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NASA NTRS1998

Standard Giant Branches in the Washington Photometric System

We have obtained CCD photometry in the Washington system C, T(sub 1) filters for some 850,000 objects associated with 10 Galactic globular clusters and 2 old open clusters. These clusters have well-known metal abundances, spanning a metallicity range of 2.5 dex from [Fe/H] approx -2.25 to +0.25 at a spacing of approx. 0.2 dex. Two independent observations were obtained for each cluster and internal checks, as well as external comparisons with existing photoelectric photometry, indicate that the final colors and magnitudes have overall uncertainties of 0.03 mag. Analogous to the method employed by Da Costa and Armandroff for V, I photometry , we then proceed to construct standard ((M(sub T),(C - T(sub 1))(sub 0)) giant branches for these clusters adopting the Lee et distance scale, using some 350 stars per globular cluster to define the giant branch. We then determine the metallicity sensitivity of the ((C - T(sub 1))(sub 0) color at a given M((sub T)(sub 1)) value. The Washington system technique is found to have three times the metallicity sensitivity of the V, I technique. At M((sub T)(sub 1)) = -2 (about a magnitude below the tip of the giant branch, roughly equivalent to M(sub I) = -3), the giant branches of 47 Tuc and M15 are separated by 1.16 magnitudes in (V - l)(sub 0) and only 0.38 magnitudes in (V - I)(sub 0). Thus, for a given photometric accuracy, metallicities can be determined three times more precisely with the Washington technique. We find a linear relationship between (C - T(sub l)(sub 0) (at M(sub T)(sub 1) = -2) and metallicity exists over the full metallicity range, with an rms of only 0.04 dex. We also derive metallicity calibrations for M(sub T)(sub 1) = -2.5 and -1.5, as well as for two other metallicity scales. The Washington technique retains almost the same metallicity sensitivity at faint magnitudes , and indeed the standard giant branches are still well separated even below the horizontal branch. The photometry is used to set upper limits in the range 0.03 - 0.09 dex for any intrinsic metallicity dispersion in the calibrating clusters. The calibrations are applicable to objects with ages approx. greater than 5 Gyr - any age effects are small or negligible for such objects. This new technique is found to have many advantages over the old two-color diagram technique for deriving metallicities from Washington photometry. In addition to only requiring 2 filters instead of 3 or 4, the new technique is generally much less sensitive to reddening and photometric errors, and the metallicity sensitivity is many times higher. The new technique is especially advantageous for metal-poor objects. The five metal-poor clusters determined by Geisler et al., using the old technique, to be much more metal-poor than previous indications, yield metallicities using the new technique which are in excellent agreement with the Zinn scale.

Geisler, Doug↗
NASA NTRS2007

Liquid Water Oceans in Ice Giants

Aptly named, ice giants such as Uranus and Neptune contain significant amounts of water. While this water cannot be present near the cloud tops, it must be abundant in the deep interior. We investigate the likelihood of a liquid water ocean existing in the hydrogen-rich region between the cloud tops and deep interior. Starting from an assumed temperature at a given upper tropospheric pressure (the photosphere), we follow a moist adiabat downward. The mixing ratio of water to hydrogen in the gas phase is small in the photosphere and increases with depth. The mixing ratio in the condensed phase is near unity in the photosphere and decreases with depth; this gives two possible outcomes. If at some pressure level the mixing ratio of water in the gas phase is equal to that in the deep interior, then that level is the cloud base. The gas below the cloud base has constant mixing ratio. Alternately, if the mixing ratio of water in the condensed phase reaches that in the deep interior, then the surface of a liquid ocean will occur. Below this ocean surface, the mixing ratio of water will be constant. A cloud base occurs when the photospheric temperature is high. For a family of ice giants with different photospheric temperatures, the cooler ice giants will have warmer cloud bases. For an ice giant with a cool enough photospheric temperature, the cloud base will exist at the critical temperature. For still cooler ice giants, ocean surfaces will result. A high mixing ratio of water in the deep interior favors a liquid ocean. We find that Neptune is both too warm (photospheric temperature too high) and too dry (mixing ratio of water in the deep interior too low) for liquid oceans to exist at present. To have a liquid ocean, Neptune s deep interior water to gas ratio would have to be higher than current models allow, and the density at 19 kbar would have to be approx. equal to 0.8 g/cu cm. Such a high density is inconsistent with gravitational data obtained during the Voyager flyby. In our model, Neptune s water cloud base occurs around 660 K and 11 kbar, and the density there is consistent with Voyager gravitational data. As Neptune cools, the probability of a liquid ocean increases. Extrasolar "hot Neptunes," which presumably migrate inward toward their parent stars, cannot harbor liquid water oceans unless they have lost almost all of the hydrogen and helium from their deep interiors.

Wiktorowicz, Sloane J.↗
NASA NTRS2018

Giant Pulse Phenomena in a High Gain Erbium Doped Fiber Amplifier

High gain Erbium Doped Fiber Amplifiers (EDFAs) are vulnerable to optical damage when unseeded, e.g. due to nonlinear effects that produce random, spontaneous Q-switched (SQS) pulses with high peak power, i.e. giant pulses. Giant pulses can damage either the components within a high gain EDFA or external components and systems coupled to the EDFA. We explore the conditions under which a reflective, polarization-maintaining (PM), core-pumped high gain EDFA generates giant pulses, provide details on the evolution of normal pulses into giant pulses, and provide results on the transient effects of giant pulses on an amplifier's fused-fiber couplers, an effect which we call Fiber Overload Induced Leakage (FOIL). While FOIL's effect on fused-fiber couplers is temporary, its damage to forward pump lasers in a high gain EDFA can be permanent.

Li, Stephen X.↗
NASA NTRS2018

Giant Pulse Phenomena in a High Gain Erbium Doped Fiber Amplifier

High gain Erbium Doped Fiber Amplifiers (EDFAs), while revolutionizing optical communications, remain vulnerable to optical damage when unseeded, e.g. due to nonlinear effects that produce random pulses with high peak power, i.e. giant pulses. Giant pulses can damage the components in a high gain EDFA or external components and systems coupled to the EDFA. We explore the conditions under which a reflective, polarization-maintaining (PM), core-pumped high gain EDFA generates giant pulses, provide details on conditions under which normal pulses evolve into giant pulses, and provide results on the transient effects of giant pulses on amplifier's fused-fiber couplers, an effect which we call Fiber Overload Induced Leakage (FOIL). While FOIL's effect on fused-fiber couplers is temporary, its damage to forward pump lasers in a high gain EDFA can be permanent.

Li, Stephen X.↗
NASA NTRSDate not supplied

Thermal Protection System to Enable Ice Giant Aerocapture Mission for Delivering Both an Orbiter and an In Situ Probe

The Ice Giants have been identified as high priority science destinations in the last Decadal Survey [1] and could benefit from aerocapture as the primary method for orbit insertion [2]. A mass-efficient aerocapture system will enable the delivery of an orbiter along with an atmospheric probe (for in situ measurements to anchor global data collected by the orbiter) and possibly a lander at Triton [3]. Aerocapture could be executed either using low L/D rigid aeroshell with lift modulation (LMA) [4] or using deployable aeroshell using drag modulation (DMA) [3]. Nearly two decades ago, a NASA-funded team performed Neptune-Triton aerocapture studies with a mid-L/D lifting configuration [5] for achieving orbit using LMA. This study showed aerocapture challenges. Due to very high peak entry conditions combined with very high heat-load, a suite of TPS materials was required and this suite was deemed problematic from a qualification perspective, due test facility limitations. In the past 20 years, progress made in GN&C for lift-guided entry missions such as MSL, Orion EFT1, Mars 2020 and the upcoming Artemis missions, and the expertise in blunt body aerodynamics at large scale (~ 5m) has led the EDL community to conclude that aerocapture is a “go do” engineering activity and most technologies are in hand to propose missions with aerocapture [6] [7]. Aerocapture using DMA, currently in development, is an option for Ice Giant Missions. While DMA is simpler in some sense, due to ballistic entry and no need for lift-guided maneuvering, it has challenges and it’s maturity is lower. LMA and DMA both require one or more ablative Thermal Protection System (TPS) materials for the rigid aeroshell element. The ablative TPS needs to be robust and mass efficient due to the high heat loads and size of the rigid aeroshell. Currently, there are capable ablative thermal protection materials, e.g., Heatshield for Extreme Entry Environments Technology (HEEET), 3-D woven Mid-Density Carbon- Phenolic (3MDCP), and PICA (Phenolic-Impregnated Carbon Ablator) that are mature, i.e., at TRL 6 or higher. NASA also invested in Conformal PICA that was matured to TRL 5. Our goal is to evaluate the applicability of high TRL TPS and consider other design options. We first establish bounding aerocapture trajectories for a wide range of arrival conditions and the associated aerothermal environment. Based on the environments, we then determine the predicted TPS mass for the aeroshell [4]. In this presentation, we will outline the process by which we establish bounding aerocapture trajectories for hyperbolic excess velocities ranging from 27 km/s to 35 km/s, which are shown to be a range of velocities that can reduce the trip time from ~14 years to 8 years. The above velocity range translates to ~12 km/s to ~24 km/s arrival velocities at the planetary entry interface [2]. The velocity reduction required to achieve orbit ranges between ~2.5 km/s to 9.5 km/s for both Neptune and Triton. Propulsive insertion alone, due to the amount of fuel required to achieve the required velocity reduction, limits the science returned [2]. We establish the bounding aerocapture trajectories for a low L/D (~ 0.4) configuration for three different ballistic coefficients. The ballistic coefficient range is determined from three different aeroshell diameters of 3m, 4m and 5m and with an entry system mass of 2200 kg. With the above range of design parameters, we then determine conservative/bounding estimates of aerothermal environments by using a combination of CFD simulations and stagnation point heating estimates [7]. This engineering approach allows us to first assess the TPS need vs. TPS capability and determine the applicability of existing TPS. Once an applicable suite of TPS is determined, the TPS thickness and mass are computed. We show that the TPS mass fraction can be as low as 5% to as high as 20%, depending on total trip time reduction and other design parameters for a range of TPS. This is a large range for TPS mass fraction. We show PICA and HEEET can indeed enable aerocapture missions, but the missions incur a mass penalty. TPS mass savings, can be further reduced with the use of conformal PICA. Advancing the development of Conformal PICA to make it robust across the entire aerothermal environment (peak heat-flux, pressure and shear) range will result in TPS mass fractions of < 10% for Ice Giant aerocapture missions such as the Neptune-Triton mission. Aerocapture allows for not only shortening the trip time but enables larger mass to be placed in orbit. Furthermore, probes deployed from orbit will benefit in reduced entry environments allowing for a lower risk TPS implementation as compared to mission designs where the probe is released prior to orbit insertion. One of the challenges for the Ice Giant community is to ensure mission designs that maximize science and allow flexibility in the placement of the entry probe. The traditional approach to release the probe ahead of the orbiter may not optimize returned science. In this presentation, we will make the case for mature TPS such as HEEET and PICA. While these materials can enable aerocapture missions, completing the development of conformal PICA and extending Conformal PICA to be more robust, will have significant impact to TPS mass efficiency and significantly enhance science return for future Gas- and Ice-Giant missions.

E Venkatapathy↗
NASA NTRS2014

Characterizing Cold Giant Planets in Reflected Light: Lessons from 50 Years of Outer Solar System Exploration and Observation

A space based coronagraph, whether as part of the WFIRST/AFTA mission or on a dedicated space telescope such as Exo-C or -S, will be able to obtain photometry and spectra of multiple gas giant planets around nearby stars, including many known from radial velocity detections. Such observations will constrain the masses, atmospheric compositions, clouds, and photochemistry of these worlds. Giant planet albedo models, such as those of Cahoy et al. (2010) and Lewis et al. (this meeting), will be crucial for mission planning and interpreting the data. However it is equally important that insights gleaned from decades of solar system imaging and spectroscopy of giant planets be leveraged to optimize both instrument design and data interpretation. To illustrate these points we will draw on examples from solar system observations, by both HST and ground based telescopes, as well as by Voyager, Galileo, and Cassini, to demonstrate the importance clouds, photochemical hazes, and various molecular absorbers play in sculpting the light scattered by solar system giant planets. We will demonstrate how measurements of the relative depths of multiple methane absorption bands of varying strengths have been key to disentangling the competing effects of gas column abundances, variations in cloud height and opacity, and scattering by high altitude photochemical hazes. We will highlight both the successes, such as the accurate remote determination of the atmospheric methane abundance of Jupiter, and a few failures from these types of observations. These lessons provide insights into technical issues facing spacecraft designers, from the selection of the most valuable camera filters to carry to the required capabilities of the flight spectrometer, as well as mission design questions such as choosing the most favorable phase angles for atmospheric characterization.

atmospheric methane abundance↗
NASA NTRS1975

Mass loss in red giants and supergiants

The circumstellar envelopes surrounding late-type giants and supergiants were studied using high resolution, photoelectric scans of strong optical resonance lines. A method for extracting the circumstellar from the stellar components of the lines allowed a quantitative determination of the physical conditions in the envelopes and the rates of mass loss at various positions in the red giant region of the HR diagram. The observed strengthening of the circumstellar spectrum with increasing luminosity and later spectral type is probably caused by an increase in the mass of the envelopes. The mass loss rate for individual stars is proportional to the visual luminosity; high rates for the supergiants suggest that mass loss is important in their evolution. The bulk of the mass return to the interstellar medium in the red giant region comes from the normal giants, at a rate comparable to that of planetary nebulae.

Sanner, F.↗
NASA NTRS1983

Chromospheric and coronal emissions from the giants in the Hyades

The visible Ca II K and International Ultraviolet Explorer spectra from the four K0 III stars (theta-1, gamma, delta, and epsilon Tau) in the Hyades, along with a field giant of similar spectral type, beta Gem, have been measured. Among the Hyades giants, the range of the high-temperature emissions can be a factor of 6 or more for C IV and an order of magnitude in the X-ray luminosity measured by Stern et al. (1981). For these presumably coeval cluster giants with similar macroscopic parameters, such as age, mass, effective temperature, gravity, and projected rotational velocity, the observed range in chromospheric and coronal emissions is not easily explained by the dominant factors thought to control these emissions in cool stars. It is possible that the emissions are time variable, on a time scale longer than six months. This would be the first evidence that giants undergo magnetic activity cycles similar to those of dwarf stars.

Baliunas, S. L.↗
NASA NTRS1986

Chromospheric activity of cool giant stars

During the seventh year of IUE twenty-six spectra of seventeen cool giant stars ranging in spectral type from K3 thru M6 were obtained. Together with spectra of fifteen stars observed during the sixth year of IUE, these low-resolution spectra have been used to: (1) examine chromospheric activity in the program stars and late type giants in general, and (2) evaluate the extent to which nonradiative heating affects the upper levels of cool giant photospheres. The stars observed in this study all have well determined TiO band strengths, angular diameters (determined from lunar occulations), bolometric fluxes, and effective temperatures. Chromospheric activity can therefore be related to effective temperatures providing a clearer picture of activity among cool giant stars than previously available. The stars observed are listed.

Steiman-Cameron, T. Y.↗
NASA NTRS1987

Giant H II regions in M81

H-alpha and VLA radio continuum observations at wavelengths of 6 and 20 cm are used to study the distribution of extinction and the distribution of giant radio H II regions along the spiral arms in M81. The radial distribution of visual extinction Av in the plane of M81 shows no trend, with an upper limit 0.1 mag/kpc for the radial extinction gradient and a mean Av of 1.1 + or - 0.4 mag. Nearly all the giant radio H II regions lie along the spiral arms or the inner H I ring. The radial distribution of the set of giant radio H II regions exhibits a strong maximum at a galactocentric distance R roughly 300 arcsec. Unless molecular hydrogen in M81 is also concentrated near R roughly 300 arcsec, the data disagree with Visser's (1980) model for star formation associated with a density wave. Some suggestions are made about how to change the ballistic particle model of Leisawitz and Bash to agree with the observed radial distribution of giant radio H II regions.

Kaufman, Michele↗
NASA NTRS1989

Theories of the origin and evolution of the giant planets

Following the accretion of solids and gases in the solar nebula, the giant planets contracted to their present sizes over the age of the solar system. It is presently hypothesized that this contraction was rapid, but not hydrodynamic; at a later stage, a nebular disk out of which the regular satellites formed may have been spun out of the outer envelope of the contracting giant planets due to a combination of total angular momentum conservation and the outward transfer of specific angular momentum in the envelope. If these hypotheses are true, the composition of the irregular satellites directly reflects the composition of planetesimals from which the giant planets formed, while the composition of the regular satellites is indicative of the composition of the less volatile components of the outer envelopes of the giant planets.

Pollack, J. B.↗
NASA NTRS1992

Giant planets: Clues on current and past organic chemistry in the outer solar system

The giant planets of the outer solar system - Jupiter, Saturn, Uranus, and Neptune - were formed in the same flattened disk of gas and dust, the solar nebula, as the terrestrial planets were. Yet, the giant planets differ in some very fundamental ways from the terrestrial planets. Despite enormous differences, the giant planets are relevant to exobiology in general and the origin of life on the Earth in particular. The giant planets are described as they are today. Their basic properties and the chemistry occurring in their atmospheres is discussed. Theories of their origin are explored and aspects of these theories that may have relevance to exobiology and the origin of life on Earth are stressed.

Pollack, James B.↗
NASA NTRS1993

The local density of halo giants

A new estimate of the local density of halo giants - 36 +/- 7 with M(V) less than 0.5 per cu kpc - is presented. This number is derived from an objective-prism survey for nearby metal-weak stars, and so is free from many of the assumptions needed to derive the local halo density in the traditional way, from high proper motion surveys. This number agrees well with estimates of the local density of halo horizontal-branch stars, but is approximately a factor of 2 smaller than the density derived by Bahcall and Casertano (1986). This may be due to the inclusion of some thick disk stars in their proper-motion selected sample. The halo density derived from giants can be expressed as a disk-to-halo ratio of 850:1 (+/- 35 percent). Using these results, a simple model is built to predict numbers of halo giants in specified directions in the Galaxy. It is shown that it performs much better than the Bahcall-Soniera model, in the specific case of halo giants. The surface brightness due to the halo at the solar radius is calculated to be 27.7 V magnitudes per sq arcsec, if the Galaxy was viewed from the outside, edge-on, thus raising the possibility of detecting light from halo field stars in other galaxies similar to our own.

Morrison, Heather L.↗
NASA NTRS1993

Giant radiating dyke swarms on Earth and Venus

On Earth, giant radiating dyke swarms are usually preserved as fan-shaped fragments which have been dismembered from their original configuration by subsequent plate tectonic rifting events. Analysis of the largest fragments and consideration of their original configuration has led to the idea that many swarms are plume related, and that dyke swarms radiate away from plume centers. Magellan radar data reveal abundant intact giant radiating swarms on Venus which are similar in scale and pattern to those on Earth. The absence of intense weathering and plate tectonic processes on Venus accounts for the preservation of the primary radiating patterns. It is characteristic of both Earth and Venus that giant radiating dikes are emplaced laterally for distances of at least 2000 km away from plume centers. At distances beyond the influence of the plume on both Earth and Venus, the radiating dyke pattern is often swept into a linear pattern aligned with the regional stress field. There is tremendous potential synergism between the characterization and analysis of terrestrial dyke swarms (where significant erosion has revealed their structure and emplacement directions at depth) and the giant swarms of Venus (where the complete circumferential structure is preserved, and the surface fracture systems above near surface dikes and the nature of the central source regions are revealed). In this study, we report on the characteristics of radial dyke swarms on Earth and Venus and draw some preliminary comparisons from the two perspectives. In summary, on both planets there is evidence for plume-related magmatic centers associated with vertical and lateral injection of magma over considerable distances (up to at least 2000 km). The abundance of very broadly radiating swarms on Venus supports the notion that the swarms on Earth were radiating over broad sectors at the time of intrusion but were dissected by later events. The Venus data show that a swarm can change from radiating (proximal) to regional (distal) subparallel orientations. An implication for Earth is that many regional linear swarms which do not have a radiating pattern may be due to fragmentation of the swarm during later plate tectonic rifting. Completion of the global classification and census of Venus features, comparison to the terrestrial synthesis, and documentation of the mode of emplacement of dikes in these environments (buffered and unbuffered conditions) should lead to additional general insight into mechanisms of formation and evolution and their relation to plumes.

Ernst, Richard E.↗
NASA NTRS1993

Chromospherically active stars. 6: Giants with compact hot companions and the barium star scenario

We have determined spectroscopic orbits for three chromospherically active giants that have hot compact companions. They are HD 160538 (K0 III + wd, P = 904 days), HD 165141 (G8 III + wd, P approximately 5200 days), and HD 185510 (K0 III + sdB, P = 20.6619 days). By fitting an IUE spectrum with theoretical models, we find the white dwarf companion of HD 165141 has a temperature of about 35000 K. Spectral types and rotational velocities have been determined for the three giants and distances have been estimated. These three systems and 39 Ceti are compared with the barium star mass-transfer scenario. The long-period mild barium giant HD 165141 as well as HD 185510 and 39 Ceti, which have relatively short periods and normal abundance giants, appear to be consistent with this scenario. The last binary, HD 160538, a system with apparently near solar abundances, a white dwarf companion, and orbital characteristics similar to many barium stars, demonstrates that the existence of a white-dwarf companion is insufficient to produce a barium star. The paucity of systems with confirmed white-dwarf companions makes abundance analyses of HD 160538 and HD 165141 of great value in examining the role of metallicity in barium star formation.

Fekel, Francis C.↗
NASA NTRS1993

Chromospherically active stars. 11: Giant with compact hot companions and the barium star scenario

We have determined spectroscopic orbits for three chromsopherically active giants that have hot compact companions. They are HD 160538 (KO III + wd, P = 904 days), HD 165141 (G8 III + wd, P approximately 5200 days), and HD 185510 (KO III + sdB, P = 20.6619 days). By fitting an IUE spectrum with theoretical models, we find the white dwarf companion of HD 165141 has a temperature of about 35,000 K. Spectral types and rotational velocities have been determined for the three giants and distances have been estimated. These three systems and 39 Ceti are compared with the barium star mass-transfer scenario. The long-period mild barium giant HD 165141 as well as HD 185510 and 39 Ceti, which have relatively short periods and normal abundance giants, appear to be consistent with this scenario. The last binary, HD 160538, a system with apparently near solar abundances, a white dwarf companion, and orbital characteristics similar to many barium stars, demonstrates that the existence of a white dwarf companion is insufficient to produce a barium star. The paucity of systems with confirmed white dwarf companions makes abundance analyses of HD 160538 and HD 165141 of great value in examining the role of metallicity in barium star formation.

Fekel, Francis C.↗
NASA NTRS1995

The tip of the red giant branch as a distance indicator for resolved galaxies. 2: Computer simulations

Based on both empirical data for the nearby galaxies, and on computer simulations, we show that measuring the position of the tip of the first-ascent red-giant branch provides a means of obtaining the distances to nearby galaxies with a precision and accuracy comparable to using Cepheids and/or RR Lyrae variables. We present an analysis of synthetic I vs (V-I) color magnitude diagrams of Population 2 systems to investigate the use of the observed discontinuity in the I-band luminosity function as a primary distance indicator. In the simulations we quantify the effects (1) signal to noise, (2) crowding, (3) population size, and (4) non-giant-branch-star contamination, on the method adopted for detecting the discontinuity,, measuring its luminosity, and estimating its uncertainity. We discuss sources of systematic error in the context of observable parameters, such as the signal-to-noise ratio and/or surface brightness. The simulations are then scaled to observed color-magnitude diagrams. It is concluded, that from the ground the tip of the red-giant-branch method can be sucessfully used to determine distances accurate to +/- 10% for galaxies out to 3 Mpc (mu approximately 27.5 mag); and from space a factor of four further in distance (mu approximately 30.6 mag) can be reached using HST. This method can be applied whereever a metal-poor population (-2.0 less than Z less than -0.7) of red-giant stars is detected (whose age is in the range 7-17 Gyr), whether that population resides in the halo of a spiral galaxy, the extended outer disk of a dwarf irregular, or in the outer periphery of an elliptical galaxy.

Madore, Barry F.↗
NASA NTRS1998

EUVE Observations of the Hyades Giants

The contractor describes EUVE and ROSAT observations of the Hyades K0 III giants theta(sup 1(vB 71 = HR 1411) and gamma$ (vB 28 = HR 1346) Tau, and ASCA observations of theta(sup 1) Tau. The coronal activity of these "clump" giants is intermediate between that of the Sun and of high-activity stars such as RS CVn systems. There is no evidence for significant short or long term variability up to several years. Modeling of the individual and combined spectra suggest that these two X-ray and EUV- bright Hyades giants resemble in their activity levels another clump giant, beta Cet, with a peak in the emission measure distribution near log T approx. 6.8, reminiscent of the Capella emission measure "bump."

Stern, Robert A.↗