W. D. Cotton

National Radio Astronomy Observatory, Charlottesville, Virginia, United States

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Publications (258)683.36 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: Very Large Array observations of the Galactic center at 7 mm have produced an image of the 30'' surrounding Sgr A* with a resolution of ~82 × 42 milliarcseconds (mas). A comparison with IR images taken simultaneously with the Very Large Telescope identifies 41 radio sources with L-band (3.8 μm) stellar counterparts. The well-known young, massive stars in the central Sgr A* cluster (e.g., IRS 16C, IRS 16NE, IRS 16SE2, IRS 16NW, IRS 16SW, AF, AFNW, IRS 34W, and IRS 33E) are detected with peak flux densities between ~0.2 and 1.3 mJy. The origin of the stellar radio emission in the central cluster is discussed in terms of ionized stellar winds with mass-loss rates in the range ~0.8-5 × 10–5M ☉ yr–1. Radio emission from eight massive stars is used as a tool for registration between the radio and infrared frames with mas precision within a few arcseconds of Sgr A* . This is similar to the established technique of aligning SiO masers and evolved stars except that radio stars lie within a few arcseconds of Sgr A*. Our data show a scatter of ~6.5 mas in the positions of the eight radio sources that appear in both the L-band and 7 mm images. Last, we use the radio and IR data to argue that members of IRS 13N are young stellar objects rather than dust clumps, supporting the hypothesis that recent star formation has occurred near Sgr A*.
    The Astrophysical Journal Letters 08/2014; 792(1):L1. · 6.35 Impact Factor
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    ABSTRACT: Very Large Array observations of the Galactic Center at 7 mm have produced an image of the 30 arcseconds surrounding Sgr A* with a resolution of 82x42 milliarcseconds (mas). A comparison with IR images taken simultaneously with the Very Large Telescope (VLT) identifies 41 radio sources with L-band (3.8 microns) stellar counterparts. The well-known young, massive stars in the central Sgr A* cluster (e.g., IRS 16C, IRS 16NE, IRS 16SE2, IRS 16NW, IRS 16SW, AF, AFNW, IRS 34W and IRS 33E) are detected with peak flux densities between 0.2 and 1.3 mJy. The origin of the stellar radio emission in the central cluster is discussed in terms of ionized stellar winds with mass-loss rates in the range 0.8-5x10^{-5} solar mass per year. Radio emission from eight massive stars is used as a tool for registration between the radio and infrared frames with mas precision within a few arcseconds of Sgr A*. This is similar to the established technique of aligning SiO masers and evolved stars except that radio stars lie within a few arcseconds of Sgr A*. Our data show a scatter of ~6.5 mas in the positions of the eight radio sources that appear in both the L-band and 7 mm images. Lastly, we use the radio and IR data to argue that members of IRS 13N are Young Stellar Objects rather than dust clumps, supporting the hypothesis that recent star formation has occurred near Sgr A*.
    07/2014;
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    ABSTRACT: We report observations using the Swift/XRT, NuSTAR, and Chandra X-ray telescopes of the transient X-ray source CXOGC J174540.0-290005, during its 2013 outburst. Due to its location in the field of multiple observing campaigns targeting Sgr A*, this is one of the best-studied outbursts of a very faint X-ray binary (VFXB; peak LX < 1036 erg/s) yet recorded, with detections in 173 ks of X-ray observations over 50 days. VFXBs are of particular interest, due to their unusually low outburst luminosities and time-averaged mass transfer rates, which are hard to explain within standard accretion physics and binary evolution. The 2013 outburst of CXOGC J174540.0-290005 peaked at Lx (2-10 keV)=5.0 × 1035 erg/s, and all data above 1034 ergs/s were well-fit by an absorbed power-law of photon index ∼ 1.7, extending from 2 keV out to ~70 keV. We discuss the implications of these observations for the accretion state of CXOGC J174540.0-290005.
    Monthly Notices of the Royal Astronomical Society 05/2014; · 5.52 Impact Factor
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    ABSTRACT: We report observations using the Swift/XRT, NuSTAR, and Chandra X-ray telescopes of the transient X-ray source CXOGC J174540.0-290005, during its 2013 outburst. Due to its location in the field of multiple observing campaigns targeting Sgr A*, this is one of the best-studied outbursts of a very faint X-ray binary (VFXB; peak $L_X<10^{36}$ erg/s) yet recorded, with detections in 173 ks of X-ray observations over 50 days. VFXBs are of particular interest, due to their unusually low outburst luminosities and time-averaged mass transfer rates, which are hard to explain within standard accretion physics and binary evolution. The 2013 outburst of CXOGC J174540.0-290005 peaked at $L_X$(2-10 keV)=$5.0\times10^{35}$ erg/s, and all data above $10^{34}$ ergs/s were well-fit by an absorbed power-law of photon index $\sim1.7$, extending from 2 keV out to $\sim$70 keV. We discuss the implications of these observations for the accretion state of CXOGC J174540.0-290005.
    04/2014;
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    ABSTRACT: We present the results of a recent re-reduction of the data from the Very Large Array (VLA) Low-frequency Sky Survey (VLSS). We used the VLSS catalogue as a sky model to correct the ionospheric distortions in the data and create a new set of sky maps and corresponding catalogue at 73.8 MHz. The VLSS Redux (VLSSr) has a resolution of 75 arcsec, and an average map rms noise level of σ ̃ 0.1 Jy beam-1. The clean bias is 0.66 × σ and the theoretical largest angular size is 36 arcmin. Six previously unimaged fields are included in the VLSSr, which has an unbroken sky coverage over 9.3 sr above an irregular southern boundary. The final catalogue includes 92 964 sources. The VLSSr improves upon the original VLSS in a number of areas including imaging of large sources, image sensitivity, and clean bias; however the most critical improvement is the replacement of an inaccurate primary beam correction which caused source flux errors which vary as a function of radius to nearest pointing centre in the VLSS.
    04/2014; 440(1).
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    ABSTRACT: Radio continuum observations of the Galactic center have been carried out in four different epochs between July and August 2011 at 7mm using the VLA in its A configuration. We combined these data and made a high dynamic range image of the inner 30" of Sgr A* with a resolution of ~82x42 milliarcseconds with an rms noise 61 microJy. After the comparison of 7mm images with H, K and L images taken with the VLT during the same epoch, we identify at least 50 radio sources. Most of these sources coincide with infrared identified stellar sources associated with the central cluster. We used the accurate position of radio stars to register the radio and infrared frames at a smaller angular distance from Sgr A* 5") than had been made in earlier studies based on SiO masers (Menten et al. 1997; Reid et al, 2003). Sensitive radio measurements should be able to potentially discover highly extincted stellar sources that are not detected at near-IR wavelengths. We discuss the origin of radio emission from stars in the central cluster. We also present dark features in Galactic Center radio images that are the imprints of envelopes of dusty stars and molecular clouds.
    01/2014;
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    ABSTRACT: The recent discovery of a dense, cold cloud (dubbed "G2") approaching Sgr A* offers an opportunity to test models of black hole accretion and its associated feedback. G2's orbit is eccentric and the cloud shows signs of tidal disruption by the black hole. High-energy emission from the Sgr A*/G2 encounter may rise toward pericenter (mid-to-late 2013, or early 2014) and continue over the next several years as the material circularizes. This encounter is also likely to enhance Sgr A*'s flare activity across the electromagnetic spectrum. We present preliminary results from our 2013 joint Chandra/XMM/VLA monitoring campaigns. Our programs aim to study the radiation properties of Sgr A* as G2 breaks up and feeds the accretion flow, to constrain the rates and emission mechanisms of faint X-ray flares, and to detect G2 itself as it is shocked and heated. We discuss the constraints these data place on theoretical models for the Sgr A*/G2 encounter and outline plans for continued monitoring with Chandra, XMM, HST, and VLA in 2014.
    01/2014;
  • Wendy M. Peters, W. D. Cotton, N. E. Kassim
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    ABSTRACT: We present the Very Large Array (VLA) Low-frequency Sky Survey Redux (VLSSr), which covers the sky above declinations δ > -30 degrees at a frequency of 74 MHz with 75" resolution and an average RMS noise of 0.1 Jy/beam. The theoretical largest angular size imaged is 36', and there are approximately 95,000 cataloged sources. We have completely re-imaged all data from the original VLSS survey leading to improvements in a number of areas. These include the application of a more accurate primary beam correction which removes substantial radially dependent flux errors present in the VLSS, and smart-windowing to reduce the clean bias by half. We look ahead to the possibility of an expanded, "VLSS generation 2", made by piggybacking observations of the planned VLA Sky Survey (VLASS) using a proposed 24/7 commensal system, called the LOw Band Observatory (LOBO). Catalogs and images for the VLSSr are available at <http://www.cv.nrao.edu/vlss/VLSSlist.shtml>.
    01/2014;
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    ABSTRACT: Thanks to high resolution radio observations it is possible to obtain a direct imaging of the innermost regions of Active Galactic Nuclei; in particular, it is possible to investigate about the jet's morphology and any proper motions, and the time evolution of physical parameters, such as flux densities and spectral index. Furthermore, with the study of the polarization properties, it is possible to obtain important information about the magnetic field structure and the emission mechanisms. In this work we present recent results about the nearby (z=0.031) TeV blazar Mrk 421. We analyzed data obtained with the Very Long Baseline Array (VLBA),both in total and polarized intensity, at twelve epochs (one observation per month from January to December 2011) at 15, 24 and 43 GHz, in the context of a broadband campaign from the radio to gamma-ray. We investigate the inner jet structure on parsec scale through the study of model-fit components for each epoch. At these frequencies the source shows a compact (about 0.13 mas, or 0.08 pc) and bright component, with a one sided jet detected out to about 10 mas. All model-fit components in the jet appear to be almost stationary during our observation period, and the spectral index is fairly flat in the core region and steepens along the jet's length. In particular, we present a preliminary study of the polarization properties for the 15 GHz dataset: we found a degree of polarization of ˜ 1% for the core region and for the C3 component, at near 1 mas from the core, we found a value of near 14%.
    12/2013;
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    ABSTRACT: There is considerable disagreement in the published 1.4-GHz radio source counts from deep surveys probing the sub-100 microJy region. Constraints on these counts have implications for studying galaxy populations and evolution, as well as the global star formation history. Here we present a statistical method for estimating the microJy and even sub-microJy source count using new deep wideband 3-GHz data in the Lockman Hole from the Jansky Very Large Array (JVLA). Using the technique known as P(D) analysis, we provide a fresh approach to the investigation of deep radio data in the form of a more robust model, with a comprehensive non-parametric error analysis. We test this method on a large-scale simulation, incorporating realistic clustering and finite source sizes. We discuss in detail our statistical methods for fitting using MCMC, handling correlations, and various systematic effects introduced from the use of wide-band radio interferometric data. Using this new approach we demonstrate that estimates and constraints on the count are possible down to a depth of 50 nJy, almost two orders of magnitude below instrumental and confusion noise. We find the differential source count near 10 microJy to have a slope of -1.7, decreasing to about -1.4 from 0.5 to 3 microJy. This yields estimates of the 3 GHz confusion noise of 1.15 to 1.3 microJy/beam rms, and a radio background temperature from discrete sources of approximately 14 mK. This is in good agreement with, and fits the data somewhat better than, the previous estimate made by fitting a single power-law model. Our counts are consistent with published evolutionary models, although some modifications may be required, e.g. a larger contribution from star-forming galaxies. With these results we are also able to constrain the peak of any possible new radio populations that would contribute to the cosmic radio background down to 50 nJy.
    11/2013; 440(3).
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    ABSTRACT: We report the results obtained for the AGN Markarian 421 by model-fitting the data in the visibility plane, studing the proper motion of jet components, the light curve, and the spectral index of the jet features. We compare the radio data with optical light curves obtained at the Steward Observatory, considering also the optical polarization information. Mrk 421 has a bright nucleus and a one-sided jet extending towards the north-west for a few parsecs. The model-fits show that brightness distribution is well described using 6-7 circular Gaussian components, four of which are reliably identified at all epochs; all components are effectively stationary except for component D, at ~0.4 mas from the core, whose motion is however subluminal. Analysis of the light curve shows two different states, with the source being brighter and more variable in the first half of 2011 than in the second half. The highest flux density is reached in February. A comparison with the optical data reveals an increase of the V magnitude and of the fractional polarization simultaneous with the enhancement of the radio activity.
    Astronomy and Astrophysics 10/2013; · 5.08 Impact Factor
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    ABSTRACT: We present U, V, and I-band images of the host galaxy of Hercules A (3C 348) obtained with HST/WFC3/UVIS. We find a network of dusty filaments which are more complex and extended than seen in earlier HST observations. The filaments are associated with a faint blue continuum light (possibly from young stars) and faint H-alpha emission. It seems likely that the cold gas and dust has been stripped from a companion galaxy now seen as a secondary nucleus. There are dusty filaments aligned with the base of the jets on both eastern and western sides of the galaxy. The morphology of the filaments is different on the two sides - the western filaments are fairly straight, while the eastern filaments are mainly in two loop-like structures. We suggest that despite the difference in morphologies, both sets of filaments have been entrained in a slow moving boundary layer outside the relativistic flow. As suggested by Fabian et al. (2008), magnetic fields in the filaments may stabilize them against disruption. We consider a speculative scenario to explain the relation between the radio source and the shock and cavities in the hot ICM seen in the Chandra data (Nulsen et al. 2005). We suggest the radio source originally (~60 Myr ago) propagated along a position angle of ~35 degrees where it created the shock and cavities. The radio source axis changed to its current orientation (~100 degrees) possibly due to a supermassive black hole merger and began its current epoch of activity about 20 Myr ago.
    The Astrophysical Journal 05/2013; 771(1). · 6.73 Impact Factor
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    ABSTRACT: CORNISH covers the 110deg2 of the northern GLIMPSE (10°<l<65°, |b|<1°) using the VLA in B and BnA configurations at 5GHz. The combination of array configuration and observing frequency results in a ~1.5" synthesized beam within a 8.9' field of view, corresponding to the FWHM primary beam. CORNISH observations of the northern GLIMPSE region were conducted using the VLA during the 2006 and 2007/2008 observing seasons. Four epochs are defined as follows: --------------------------------------------------------------------- Epoch Dates Notes --------------------------------------------------------------------- I 2006 Jul 12 -> 2006 Sep 16 VLA antennas only, storms II 2007 Sep 28 -> 2007 Oct 6 VLA + EVLA antennas, low Decl. IIIa 2007 Oct 27 -> 2008 Feb 4 Dec. Range: -14.9° -10.5° Range: 16.1° -> 21.1° IIIb 2007 Oct 27 -> 2008 Feb 4 Dec. Range: +14.2° +29.1° Range: 48.9° -> 65.5° --------------------------------------------------------------------- (1 data file).
    VizieR Online Data Catalog. 05/2013;
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    ABSTRACT: We report the discovery of a widespread population of collisionally excited methanol J = 4–1 to 30 E sources at 36.2 GHz from the inner 66' × 18' (160 × 43 pc) of the Galactic center. This spectral feature was imaged with a spectral resolution of 16.6 km s–1 taken from 41 channels of a Very Large Array continuum survey of the Galactic center region. The revelation of 356 methanol sources, most of which are maser candidates, suggests a large abundance of methanol in the gas phase in the Galactic center region. There is also spatial and kinematic correlation between SiO (2-1) and CH3OH emission from four Galactic center clouds: the +50 and +20 km s–1 clouds and G0.13–0.13 and G0.25 + 0.01. The enhanced abundance of methanol is accounted for in terms of induced photodesorption by cosmic rays as they travel through a molecular core, collide, dissociate, ionize, and excite Lyman Werner transitions of H2. A time-dependent chemical model in which cosmic rays drive the chemistry of the gas predicts CH3OH abundance of 10–8 to 10–7 on a chemical timescale of 5 × 104 to 5 × 105 years. The average methanol abundance produced by the release of methanol from grain surfaces is consistent with the available data.
    The Astrophysical Journal Letters 02/2013; 764(2):L19. · 6.35 Impact Factor
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    ABSTRACT: We report the discovery of a widespread population of collisionally excited methanol J = 4_{-1} to 3$_0 E sources at 36.2 GHz from the inner 66'x18' (160x43 pc) of the Galactic center. This spectral feature was imaged with a spectral resolution of ~16.6 km/s taken from 41 channels of a VLA continuum survey of the Galactic center region. The revelation of 356 methanol sources, most of which are maser candidates, suggests a large abundance of methanol in the gas phase in the Galactic center region. There is also spatial and kinematic correlation between SiO (2--1) and CH3OH emission from four Galactic center clouds: the +50 and +20 km/s clouds and G0.13-0.13 and G0.25+0.01. The enhanced abundance of methanol is accounted for in terms of induced photodesorption by cosmic rays as they travel through a molecular core, collide, dissociate, ionize, and excite Lyman Werner transitions of H2. A time-dependent chemical model in which cosmic rays drive the chemistry of the gas predicts CH3OH abundance of 10^{-8} to 10^{-7} on a chemical time scale of 5x10^4 to 5x10^5 years. The average methanol abundance produced by the release of methanol from grain surfaces is consistent with the available data.
    01/2013;
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    ABSTRACT: The ARCADE 2 balloon experiment has reported a 3 GHz sky brightness that is 65 +/- 8 mK in excess of the CMB which is much greater than the ~13 mK that can be explained by the known population of radio sources. We have used the Karl Jansky Very Large Array to image one primary beam at 3 GHz with 8 arcsecond resolution and 1.0 μJy per beam rms noise near the pointing center. Our image is confusion limited with an rms confusion noise of ~1.2 μJy per beam. Modeling the distribution of confusion noise suggests that any excess background must be very smooth, so any hypothetical population of discrete sources that can account for the ARCADE result must be very numerous and weaker than ~ 30 nanoJy. If the ARCADE results are correct, the number of weak radio sources would be several orders of magnitude greater than the faintest galaxies in the Hubble Ultra Deep Field.
    01/2013;
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    ABSTRACT: The CORNISH project is the highest resolution radio continuum survey of the Galactic plane to date. It is the 5 GHz radio continuum part of a series of multi-wavelength surveys that focus on the northern GLIMPSE region (10 deg < l < 65 deg), observed by the Spitzer satellite in the mid-infrared. Observations with the Very Large Array in B and BnA configurations have yielded a 1.5" resolution Stokes I map with a root-mean-squared noise level better than 0.4 mJy/beam. Here we describe the data-processing methods and data characteristics, and present a new, uniform catalogue of compact radio-emission. This includes an implementation of automatic deconvolution that provides much more reliable imaging than standard CLEANing. A rigorous investigation of the noise characteristics and reliability of source detection has been carried out. We show that the survey is optimised to detect emission on size scales up to 14" and for unresolved sources the catalogue is more than 90 percent complete at a flux density of 3.9 mJy. We have detected 3,062 sources above a 7-sigma detection limit and present their ensemble properties. The catalogue is highly reliable away from regions containing poorly-sampled extended emission, which comprise less than two percent of the survey area. Imaging problems have been mitigated by down-weighting the shortest spacings and potential artefacts flagged via a rigorous manual inspection with reference to the Spitzer infrared data. We present images of the most common source types found: regions, planetary nebulae and radio-galaxies. The CORNISH data and catalogue are available online at http://cornish.leeds.ac.uk
    The Astrophysical Journal Supplement Series 11/2012; 205(1). · 16.24 Impact Factor
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    ABSTRACT: The compact radio source Sgr A* is coincident with a 4 Multiplication-Sign 10{sup 6} M{sub Sun} black hole at the dynamical center of the Galaxy and is surrounded by dense orbiting ionized and molecular gas. We present high-resolution radio continuum images of the central 3' and report a faint continuous linear structure centered on Sgr A* with a P.A. {approx} 60 Degree-Sign . The extension of this feature appears to be terminated symmetrically by two linearly polarized structures at 8.4 GHz, {approx}75'' from Sgr A*. A number of weak blobs of radio emission with X-ray counterparts are detected along the axis of the linear structure. The linear structure is best characterized by a mildly relativistic jet from Sgr A* with an outflow rate 10{sup -6} M{sub Sun} yr{sup -1}. The near and far sides of the jet are interacting with orbiting ionized and molecular gas over the last 1-3 hundred years and are responsible for a 2'' hole, the 'minicavity', characterized by disturbed kinematics, enhanced Fe II/III line emission, and diffuse X-ray gas. The estimated kinetic luminosity of the outflow is {approx}1.2 Multiplication-Sign 10{sup 41} erg s{sup -1}, so the interaction with the bar may be responsible for the Galactic center X-ray flash inferred to be responsible for much of the fluorescent Fe K{alpha} line emission from the inner 100 pc of the Galaxy.
    The Astrophysical Journal Letters 10/2012; 758(1). · 6.35 Impact Factor
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    J. F. Helmboldt, W. M. Lane, W. D. Cotton
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    ABSTRACT: The results of a climatological study of ionospheric disturbances derived from observations of cosmic sources from the Very Large Array (VLA) Low-frequency Sky Survey (VLSS) are presented. We have used the ionospheric corrections applied to the 74 MHz interferometric data within the VLSS imaging process to obtain fluctuation spectra for the total electron content (TEC) gradient on spatial scales from a few to hundreds of kilometers and temporal scales from less than one minute to nearly an hour. The observations sample nearly all times of day and all seasons. They also span latitudes and longitudes from 28 deg. N to 40 deg. N and 95 deg. W to 114 deg. W, respectively. We have binned and averaged the fluctuation spectra according to time of day, season, and geomagnetic (Kp index) and solar (F10.7) activity. These spectra provide a detailed, multi-scale account of seasonal and intraday variations in ionospheric activity with wavelike structures detected at wavelengths between about 35 and 250 km. In some cases, trends between spectral power and Kp index and/or F10.7 are also apparent. In addition, the VLSS observations allow for measurements of the turbulent power spectrum down to periods of 40 seconds (scales of ~0.4 km at the height of the E-region). While the level of turbulent activity does not appear to have a strong dependence on either Kp index or F10.7, it does appear to be more pronounced during the winter daytime, summer nighttime, and near dusk during the spring.
    Radio Science 09/2012; 47(5). · 1.00 Impact Factor
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    ABSTRACT: High-resolution radio observations are ideal for constraining the value of physical parameters in the inner regions of active-galactic-nucleus jets and complement results on multiwavelength (MWL) observations. This study is part of a wider multifrequency campaign targeting the nearby TeV blazar Markarian 421 (z=0.031), with observations in the sub-mm (SMA), optical/IR (GASP), UV/X-ray (Swift, RXTE, MAXI), and gamma rays (Fermi-LAT, MAGIC, VERITAS). We investigate the jet's morphology and any proper motions, and the time evolution of physical parameters such as flux densities and spectral index. The aim of our wider multifrequency campaign is to try to shed light on questions such as the nature of the radiating particles, the connection between the radio and gamma-ray emission, the location of the emitting regions and the origin of the flux variability. We consider data obtained with the Very Long Baseline Array (VLBA) over twelve epochs (one observation per month from January to December 2011) at 15 GHz and 24 GHz. We investigate the inner jet structure on parsec scales through the study of model-fit components for each epoch. The structure of Mrk 421 is dominated by a compact (~0.13 mas) and bright component, with a one-sided jet detected out to ~10 mas. We identify 5-6 components in the jet that are consistent with being stationary during the 12-month period studied here. Measurements of the spectral index agree with those of other works: they are fairly flat in the core region and steepen along the jet length. Significant flux-density variations are detected for the core component. From our results, we draw an overall scenario in which we estimate a viewing angle 2{\deg} < theta < 5{\deg} and a different jet velocity for the radio and the high-energy emission regions, such that the respective Doppler factors are {\delta}r ~3 and {\delta}h.e. ~14.
    Astronomy and Astrophysics 08/2012; · 5.08 Impact Factor

Publication Stats

3k Citations
683.36 Total Impact Points

Institutions

  • 1981–2014
    • National Radio Astronomy Observatory
      Charlottesville, Virginia, United States
  • 2012
    • University of Sydney
      • Sydney Institute of Astronomy (SIfA)
      Sydney, New South Wales, Australia
  • 2007–2008
    • Northwestern University
      • Department of Physics and Astronomy
      Evanston, Illinois, United States
  • 2003
    • Netherlands Institute for Radio Astronomy
      Dwingelo, Drenthe, Netherlands
  • 1996–2003
    • University of Bologna
      • Department of Physics and Astronomy DIFA
      Bolonia, Emilia-Romagna, Italy
  • 2000
    • Leiden University
      Leyden, South Holland, Netherlands
    • University of Virginia
      • Department of Astronomy
      Charlottesville, Virginia, United States
  • 1984
    • Instituto Nacional de Técnica Aeroespacial
      Torrejon de Ardos, Madrid, Spain
  • 1982
    • Cornell University
      Ithaca, New York, United States
  • 1980–1982
    • Massachusetts Institute of Technology
      Cambridge, Massachusetts, United States