The Virgin Mary, Creation, Incarnation, and Redemption: From the Church Fathers to Chiara Lubich

This article discusses a series of texts on the Virgin Mary that are to be found among the writings by Chiara Lubich known as “Paradise ’49,” which describe the mystical illuminations that she, together with some of her first companions, experienced between 1949 and 1951. I begin by considering illuminations on Mary’s role as Theotokos, the Mother or Bearer of God, and then discuss the part she plays in the Redemption as the Desolata, or Desolate One. I conclude with some remarks about Lubich’s vision of Mary in relation to the Trinity, humanity, and creation (of which Mary is the highest synthesis). I show how Lubich partakes entirely in the tradition that begins with church fathers such as Justin Martyr and Irenaeus, who write of the Virgin as the New Eve in the third century. Yet, I argue, Lubich’s insights add something new, particularly with regard to her understanding of the relationship between Jesus’s cry of forsakenness on the cross and Mary’s desolation as she participates in the agony of her Son and assents to the loss of her divine motherhood. I seek to show that Lubich’s new understanding of these events has profound implications for a variety of doctrinal matters concerning Mary, including her freedom from sin, her co-operation in the Redemption, and her role in actualizing the grace unleashed by Christ’s sacrifice. But more important than this in some respects, Lubich shows us how it is through losing God out of love for God that Mary, in her desolation, most fully mirrors the kenosis that lies at the heart of the perichoretic relations of the Trinity and offers us a model of how we may live Trinitarian love on earth and participate as cocreators in the renewal and transformation of Creation

Moments of the eigenvalue densities and of the secular coefficients of β-ensembles

© 2017 IOP Publishing Ltd & London Mathematical Society.We compute explicit formulae for the moments of the densities of the eigenvalues of the classical β-ensembles for finite matrix dimension as well as the expectation values of the coefficients of the characteristic polynomials. In particular, the moments are linear combinations of averages of Jack polynomials, whose coefficients are related to specific examples of Jack characters

Magnetic resonance imaging detects significant sex differences in human myocardial strain

<p>Abstract</p> <p>Background</p> <p>The pathophysiology responsible for the significant outcome disparities between men and women with cardiac disease is largely unknown. Further investigation into basic cardiac physiological differences between the sexes is needed. This study utilized magnetic resonance imaging (MRI)-based multiparametric strain analysis to search for sex-based differences in regional myocardial contractile function.</p> <p>Methods</p> <p>End-systolic strain (circumferential, longitudinal, and radial) was interpolated from MRI-based radiofrequency tissue tagging grid point displacements in each of 60 normal adult volunteers (32 females).</p> <p>Results</p> <p>The average global left ventricular (LV) strain among normal female volunteers (n = 32) was significantly larger in absolute value (functionally better) than in normal male volunteers (n = 28) in both the circumferential direction (Male/Female = -0.19 ± 0.02 vs. -0.21 ± 0.02; p = 0.025) and longitudinal direction (Male/Female = -0.14 ± 0.03 vs. -0.16 ± 0.02; p = 0.007).</p> <p>Conclusions</p> <p>The finding of significantly larger circumferential and longitudinal LV strain among normal female volunteers suggests that baseline contractile differences between the sexes may contribute to the well-recognized divergence in cardiovascular disease outcomes. Further work is needed in order to determine the pathologic changes that occur in LV strain between women and men with the onset of cardiovascular disease.</p

A Spatially Resolved Study of the Synchrotron Emission and Titanium in Tycho's Supernova Remnant with NuSTAR

We report results from deep observations (~750 ks) of Tycho's supernova remnant (SNR) with NuSTAR. Using these data, we produce narrow-band images over several energy bands to identify the regions producing the hardest X-rays and to search for radioactive decay line emission from 44Ti. We find that the hardest (>10 keV) X-rays are concentrated in the southwest of Tycho, where recent Chandra observations have revealed high emissivity "stripes" associated with particles accelerated to the knee of the cosmic-ray spectrum. We do not find evidence of 44Ti, and we set limits on its presence and distribution within the SNR. These limits correspond to a upper-limit 44Ti mass of M44 < 2.4x10^-4 M_sun for a distance of 2.3 kpc. We perform spatially resolved spectroscopic analysis of sixty-six regions across Tycho. We map the best-fit rolloff frequency of the hard X-ray spectra, and we compare these results to measurements of the shock expansion and ambient density. We find that the highest energy electrons are accelerated at the lowest densities and in the fastest shocks, with a steep dependence of the roll-off frequency with shock velocity. Such a dependence is predicted by models where the maximum energy of accelerated electrons is limited by the age of the SNR rather than by synchrotron losses, but this scenario requires far lower magnetic field strengths than those derived from observations in Tycho. One way to reconcile these discrepant findings is through shock obliquity effects, and future observational work is necessary to explore the role of obliquity in the particle acceleration process.Comment: 12 pages, 12 figures, ApJ in pres

Broadband X-ray Imaging and Spectroscopy of the Crab Nebula and Pulsar with NuSTAR

We present broadband (3 -- 78 keV) NuSTAR X-ray imaging and spectroscopy of the Crab nebula and pulsar. We show that while the phase-averaged and spatially integrated nebula + pulsar spectrum is a power-law in this energy band, spatially resolved spectroscopy of the nebula finds a break at $\sim$9 keV in the spectral photon index of the torus structure with a steepening characterized by $\Delta\Gamma\sim0.25$. We also confirm a previously reported steepening in the pulsed spectrum, and quantify it with a broken power-law with break energy at $\sim$12 keV and $\Delta\Gamma\sim0.27$. We present spectral maps of the inner 100\as\ of the remnant and measure the size of the nebula as a function of energy in seven bands. These results find that the rate of shrinkage with energy of the torus size can be fitted by a power-law with an index of $\gamma = 0.094\pm 0.018$, consistent with the predictions of Kennel and Coroniti (1984). The change in size is more rapid in the NW direction, coinciding with the counter-jet where we find the index to be a factor of two larger. NuSTAR observed the Crab during the latter part of a $\gamma$-ray flare, but found no increase in flux in the 3 - 78 keV energy band

Locating the most energetic electrons in Cassiopeia A

We present deep ($>$2.4 Ms) observations of the Cassiopeia A supernova remnant with {\it NuSTAR}, which operates in the 3--79 keV bandpass and is the first instrument capable of spatially resolving the remnant above 15 keV. We find that the emission is not entirely dominated by the forward shock nor by a smooth "bright ring" at the reverse shock. Instead we find that the $>$15 keV emission is dominated by knots near the center of the remnant and dimmer filaments near the remnant's outer rim. These regions are fit with unbroken power-laws in the 15--50 keV bandpass, though the central knots have a steeper ($\Gamma \sim -3.35$) spectrum than the outer filaments ($\Gamma \sim -3.06$). We argue this difference implies that the central knots are located in the 3-D interior of the remnant rather than at the outer rim of the remnant and seen in the center due to projection effects. The morphology of $>$15 keV emission does not follow that of the radio emission nor that of the low energy ($<$12 keV) X-rays, leaving the origin of the $>$15 keV emission as an open mystery. Even at the forward shock front we find less steepening of the spectrum than expected from an exponentially cut off electron distribution with a single cutoff energy. Finally, we find that the GeV emission is not associated with the bright features in the {\it NuSTAR} band while the TeV emission may be, suggesting that both hadronic and leptonic emission mechanisms may be at work.Comment: 12 pages, 11 figures, accepted for publication in Ap

High-Energy X-ray Imaging of the Pulsar Wind Nebula MSH~15-52: Constraints on Particle Acceleration and Transport

We present the first images of the pulsar wind nebula (PWN) MSH 15-52 in the hard X-ray band (>8 keV), as measured with the Nuclear Spectroscopic Telescope Array (NuSTAR). Overall, the morphology of the PWN as measured by NuSTAR in the 3-7 keV band is similar to that seen in Chandra high-resolution imaging. However, the spatial extent decreases with energy, which we attribute to synchrotron energy losses as the particles move away from the shock. The hard-band maps show a relative deficit of counts in the northern region towards the RCW 89 thermal remnant, with significant asymmetry. We find that the integrated PWN spectra measured with NuSTAR and Chandra suggest that there is a spectral break at 6 keV which may be explained by a break in the synchrotron-emitting electron distribution at ~200 TeV and/or imperfect cross calibration. We also measure spatially resolved spectra, showing that the spectrum of the PWN softens away from the central pulsar B1509-58, and that there exists a roughly sinusoidal variation of spectral hardness in the azimuthal direction. We discuss the results using particle flow models. We find non-monotonic structure in the variation with distance of spectral hardness within 50" of the pulsar moving in the jet direction, which may imply particle and magnetic-field compression by magnetic hoop stress as previously suggested for this source. We also present 2-D maps of spectral parameters and find an interesting shell-like structure in the NH map. We discuss possible origins of the shell-like structure and their implications.Comment: 15 pages, 9 figures, accepted for publication in Ap

The Hard X-Ray View of the Young Supernova Remnant G1.9+0.3

NuSTAR observed G1.9+0.3, the youngest known supernova remnant in the Milky Way, for 350 ks and detected emission up to $\sim$30 keV. The remnant's X-ray morphology does not change significantly across the energy range from 3 to 20 keV. A combined fit between NuSTAR and CHANDRA shows that the spectrum steepens with energy. The spectral shape can be well fitted with synchrotron emission from a power-law electron energy distribution with an exponential cutoff with no additional features. It can also be described by a purely phenomenological model such as a broken power-law or a power-law with an exponential cutoff, though these descriptions lack physical motivation. Using a fixed radio flux at 1 GHz of 1.17 Jy for the synchrotron model, we get a column density of N$_{\rm H}$ = $(7.23\pm0.07) \times 10^{22}$ cm$^{-2}$, a spectral index of $\alpha=0.633\pm0.003$, and a roll-off frequency of $\nu_{\rm rolloff}=(3.07\pm0.18) \times 10^{17}$ Hz. This can be explained by particle acceleration, to a maximum energy set by the finite remnant age, in a magnetic field of about 10 $\mu$G, for which our roll-off implies a maximum energy of about 100 TeV for both electrons and ions. Much higher magnetic-field strengths would produce an electron spectrum that was cut off by radiative losses, giving a much higher roll-off frequency that is independent of magnetic-field strength. In this case, ions could be accelerated to much higher energies. A search for $^{44}$Ti emission in the 67.9 keV line results in an upper limit of $1.5 \times 10^{-5}$ $\,\mathrm{ph}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$ assuming a line width of 4.0 keV (1 sigma).Comment: 9 pages, 6 figures, accepted Ap

NuSTAR study of Hard X-Ray Morphology and Spectroscopy of PWN G21.5-0.9

We present NuSTAR high energy X-ray observations of the pulsar wind nebula (PWN)/supernova remnant G21.5-0.9. We detect integrated emission from the nebula up to ~40 keV, and resolve individual spatial features over a broad X-ray band for the first time. The morphology seen by NuSTAR agrees well with that seen by XMM-Newton and Chandra below 10 keV. At high energies NuSTAR clearly detects non-thermal emission up to ~20 keV that extends along the eastern and northern rim of the supernova shell. The broadband images clearly demonstrate that X-ray emission from the North Spur and Eastern Limb results predominantly from non-thermal processes. We detect a break in the spatially integrated X-ray spectrum at ~9 keV that cannot be reproduced by current SED models, implying either a more complex electron injection spectrum or an additional process such as diffusion compared to what has been considered in previous work. We use spatially resolved maps to derive an energy-dependent cooling length scale, $L(E) \propto E^{m}$ with $m = -0.21 \pm 0.01$. We find this to be inconsistent with the model for the morphological evolution with energy described by Kennel & Coroniti (1984). This value, along with the observed steepening in power-law index between radio and X-ray, can be quantitatively explained as an energy-loss spectral break in the simple scaling model of Reynolds (2009), assuming particle advection dominates over diffusion. This interpretation requires a substantial departure from spherical magnetohydrodynamic (MHD), magnetic-flux-conserving outflow, most plausibly in the form of turbulent magnetic-field amplification.Comment: 13 pages, 8 figures, 1 table, Accepted for publication in the Astrophysical Journa