A Small Contribution to Catalan′s Equation

AbstractUsing recent results on linear forms in logarithms of algebraic numbers, we prove that any solution of the equation xp − yq = ϵ, where ϵ = ± 1, p and q are odd primes, and p > q satisfies p < 3.42 · 1028 and q < 5.6 · 1019. We also combine our work with some results of Altonen and Inkeri to determine the six cases with q ≤ 37 for which this equation may have solutions

Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets

The spins of ten stellar black holes have been measured using the continuum-fitting method. These black holes are located in two distinct classes of X-ray binary systems, one that is persistently X-ray bright and another that is transient. Both the persistent and transient black holes remain for long periods in a state where their spectra are dominated by a thermal accretion disk component. The spin of a black hole of known mass and distance can be measured by fitting this thermal continuum spectrum to the thin-disk model of Novikov and Thorne; the key fit parameter is the radius of the inner edge of the black hole's accretion disk. Strong observational and theoretical evidence links the inner-disk radius to the radius of the innermost stable circular orbit, which is trivially related to the dimensionless spin parameter a_* of the black hole (|a_*| < 1). The ten spins that have so far been measured by this continuum-fitting method range widely from a_* \approx 0 to a_* > 0.95. The robustness of the method is demonstrated by the dozens or hundreds of independent and consistent measurements of spin that have been obtained for several black holes, and through careful consideration of many sources of systematic error. Among the results discussed is a dichotomy between the transient and persistent black holes; the latter have higher spins and larger masses. Also discussed is recently discovered evidence in the transient sources for a correlation between the power of ballistic jets and black hole spin.Comment: 30 pages. Accepted for publication in Space Science Reviews. Also to appear in hard cover in the Space Sciences Series of ISSI "The Physics of Accretion onto Black Holes" (Springer Publisher). Changes to Sections 5.2, 6.1 and 7.4. Section 7.4 responds to Russell et al. 2013 (MNRAS, 431, 405) who find no evidence for a correlation between the power of ballistic jets and black hole spi

The balance of power: accretion and feedback in stellar mass black holes

In this review we discuss the population of stellar-mass black holes in our galaxy and beyond, which are the extreme endpoints of massive star evolution. In particular we focus on how we can attempt to balance the available accretion energy with feedback to the environment via radiation, jets and winds, considering also possible contributions to the energy balance from black hole spin and advection. We review quantitatively the methods which are used to estimate these quantities, regardless of the details of the astrophysics close to the black hole. Once these methods have been outlined, we work through an outburst of a black hole X-ray binary system, estimating the flow of mass and energy through the different accretion rates and states. While we focus on feedback from stellar mass black holes in X-ray binary systems, we also consider the applicability of what we have learned to supermassive black holes in active galactic nuclei. As an important control sample we also review the coupling between accretion and feedback in neutron stars, and show that it is very similar to that observed in black holes, which strongly constrains how much of the astrophysics of feedback can be unique to black holes.Comment: To be published in Haardt et al. Astrophysical Black Holes. Lecture Notes in Physics. Springer 201

PROFIT: a new alternative for emission-line PROfile FITting

I briefly describe a simple routine for emission-line profiles fitting by Gaussian curves or Gauss-Hermite series. The PROFIT (line-PROfile FITting) routine represent a new alternative for use in fits data cubes, as those from Integral Field Spectroscopy or Fabry-Perot Interferometry, and may be useful to better study the emission-line flux distributions and gas kinematics in distinct astrophysical objects, such as the central regions of galaxies and star forming regions. The PROFIT routine is written in IDL language and is available at http://www.ufsm.br/rogemar/software.html. The PROFIT routine was used to fit the [Fe II]1.257um emission-line profiles for about 1800 spectra of the inner 350 pc of the Seyfert galaxy Mrk1066 obtained with Gemini NIFS and shows that the line profiles are better reproduced by Gauss-Hermite series than by the commonly used Gaussian curves. The two-dimensional map of the h_3 Gauss-Hermite moment shows its highest absolute values in regions close to the edge of the radio structure. These high values may be originated in an biconical outflowing gas associated with the radio jet - previously observed in the optical [O III] emission. The analysis of this kinematic component indicates that the radio jet leaves the center of the galaxy with the north-west side slightly oriented towards us and the south-east side away from us, being partially hidden by the disc of the galaxy.Comment: Accepted for publication Astrophysics & Space Science - 7 pges; 4 Fig

An overview of jets and outflows in stellar mass black holes

In this book chapter, we will briefly review the current empirical understanding of the relation between accretion state and and outflows in accreting stellar mass black holes. The focus will be on the empirical connections between X-ray states and relativistic (`radio') jets, although we are now also able to draw accretion disc winds into the picture in a systematic way. We will furthermore consider the latest attempts to measure/order jet power, and to compare it to other (potentially) measurable quantities, most importantly black hole spin.Comment: Accepted for publication in Space Science Reviews. Also to appear in the Space Sciences Series of ISSI - The Physics of Accretion on to Black Holes (Springer Publisher

Measuring Black Hole Spin using X-ray Reflection Spectroscopy

I review the current status of X-ray reflection (a.k.a. broad iron line) based black hole spin measurements. This is a powerful technique that allows us to measure robust black hole spins across the mass range, from the stellar-mass black holes in X-ray binaries to the supermassive black holes in active galactic nuclei. After describing the basic assumptions of this approach, I lay out the detailed methodology focusing on "best practices" that have been found necessary to obtain robust results. Reflecting my own biases, this review is slanted towards a discussion of supermassive black hole (SMBH) spin in active galactic nuclei (AGN). Pulling together all of the available XMM-Newton and Suzaku results from the literature that satisfy objective quality control criteria, it is clear that a large fraction of SMBHs are rapidly-spinning, although there are tentative hints of a more slowly spinning population at high (M>5*10^7Msun) and low (M<2*10^6Msun) mass. I also engage in a brief review of the spins of stellar-mass black holes in X-ray binaries. In general, reflection-based and continuum-fitting based spin measures are in agreement, although there remain two objects (GROJ1655-40 and 4U1543-475) for which that is not true. I end this review by discussing the exciting frontier of relativistic reverberation, particularly the discovery of broad iron line reverberation in XMM-Newton data for the Seyfert galaxies NGC4151, NGC7314 and MCG-5-23-16. As well as confirming the basic paradigm of relativistic disk reflection, this detection of reverberation demonstrates that future large-area X-ray observatories such as LOFT will make tremendous progress in studies of strong gravity using relativistic reverberation in AGN.Comment: 19 pages. To appear in proceedings of the ISSI-Bern workshop on "The Physics of Accretion onto Black Holes" (8-12 Oct 2012). Revised version adds a missing source to Table 1 and Fig.6 (IRAS13224-3809) and corrects the referencing of the discovery of soft lags in 1H0707-495 (which were in fact first reported in Fabian et al. 2009

Current Status of Simulations

As the title suggests, the purpose of this chapter is to review the current status of numerical simulations of black hole accretion disks. This chapter focuses exclusively on global simulations of the accretion process within a few tens of gravitational radii of the black hole. Most of the simulations discussed are performed using general relativistic magnetohydrodynamic (MHD) schemes, although some mention is made of Newtonian radiation MHD simulations and smoothed particle hydrodynamics. The goal is to convey some of the exciting work that has been going on in the past few years and provide some speculation on future directions.Comment: 15 pages, 14 figures, to appear in the proceedings of the ISSI-Bern workshop on "The Physics of Accretion onto Black Holes" (8-12 October 2012

On the Crustal Matter of Magnetars

We have investigated some of the properties of dense sub-nuclear matter at the crustal region (both the outer crust and the inner crust region) of a magnetar. The relativistic version of Thomas-Fermi (TF) model is used in presence of strong quantizing magnetic field for the outer crust matter. The compressed matter in the outer crust, which is a crystal of metallic iron, is replaced by a regular array of spherically symmetric Wigner-Seitz (WS) cells. In the inner crust region, a mixture of iron and heavier neutron rich nuclei along with electrons and free neutrons has been considered. Conventional Harrison-Wheeler (HW) and Bethe-Baym-Pethick (BBP) equation of states are used for the nuclear mass formula. A lot of significant changes in the characteristic properties of dense crustal matter, both at the outer crust and the inner crust, have been observed.Comment: 29 pages REVTEX manuscript, 15 .eps figures (included

A Millennium Learning Goal for education post‐2015: a question of outcomes or processes

As the target year for the current Millennium Development Goal of universal completion of primary education approaches, three World Bank economists have proposed its replacement with a Millennium Learning Goal. This is part of a trend of increased privileging of learning outcomes. The proposal is assessed from the perspective of human rights-based and social justice conceptualisations of education quality. A Millennium Learning Goal may enhance information on inclusion, conceived as equal opportunity to achieve learning outcomes. However, there is a danger that it would be misused to generate high stakes tests that can be detrimental to the achievement of goals that are not readily measurable and hence to the relevance of education. It is argued that a process goal with qualitative targets for the assessment of learning, for the monitoring of educational processes and for the processes by which learning goals are determined would be more appropriate for the international level.As the target year for the current Millennium Development Goal of universal completion of primary education approaches, three World Bank economists have proposed its replacement with a Millennium Learning Goal. This is part of a trend of increased privileging of learning outcomes. The proposal is assessed from the perspective of human rights-based and social justice conceptualisations of education quality. A Millennium Learning Goal may enhance information on inclusion, conceived as equal opportunity to achieve learning outcomes. However, there is a danger that it would be misused to generate high stakes tests that can be detrimental to the achievement of goals that are not readily measurable and hence to the relevance of education. It is argued that a process goal with qualitative targets for the assessment of learning, for the monitoring of educational processes and for the processes by which learning goals are determined would be more appropriate for the international level