Globular Cluster Systems in Brightest Cluster Galaxies. III: Beyond Bimodality

We present new deep photometry of the rich globular cluster (GC) systems around the Brightest Cluster Galaxies UGC 9799 (Abell 2052) and UGC 10143 (Abell 2147), obtained with the HST ACS and WFC3 cameras. For comparison, we also present new reductions of similar HST/ACS data for the Coma supergiants NGC 4874 and 4889. All four of these galaxies have huge cluster populations (to the radial limits of our data, comprising from 12000 to 23000 clusters per galaxy). The metallicity distribution functions (MDFs) of the GCs can still be matched by a bimodal-Gaussian form where the metal-rich and metal-poor modes are separated by ~0.8 dex, but the internal dispersions of each mode are so large that the total MDF becomes very broad and nearly continuous from [Fe/H] = -2.4 to Solar. There are, however, significant differences between galaxies in the relative numbers of \emph{metal-rich} clusters, suggesting that they underwent significantly different histories of mergers with massive, gas-rich halos. Lastly, the proportion of metal-poor GCs rises especially rapidly outside projected radii R > 4 R_eff, suggesting the importance of accreted dwarf satellites in the outer halo. Comprehensive models for the formation of GCs as part of the hierarchical formation of their parent galaxies will be needed to trace the systematic change in structure of the MDF with galaxy mass, from the distinctly bimodal form in smaller galaxies up to the broad continuum that we see in the very largest systems.Comment: In press for Astrophysical Journa

Subordination and Radius Problems for Certain Starlike Functions

We study the following class of starlike functions $$\mathcal{S}^*_{\wp}:=\left\{f\in\mathcal{A}: {zf'(z)}/{f(z)}\prec\ 1+ze^z=:\wp(z) \right\},$$ that are associated with the cardioid domain $\wp(\mathbb{D})$, by deriving certain convolution results, radius problems, majorization result, radius problems in terms of coefficients and differential subordination implications. Consequently, we establish some interesting generalizations of our results for the Ma-Minda class of starlike functions $\mathcal{S}^{*}(\psi)$. We also provide, the set of extremal functions maximizing $\Re\Phi\left(\log{(f(z)/z)}\right)$ or $\left|\Phi\left(\log{(f(z)/z)}\right)\right|$ for functions in $\mathcal{S}^{*}(\psi)$, where $\Phi$ is a non-constant entire function. Further T. H. MacGregor's result for the class $\mathcal{S}^{*}(\alpha)$ and $\mathcal{S}^*_{\wp}$ are obtained as special case to our result

Pseudospin entanglement and Bell test in graphene

We propose a way of producing and detecting pseudospin entanglement between electrons and holes in graphene. Electron-hole pairs are produced by a fluctuating potential and their entanglement is demonstrated by a current correlation measurement. The chirality of electrons in graphene facilitates a well-controlled Bell test with (pseudo-)spin projection angles defined in real space.Comment: 9 pages, 2 figures; v2 with slightly modified abstract and introductio