78\pm0.03$. From our bolometric luminosity and an age of 23$\pm$3 Myr, hot-start evolutionary tracks give a mass of 12.7$\pm$0.3 $M_{Jup}$, radius of 1.45$\pm$0.02 $R_{Jup}$, and $T_{eff}$ of 1708$\pm$23 K (model-dependent errors not included). Our empirically-determined luminosity is in agreement with values from atmospheric models (typically $-3.8$ dex), but brighter than values from the field-dwarf bolometric correction (typically $-3.9$ dex), illustrating the limitations in comparing young exoplanets to old brown dwarfs.Comment: Accepted to ApJ. 27 pages, 22 figures, 19 table

Resolving the Dusty Circumstellar Structure of the Enigmatic Symbiotic Star CH Cygni with the MMT Adaptive Optics System

We imaged the symbiotic star CH Cyg and two PSF calibration stars using the unique 6.5m MMT deformable secondary adaptive optics system. Our high-resolution (FWHM=0.3"), very high Strehl (98%+-2%) mid-infrared (9.8 and 11.7 um) images of CH Cyg allow us to probe finer length scales than ever before for this object. CH Cyg is significantly extended compared to our unresolved PSF calibration stars (Mu UMa and Alpha Her) at 9.8 and 11.7 um. We estimated the size of the extension by convolving a number of simple Gaussian models with the Mu UMa PSF and determining which model provided the best fit to the data. Adopting the Hipparcos distance for this object of 270 pc, we found a nearly Gaussian extension with a FWHM at 9.8 um of ~40.5+-2.7 AU (0.15+-0.01") and a FWHM at 11.7 um of 45.9+-2.7 AU (0.17+-0.01"). After subtracting out the Gaussian component of the emission (convolved with our PSF), we found a faint \~0.7" asymmetric extension which peaks in flux ~0.5" north of the stars. This extension is roughly coincident with the northern knotlike feature seen in HST WFPC2 images obtained in 1999.Comment: 18 pages, 7 figures, accepted by the Astrophysical Journa

Status of MagAO and review of astronomical science with visible light adaptive optics

We review astronomical results in the visible (lambda <1 micron) with adaptive optics and note the status the MagAO system and the recent upgrade to visible camera's Simultaneous/Spectra Differential Imager (SDI to SDI+) mode. Since mid-2013 there has been a rapid increase visible AO with over 50 refereed science papers published in just 2015-2016 timeframe. The main focus of this paper is another large (D=6.5m Magellan telescope) AO system (MagAO) which has been very productive in the visible (particularly at the H-alpha emission line). MagAO is an advanced Adaptive Secondary Mirror (ASM) AO system at the Magellan in Chile. This ASM secondary has 585 actuators with <1 msec response times (0.7 ms typically). MagAO utilizes a 1 kHz pyramid wavefront sensor (PWFS). The relatively small actuator pitch (~22 cm/subap, 300 modes, upgraded to 30 pix dia. PWFS) allows moderate Strehls to be obtained in the visible (0.63-1.05 microns). Long exposures (60s) achieve <30mas resolutions and 30% Strehls at 0.62 microns (r') with the VisAO camera (0.5-1.0 microns) in 0.5" seeing with bright R < 9 mag stars (~10% Strehls can be obtained on fainter R~12 mag guide stars). Differential Spectral Imaging (SDI) at H-alpha has been very important for accreting exoplanet detection. There is also a 1-5micron science camera (Clio; Morzinski et al. 2016). These capabilities have led to over 35 MagAO refereed science publications. Here we review the key steps to having good performance in the visible and review the exciting new AO visible science opportunities and science results. The recent rapid increase in the scientific publications and power of visible AO is due to the maturity of the next-generation of AO systems and our new ability probe circumstellar regions with very high (10-30 mas) spatial resolutions that would otherwise require much larger (>10m) diameter telescopes in the infrared.Comment: 18 pages, Proc. SPIE 10703, Adaptive Optics IV, June 2018 Austin TX. arXiv admin note: substantial text overlap with arXiv:1407.509

Into the Blue: AO Science with MagAO in the Visible

We review astronomical results in the visible ({\lambda}<1{\mu}m) with adaptive optics. Other than a brief period in the early 1990s, there has been little astronomical science done in the visible with AO until recently. The most productive visible AO system to date is our 6.5m Magellan telescope AO system (MagAO). MagAO is an advanced Adaptive Secondary system at the Magellan 6.5m in Chile. This secondary has 585 actuators with < 1 msec response times (0.7 ms typically). We use a pyramid wavefront sensor. The relatively small actuator pitch (~23 cm/subap) allows moderate Strehls to be obtained in the visible (0.63-1.05 microns). We use a CCD AO science camera called "VisAO". On-sky long exposures (60s) achieve <30mas resolutions, 30% Strehls at 0.62 microns (r') with the VisAO camera in 0.5" seeing with bright R < 8 mag stars. These relatively high visible wavelength Strehls are made possible by our powerful combination of a next generation ASM and a Pyramid WFS with 378 controlled modes and 1000 Hz loop frequency. We'll review the key steps to having good performance in the visible and review the exciting new AO visible science opportunities and refereed publications in both broad-band (r,i,z,Y) and at Halpha for exoplanets, protoplanetary disks, young stars, and emission line jets. These examples highlight the power of visible AO to probe circumstellar regions/spatial resolutions that would otherwise require much larger diameter telescopes with classical infrared AO cameras.Comment: 14 pages, 8 figures, to appear in Proc. SPIE 914

Mid-Infrared Imaging of the Post-AGB Star AC Herculis with the MMT Adaptive Optics System

We utilized the MMT's unique deformable secondary adaptive optics system to produce high-resolution (FWHM=0.3"), very high Strehl mid-infrared (9.8, 11.7 & 18 micron) images of the post-AGB star AC Her. The very high (98+/-2%) Strehls achieved with Mid-IR AO led naturally to an ultra-stable PSF independent of airmass, seeing, or location on the sky. We find no significant difference between AC Her's morphology and our unresolved PSF calibration stars (mu UMa & alpha Her) at 9.8, 11.7, & 18 microns. Our current observations do not confirm any extended Mid-IR structure around AC Her. These observations are in conflict with previously reported Keck (seeing-limited) 11.7 and 18 micron images which suggested the presence of a resolved ~0.6" edge-on circumbinary disk. We conclude that AC Her has no extended Mid-IR structure on scales greater than 0.2" (R<75 AU). These first results of Mid-IR AO science are very encouraging for future high accuracy Mid-IR imaging with this technique.Comment: To appear in the November 20, 2003 issue of the Astrophysical Journal Letters. The preprint has 7 pages and 3 figures (one in color; but prints OK in B&W