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Stellar evolution calculations with variable abundance ratios were used to gauge the effects on temperatures, luminosities, and lifetimes in various phases. Individual elements C, N, O, Mg, Si, and Fe were included. Most of the effect relevant to integrated light models is contained in the temperature variable, as opposed to the timescale or luminosity. We derive a recipe for including abundance-sensitive temperature effects that is applicable to existing isochrone grids. The resultant enhanced isochrones are incorporated into composite stellar population models and compared with galaxy data from the Sloan Digital Sky Survey. A severe oxygen-age degeneracy is apparent, 2 - 3 Gyr per 0.1 dex in [O/R], where R represents a heavy element such as Fe. Over the range of early-type galaxy velocity dispersion, the spans of all abundance ratios are reduced but the age range increases, systematically older. Allowing Fe-peak elements the freedom to vary accentuates this increase of age span. Overall, these results sharpen the age-mass correlation known as downsizing but decrease the steepness of abundance ratio gradients. Both of these observations, in turn, imply a more robust contribution from gas free mergers in the histories of typical elliptical galaxies., Comment: 10 pages, 12 figures, 4 tables, accepted to MNRAS, 2022 Jan 26

The tip of the red giant branch is one of the widely used distance measurement methods for the relatively nearby galaxies where the bright individual stars are resolved. Most of the earlier works have used the Photometry in the I-band such as HST ACS/WFC F814W or F850LP for the RGB tip method. Here we look into the RGB tip magnitudes in J-band such as HST WFC3/IR F110W and JWST NIRCam/WF F115W for a wide range of age and metallicity. We find that the J-band (HST WFC3/IR F110W and JWST NIRCam/WF F115W) RGB tip magnitudes do not significantly change compared to that of the I-band (HST ACS/WFC F814W, F850LP) for a wide range of metallicity at given age. Moreover, HST WFC3/IR F110W RGB tip magnitudes stay constant within 0.005 magnitudes for stellar populations with old ages (age > 5 Gyr) at given metallicity., Comment: 4 pages, 3 figures, to appear in the Research Notes of the AAS

We study the inner-most stable circular orbit(ISCO) of Kerr black hole in MOdified gravity(Kerr-MOG black hole) which is one of the exact solution of the field equation of modified gravity in strong gravity regime. Kerr-MOG black hole is constructed commonly known kerr metric in Boyer-Lindquist coordinate by adding repulsive parameter like Yukawa force which explained in quantum gravity. We explore what is some differences of the ISCOs of Kerr-MOG black hole and kerr black hole., Comment: 5pages, 5figures

Embedded diagrams are drawn for investigating the black hole of Kerr and non-Kerr metric. Kerr black holes are characterized by masses $M$ and spin parameters $a$. Non-Kerr black holes also are characterized by the deformation parameters $\epsilon$, which is related to shape of the black hole, in addition to their masses and spins. In this paper, we investigate the behavior of non-Kerr black holes compared with Kerr black holes in the parameter space of ($a$,$\epsilon$) using embedded diagrams. The event horizons and the naked singularity of non-Kerr BHs are discussed in detail., Comment: 4 pages, 6 figures

We present new calibrations of the near-infrared surface brightness fluctuation (SBF) distance method for the F110W (J) and F160W (H) bandpasses of the Wide Field Camera 3 Infrared Channel (WFC3/IR) on the Hubble Space Telescope. The calibrations are based on data for 16 early-type galaxies in the Virgo and Fornax clusters observed with WFC3/IR and are provided as functions of both the optical (g-z) and near-infrared (J-H) colors. The scatter about the linear calibration relations for the luminous red galaxies in the sample is approximately 0.10 mag, corresponding to a statistical error of 5% in distance. Our results imply that the distance to any suitably bright elliptical galaxy can be measured with this precision out to about 80 Mpc in a single-orbit observation with WFC3/IR, making this a remarkably powerful instrument for extragalactic distances. The calibration sample also includes much bluer and lower-luminosity galaxies than previously used for IR SBF studies, revealing interesting population differences that cause the calibration scatter to increase for dwarf galaxies., Comment: 19 pages, 11 figures; version accepted for publication in the Astrophysical Journal; revised version contains a number of clarifications and additional references

The remarkable scientific return and legacy of LSST, in the era that it will define, will not only be realized in the breakthrough science that will be achieved with catalog data. This Big Data survey will shape the way the entire astronomical community advances -- or fails to embrace -- new ways of approaching astronomical research and data. In this white paper, we address the NRC template questions 4,5,6,8 and 9, with a focus on the unique challenges for smaller, and often under-resourced, institutions, including institutions dedicated to underserved minority populations, in the efficient and effective use of LSST data products to maximize LSST's scientific return., Comment: White paper submitted to the National Research Council Committee on a Strategy Optimize the U.S. OIR System in the Era of the LSST, 3 pages

Result diversification is an important aspect in web-based search, document summarization, facility location, portfolio management and other applications. Given a set of ranked results for a set of objects (e.g. web documents, facilities, etc.) with a distance between any pair, the goal is to select a subset $S$ satisfying the following three criteria: (a) the subset $S$ satisfies some constraint (e.g. bounded cardinality); (b) the subset contains results of high "quality"; and (c) the subset contains results that are "diverse" relative to the distance measure. The goal of result diversification is to produce a diversified subset while maintaining high quality as much as possible. We study a broad class of problems where the distances are a metric, where the constraint is given by independence in a matroid, where quality is determined by a monotone submodular function, and diversity is defined as the sum of distances between objects in $S$. Our problem is a generalization of the {\em max sum diversification} problem studied in \cite{GoSh09} which in turn is a generaliztion of the {\em max sum $p$-dispersion problem} studied extensively in location theory. It is NP-hard even with the triangle inequality. We propose two simple and natural algorithms: a greedy algorithm for a cardinality constraint and a local search algorithm for an arbitary matroid constraint. We prove that both algorithms achieve constant approximation ratios.

We introduce a new regression problem which we call the Sum-Based Hierarchical Smoothing problem. Given a directed acyclic graph and a non-negative value, called target value, for each vertex in the graph, we wish to find non-negative values for the vertices satisfying a certain constraint while minimizing the distance of these assigned values and the target values in the lp-norm. The constraint is that the value assigned to each vertex should be no less than the sum of the values assigned to its children. We motivate this problem with applications in information retrieval and web mining. While our problem can be solved in polynomial time using linear programming, given the input size in these applications such a solution might be too slow. We mainly study the \ell_1-norm case restricting the underlying graphs to rooted trees. For this case we provide an efficient algorithm, running in O(n^2) time. While the algorithm is purely combinatorial, its proof of correctness is an elegant use of linear programming duality. We believe that our approach may be applicable to similar problems, where comparable hierarchical constraints are involved, e.g. considering the average of the values assigned to the children of each vertex. While similar in flavor to other smoothing problems like Isotonic Regression (see for example [Angelov et al. SODA'06]), our problem is arguably richer and theoretically more challenging.

Spectral feature index diagrams with integrated globular clusters and simple stellar population models often show that some clusters have weak H beta, so weak that even the oldest models cannot match the observed feature depths. In this work, we rule out the possibility that abundance mixture effects are responsible for the weak indices unless such changes operate to cool the entire isochrone. We discuss this result in the context of other explanations, including horizontal branch morphology, blue straggler populations, and nebular or stellar emission fill-in, finding a preference for flaring in M giants as an explanation for the H beta anomaly., Comment: Submitted to the AJ

We present simple stellar population (SSP) models with scaled-solar and alpha-element enhanced abundances. The SSP models are based on the Dartmouth Stellar Evolution Database, our library of synthetic stellar spectra, and a detailed systematic variation of horizontal-branch (HB) morphology with age and metallicity. In order to test the relative importance of a variety of SSP model ingredients, we compare our SSP models with integrated spectra of 41 Milky Way Globular Clusters (MWGCs) from Schiavon et al. (2005). Using the Mg b and Ca4227 indices, we confirm that Mg and Ca are enhanced by about +0.4 and +0.2 dex, respectively, in agreement with results from high resolution spectra of individual stars in MWGCs. Balmer lines, particularly Hgamma and Hdelta, of MWGCs are reproduced by our alpha-enhanced SSP models not only because of the combination of isochrone and spectral effects but also because of our reasonable HB treatment. Moreover, it is shown that the Mg abundance significantly influences Balmer and iron line indices. Finally, the investigation of power-law initial mass function (IMF) variations suggests that an IMF much shallower than Salpeter is unrealistic because the Balmer lines are too strong on the metal-poor side to be compatible with observations., Comment: 38 pages, 18 figures, AJ accepted. Models are available from http://astro.wsu.edu/hclee/sp_LWD09.html and http://astro.wsu.edu/hclee/sp.html

Promoting racial and ethnic diversity is critically important to the future success and growth of the field of astronomy. The raw ability, drive and interest required to excel in the field is distributed without regard to race, gender, or socioeconomic background. By not actively promoting diversity in our field we risk losing talented people to other professions (or losing them entirely), which means that there will be astronomical discoveries that simply won't get made. There is demonstrated evidence that STEM fields benefit from diverse perspectives on problems that require more complex thought processes. This is especially relevant to a field like astronomy where more and more work is being done collaboratively. The lack of notable growth in African American, Hispanic, and Native American representation in astronomy indicates that the 'pipeline' for these individuals is systemically leaky at critical junctures. Substantially more effort must be directed toward improving the educational and career development of minorities to insure that these potential colleagues are supported through the process. However, simply recognizing that the pipeline is faulty is woefully inadequate. There must be very specific, targeted solutions to help improve the situation. With this in mind, we offer two position papers addressing specific areas of improvement that we identify as (a) essential for any foreseeable progress in the field, and (b) attainable in the 2010-2020 decade. These position papers focus primarily on African Americans, Hispanics, and Native Americans. Although we do not directly address issues of Asian Americans, Pacific Islanders, and other groups, many of the recommendations made here can be adapted to address issues faced by these groups as well., Comment: 5 pages, An Astro2010 Decadal Survey State of the Profession Position Paper

In order to attract, recruit and retain underrepresented minority students to pursue Astronomy and related fields, we must ensure that there continues to be a well qualified pool of graduate and undergraduate students from which to recruit. This required pool of people are today's elementary, middle and high school students. The Astronomy community must be proactive in demonstrating the importance of pursing scientific study and careers to these students and their parents. Only by actively engaging these communities can U.S Astronomy hope to increase the numbers of minority PhDs and continue to be a leader in Astronomical discovery and knowledge., Comment: cover page + 8 pages, An Astro2010 Decadal Survey State of the Profession Position Paper

If the ethnic makeup of the astronomy profession is to achieve parity with the general population within one generation (~30 years), the number of underrepresented minorities earning graduate degrees in astronomy and astrophysics must increase in the coming decade by a factor of 5 to 10. To accomplish this, the profession must develop and invest in mechanisms to more effectively move individuals across critical educational junctures to the PhD and beyond. Early and continuous research engagement starting in the undergraduate years is critical to this vision, in which the federally funded research internship programs (e.g. NSF REU, NASA GSRP) and national centers/observatories play a vital role. Regionally based partnerships with minority-serving institutions (MSIs) are crucial for tapping extant pools of minority talent, as are post-baccalaurate and/or masters degree "bridging" programs that provide critical stepping stones to the PhD. Because of the strong undergraduate physics, engineering, and computer science backgrounds of many students from MSIs, we suggest that instrument development and large scale computing/data-mining are particularly promising avenues for engagement in the coming decade., Comment: cover page + 15 pages, An Astro2010 Decadal Survey State of the Profession Position Paper

We investigate the effects of alpha-element enhancement and the thermally pulsing-asymptotic giant branch (TP-AGB) stars on the surface brightness fluctuation (SBF) magnitudes and broadband colors of simple stellar populations and compare to the empirical calibrations. We consider a broad range of ages and metallicities using the recently updated Teramo BaSTI isochrones. We find that the alpha-element enhanced I-band SBF magnitudes are about 0.35 mag brighter and their integrated V - I colors are about 0.02 mag redder, mostly because of oxygen enhancement effects on the upper red giant branch and asymptotic giant branch. We also demonstrate, using both the Teramo BaSTI and Padova isochrones, the acute sensitivity of SBF magnitudes to the presence of TP-AGB stars, particularly in the near-IR, but in the I-band as well. Empirical SBF trends therefore hold great promise for constraining this important but still highly uncertain stage of stellar evolution. In a similar vein, non-negligible disparities are found among several different models available in the literature due to intrinsic model uncertainties., Comment: Accepted for publication in the Astrophysical Journal, 15 figures

We are developing a brand new stellar population models with flexible chemistry (isochrones plus stellar colors and spectra) in order to set a new standard of completeness and excellence. Here we present preliminary results to assess the effects of stellar evolution models and stellar model atmosphere to the well-known Lick indices at constant heavy element mass fraction Z that self-consistently account for varying heavy element mixtures. We have enhanced chemical elements one by one. Our ultimate goal is to demonstrate 10% absolute mean ages for a sample of local galaxies derived from an integrated light spectrum., Comment: To appear in the proceedings for IAU symposium 241. "Stellar Populations as Building Blocks of Galaxies", Editors: R.F. Peletier, A. Vazdekis

We present the effects due to alpha-element enhancement on surface brightness fluctuation magnitudes and broad-band colors in order to investigate the calibration zero-point. We study these effects at ages covering 0.1 to 13 Gyr and metallicities of Z=0.0003 to 0.04 using the Teramo group's isochrones, BaSTI. Our preliminary results indicate that alpha-enhanced models are needed to match massive red galaxies while solar-scaled models are fine for dwarf blue galaxies to reproduce their independently estimated ages and metallicities., Comment: To appear in the proceedings for IAU symposium 241. "Stellar Populations as Building Blocks of Galaxies", Editors: R.F. Peletier, A. Vazdekis. Relevant materials are also at http://astro.wsu.edu/hclee/hclee_208_AAS_10_07.pdf and http://www.astro.rug.nl/~sctrager/FTSPM/Lee_alpha.pdf

In integrated-light, some color-color diagrams that use optical and near-infrared photometry show surprisingly orthogonal grids as age and metallicity are varied, and they are coming into common usage for estimating the average age and metallicity of spiral galaxies. In this paper we reconstruct these composite grids using simple stellar population models from several different groups convolved with some plausible functional forms of star formation histories at fixed metallicity. We find that the youngest populations present (t<2 Gyr) dominate the light, and because of their presence the age-metallicity degeneracy can be partially broken with broad-band colors, unlike older populations. The scatter among simple stellar population models by different authors is, however, large at ages t<2 Gyr. The dominant uncertainties in stellar population models arise from convective core overshoot assumptions and the treatment of the thermally pulsing asymptotic giant branch phase and helium abundance may play a significant role at higher metallicities. Real spiral galaxies are unlikely to have smooth, exponential star formation histories, and burstiness will cause a partial reversion to the single-burst case, which has even larger model-to-model scatter. Finally, it is emphasized that the current composite stellar population models need some implementation of chemical enrichment histories for the proper analysis of the observational data., Comment: 33 pages, 15 figures. Accepted to ApJ (Apr 2007). The major surgery was Fig. 14

The delta N formula that relates the final curvature perturbation on comoving slices to the inflaton perturbation on flat slices after horizon crossing is a powerful and intuitive tool to compute the curvature perturbation spectrum from inflation. However, it is customarily assumed further that the conventional slow-roll condition is satisfied, and satisfied by all components, during horizon crossing. In this paper, we develop a new delta N formalism for multi-component inflation that can be applied in the most general situations. This allows us to generalize the idea of general slow-roll inflation to the multi-component case, in particular only applying the general slow-roll condition to the relevant component. We compute the power spectrum of the curvature perturbation in multi-component general slow-roll inflation, and find that under quite general conditions it is invertible., Comment: 24 pages, no figure

All 25 Lick/IDS spectral indices have been computed for the integrated light of simple stellar populations over broad ranges of age and metallicity and with effects from horizontal-branch stars fully implemented. For Balmer indices a significant response was noted for Hgamma and Hdelta when a-elements are enhanced, but Hbeta is rather a-insensitive. We also find that our 5 Gyr and 12 Gyr models of Hgamma and Hdelta overlap in the metal-poor regime because of changing populations of blue horizontal-branch stars. Furthermore, for populations younger than 1 Gyr, Balmer lines become weaker in the metal-poor regime because the main-sequence turnoff is hotter than 10,000 K. We present models at fixed [Fe/H] (rather than fixed heavy element mass fraction Z), and compare to Milky Way globular clusters that have independently estimated mean [Fe/H] and [a/Fe]. Comparison of our models with observations of Milky Way and M31 globular clusters in index-index space are favorable, tracing the observations at a model age of 12 Gyr without any zero-point shifts that are needed by some other models. Contrary to the literature values, the Milky Way globular cluster NGC 6553 appears more metal-rich than NGC 6528 from metal indices. We present Hdelta and Hgamma Lick/IDS indices for the Lick/IDS sample of galaxies. We confirm the well-known enhancement of Mg and Na relative to Fe and Ca among early-type galaxies, and its increase with increasing velocity dispersion. There are distinct differences between globular clusters and galaxies in diagrams involving CN1 and CN2, hinting that the globular cluster environment may be a special one in terms of the amount of N incorporated into stars. (abridged), Comment: 41 pages, 19 figures, ApJS, in press. Models and high-order Balmer line indices of Lick galaxies are available at http://astro.wsu.edu/hclee/sp.html

We propose a general inverse formula for extracting inflationary parameters from the observed power spectrum of cosmological perturbations. Under the general slow-roll scheme, which helps to probe the properties of inflation in a model independent way, we invert the leading order, single field, power spectrum formula. We also give some physically interesting examples to demonstrate its wide applicability and illuminate its properties., Comment: 8 pages, no figure ; References expanded

The rotation curves of low surface brightness (LSB) galaxies suggest that they possess significantly higher mass-to-light (M/L) ratios than their high surface brightness counterparts, indicating that LSB galaxies may be dark matter dominated. This interpretation is hampered by the difficulty of disentangling the disc and dark halo contributions from the disc dynamics of LSB galaxies. Recently, Fuchs (2002) has attempted such a disentanglement using spiral arm density wave and swing amplification theory, allowing an independent measurement of the disc mass; this work suggests that LSB discs are significantly more massive than previously believed. This would considerably reduce the amount of matter required in the dark halos in fitting the rotation curves. Interestingly, the high mass-to-light ratios derived for the discs appear inconsistent with standard stellar population synthesis models. In this paper, we investigate whether the high M/L ratios for the Fuchs LSB discs might be understood by adopting a very ``bottom heavy'' initial mass function (IMF). We find that an IMF with a power law exponent of around alpha=3.85 (compared to the standard Salpeter IMF, alpha=2.35) is sufficient to explain the unusually high M/L ratios of the Fuchs sample. Within the context of the models, the blue colours ((B-R)_0 < 1.0) of the sample galaxies result from being metal-poor ([Fe/H] = -1.5 ~ -1.0) and having undergone recent (~1-3 Gyr ago) star formation., Comment: 6 pages, 5 figures, accepted for publication in MNRAS

The primary present-day observables upon which theories of galaxy evolution are based are a system's morphology, dynamics, colour, and chemistry. Individually, each provides an important constraint to any given model; in concert, the four represent a fundamental (intractable) boundary condition for chemodynamical simulations. We review the current state-of-the-art semi-analytical and chemodynamical models for the Milky Way, emphasising the strengths and weaknesses of both approaches., Comment: 16 pages, 9 figures, 1 table, LaTeX (emulatepasa.sty). Invited Review, accepted for publication in the Publications of the Astronomical Society of Australia, Vol 20, Num 4 (2003)