VIMAP: an Interactive Program Providing Radio Spectral Index Maps of Active Galactic Nuclei
aa r X i v : . [ a s t r o - ph . I M ] O c t Journal of the Korean Astronomical Society preprint - no DOI assigned : 1 ∼
5, 2014 September pISSN: 1225-4614 · eISSN: 2288-890X The Korean Astronomical Society (2014) http://jkas.kas.org
VIMAP: AN I NTERACTIVE P ROGRAM P ROVIDING R ADIO S PECTRAL I NDEX M APS OF A CTIVE G ALACTIC N UCLEI
Jae-Young Kim and Sascha Trippe
Department of Physics and Astronomy, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-742, Korea; [email protected]; [email protected]
Received September 5, 2014; accepted October 10, 2014
Abstract:
We present a GUI-based interactive Python program,
VIMAP , which generates radio spectralindex maps of active galactic nuclei (AGN) from Very Long Baseline Interferometry (VLBI) maps obtainedat different frequencies.
VIMAP is a handy tool for the spectral analysis of synchrotron emission fromAGN jets, specifically of spectral index distributions, turn-over frequencies, and core-shifts. In general,the required accurate image alignment is difficult to achieve because of a loss of absolute spatial coordinateinformation during VLBI data reduction (self-calibration) and/or intrinsic variations of source structure asfunction of frequency. These issues are overcome by
VIMAP which in turn is based on the two-dimensionalcross-correlation algorithm of Croke & Gabuzda (2008). In this paper, we briefly review the problem ofaligning VLBI AGN maps, describe the workflow of
VIMAP , and present an analysis of archival VLBImaps of the active nucleus 3C 120.
Key words:
Galaxies: active — Radio continuum: galaxies — Methods: data analysis; numerical —Techniques: interferometric
1. I
NTRODUCTION
Active galactic nuclei (AGN) emit strong radio con-tinuum synchrotron radiation and show spatial struc-ture at scales ranging from sub-parsecs to kiloparsecs.Typical features are a core and outflows, especiallyjets, of usually complex structure. Multiple theoret-ical and observational studies indicate that the ac-cretion of gas onto rotating supermassive black holesand acceleration of the accreted matter by magneto-hydrodynamical processes is responsible for launchingrelativistic outflows and powering the observed high-energy synchrotron radiation (see, e.g., Boettcher et al.2012 for a recent review).Multi-frequency Very Long Baseline Interferometry(VLBI) observations are crucial for studying the physicsand evolution of the outflows of AGN. Synchrotronradiation is characterized by its spectral index, α ≡ log( S ν /S ν ) / log( ν /ν ), where S ν is the flux at fre-quency ν and ν and ν are two different observingfrequencies with ν > ν . Measurements of the spatialdistribution of α provide valuable physical information.Walker et al. (2000) revealed the spatial geometry ofionized gas associated with the accretion disk of 3C 84by analyzing its continuum absorption spectra. Frommet al. (2013) interpreted a radio flare in CTA 102 asinteraction of a traveling shock with a stationary struc-ture (potentially a recollimation shock). O’Sullivan &Gabuzda (2009) measured particle densities and mag-netic field strengths in the parsec-scale jets of six activegalaxies in order to test the classical model of AGNjets proposed by Blandford & K¨onigl (1979). Analysesof the structural and spectral variability of radio jets Corresponding author:
S. Trippe complement single-dish studies of temporal AGN vari-ability (e.g., Park & Trippe 2012, 2014; Kim & Trippe2013) and of the interplay between accretion and jetformation (e.g., Allen et al. 2006; Trippe 2014).In practice, obtaining spatially resolved spectral in-dex information for AGN outflows is challenging mainlyfor two reasons. Firstly, an AGN core corresponds toa radio photosphere, e.g., an optical depth τ ν = 1 sur-face, for which the observed position is a function offrequency (a phenomenon known as core-shift effect;Lobanov 1998). Secondly, phase self-calibration, whichis an important step in VLBI data reduction, removesabsolute coordinate information (Kameno et al. 2003;Kadler et al. 2004). Both effects imply the need fora careful spatial alignment of radio maps obtained atdifferent frequencies. Traditionally, two methods foraligning multi-frequency VLBI images have been used.The first one uses optically thin compact components,which are assumed to not change their positions as func-tion of frequency, as reference points in a map (e.g.,Kadler et al. 2004). The second method employs spa-tial correlations of optically thin extended jet structurefor achieving alignment and/or for measuring the core-shift (Walker et al. 2000; Croke & Gabuzda 2008).Currently, standard radio astronomical softwarepackages, especially AIPS , CASA , and Difmap (Shep-herd 1997) lack specialized tasks dedicated to imagealignment. Motivated by this, we developed a highlyinteractive graphical user interface (GUI) based Pythonprogram,
VIMAP , which adopts the two-dimensionalcross-correlation scheme of Croke & Gabuzda (2008).
VIMAP is open to the public and is capable of perform- Maintained by the National Radio Astronomical Observatoryof the USA. Kim & Trippe ing map alignment and the generation of spectral indexmaps in a straightforward manner. In Section 2 weoutline how
VIMAP works. In Section 3 we present ananalysis of archival VLBI maps of the AGN 3C 120 fordemonstration.
2. T HE VIMAP W
ORKFLOW
VIMAP is written in Python version 2.7.3 and uses thefollowing well-known numerical and astronomical add-on packages: • Numpy version 1 . . • Scipy version 0 . . • Matplotlib version 1 . . • PyFITS version 3 . . • wxPython version 2 . . . These packages are available from the correspondingweb sites.
VIMAP itself, plus supplementary informa-tion material, is freely available on the Internet. In order to begin the analysis, the sizes (in pixels) andpixel scales (angular extension of a pixel) of the twomaps need to be made equal. Once this is achieved,the map obtained at frequency ν > ν needs to beconvolved with the restoring beam of the map obtainedat the frequency ν , or has to be reconstructed from its δ function CLEAN components using the beam of themap at ν . This is easily achieved using the standard AIPS and/or
Difmap data reduction packages. The pixelscale should be much smaller than the synthesized beamsize at ν ; we recommend a size of 1/20 (or less) of thebeam size. In general, AGN cores need to be excluded from im-age alignment calculations because their positions mayvary as function of frequency. In
VIMAP , users canplace an elliptical mask onto a core with variable (i)center position, (ii) semimajor/minor axis lengths, and(iii) orientation. Depending on how well the core canbe identified and separated from the outflows in a givenmap, it may be necessary to iterate the alignment sev-eral times with different choices of masks.
The relative shift between two images is estimated viaa two-dimensional cross-correlation. The definition of http://matplotlib.org − − − − − RA [mas] − − − D EC [ m a s ] − − − − − RA [mas] − − − D EC [ m a s ]
12 GHz − − − − − RA [mas] − − − D EC [ m a s ]
12 GHzCONV
Figure 1.
VLBI maps of the active galaxy 3C 120 at 8 and12 GHz. Contour levels decrease by factors of √ Top : 8-GHzmap. The peak intensity is 0.70 Jy / beam with the lowestcontour corresponding to 0.9% of the peak value. Center :12-GHz map. The peak intensity is 0.96 Jy / beam with thelowest contour level corresponding to 0.6% of the peak value. Bottom : Same as center panel, but using the restoring beamof the 8-GHz map. The peak intensity is then increased to1.09 Jy / beam. the correlation coefficient r xy implemented in VIMAP is r xy = P i,j ( I ν ,ij − I ν )( I ν ,ij − I ν ) rhP i,j ( I ν ,ij − I ν ) i hP i,j ( I ν ,ij − I ν ) i (1) (Croke & Gabuzda 2008) where I ν , ,ij is the intensityat frequency ν , and at spatial coordinate ( i, j ), I ν , is the mean intensity of a map at ν , . IMAP: Program Providing Radio Spectral Index Maps of AGN −30 −20 −10 0 10 20 shift in RA [Pixel] −20−1001020 s h i f t i n D E C [ P i x e l ] Result of 2D Correlation
Figure 2.
2D cross-correlation map; the color scales indicatesthe value of the correlation coefficient. Offsets are in unitsof pixels. The 12-GHz map is shifted relative to the 8-GHzmap. Black contours correspond to correlation values of 0.7,0.73, 0.76, 0.79, etc.
The output of the cross-correlation analysis is a 2Dmap displaying the correlation coefficient r xy as func-tion of relative offsets in right ascension (RA) and dec-lination (DEC). The spatial shift between the images isgiven by the location of the maximum value of r xy . Ifnecessary, VIMAP users can set offsets manually.
Eventually,
VIMAP generates a spectral index mapshowing the index α (as defined in the introduction)as function of position, as well as a spectral index errormap.The spectral index error map is based on the assump-tion that the uncertainty of the flux density in eachof the two radio maps used is a combination of (i) asystematic error coming from imperfect visibility am-plitude calibration and (ii) random thermal noise fromthe observed source, sky, and instruments. This impliesa total intensity error σ ν,ij , as function of frequency ν and image location ( i, j ), of σ ν,ij = δ ν I ν,ij + RM S ν,ij . (2)Here δ ν . . RM S ν,ij is the root-mean-squared thermal noise.
RM S ν,ij can be measured inempty regions of an image. The factor δ ν may be knowna priori for a given interferometer; if not, it can be esti-mated by measuring the flux from a compact flux cal-ibrator and cross-comparison to results found by otherobservatories. Eventually, the uncertainty of the spec-tral index α ij – i.e., the final spectral index error map Err ( α ν , ,ij ) – is found via standard error propagation: Err ( α ν , ,ij ) = 1log( ν /ν ) × " σ ν ,ij I ν ,ij + σ ν ,ij I ν ,ij / . (3) Table 1
Parameters of two VLBA data sets used for demonstration.Frequency Beam size a Noise b (GHz) (mas) (mJy/beam)8.4 1 . × .
92 2.112.1 1 . × .
64 1.7
Notes.
Target: 3C 120. Observing date: May 24, 2006. Bothmaps have a size of 1024 × Table 2
Shift of the 12-GHz map relative to the 8-GHz map.Shift in RA (pixels) -3Shift in DEC (pixels) 12D shift (mas) 0.158Maximum r xy When generating the final spectral index map,
VIMAP employs two cutoffs that exclude trivial or un-physical spectral index values: (i) a marginal intensityboundary, outside of which the source flux is assumedto be too weak for extracting spectral index informa-tion; and (ii) an upper limit on the error on α ij .
3. A
PPLICATION
In the following, we provide an analysis of a VLBI dataset with
VIMAP . We used two Very Long Baseline Ar-ray (VLBA) maps of the AGN 3C 120 obtained in 2006at 8.4 and 12.1 GHz, respectively. We obtained rawdata from the archive of the MOJAVE program (Lis-ter et al. 2009) and converted them into images usingthe modelfit task of Difmap . Observation details andintensity maps are provided in Table 1 and Figure 1,respectively.In each map, we covered the core (cf. Section 2.3)with an elliptical mask about three times the size of therestoring beam in order to ensure that optically thickregions do not affect the correlation. After this,
VIMAP calculated the normalized 2D cross-correlation for thetwo input maps (cf. Equation 1) and saved the resultant r xy array (Figure 2). The maximum correlation ( ≈ ≈ .
9% of the peak value of the 8-GHzmap and an upper limit on the spectral index error of0.5. Spectral index maps before and after image align-ment are shown in Figure 3; the impact of the offsetbetween the input maps is evident. Figure 4 providesthe spectral index error map (top panel) and the evolu-tion of the spectral index along a one-dimensional cutfollowing the jet (center and bottom panels). At leastthree features should be noted: (i) Up to 2 mas fromthe core ( ≈ beam size; first red star from the core inthe center panel of Figure 4), the α profile obtained Kim & Trippe − − − − − RA [mas] − − − D EC [ m a s ] Without Correction − . − . − . − . − . . . . . . . − − − − − RA [mas] − − − D EC [ m a s ] With Correction − . − . − . − . − . . . . . . . Figure 3.
Maps of spectral index α (color scale) of 3C 120before (top) and after (bottom) correcting for the offset be-tween the maps. The impact of the offset is evident. after image alignment rapidly decreases, whereas theprofile obtained without alignment is rather flat. (ii)About 3 mas from the core (second red star), the spec-tral index obtained without image alignment jumps upto ≈
1. Without image alignment, this feature mightbe incorrectly interpreted as an overdensity in the jet.(iii) About the same holds for the spectral index from7 mas to around 10 mas (third to fourth red star).
4. S
UMMARY
We report the development of a GUI-based interactivePython program,
VIMAP , for generating radio spectralindex maps of active galactic nuclei from VLBI radiomaps obtained at two different frequencies. For thecrucial task of accurate spatial alignment of the inputmaps we employ the 2D cross-correlation algorithm ofCroke & Gabuzda (2008). As yet, such a tool has notbeen available in the frame of standard radio interfer-ometric data processing packages like
AIPS or CASA .Our approach complements the method of image align-ment via cross-identification of jet model components(Kameno et al. 2003; Kadler et al. 2004). As noted ex-plicitly by Kadler et al. (2004) (in their Section 4), themodel component approach depends on a reliable cross-identification of optically thin jet components whichis not always possible.
VIMAP offers a higher degreeof flexibility because it does not rely on such cross- We note that Croke & Gabuzda (2008) presented a C softwareprogram dedicated to the same purpose. However, their pro-gram comes with additional
AIPS dependencies which make itunsuitable for interactive data processing. − − − − − RA [mas] − − − D EC [ m a s ] Error Distribution . . . . . . . . . . . − − − − − RA [mas] − − − D EC [ m a s ] Spectral Evolution − . − . − . − . − . . . . . . . Distance from Core [mas] − − S p e c t r a l I n d e x With CorrectionWithout Correction
Figure 4.
Top : Spectral index error map, assuming δ ν = 0 . Center :Same as the lower panel of Figure 3. The magenta lineindicates a 1D cut through the α map along which the evo-lution of the index is analyzed. Red stars on the magentaline indicate locations of notable features shown in the bot-tom panel. Bottom : 1D spectral index profile along the cutindicated in the center panel, before and after correcting forthe offset between the 8-GHz and 12-GHz maps. identifications and, in fact, does not even require mod-elling but may be applied to deconvolved (CLEANed)maps immediately. A detailed comparison of the twoapproaches is provided by Fromm et al. (2013) (theirSection 2.1).A key feature of
VIMAP is its interactive GUI-basedapproach depending only on few standard, freely avail-able, Python packages. Accordingly,
VIMAP providesusers with a new tool capable of handling large amountsof multi-frequency VLBI data in a straightforward man-
IMAP: Program Providing Radio Spectral Index Maps of AGN si-multaneous multi-frequency observations, and the KVNand VERA Array (KaVA) (Niinuma et al. 2014). A CKNOWLEDGMENTS
This work made use of data from the MOJAVE AGNmonitoring database (Lister et al. 2009) and of the
AIPS and
Difmap software packages provided by the NationalRadio Astronomical Observatory of the USA. We ac-knowledge financial support from the Korean NationalResearch Foundation (NRF) via Basic Research Grant2012-R1A1A2041387. R EFERENCES
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