Fluoride ion reactions of fluorocarbon derivations Final report

Relative reactivity of unsaturated fluorocarbon derivatives toward cesium fluorid

Simultaneous spectral and reverberation modelling of relativistic reflection in Mrk 335

We present an X-ray spectral and timing model to investigate the broad and variable iron line seen in the high flux state of Mrk 335. The model consists of a variable X-ray source positioned along the rotation axis of the black hole that illuminates the accretion disc producing a back-scattered, ionized reflection spectrum. We compute time lags including full dilution effects and perform simultaneous fitting of the 2-10 keV spectrum and the frequency-dependent time lags of 2.5-4 vs. 4-6.5 keV bands. The best-fitting parameters are consistent with a black hole mass of approximately 1.3 x 10^7 M_sun, disc inclination of 45 degrees and the photon index of the direct continuum of 2.4. The iron abundance is 0.5 and the ionization parameter is 10^3 erg cm / s at the innermost part of the disc and decreases further out. The X-ray source height is very small, approximately 2 r_g. Furthermore, we fit the Fe L lags simultaneously with the 0.3-10 keV spectrum. The key parameters are comparable to those previously obtained. We also report the differences below 2 keV using the xillver and reflionx models which could affect the interpretation of the soft excess. While simultaneously fitting spectroscopic and timing data can break the degeneracy between the source height and the black hole mass, we find that the measurements of the source height and the central mass significantly depend on the ionization state of the disc and are possibly model-dependent.Comment: 11 pages, 8 figures, accepted for publication in MNRA

The complex geomety of a domain related to μ\mu-synthesis

We describe the basic complex geometry and function theory of the {\em pentablock} $\mathcal{P}$, which is the bounded domain in $\mathbb{C}^3$ given by $$\mathcal{P}= \{(a_{21}, \mathrm{tr} A, \det A): A= \begin{bmatrix} a_{ij}\end{bmatrix}_{i,j=1}^2 \in \mathbb{B}\}$$ where $\mathbb{B}$ denotes the open unit ball in the space of $2\times 2$ complex matrices. We prove several characterizations of the domain. We describe its distinguished boundary and exhibit a $4$-parameter group of automorphisms of $\mathcal{P}$. We show that $\mathcal{P}$ is intimately connected with the problem of $\mu$-synthesis for a certain cost function $\mu$ on the space of $2\times 2$ matrices defined in connection with robust stabilization by control engineers. We demonstrate connections between the function theories of $\mathcal{P}$ and $\mathbb{B}$. We show that $\mathcal{P}$ is polynomially convex and starlike.Comment: 36 pages, 2 figures. This version contains corrections of some inaccuracies and an expanded argument for Proposition 12.

X-ray time lags in AGN: inverse-Compton scattering and spherical corona model

We develop a physically motivated, spherical corona model to investigate the frequency-dependent time lags in AGN. The model includes the effects of Compton up-scattering between the disc UV photons and coronal electrons, and the subsequent X-ray reverberation from the disc. The time lags are associated with the time required for multiple scatterings to boost UV photons up to soft and hard X-ray energies, and the light crossing time the photons take to reach the observer. This model can reproduce not only low-frequency hard and high-frequency soft lags, but also the clear bumps and wiggles in reverberation profiles which should explain the wavy-residuals currently observed in some AGN. Our model supports an anti-correlation between the optical depth and coronal temperatures. In case of an optically thin corona, time delays due to propagating fluctuations may be required to reproduce observed time lags. We fit the model to the lag-frequency data of 1H0707-495, Ark 564, NGC 4051 and IRAS 13224-3809 estimated using the minimal bias technique so that the observed lags here are highest-possible quality. We find their corona size is ~7-15 r_g having the constrained optical depth ~2-10. The coronal temperature is ~150-300 keV. Finally, we note that the reverberation wiggles may be signatures of repeating scatters inside the corona that control the distribution of X-ray sources.Comment: 15 pages, 10 figures, accepted for publication in MNRA

Iron line profiles including emission from within the innermost stable orbit of a black hole accretion disc

Reynolds & Begelman (1997) have recently proposed a model in which the broad and extremely redshifted iron line seen during a deep minimum of the light curve of the Seyfert 1 galaxy MCG-6-30-15 originates from matter spiralling into a Schwarzschild black hole, contrary to previous claims that the black hole may be spinning rapidly (Iwasawa et al 1996; Dabrowski et al 1997). Here we calculate in detail the X-ray spectrum produced by their model using the full reflected continuum emission, including absorption features. This calculation takes into account the doppler and relativistic effects. For the range of parameters we consider, we find that the spectrum should show a large photoelectric absorption edge of iron, which is not seen in the data. The absorption edge is a consequence of the line emitting matter within the innermost stable orbit being highly ionized, and is largely independent of the parameters chosen for their model. If we restrict our attention to the 3-10 keV band we may effectively remove this absorption edge by fitting a steeper power law, but this results in a significant underprediction of the 0.4-0.5 keV flux. We conclude that the data on MCG-6-30-15 are more consistent with the Kerr than the Schwarzschild model.Comment: 5 pages with 5 postscript figures. Accepted for publication in MNRA

Defect energy of infinite-component vector spin glasses

We compute numerically the zero temperature defect energy, Delta E, of the vector spin glass in the limit of an infinite number of spin components m, for a range of dimensions 2 <= d <= 5. Fitting to Delta E ~ L^theta, where L is the system size, we obtain: theta = -1.54 (d=2), theta = -1.04 (d=3), theta = -0.67 (d=4) and theta = -0.37 (d=5). These results show that the lower critical dimension, d_l (the dimension where theta changes sign), is significantly higher for m=infinity than for finite m (where 2 < d_l < 3).Comment: 4 pages, 5 figure