VLBI Observations of SN 2009bb
M. F. Bietenholz, A. M. Soderberg, N. Bartel, S. P. Ellingsen, S. Horiuchi, C. J. Phillips, A. K. Tzioumis, M. H. Wieringa, N. N. Chugai
aa r X i v : . [ a s t r o - ph . H E ] S e p Draft version October 15, 2018
Preprint typeset using L A TEX style emulateapj v. 11/10/09
VLBI OBSERVATIONS OF THE TYPE I B/C SUPERNOVA 2009bb
M. F. Bietenholz , A. M. Soderberg , N. Bartel , S. P. Ellingsen , S. Horiuchi , C. J. Phillips , A. K.Tzioumis , M. H. Wieringa and N. N. Chugai Draft version October 15, 2018
ABSTRACTWe report on VLBI, as well as VLA radio observations of the Type Ib/c supernova 2009bb. Thehigh radio luminosity of this supernova seems to require relativistic outflow, implying that the earlyradio emission was “engine-driven”, that is driven by collimated outflow from a compact object, eventhough no gamma-ray emission was seen. The radio light curve shows a general decline, with a “bump”near t = 52 d, seen most prominently at 5 GHz. The lightcurve bump could be either engine-driven,or it might represent the turn-on of the normal radio emission from a supernova, driven by interactionwith the CSM rather than by the engine. We undertook VLBI observations to resolve SN 2009bb’srelativistic outflow. Our observations constrain the angular outer radius at an age of 85 d to be < .
64 mas, corresponding to < × cm and an average apparent expansion speed of < . c .This result is consistent with the moderately relativistic ejecta speeds implied by the radio luminosityand spectrum. Subject headings: supernovae: individual (SN2009bb) — radio continuum: general — gamma rays:bursts INTRODUCTION
Supernova SN 2009bb was discovered by theChilean Automatic Supernova Search Program (CHASE;Pignata et al. 2009b,a) on 2009 March 29.9 UT, in thenearby spiral galaxy NGC 3278. The radial velocity ofNGC 3278 is 2964 km s − (Paturel et al. 2003), and inwhat follows we will use a round distance of 40 Mpc forthe galaxy and the supernova. SN 2009bb is in a re-gion of high star-formation, approximately 4.2 kpc fromthe center of the galaxy in projection (Levesque et al.2010). Stritzinger et al. (2009) obtained an optical spec-trum which showed no evidence for hydrogen, and thusSN 2009bb was classified as type I b/c. The shock break-out date is well constrained to be March 19 ± VeryLarge Array (VLA) on April 5.2 UT, at time aftershock breakout, t of 17 d. The 8.5-GHz flux den-sity was 24 . ± . ∼ × erg s − Hz − , which is larger than that ob-served for any other SN I b/c at a similar time af- Hartebeesthoek Radio Observatory, PO Box 443, Krugers-dorp, 1740, South Africa Dept. of Physics and Astronomy, York University, Toronto,M3J 1P3, Ontario, Canada Harvard-Smithsonian Center for Astrophysics, Theory Divi-sion, 60 Garden Street, Cambridge, MA 02138, US Hubble Fellow School of Mathematics and Physics, University of Tasmania,Hobart, Tasmania, Australia Canberra Deep Space Communication Complex, P.O. Box1035, Tuggeranong, ACT 2901, Australia Australia Telescope National Facility, Epping NSW, Aus-tralia Institute of Astronomy, RAS, Pyatnitskaya 48, Moscow119017, Russia The National Radio Astronomy Observatory is a facility ofthe National Science Foundation operated under cooperative agree-ment by Associated Universities, Inc. We use t to refer to time in the observer frame. ter shock breakout (see Soderberg et al. 2010b, 2006b;Berger et al. 2003). Subsequent VLA observations con-firmed the initially high flux density and showed a power-law decay, with the flux density at 8.5 GHz, S . ∝ t − . (Soderberg et al. 2010b). Similar decay rates areseen for other Type I b/c SNe, but also for the near-est gamma-ray burst, GRB 980425. These radio obser-vations gave a position for SN 2009bb of 10 h m . s − ◦ ′ . ′′ ′′ in eachcoordinate. We give this position, and all others in thispaper using J2000 coordinates.Radio emission in a supernova is generated by theshocks formed as the ejecta interact with the circumstel-lar material (CSM). Radio emission therefore traces thefastest ejecta, unlike the optical emission, which tracesthe massive but more slowly-moving bulk of the ejecta.Strong radio emission consequently is a sign of particu-larly strong interaction with the CSM, which can be dueeither to a particularly dense CSM, such as is seen forthe radio-luminous Type II SNe, or to particularly strongshocks which are caused by relativistic ejecta, whetherthose latter are collimated or not.Type I b/c SNe like SN 2009bb are of special inter-est because GRBs have been shown to be associatedwith them (e.g., Galama et al. 1998; Stanek et al. 2003;Malesani et al. 2004; Pian et al. 2006; Cobb et al. 2010;Starling et al. 2010). While the optical luminosities ofType I b/c SNe and those associated with GRBs over-lap, the GRBs are distinguished by having powerful non-thermal “afterglow” emission. In the radio, the after-glow typically peaks a few days after the explosion, andGRB radio luminosities are observed to be up to a mil-lion times higher than those of ordinary Type I b/cSNe (Soderberg et al. 2006a). This bright emission isthe observational manifestation of the substantial en-ergy coupled to relativistic velocities in GRBs. How-ever, GRBs are rare events, and Soderberg et al. (2006b)showed that less than 3% of all Type I b/c SNe have sim- Bietenholz et alilarly relativistic outflows. The presence of relativisticejecta, therefore, makes a supernova of particular inter-est. The physical mechanism that distinguishes ordinaryType I b/c SNe from GRB-SNe remains unknown anddetailed studies of relativistic Type I b/c SNe are there-fore required to make progress.In particular, Soderberg et al. (2010b) showed thatSN 2009bb’s high radio luminosity requires a substan-tial relativistic outflow powered by a “central engine”, inother words a black hole or a neutron star surroundedby an accretion disk which produces collimated outflow.The radio spectrum as measured at the VLA and theGiant Meterwave Radio Telescope (GMRT) is well fitby a synchrotron self-absorption (SSA) spectrum. Thehigh luminosity and relatively low turnover frequencyof ∼ t = 20 d then imply a blastwave radiusof 4 . × cm (Soderberg et al. 2010b) and therefore amean apparent expansion speed of 0 . ± . c , assum-ing equipartition of energy between electrons and mag-netic fields. Note that these are minimum values for thesize and expansion velocity, since both deviations fromequipartition, and the presense of free-free absorption(FFA) in addition to SSA would result in larger values.No gamma-ray counterpart was detected, but an off-axisviewing angle or a low fluence burst cannot be excluded.SN 2009bb differs from GRBs in that it occurred in ahigh-metallicity environment (Levesque et al. 2010).For relatively nearby SNe, a direct measurement ofthe size of the shockwave is possible with very-long-baseline interferometry (VLBI) observations. Such ameasurement provides a model-independent way of mea-suring the expansion speed and therefore determiningthe presence or absence of relativistic ejecta, and pos-sibly also determining the emission geometry and test-ing the assumption of equipartition. Unfortunately, SNewhich are both sufficiently nearby and radio-bright toallow VLBI imaging are rare events. Relativistic ex-pansion was clearly detected using VLBI in the caseof GRB 030329 (Taylor et al. 2004). In the case ofSNe not associated with GRBs, however, the VLBIobservations so far have confirmed the rarity of rela-tivistic ejecta: VLBI observations of two Type I b/cSNe which were suspected of having relativistic ejecta,SN 2008D and SN 2001em, showed only subluminalexpansion (Bietenholz et al. 2009; Paragi et al. 2008;Schinzel et al. 2009; Bietenholz & Bartel 2007, 2005;Paragi et al. 2005). In the case of SN 2007gr, relativis-tic expansion was claimed by Paragi et al. (2010), butSoderberg et al. (2010a) showed that a more conservativeinterpretation of a normal, non-relativistic supernova canalso be reconciled with the VLBI measurements, and pro-vides a more natural explanation of the relatively low ra-dio and X-ray luminosity. Optical and infra-red spectraalso suggest a modest ejected mass and explosion energy(Mazzali et al. 2010), whereas relativistic ejecta are usu-ally accompanied by large ejected masses and explosionenergies. OBSERVATIONS
We obtained both VLA total-flux-density and VLBIimaging observations of SN 2009bb. The VLA observa-tions were obtained in two ways. Firstly, by using theVLA as a standalone interferometer in parallel with theuse of the phased VLA as part of our VLBI array on 2009 June 10 - 11, described below. These observations wereat 8.4 GHz in the CnB array configuration. Secondly,as part of a regular VLA monitoring program for TypeI b/c supernovae (AS983; PI Soderberg) on 2009 Octo-ber 23, at both 8.4 and 5.0 GHz, and with the array inthe D configuration. The observations were reduced in astandard manner, with the flux density scale being set byobservations of 3C 286, and VCS4 J1036-3744 (hereafterJ1036-3744; also known as QSO B1034-374) being usedfor phase-referencing.The VLBI observations were carried out at 8.4 GHz,and lasted for 10 hours with a midpoint of 2009 June12.1 UT, or t = 85 d. Our VLBI array consisted of theNRAO VLBA (10 × − , with the exceptionof the Tidbinbilla antenna, at which we only recordedleft circular polarization (IEEE convention). The VLBIdata were correlated with NRAO’s VLBA processor, andthe analysis carried out with NRAO’s Astronomical Im-age Processing System (AIPS). The initial flux densitycalibration was done through measurements of the sys-tem temperature at each telescope, and then improvedthrough selfcalibration of the reference source. A correc-tion was made for the dispersive delay due to the iono-sphere using the AIPS task TECOR, although the effectat our frequency is not large.We phase-referenced our VLBI observations to J1036-3744, for which we use the position from theFourth VLBA calibrator survey of 10 h m . s − ◦ ′ . ′′ ∼ ∼ ◦ in elevation at the BR,HN and NL antennas of the VLBA, therefore we did notuse the data from these antennas in the final analysis.The majority of our remaining visibility measurementswere made at relatively low elevations, with less than25% of our individual visibility measurements being ob-tained with both antennas observing at elevations > ◦ .We show the final u - v -coverage obtained in Figure 1.For both imaging and model-fitting of the VLBI datafor SN 2009bb, we reduced the weights of the VLA by afactor of 4. As the VLA is more than an order of magni-tude more sensitive than any of the remainder of the an-tennas, the fraction of visibilities involving the VLA willhave much higher weight and thus dominate. Althoughreducing the VLA weights incurs a penalty in statisticalefficiency, it improves the stability of both imaging andmodelfitting. RESULTS
VLA Total Flux Density
We describe first the results from the reduction of the8.4 GHz VLA interferometric data. Our flux-density un-certainties include both statistical standard errors and anLBI Observations of SN 2009bb 3 M e g a W av l ng t h Mega Wavlngth300 200 100 0 -100 -200 -3003002001000-100-200-300
20 Mega Wavlngth
Fig. 1.—
The u - v -coverage obtained for our VLBI observatingrun for SN 2009bb on 2009 June 10 - 11 at 8.4 GHz after editingand excluding measurements with antenna elevations below 12 ◦ .The inset shows a detail of the ±
10 M λ × ± λ central region ofthe u - v plane showing the coverage of the shortest baselines. D E C L I NA T I O N ( J2000 ) RIGHT ASCENSION (J2000)10 31 38 37 36 35 34 33-39 57 00153045
SN 2009bb
Fig. 2.—
An 8.4-GHz VLA image of NGC 3278 on 2009 June12. SN 2009bb is indicated. The contours are at − .
1, 0.1,0.14, 0.20, 0.28, 0.5, 1.0, and 2.5 mJy bm − , and the greyscaleis labeled in mJy bm − . The peak brightness in this sub-imagewas 2640 µ Jy bm − , the background rms 31 µ Jy bm − , andthe FWHM of the convolving beam, indicated at lower left, was3 . ′′ × . ′′ at p.a. 14 ◦ . The position of the galaxy center(Paturel et al. 2003) is indicated by a cross. assumed 5% uncertainty in the flux density scale, addedin quadrature. For our calibrator source, J1036-3744, weobtained a flux density of 0 . ± .
04 Jy.We show the VLA image of NGC 3278 and SN 2009bbin Figure 2. The presence of a small amount of extendedemission due to the galaxy NGC 3278 is apparent.By fitting an elliptical Gaussian of the same dimensionsas the restoring beam and a zero level, we determine the8.4-GHz flux density of SN 2009bb at t = 85 d to be2 . ± .
19 mJy, where our uncertainty includes a contri- bution due to the uncertainty in estimating the zero-level(as well as the aforementioned 5% uncertainty in the flux-density scale, all added in quadrature). We estimate thecontribution from NGC 3278 to be 240 ± µ Jy bm − at our resolution of 3 . ′′ × . ′′ (FWHM).For our subsequent VLA observations on 2009 Oct. 23,the array was in the lowest-resolution D array configura-tion with a synthesized beamwidth of 31 ′′ × ′′ at 8.4 GHzand 47 ′′ × ′′ at 5.0 GHz. The subtraction of the galaxycomponent of the radio emission was not straightforward.We accomplished it by using the image of SN 2009bb andNGC 3278 made on 12 June 2009 (Figure 2), which hadadequate resolution and good u - v coverage, as a tem-plate. We assume that NGC 3278 does not change withtime, and that any change in the image between June andOctober is therefore due to SN 2009bb. We convolved thetemplate image to the resolution of the new ones, and inthe case of 5 GHz, scaled the brightness distribution byan assumed spectral index of − .
6, and then determinedthe change in the flux density of SN 2009bb. We find theflux density of SN 2009bb on 2009 Oct. 23 ( t = 218 d)was 0 . ± .
24 mJy at 8.4 GHz and 1 . ± . t = 85 d, 8.4 GHz) shows no noticeable dis-crepancy with the remainder of the observed light curve.A bump in the light curves is observed near t ≃
52 d.It is most prominent in the 5-GHz light curve, whichshows an increase by almost a factor of 2, reaching a localmaximum of 12 mJy at t ≃
52 d, which corresponds to aspectral luminosity of 2.3 × erg s − Hz − . A similaralthough smaller relative increase is seen at 8.4 GHz,with the peak occurring perhaps slightly earlier.A weighted least-squares fit to all the data up to t =220 d shows that on average, the flux density decaysas follows: S . ∝ t − . ± . and S ∝ t − . ± . .There is a possible flattening of the flux density decayat the very latest times ( t >
100 d), although due to thedifficulty of galaxy subtraction the reality of any late-time flattening is difficult to confirm. While the overallaverage decay rate is significantly flatter at 5 GHz thanat 8.4 GHz, this is largely due to the bump being moreprominent at 5 GHz, with the decay rates being similarat both frequencies after the bump.
VLBI
We now discuss the results of the VLBI observations,turning first to our phase-calibrator source, J1036-3744,as the results obtained for it will inform our interpre-tation of the SN 2009bb results. From a deconvolved(CLEAN) image of J1036-3744, we recovered a total fluxdensity of 687 mJy, with an background rms brightnessof 1.6 mJy bm − . The image is dynamic-range limited,rather than limited by thermal noise. The total flux den-sity recovered is 10% less than the flux density measuredat the VLA. It is possible this discrepancy is due to10% of the flux density being at spatial scales too largefor VLBI but too small for the VLA (0 . ′′ ∼ . ′′ ), Bietenholz et al Fig. 3.—
The 4.8 and 8.4-GHz radio light curve of SN 2009bbfrom VLA measurements. The measurements are described in thispaper or in Soderberg et al. (2010b). Our uncertainties includean estimated 5% uncertainty in the VLA flux-density scale and acontribution from the galaxy subtraction. The VLA flux densitymeasurement corresponding to our VLBI observations is circled.For better visibility, we have shifted the 5-GHz points very slightlyin time so as to avoid overlapping error bars. We also indicate therange of flux densities recovered from the VLBI observations toillustrate the discrepancy between them and the VLA flux densities(see appendix for details). although it is not uncommon to see such discrepanciesbetween the flux density scales for VLBI, determinedfrom the system-temperature measurements, from themore accurate one for VLA measurements, determinedby observations of calibrator sources such as 3C 286. Theresidual delays and delay-rates we found for J1036-3744were moderate, being mostly <
40 nsec and < − u - v taper of30% at 120 M λ had a total clean flux density of 740 µ Jy, apeak brightness of 610 µ Jy bm − , and a background rmsbrightness of 130 µ Jy bm − . We tried different weightingschemes and u - v tapers, but in no case was the total cleanflux density greater than 800 µ Jy.For marginally resolved sources, such as SN 2009bb,the best values for the source size and VLBI flux den-sity come from fitting models directly to the visibilitydata, rather than imaging. We choose as a model theprojection of an optically-thin spherical shell of uniformvolume emissivity, with an outer radius of 1 . × the in-ner one . Such a model has been found to be appropri-ate for other radio supernovae (see e.g., Bietenholz et al.2003; Bartel & Bietenholz 2008). For a partially resolvedsource such as SN 2009bb, the exact model geometry is Our results do not depend significantly on the assumed shellthickness, as the effect of reasonable thicknesses different than theassumed one is considerably less than our stated uncertainties. not critical, and our shell model will give a reasonableestimate of the size of any circularly symmetric source,with a scaling factor of order unity dependent on theexact morphology (see discussion in Bartel et al. 2002).The Fourier transform of this shell model is then fit tothe visibility measurements by least squares.For the interested reader, we give the details of themodelfitting results in the appendix. Fitting such amodel to the strictly phase-referenced visibilities forSN 2009bb gives our most accurate estimate of its cen-ter position, which is 10 h m . s − ◦ ′ . ′′ ∼
50% of that measured at the VLA. This discrepancymight suggest that the source is over-resolved by theVLBI observations, or, more precisely, that the missingflux density is at angular scales too large to be seen in theVLBI observations, but smaller than the VLA resolution.The VLBI observations had reasonable u - v coverage evenfor baselines as short as 10 M λ (see inset in Figure 1),and are therefore sensitive to structure up to ∼
20 mas inangular size, while the VLA resolution was ∼ ′′ . If thediscrepancy between the VLA and VLBI flux densities isto be ascribed to a source resolved in VLBI, then its sizeshould therefore be in the range of 20 mas to 3 ′′ . Theminimum angular size makes it unlikely that such hypo-thetical structure could be related to SN 2009bb, sincefor a supernova age of 85 d and the distance 40 Mpc,the implied apparent expansion speed is > c , whichwe consider improbable.Another possibility is a source of radio emission unre-lated to SN 2009bb but coincidentally so close as to bewithin the VLA beamwidth. We consider also this pos-sibility to be unlikely. A flux density of at least 1 mJy isrequired to explain the discrepancy, while the brightest ofNGC 3278’s galactic radio emission seen at the VLA wasonly ∼ µ Jy bm − , and appears well-resolved (Fig-ure 2). It would seem improbable therefore that therewould be such a bright and compact unrelated source ofemission located so close to SN 2009bb.The third possibility, which we consider most likely,is that there is substantial decorrelation in the VLBImeasurements, due to uncorrected differences in atmo-spheric delay between SN 2009bb and the phase-referencesource . In other words, the phase-calibration forSN 2009bb is of poor quality. Any determination of thesource size must therefore be interpreted with caution.For a sufficiently strong source, the phase calibrationcould be improved by selfcalibration. SN 2009bb, how-ever, was not bright enough to allow conventional selfcali-bration using an image. As an alternative, we introducedthe antenna phases as free parameters in the u - v planemodelfit. Unfortunately, due to the poor u - v coverageand the low signal-to-noise ratio, we were only able toobtain an upper limit of 0.64 mas to the source radiuswith this procedure. We found, however, that even withthis effective phase selfcalibration, we were not able to re-cover more than about half of the VLA flux density. Our We note that inaccuracies in the correlator model could alsocause coherence loss, but are typically considerably smaller thanthe un-modelled contributions of the atmosphere.
LBI Observations of SN 2009bb 5
TABLE 1Size Estimates for SN 2009bb
Age (days) a
20 52 81 145Radius b ( × cm) 4.4 8.0 22 26Angular Radius (mas) c a Age in days since shock breakout. b Linear size computed from radio spectrum by as-suming SSA to be the dominant absorption mecha-nism. Radio spectra in Soderberg et al. (2010b). c Angular radius (for D = 40 Mpc). upper limit on SN 2009bb’s angular size is not a formalstatistical limit because of various assumptions made inits derivation, but it is intended as a 3 σ limit, and shouldbe reasonably robust. We describe the exact procedureby which we arrive at this limit in the appendix for theinterested reader.Since the age of SN 2009bb at the time of our VLBIobservations was 85 d, using a distance of 40 Mpc as wellas assuming circular symmetry, this limit on the angularradius allows us to obtain a corresponding upper limiton the apparent expansion speed of 1 . c . DISCUSSION
We have made VLA and VLBI observations of the typeI b/c supernova 2009bb. This supernova was of par-ticular interest because the high level of radio emissionshowed that substantial material was ejected at relativis-tic speeds (Soderberg et al. 2010b). We discuss first theevolution of the radio light curve as revealed by our VLAmeasurements of the total flux density
Radio Light Curve Evolution
Our new data reveal a continuing decline of the radiolight curve of SN 2009bb at late times (Figure 3). By as-suming that the turnover in the radio spectrum is due toSSA, we can estimate the size at different epochs from thefour radio spectra published in Soderberg et al. (2010b).We give these values of the radius, along with the corre-sponding values angular radius and the average expan-sion velocity as a fraction of c in Table 1. These are mini-mum radii: if the spectral turnover were due to, for exam-ple, FFA rather than SSA, the supernova would be larger.However, our VLBI measurement gives a 3 σ upper limiton the radius of 0.64 mas at t = 85 d, which rules out aradius much larger than those derived from SSA. In thecase of SN 2009bb, much larger sizes and expansion ve-locities are probably ruled out also on energetic grounds,as Soderberg et al. (2010b) showed that the above sizeestimates imply an energy of (1 . ± . × erg coupledto relativstic ejecta, and much larger amounts of energycoupled to the relativistic ejecta are improbable. Moregenerally, Chevalier (1998) shows that SSA is probablythe dominant absorption mechanism for Type I b/c SNe.In summary, we think it unlikely that the sizes or veloc-ities in Table 1 are substantially in error. These radiusvalues suggests deceleration between t = 20 d and 52 d,but possibly a re-acceleration between t = 50 d and 81 d,and a relatively constant speed expansion since then.A bump is visible in the light curves, which is mostprominent at 5 GHz, where it peaks at t ≃
52 d,and the flux density increases by a factor of ∼ ∼ × erg s − Hz − .What is the origin of this bump? As mentioned,SN 2009bb was distinguished by having mildly rel-ativistic ejecta. One hypothesis is that the bumpcould be driven by the “engine”, in other words rep-resent a renewed injection of energy: similar bumps inthe lightcurve were seen for GRB 980425/SN 1998bw(Kulkarni et al. 1998; Li & Chevalier 1999) during therelativistic phase, and are thought to be engine-driven.The fact that the SSA sizes derived above suggest a re-acceleration between t =50 d and 82 d would be consistentwith this interpretation, in other words that there was arenewed energy input at the forward shock somewherearound t = 50 d.Alternatively, the bump may be related to the colli-sion between the bulk of the ejecta, which are almostundecelerated, with the leading blast wave, which wasinitially relativistic but decelerates as it sweeps up thestellar wind. It is not straightforward to predict the out-come of this collision because it essentially depends onthe poorly known distributions of density and velocityin the mildly relativistic, outermost layers of SN ejecta.We note, however, that this scenario is similar in manyrespects to that of the bump representing renewed en-ergy input by the engine: in both cases the bump in thelight curve is the result of the collision between the asyet undecelerated inner shell and the decelerating exter-nal shock. The difference may be in a possible deviationfrom a spherical symmetry, which is expected to be largerin the scenario of recurrent jets than in the present case.To summarize, we consider the bump in the light curvelikely to be engine-driven, although the collision of themain ejecta with the external shock wave is not excluded.Interestingly, even the case that bump is engine-driven,i.e., due to recurrent jet activity, the collision of themain SN ejecta with the decelerating blast wave is un-avoidable. Such a collision might therefore be expectedin supernovae similar to SN 2009bb or SN 1998bw at t = 50 ∼
100 d, and may produce detectable effects inthe radio lightcurves.
Source Size Derived from VLBI Observations
The primary goal of our VLBI observations was to setlimits on the expansion speed by measuring the angularsize of SN 2009bb. Unfortunately, the southern decli-nation of the source meant that it was at low elevationfor most of our VLBI array, which limited the quality ofthe data obtained, and consequently the accuracy of thedetermination of the source’s angular size.We obtained an estimate of the source outer angularradius between 0 and 0.64 mas, suggesting average ap-parent expansion speeds between 0 and 1 . c , with thelimits intended to represent a 3 σ range (see § t = 85 d of < × cmand a bulk Lorentz factor of < . t NR ≃ t ≃ t =20 d, the radius of the supernova was ∼ × cm. Ifwe assume a standard Sedov-von Neumann-Taylor evo-lution (see e.g., Granot & Loeb 2003) after t = 20 d, wewould expect a radius at the time of our VLBI observa-tions ( t = 85 d) of ∼ × cm which is well within ourobservational limits on radius.VLBI observations of SNe such as SN 2009bb are cru-cial to directly measuring the expansion speeds and per-haps the geometry of the radio emission, and thus im-portant to confirming a jet model. However, such VLBIobservations are difficult and generally limited by theavailable sensitivity and u - v coverage, especially if thesupernova is at a southern declination. They should be-come easier in the future with the planned increases insensitivity of the VLBA (Ulvestad et al. 2010), and byfuture availability of South African and Australian SKApathfinder instruments, MeerKAT (Booth et al. 2009)and ASKAP (Johnston et al. 2008) respectively, as VLBIstations. APPENDIX
In this appendix, we describe in detail how we arrivedat the upper limit on the angular size of SN 2009bb fromthe VLBI observations. We first made an image from thestrictly phase-referenced VLBI data for SN 2009bb, us-ing robust weighting and dropping any data taken withtelescope elevations below 12 ◦ . We found a peak bright-ness of only 610 µ Jy bm − for a convolving beam of3 . × . ◦ (FWHM). Even if we restrictourselves to the baseline-lengths of <
10 M λ ,we founda peak brightness of only 800 ± µ Jy bm − , with aconvolving beam size of 42 ×
10 mas. We note however,that due to the uneven u - v coverage, the sidelobe levelsare quite high, reaching peaks > § ± µ Jy with an outer angular ra-dius, θ o , of 0.47 mas, and a best-fit center position of10 h m . s − ◦ ′ . ′′ § µ Jy recovered fromstrictly phase-referenced data is considerably below thevalue of 2 . ± .
19 mJy measured at the VLA ( § § ◦ away on the sky, with the difference being predominatelyin declination. Any un-modeled elevation dependence ofthe delay will therefore result in errors in the delay forSN 2009bb, and poor phase-referencing. The situtionfor SN 2009bb is particularly bad since the difference insource position is mostly in declination and since the ob-servations are mostly at low elevation where the airmassis large. Self calibration in phase would in principle allowimproving the calibration of the supernova visibilities, al-though it does have the drawback of introducing biases(see e.g., Massi & Aaron 1999; Mart´ı-Vidal & Marcaide2008), which can be severe in the case of low signal-to-noise.As our signal-to-noise ratio is too low for traditionalselfcalibration using images, we instead introduce thephases of the complex antenna gains as free parametersin the model-fitting procedure, using a slightly modifiedversion of the AIPS task OMFIT. This procedure hasthe advantage of allowing a more quantitative measureof the goodness-of-fit than traditional selfcalibration us-ing images. Due to the low signal-to-noise, we fitted foronly a single phase solution common all 8 intermediate-frequency channels. We fix the source position at thebest-fit position obtained above, and let the antennaphases vary on a 30-min timescale. The best fit model forSN 2009bb obtained in this way had θ o = 0 . +0 . − . masand a flux density of 1 . ± .
07 mJy (statistical uncer-tainties). Even in this case, the total flux density in themodel was only 54% of that measured at the VLA.For a partly resolved source, the fitted source sizeis generally also correlated with the antenna amplitudegains. We tested for an additional uncertainty due tomis-calibration of the antenna amplitude gains by arti-ficially varying individual antenna gains by ± θ o was 0.05 mas. Adding this to theabove uncertainties in quadrature results in a value for θ o of 0 . +0 . − . mas.As mentioned, selfcalibration can introduce biases. Totest for this possibility, we calculated simulated visibili-ties from models with various values of θ o and randomnoise at a level corresponding to that in our observa-tions. We then fit these simulated visibilities using thesame procedure as above, including the addition of theantenna phases as free parameters. These tests suggeststhat the true value of θ o is in fact ∼
18% higher thanthat determined from the fitting. For simplicity, we car-ried out this test using a disk, rather than a sphericalshell model, that the relative bias in θ o should be verysimilar. In other words, selfcalibration tends to make thesource appear more compact.Correcting for this bias, we thus arrive at a final, unbi-ased estimate of θ o for SN 2009bb of 0 . +0 . − . mas, witha 3 σ upper limit of 0.59 mas. However as noted above,even with phase-selfcalibration, the fitted flux density isstill notably below that measured by the VLA, whichsuggests the presence of further decorrelation (or someother source of error). As the signal-to-noise is alreadylower than is generally considered safe for selfcalibration,using a shorter solution interval is not advisable.LBI Observations of SN 2009bb 7As a final test, we fixed the model flux density at2.0 mJy, a round value slightly below but near that mea-sured by the VLA, and again fitted a model of the sourceas well as the antenna gain-phases. We find that the bestfit to the VLBI visibilities is not much larger than theabove estimates, having θ o = 0 . +0 . − . mas, with a sta-tistical 3 σ upper limit of 0.64 mas. We note that forcingsuch a large flux density on the model results in a signif-icant increase in χ over models with lower flux density.The VLBI visibilities, therefore, seem to robustly sug-gest a total flux density for SN 2009bb of .
50% ofthat observed at the VLA. Given this inconsistency, thebiases involved in phase-selfcalibration, and the likeli-hood of coherence losses not accounted for by our phase-selfcalibration, we suggest a probable range for the outerradius of SN 2009bb of 0 < θ o < .
64 mas. The failureto recover the total flux density suggests the possibilitythat significant decorrelation remains in the VLBI data,but such decorrelation is more likely to increase the ap-parent size of the source than decrease it, so our upperlimit on the angular size should be robust.A very similar phenomenon was seen in the case ofSN 2007gr. Also for this SN, the flux density recoveredfrom VLBI observations was considerably lower than thetotal flux density measured by a connected-element inter- ferometer. Initially, this discrepancy was interpreted assuggesting a large source size and thus relativistic expan-sion (Paragi et al. 2010). This was somewhat surprising,given that SN 2007gr’s peak 8.4-GHz spectral luminos-ity was relatively low, being ∼
500 times lower than thatof SN 2009bb. Soderberg et al. (2010a) showed that theradio lightcurves and the lack of detectable X-ray emis-sion were fully consistent with a normal, non-relativisticSN, but were in fact hard to reconcile with relativisticexpansion. They also re-examined the SN 2007gr VLBIdata and showed that the low VLBI flux density was ob-served on both short and long baselines, and if it wasto be explained by a large, heavily-resolved source, re-quired very large apparent expansion velocities of > c .They conclude that coherence losses which were largerthan normal but not improbably so provided an expla-nation which as plausible as the original one of modestlyrelativistic expansion for SN 2007gr. In the present caseof SN 2009bb, some loss of coherence is not unexpected,given that the southern declination of the source neces-sitated observations made mostly at low elevation.Research at York University was partly supported byNSERC. We have made use of NASA’s AstrophysicsData System Bibliographic Services..They conclude that coherence losses which were largerthan normal but not improbably so provided an expla-nation which as plausible as the original one of modestlyrelativistic expansion for SN 2007gr. In the present caseof SN 2009bb, some loss of coherence is not unexpected,given that the southern declination of the source neces-sitated observations made mostly at low elevation.Research at York University was partly supported byNSERC. We have made use of NASA’s AstrophysicsData System Bibliographic Services.