Coverage with k-transmitters in the presence of obstacles

For a fixed integer k ≥ 0, a k-transmitter is an omnidirectional wireless transmitter with an infinite broadcast range that is able to penetrate up to k “walls”, represented as line segments in the plane. We develop lower and upper bounds for the number of k-transmitters that are necessary and sufficient to cover a given collection of line segments, polygonal chains and polygons.Postprint (published version

Space Telescope and Optical Reverberation Mapping Project. VII. Understanding the Ultraviolet Anomaly in NGC 5548 with X-Ray Spectroscopy

During the Space Telescope and Optical Reverberation Mapping Project observations of NGC 5548, the continuum and emission-line variability became decorrelated during the second half of the six-month-long observing campaign. Here we present Swift and Chandra X-ray spectra of NGC 5548 obtained as part of the campaign. The Swift spectra show that excess flux (relative to a power-law continuum) in the soft X-ray band appears before the start of the anomalous emission-line behavior, peaks during the period of the anomaly, and then declines. This is a model-independent result suggesting that the soft excess is related to the anomaly. We divide the Swift data into on- and off-anomaly spectra to characterize the soft excess via spectral fitting. The cause of the spectral differences is likely due to a change in the intrinsic spectrum rather than to variable obscuration or partial covering. The Chandra spectra have lower signal-to-noise ratios, but are consistent with the Swift data. Our preferred model of the soft excess is emission from an optically thick, warm Comptonizing corona, the effective optical depth of which increases during the anomaly. This model simultaneously explains all three observations: the UV emission-line flux decrease, the soft-excess increase, and the emission-line anomaly

Space Telescope and Optical Reverberation Mapping Project. VI. : reverberating disk models for NGC 5548

D.A.S. and K.D.H. acknowledge support from the UK Science and Technology Facilities Council through grant ST/K502339/1 and ST/J001651/1.We conduct a multiwavelength continuum variability study of the Seyfert 1 galaxy NGC 5548 to investigate the temperature structure of its accretion disk. The 19 overlapping continuum light curves (1158 Å to 9157 Å) combine simultaneous Hubble Space Telescope, Swift, and ground-based observations over a 180 day period from 2014 January to July. Light-curve variability is interpreted as the reverberation response of the accretion disk to irradiation by a central time-varying point source. Our model yields the disk inclination i = 36° ± 10°, temperature T1 =(44 ± 6) x 103 K at 1 light day from the black hole, and a temperature–radius slope (T α r-α) of α = 0.99 ± 0.03. We also infer the driving light curve and find that it correlates poorly with both the hard and soft X-ray light curves, suggesting that the X-rays alone may not drive the ultraviolet and optical variability over the observing period. We also decompose the light curves into bright, faint, and mean accretion-disk spectra. These spectra lie below that expected for a standard blackbody accretion disk accreting at L/LEdd=0.1.PostprintPeer reviewe

Space Telescope and Optical Reverberation Mapping Project. XII. broad-line region modeling of NGC 5548.

We present geometric and dynamical modeling of the broad line region (BLR) for the multi-wavelength reverberation mapping campaign focused on NGC 5548 in 2014. The data set includes photometric and spectroscopic monitoring in the optical and ultraviolet, covering the Hβ, C iv, and Lyα broad emission lines. We find an extended disk-like Hβ BLR with a mixture of near-circular and outflowing gas trajectories, while the C iv and Lyα BLRs are much less extended and resemble shell-like structures. There is clear radial structure in the BLR, with C iv and Lyα emission arising at smaller radii than the Hβ emission. Using the three lines, we make three independent black hole mass measurements, all of which are consistent. Combining these results gives a joint inference of ${\mathrm{log}}_{10}({M}_{\mathrm{BH}}/{M}_{\odot })={7.64}_{-0.18}^{+0.21}$. We examine the effect of using the V band instead of the UV continuum light curve on the results and find a size difference that is consistent with the measured UV–optical time lag, but the other structural and kinematic parameters remain unchanged, suggesting that the V band is a suitable proxy for the ionizing continuum when exploring the BLR structure and kinematics. Finally, we compare the Hβ results to similar models of data obtained in 2008 when the active galactic nucleus was at a lower luminosity state. We find that the size of the emitting region increased during this time period, but the geometry and black hole mass remained unchanged, which confirms that the BLR kinematics suitably gauge the gravitational field of the central black hole

Space Telescope and Optical Reverberation Mapping Project.VI. Reverberating Disk Models for NGC 5548

We conduct a multiwavelength continuum variability study of the Seyfert 1 galaxy NGC 5548 to investigate the temperature structure of its accretion disk. The 19 overlapping continuum light curves ($1158\,\mathring{\rm A}$ to $9157\,\mathring{\rm A}$) combine simultaneous Hubble Space Telescope, Swift, and ground-based observations over a 180 day period from 2014 January to July. Light-curve variability is interpreted as the reverberation response of the accretion disk to irradiation by a central time-varying point source. Our model yields the disk inclination $i=36^\circ \pm 10^\circ$, temperature ${T}_{1}=(44\pm 6)\times {10}^{3}$ K at 1 light day from the black hole, and a temperature–radius slope ($T\propto {r}^{-\alpha }$) of $\alpha =0.99\pm 0.03$. We also infer the driving light curve and find that it correlates poorly with both the hard and soft X-ray light curves, suggesting that the X-rays alone may not drive the ultraviolet and optical variability over the observing period. We also decompose the light curves into bright, faint, and mean accretion-disk spectra. These spectra lie below that expected for a standard blackbody accretion disk accreting at $L/{L}_{\mathrm{Edd}}=0.1$.<br/

Space telescope and optical reverberation mapping project. IV. Anomalous behavior of the broad ultraviolet emission lines in NGC 5548

During an intensive Hubble Space Telescope (HST) Cosmic Origins Spectrograph (COS) UV monitoring campaign of the Seyfert 1 galaxy NGC 5548 performed from 2014 February to July, the normally highly correlated far UV continuum and broad emission line variations decorrelated for ∼60-70 days, starting ∼75 days after the first HST/COS observation. Following this anomalous state, the flux and variability of the broad emission lines returned to a more normal state. This transient behavior, characterized by significant deficits in flux and equivalent width of the strong broad UV emission lines, is the first of its kind to be unambiguously identified in an active galactic nucleus reverberation mapping campaign. The largest corresponding emission line flux deficits occurred for the high ionization, collisionally excited lines C iv and Si iv(+O iv]), and also He ii(+O iii]), while the anomaly in Lywas substantially smaller. This pattern of behavior indicates a depletion in the flux of photons with Eph > 54 eV relative to those near 13.6 eV. We suggest two plausible mechanisms for the observed behavior: (i) temporary obscuration of the ionizing continuum incident upon broad line region (BLR) clouds by a moving veil of material lying between the inner accretion disk and inner (BLR), perhaps resulting from an episodic ejection of material from the disk, or (ii) a temporary change in the intrinsic ionizing continuum spectral energy distribution resulting in a deficit of ionizing photons with energies >54 eV, possibly due to a transient restructuring of the Comptonizing atmosphere above the disk. Current evidence appears to favor the latter explanation.Publisher PDFPeer reviewe

Space Telescope and Optical Reverberation Mapping Project. IX. Velocity–Delay Maps for Broad Emission Lines in NGC 5548

In this contribution, we achieve the primary goal of the active galactic nucleus (AGN) STORM campaign by recovering velocity–delay maps for the prominent broad emission lines (Lyα, C iv, He ii, and Hβ) in the spectrum of NGC 5548. These are the most detailed velocity–delay maps ever obtained for an AGN, providing unprecedented information on the geometry, ionization structure, and kinematics of the broad-line region. Virial envelopes enclosing the emission-line responses show that the reverberating gas is bound to the black hole. A stratified ionization structure is evident. The He ii response inside 5–10 lt-day has a broad single-peaked velocity profile. The Lyα, C iv, and Hβ responses extend from inside 2 to outside 20 lt-day, with double peaks at ±2500 km s−1 in the 10–20 lt-day delay range. An incomplete ellipse in the velocity–delay plane is evident in Hβ. We interpret the maps in terms of a Keplerian disk with a well-defined outer rim at R = 20 lt-day. The far-side response is weaker than that from the near side. The line-center delay $\tau =(R/c)(1-\sin i)\approx 5$ days gives the inclination i ≈ 45°. The inferred black hole mass is MBH ≈ 7 × 107 M⊙. In addition to reverberations, the fit residuals confirm that emission-line fluxes are depressed during the "BLR Holiday" identified in previous work. Moreover, a helical "Barber-Pole" pattern, with stripes moving from red to blue across the C iv and Lyα line profiles, suggests azimuthal structure rotating with a 2 yr period that may represent precession or orbital motion of inner-disk structures casting shadows on the emission-line region farther out

Space Telescope and Optical Reverberation Mapping Project. VII. Understanding the Ultraviolet Anomaly in NGC 5548 with X-Ray Spectroscopy

During the Space Telescope and Optical Reverberation Mapping Project observations of NGC 5548, the continuum and emission-line variability became decorrelated during the second half of the six-month-long observing campaign. Here we present Swift and Chandra X-ray spectra of NGC 5548 obtained as part of the campaign. The Swift spectra show that excess flux (relative to a power-law continuum) in the soft X-ray band appears before the start of the anomalous emission-line behavior, peaks during the period of the anomaly, and then declines. This is a model-independent result suggesting that the soft excess is related to the anomaly. We divide the Swift data into on- and off-anomaly spectra to characterize the soft excess via spectral fitting. The cause of the spectral differences is likely due to a change in the intrinsic spectrum rather than to variable obscuration or partial covering. The Chandra spectra have lower signal-to-noise ratios, but are consistent with the Swift data. Our preferred model of the soft excess is emission from an optically thick, warm Comptonizing corona, the effective optical depth of which increases during the anomaly. This model simultaneously explains all three observations: the UV emission-line flux decrease, the soft-excess increase, and the emission-line anomaly

Photoproduction of K+ K- Pairs in Ultraperipheral Collisions

K+K- pairs may be produced in photonuclear collisions, either from the decays of photoproduced φ(1020) mesons or directly as nonresonant K+K- pairs. Measurements of K+K- photoproduction probe the couplings between the φ(1020) and charged kaons with photons and nuclear targets. The kaon-proton scattering occurs at energies far above those available elsewhere. We present the first measurement of coherent photoproduction of K+K- pairs on lead ions in ultraperipheral collisions using the ALICE detector, including the first investigation of direct K+K- production. There is significant K+K- production at low transverse momentum, consistent with coherent photoproduction on lead targets. In the mass range 1.1&lt;1.4 GeV/c2 above the φ(1020) resonance, for rapidity |yKK|&lt;0.8 and pT,KK&lt;0.1 GeV/c, the measured coherent photoproduction cross section is dσ/dy=3.37±0.61(stat)±0.15(syst) mb. The center-of-mass energy per nucleon of the photon-nucleus (Pb) system WγPb,n ranges from 33 to 188 GeV, far higher than previous measurements on heavy-nucleus targets. The cross section is larger than expected for φ(1020) photoproduction alone. The mass spectrum is fit to a cocktail consisting of φ(1020) decays, direct K+K- photoproduction, and interference between the two. The confidence regions for the amplitude and relative phase angle for direct K+K- photoproduction are presented