PROMISSORY ESTOPPEL: PRINCIPLE FROM PRECEDENTS: I

The doctrine of promissory estoppel is an outstanding modem example of the way in which the Anglo-American legal system develops significant rules and principles out of the day-to-day decisions of our courts. Progress in the law comes about through the formulation and acceptance of generalizations. However, merely stating the results of a number of different instances does not result in clarification and simplification. That comes only when the precedents are studied with a view to discovering the \u27\u27binding thread of principle that runs through them all. Such a principle, if discovered in the course of the appraisal of a series of cases, will make for a more ready understanding of the cases which have already been decided. Even more important, however, is the future use which can be made of the principle thus discovered. It may thereafter be employed in variant and diverse fact situations to produce workable, logical and rational solutions to problems which had previously been solved only by resort to fiction or by the use of historical anomalies and conceptual distortions. As Cohen has so aptly remarked, A legal system that works with general principles has powerful instruments .... [A] generalized jurisprudence enlarges the law\u27s control over the diversity of legal situations. It is like fishing with large nets instead of with single lines

The Contribution of TP-AGB and RHeB Stars to the Near-IR Luminosity of Local Galaxies: Implications for Stellar Mass Measurements of High Redshift Galaxies

Using high spatial resolution HST WFC3 and ACS imaging of resolved stellar populations, we constrain the contribution of thermally-pulsing asymptotic giant branch (TP-AGB) stars and red helium burning (RHeB) stars to the 1.6 um near-infrared (NIR) luminosities of 23 nearby galaxies. The TP-AGB phase contributes as much as 17% of the integrated F160W flux, even when the red giant branch is well populated. The RHeB population contribution can match or even exceed the TP-AGB contribution, providing as much as 21% of the integrated F160W light. The NIR mass-to-light (M/L) ratio should therefore be expected to vary significantly due to fluctuations in the star formation rate over timescales from 25 Myr to several Gyr. We compare our observational results to predictions based on optically derived star formation histories and stellar population synthesis (SPS) models, including models based on the Padova isochrones (used in popular SPS programs). The SPS models generally reproduce the expected numbers of TP-AGB stars in the sample. The same SPS models, however, give a larger discrepancy in the F160W flux contribution from the TP-AGB stars, over-predicting the flux by a weighted mean factor of 2.3 +/-0.8. This larger offset is driven by the prediction of modest numbers of high luminosity TP-AGB stars at young (<300 Myrs) ages. The best-fit SPS models simultaneously tend to under-predict the numbers and fluxes of stars on the RHeB sequence, typically by a factor of 2.0+/-0.6 for galaxies with significant numbers of RHeBs. Coincidentally, over-prediction of the TP-AGB and under-prediction of the RHeBs result in a NIR M/L ratio largely unchanged for a rapid star formation rate. However, the NIR-to-optical flux ratio of galaxies could be significantly smaller than AGB-rich models would predict, an outcome that has been observed in some intermediate redshift post-starburst galaxies. (Abridged)Comment: 28 Pages, 12 Figures, 5 Tables, Accepted for Publication in the Astrophysical Journa

The ACS Nearby Galaxy Survey Treasury IX. Constraining asymptotic giant branch evolution with old metal-poor galaxies

In an attempt to constrain evolutionary models of the asymptotic giant branch (AGB) phase at the limit of low masses and low metallicities, we have examined the luminosity functions and number ratio between AGB and red giant branch (RGB) stars from a sample of resolved galaxies from the ACS Nearby Galaxy Survey Treasury (ANGST). This database provides HST optical photometry together with maps of completeness, photometric errors, and star formation histories for dozens of galaxies within 4 Mpc. We select 12 galaxies characterized by predominantly metal-poor populations as indicated by a very steep and blue RGB, and which do not present any indication of recent star formation in their color--magnitude diagrams. Thousands of AGB stars brighter than the tip of the RGB (TRGB) are present in the sample (between 60 and 400 per galaxy), hence the Poisson noise has little impact in our measurements of the AGB/RGB ratio. We model the photometric data with a few sets of thermally pulsing AGB (TP-AGB) evolutionary models with different prescriptions for the mass loss. This technique allows us to set stringent constraints to the TP-AGB models of low-mass metal-poor stars (with M<1.5 Msun, [Fe/H]<~-1.0). Indeed, those which satisfactorily reproduce the observed AGB/RGB ratios have TP-AGB lifetimes between 1.2 and 1.8 Myr, and finish their nuclear burning lives with masses between 0.51 and 0.55 Msun. This is also in good agreement with recent observations of white dwarf masses in the M4 old globular cluster. These constraints can be added to those already derived from Magellanic Cloud star clusters as important mileposts in the arduous process of calibrating AGB evolutionary models.Comment: To appear in ApJ, a version with better resolution is in http://stev.oapd.inaf.it/~lgirardi/rgbagb.pd

Cellular Structures for Computation in the Quantum Regime

We present a new cellular data processing scheme, a hybrid of existing cellular automata (CA) and gate array architectures, which is optimized for realization at the quantum scale. For conventional computing, the CA-like external clocking avoids the time-scale problems associated with ground-state relaxation schemes. For quantum computing, the architecture constitutes a novel paradigm whereby the algorithm is embedded in spatial, as opposed to temporal, structure. The architecture can be exploited to produce highly efficient algorithms: for example, a list of length N can be searched in time of order cube root N.Comment: 11 pages (LaTeX), 3 figure

Resolved Near-infrared Stellar Populations in Nearby Galaxies

We present near-infrared (NIR) color-magnitude diagrams (CMDs) for the resolved stellar populations within 26 fields of 23 nearby galaxies (≲ 4 Mpc), based on images in the F110W and F160W filters taken with the Wide-Field Camera 3 (WFC3) on the Hubble Space Telescope (HST). The CMDs are measured in regions spanning a wide range of star formation histories, including both old dormant and young star-forming populations. We match key NIR CMD features with their counterparts in more familiar optical CMDs, and identify the red core helium-burning (RHeB) sequence as a significant contributor to the NIR flux in stellar populations younger than a few 100 Myr old. The strength of this feature suggests that the NIR mass-to-light ratio can vary significantly on short timescales in star-forming systems. The NIR luminosity of star-forming galaxies is therefore not necessarily proportional to the stellar mass. We note that these individual RHeB stars may also be misidentified as old stellar clusters in images of nearby galaxies. For older stellar populations, we discuss the CMD location of asymptotic giant branch (AGB) stars in the HST filter set and explore the separation of AGB subpopulations using a combination of optical and NIR colors. We empirically calibrate the magnitude of the NIR tip of the red giant branch in F160W as a function of color, allowing future observations in this widely adopted filter set to be used for distance measurements. We also analyze the properties of the NIR red giant branch (RGB) as a function of metallicity, showing a clear trend between NIR RGB color and metallicity. However, based on the current study, it appears unlikely that the slope of the NIR RGB can be used as an effective metallicity indicator in extragalactic systems with comparable data. Finally, we highlight issues with scattered light in the WFC3, which becomes significant for exposures taken close to a bright Earth limb

A Global Star Forming Episode in M31 2-4 Gyr Ago

We have identified a major global enhancement of star formation in the inner M31 disk that occurred between 2-4 Gyr ago, producing $\sim$60% of the stellar mass formed in the past 5 Gyr. The presence of this episode in the inner disk was discovered by modeling the optical resolved star color-magnitude diagrams of low extinction regions in the main disk of M31 (3$<$R$<$20 kpc) as part of the Panchromatic Hubble Andromeda Treasury. This measurement confirms and extends recent measurements of a widespread star formation enhancement of similar age in the outer disk, suggesting that this burst was both massive and global. Following the galaxy-wide burst, the star formation rate of M31 has significantly declined. We briefly discuss possible causes for these features of the M31 evolutionary history, including interactions with M32, M33 and/or a merger.Comment: 12 pages, 2 tables, 6 figures, accepted for publication in Ap