ALMA and VLA Observations of EX Lupi in its Quiescent State
Jacob Aaron White, Á. Kóspál, A. G. Hughes, P. Ábrahám, V. Akimkin, A. Banzatti, L. Chen, F. Cruz-Sáenz de Miera, A. Dutrey, M. Flock, S. Guilloteau, A. S. Hales, T. Henning, K. Kadam, D. Semenov, A. Sicilia-Aguilar, R. Teague, E. I. Vorobyov
DDraft version October 1, 2020
Typeset using L A TEX twocolumn style in AASTeX62
ALMA and VLA Observations of EX Lupi in its Quiescent State
Jacob Aaron White,
1, 2, 3 ´A. K´osp´al,
3, 4, 5
A.G. Hughes, P. ´Abrah´am,
3, 5
V. Akimkin, A. Banzatti, L. Chen, F. Cruz-S´aenz de Miera, A. Dutrey, M. Flock, S. Guilloteau, A.S. Hales,
10, 11
T. Henning, K. Kadam, D. Semenov,
4, 12
A. Sicilia-Aguilar, R. Teague, and E.I. Vorobyov
15, 7 National Radio Astronomy Observatory, 520 Edgemont Rd., Charlottesville, VA, 22903, USA Jansky Fellow of the National Radio Astronomy Observatory Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, Konkoly-Thege Mikl´os ´ut 15-17, 1121 Budapest, Hungary Max Planck Institute for Astronomy, K¨onigstuhl 17, D-69117 Heidelberg, Germany ELTE E¨otv¨os Lor´and University, Institute of Physics, P´azm´any P´eter s´et´any 1/A, 1117 Budapest, Hungary Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Rd., Vancouver, BC V6T 1T7, Canada Institute of Astronomy, Russian Academy of Sciences, Pyatnitskaya str. 48, 119017, Russia Texas State University, Department of Physics, RFM Building 3227, 601 University Drive, San Marcos, TX 78666, USA Laboratoire d’Astrophysique de Bordeaux, Universit´e de Bordeaux, CNRS, B18N, All´ee Geoffroy Saint-Hilaire, 33615, Pessac,France Joint ALMA Observatory, Avenida Alonso de C´ordova 3107, Vitacura 7630355, Santiago, Chile National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA Department of Chemistry, Ludwig Maximilian University, Butenandtstr. 5-13, 81377 Munich, Germany SUPA, School of Science and Engineering, University of Dundee, Nethergate, DD1 4HN, Dundee, UK Center for Astrophysics — Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA University of Vienna, Department of Astrophysics, Vienna 1180, Austria (Received -; Revised -; Accepted -)
Submitted to ApJABSTRACTExtreme outbursts in young stars may be a common stage of pre-main-sequence stellar evolution.These outbursts, caused by enhanced accretion and accompanied by increased luminosity, can alsostrongly impact the evolution of the circumstellar environment. We present ALMA and VLA ob-servations of EX Lupi, a prototypical outburst system, at 100 GHz, 45 GHz, and 15 GHz. We usethese data, along with archival ALMA 232 GHz data, to fit radiative transfer models to EX Lupi’scircumstellar disk in its quiescent state following the extreme outburst in 2008. The best fit modelsshow a compact disk with a characteristic dust radius of 45 au and a total mass of 0.01 M (cid:12) . Ourmodeling suggests grain growth to sizes of at least 3 mm in the disk, possibly spurred by the recentoutburst, and an ice line that has migrated inward to 0 . − . Keywords:
FU Orionis stars (553), Millimeter astronomy (1061), Pre-main sequence stars (1290), Pro-toplanetary disks (1300), Radio continuum emission(1340), Radio interferometry (1346),Stellar accretion disks (1579) INTRODUCTION
Corresponding author: J.A. [email protected]
Giant molecular clouds are the nurseries in which starsare born. The earliest phases of mass accumulation takeplace in the densest regions of the cloud cores and the ro-tation of these in-falling cores can lead to the formationof young stellar objects (YSOs) embedded in accretiondisks. a r X i v : . [ a s t r o - ph . E P ] S e p White et al.
A growing number of YSOs have been observed tohave extreme outbursts (e.g., Audard et al. 2014), in-creasing the brightness by up to several magnitudesand the total luminosity by a factor of 10 − − (cid:12) , 0.7L (cid:12) quiescent luminosity) located 157 . ± . . × − M (cid:12) .K´osp´al, et al. (2020) used spectropolarimetric monitor-ing of EX Lupi post-outburst with the Canada-FranceHawaii Telescope (CFHT) to place constraints on thestellar magnetic fields. Their preliminary analysis sug-gests the surface magnetic field is 3 kG, stronger thanwhat has been observed for some embedded FUor/EXorobjects (e.g., 1 kG observed in FU Orionis Donati et al.2005) and more in line with what is seen in Classical TTauri stars with field strengths of up to a few kG (Johns-Krull 2007; Bouvier et al. 2007; Johns-Krull et al. 2009).The strength and stability of the stellar magnetic fieldin EX Lupi can influence the stability of the accretioncolumns (Sicilia-Aguilar et al. 2015) and has significantimplications on possible outburst mechanisms.In this paper, we present long wavelength observationsof EX Lupi. In Sec. 2, we describe the data and calibra-tion procedures. In Sec. 3, we outline the model fittingapproach used and in Sec. 4 we discuss the results. OBSERVATIONSThe analysis presented here uses a combination of newradio observations with the
NSF’s Karl G. Jansky VeryLarge Array (VLA), new ALMA 100 GHz observations,and ALMA 232 GHz data from literature (Hales et al.2018). All of the observations are summarized in Table 1and the new ones are detailed below.2.1.
VLA Observations
The VLA observations (ID 19A-145, PI White) werecentered on EX Lupi using J2000 coordinates RA =16 h m . s and δ = − ◦ (cid:48) . (cid:48)(cid:48)
10. The Schedul-ing Blocks (SB) for each observation were executed ondifferent days but all used the B configuration with 26antennas and baselines ranging from 0.21 to 11.1 km.Quasar J1607-3331 was used for bandpass and gain cal-ibration. Quasar 3C286 was used as a flux calibrationsource. Data were reduced using the
CASA 5.4.1 pipeline,which included bandpass, flux, and phase calibrations(McMullin et al. 2007). The absolute flux calibration ofthe VLA at these wavelengths is typically ∼ Allof the SBs used the same sources for calibration. For a note on the VLA flux calibration uncertainty, see sci-ence.nrao.edu/facilities/vla/docs/manuals/oss/performance/fdscale.
LMA and VLA Observations of EX Lupi Table 1.
Summary of the observations. The ALMA 232 GHz data is from Hales et al. (2018) with no additional calibrationprocedures. The peak fluxes were measured from the CLEANed images and the total flux was calculated in the
CASA task uvmodelfit . The stated uncertainties do not include the absolute flux calibration uncertainty, which is ≤
10% at these frequenciesfor ALMA and ≤
5% for VLA. ∗ The 45 GHz VLA observations resulted in a non-detection, therefore we include a 3 σ upperlevel limit on the peak flux. 232 GHz 100 GHz 45 GHz 15 GHzFacility ALMA ALMA VLA VLAObservation Date 2016 Jul 25 2018 Jan 27, Mar 17, Mar 19 2019 May 13, Jul 10 2019 Mar 09Flux Calibrator J1427-4206 J1427-4206, J1517-2422 3C286 3C286Beam Size 0 . (cid:48)(cid:48) × . (cid:48)(cid:48)
26 1 . (cid:48)(cid:48) × . (cid:48)(cid:48)
81 0 . (cid:48)(cid:48) × . (cid:48)(cid:48)
16 1 . (cid:48)(cid:48) × . (cid:48)(cid:48) . ◦ . ◦ . ◦ . ◦ σ rms − − − − Peak Flux 8.8 mJy beam − − < . ∗ mJy beam − − Total Flux 17 . ± .
15 mJy 2 . ± .
013 mJy - 0 . ± .
008 mJy
The 15 GHz data from the VLA were acquired inSemester 19A on 2019 March 09 and had a total on-source time of 948 s. The observations used a Ku Bandtuning setup with 3 × CASA ’s CLEAN algorithm down to a threshold of the RMS noise. The 15 GHz observations achieve asensitivity of 7 µ Jy beam − . The size of the resultingsynthesized beam is 1 . (cid:48)(cid:48) × . (cid:48)(cid:48)
42 ( ∼
180 au) at a posi-tion angle of 10 . ◦ . Due to the large beam, the emissionis only marginally resolved along the minor axis of thebeam. The peak flux is 0 .
044 mJy beam − as mea-sured in the CLEANed image. We used the CASA task uvmodelfit and a disk model to obtain a total flux of0 . ± .
008 mJy.The 45 GHz VLA data were acquired on 2019 May 13and 2019 July 10 and had a total combined on-sourcetime of 2345 s. Both 45 GHz SBs used a Q Band tuningsetup with 4 × .
048 GHz basebands and rest frequencycenters of 41 GHz, 43 GHz, 47 GHz, and 49 GHz. Thisgives an effective frequency of 45 GHz (6.7 mm) for theQ band. The 45 GHz observations were concatenated in
CASA and the data were imaged with a natural weight-ing and cleaned using the
CLEAN algorithm down toa threshold of the RMS noise. Together, these dataachieve a sensitivity of 43 µ Jy beam − . The resultingsynthesized beam is 0 . (cid:48)(cid:48) × . (cid:48)(cid:48)
16 ( ∼
40 au) at a positionangle of 10 . ◦ .The low declination of EX Lupi leads to an elongatedsynthesized beam with the VLA (EX Lupi is locatedat δ = − ◦ and the VLA is at a latitude of 34 ◦ N).The atmospheric fluctuations at low altitude can also bemuch greater, leading to a poorer phase calibration and thus impacting the quality of the reconstructed images.These factors, coupled with less time on source thaninitially requested for the Q Band, led to a non-detectionat 45 GHz. We note that this does not necessarily meanthe disk is not observable at these frequencies.2.2.
ALMA Observations
EX Lupi was observed with ALMA (2017.1.00224.S,PI K´osp´al) on 2018 January 27, March 17, and March 19with a phase center of RA= 16 h m . s δ = − ◦ (cid:48) . (cid:48)(cid:48)
4. The total on-source integration time was 11640s. The nominal antenna configuration was C43-4, withbaselines between 14 m and 1398 m. Two spectral setupswere used with spectral windows for different molecularlines (which will be presented in a later paper). In bothsetups, a 1.875 GHz wide window was centered at 100.2GHz (2.99 mm) to measure the continuum emission ofEX Lupi. The data were manually calibrated using the
CASA 5.4.1 pipeline. The procedure included offline wa-ter vapor radiometer calibration, system temperaturecorrection, and bandpass, phase and amplitude calibra-tions. Quasars J1427 − − − uvcontsub routine in CASA to obtainthe continuum emission.The 100 GHz observations were concatenated in
CASA and the data were imaged with a natural weightingand CLEANed using the
CLEAN algorithm down toa threshold of the RMS noise. Together, these dataachieve a sensitivity of 13 µ Jy beam − . The resulting White et al. synthesized beam is 1 . (cid:48)(cid:48) × . (cid:48)(cid:48)
81 ( ∼
150 au) at a po-sition angle of 87 . ◦ . The disk is marginally resolved.The peak flux is 1 .
98 Jy beam − as measured in theCLEANed image. We used the CASA task uvmodelfit anda disk model to obtain a total flux of 2 . ± . µ Jy.2.3.
Literature Data
In addition to the new ALMA and VLA data pre-sented here, we also use the ALMA 232 GHz continuumdata from Hales et al. (2018) in our analysis. The obser-vations were made on 2016 July 25, have a CLEANedsynthesized beam of 0 . (cid:48)(cid:48) × . (cid:48)(cid:48)
26, and sensitivity of σ rms = 38 µ Jy beam − . The disk was well resolvedat this frequency. No further calibration or processingwas performed outside the procedure listed in Hales etal. (2018). MODEL FITTINGTo constrain the parameters of the dust in EX Lupi’scircumstellar disk, we followed a radiative transfer (RT)model fitting approach similar to Hales et al. (2018).We use the RT code
RADMC-3D 0.41 (Dullemond et al.2012) with the Python interface radmc3dPy to set thecode input parameters for a given disk model. We keepthe following parameters fixed in the fitting procedure:inclination i = 32 ◦ , position angle PA= 65 ◦ , and innerdisk radius r = 0 .
05 au (Hales et al. 2018); flaring pa-rameter ψ = 0 .
09 (Sipos et al. 2009); stellar temperatureT = 3859 K and stellar radius R = 1 . (cid:12) (Frasca etal. 2017).We adopt a disk model similar to that of a typical TTauri protoplanetary disk (Andrews et al. 2009) with adisk density given by: ρ = Σ( r, φ ) H p (cid:112) (2 π ) exp (cid:18) − z H p (cid:19) , (1)where Σ is the surface density profile, H p is the pressurescale height, and z is the height above the disk midplane.The disk’s surface density profile follow a power-law pro-file with an exponential outer tapering:Σ( r ) = Σ (cid:18) rR c (cid:19) − γ exp (cid:40) − (cid:18) rR c (cid:19) − γ (cid:41) , (2)where Σ is the surface density at the inner radius of0.05 au, R c is the characteristic radius of the disk, and γ is the power-law exponent of the radial surface densityprofile. The pressure scale height is defined as: H p = h c (cid:16) r
100 au (cid:17) ψ , (3) where ψ is the disk flaring parameter and h c is the ratioof the pressure scale height over radius at 100 au (seeHales et al. 2018).In order to converge on the best fit disk parameters, weuse a Metropolis-Hastings Markov Chain Monte Carlo(MCMC) model fitting approach. The free parametersconsidered in the modeling are: the total disk mass witha gas-to-dust ratio of 100:1, M disk , characteristic radius, R c , power law exponent of the surface density profile, γ , and scale height ratio at 100 au, h c . We perform theMCMC modelling in the image plane (see, e.g., Boothet al. 2016; White et al. 2017). After a trial model isselected, we use RADMC-3D and the mctherm commandto calculate the dust temperature and then use the im-age command to generate a ray-traced continuum im-age projected to the inclination and position angle ofthe disk. The image is then attenuated by the primarybeam and convolved with the dirty beam for a given ob-servational setup. A χ for each trial model is calculatedas χ = ( Data − M odel ) σ , (4)where σ is the observed σ rms for a given observation mul-tiplied by the synthetic beam size in pixels (see Boothet al. 2016). To fit multiple wavelength’s data simulta-neously, the χ at each wavelength needs to be calcu-lated and weighted. We adopt an equal weighting foreach wavelength, and all of the χ values are averagedtogether. A given trial model is then accepted if a ran-dom number drawn from a uniform distribution [0,1] isless than α , where α = min( e ( χ i − χ i +1 ) , . (5)Fitting the 232 GHz, 100 GHz, and 15 GHz data si-multaneously requires a dust opacity file extended tolarger grain sizes. We use the OpacityTool3 program (Toon& Ackerman 1981; Woitke et al. 2016) to get more realis-tic dust absorption and scattering parameters. This pro-gram calculates dust opacities by using a volume mix-ture of 60% amorphous silicates (e.g., Dorschner et al.1995), 15% amorphous carbon (e.g. Zubko et al. 1996),and a 25% porosity. Bruggeman mixing is used to cal-culate an effective refractory index and a distribution ofhollow spheres with a maximum hollow ratio of 0.8 (Minet al. 2005) is included to avoid Mie theory scatteringartifacts. We further assume the disk is populated by0 . − µ m grains following a power-law size distri-bution of s − . . The OpacityTool Software was obtained fromhttps://dianaproject.wp.st-andrews.ac.uk/data-results-downloads/fortran-package/
LMA and VLA Observations of EX Lupi χ and could only beginobtaining reasonable results if the weighting for the 15GHz data was set to an arbitrarily small value. This in-dicates that the approach is not well suited for fitting allthree datasets simultaneously, or that there are differentemission mechanisms at longer wavelengths. Therefore,we decided to exclude the 15 GHz data and discuss otherapproaches to fitting it in Sec.4.1.To constrain the properties of the 232 GHz and 100GHz observations, we use all the same approach andassumptions outlined above but change the particle sizepopulation to 0 . − µ m grains. We adopted anequal weighting for the two data sets and ran an MCMCfit with 100 × DISCUSSION4.1.
Model Fitting Results
Our RT models of the 232 and 100 GHz ALMA datawere able to well reproduce the observations. When fit-ting both of the datasets simultaneously, we find mostprobable values of: M disk = 0 .
01 M (cid:12) , R c = 45 au, γ = 0 .
25, and h c = 2 . α . − . = 2 . ± .
11 (the uncertaintyincludes a 10% absolute flux calibration uncertainty ateach frequency). The spectral index is consistent with2 . ± .
47 as reported in Hales et al. (2018) and calcu-lated within the ALMA Band 6 spectral windows. Ex-trapolating the peak flux of the 100 GHz data to 45GHz, along with the new beam size and α = 2 .
2, givesa peak flux lower than the achieved σ rms of the 45 GHzobservations. This calculated flux shows that the non-detection at 45 GHz is not useful for constraining thethermal disk properties. If the 15 GHz observations are tracing the thermalemission from large grains, then it is possible these largegrains are located at a different area of the disk thanthe smaller grains probed by ALMA. To test this, wetried fitting the VLA 15 GHz data alone with the sameRT approach as for the ALMA datasets. This approachallows for a different disk geometry of the large grains,but still requires the total flux to be well fit to the data.We note though that due to the large beam size at 15GHz, the disk is not resolved along the major axis andwould be only marginally resolved along the minor axis.The results are summarized in Table 2, the best fit modeland residuals are shown in Fig. 3, and the PDF is shownin Fig. 4.While the 15 GHz only model does indeed well repro-duce the data, the resulting disk parameters seem im-probable. As segregation by grain size is possible due toradial drift and settling, a different disk geometry aloneis not immediately disqualifying. The scale height, how-ever, seems un-physically large at 89 au. Larger grainswould be expected to settle in the midplane of the disk,meaning the scale height would likely be the same orsmaller than is observed with the mm grains. The bestfit total disk mass is also 3 . × larger than when fittingto the mm data alone. Such a disk may have emissionat 45 GHz, depending on the spectral index, and we re-port a non-detection at 45 GHz. We conclude that eventhough a thermal emission model can technically fit thedata well at 15 GHz, the resulting disk parameters to doso are highly improbable. Alternate sources of 15 GHzemission are explored in Sec. 4.3.4.2. Millimeter Observations & Grain Growth
EX Lupi lies between the Lupus 3 and Lupus 4 starforming regions (Cambr´esy 1999). ALMA surveys ofprotoplanetary disks in the Lupus star forming regionshave found total disk masses to be ∼ − M (cid:12) (Ansdellet al. 2016). Our model fitting finds a total disk massnearly an order of magnitude higher, assuming a gas-to-dust ratio of 100:1. The mass discrepancy could bedue to the assumptions made in the mass calculation inAnsdell et al. (2016) such as the optical depth and thathere we include a full RT calculation. The actual gas-to-dust ratio in EX Lupi could also be much lower thanassumed. If the difference in the masses is indeed real,it could be explained by EX Lupi being younger, moreheavily accreting, or from an inherent difference in thedisks of EXor/FUor-type system from that of typicalprotoplanetary disks. EX Lupi’s disk mass is smallerthan that of FUors, as expected, but the characteristicradius is similar. Other ALMA studies have found thatEXor/FUor disks tend to be more compact than that White et al.
Table 2.
Summary of the most probable model parameters and the corresponding 95% confidence intervals from the posteriordistributions in brackets. The first row is the ALMA 232 GHz and 100 GHz data fit simultaneously, the second row is the 15GHz VLA data fit alone, the third row is fitting a point source model on top of the RT calculated 15 GHz disk emission. Thedisk mass is the total disk mass assuming a gas-to-dust ratio of 100:1. The scale height is measured at 100 au (see Hales et al.2018). Dataset(s) Disk Mass Characteristic Radius γ Scale Height(M (cid:12) ) (au) (au)232 GHz + 100 GHz 0.0099 45 0.25 2.5[0.0067, 0.012] [39, 68] [ − .
36, 0.77] [1.9, 3.8]15 GHz 0.035 56 0.12 89[0.011, 0.053] [13, 140] [ − .
8, 1.2] [21, 98]Dataset Flux X-offset Y-offset(mJy) ( (cid:48)(cid:48) ) ( (cid:48)(cid:48) )15 GHz 0.055 0.025 0.26[0.045, 0.066] [ − .
09, 0.11] [ − . of typical protoplanetary disks (e.g., Cieza et al. 2018,K´osp´al et al. in prep.).EX Lupi experienced an outburst in 2008 and hassince returned to a quiescent state. Therefore, all ofthe ALMA and VLA data presented here are indicativeof a post-outburst circumstellar environment. ´Abrah´amet al. (2009) found that the outburst increased the crys-tallinity of the disk grains and transported them fromthe inner regions to the outer regions. Their work showsthat even a short-lived outburst, such as an EXor-typeoutburst, can have observable effects on the circumstel-lar disk.The water ice line (or snow line) is the radial locationin a disk where water reaches its condensation temper-ature and freezes out on to grains in the disk. The ex-act temperature at which this occurs depends on otherdisk properties, such as gas pressure, but is typically be-tween 150 to 175 K in the midplane of a disk (Lecar etal. 2006). EX Lupi’s recent outburst increased the bolo-metric luminosity by about 36 × ( ´Abrah´am et al. 2009).This enhanced luminosity can heat the disk and pushthe ice line(s) out to further radial distances. This wasobserved in ALMA observations of V883 Ori, where theice line moved from a presumed 1 − −
30 au on the surface of the disk and 1 − Spitzer observa-tions of the H O spectra, Banzatti et al. (2012) find the ice line moved from 1.3 au during outburst to 0.6 auafter outburst.Our RT modeling shows that the ice line is now lo-cated at 3 − . − . µ m of κ = 52 . / g. Therelaxation time curve is shown in Fig. 5.The black line represents the relaxation timescale inyears for the best fit disk model as a function of radialposition in the disk, with the outburst and post-outburstice lines indicated in gray. This curve shows that EXLupi’s recent outburst, of duration of ∼ ∼
10 yr time between theend of the outburst and the observations is more thanenough to relax the disk up to 10 au to a new thermalstate.An ice line can be a source of turbulence in a disk,around which grain growth can occur (e.g., Brauer et al.2008; Ros & Johansen 2013; Zhang et al. 2015). There-
LMA and VLA Observations of EX Lupi Figure 1. Top:
Dirty image, best fit RT model, and residuals for the ALMA 232 GHz observations.
Bottom:
Dirty image,best fit RT model, and residuals for the ALMA 100 GHz observations. The two datasets were fit simultaneously with equalweighting. The black ellipses in the bottom left of each figure represent the synthesized beam. fore as the ice line moves inwards after an outburst itprovides a potential mechanism to spur grain growththroughout the disk. The associated timescales for wa-ter to deposit onto grains near the ice line will be muchshorter than the relaxation timescale outlined above,meaning grain growth from water freeze-out or depo-sition can be commensurate with the moving positionof the ice line (e.g., Brown & Charnley 1990). Ther-mal grains are inefficient emitters at wavelengths longerthan their grain size. Therefore, using the detection ofthe disk in the ALMA 100 GHz data, and calculatedspectral index of α = 2 . ± .
01 indicating the diskis optically thin, we infer that grains of at least 3 mm may be present in the disk post-outburst. Our RT mod-els include grains of sizes up to 1 cm. While this isnot a confirmation of 1 cm grains it does indicate thedata is at least consistent with the presence of up to1 cm grains. Significant grain growth is possible withEX Lupi’s evolving ice line, although we note that thereis no pre-outburst ALMA and VLA data to compare itto. If EXor-like outbursts, which are short lived andcan repeat many times during pre-main-sequence stel-lar evolution (e.g., Vorobyov & Basu 2015; White et al.2019), are indeed common for most stars then appre-ciable grain growth can occur throughout the disk bothearly and often. Quick and abundant grain growth to
White et al.
Figure 2.
Posterior distribution of the best fit model for fitting the ALMA 232 GHz and 100 GHz simultaneously. The mostprobable values for each parameter are denoted by the blue lines. mm-cm sized particles is an important step in the planetformation process and can drive the growth of largerplanets and planetesimals (e.g., Morbidelli & Raymond2016; Johansen & Lambrechts 2017; Hughes & Boley2017). Significant early grain growth and the presenceof planetesimals is also a possible explanation for thegaps seen in HL Tau (Brogan et al. 2015) or surveys ofnearby protoplanetary disks with the ALMA DSHARPsurvey (e.g., Andrews et al. 2018).4.3.
Long Wavelength Central Emission
In Sec. 3, we concluded that the 15 GHz VLA data islikely dominated by something other than thermal diskemission. A more likely scenario is that at 15 GHz we areseeing thermal disk emission plus a combination of non-thermal disk emission, stellar winds, jets, or stellar emis-sion. To test this scenario, we can fit a point source emis-sion model on top of the thermal disk emission. Giventhe resolution of the 15 GHz data (1 . (cid:48)(cid:48) × . (cid:48)(cid:48) ∼ .
001 mJy. Starting with this disk model, the “addi-tional” emission required to reproduce the data can beassumed to be coming from approximately the center ofthe disk. This leaves only 3 free parameters: the fluxof the central emission, the X-offset, and the Y-offset.We adopt an MCMC modelling approach similar to theone outlined in Sec. 3 but now just add the flux of thecentral emission on top of the already calculated RTmodel. The results are summarized in Table 2, the bestfit model and residuals are shown in Fig. 6, and the PDFis shown in Fig. 7. We find a most probable flux of 0.055mJy, an X-offset of 0 . (cid:48)(cid:48) . (cid:48)(cid:48)
26. Dueto the nature of the large beam at 15 GHz (1 . (cid:48)(cid:48) × . (cid:48)(cid:48) LMA and VLA Observations of EX Lupi Figure 3. Left:
VLA 15 GHz dirty image.
Middle:
15 GHz RT disk model
Right:
Data minus model residuals. The blackellipses in the bottom left of each figure represent the synthesized beam. the location of the central emission flux is still broadlyconsistent with being peaked on the star itself.4.3.1.
Role of the Magnetic Field
Some of the most promising outburst theories for EX-ors rely on the role of the magnetic field. Armitage(2016) predicted that the outbursts could be explainedby changes in the polarity and strength of the stellarmagnetic fields at the kG-level. In a competing scenario,D’Angelo & Spruit (2012) proposed an instability whichcan lead to quasi-periodic oscillations in the inner diskand associated recurrent outbursts. This instability canoccur when the accretion disk is truncated close to theco-rotation radius by the strong magnetic field of thestar. Stable accretion columns linked to a very strongmagnetic field in EX Lupi were noted in Sicilia-Aguilaret al. (2015).In principle, if kG-level stellar magnetic fields werepresent in EX Lupi then there could be significant non-thermal emission that would yield brightness tempera-tures easily detectable at long wavelengths with VLA.The central emission flux of 0.055 mJy corresponds to aRayleigh-Jeans brightness temperature of T B ≈ × K, assuming the size of the emitting region is uniformlyspread out over the surface of the star (we note thatdepending on the emission mechanism the actual emit-ting region could range from a small localized area ofthe star to several stellar radii). This brightness tem-perature is much larger than the effective temperatureof EX Lupi ( T = 3859 K), which indicates that signif-icant non-thermal stellar emission could be present as was seen in optical line emission (e.g., Sicilia-Aguilar etal. 2012).One potential source of such large brightness temper-atures is synchrotron emission from relativistic or nearlyrelativistic electrons being accelerated by EX Lupi’smagnetic field. If synchrotron emission is present, thenthe flux should peak near the critical frequency (e.g.,Hughes et al. 2019), ν crit = γ qB πm e , (6)where γ is the Lorentz factor and is assumed to be ∼
1, q is the electron charge, B is the magnetic fieldstrength, and m e is the electron mass (we note that γ here is not the same as the disk power-law exponentused in Eqn. 2). Adopting a magnetic field strengthof 3 kG gives ν crit = 8 . γ = 1 .
34, then ν crit = 15 GHz.Alternatively, Armitage (2016) predict that significantchanges in magnetic field strength could be a driver forthe episodic accretion in EXor-type stars. Therefore,the magnetic field strength could potentially be differ-ent than measured previously with CFHT (K´osp´al, etal. 2020). If this is indeed the case, and ν crit is ∼ ∼ . White et al.
Figure 4.
Posterior distribution of the best fit model of the 15 GHz emission alone shown in Fig. 3. The most probable valuesare denoted by the blue lines. quency ν , is given by: T e ≈ (cid:16) πm e νqB (cid:17) / m e c k (7)where k is the Boltzmann constant. This yields 2 − × K, depending on which value for the magnetic fieldis used. The electron temperature is about a factor of50 larger than the observed brightness temperature im-plying the emission is optically thin. At face value, syn-chrotron emission is a potential source of the 15 GHzemission. An important consideration though is thatthe size of the emitting region could be extended muchfurther from the stellar surface. At further stellar sepa-rations, the magnetic field strength will become weakercausing ν crit to fall below 15 GHz and the expected syn-chrotron emission at 15 GHz to be much lower as well.While EX Lupi is indeed still a pre-main-sequencestar, its spectral classification is M0 and its mass in-dicates that when it reaches the main-sequence it will still be an M-type star. M-type stars are notorious forflares and magnetic activity, but were not observed at ra-dio wavelengths until recent technological advancements(Berger et al. 2001). While the exact emission mecha-nisms are still debated, they are thought to be primar-ily due to electron cyclotron maser instabilities (ECMI)and/or gyrosynchrotron emission.ECMI emission is similar to the auroral emission ob-served on most solar system planets (Turnpenney et al.2018). If the 15 GHz emission in EX Lupi was due toECMI, then the emission is expected to peak at the fun-damental critical frequency of ν crit = 8 . ν crit ∼
15 GHz, ECMI is a highly unlikely
LMA and VLA Observations of EX Lupi Figure 5.
The relaxation time in years as a function ofdisk radii along the midplane for the best fit RT model of EXLupi (see Eqns. 10-13 in Flock et al. 2017). The locations ofthe ice line along the disk midplane both during ( ´Abrah´amet al. 2009) and post-outburst are also denoted in gray. source of the 15 GHz emission due to the required sta-bility.If the 15 GHz emission in EX Lupi was due to gy-rosynctrotron emission, then it is likely due to magneticreconnection events releasing a large number of ener-getic particles (e.g., Williams et al. 2014; Hughes et al.2019). The surface of a pre-main-sequence accreting M-type star, such as EX Lupi, is undoubtedly a turbulentenvironment where these processes could dominate. Theexpected emission at 15 GHz depends on the size of theemitting region (which is typically much smaller thanthe stellar radius), the magnetic field strength, and theelectron energy index δ . Assuming the gyrosynchrotronemission is optically thin, then the spectral index can beused as a tracer for δ . Following Hughes et al. (2019),the relation between all of these parameters is given by: R em = 132 (cid:16) dpc (cid:17)(cid:16) GHzν (cid:17)(cid:115) F µJy T eff , (8)where R em is the emitting region in units of R (cid:12) , F µ Jy is the observed flux in µ Jy, and T eff is given by: T eff = 2 . × (sin θ ) − . − . δ − . δ (cid:16) νν crit (cid:17) . . δ (9)where θ is assumed to be ∼ ◦ (see Dulk 1985, forthe derivation and further details on the relationship be-tween expected flux and the size of the emitting region).Fig. 8 shows the size of the emitting region and magneticfield strength for various values of δ (which cannot be constrained with the available data). If we assume atypical lower level limit of δ ∼ − ∼ . − . (cid:12) . This is a sig-nificant fraction of the stellar surface (R ∗ = 1 . (cid:12) )and much larger than is typically expected for main-sequence M-dwarf stars which have reconnection regionstypically of order 0 .
01 R (cid:12) . If δ >
2, which is typicallythe case in M-dwarfs, then the size of the emitting regionquickly becomes larger than the star. EX Lupi could,however, have a very small value of δ or have the gy-rosynchrotron emission come from a large area whereit is actively accreting disk material. Follow-up obser-vations at higher/lower frequencies will enable spectralindex constraints, and thus a value for δ , to better de-termine if gyrosynchrotron is a potential source of theobserved 15 GHz emission.4.3.2. Radio Jets and Non-thermal Disk Emission
Some EXor/FUor systems also have very bright radiojets (e.g., Z CMa and L1551 IRS 5, Poetzel et al. 1989;Rodr´ıguez et al. 2003). While EX Lupi did show signif-icant X-ray activity leading up to and during the mostrecent outburst, the emission is most likely stemmingfrom accretion shocks instead of jets (see, e.g., Grosso etal. 2010). No radio jets have been previously reportedin EX Lupi. If the 15 GHz emission was indeed dueto a radio jet, then we would expect it to have an ap-proximately flat spectral index leading it to possibly bedetectable at 45 GHz. Since we did not detect anythingat 45 GHz, and no radio jet was reported previously, wenote the likelihood of the 15 GHz emission being jet-driven is low.Centrally located disk winds are another possiblesource of long wavelength emission. K´osp´al et al. (2011)found that the hydrogen emission within 1 au is likelydue to disk winds in EX Lupi. In optical line spectra,there is further evidence of disk winds in both outburstand quiescence (Sicilia-Aguilar et al. 2012, 2015; Ban-zatti et al. 2019). Hales et al. (2018) observed large scaleasymmetries in the outer CO gas disk which could bedue to a molecular outflow. Similar to jets, disk windswould likely be peaked at frequencies <
15 GHz andhave a flat to slightly positive spectral index. Follow-up observations at <
15 GHz are necessary in order tomeasure the spectral index and determine if winds orjets are a possible source of observed emission.Free-free emission from an ionized disk, typically moreprevalent in the latter stages of disk dissipation whenphotoevaporation becomes significant, can come fromEUV and X-ray irradiation. EX Lupi had significantX-ray activity before and during the outburst, which2
White et al.
Figure 6. Left:
VLA 15 GHz dirty image.
Middle:
15 GHz RT disk model (as calculated from fitting to both ALMAdatasets) added to the best fit central emission model.
Right:
Data minus model residuals. The black ellipses in the bottomright represents the synthesized beam. could have significantly ionized its inner disk. Althoughunlikely, if this irradiation continued after the outburstended then free-free emission could still be present in theEX Lupi system. Free-free emission can also arise fromaccretion shocks propagating through the disk when theaccretion rate becomes much larger (e.g., Hartmann &Kenyon 1996). Sicilia-Aguilar et al. (2015) find evidenceof accretion shocks via optical spectroscopy and Grossoet al. (2010) noted that the X-ray emission seen in EXLupi is also likely due to accretion shocks. The X-rayluminosity of EX Lupi was 1 . × erg s − duringthe outburst (Grosso et al. 2010). Using the relation forX-ray luminosity to expected radio flux from free-freeemission outlined in Pascucci et al. (2012): F . cm = 2 . × − (cid:16) d (cid:17) L x [ µJy ] , (10)where F . is the 3.5 cm flux, d is the distance to thesource in pc and L X is the X-ray luminosity in erg s − ,we find an expected flux of 4.3 µ Jy. Free-free emissionshould have an approximately flat spectral index mean-ing the expected flux at 15 GHz (2 cm) should also be ∼ . µ Jy. It is therefore possible that free-free emissionaccounts for up to 10% of the observed 15 GHz flux. Wenote though that since the post-outburst X-ray luminos-ity should be lower than that observed by Grosso et al.(2010), the expected post-outburst radio flux should belower as well.Considering all of the potential sources of the 15 GHzemission, we find that the most likely scenario is acombination of (gyro)synchrotron and free-free emission. We note though that follow-up observations at lower fre-quencies are needed to confirm the spectral index. Itis indeed possible that there is a combination of moreemission mechanisms present at 15 GHz. In order to dis-entangle all the potential sources of emission, 1 −
15 GHzobservations with both high angular resolution and sen-sitivity are necessary. The VLA is currently the leadingfacility in this regime and the observations presented arealready pushing the limits of its capabilities. Therefore,proposed future facilities, such as the ngVLA (White etal. 2018), will be key to fully understanding the under-lying emission mechanisms in EX Lupi and connectingthem in the broader context of EXor/FUors in general. SUMMARYIn this paper, we presented ALMA and VLA con-tinuum observations of the EX Lupi disk in its post-outburst state. We fit radiative transfer models of thecircumstellar dust and find the models are consistentwith grain growth up to at least 3 mm, and possibly ashigh as 1 cm. The grain growth could have been spurredby the recent outburst, which ended in 2008. The best fitdisk model has an ice line located at 0 . − . (cid:12) , accompanied by a relatively compactcharacteristic dust radius of 45 au. The size is in agree-ment with other studies that find EXor/FUor disks to LMA and VLA Observations of EX Lupi Figure 7.
Posterior distribution of the 15 GHz central emission on top of the RT calculated disk emission from the ALMAdata. The most probable values are denoted by the blue lines. be more compact than that of typical protoplanetarydisks.We find a best fit flux of 0.055 mJy at 15 GHz, signifi-cantly more than can be explained by thermal disk emis-sion alone. We explored several potential sources of theemission and conclude that it is likely primarily due to(gyro)synchrotron emission coming from strong stellarmagnetic fields and/or non-negligible free-free emissionfrom accretion shocks and disk heating through X-rayemission.We thank the anonymous referee for feedback thatimproved this paper. This project received supportfrom the European Research Council (ERC) under theEuropean Union’s Horizon 2020 research and innova-tion program under grant agreement No 716155 (SAC-CRED). DS acknowledges support by the DeutscheForschungsgemeinschaft through SPP 1833: “Buildinga Habitable Earth” (SE 1962/6-1). EV and VA ac- knowledge the support of the Large Scientific Project ofthe Russian Ministry of Science and Higher Education“Theoretical and experimental studies of the forma-tion and evolution of extrasolar planetary systems andcharacteristics of exoplanets” (No. 13.1902.21.0039).On behalf of the SACCRED project we are thankfulfor the usage of MTA Cloud (https://cloud.mta.hu/)that helped us achieving the results published in thispaper. This paper makes use of the ALMA datafrom projects ADS/JAO.ALMA
White et al.
Figure 8.
The size of the emitting region and magneticfield strength for various electron energy indices, δ , assuminggyrosynchrotron emission at 15 GHz. The solid black line at δ = 2 represents a typical lower level estimate for δ . ence Foundation operated under cooperative agreementby Associated Universities, Inc. Facilities:
ALMA, VLA
Software:
CASA 5.4.1 (McMullin et al. 2007)REFERENCES ´Abrah´am, P., Juh´asz, A., Dullemond, C.P., et al., 2009,Nat, 459(7244), pp.224-226.´Abrah´am, P., Chen, L., K´osp´al, ´A., et al., 2019, ApJ,887(2), p.156.Andrews, S.M., Wilner, D.J., Hughes, A.M., et al., 2009,ApJ, 700(2), p.1502.Andrews, S.M., Huang, J., P´erez, L.M., et al., 2018, ApJL,869(2), p.L41.Ansdell, M., Williams, J.P., van der Marel, N., et al., 2016,ApJ, 828(1), p.46.Armitage, P.J., 2016, ApJL, 833(2), p.L15.Audard, M., ´Abrah´am, P., Dunham, M.M., et al., 2014,Protostars & Planets VI, 387.Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., etal. 2013, A&A, 558, A33Bailer-Jones, C.A.L., Rybizki, J., Fouesneau, M., et al.,2018, AJ, 156(2), p.58.Banzatti, A., Meyer, M.R., Bruderer, S., et al., 2012, ApJ,745(1), p.90.Banzatti, A., Pascucci, I., Edwards, S., et al., 2019, ApJ,870(2), p.76.Baryshev, A.M., Hesper, R., Mena, F.P., et al., 2015, A&A,577, A129Berger, E., Ball, S., Becker, K. M., et al. 2001, Natur, 410,338Booth, M., Jord´an, A., Casassus, S., et al., MNRAS,460(1), pp.L10-L14. Bouvier, J., Alencar, S. H. P., Harries, T. J., et al., 2007,Protostars & Planets VBrauer, F., Henning, T., & Dullemond, C.P., 2008, A&A,487(1), pp.L1-L4.Brogan, C.L., P´erez, L.M., Hunter, T.R., et al., 2015,ApJL, 808(1), p.L3.Brown, P.D. & Charnley, S.B., 1990, MNRAS, 244,pp.432-443.Cambr´esy, L. 1999, A&A, 345, 965Cieza, L.A., Casassus, S., Tobin, J., et al., 2016, Nature,535(7611), p.258.Cieza, L. A., Ru´ız-Rodr´ıguez, D., Perez, S., et al. 2018,MNRAS, 474, 4347D’Angelo, C. R., Spruit, H. C., 2012, MNRAS, 420, 416Donati, J., Paletou, F., Bouvier, J. et al., 2005, Nat., 438,466-469Dorschner, J., Begemann, B., Henning, T., et al., 1995,A&A, 300, 503Dulk, G. A., 1985, ARA&A, 23, 169Dullemond, C.P., Juh´asz, A., Pohl, A., et al. , 2012,Astrophysics Source Code Library, ascl:1202.015Flock, M., Nelson, R.P., Turner, N.J., et al., 2017, ApJ,850(2), p.131.Frasca, A., Biazzo, K., Alcala, J. M., et al. 2017, A&A, 602,A33Grosso, N., Hamaguchi, K., Kastner, J.H., et al., 2010,A&A, 522, p.A56.
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