Here we present the weak-lensing results for A1758, which is known to consist of four subclusters undergoing two separate mergers, A1758N and A1758S. Weak-lensing results for A1758N agree with ...previous weak-lensing results for clusters 1E0657-558 (Bullet cluster) and MACS J0025.4-1222, whose X-ray gas components were found to be largely separated from their clusters' gravitational potentials. A1758N has a geometry that is different from previously published mergers in that one of its X-ray peaks overlays the corresponding gravitational potential and the other X-ray peak is well separated from its cluster's gravitational potential. The weak-lensing mass peaks of the two northern clusters are separated at the 2.5sigma level. We estimate the combined mass of the clusters in A1758N to be (2.2 + or - 0.5) x 10 super(15) M sub(sm circle in circle) and r sub(200) = 2300 sub(-130) super(+100) kpc. We also detect seven strong-lensing candidates, two of which may provide information that would improve the mass measurements of A1758N.
Aims. Since the CGRO operation in 1991–2000, one of the primary unresolved questions about the blazar γ-ray emission has been its possible correlation with the low-energy (in particular optical) ...emission. To help answer this problem, the Whole Earth Blazar Telescope (WEBT) consortium has organized the GLAST-AGILE Support Program (GASP) to provide the optical-to-radio monitoring data to be compared with the γ-ray detections by the AGILE and GLAST satellites. This new WEBT project started in early September 2007, just before a strong γ-ray detection of 0716+714 by AGILE. Methods. We present the GASP-WEBT optical and radio light curves of this blazar obtained in July–November 2007, about various AGILE pointings at the source. We construct NIR-to-UV spectral energy distributions (SEDs), by assembling GASP-WEBT data together with UV data from the Swift ToO observations of late October. Results. We observe a contemporaneous optical-radio outburst, which is a rare and interesting phenomenon in blazars. The shape of the SEDs during the outburst appears peculiarly wavy because of an optical excess and a UV drop-and-rise. The optical light curve is well sampled during the AGILE pointings, showing prominent and sharp flares. A future cross-correlation analysis of the optical and AGILE data will shed light on the expected relationship between these flares and the γ-ray events.
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Prompted by a high optical state in 2007 September, the Whole Earth Blazar Telescope consortium organized an intensive optical, near-IR (JHK) and radio observing campaign on the intermediate BL Lac ...object 3C 66A throughout the fall and winter of 2007-2008. In this paper, we present data from 28 observatories in 12 countries, covering the observing season from late 2007 July through 2008 February. The source remained in a high optical state throughout the observing period and exhibited several bright flares on timescales of ~10 days. This included an exceptional outburst around 2007 September 15-20, reaching a peak brightness at R~ 13.4. Our campaign revealed microvariability with flux changes up to |dR/dt|~ 0.02 mag hr-1. Our observations do not reveal evidence for systematic spectral variability in the overall high state covered by our campaign, in agreement with previous results. In particular, we do not find evidence for spectral hysteresis in 3C 66A for which hints were found in an earlier campaign in a somewhat lower flux state. We also did not find any evidence for spectral lags in the discrete correlation functions between different optical bands. We infer a value of the magnetic field in the emission region of B~ 19 e 2/7 B t-6/7 h D 13/7 1 G, where eB is the magnetic field equipartition fraction, t h is the shortest observed variability timescale in units of hours, and D 1 is the Doppler factor in units of 10. From the lack of systematic spectral variability, we can derive an upper limit on the Doppler factor, D <= 28 t-1/8 h e 3/16 B . This is in perfect agreement with superluminal motion measurements with the VLBI/VLBA of bapp <= 27 and argues against models with very high Lorentz factors of 50, required for a one-zone synchrotron-self-Compton interpretation of some high-frequency-peaked BL Lac objects detected at TeV g-ray energies.
Context. BL Lacertae is the prototype of the blazar subclass named after it. Yet, it has occasionally shown a peculiar behaviour that has questioned a simple interpretation of its broad-band emission ...in terms of synchrotron plus synchrotron self-Compton (SSC) radiation. Aims. In the 2007–2008 observing season we carried out a new multiwavelength campaign of the Whole Earth Blazar Telescope (WEBT) on BL Lacertae, involving three pointings by the XMM-Newton satellite in July and December 2007, and January 2008, to study its emission properties, particularly in the optical-X-ray energy range. Methods. The source was monitored in the optical-to-radio bands by 37 telescopes. The brightness level was relatively low. Some episodes of very fast variability were detected in the optical bands. Flux changes had larger amplitude at the higher radio frequencies than at longer wavelengths. Results. The X-ray spectra acquired by the EPIC instrument onboard XMM-Newton are well fitted by a power law with photon index $\Gamma \sim 2$ and photoelectric absorption exceeding the Galactic value. However, when taking into account the presence of a molecular cloud on the line of sight, the EPIC data are best fitted by a double power law, implying a concave X-ray spectrum. The spectral energy distributions (SEDs) built with simultaneous radio-to-X-ray data at the epochs of the XMM-Newton observations suggest that the peak of the synchrotron emission lies in the near-IR band, and show a prominent UV excess, besides a slight soft-X-ray excess. A comparison with the SEDs corresponding to previous observations with X-ray satellites shows that the X-ray spectrum is very variable, since it can change from extremely steep to extremely hard, and can be more or less curved in intermediate states. We ascribe the UV excess to thermal emission from the accretion disc, and the other broad-band spectral features to the presence of two synchrotron components, with their related SSC emission. We fit the thermal emission with a black body law and the non-thermal components by means of a helical jet model. The fit indicates a disc temperature $ \ga$$ 20\,000 \rm \, K$ and a luminosity $ \ga$$ 6 \times 10^{44} ~\rm erg \, s^{-1}$.
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In 2007-2008 we carried out a new multiwavelength campaign of the Whole Earth Blazar Telescope (WEBT) on BL Lacertae, involving three pointings by the XMM-Newton satellite, to study its emission ...properties. The source was monitored in the optical-to-radio bands by 37 telescopes. The brightness level was relatively low. Some episodes of very fast variability were detected in the optical bands. The X-ray spectra are well fitted by a power law with photon index of about 2 and photoelectric absorption exceeding the Galactic value. However, when taking into account the presence of a molecular cloud on the line of sight, the data are best fitted by a double power law, implying a concave X-ray spectrum. The spectral energy distributions (SEDs) built with simultaneous radio-to-X-ray data at the epochs of the XMM-Newton observations suggest that the peak of the synchrotron emission lies in the near-IR band, and show a prominent UV excess, besides a slight soft-X-ray excess. A comparison with the SEDs corresponding to previous observations with X-ray satellites shows that the X-ray spectrum is extremely variable. We ascribe the UV excess to thermal emission from the accretion disc, and the other broad-band spectral features to the presence of two synchrotron components, with their related SSC emission. We fit the thermal emission with a black body law and the non-thermal components by means of a helical jet model. The fit indicates a disc temperature greater than 20000 K and a luminosity greater than 6 x 10^44 erg/s.
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The Riemann zeta function is defined as $\mathrm{\zeta }\left(\mathrm{z}\right)=\sum _{\mathrm{k}=1}^{\mathrm{\infty }}{\mathrm{k}}^{-\mathrm{z}}$, where Re(z) > 1. The reader may be familiar with ...Euler's method of computing $\mathrm{\zeta }\left(2\right)=\sum _{\mathrm{k}=1}^{\mathrm{\infty }}\frac{1}{{\mathrm{k}}^{2}}=\frac{{\mathrm{\pi }}^{2}}{6}$ which compares the Weierstrass product and Taylor series for sin x/x. By going to the complex plane, this technique can be generalized to find a formula for ζ(2n), where 2n is a positive even integer. The approach is elementary in nature, employing facts from standard undergraduate mathematics courses including complex analysis, abstract algebra, and discrete mathematics.
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The concept of a free Hopf algebra generated by a coalgebra was introduced by Takeuchi to provide an example of a Hopf algebra with a non-bijective antipode. In general, this free Hopf algebra is not ...generated as an algebra by the coalgebra. In this paper, we construct a class of Hopf algebras, including SLq(2), which are generated as algebras by a coalgebra and which satisfy a useful universality condition.
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Aims. The Whole Earth Blazar Telescope (WEBT) consortium has been monitoring the blazar 3C 454.3 from the radio to the optical bands since 2004 to study its emission variability properties. Methods. ...We present and analyse the multifrequency results of the 2007-2008 observing season, including XMM-Newton observations and near-IR spectroscopic monitoring, and compare the recent emission behaviour with the past one. The historical mm light curve is presented here for the first time. Results. In the optical band we observed a multi-peak outburst in July-August 2007, and other faster events in November 2007-February 2008. During these outburst phases, several episodes of intranight variability were detected. A mm outburst was observed starting from mid 2007, whose rising phase was contemporaneous to the optical brightening. A slower flux increase also affected the higher radio frequencies, the flux enhancement disappearing below 8 GHz. The analysis of the optical-radio correlation and time delays, as well as the behaviour of the mm light curve, confirm our previous predictions, suggesting that changes in the jet orientation likely occurred in the last few years. The historical multiwavelength behaviour indicates that a significant variation in the viewing angle may have happened around year 2000. Colour analysis confirms a general redder-when-brighter trend, which reaches a “saturation” at R ~ 14 and possibly turns into a bluer-when-brighter trend in bright states. This behaviour is due to the interplay of different emission components, the synchrotron one possibly being characterised by an intrinsically variable spectrum. All the near-IR spectra show a prominent Hα emission line (EWobs = 50-120 Å), whose flux appears nearly constant, indicating that the broad line region is not affected by the jet emission. We show the broad-band SEDs corresponding to the epochs of the XMM-Newton pointings and compare them to those obtained at other epochs, when the source was in different brightness states. A double power-law fit to the EPIC spectra including extra absorption suggests that the soft-X-ray spectrum is concave, and that the curvature becomes more pronounced as the flux decreases. This connects fairly well with the UV excess, which becomes more prominent with decreasing flux. The most obvious interpretation implies that, as the beamed synchrotron radiation from the jet dims, we can see both the head and the tail of the big blue bump. The X-ray flux correlates with the optical flux, suggesting that in the inverse-Compton process either the seed photons are synchrotron photons at IR-optical frequencies or the relativistic electrons are those that produce the optical synchrotron emission. The X-ray radiation would thus be produced in the jet region from where the IR-optical emission comes.
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