The X-ray Jet in Centaurus A: Clues on the Jet Structure and Particle Acceleration

We report detailed studies of the X-ray emission from the kpc scale jet in the nearest active galaxy, Cen A. 41 compact sources were found within the jet, 13 of which were newly identified. We construct the luminosity function for the detected jet-knots and argue that the remaining emission is most likely to be truly diffuse, rather than resulting from the pile-up of unresolved faint knots. The transverse jet profile reveals that the extended emission has the intensity peak at the jet boundaries. We note that limb-brightened jet morphologies have been observed previously at radio frequencies in some jet sources, but never so clearly at higher photon energies. Our result therefore supports a stratified jet model, consisting of a relativistic outflow including a boundary layer with a velocity shear. In addition, we found that the X-ray spectrum of the diffuse component is almost uniform across and along the jet. We discuss this spectral behavior within a framework of shock and stochastic particle acceleration processes. We note some evidence for a possible spectral hardening at the outer sheath of the jet. Due to the limited photon statistics of the present data, further deep observations of Cen A are required to determine the reality of this finding, however we note that the existence of the hard X-ray features at outer jet boundaries would provide an important challenge to theories for the evolution of ultra-relativistic particles within the jets.Comment: 27page, 8 figures, ver2, accepted for publication in the Ap

On the Interaction of the PKS B1358-113 Radio Galaxy with the Abell 1836 Cluster

[abridged] Here we present the analysis of multifrequency data gathered for the FRII radio galaxy PKS B1358-113, hosted in the brightest cluster galaxy of Abell 1836. The galaxy harbors one of the most massive black holes known to date and our analysis of the optical data reveals that this black hole is only weakly active. Based on new Chandra and XMM-Newton X-ray observations and archival radio data we derive the preferred range for the jet kinetic luminosity $\sim (0.5-3) \times 10^{45}$ erg s$^{-1}$. This is above the values implied by various scaling relations proposed for radio sources in galaxy clusters, being instead very close to the maximum jet power allowed for the given accretion rate. We constrain the radio source lifetime as $\sim 40-70$ Myrs, and the total amount of deposited jet energy $\sim (2-8) \times 10^{60}$\,ergs. The detailed analysis of the X-ray data provides indication for the presence of a bow-shock driven by the expanding radio lobes into the Abell 1836 cluster environment, with the corresponding Mach number $\sim 2-4$. This, together with the recently growing evidence that powerful FRII radio galaxies may not be uncommon in the centers of clusters at higher redshifts, supports the idea that jet-induced shock heating may indeed play an important role in shaping the properties of clusters, galaxy groups, and galaxies in formation. We speculate on a possible bias against detecting jet-driven shocks in poorer environments, resulting from an inefficient electron heating at the shock front, combined with a relatively long electron-ion equilibration timescale.Comment: Version accepted to Ap

No Tradeoff between Coherence and Sub-Poissonianity for Heisenberg-Limited Lasers

The Heisenberg limit to laser coherence $\mathfrak{C}$ -- the number of photons in the maximally populated mode of the laser beam -- is the fourth power of the number of excitations inside the laser. We generalize the previous proof of this upper bound scaling by dropping the requirement that the beam photon statistics be Poissonian (i.e., Mandel's $Q=0$). We then show that the relation between $\mathfrak{C}$ and sub-Poissonianity ($Q<0$) is win-win, not a tradeoff. For both regular (non-Markovian) pumping with semi-unitary gain (which allows $Q\xrightarrow{}-1$), and random (Markovian) pumping with optimized gain, $\mathfrak{C}$ is maximized when $Q$ is minimized.Comment: This is a companion letter to the manuscript entitled "Optimized Laser Models with Heisenberg-Limited Coherence and Sub-Poissonian Beam Photon Statistics", arxiv:2208.14082. 6 pages, 2 figure

Optimized Laser Models with Heisenberg-Limited Coherence and Sub-Poissonian Beam Photon Statistics

Recently it has been shown that it is possible for a laser to produce a stationary beam with a coherence (quantified as the mean photon number at spectral peak) which scales as the fourth power of the mean number of excitations stored within the laser, this being quadratically larger than the standard or Schawlow-Townes limit [1]. Moreover, this was analytically proven to be the ultimate quantum limit (Heisenberg limit) scaling under defining conditions for CW lasers, plus a strong assumption about the properties of the output beam. In Ref. [2], we show that the latter can be replaced by a weaker assumption, which allows for highly sub-Poissonian output beams, without changing the upper bound scaling or its achievability. In this Paper, we provide details of the calculations in Ref. [2], and introduce three new families of laser models which may be considered as generalizations of those presented in that work. Each of these families of laser models is parameterized by a real number, $p$, with $p=4$ corresponding to the original models. The parameter space of these laser families is numerically investigated in detail, where we explore the influence of these parameters on both the coherence and photon statistics of the laser beams. Two distinct regimes for the coherence may be identified based on the choice of $p$, where for $p>3$, each family of models exhibits Heisenberg-limited beam coherence, while for $p<3$, the Heisenberg limit is no longer attained. Moreover, in the former regime, we derive formulae for the beam coherence of each of these three laser families which agree with the numerics. We find that the optimal parameter is in fact $p\approx4.15$, not $p=4$.Comment: This is a companion manuscript to the letter entitled "No Tradeoff between Coherence and Sub-Poissonianity for Heisenberg-Limited Lasers", arxiv:2208.14081. 22 pages, 11 figure

Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property

The AMP Markov property is a recently proposed alternative Markov property for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced LWF Markov property that is coherent with data-generation by natural block-recursive regressions. In this paper, we show that maximum likelihood estimates in Gaussian AMP chain graph models can be obtained by combining generalized least squares and iterative proportional fitting to an iterative algorithm. In an appendix, we give useful convergence results for iterative partial maximization algorithms that apply in particular to the described algorithm.Comment: 15 pages, article will appear in Scandinavian Journal of Statistic

Casimir effect for tachyonic fields

In this paper we examine Casimir effect in the case of tachyonic field, which is connected with particles with negative four-momentum square. We consider here only the case of one dimensional, scalar field. In order to describe tachyonic field, we use the absolute synchronization scheme preserving Lorentz invariance. The renormalized vacuum energy is calculated by means of Abel-Plana formula. Finaly, the Casimir energy and Casimir force as the functions of distance are obtained. In order to compare the resulting formula with the standard one, we calculate the Casimir energy and Casimir force for massive, scalar field.Comment: 7 pages, 9 figure

On QBF Proofs and Preprocessing

QBFs (quantified boolean formulas), which are a superset of propositional formulas, provide a canonical representation for PSPACE problems. To overcome the inherent complexity of QBF, significant effort has been invested in developing QBF solvers as well as the underlying proof systems. At the same time, formula preprocessing is crucial for the application of QBF solvers. This paper focuses on a missing link in currently-available technology: How to obtain a certificate (e.g. proof) for a formula that had been preprocessed before it was given to a solver? The paper targets a suite of commonly-used preprocessing techniques and shows how to reconstruct certificates for them. On the negative side, the paper discusses certain limitations of the currently-used proof systems in the light of preprocessing. The presented techniques were implemented and evaluated in the state-of-the-art QBF preprocessor bloqqer.Comment: LPAR 201

Small-scale anisotropy of cosmic rays above 10^19eV observed with the Akeno Giant Air Shower Array

With the Akeno Giant Air Shower Array (AGASA), 581 cosmic rays above 10^19eV, 47 above 4 x 10^19eV, and 7 above 10^20eV are observed until August 1998. Arrival direction distribution of these extremely high energy cosmic rays has been studied. While no significant large-scale anisotropy is found on the celestial sphere, some interesting clusters of cosmic rays are observed. Above 4 x 10^19eV, there are one triplet and three doublets within separation angle of 2.5^o and the probability of observing these clusters by a chance coincidence under an isotropic distribution is smaller than 1 %. Especially the triplet is observed against expected 0.05 events. The cos(\theta_GC) distribution expected from the Dark Matter Halo model fits the data as well as an isotropic distribution above 2 x 10^19eV and 4 x 10^19eV, but is a poorer fit than isotropy above 10^19eV. Arrival direction distribution of seven 10^20eV cosmic rays is consistent with that of lower energy cosmic rays and is uniform. Three of seven are members of doublets above about 4 x 10^19eV.Comment: 40 pages, 12 figure, AASTeX *** Authors found a typo on Table 2 -- Energy of event 94/07/06 **

Particle-unstable nuclei in the Hartree-Fock theory

Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the resonant states become square integrable. The method is implemented with Skyrme effective interactions. Several Skyrme parametrizations are tested on four unstable nuclei: 10He, 12O, 26O and 28O.Comment: 5 pages, LaTeX, submitted to Phys. Rev. Let

Permutable entire functions satisfying algebraic differential equations

It is shown that if two transcendental entire functions permute, and if one of them satisfies an algebraic differential equation, then so does the other one.Comment: 5 page