From Baking a Cake to Solving the Schrodinger Equation

The primary emphasis of this study has been to explain how modifying a cake recipe by changing either the dimensions of the cake or the amount of cake batter alters the baking time. Restricting our consideration to the genoise, one of the basic cakes of classic French cuisine, we have obtained a semi-empirical formula for its baking time as a function of oven temperature, initial temperature of the cake batter, and dimensions of the unbaked cake. The formula, which is based on the Diffusion equation, has three adjustable parameters whose values are estimated from data obtained by baking genoises in cylindrical pans of various diameters. The resulting formula for the baking time exhibits the scaling behavior typical of diffusion processes, i.e. the baking time is proportional to the (characteristic length scale)^2 of the cake. It also takes account of evaporation of moisture at the top surface of the cake, which appears to be a dominant factor affecting the baking time of a cake. In solving this problem we have obtained solutions of the Diffusion equation which are interpreted naturally and straightforwardly in the context of heat transfer; however, when interpreted in the context of the Schrodinger equation, they are somewhat peculiar. The solutions describe a system whose mass assumes different values in two different regions of space. Furthermore, the solutions exhibit characteristics similar to the evanescent modes associated with light waves propagating in a wave guide. When we consider the Schrodinger equation as a non-relativistic limit of the Klein-Gordon equation so that it includes a mass term, these are no longer solutions.Comment: 23 pages, 10 Postscript figure

Dyons, Superstrings, and Wormholes: Exact Solutions of the Non-Abelian Dirac-Born-Infeld Action

We construct dyon solutions on coincident D4-branes, obtained by applying T-duality transformations to type I SO(32) superstring theory in 10 dimensions. These solutions, which are exact, are obtained from an action comprising the non-Abelian Dirac-Born-Infeld action and a Wess-Zumino-like action. When one spatial dimension of the D4-branes is taken to be vanishingly small, the dyons are analogous to the ’t Hooft/Polyakov monopole residing in a 3+1-dimensional spacetime, where the component of the Yang-Mills potential transforming as a Lorentz scalar is reinterpreted as a Higgs boson transforming in the adjoint representation of the gauge group. Applying a T-duality transformation to the vanishingly small spatial dimension, we obtain a collection of D3-branes, not all of which are coincident. Two of the D3-branes, distinct from the others, acquire intrinsic, finite curvature and are connected by a wormhole. The dyons possess electric and magnetic charges whose values on each D3-brane are the negative of one another. The gravitational effects, which arise after the T-duality transformation, occur despite the fact that the action of the system does not explicitly include the gravitational interaction. These solutions provide a simple example of the subtle relationship between the Yang-Mills and gravitational interactions, that is, gauge/gravity duality

Structure of the Draco Dwarf Spheroidal Galaxy

This article studies the structure of the Draco dwarf spheroidal galaxy with an emphasis on the question of whether the spatial distribution of its stars has been affected by the tidal interaction with the Milky Way, using R- and V-band CCD photometry for eleven fields. The article reports coordinates for the center, a position angle of the major axis, and the ellipticity. It also reports the results of searches for asymmetries in the structure of Draco. These results, and searches for a ``break'' in the radial profile and for the presence of principal sequences of Draco in a color-magnitude diagram for regions more than 50 arcmin from the center, yield no evidence that tidal forces from the Milky Way have affected the structure of Draco.Comment: 25 pages, 11 figures, 3 tables. Accepted for publication in A

Magellan/M2FS Spectroscopy of Galaxy Clusters: Stellar Population Model and Application to Abell 267

We report the results of a pilot program to use the Magellan/M2FS spectrograph to survey the galactic populations and internal kinematics of galaxy clusters. For this initial study, we present spectroscopic measurements for $223$ quiescent galaxies observed along the line of sight to the galaxy cluster Abell 267 ($z\sim0.23$). We develop a Bayesian method for modeling the integrated light from each galaxy as a simple stellar population, with free parameters that specify redshift ($v_\mathrm{los}/c$) and characteristic age, metallicity ($\mathrm{[Fe/H]}$), alpha-abundance ($[\alpha/\mathrm{Fe}]$), and internal velocity dispersion ($\sigma_\mathrm{int}$) for individual galaxies. Parameter estimates derived from our 1.5-hour observation of A267 have median random errors of $\sigma_{v_\mathrm{los}}=20\ \mathrm{km\ s^{-1}}$, $\sigma_{\mathrm{Age}}=1.2\ \mathrm{Gyr}$, $\sigma_{\mathrm{[Fe/H]}}=0.11\ \mathrm{dex}$,$\sigma_{[\alpha/\mathrm{Fe}]}=0.07\ \mathrm{dex}$, and$\sigma_{\sigma_\mathrm{int}}=20\ \mathrm{km\ s^{-1}}$. In a companion paper, we use these results to model the structure and internal kinematics of A267.Comment: 16 pages, 11 figures, accepted for publication in The Astronomical Journa

How Lyman Alpha Emission Depends On Galaxy Stellar Mass

In this work, we show how the stellar mass (M) of galaxies affects the 3<z<4.6 Ly-alpha equivalent width (EW) distribution. To this end, we design a sample of 629 galaxies in the M range 7.6 < logM/Msun < 10.6 from the 3D-HST/CANDELS survey. We perform spectroscopic observations of this sample using the Michigan/Magellan Fiber System, allowing us to measure Ly-alpha fluxes and use 3D-HST/CANDELS ancillary data. In order to study the Ly-alpha EW distribution dependence on M, we split the whole sample in three stellar mass bins. We find that, in all bins, the distribution is best represented by an exponential profile of the form dN(M)/dEW= A(M)exp(-EW/W0(M))/W0(M). Through a Bayesian analysis, we confirm that lower M galaxies have higher Ly-alpha EWs. We also find that the fraction A of galaxies featuring emission and the e-folding scale W0 of the distribution anti- correlate with M, recovering expressions of the forms A(M)= -0.26(.13) logM/Msun+3.01(1.2) and W0(M)= -15.6(3.5) logM/Msun +166(34). These results are crucial for proper interpretation of Ly-alpha emission trends reported in the literature that may be affected by strong M selection biases.Comment: 4 pages, 5 figure

AGB Sodium Abundances in the Globular Cluster 47 Tucanae (NGC 104)

A recent analysis comparing the [Na/Fe] distributions of red giant branch (RGB) and asymptotic giant branch (AGB) stars in the Galactic globular cluster NGC 6752 found that the ratio of Na-poor to Na-rich stars changes from 30:70 on the RGB to 100:0 on the AGB. The surprising paucity of Na-rich stars on the AGB in NGC 6752 warrants additional investigations to determine if the failure of a significant fraction of stars to ascend the AGB is an attribute common to all globular clusters. Therefore, we present radial velocities, [Fe/H], and [Na/Fe] abundances for 35 AGB stars in the Galactic globular cluster 47 Tucanae (47 Tuc; NGC 104), and compare the AGB [Na/Fe] distribution with a similar RGB sample published previously. The abundances and velocities were derived from high resolution spectra obtained with the Michigan/Magellan Fiber System (M2FS) and MSpec spectrograph on the Magellan-Clay 6.5m telescope. We find the average heliocentric radial velocity and [Fe/H] values to be =-18.56 km s^-1 (sigma=10.21 km s^-1) and =-0.68 (sigma=0.08), respectively, in agreement with previous literature estimates. The average [Na/Fe] abundance is 0.12 dex lower in the 47 Tuc AGB sample compared to the RGB sample, and the ratio of Na-poor to Na-rich stars is 63:37 on the AGB and 45:55 on the RGB. However, in contrast to NGC 6752, the two 47 Tuc populations have nearly identical [Na/Fe] dispersion and interquartile range values. The data presented here suggest that only a small fraction <20% of Na-rich stars in 47 Tuc may fail to ascend the AGB. Regardless of the cause for the lower average [Na/Fe] abundance in AGB stars, we find that Na-poor stars and at least some Na-rich stars in 47 Tuc evolve through the early AGB phase. [abridged]Comment: Accepted for publication in the Astronomical Journal; 15 pages; 8 figures; 4 table

Mapping the Galactic Halo. V. Sgr dSph Tidal Debris 60 degrees from the Main Body

As part of the Spaghetti Project Survey (SPS) we have detected a concentration of giant stars well above expectations for a smooth halo model. The position (l~350, b~50) and distance (~50 kpc) of this concentration match those of the Northern over-density detected by SDSS (Yanny et al. 2000, Ivezic et al. 2000). We find additional evidence for structure at ~80 kpc in the same direction. We present radial velocities for many of these stars, including the first published results from the 6.5m Magellan telescope. The radial velocities for stars in these structures are in excellent agreement with models of the dynamical evolution of the Sgr dwarf tidal debris, whose center is 60 degrees away. The metallicity of stars in these streams is lower than that of the main body of the Sgr dwarf, which may indicate a radial metallicity gradient prior to disruption.Comment: 10 pages, 3 figures accepted in Astrophysical Journal Letter

Absolute Magnitudes and Colors of RR Lyrae stars in DECam Passbands from Photometry of the Globular Cluster M5

We characterize the absolute magnitudes and colors of RR Lyrae stars in the globular cluster M5 in the ugriz filter system of the Dark Energy Camera (DECam). We provide empirical Period-Luminosity (P-L) relationships in all 5 bands based on 47 RR Lyrae stars of the type ab and 14 stars of the type c. The P-L relationships were found to be better constrained for the fundamental mode RR Lyrae stars in the riz passbands, with dispersion of 0.03, 0.02 and 0.02 magnitudes, respectively. The dispersion of the color at minimum light was found to be small, supporting the use of this parameter as a means to obtain accurate interstellar extinctions along the line of sight up to the distance of the RR Lyrae star. We found a trend of color at minimum light with pulsational period that, if taken into account, brings the dispersion in color at minimum light to < 0.016 magnitudes for the (r-i), (i-z), and (r-z) colors. These calibrations will be very useful for using RR Lyrae stars from DECam observations as both standard candles for distance determinations and color standards for reddening measurements.Comment: Accepted for publication in A