The structure of the solutions to semilinear equations at a critical exponent

This paper is concerned with the structure of the solutions to subcritical elliptic equations related to the Matukuma equation. In certain cases the complete structure of the solution set is known, and is comparable to that of the original Matukuma equation. Here we derive sufficient conditions for a more complicated solution set consisting of; (i) crossing solutions for small initial conditions and large initial conditions; (ii) at least one open interval of slowly decaying solutions; and (iii) at least two rapidly decaying solutions. As a consequence we obtain multiplicity results for rapidly decaying, or minimal solutions

Complex X-ray spectral variability in Mkn 421 observed with XMM-Newton

The bright blazar Mkn 421 has been observed four times for uninterrupted durations of ~ 9 - 13 hr during the performance verification and calibration phases of the XMM-Newton mission. The source was strongly variable in all epochs, with variability amplitudes that generally increased to higher energy bands. Although the detailed relationship between soft (0.1 - 0.75 keV) and hard (2 - 10 keV) band differed from one epoch to the next, in no case was there any evidence for a measurable interband lag, with robust upper limits of $| \tau | < 0.08$ hr in the best-correlated light curves. This is in conflict with previous claims of both hard and soft lags of ~1 hr in this and other blazars. However, previous observations suffered a repeated 1.6 hr feature induced by the low-Earth orbital period, a feature that is not present in the uninterrupted XMM-Newton data. The new upper limit on $|\tau|$ leads to a lower limit on the magnetic field strength and Doppler factor of B \delta^{1/3} \gs 4.7 G, mildly out of line with the predictions from a variety of homogeneous synchrotron self-Compton emission models in the literature of $B \delta^{1/3} = 0.2 - 0.8$ G. Time-dependent spectral fitting was performed on all epochs, and no detectable spectral hysteresis was seen. We note however that the source exhibited significantly different spectral evolutionary behavior from one epoch to the next, with the strongest correlations in the first and last and an actual divergance between soft and hard X-ray bands in the third. This indicates that the range of spectral variability behavior in Mkn 421 is not fully described in these short snippets; significantly longer uninterrupted light curves are required, and can be obtained with XMM-Newton.Comment: 21 pages, 4 figures, accepted for ApJ, scheduled for August 1, 200

Potential for cogeneration of heat and electricity in California industry, phase 2

The nontechnical issues of industrial cogeneration for 12 California firms were analyzed under three categories of institutional settings: (1) industrial ownership without firm sales of power; (2) industrial ownership with firm sales of power; and (3) utility or third party ownership. Institutional issues were analyzed from the independent viewpoints of the primary parties of interest: the industrial firms, the electric utilities and the California Public utilities Commission. Air quality regulations and the agencies responsible for their promulgation were examined, and a life cycle costing model was used to evaluate the economic merits of representative conceptual cogeneration systems at these sites. Specific recommendations were made for mitigating measures and regulatory action relevant to industrial cogeneration in California

High Temporal Resolution XMM Monitoring of PKS 2155-304

The bright, strongly variable BL Lac object PKS 2155-304 was observed by XMM for two essentially uninterrupted periods of ~11 and 16 hr on 30-31 May 2000. The strongest variations occurred in the highest energy bands. After scaling for this effect, the three softest bands (0.1-1.7 keV) showed strong correlation with no measurable lag to reliable limits of \tau \ls 0.3 hr. However, the hardest band (~3 keV) was less well-correlated with the other three, especially on short time scales, showing deviations of ~10-20% in ~1 hr although, again, no significant interband lag was detected. This result and examination of previous ASCA and BeppoSAX cross-correlation functions suggest that previous claims of soft lags on time scales of 0.3-4 hr could well be an artifact of periodic interruptions due to Earth-occultation every 1.6 hr. Previous determinations of the magnetic field/bulk Lorentz factor were therefore premature, as these data provide only a lower limit of B \gamma^{1/3} \gs 2.5 G. The hardest band encompasses the spectral region above the high-energy break; its enhanced variability could be indicating that the break energy of the synchrotron spectrum, and therefore of the underlying electron energy distribution, changes independently of the lower energies.Comment: 13 pages, 3 figures, accepted by Ap

The Double Quasar HE1104-1805: a case study for time delay determination with poorly sampled lightcurves

We present a new determination of the time delay of the gravitational lens system HE1104-1805 ('Double Hamburger') based on a previously unpublished dataset. We argue that the previously published value of dt_(A-B)=0.73 years was affected by a bias of the employed method. We determine a new value of dt_(A-B)=0.85+/-0.05 years (2 sigma confidence level), using six different techniques based on non interpolation methods in the time domain. The result demonstrates that even in the case of poorly sampled lightcurves, useful information can be obtained with regard to the time delay. The error estimates were calculated through Monte Carlo simulations. With two already existing models for the lens and using its recently determined redshift, we infer a range of values of the Hubble parameter: Ho=48+/-4 km/s Mpc^-1 (2 sigma) for a singular isothermal ellipsoid (SIE) and Ho=62+/-4 km/s Mpc^-1 (2 sigma) for a constant mass-to-light ratio plus shear model (M/L+gamma). The possibly much larger errors due to systematic uncertainties in modeling the lens potential are not included in this error estimate.Comment: 11 pages, 15 figures, accepted by Astronomy and Astrophysic

Progress in understanding Blazars from BeppoSAX observations

Results obtained with BeppoSAX observations of blazars within various collaborative programs are presented. The spectral similarity "paradigm", whereby the spectral energy distributions of blazars follow a sequence, leading to a unified view of the whole population, is briefly illustrated. We concentrate on recent observations of flares and associated spectral variability for three objects at the "blue" end of the spectral sequence, namely PKS 2155-304, Mkn 421 and Mkn 501. The results are discussed in terms of a general analytic synchrotron self-Compton interpretation of the overall spectrum. The physical parameters of the quasi-stationary emission region can be derived with some confidence, while the variability mechanism(s) must be complex.Comment: 10 pages, 8 figures, to be published in the Proceedings of the 32nd COSPAR Meeting, Nagoya, 12-19 July 199

The Remarkably Featureless High Resolution X-ray Spectrum of Mrk 478

An observation of Mrk 478 using the Chandra Low Energy Transmission Grating Spectrometer is presented. The source exhibited 30-40% flux variations on timescales of order 10000 s together with a slow decline in the spectral softness over the full 80 ks observation. The 0.15--3.0 keV spectrum is well fitted by a single power law with photon index of Gamma = 2.91 +/- 0.03. Combined with high energy data from BeppoSAX, the spectrum from 0.15 to 10 keV is well fit as the sum of two power laws with Gamma = 3.03 +/- 0.04, which dominates below 2 keV and 1.4 +/- 0.2, which dominates above 2 keV (quoting 90% confidence uncertainties). No significant emission or absorption features are detected in the high resolution spectrum, supporting our previous findings using the Extreme Ultraviolet Explorer but contradicting the claims of emission lines by Hwang & Bowyer (1997). There is no evidence of a warm absorber, as found in the high resolution spectra of many Sy 1 galaxies including others classified as narrow line Sy 1 galaxies such as Mrk 478. We suggest that the X-ray continuum may result from Comptonization of disk thermal emission in a hot corona through a range of optical depths.Comment: 21 pages, 7 figures; accepted for publication in the Astronomical Journa

Connection between the Accretion Disk and Jet in the Radio Galaxy 3C 111

We present the results of extensive multi-frequency monitoring of the radio galaxy 3C 111 between 2004 and 2010 at X-ray (2.4--10 keV), optical (R band), and radio (14.5, 37, and 230 GHz) wave bands, as well as multi-epoch imaging with the Very Long Baseline Array (VLBA) at 43 GHz. Over the six years of observation, significant dips in the X-ray light curve are followed by ejections of bright superluminal knots in the VLBA images. This shows a clear connection between the radiative state near the black hole, where the X-rays are produced, and events in the jet. The X-ray continuum flux and Fe line intensity are strongly correlated, with a time lag shorter than 90 days and consistent with zero. This implies that the Fe line is generated within 90 light-days of the source of the X-ray continuum. The power spectral density function of X-ray variations contains a break, with steeper slope at shorter timescales. The break timescale of 13 (+12,-6) days is commensurate with scaling according to the mass of the central black hole based on observations of Seyfert galaxies and black hole X-ray binaries (BHXRBs). The data are consistent with the standard paradigm, in which the X-rays are predominantly produced by inverse Compton scattering of thermal optical/UV seed photons from the accretion disk by a distribution of hot electrons --- the corona --- situated near the disk. Most of the optical emission is generated in the accretion disk due to reprocessing of the X-ray emission. The relationships that we have uncovered between the accretion disk and the jet in 3C 111, as well as in the FR I radio galaxy 3C 120 in a previous paper, support the paradigm that active galactic nuclei and Galactic BHXRBs are fundamentally similar, with characteristic time and size scales proportional to the mass of the central black holeComment: Accepted for publication in ApJ. 18 pages, 17 figures, 11 tables (full machine readable data-tables online in ApJ website