Modified fast frequency acquisition via adaptive least squares algorithm

A method and the associated apparatus for estimating the amplitude, frequency, and phase of a signal of interest are presented. The method comprises the following steps: (1) inputting the signal of interest; (2) generating a reference signal with adjustable amplitude, frequency and phase at an output thereof; (3) mixing the signal of interest with the reference signal and a signal 90 deg out of phase with the reference signal to provide a pair of quadrature sample signals comprising respectively a difference between the signal of interest and the reference signal and a difference between the signal of interest and the signal 90 deg out of phase with the reference signal; (4) using the pair of quadrature sample signals to compute estimates of the amplitude, frequency, and phase of an error signal comprising the difference between the signal of interest and the reference signal employing a least squares estimation; (5) adjusting the amplitude, frequency, and phase of the reference signal from the numerically controlled oscillator in a manner which drives the error signal towards zero; and (6) outputting the estimates of the amplitude, frequency, and phase of the error signal in combination with the reference signal to produce a best estimate of the amplitude, frequency, and phase of the signal of interest. The preferred method includes the step of providing the error signal as a real time confidence measure as to the accuracy of the estimates wherein the closer the error signal is to zero, the higher the probability that the estimates are accurate. A matrix in the estimation algorithm provides an estimate of the variance of the estimation error

Scale invariant jets: from blazars to microquasars

Black holes, anywhere in the stellar-mass to supermassive range, are often associated with relativistic jets. Models suggest that jet production may be a universal process common in all black hole systems regardless of their mass. Although in many cases observations support such hypotheses for microquasars and Seyfert galaxies, little is known on whether boosted blazar jets also comply with such universal scaling laws. We use uniquely rich multiwavelength radio light curves from the F-GAMMA program and the most accurate Doppler factors available to date to probe blazar jets in their emission rest frame with unprecedented accuracy. We identify for the first time a strong correlation between the blazar intrinsic broad-band radio luminosity and black hole mass, which extends over $\sim$ 9 orders of magnitude down to microquasars scales. Our results reveal the presence of a universal scaling law that bridges the observing and emission rest frames in beamed sources and allows us to effectively constrain jet models. They consequently provide an independent method for estimating the Doppler factor, and for predicting expected radio luminosities of boosted jets operating in systems of intermediate or tens-of-solar mass black holes, immediately applicable to cases as those recently observed by LIGO.Comment: 13 pages, 4 figures, accepted for publication in AP

Photospheric Electric Fields and Energy Fluxes in the Eruptive Active Region NOAA 11158

How much electromagnetic energy crosses the photosphere in evolving solar active regions? With the advent of high-cadence vector magnetic field observations, addressing this fundamental question has become tractable. In this paper, we apply the "PTD-Doppler-FLCT-Ideal" (PDFI) electric field inversion technique of Kazachenko et al. (2014) to a 6-day HMI/SDO vector magnetogram and Doppler velocity sequence, to find the electric field and Poynting flux evolution in active region NOAA 11158, which produced an X2.2 flare early on 2011 February 15. We find photospheric electric fields ranging up to $2$ V/cm. The Poynting fluxes range from $[-0.6$ to $2.3]\times10^{10}$ ergs$\cdot$cm$^{-2}$s$^{-1}$, mostly positive, with the largest contribution to the energy budget in the range of $[10^9$-$10^{10}]$ ergs$\cdot$cm$^{-2}$s$^{-1}$. Integrating the instantaneous energy flux over space and time, we find that the total magnetic energy accumulated above the photosphere from the initial emergence to the moment before the X2.2 flare to be $E=10.6\times10^{32}$ ergs, which is partitioned as $2.0$ and $8.6\times10^{32}$ ergs, respectively, between free and potential energies. Those estimates are consistent with estimates from preflare non-linear force-free field (NLFFF) extrapolations and the Minimum Current Corona estimates (MCC), in spite of our very different approach. This study of photospheric electric fields demonstrates the potential of the PDFI approach for estimating Poynting fluxes and opens the door to more quantitative studies of the solar photosphere and more realistic data-driven simulations of coronal magnetic field evolution.Comment: 51 pages, 10 figures, accepted by ApJ on August 11, 201

Constraining the limiting brightness temperature and Doppler factors for the largest sample of radio bright blazars

Relativistic effects dominate the emission of blazar jets complicating our understanding of their intrinsic properties. Although many methods have been proposed to account for them, the variability Doppler factor method has been shown to describe the blazar populations best. We use a Bayesian hierarchical code called {\it Magnetron} to model the light curves of 1029 sources observed by the Owens Valley Radio Observatory's 40-m telescope as a series of flares with an exponential rise and decay, and estimate their variability brightness temperature. Our analysis allows us to place the most stringent constraints on the equipartition brightness temperature i.e., the maximum achieved intrinsic brightness temperature in beamed sources which we found to be $\rm \langle T_{eq}\rangle=2.78\times10^{11}K\pm26\%$. Using our findings we estimated the variability Doppler factor for the largest sample of blazars increasing the number of available estimates in the literature by almost an order of magnitude. Our results clearly show that $\gamma$-ray loud sources have faster and higher amplitude flares than $\gamma$-ray quiet sources. As a consequence they show higher variability brightness temperatures and thus are more relativistically beamed, with all of the above suggesting a strong connection between the radio flaring properties of the jet and $\gamma$-ray emission.Comment: 14 pages, 8 figures, accepted for publication in AP

Central Masses and Broad-Line Region Sizes of Active Galactic Nuclei: I. Comparing the Photoionization and Reverberation Techniques

The masses and emission-line region sizes of Active Galactic Nuclei (AGNs) can be measured by ``reverberation-mapping'' (measuring the lag of the emission-line luminosity after changes in the continuum). We use tis technique to calibrate similar size and mass estimates made by photoionization models of the AGN line-emitting regions. We compile a sample of 19 AGNs with reliable reverberation and spectroscopy data, twice the number available previously. The data provide strong evidence that the BLR size and the emission-line width measure directly the central mass. Two methods are used to estimate the distance of the broad emission-line region (BLR) from the ionizing source: the photoionization method (available for many AGNs but has large intrinsic uncertainties), and the reverberation method (gives very reliable distances, but available for only a few objects). The distance estimate is combined with the velocity dispersion, derived from the broad Hb line profile, to estimate the virial mass. Comparing the central masses calculated with the reverberation method to those calculated using a photoionization model, we find a highly significant, nearly linear correlation. This provides a calibration of the photoionization method on the objects with presently available reverberation data, which should enable mass estimates for all AGNs with measured Hb line width. Comparing the BLR sizes given by the two methods also enables us to estimate the ionizing EUV luminosity which is directly unobservable. We find it to be typically ten times the visible (monochromatic luminosity at 5100A). The inferred Eddington ratio of the individual objects in our sample are 0.001-0.03 (visible luminosity) and 0.01-0.3 (ionizing luminosity).Comment: 27 pages Latex, 8 figures. Accepted for publication in the Astrophysical Journa

Twenty Years of Timing SS433

We present observations of the optical ``moving lines'' in spectra of the Galactic relativistic jet source SS433 spread over a twenty year baseline from 1979 to 1999. The red/blue-shifts of the lines reveal the apparent precession of the jet axis in SS433, and we present a new determination of the precession parameters based on these data. We investigate the amplitude and nature of time- and phase-dependent deviations from the kinematic model for the jet precession, including an upper limit on any precessional period derivative of $\dot P < 5 \times 10^{-5}$. We also dicuss the implications of these results for the origins of the relativistic jets in SS433.Comment: 21 pages, including 9 figures. To appear in the Astrophysical Journa

Why should we correct reported pulsation frequencies for stellar line-of-sight Doppler velocity shifts?

In the age of Kepler and Corot, extended observations have provided estimates of stellar pulsation frequencies that have achieved new levels of precision, regularly exceeding fractional levels of a few parts in $10^{4}$. These high levels of precision now in principle exceed the point where one can ignore the Doppler shift of pulsation frequencies caused by the motion of a star relative to the observer. We present a correction for these Doppler shifts and use previously published pulsation frequencies to demonstrate the significance of the effect. We suggest that reported pulsation frequencies should be routinely corrected for stellar line-of-sight velocity Doppler shifts, or if a line-of-sight velocity estimate is not available, the frame of reference in which the frequencies are reported should be clearly stated.Comment: 5 pages, 1 figure, accepted for publication in MNRAS Letter