Embedded Diagrams of Kerr and Non-Kerr black Holes

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 figure

Age Estimation of Extragalactic Globular Cluster Systems Using H beta Index

After taking into account, for the first time, the detailed systematic variation of horizontal-branch (HB) morphology with age and metallicity, our population synthesis models show that the integrated H beta index is significantly affected by the presence of blue HB stars. Our models indicate that the strength of the H beta index increases as much as 0.75 A due to blue HB stars. According to our models, a systematic difference between the globular cluster system in the Milky Way Galaxy and that in NGC 1399 in the H beta vs. Mg2 diagram is understood if globular cluster systems in giant elliptical galaxies are couple of billion years older, in the mean, than the Galactic counterpart.Comment: 3 pages, 2 figures. Contribution to `Astrophysical Ages and Timescales' ASP Conf. Ser., Eds. T. von Hippel, N. Manset, C. Simpson, EPS files are available at http://csaweb.yonsei.ac.kr/~hclee/Hawai

Nonlinear Color-Metallicity Relations of Globular Clusters. VIII. Reproducing Color Distributions of Individual Globular Cluster Systems in the Virgo and Fornax Galaxy Clusters

The color distributions of globular clusters (GCs) in individual early-type galaxies show great diversity in their morphology. Based on the conventional "linear" relationship between the colors and metallicities of GCs, the GC metallicity distributions inferred from colors and in turn their formation histories, should be as diverse as they appear. In contrast, here we show that an alternative scenario rooted in the "nonlinear" nature of the metallicity-to-color transformation points to a simpler and more coherent picture. Our simulations of the color distributions for $\sim$80 GC systems in early-type galaxies from the ACS Virgo and Fornax Cluster Surveys suggest that the majority ($\sim$70$\%$) of early-type galaxies have old ($\sim$13 Gyr) and coeval GCs. Their variety in the color distribution morphology stems mainly from one parameter, the mean metallicity of a GC system. Furthermore, the color distributions of the remaining ($\sim$30$\%$) GC systems are also explained by the nonlinearity scenario, assuming additional young or intermediate-age GCs with a number fraction of $\sim$20$\%$ of underlying old GCs. Our results reinforce the nonlinearity explanation for the GC color bimodality and provide a new perspective on early-type galaxy formation in the cluster environment, such as the Virgo and Fornax galaxy clusters.Comment: 33 pages, 7 figures, 3 tables, accepted for publication in ApJ

A general framework for compressed sensing and parallel MRI using annihilating filter based low-rank Hankel matrix

Parallel MRI (pMRI) and compressed sensing MRI (CS-MRI) have been considered as two distinct reconstruction problems. Inspired by recent k-space interpolation methods, an annihilating filter based low-rank Hankel matrix approach (ALOHA) is proposed as a general framework for sparsity-driven k-space interpolation method which unifies pMRI and CS-MRI. Specifically, our framework is based on the fundamental duality between the transform domain sparsity in the primary space and the low-rankness of weighted Hankel matrix in the reciprocal space, which converts pMRI and CS-MRI to a k-space interpolation problem using structured matrix completion. Using theoretical results from the latest compressed sensing literatures, we showed that the required sampling rates for ALOHA may achieve the optimal rate. Experimental results with in vivo data for single/multi-coil imaging as well as dynamic imaging confirmed that the proposed method outperforms the state-of-the-art pMRI and CS-MRI

Yonsei evolutionary population synthesis (YEPS). II. Spectro-photometric evolution of helium-enhanced stellar populations

The discovery of multiple stellar populations in Milky Way globular clusters (GCs) has stimulated various follow-up studies on helium-enhanced stellar populations. Here we present the evolutionary population synthesis models for the spectro-photometric evolution of simple stellar populations (SSPs) with varying initial helium abundance ($Y_{\rm ini}$). We show that $Y_{\rm ini}$ brings about {dramatic} changes in spectro-photometric properties of SSPs. Like the normal-helium SSPs, the integrated spectro-photometric evolution of helium-enhanced SSPs is also dependent on metallicity and age for a given $Y_{\rm ini}$. {We discuss the implications and prospects for the helium-enhanced populations in relation to the second-generation populations found in the Milky Way GCs.} All of the models are available at \url{http://web.yonsei.ac.kr/cosmic/data/YEPS.htm}.Comment: Accepted for publication in ApJ, 21 pages, 12 figures, 3 table

Which Contrast Does Matter? Towards a Deep Understanding of MR Contrast using Collaborative GAN

Thanks to the recent success of generative adversarial network (GAN) for image synthesis, there are many exciting GAN approaches that successfully synthesize MR image contrast from other images with different contrasts. These approaches are potentially important for image imputation problems, where complete set of data is often difficult to obtain and image synthesis is one of the key solutions for handling the missing data problem. Unfortunately, the lack of the scalability of the existing GAN-based image translation approaches poses a fundamental challenge to understand the nature of the MR contrast imputation problem: which contrast does matter? Here, we present a systematic approach using Collaborative Generative Adversarial Networks (CollaGAN), which enable the learning of the joint image manifold of multiple MR contrasts to investigate which contrasts are essential. Our experimental results showed that the exogenous contrast from contrast agents is not replaceable, but other endogenous contrast such as T1, T2, etc can be synthesized from other contrast. These findings may give important guidance to the acquisition protocol design for MR in real clinical environment.Comment: 32 pages, 6 figure

Thermally activated switching of perpendicular magnet by spin-orbit spin torque

We theoretically investigate the threshold current for thermally activated switching of a perpendicular magnet by spin-orbit spin torque. Based on the Fokker-Planck equation, we obtain an analytic expression of the switching current, in agreement with numerical result. We find that thermal energy barrier exhibits a quasi-linear dependence on the current, resulting in an almost linear dependence of switching current on the log-scaled current pulse-width even below 10 ns. This is in stark contrast to standard spin torque switching, where thermal energy barrier has a quadratic dependence on the current and the switching current rapidly increases at short pulses. Our results will serve as a guideline to design and interpret switching experiments based on spin-orbit spin torqueComment: 18 pages, 4 figure

Threshold current for switching of a perpendicular magnetic layer induced by spin Hall effect

We theoretically investigate the switching of a perpendicular magnetic layer by in-plane charge current due to the spin Hall effect. We find that, in the high damping regime, the threshold switching current is independent of the damping constant, and is almost linearly proportional to both effective perpendicular magnetic anisotropy field and external in-plane field applied along the current direction. We obtain an analytic expression of the threshold current, in excellent agreement with numerical results. This expression can be used to determine the physical quantities associated with spin Hall effect, and to design relevant magnetic devices based on the switching of perpendicular magnetic layers.Comment: 16 pages, 3 figure

Nonlinear Color--Metallicity Relations of Globular Clusters. VI. On Calcium II Triplet Based Metallicities of Globular Clusters in Early-type Galaxies

The metallicity distribution function of globular clusters (GCs) in galaxies is a key to understanding galactic formation and evolution. The calcium II triplet (CaT) index has recently become a popular metal abundance indicator thanks to its sensitivity to GC metallicity. Here we revisit and assess the reliability of CaT as a metallicity indicator using our new stellar population synthesis simulations based on empirical, high-resolution fluxes. The model shows that the CaT strength of old ($>$ 10 Gyr) GCs is proportional to ${\rm [Fe/H]}$ below $-0.5$. In the modest metal-rich regime, however, CaT does not increase anymore with ${\rm [Fe/H]}$ due to the little contribution from coolest red giant stars to the CaT absorption. The nonlinear nature of the color--$CaT$ relation is confirmed by the observations of GCs in nearby early-type galaxies. This indicates that the CaT should be used carefully when deriving metallicities of metal-rich stellar populations. Our results offer an explanation for the observed sharp difference between the color and $CaT$ distributions of GCs in the same galaxies. We take this as an analogy to the view that metallicity--color and metallicity--Lick index nonlinearity of GCs is primarily responsible for their observed "bimodal" distributions of colors and absorption indices.Comment: 27 pages, 10 figures, 2 tables, accepted for publication in Ap

Horizontal-Branch Stars as an Age Indicator

Surface temperature distribution of horizontal-branch (HB) stars is very sensitive to age in old stellar systems, which makes it an attractive age indicator. In this paper, we present the recent revision of our model calculations for the HB morphology of globular clusters. The result is more updated version of our earlier models (Lee, Demarque, & Zinn 1994), which suggests that the HB morphology is more sensitive (\sim 40%) to age. We also present our new model calculations on the effect of HB stars in dating old stellar systems using the H$\beta$ index. Our results indicate that the effect of HB stars is rather strong, and suggest a possibility for the systematic difference in age between the globular clusters in the Milky Way Galaxy and those in giant elliptical galaxies. Finally, we compare these results with the relative ages estimated from our far-UV dating technique for giant elliptical galaxies.Comment: 10 pages, 2 figures, Invited paper presented at the workshop on "Spectrophotometric Dating of Stars & Galaxies", held at Annapolis, MD, USA, in April 25-29, 199