Can we use Weak Lensing to Measure Total Mass Profiles of Galaxies on 20 kiloparsec Scales?

Current constraints on dark matter density profiles from weak lensing are typically limited to radial scales greater than 50-100 kpc. In this paper, we explore the possibility of probing the very inner regions of galaxy/halo density profiles by measuring stacked weak lensing on scales of only a few tens of kpc. Our forecasts focus on scales smaller than the equality radius (Req) where the stellar component and the dark matter component contribute equally to the lensing signal. We compute the evolution of Req as a function of lens stellar mass and redshift and show that Req=7-34 kpc for galaxies with the stellar mass of 10^{9.5}-10^{11.5} solar masses. Unbiased shear measurements will be challenging on these scales. We introduce a simple metric to quantify how many source galaxies overlap with their neighbours and for which shear measurements will be challenging. Rejecting source galaxies with close-by companions results in about a 20 per cent decrease in the overall source density. Despite this decrease, we show that Euclid and WFIRST will be able to constrain galaxy/halo density profiles at Req with signal-to-noise ratio >20 for the stellar mass of >10^{10} solar masses. Weak lensing measurements at Req, in combination with stellar kinematics on smaller scales, will be a powerful means by which to constrain both the inner slope of the dark matter density profile as well as the mass and redshift dependence of the stellar initial mass function.Comment: 19 pages, 14 figures, 3 tables, submitted to MNRAS, included the referee comment

Magnetic field generation by the Weibel instability at temperature gradients in collisionless plasmas

The Weibel instability could be responsible for the generation of magnetic fields in various objects such as gamma-ray bursts, jets from active galactic nuclei, and clusters of galaxies. Using numerical simulations, the development of the Weibel instability at a temperature gradient is studied. It is found that current sheets are first generated at the gradient, and then they are rounded off and turn into current filaments. During this process, return currents are generated around the filaments and they prevent filaments from merger. The magnetic fields around the filaments persist at least until t~8000/\omega_p, where \omega_p is the plasma frequency, and it is very likely that they survive for a much longer time.Comment: Physics of Plasmas in pres

Radial Bargmann representation for the Fock space of type B

Let $\nu_{\alpha,q}$ be the probability and orthogonality measure for the $q$-Meixner-Pollaczek orthogonal polynomials, which has appeared in \cite{BEH15} as the distribution of the $(\alpha,q)$-Gaussian process (the Gaussian process of type B) over the $(\alpha,q)$-Fock space (the Fock space of type B). The main purpose of this paper is to find the radial Bargmann representation of $\nu_{\alpha,q}$. Our main results cover not only the representation of $q$-Gaussian distribution by \cite{LM95}, but also of $q^2$-Gaussian and symmetric free Meixner distributions on $\mathbb R$. In addition, non-trivial commutation relations satisfied by $(\alpha,q)$-operators are presented.Comment: 13 pages, minor changes have been mad

Double solid twistor spaces: the case of arbitrary signature

In a recent paper (math.DG/0701278) we constructed a series of new Moishezon twistor spaces which is a kind of variant of the famous LeBrun twistor spaces. In this paper we explicitly give projective models of another series of Moishezon twistor spaces on nCP^2 for arbitrary n>2, which can be regarded as a generalization of the twistor spaces of a 'double solid type' on 3CP^2 studied by Kreussler, Kurke, Poon and the author. Similarly to the twistor spaces of 'double solid type' on 3CP^2, projective models of present twistor spaces have a natural structure of double covering of a CP^2-bundle over CP^1. We explicitly give a defining polynomial of the branch divisor of the double covering whose restriction to fibers are degree four. If n>3 these are new twistor spaces, to the best of the author's knowledge. We also compute the dimension of the moduli space of these twistor spaces. Differently from math.DG/0701278, the present investigation is based on analysis of pluri-(half-)anticanonical systems of the twistor spaces.Comment: 30 pages, 3 figures; v2: title changed (the original title was "Explicit construction of new Moishezon twistor spaces, II".

Degenerations of LeBrun twistor spaces

We investigate various limits of the twistor spaces associated to the self-dual metrics on n CP ^2, the connected sum of the complex projective planes, constructed by C. LeBrun. In particular, we explicitly present the following 3 kinds of degenerations whose limits of the metrics are: (a) LeBrun metrics on (n-1) CP ^2$, (b) (Another) LeBrun metrics on the total space of the line bundle O(-n) over CP ^1 (c) The hyper-Kaehler metrics on the small resolution of rational double points of type A_{n-1}, constructed by Gibbons and Hawking.Comment: 21 pages, 7 figures. V2: A new section added at the end of the article. V3: Reference slightly update

Deformation of LeBrun's ALE metrics with negative mass

In this article we investigate deformations of a scalar-flat K\"ahler metric on the total space of complex line bundles over CP^1 constructed by C. LeBrun. In particular, we find that the metric is included in a one-dimensional family of such metrics on the four-manifold, where the complex structure in the deformation is not the standard one.Comment: 20 pages, no figure. V2: added two references, filled a gap in the proof of Theorem 1.2. V3: corrected a wrong statement about Kuranishi family of a Hirzebruch surface stated in the last paragraph in the proof of Theorem 1.2, and fixed a relevant error in the proof. Also added a reference [24] about Kuranishi family of Hirzebruch surface

Horizontal symmetry in Higgs sector of GUT with U(1)_A symmetry

In a series of papers, we pointed out that an anomalous $U(1)_A$ gauge symmetry naturally solves various problems in grand unified theories (GUTs) and that a horizontal gauge symmetry, $SU(2)_H$ or $SU(3)_H$, not only realizes the unification of three generation quarks and leptons in fewer multiplets but also solves the supersymmetric flavor problem. In this paper, we examine the possibility that the Higgs sectors of the GUT symmetry and of the horizontal symmetry are unified, that is, there are some Higgs fields whose vacuum expectation values (VEVs) break both the GUT gauge symmetry and the horizontal symmetry at the same time. Although the scale of the VEVs become too large to suppress the flavor changing neutral current processes sufficiently, the unification is possible. In addition, for the $SU(3)_H$ models, the $SU(3)_H$ gauge anomaly is cancelled in the unified models without introducing additional fields in contrast with the previous models in which the Higgs sectors are not unified.Comment: 35 page

Gauge Coupling Unification in GUT with Anomalous U(1) Symmetry

We show that in the framework of grand unified theory (GUT) with anomalous $U(1)_A$ gauge symmetry, the success of the gauge coupling unification in the minimal SU(5) GUT is naturally explained, even if the mass spectrum of superheavy fields does not respect SU(5) symmetry. Because the unification scale for most realizations of the theory becomes smaller than the usual GUT scale, it suggests that the present level of experiments is close to that sufficient to observe proton decay via dimension 6 operators, $p\to e+\pi$.Comment: 4 pages, RevTeX, to appear in Phys.Rev.Let

Intratumoural mRNA expression of genes from the oestradiol metabolic pathway and clinical and histopathological parameters of breast cancer

INTRODUCTION: The expression of the oestrogen receptor (ER) is one of the more important clinical parameters of breast cancer. However, the relationship between the ER and its ligand, oestradiol, and the enzymes that synthesise it are not well understood. The expression of mRNA transcripts of members of the oestradiol metabolic and signalling pathways including the ER was studied in detail. METHOD: mRNA transcripts for aromatase (CYP19), 17-β-hydroxysteroid dehydrogenase I, 17-β-hydroxysteroid dehydrogenase II, ERα, ERβ, steroid sulfatase (STS), oestradiol sulfotransferase (EST), cyclin D(1 )(CYCLD1) and ERBB2 were fluorometrically quantified by competitive RT-PCR using an internal standard in 155 breast carcinomas. In addition, the transcripts of CYP19 were analysed for alternative splicing/usage of exon 1 and an alternative poly A tail. RESULTS: A great variability of expression was observed, ranging from 0 to 2376 amol/mg RNA. The highest levels were observed for STS and EST, and the lowest levels (close to zero) were observed for the 17-β-hydroxysteroid dehydrogenase isoenzymes. The levels of mRNA expression were analysed with respect to clinical and histopathological parameters as well as for disease-free survival. High correlation of the mRNA expression of STS, EST and 17-β-hydroxysteroid dehydrogenase in the tumours suggested a common regulation, possibly by their common metabolite (oestradiol). Hierarchical clustering analysis in the 155 patients resulted in two main clusters, representing the ERα-negative and ERα-positive breast cancer cases. The mRNA expression of the oestradiol metabolising enzymes did not follow the expression of the ERα in all cases, leading to the formation of several subclasses of tumours. Patients with no expression of CYP19 and patients with high levels of expression of STS had significantly shorter disease-free survival time (P > 0.0005 and P < 0.03, respectively). Expression of ERβ mRNA was a better prognostic factor than that of ERα in this material. CONCLUSION: Our results indicate the importance of CYP19 and the enzymes regulating the oestrone sulfate metabolism as factors of disease-free survival in breast cancer, in addition to the well-known factors ER and ERBB2

Sliding Singlet Mechanism Revisited

We show that the unification of the doublet Higgs in the standard model (SM) and the Higgs to break the grand unified theory (GUT) group stabilizes the sliding singlet mechanism which can solve the doublet-triplet (DT) splitting problem. And we generalize this attractive mechanism to apply it to many unified scenarios. In this paper, we try to build various concrete E_6 unified models by using the generalized sliding singlet mechanism.Comment: 13 page