Rm Sp Research Articles

The eROSITA Final Equatorial-Depth Survey (eFEDS) – Splashback radius of X-ray galaxy clusters using galaxies from HSC survey

ABSTRACT We present the splashback radius measurements around the SRG/eROSITA eFEDS X-ray selected galaxy clusters by cross-correlating them with HSC S19A photometric galaxies. The X-ray selection is expected to be less affected by systematics related to projection that affects optical cluster finder algorithms. We use a nearly volume-limited sample of 109 galaxy clusters selected in 0.5–2.0 keV band having luminosity $L_X \gt 10^{43.5}\, {\rm erg \, s}^{-1}\, h^{-2}$ within the redshift z < 0.75 and obtain measurements of the projected cross-correlation with a signal to noise of 17.43. We model our measurements to infer a 3D profile and find that the steepest slope is sharper than −3 and associate the location with the splashback radius. We infer the value of the 3D splashback radius $r_{\rm sp} = 1.45^{+0.30}_{-0.26}\, h^{-1}\, {\rm Mpc}$ . We also measure the weak-lensing signal of the galaxy clusters and obtain halo mass $\log [M_{\rm 200m}/ h^{-1}\, {\rm M_\odot }] = 14.52 \pm 0.06$ using the HSC-S16A shape catalogue data at the median redshift z = 0.46 of our cluster sample. We compare our rsp values with the spherical overdensity boundary $r_{\rm 200m} = 1.75 \pm 0.08\, h^{-1} \, {\rm Mpc}$ based on the halo mass, which is consistent within 1.2σ with the ΛCDM predictions. Our constraints on the splashback radius, although broad, are the best measurements thus far obtained for an X-ray selected galaxy cluster sample.

Detecting the stochastic gravitational wave background with the TianQin detector

The detection of stochastic gravitational wave background (SGWB) is among the leading scientific goals of the space-borne gravitational wave observatory, which would have significant impact on astrophysics and fundamental physics. In this work, we developed a data analysis software, \texttt{TQSGWB}, which can extract isotropic SGWB using the Bayes analysis method based on the TianQin detector. We find that for the noise cross spectrum, there are imaginary components and they play an important role in breaking the degeneracy of the position noise in the common laser link. When the imaginary corrections are considered, the credible regions of the position noise parameters are reduced by two orders of magnitude. We demonstrate that the parameters of various signals and instrumental noise could be estimated directly in the absence of a Galactic confusion foreground through Markov chain Monte Carlo sampling. With only a three-month observation, we find that TianQin could be able to confidently detect SGWBs with energy density as low as $\Omega_{\rm PL} = 1.3 \times 10^{-12}$, $\Omega_{\rm Flat} = 6.0 \times 10^{-12}$, and $\Omega_{\rm SP} = 9.0 \times 10^{-12}$, for power-law, flat, and single-peak models respectively.

Shocks in the stacked Sunyaev-Zel’dovich profiles of clusters II: Measurements from SPT-SZ + Planck Compton-y map

ABSTRACT We search for the signature of cosmological shocks in stacked gas pressure profiles of galaxy clusters using data from the South Pole Telescope (SPT). Specifically, we stack the latest Compton-y maps from the 2500 deg2 SPT-SZ survey on the locations of clusters identified in that same data set. The sample contains 516 clusters with mean mass $\langle M_{\rm 200m}\rangle = 10^{14.9} \, {\rm M}_\odot$ and redshift 〈z〉 = 0.55. We analyse in parallel a set of zoom-in hydrodynamical simulations from the three hundred project. The SPT-SZ data show two features: (i) a pressure deficit at R/R200m = 1.08 ± 0.09, measured at 3.1σ significance and not observed in the simulations, and; (ii) a sharp decrease in pressure at R/R200m = 4.58 ± 1.24 at 2.0σ significance. The pressure deficit is qualitatively consistent with a shock-induced thermal non-equilibrium between electrons and ions, and the second feature is consistent with accretion shocks seen in previous studies. We split the cluster sample by redshift and mass, and find both features exist in all cases. There are also no significant differences in features along and across the cluster major axis, whose orientation roughly points towards filamentary structure. As a consistency test, we also analyse clusters from the Planck and Atacama Cosmology Telescope Polarimeter surveys and find quantitatively similar features in the pressure profiles. Finally, we compare the accretion shock radius ($R_{\rm sh,\, acc}$) with existing measurements of the splashback radius (Rsp) for SPT-SZ and constrain the lower limit of the ratio, $R_{\rm sh,\, acc}/R_{\rm sp}\gt 2.16 \pm 0.59$.

Siegel modular forms of weight 13 and the Leech lattice

For g=8,12,16 and 24 , there is a nonzero alternating g -multilinear form on the {\rm Leech} lattice, unique up to a scalar, which is invariant by the orthogonal group of {\rm Leech} . The harmonic Siegel theta series built from these alternating forms are Siegel modular cuspforms of weight 13 for {\rm Sp}_{2g}(\mathbb{Z}) . We prove that they are nonzero eigenforms, determine one of their Fourier coefficients, and give informations about their standard {\rm L} -functions. These forms are interesting since, by a recent work of the authors, they are the only nonzero Siegel modular forms of weight 13 for {\rm Sp}_{2n}(\mathbb{Z}) , for any n\geq 1 .

First Order Transitions Between the Gapped Spin-Liquid and Ferrimagnetic Phases in \((1/2,1/2,1)\) Mixed Diamond Chains with Bond Alternation

The ground-state phases of mixed diamond chains with bond alternation $\delta$, and ($S, \tau^{(1)}, \tau^{(2)})=(1/2,1/2,1)$, where $S$ is the magnitude of vertex spins, and $\tau^{(1)}$ and $\tau^{(2)}$ are those of apical spins, are investigated. The two apical spins in each unit cell are connected by an exchange coupling $\lambda$. The exchange couplings between the apical spins and the vertex spins take the values $1+\delta$ and $1-\delta$ alternatingly. This model has an infinite number of local conservation laws. For large $\lambda$ and $\delta \neq 0$, the ground state is equivalent to that of the spin $1/2$ chain with bond alternation. Hence, the ground state is a gapped spin liquid. This energy gap vanishes for $\delta=0$. With the decrease of $\lambda$, the ground state undergoes a transition at $\lambda=\lambda_{\rm c0}(\delta)$ to a series of ferrimagnetic phases with a spontaneous magnetization $m_{\rm sp}=1/p$ per unit cell where $p$ is a positive integer. It is found that this transition is a first order transition for $\delta\neq 0$ with a discontinuous change in $m_{\rm sp}$, while no discontinuity is found for $\delta=0$. The critical behaviors of $m_{\rm sp}$ and $\lambda_{\rm c0}(\delta)$ around the critical point $(\delta,\lambda) =(0, \lambda_{\rm c0}(\delta))$ are also discussed analytically.

F(R)gravity after the detection of the orbital precession of the S2 star around the Galactic Center massive black hole

The GRAVITY Collaboration achieved the remarkable detection of the orbital precession of the S2 star around the Galactic centre supermassive black hole, providing yet another proof of the validity of the General Relativity. The departure from the Schwarzschild precession is encoded in the parameter $f_{\rm SP}$ which multiplies the predicted general relativistic precession. Such a parameter results to be $f_{\rm SP}=1.10\pm0.19$, which is consistent with General Relativity ($f_{\rm SP}=1$) at 1$\sigma$ level. Nevertheless, this parameter may also hide an effect of modified theories of gravity. Thus, we consider the orbital precession due to the Yukawa-like gravitational potential arising in the weak field limit of $f(R)$-gravity, and we use the current bound on the $f_{\rm SP}$ to constrain the strength and the scale length of the Yukawa-like potential. No deviation from GR are revealed at scale of $\lambda<6300$ AU with the strength of the Yukawa potential restricted to $\delta = -0.01_{-0.14}^{+0.61}$.

Word images in symmetric and classical groups of Lie type are dense

Let $w\in\mathbf F_k$ be a non-trivial word and denote by $w(G)\subseteq G$ the image of the associated word map $w\colon G^k\to G$. Let $G$ be one of the finite groups ${\rm S}_n,{\rm GL}_n(q),{\rm Sp}_{2m}(q),{\rm GO}_{2m}^\pm(q),{\rm GO}_{2m+1}(q),{\rm GU}_n(q)$ ($q$ a prime power, $n\geq 2$, $m\geq 1$), or the unitary group ${\rm U}_n$ over $\mathbb C$. Let $d_G$ be the normalized Hamming distance resp. the normalized rank metric on $G$ when $G$ is a symmetric group resp. one of the other classical groups and write $n(G)$ for the permutation resp. Lie rank of $G$. For $\varepsilon>0$, we prove that there exists an integer $N(\varepsilon,w)$ such that $w(G)$ is $\varepsilon$-dense in $G$ with respect to the metric $d_G$ if $n(G)\geq N(\varepsilon,w)$. This confirms metric versions of a conjectures by Shalev and Larsen. Equivalently, we prove that any non-trivial word map is surjective on a metric ultraproduct of groups $G$ from above such that $n(G)\to\infty$ along the ultrafilter. As a consequence of our methods, we also obtain an alternative proof of the result of Hui-Larsen-Shalev that $w_1({\rm SU}_n)w_2({\rm SU}_n)={\rm SU}_n$ for non-trivial words $w_1,w_2\in\mathbf F_k$ and $n$ sufficiently large.

Infinite Series of Ferrimagnetic Phases Emergent from the Gapless Spin Liquid Phase of Mixed Diamond Chains

The ground-state phases of mixed diamond chains with ($S, \tau^{(1)}, \tau^{(2)})=(1/2,1/2,1)$, where $S$ is the magnitude of vertex spins, and $\tau^{(1)}$ and $\tau^{(2)}$ are those of apical spins, are investigated. The apical spins $\tau^{(1)}$ and $\tau^{(2)}$ are connected with each other by an exchange coupling $\lambda$. Other exchange couplings are set equal to unity. This model has an infinite number of local conservation laws. For large $\lambda$, the ground state is equivalent to that of the uniform spin $1/2$ chain. Hence, the ground state is a gapless spin liquid. For $\lambda \leq 0$, the ground state is a Lieb-Mattis ferrimagnetic phase with spontaneous magnetization $m_{\rm sp}=1$ per unit cell. For intermediate $\lambda$, we find a series of ferrimagnetic phases with $m_{\rm sp}=1/p$ where $p$ takes positive integer values. The phases with $p \geq 2$ are accompanied by the spontaneous breakdown of the $p$-fold translational symmetry. It is suggested that the phase with arbitrarily large $p$, namely infinitesimal spontaneous magnetization, is allowed as $\lambda$ approaches the transition point to the gapless spin liquid phase.

FORMAL DEGREES AND LOCAL THETA CORRESPONDENCE: QUATERNIONIC CASE

In this paper, we determine a constant occurring in a local analogue of the Siegel-Weil formula, and describe the behavior of the formal degrees under the local theta correspondence for quaternionic dual pairs of almost equal rank over a non-Archimedean local field of characteristic $0$. As an application, we prove the formal degree conjecture of Hiraga-Ichino-Ikeda for the non-split inner forms of ${\rm Sp}_4$ and ${\rm GSp}_4$.

CNN-Based Target Detection and Classification When Sparse SAR Image Dataset is Available

Synthetic aperture radar (SAR) is an earth observation technology that can obtain high-resolution image in all-weather and all-time conditions, and hence, has been widely used in civil and military applications. SAR target detection and classification are the key processes for the detailed feature information extraction of the interested target. Compared with traditional matched filtering (MF) recovered result, sparse SAR image has lower sidelobes, noise, and clutter. Thus, it will theoretically has better performance in target detection and classification. In this article, we propose a novel sparse SAR image based target detection and classification framework. This novel framework first obtains the sparse SAR image dataset by complex approximate message passing (CAMP), which is an <inline-formula><tex-math notation="LaTeX">$L_1$</tex-math></inline-formula>-norm regularization sparse imaging method. Different from other regularization recovery algorithms, CAMP can output not only a sparse solution, but also a nonsparse estimation of considered scene that well preserves the statistical characteristic of the image when protruding the target. Then, we detect and classify the targets by using the convolutional neural network based technologies from the sparse SAR image datasets constructed by the sparse and nonsparse solutions of CAMP, respectively. For clarify, these two kinds of sparse SAR image datasets are named as <inline-formula><tex-math notation="LaTeX">$\mathcal {D}_{\rm Sp}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$\mathcal {D}_{\rm Nsp}$</tex-math></inline-formula>. Experimental results show that under standard operating conditions, the proposed framework can obtain 92.60&#x0025; and 99.29&#x0025; mAP on Faster RCNN and YOLOv3 by using the <inline-formula><tex-math notation="LaTeX">$\mathcal {D}_{\rm Nsp}$</tex-math></inline-formula> sparse SAR image dataset. Under extended operating conditions, the mAP value of Faster RCNN and YOLOv3 are 95.69&#x0025; and 89.91&#x0025; mAP, respectively. These values based on the <inline-formula><tex-math notation="LaTeX">$\mathcal {D}_{\rm Nsp}$</tex-math></inline-formula> dataset are much higher than the classified result based on the corresponding MF dataset.

Quenched Galaxies in Clusters of Galaxies and Their Outskirts

Based on the SDSS data, the properties of galaxies with quenched star formation (QGs) within the "splashback"-radius of galaxy clusters $R_{\rm sp}$ and beyond it have been studied. We used a sample of 40 groups and galaxy clusters and a sample of field galaxies at $0.02<z<0.045$. The radii $R_{\rm sp}$ were defined from the observed integrated distribution of the number of galaxies as a function of the squared distance from the center of the galaxy systems. We show that in galaxy clusters 72% of the QGs we have found are within $R_{\rm sp}$. About 40% of these galaxies are late-type ones with ${frac}DeV < 0.8$. Approximately 80% of galaxies with quenched star formation have stellar masses in the range of $\log M_*/M_{\odot} = [10; 11]$. We found that QGs of late types and of early types in a less degree have maximum angular radii $R_{90,r}$ and $R_{50,r}$ near the "splashback"-radius of groups and clusters of galaxies. Our results confirm the assumption that in the filaments directed toward clusters, the quenched galaxies are more massive near the boundaries of clusters of galaxies than at the outskirts.

Statistical Mechanics of Confined Polymer Networks

We show how the theory of the critical behaviour of $d$-dimensional polymer networks of arbitrary topology can be generalized to the case of networks confined by hyperplanes. This in particular encompasses the case of a single polymer chain in a bridge configuration. We further define multi-bridge networks, where several vertices are in local bridge configurations. We consider all cases of ordinary, mixed and special surface transitions, and polymer chains made of self-avoiding walks, or of mutually-avoiding walks, or at the tricritical $\Theta$-point. In the $\Theta$-point case, generalising the good-solvent case, we relate the critical exponent for simple bridges, $\gamma_b^{\Theta}$, to that of terminally-attached arches, $\gamma_{11}^{\Theta},$ and to the correlation length exponent $\nu^{\Theta}.$ We find $\gamma_b^{\Theta} = \gamma_{11}^{\Theta}+\nu^{\Theta}.$ In the case of the special transition, we find $\gamma_b^{\Theta}({\rm sp}) = \frac{1}{2}[\gamma_{11}^{\Theta}({\rm sp})+\gamma_{11}^{\Theta}]+\nu^{\Theta}.$ For general networks, the explicit expression of configurational exponents then naturally involve bulk and surface exponents for multiple random paths. In two-dimensions, we describe their Euclidean exponents from a unified perspective, using Schramm-Loewner Evolution (SLE) in Liouville quantum gravity (LQG), and the so-called KPZ relation between Euclidean and LQG scaling dimensions. This is done in the case of ordinary, mixed and special surface transitions, and of the $\Theta$-point. We provide compelling numerical evidence for some of these results both in two- and three-dimensions.

Diagram involutions and homogeneous Ricci-flat metrics

We introduce a combinatorial method to construct indefinite Ricci-flat metrics on nice nilpotent Lie groups. We prove that every nilpotent Lie group of dimension $\leq6$, every nice nilpotent Lie group of dimension $\leq7$ and every two-step nilpotent Lie group attached to a graph admits such a metric. We construct infinite families of Ricci-flat nilmanifolds associated to parabolic nilradicals in the simple Lie groups ${\rm SL}(n)$, ${\rm SO}(p,q)$, ${\rm Sp}(n,\mathbb R)$. Most of these metrics are shown not to be flat.

Galaxy Clusters and Their Outskirts: the “Red Sequence”, Star Formation Rate, Stellar Mass

We study the outskirts ($R<3R_{200c}$) of 40 groups and clusters of galaxies of the local Universe ($0.02<z<0.045$) with 300~km~s$^{-1}<\sigma<950$~km~s$^{-1}$. Using the SDSS DR10 catalog data, we measured the stellar mass of galaxy clusters in accordance with the previously determined $K_s$-luminosity (2MASX data) and found their correlation in the form $M_*/M_{\odot} \propto (L_K/L_{\odot})^{1.010\pm0.004}$ ($M_K<-21\,.\!\!^{\rm m}5$, $R<R_{200c}$). We also found the dependence of the galaxy cluster stellar mass on halo mass: $M_*/M_{\odot} \propto (M_{200c}/M_{\odot})^{0.77\pm0.01}$}. Our results show that the fraction of galaxies with quenched star formation ($M_K<-21\,.\!\!^{\rm m}5$) is maximal in the central regions of the galaxy clusters and equals, on the average, $0.81\pm0.02$; it decreases to $0.44\pm0.02$ outside of the projected radius $R_{sp}$ ($2<R/R_{200c}<3$), which we found from the observed profile, but still remains higher than that in the field by 27\%. The fraction of early-type "red sequence" galaxies decreases from $0.54\pm0.02$ in the center to $0.24\pm0.01$ beyond $R_{\rm sp}$, reaching its field value.

Impact of magnetic-field fluctuations on measurements of the chiral magnetic effect in collisions of isobaric nuclei

We investigate the properties of electromagnetic fields in isobaric $_{44}^{96}\textrm{Ru}+\,_{44}^{96}\textrm{Ru}$ and $_{40}^{96}\textrm{Zr}+\,_{40}^{96}\textrm{Zr}$ collisions at $\sqrt{s}$ = 200 GeV by using a multiphase transport model, with special emphasis on the correlation between magnetic field direction and participant plane angle $\Psi_{2}$ (or spectator plane angle $\Psi_{2}^{\rm SP}$), i.e. $\langle{\rm cos}\ 2(\Psi_B - \Psi_{2})\rangle$ [or $\langle{\rm cos}\ 2(\Psi_B - \Psi_{2}^{\rm SP})\rangle$]. We confirm that the magnetic fields of $_{44}^{96}\textrm{Ru}+\,_{44}^{96}\textrm{Ru}$ collisions are stronger than those of $_{40}^{96}\textrm{Zr}+\,_{40}^{96}\textrm{Zr}$ collisions due to their larger proton fraction. We find that the deformation of nuclei has a non-negligible effect on $\langle{\rm cos}\ 2(\Psi_B - \Psi_{2})\rangle$ especially in peripheral events. Because the magnetic-field direction is more strongly correlated with $\Psi_{2}^{\rm SP}$ than with $\Psi_{2}$, the relative difference of the chiral magnetic effect observable with respect to $\Psi_{2}^{\rm SP}$ is expected to be able to reflect much cleaner information about the chiral magnetic effect with less influences of deformation.

Quaternionic toric manifolds

In the present paper we introduce and study a new notion of toric manifold in the quaternionic setting. We develop a construction with which, starting from appropriate $m$-dimensional Delzant polytopes, we obtain manifolds of real dimension $4m$, acted on by $m$ copies of the group ${\rm Sp}(1)$ of unit quaternions. These manifolds are quaternionic regular and can be endowed with a $4$-plectic structure and a generalized moment map. Convexity properties of the image of the moment map are studied. Quaternionic toric manifolds appear to be a large enough class of examples where one can test and study new results in quaternionic geometry.

M*/L gradients driven by IMF variation: large impact on dynamical stellar mass estimates

Within a galaxy the stellar mass-to-light ratio $\Upsilon_*$ is not constant. Spatially resolved kinematics of nearby early-type galaxies suggest that allowing for a variable initial mass function (IMF) returns significantly larger $\Upsilon_*$ gradients than if the IMF is held fixed. If $\Upsilon_*$ is greater in the central regions, then ignoring the IMF-driven gradient can overestimate $M_*^{\rm dyn}$ by as much as a factor of two for the most massive galaxies, though stellar population estimates $M_*^{\rm SP}$ are also affected. Large $\Upsilon_*$-gradients have four main consequences: First, $M_*^{\rm dyn}$ cannot be estimated independently of stellar population synthesis models. Second, if there is a lower limit to $\Upsilon_*$ and gradients are unknown, then requiring $M_*^{\rm dyn}=M_*^{\rm SP}$ constrains them. Third, if gradients are stronger in more massive galaxies, then $M_*^{\rm dyn}$ and $M_*^{\rm SP}$ can be brought into agreement, not by shifting $M_*^{\rm SP}$ upwards by invoking constant bottom-heavy IMFs, as advocated by a number of recent studies, but by revising $M_*^{\rm dyn}$ estimates in the literature downwards. Fourth, accounting for $\Upsilon_*$ gradients changes the high-mass slope of the stellar mass function $\phi(M_*^{\rm dyn})$, and reduces the associated stellar mass density. These conclusions potentially impact estimates of the need for feedback and adiabatic contraction, so our results highlight the importance of measuring $\Upsilon_*$ gradients in larger samples.

Infrared fixed point physics in SO(Nc) and Sp(Nc) gauge theories

We study properties of asymptotically free vectorial gauge theories with gauge groups $G={\rm SO}(N_c)$ and $G={\rm Sp}(N_c)$ and $N_f$ fermions in a representation $R$ of $G$, at an infrared (IR) zero of the beta function, $\alpha_{IR}$, in the non-Abelian Coulomb phase. The fundamental, adjoint, and rank-2 symmetric and antisymmetric tensor fermion representations are considered. We present scheme-independent calculations of the anomalous dimensions of (gauge-invariant) fermion bilinear operators $\gamma_{\bar\psi\psi,IR}$ to $O(\Delta_f^4)$ and of the derivative of the beta function at $\alpha_{IR}$, denoted $\beta'_{IR}$, to $O(\Delta_f^5)$, where $\Delta_f$ is an $N_f$-dependent expansion variable. It is shown that all coefficients in the expansion of $\gamma_{\bar\psi\psi,IR}$ that we calculate are positive for all representations considered, so that to $O(\Delta_f^4)$, $\gamma_{\bar\psi\psi,IR}$ increases monotonically with decreasing $N_f$ in the non-Abelian Coulomb phase. Using this property, we give a new estimate of the lower end of this phase for some specific realizations of these theories.

Analytic continuation of Wolynes theory into the Marcus inverted regime.

The Wolynes theory of electronically nonadiabatic reaction rates [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] is based on a saddle point approximation to the time integral of a reactive flux autocorrelation function in the nonadiabatic (golden rule) limit. The dominant saddle point is on the imaginary time axis at tsp=iλspℏ, and provided λsp lies in the range -β/2≤λsp≤β/2, it is straightforward to evaluate the rate constant using information obtained from an imaginary time path integral calculation. However, if λsp lies outside this range, as it does in the Marcus inverted regime, the path integral diverges. This has led to claims in the literature that Wolynes theory cannot describe the correct behaviour in the inverted regime. Here we show how the imaginary time correlation function obtained from a path integral calculation can be analytically continued to λsp<-β/2, and the continuation used to evaluate the rate in the inverted regime. Comparison with exact golden rule results for a spin-boson model and a more demanding (asymmetric and anharmonic) model of electronic predissociation shows that the theory is just as accurate in the inverted regime as it is in the normal regime.

Maximal representations, non-Archimedean Siegel spaces, and buildings

Let $\mathbb F$ be a real closed field. We define the notion of a maximal framing for a representation of the fundamental group of a surface with values in ${\rm Sp}(2n,\mathbb F)$. We show that ultralimits of maximal representations in ${\rm Sp}(2n,\mathbb R)$ admit such a framing, and that all maximal framed representations satisfy a suitable generalisation of the classical Collar Lemma. In particular this establishes a Collar Lemma for all maximal representations into ${\rm Sp}(2n,\mathbb R)$. We then describe a procedure to get from representations in ${\rm Sp}(2n,\mathbb F)$ interesting actions on affine buildings, and, in the case of representations admitting a maximal framing, we describe the structure of the elements of the group acting with zero translation length.