VLA Observations of DG Tau's Radio Jet: A highly collimated thermal outflow
C. Lynch, R. L. Mutel, M. Güdel, T. Ray, S. L. Skinner, P. C. Schneider, K. G. Gayley
VVLA Observations of DG Tau’s Radio Jet: A highly collimated thermal outflow
C. Lynch , R. L. Mutel , M. G¨udel , T. Ray , S. L. Skinner , P. C. Schneider & K. G. Gayley Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52240, USA Department of Astrophysics, University of Vienna, Vienna, AT Dublin Institute for Advanced Studies, Astronomy and Astrophysics Section, 31 FitzwilliamPlace, Dublin 2, Ireland Center for Astrophysics and Space Astronomy, University of Colorado, Boulder, Colorado 80309,USA Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
ABSTRACT
The active young protostar DG Tau has an extended jet that has been well studiedat radio, optical, and X-ray wavelengths. We report sensitive new VLA full-polarizationobservations of the core and jet between 5 GHz and 8 GHz. Our high angular resolutionobservation at 8 GHz clearly shows an unpolarized inner jet with a size 42 AU (0.35 (cid:48)(cid:48) )extending along a position angle similar to the optical-X ray outer jet. Using ournearly coeval 2012 VLA observations, we find a spectral index α = +0 . ± .
05, whichcombined with the lack of polarization, is consistent with bremsstrahlung (free-free)emission, with no evidence for a non-thermal coronal component. By identifying theend of the radio jet as the optical depth unity surface, and calculating the resultingemission measure, we find our radio results are in agreement with previous optical linestudies of electron density and consequent mass-loss rate. We also detect a weak radioknot at 5 GHz located 7 (cid:48)(cid:48) from the base of the jet, coincident with the inner radioknot detected by Rodr´ıguez et al. (2012) in 2009 but at lower surface brightness. Weinterpret this as due to expansion of post-shock ionized gas in the three years betweenobservations.
1. Introduction
The evolution of a young stellar object (YSO) involves not only mass accretion, through acircumstellar molecular disk, but also the loss of angular momentum and mass flux through anarrowly collimated jet, thought to be launched close to the YSO. Magnetic fields are suspected ofplaying an important role in both the launching and collimation of these jets (Pudritz et al. 2012;Cai et al. 2008). However, the processes through which these fields act are not well understood(e.g. Carrasco-Gonzalez et al. 2010). a r X i v : . [ a s t r o - ph . S R ] F e b − . In addition, about10 have been discovered to have X-ray emission. These X-rays most likely trace the fastest shocksin the jets of YSOs. If the material in the YSO jet is heated to X-ray emitting temperatures byshocks, shock velocities around 500 km s − required (Schneider et al. 2011).A large number of the compact jets associated with YSOs have been detected at radio wave-lengths. The dominant radio emission mechanism is thought to be thermal bremsstrahlung fromthe shock-heated gas. However, evidence for non-thermal emission from several YSOs has also beendiscovered. Polarization has been associated with several YSOs, including objects in the ρ Ophiuchimolecular cloud (Andre et al. 1988; White et al. 1992; Andre et al. 1992), the Taurus-Auriga molec-ular cloud (Phillips et al. 1993; Skinner 1993; Feigelson et al. 1994; Ray et al. 1997), the R CoronaeAustralis region (Choi et al. 2008), the Orion region (Zapata et al. 2004), and HH 7-11 (Rodr´ıguezet al. 1999). Furthermore, a few YSOs have been associated with linearly polarized radio emission,these include HH 80-81 (Carrasco-Gonzalez et al. 2010), HD 283447 (Phillips et al. 1996), andthe Orion Streamers (Yusef-Zadeh et al. 1990). Additional characteristics of non-thermal emission,including strong variation in flux density on timescales of hours to days, a negative spectral index,and VLBI measurements of high brightness temperatures ( T B (cid:29) K), have also been found(Curiel et al. 1993; Hughes 1997; Andre et al. 1992; Wilner et al. 1999; Rodr´ıguez et al. 2005). Asuggested source of this non-thermal emission is the gyrosynchrotron mechanism (Andre 1996).Non-thermal emission is almost always associated with the more evolved weak-lined T Tauristars (WTTS). This is consistent with the idea that the non-thermal coronal emission is revealedonly after the optically thick mass outflows have evolved away (Eisl¨offel et al. 2000). However, thisidea may be too simple: Apparently non-thermal emission has recently been reported from severalless-evolved YSO’s that have infrared evidence for a disk (Osten & Wolk 2009).This paper focuses on DG Tau, a highly active CTTS driving a well studied energetic bipolarjet. Located in the Taurus Molecular Cloud (estimated distance 140 pc; Torres et al. (2009)), DGTau is of spectral type K5-M0, with a mass of 0.67 M (cid:12) , a luminosity of 1.7 L (cid:12) and an estimated ageof 3 × yr (Kitamura et al. 1996b; G¨udel et al. 2007). It was one of the first T Tauri stars to be 3 –associated with an optical jet (Mundt & Fried 1983) and has been studied extensively with adaptiveoptics, interferometry and the Hubble Space T elescope . The “micro-jet”, associated with the HH158 knot, extends out to 12”(e.g. Eisl¨offel & Mundt 1998) at a position angle of 223 ◦ (Lavalleyet al. 1997). Eisl¨offel & Mundt (1998) calculated the proper motion of 4 knots observed in theHH 158 jet located at distances between 2 . (cid:48)(cid:48) -10 . (cid:48)(cid:48) ( 350-1400 au), velocities around 150 km s − .Furthermore, Dougados et al. (2000) calculated the proper motions of knots located within 4 . (cid:48)(cid:48) from the source of the HH 158 jet; they determine velocities of ∼
200 km s − .The jet of DG Tau has an onion-like structure within 500 AU of the star, where faster,highly collimated gas is nested in wider slower material, with maximum bulk gas speeds reach-ing 500 km s − (Bacciotti et al. 2000; Lavalley-Fouquet et al. 2000). This velocity structure isexpected if the jet material is launched from a range of disk radii (Agra-Amboage et al. 2011).Moreover, for the slower jet material in the jet the velocity between the two sides of the jet isbetween 6-15 km s − ; this velocity shift may indicate that the jet is rotating (Bacciotti et al. 2002).Using [Fe II] observations and averaging over the central 1 . (cid:48)(cid:48) , the mass-loss rate from the highvelocity gas is determined to be (1.6 ± × − M (cid:12) yr − and from the medium velocity gas(1.7 ± × − M (cid:12) yr − , giving a total mass-loss rate for the velocity range of 50 to 300 km s − of (3.3 ± × − M (cid:12) yr − . However, this value is a lower limit to the mass-loss rate from theatomic component of the jet since the [Fe II] emission does not probe the whole range of velocitiesseen at optical wavelengths (Agra-Amboage et al. 2011). The mass-loss rate of DG Tau has alsobeen estimated using [OI] λ × − M (cid:12) yr − (Hartigan et al. 1995). The mostrecent estimate for the mass loss through the jet atomic component is Maurri et al. (2012), with˙ M = (1 . ± . × − M (cid:12) yr − . Near-infrared evidence for a counter-jet has been reported byPyo et al. (2003). The redshifted emission appears suddenly at -0 . (cid:48)(cid:48) which suggests that the innerpart of the counter-jet is hidden behind an optically thick circumstellar disk.DG Tau shows strong millimeter continuum emission thought to arise from a compact dustdisk around the star. Assuming a dust opacity coefficient κ ν =0.02-0.05 cm g − at 147 GHz, thespectrum is consistent with thermal emission from a disk having a radius of about 110 AU and amass 0.01-0.06 M (cid:12) (Kitamura et al. 1996b). At larger scales, CO observations have revealed agas disk with radius of 2800 au, oriented with its major axis perpendicular to the jet of DG Tau(Kitamura et al. 1996a).The X-ray jet of DG Tau was first discovered by G¨udel et al. (2005) using a
Chandra
ACIS-Sobservation, which showed very faint soft emission along the jet out to a distance of about 5 . (cid:48)(cid:48) tothe SW with position angle 225 ◦ . In addition, G¨udel et al. (2005) found that DG Tau reveals anew type of X-ray spectrum that includes two emission components with vastly different absorbingcolumn densities: A weakly attenuated soft spectral component associated with a plasma withelectron temperatures of no more than a few MK and a strongly absorbed hard spectral componentassociated with a hot plasma of several tens of MK.The soft X-ray component is thought to originateat the base of the jet where the first shocks form, while the hard component is attributed to emissionarising from a magnetospheric corona. Moreover, Schneider & Schmitt (2008) demonstrated that 4 –the soft and hard X-ray components have a separation of ∼ . (cid:48)(cid:48) and that the soft X-ray emissionis coincident with emission from optical lines indicating that this X-ray component is indeed fromthe jet.There are few previous radio observations of DG Tau. It was first detected in a VLA surveyof the Taurus-Auriga region at 5 GHz (Cohen et al. 1982). Further observations at 15 GHz and1.5 GHz (Cohen & Bieging 1986) found that the structure is elongated. Cohen & Bieging (1986)suggested that the radio structure and spectrum is consistent with free-free emission from ionizedgas in an outflowing jet. Rodr´ıguez et al. (2012) reported radio knots in the extended jet at0 . (cid:48)(cid:48) and 6 . (cid:48)(cid:48) respectively. They determine that these radio components were coincident withpreviously detected optical knots.In this paper we present the results of a Jansky Very Large Array (VLA) multi-frequencycampaign of DG Tau. The goals of these observations were to determine the morphology of theinner jet, search for possible non-thermal coronal radio emission, and investigate the nature of theradio knots at large distance from the star.
2. VLA Observations
The radio campaign comprised three observing epochs between June 2011 and April 2012.The June 18, 2011 observation used two 128 MHz bands centered on 8.33 GHz and 8.46 GHz inA configuration. In 2012 we conducted two C-array observations using the newly-available 2 GHzbandwidth capability of the VLA. The March 22, 2012 observation spanned the frequency rangeof 4.5 GHz to 6.5 GHz, while the April 15, 2012 observation spanned 7.9 GHz to 9.9 GHz. Thedetails of these observations are listed in Table 1.For all three observations both the receiver bandpass correction and the absolute flux density The VLA is operated by the National Radio Astronomy Observatory, which is a facility of the National ScienceFoundation operated under cooperative agreement by Associated Universities, Inc.
Table 1. VLA ResultsEpoch Array Freq BW Time Total flux Peak flux Sky RMS Θ
F W HM (GHz) (GHz) (min) (mJy) (mJy/beam) ( µ Jy) (arcsec)2000.83 A 43.3 0.1 240 3.9 0.6 100 0.05 × × × ×
3. Results3.1. Imaging the DG Tau Jet
After flagging bad visibilities and applying the normal amplitude and phase calibration, cleanmaps in total intensity (Stokes I , see Figure 1), circularly polarized intensity (Stokes V ) and linearpolarized intensity were produced using the standard CASA data calibration procedures. The peakand integrated flux density of both the total and polarized intensity was obtained using the CASAtask IMFIT (see Table 1). We did not detect either circular or linear polarization, with upperlimits 0.03 mJy beam − (3%) for circular and 0.02 mJy beam − (2%) for linear polarization. Boththe rising spectral index and lack of polarization suggest that any non-thermal coronal componentis absent or very weak.The A-array 8 GHz total intensity contour map at epoch 2011.46 is shown in Figure 1. Inthis high-angular resolution image, the emission extends approximately 0.35 (cid:48)(cid:48) SW in approximatelysame direction as the optical jet. Both the asymmetry and elongation of the emission suggestthat the source is the collimated jet mapped by optical observations (Bacciotti et al. 2000; Agra-Amboage et al. 2011) which have resolved the inner jet to within 0 . (cid:48)(cid:48) of the central source anddetermined that collimation must occur within this region.The 2012 observations were taken in C-array, with much lower angular resolution but highersensitivity to larger, low-surface brightness components. Contour maps of the 5 GHz (epoch2012.22) and 8 GHz (epoch 2012.29) observations are shown in Figure 2. The location of thecentral source for the 2012.22 (5.5 GHz) observation is coincident with the 2012.29 (8.5 GHz) cen-tral source within the centroid uncertainty ( ± . (cid:48)(cid:48) ). Note that the integrated flux density at8 GHz apparently increased 17% from epoch 2011.46 to 2012.29, but it is possible that the increaseresults from faint extended structure over-resolved by the smaller beam at epoch 2011.46 (cf. Table1). The 5.5 GHz map shows a component (labeled A) extending ∼ (cid:48)(cid:48) SW whose centroid is coin-cident with a much weaker feature seen in the 8.5 GHz map. This component is nearly coincidentwith the knot component reported by Rodr´ıguez et al. (2012) but at a much lower flux density; wediscuss this in more detail in section 4.3. 6 –Fig. 1.—: VLA 8 GHz naturally-weighted contour map of DG Tau’s inner jet at epoch 2011.46.The contours are -3, 3, 6, 10, 15, 20, 25, 30, 35, and 40 × µ Jy beam − , the RMS noise level ofthe image. The restoring beam is shown in the bottom left corner with dimensions given in Table 1.There is also a more distant feature in the 5 GHz map (labeled C) with a flux density S ∼ µ Jy about 14 (cid:48)(cid:48) from the stellar position, but well-displaced from the jet axis. This feature is alsoweakly seen in the Rodriguez et al. map, and is certainly real. We do not know if it is associatedwith the DG Tau jet, although it is unlikely that an unrelated background source this strong wouldbe located this close to the jet. We speculate that the feature may be a part of an extended bow 7 – (a)
A C AC (b) Fig. 2.—: VLA contour maps of DG Tau during the two spring 2012 observations. The 8.5 GHzmap at epoch 2012.29 is shown on the right, while the 4.5-6.5 GHz emission (epoch 2012.22) map ison the left. Both maps were made used natural weighting with contour levels -3, 3, 4, 6, 8, 10, 12,15, 20, 40, and 60 × µ Jy beam − , the RMS values of the respective maps. The restoringbeam for each map is given in the bottom left corner with the dimensions given in Table 1. Thecross indicates the location of knot A detected byRodr´ıguez et al. (2012) in 2009 radio observations.Feature C, located ∼ . (cid:48)(cid:48) SW of the inner centriod, is visible in both 2012 maps and on the 2009map of Rodr´ıguez et al. (2012), but is displaced from the optical jet.shock associated with the optical knot seen near 13 (cid:48)(cid:48) (Rodr´ıguez et al. 2012), but do not discuss itfurther in this paper.
Figure 3 shows a radio spectrum of DG Tau using our VLA data, previously published radiodata (Cohen et al. 1982; Cohen & Bieging 1986; Rodr´ıguez et al. 2012), and an archival VLAobservation of DG Tau at 43 GHz (project code AW545, PI David Wilner) that we calibratedand mapped. The spectrum monotonically increases over the frequency range of 4.5 to 43 GHz.However, it is clear from the multiple observations at 8.5 GHz and 4.5 GHz that the flux densityis significantly variable over a period of years. Therefore we use only our nearly coeval 2012observations to fit a power-law to the spectrum, giving a spectral index α = 0.46 ± α = 0 . ± . . (cid:48)(cid:48) from the central source. The points are derived values of electrondensity and velocity from (Maurri et al. 2012).
4. Discussion4.1. Comparison between radio and optically-derived electron densities
Free-free emission depends only on the plasma temperature, the observing frequency, and thelinear emission measure i.e., the square of the electron density integrated along the line of sightto the observer. If the plasma temperature is known (e.g., from optical line observations), andthe optical depth at a given location can be estimated (e.g., from source structure), the emissionmeasure at that location can be estimated. The entire detected radio jet is the optically thicksurface. We therefore identify the outermost detectable region of the radio jet with the unityoptical depth surface ( τ = 1). We then can calculate the emission measure and compare withestimates of electron density and jet width at this location based on optical line ratios.Inspection of Figure 1 shows that the radio emission becomes undetectable ∼ . (cid:48)(cid:48) (50 AUprojected) from the base of the jet. Assuming a thermal jet, this should correspond to the τ = 1surface, meaning inside ∼ . (cid:48)(cid:48) the jet is fully optically thick while outside this distance the jetis optically thin. The temperature of the jet gas is not well-constrained, but if the jet is launchedvia a quasi-steady centrifugal MHD disk wind, as suggested by the transverse velocity gradients(Bacciotti et al. 2002), the gas temperature should be not much higher than the photospherictemperature (4800 K). However, the innermost, high-velocity core is likely shock-heated and mayhave a temperature near 8000 K, typical to other stellar jets. The lower-speed, broader flowassociated with warm molecular emission is cooler, with a temperature of 2000 K, determined frominfrared line ratios (Takami et al. 2004). In the following we assume a mean temperature acrossthe flow T = 5000 K. 10 –The free-free optical depth can be written τ ( ν, T, EM ) = 1 . (cid:16) ν GHz (cid:17) − . (cid:18) T K (cid:19) − . (cid:18) EM10 cm − (cid:19) (1)Assuming τ = 1 at ν = 8.5 GHz, the emission measure at 0.35 (cid:48)(cid:48) is EM ≡ (cid:90) n e ds = 3 . × cm − (2)High angular resolution observations of optical line ratios have be used to determine boththe electron density and jet width as a function of velocity bin along the jet (e.g., Coffey et al.2008; Maurri et al. 2012). By combining these measurements, we can estimate the axial electrondensity profile. Figure 4(a) shows a simple Gaussian fit to the electron density as a function of axialdistance, where the points represent the mean density in each velocity bin and the uncertainties arethe FWHM width uncertainty in each bin, using data from Maurri et al. (2012). We have combinedthese measurements to fit a simple analytic function to the electron density as a function of jetaxial distance ρ , n e ( ρ ) = n e − (cid:16) ρρe (cid:17) (3)where n = 2 . × cm − and ρ e = 5.5 au. Integrating this density profile, we find a linearemission measure EM = 3 . × cm − , in excellent agreement with the radio data. We next use the axial electron density derived in the previous subsection to estimate themass-loss rate of the ionized component of the jet outflow at τ = 1 (50 AU projected distance).Figure 4(b) shows a Gaussian fit to the FWHM widths of the velocity bins given in Maurri et al.(2012), V ( ρ ) = V e − (cid:16) ρρv (cid:17) (4)where V = 400 km s − , and ρ v = 12 au. Using this velocity profile, along with the density profiledetermined in the previous sub-section, we determine the mass-flux of the ionized gas at 50 AUprojected distance, ˙ M = 2 π m i (cid:90) ∞ V ( ρ ) n e ( ρ ) ρ dρ. (5)where m i ∼ . m p is the average ion mass. Using the approximate analytic models shown inFigure 4 for n e ( ρ ) and V ( ρ ), we find mass flux ˙ M ∼ × − M (cid:12) yr − , with more than half ofthe mass flux in the high-velocity component within 5 AU of the jet center. Since the high-velocitycomponent is almost completely ionized (Maurri et al. 2012), this mass-loss estimate should be lessthan a factor of two smaller than the mass-loss of both the ionized and neutral gas. 11 –Recent mass loss estimates of the DG Tau jet include that of Agra-Amboage et al. (2011),˙ M = (3 . ± . × − M (cid:12) yr − and Maurri et al. (2012), ˙ M = (1 . ± . × − M (cid:12) yr − .While these are both somewhat lower than the present model prediction, the differences are probablynot significant given the poorly-constrained functional forms used for the axial density and velocityprofiles. Radio observations of DG Tau at epoch 2009.6 (Rodr´ıguez et al. 2012) show a radio knotlocated approximately 7 (cid:48)(cid:48) along the jet with an integrated flux density 150 µ Jy, coincident with anoptical [S II] knot. There is also a much weaker feature near 12 (cid:48)(cid:48) , also coincident with an opticalknot. If these radio structures are associated with shock-compressed gas in the jet flow, we wouldexpect them to evolve both in flux and position on the dynamical timescale of the shock and theexpanding post-shock gas.Our observations confirm the existence of the inner knot. Figure 5 shows 5.4 GHz and 8.5 GHzimages of DG Tau at epochs 2012.22 and 2012.29 respectively. At each frequency we show mapsmade with two different uv-plane density weighting functions: uniform weighting to maximizeangular resolution (panels c, d), and natural (a.k.a. unity) weighting to maximize sensitivity tolow-brightness features (panels a, b). The locations of the 7 (cid:48)(cid:48) knot (labeled A) and 12 (cid:48)(cid:48) knot (labeledB) detected by Rodr´ıguez et al. (2012) are indicated by crosses. Both the 8.5 and 5.4 GHz naturalweighted maps show radio emission coincident with knot A but not with knot B. We did not detecteither knot A or B in our epoch 2011.46 A-array observation, probably because the knots wereover-resolved, as discussed below.
The DG Tau jet optical knots move outward with sky-plane proper motions ∼ . (cid:48)(cid:48) per year( V ∼
200 km/s), at least within 10 arcsec of the stellar position (Eisl¨offel & Mundt 1998; Dougadoset al. 2000). Rodr´ıguez et al. (2012) found radio knots that are approximately cospatial withthe optical knots, and also move with this speed, suggesting that the radio and optical knots aretwo manifestations of the same traveling shocks. Here we examine whether our more recent knotobservations are consistent with this hypothesis. We consider only the motion of knot A, since wedid not detect knot B at any epoch. Note that all positions discussed below are angular separationsfrom the stellar position in the sky plane. 12 –
A BC (a)
A BC (c) (b)
A BC (d)
A BC
Fig. 5.—: DG Tau contour maps at 8 GHz (a, c) and 5 GHz (b, d) at epochs 2012.29 and 2012.22respectively. The two maps in the first column of this figure, (a) & (b), are made using naturalweighting. The contour levels are -3, 3, 4, 6, 10, 20, 40, 60, 80, 100, 120, and 140 times the RMSin each map; the RMS and beam dimensions are given in Table (1). The second column maps,(c) & (d), are made using uniform weighting in order to maximize angular resolution of the maps.The contour levels are -3, 3, 6, 10, 20, 40, and 60 times the RMS in each map. The RMS for (c)is 15 µ Jy with beam dimensions 1 . (cid:48)(cid:48) × . (cid:48)(cid:48) ; (d) has a RMS of 13 µ Jy and beam dimensions of2 . (cid:48)(cid:48) × . (cid:48)(cid:48) . The crosses in each of these maps indicate the locations of the two knots detected byRodr´ıguez et al. (2012). 13 –Fig. 6.—: Projected knot location along jet vs. epoch (solid line) with observed centroid locationsat epochs 2009.63 and 2012.22 14 –Using the Rodr´ıguez et al. (2012) calculated speed V = 198 km s − and their 2009.62 positionfor knot A, the expected position at epochs 2011.22 and 2011.29 is 7 . (cid:48)(cid:48) . We fit single-componentGAUssian models to knot A in the 5.5 GHz image. At 5.5 GHz, knot A has a centroid position7 . (cid:48)(cid:48) ± . (cid:48)(cid:48) , while at 8.5 GHz it is 7 . (cid:48)(cid:48) ± . (cid:48)(cid:48) (Figure 6). Both positions agree with the predictedproper motion, but the fractional uncertainty is large, 37% in the higher resolution 8.5 GHz image.The optical position of knot A has recently been determined from HST STIS observations atepoch 2011.13 (Schneider et al. 2012, in preparation). Fitting a Gaussian to the spatial profile ofthe [S II] 6731˚ A line within v = -265 ±
65 km/s results in a distance 7 . (cid:48)(cid:48) ± . (cid:48)(cid:48) , compared with apredicted position 7 . (cid:48)(cid:48) using the Rodr´ıguez et al. (2012) proper motion. The measured position isonly slightly offset from the predicted position, and could indicate that the peak radio and opticalintensities occur along different lines of sight in the shocked emission region. This is plausible,since the radio and optical line emergent intensities have different dependencies on the density andtemperature of the gas. In addition to moving with the predicted proper motion, the flux density of knot A decreaseddramatically. In order to avoid differences associated with spectral index and angular resolution,we can compare the epoch 2009.63 measurement of Rodr´ıguez et al. (2012) with our 2012.29 ob-servation, both of which were at 8.5 GHz and had the same angular resolution (VLA at C-array).The epoch 2009.63 integrated flux was (150 ± µ Jy while the 2012.29 integrated flux was(46 ± µ Jy, both measured using naturally-weighted maps. This is a 70% decrease in 2.7 years,and is certainly real given the matched frequency and angular resolutions of the two observations.This behavior is not unprecedented: Radio knots in several other YSO jets have been observed todecrease with time and become undetectable within years of their initial ejection (e.g. Mart´ı et al.1998). The total flux density at 5.5 GHz (epoch 2012.22) was (73 ± µ Jy. This implies aspectral index − . ± .
4, consistent with optically thin thermal emission, but highly uncertainbecause of the large uncertainty in each measurement, and the differing angular resolutions.Rodr´ıguez et al. (2012) proposed a model consisting of periodic generation of shocks movingoutward at at projected speed 200 km s − in a conical outflow. The model predicts a periodicvariation of knot flux density caused by corresponding periodic velocity variations in a bipolaroutflow. Fig. 8 of Rodr´ıguez et al. (2012) predicts a flux for knot A near that observed at epoch2012.29, but occurring 1.5 years after the flux level observed at epoch 2009.63 rather than 2.7years. However, since their model is parameterized by several geometrical parameters which arenot well-constrained, a detailed comparison is not appropriate with only a single additional fluxmeasurement. Instead, guided by Occam’s razor, we interpret the flux decrease using a much simplerconceptual model of an expanding volume of post-shock gas characterized by a single variable, theelectron density. 15 –Fig. 7.—: (a) DG Tau knot A flux density vs. epoch calculated using optically thin expandingsphere model (see text), with observed values at epochs 2009.63 (Rodr´ıguez et al. 2012) and 2012.22(this paper). (b) Model electron density vs. projected axial distance (arc sec) at epochs 2009.63(solid line) and 2012.22 (dashed line). (c) Model surface brightness vs. epoch (solid line) withobserved values ( • ) and upper limits ( × ). (d) Optical depth at 5 GHz (solid line) and 8 GHz(dashed line) vs. epoch, confirming the optically-thin model assumption. 16 –We model the knot as an optically-thin, free-free emitting isotropic sphere whose density scalesexponentially with radial distance ρ , n e ( ρ ) = Nρ F √ π exp (cid:34) − ln (2) (cid:18) ρρ F (cid:19) (cid:35) , (6)where 2 ρ F is the full width at half maximum scale, and the normalization ensures that the integrateddensity is a constant N , i.e., the total number of electrons does not change as the sphere expands.We also assume the knot is isothermal, a simplistic but reasonable assumption since for optically-thin emission, the flux density dependence on temperature is much smaller than for density ( S ∝ T − . n e ). We assume T = 10 K, based on optical line ratio observations (Agra-Amboage et al.2011). The sphere is assumed to expand linearly with time, ρ ( t ) = ρ + ˙ ρ ( t − t ).The flux and size of the sphere were calculated as a function of time and compared withobservations. We solved for best-fit model parameters N = 4 . × , ρ = 336 AU(2 . (cid:48)(cid:48) at d= 140 pc), and ˙ ρ = 21 AU yr − (0.15 (cid:48)(cid:48) yr − ). Figure 7 shows the flux density, electron densityprofile, surface brightness, and optical depth as a function of epoch for the fitted model, along withobserved values and upper limits. The agreement is well within the measurement uncertainty ofthe radio knot at all epochs, and has τ (cid:28)
1, as expected.Maurri et al. (2012) measure electron densities n e ∼ cm − along the jet at a projecteddistance near 4-5 (cid:48)(cid:48) . For a conical flow with constant ionization fraction, the density scales as r − ,so we expect n e ∼
500 cm − outside the radio knot at a projected distance of 7 (cid:48)(cid:48) . According to themodel, the maximum knot density varied from 2000 to 1000 cm − from epochs 2009.6 – 2012.2,implying a density enhancement factor of 4 in 2009.6, decreasing to 2 in 2012.2. Assuming thatthe present expansion continues, the model predicts that the density contrast will vanish and thatthe knot will disappear within a few years.
5. Summary
We report multi-epoch VLA observations of the pre-main sequence star DG Tau’s radio jet.The radio spectrum ( α = 0 . ± (cid:48)(cid:48) (50 AU projected distance) is the τ = 1 surface, we calculate the column emissionmeasure. Assuming an ’onion skin’ ionization model and azimuthal symmetry, we find that themean electron density in the centre of the jet is ¯n = 2.5 × cm − . This agrees well with opticalestimates at this location (Maurri et al. 2012). We model the electron density and velocity axialprofiles to calculate the mass loss of the ionized component, ˙ M ion ∼ × − M (cid:12) yr − , withmore than half of the mass flux in the high-velocity component within 5 AU of the jet center.This mass loss is comparable to the total mass loss calculated using optical line observations (e.g.,Agra-Amboage et al. 2011; Maurri et al. 2012), indicating that most of the mass loss in the jet atthis location is in the ionized component. 17 –We confirm the existence of a radio knot near 7 (cid:48)(cid:48) recently reported by Rodr´ıguez et al. (2012).The knot proper motion is consistent with a projected speed V = 200 km s − , as suggested byRodr´ıguez et al. (2012) and previous optical estimates. The flux density of the knot dramaticallydecreased between 2009.6 and 2012.2. We present a simple model for radio emission from theknot consisting of an optically-thin ionized sphere which expands linearly with time. The modelpredicts that the FWHM size of the radio knot increases from 340 AU (2.4 (cid:48)(cid:48) ) to 390 AU (2.75 (cid:48)(cid:48) )from 2009.6 to 2012.2, while the central electron density decreases from 2000 to 1000 cm − . Theresulting radio flux decreases from 150 µ Jy to 50 µ Jy, in agreement with observations. By scalingfrom previously published density measurements at closer distances along the jet, we find that thedensity enhancement factor of the knot decreased from 4 in 2009.6 to 2 in 2012.2, and that theknot will disappear completely within a few years.
REFERENCES
Agra-Amboage, V., Dougados, C., Cabrit, S., & Reunanen, J. 2011, A&A, 532, A59Andre, P. 1996, ASP Conference Series, 93, 273Andre, P., Deeney, B. D., Phillips, R. B., & Lestrade, J.-F. 1992, ApJ, 401, 667Andre, P., Montmerle, T., Feigelson, E. D., Stine, P. C., & Klein, K. 1988, ApJ, 335, 940Bacciotti, F., Eisl¨offel, J., & Ray, T. P. 1999, A&A, 350, 917Bacciotti, F., Mundt, R., Ray, T. P., Eisl¨offel, J., Solf, J., & Camezind, M. 2000, ApJ, 537, L49Bacciotti, F., Ray, T. P., Mundt, R., Eisl¨offel, J., & Solf, J. 2002, ApJ, 576, 222Bacciotti, F., Ray, T. P., Mundt, R., Eisl¨offel, J., & Solf, J. 2002, ApJ, 576, 222Cai, M. J., Shang, H., Lin, H.-H., & Shu, F. H. 2008, ApJ, 672, 489Carrasco-Gonzalez, C., Rodriguez, L. F., Anglada, G., Marti, J., Torrelles, J. M., & Osorio, M.2010, Science, 330, 1209Choi, M., Hamaguchi, K., Lee, J.-E., & Tatematsu, K. 2008, ApJ, 687, 406Coffey, D., Bacciotti, F., & Podio, L. 2008, ApJ, 689, 1112Cohen, M., & Bieging, J. 1986, AJ, 92, 1396Cohen, M., Bieging, J. H., & Schwartz, P. R. 1982, ApJ, 253, 707Curiel, S., Rodriguez, L. F., Moran, J. M., & Canto, J. 1993, ApJ, 415, 191Dougados, C., Cabrit, S., Lavalley, C., & M´enard, F. 2000, A&A, 357, L61 18 –Eisl¨offel, J., & Mundt, R. 1998, AJ, 115, 1554Eisl¨offel, J., Mundt, R., Ray, T. P., & Rodriguez, L. F. 2000, Protostars and Planets IV, 815Feigelson, E. D., Welty, A. D., Imhoff, C. L., Hall, J. C., Etzel, P. B., & Phillips, R. B.and Londsdale,C. J. 1994, ApJ, 432, 373G¨udel, M., Skinner, S. L., Briggs, K. R., Audard, M., Arzner, K., & Telleschi, A. 2005, ApJ, 626,L53G¨udel, M., Telleschi, A., Audard, M., Skinner, S. L., Briggs, K. R., Palla, F., & Dougados, C. 2007,A&A, 468, 515Hartigan, P., Edwards, S., & Ghandour, L. 1995, The Astrophysical Journal, 452, 736Hughes, V. A. 1997, ApJ, 481, 857Kitamura, Y., Kawabe, R., & Saito, M. 1996a, ApJ, 457, 277—. 1996b, ApJ, 465, L137Lavalley, C., Cabrit, S., Dougados, C., Ferruit, P., & Bacon, R. 1997, A&A, 327, 671Lavalley-Fouquet, C., Cabrit, S., & Dougados, C. 2000, A&A, 356, L41Mart´ı, J., Rodr´ıguez, L. F., & Reipurth, B. 1998, ApJ, 502, 337Maurri, L., Bacciotti, F., Podio, L., Eisoffel, J., Ray, T., Mundt, R., Locatelli, U., & Coffey, D.2012, Astron. Astrophys., submittedMcGroarty, F., & Ray, T. P. 2004, A&A, 420, 975McGroarty, F., Ray, T. P., & Froebrich, D. 2007, A&A, 467, 1197Mundt, R., & Fried, J. W. 1983, ApJ, 274, L83Osten, R. A., & Wolk, S. J. 2009, ApJ, 691, 1128Phillips, R. B., Lonsdale, C. J., & Feigelson, E. D. 1993, ApJ, 403, L43Phillips, R. B., Lonsdale, C. J., Feigelson, E. D., & Deeney, B. D. 1996, AJ, 111, 918Pudritz, R. E., Hardcastle, M. J., & Gabuzda, D. C. 2012, Space Sci. Rev., 169, 27Pyo, T.-S., Kobayashi, N., Hayashi, M., Terada, H., Goto, M., Takami, H., Takato, N., Gaessler,W., Usuda, T., Yamashita, T., Tokunaga, A. T., Hayano, Y., Kamata, Y., Iye, M., &Minowa, Y. 2003, ApJ, 590, 340Ray, T. P., Muxlow, T. W. B., Axon, D. J., Brown, A., Corcoran, D., Dyson, J., & Mundt, R.1997, Nature, 385, 415 19 –Reynolds, S. P. 1986, ApJ, 304, 713Rodr´ıguez, L. F., Anglada, G., & Curiel, S. 1999, ApJ, 125, 427Rodr´ıguez, L. F., Garay, G., Brooks, K. J., & Mardones, D. 2005, ApJ, 629, 953Rodr´ıguez, L. F., Gonz´alez, R. F., Raga, A. C., Cant´o, J., Riera, A., Loinard, L., Dzib, S. A., &Zapata, L. A. 2012, A&A, 537, A123Schneider, P. C., G¨unther, H. M., & Schmitt, J. H. M. M. 2011, A&A, 530, A123Schneider, P. C., & Schmitt, J. H. M. M. 2008, A&A, 488, L13Skinner, S. L. 1993, ApJ, 408Takami, M., Chrysostomou, A., Ray, T. P., Davis, C., Dent, W. R. F., Bailey, J., Tamura, M., &Terada, H. 2004, A&A, 416, 213Torres, R. M., Loinard, L., Mioduszewski, A. J., & Rodr´ıguez, L. F. 2009, ApJ, 698, 242White, S. M., Pallavicini, R., & Kundu, M. R. 1992, A&A, 259, 149Wilner, D. J., Reid, M. J., & Menten, K. M. 1999, ApJ, 513, 775Yusef-Zadeh, F., Cornwell, T. J., Reipurth, B., & Roth, M. 1990, ApJ, 348, L61Zapata, L. A., Rodriguez, L. F., & Kurtz, S. E. 2004, ApJ, 127, 2252