Magnetic topologies of young suns: The weak-line T Tauri stars TWA 6 and TWA 8A
C. A. Hill, C. P. Folsom, J.-F. Donati, G. J. Herczeg, G. A. J. Hussain, S. H. P. Alencar, S. G. Gregory, MaTYSSE collaboration
MMNRAS , 1–27 (2018) Preprint 20 February 2019 Compiled using MNRAS L A TEX style file v3.0
Magnetic topologies of young suns:The weak-line T Tauri stars TWA 6 and TWA 8A
C. A. Hill (cid:63) , C. P. Folsom , J.-F. Donati , G. J. Herczeg , G. A. J. Hussain , ,S. H. P. Alencar , S. G. Gregory and the MaTYSSE collaboration. IRAP, Universit´e de Toulouse, CNRS, UPS, CNES, 14 Avenue Edouard Belin, Toulouse, F-31400, France Kavli Institute for Astronomy and Astrophysics, Peking University, Yi He Yuan Lu 5, Haidian Qu, Beijing 100871, China ESO, Karl-Schwarzschild-Str. 2, D-85748 Garching, Germany Departamento de F`ısica - ICEx-UFMG, Av. Antˆonio Carlos, 6627, 30270–901 Belo Horizonte, MG, Brazil University of St Andrews, St Andrews, KY16 9SS, UK
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We present a spectropolarimetric study of two weak-line T Tauri stars (wTTSs),TWA 6 and TWA 8A, as part of the MaTYSSE (Magnetic Topologies of Young Starsand the Survival of close-in giant Exoplanets) program. Both stars display significantZeeman signatures that we have modelled using Zeeman Doppler Imaging (ZDI). Themagnetic field of TWA 6 is split equally between poloidal and toroidal components,with the largest fraction of energy in higher-order modes, with a total unsigned fluxof 840 G, and a poloidal component tilted ◦ from the rotation axis. TWA 8A hasa 70 per cent poloidal field, with most of the energy in higher-order modes, with anunsigned flux of 1.4 kG (with a magnetic filling factor of 0.2), and a poloidal fieldtilted ◦ from the rotation axis. Spectral fitting of the very strong field in TWA 8A(in individual lines, simultaneously for Stokes I and V ) yielded a mean magnetic fieldstrength of . ± . kG. The higher field strengths recovered from spectral fittingsuggests that a significant proportion of magnetic energy lies in small-scale fields thatare unresolved by ZDI. So far, wTTSs in MaTYSSE appear to show that the poloidal-field axisymmetry correlates with the magnetic field strength. Moreover, it appearsthat classical T Tauri stars (cTTSs) and wTTSs are mostly poloidal and axisymmet-ric when mostly convective and cooler than ∼ K, with hotter stars being lessaxisymmetric and poloidal, regardless of internal structure.
Key words: stars: magnetic fields – techniques: polarimetric – stars: formation –stars: imaging – stars: individual: TWA 6 – stars: individual: TWA 8A
During the first few hundred thousand years of low-massstar formation, class-I pre-main sequence (PMS) stars ac-crete significant amounts of material from their surround-ing dusty envelopes. After around 0.5 Myr, these protostarsemerge from their dusty cocoons and are termed classicalT Tauri stars (cTTSs / class-II PMS stars) if they are stillaccreting from their surrounding discs, or weak-line T Tauristars (wTTSs / class-III PMS stars) if they have exhaustedthe gas from the inner disc cavity. During the PMS phase,stellar magnetic fields have their largest impact on the evo-lution of the star. These fields control accretion processesand trigger outflows/jets (Bouvier et al. 2007), dictate the (cid:63)
E-mail: [email protected] star’s angular momentum evolution by enforced spin-downthrough star-disc coupling (e.g., Davies et al. 2014), andalter disc dynamics and planet formation (Baruteau et al.2014). Moreover, as PMS stars are gravitationally contract-ing towards the MS, the change in stellar structure from fullyto partly convective is expected to alter the stellar dynamomechanism and the resulting magnetic field topology.Previous work through the MaPP (Magnetic Protostarsand Planets) survey revealed that the large-scale topologiesof 11 cTTSs remained relatively simple and mainly poloidalwhen the host star is still fully or largely convective, but be-come much more complex when the host star turns mostlyradiative (Gregory et al. 2012; Donati et al. 2013). This sur-vey concluded that these fields likely originated from a dy-namo, varying over time-scales of a few years (Donati et al. © a r X i v : . [ a s t r o - ph . S R ] F e b C. A. Hill et al. ± Myr (Bell et al. 2015), is in tran-sition between the T Tauri and the post T Tauri phase, andthus provides a very interesting period in which to study theproperties of the member stars as they spin-up towards theZAMS. Our phase-resolved spectropolarimetric observationsare documented in Section 2, with the stellar and disc prop-erties presented in Section 3. We discuss the spectral energydistributions, several emission lines, and the accretion statusof both stars in Section 3.2. In Section 4 we present our re-sults after applying our tomographic modelling technique tothe data. In Section 5 we present our results of our spectralfitting to the Stokes I and Stokes V spectra, and in Section 6we discuss our analysis of the filtered RV curves. Finally, wediscuss and summarize our results and their implications forlow-mass star and planet formation in Section 7. Spectropolarimetric observations of TWA 6 were taken inFebruary 2014, with observations of TWA 8A taken inMarch and April 2015, both using ESPaDOnS at the 3.6-m CFHT. Spectra from ESPaDOnS span the entire opticaldomain (from 370–1000 nm) at a resolution of 65,000 (i.e.,a resolved velocity element of 4.6 kms − ) over the full wave-length range, in both circular or linear polarization (Donati2003).A total of 22 circularly-polarized (Stokes V ) and unpo-larized (Stokes I ) spectra were collected for TWA 6 over atimespan of 16 nights, corresponding to around 29.6 rotationcycles (where P rot = . d, Kiraga 2012). Time samplingwas fairly regular, with the longest gap of 6 nights occurringtowards the end of the run. For TWA 8A, 15 spectra werecollected with regular time sampling over a 15 night times- pan, corresponding to around 3.2 rotation cycles (where P rot = 4.638 d, Kiraga 2012).All polarization spectra consist of four individual sub-exposures (each lasting 406 s for TWA 6, and 1115 s forTWA 8A), taken in different polarimeter configurations toallow the removal of all spurious polarization signatures atfirst order. All raw frames were processed using the LibreESpRIT software package, which performs bias subtraction,flat fielding, wavelength calibration, and optimal extractionof (un)polarized ´echelle spectra, as described in the previ-ous papers of the series (Donati et al. 1997, also see Donatiet al. 2010, 2011, 2014), to which the reader is referred formore information. The peak signal-to-noise ratios (S/N, per2.6 kms − velocity bin) achieved on the collected spectrarange between 111–197 (median 164) for TWA 6, and 209–369 (median 340) for TWA 8A, depending on weather/seeingconditions. All spectra are automatically corrected for spec-tral shifts resulting from instrumental effects (e.g., mechan-ical flexures, temperature or pressure variations) using at-mospheric telluric lines as a reference. This procedure pro-vides spectra with a relative RV precision of better than0.030 kms − (e.g. Moutou et al. 2007; Donati et al. 2008). Ajournal of all observations is presented in Table 1 for bothstars. Both stars are part of the TW Hya association (TWA, e.g.,Jayawardhana et al. 1999; Webb et al. 1999; Donaldson et al.2016), one of the closest young star associations at a distanceof (cid:39) pc (e.g., Zuckerman & Song 2004). Furthermore, atan age of ± Myr (Bell et al. 2015), TWA is at a crucialevolutionary phase where star-disk interactions have ceased,and where the T Tauri stars are rapidly spinning up as theycontinue their gravitational contraction towards the mainsequence (e.g., Rebull et al. 2004).Both stars are classed as T Tauri due to strongLi i − ) and0.38 ˚A (17 kms − ) for TWA 6 and TWA 8A, respectively(slightly lower than the 0.56 ˚A and 0.53 ˚A found by Torreset al. 2003). Furthermore, our spectra show that the strengthof Li i . ± . d period of Lawson & Crause (2005), andthe . ± . d period of Skelly et al. (2008). ForTWA 8A, we adopt the photometric period of 4.638 d (Ki-raga 2012), in excellent agreement with the . ± . dperiod found by Lawson & Crause (2005), the . ± . dperiod of Messina et al. (2010), and the 4.639 d period foundby applying a Lomb-Scargle periodogram analysis to Super-WASP photometric data (Butters et al. 2010). The rota-tional cycles of TWA 6 and TWA 8A (denoted E and E MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A Table 1.
Journal of ESPaDOnS observations of TWA 6 (first22 rows) and TWA 8A (last 15 rows), each consisting of a se-quence of 4 subexposures lasting 406 s and 1115 s for TWA 6and TWA 8A, respectively. Columns 1–4 list (i) the UT date ofthe observation, (ii) the corresponding UT time at mid exposure,(iii) the Barycentric Julian Date (BJD), and (iv) the peak signal-to-noise ratio (per 2.6 kms − velocity bin) of each observation.Columns 5 and 6 respectively list the S/N in Stokes I LSD pro-files (per 1.8 kms − velocity bin), and the rms noise level (relativeto the unpolarized continuum level I c and per 1.8 kms − velocitybin) in the Stokes V LSD profiles. Column 6 indicates the rota-tional cycle associated with each exposure, using the ephemeridesgiven in Equation 1.Date UT BJD S/N S/N lsd σ lsd Cycle(2014) (hh:mm:ss) (2456693.9+) (0.01%)Feb 04 11:15:00 0.07239 160 1796 5.6 0.151Feb 04 12:17:52 0.11605 184 2260 4.5 0.232Feb 07 10:28:34 3.04027 134 1619 6.2 5.638Feb 07 11:30:04 3.08299 131 1559 6.4 5.717Feb 07 13:04:25 3.14851 158 1849 5.4 5.838Feb 09 09:27:53 4.99822 168 1990 5.1 9.258Feb 09 10:46:58 5.05313 169 1973 5.1 9.359Feb 09 11:48:45 5.09605 132 1639 6.1 9.439Feb 10 11:08:25 6.06807 163 1914 5.3 11.236Feb 10 12:10:38 6.11128 178 2126 4.7 11.316Feb 11 09:37:38 7.00507 183 2273 4.4 12.968Feb 11 11:05:43 7.06624 197 2461 4.1 13.081Feb 11 11:54:04 7.09981 169 1922 5.2 13.143Feb 12 09:21:45 7.99407 164 1933 5.2 14.797Feb 12 11:22:19 8.07780 159 1869 5.4 14.951Feb 12 12:49:30 8.13834 160 1855 5.4 15.063Feb 13 10:35:31 9.04533 111 1514 6.6 16.740Feb 13 13:06:11 9.14997 180 2094 4.8 16.934Feb 19 09:23:25 14.99545 160 1847 5.4 27.741Feb 19 10:51:16 15.05645 181 2223 4.5 27.853Feb 19 12:29:16 15.12451 192 2387 4.2 27.979Feb 20 12:06:25 16.10867 137 1345 7.5 29.799(2015) (2457107.9+)Mar 25 11:43:05 0.06756 338 3847 2.6 0.020Mar 26 11:04:43 1.04090 343 3812 2.6 0.230Mar 27 11:40:03 2.06545 340 3863 2.6 0.451Mar 28 11:30:18 3.05868 341 3841 2.6 0.665Mar 29 12:16:00 4.09040 302 3348 3.0 0.887Mar 30 11:49:48 5.07220 369 4244 2.4 1.099Mar 31 08:28:33 5.93245 357 4071 2.5 1.285Apr 01 08:26:55 6.93130 349 3960 2.5 1.500Apr 03 11:25:50 9.05552 253 2670 3.8 1.958Apr 04 11:34:15 10.06136 355 4091 2.5 2.175Apr 05 08:42:10 10.94184 332 3764 2.7 2.365Apr 06 08:30:36 11.93379 353 4013 2.5 2.579Apr 08 09:13:10 13.97061 202 1754 5.7 3.018Apr 09 07:18:42 14.90036 253 2819 3.6 3.218Apr 09 08:45:35 14.95143 309 3621 2.8 3.229 in Equation 1) are computed from Barycentric Julian Dates(BJDs) according to the (arbitrary) ephemerides:BJD (d) = . + . E (for TWA 6)BJD (d) = . + . E (for TWA 8A) (1) To determine the T eff and log g of our target stars, we ap-plied our automatic spectral classification tool (discussed inDonati et al. 2012) to several of the highest S/N spectra forboth stars. We fit the observed spectrum using multiple win-dows in the wavelength ranges 515–520 nm and 600–620 nm(using Kurucz model atmospheres, Kurucz 1993), in a sim-ilar way to the method of Valenti & Fischer (2005). Thisprocess yields estimates of T eff and log g , where the opti-mum parameters are those that minimize χ , with errorsbars determined from the curvature of the χ landscape atthe derived minimum.For TWA 6, we find that T eff = ± K and log g = . ± . (with g in cgs units). While two-temperaturemodelling such as that carried out by Gully-Santiago et al.(2017) would provide a better estimate of T eff and the frac-tional spot coverage, for our purposes, a homogeneous modelis sufficient. For TWA 6, we adopt the V and B magnitudesof . ± . and . ± . from (Messina et al. 2010),and assuming a spot coverage of the visible stellar hemi-sphere of ∼ per cent (typical for such active stars, seeSection 4), we derive an unspotted V magnitude of . ± . .We note that assuming a different spot coverage (such as 0or 50 per cent) places our derived parameters within ourquoted error bars. Using the relation from Pecaut & Ma-majek (2013), the expected visual bolometric correction forTWA 6 is BC v = − . ± . , and as there is no evidenceof extinction to TWA members (e.g. Stelzer et al. 2013), weadopt A v = . Combining V , BC v , A v and the trigonomet-ric parallax distance found by Gaia of . ± . pc (cor-responding to a distance modulus of . ± . , Gaia Col-laboration et al. 2016, 2018, in excellent agreement with the . ± . pc of Donaldson et al. 2016), we obtain an absolutebolometric magnitude of . ± . , or equivalently, a loga-rithmic luminosity relative to the Sun of − . ± . . Whencombined with the photospheric temperature obtained pre-viously, we obtain a radius of . ± . R (cid:12) .Coupling P rot (see Equation 1) with the measured v sin i of . ± . kms − (see Section 4), we can infer that R (cid:63) sin i is equal to . ± . R (cid:12) , where R (cid:63) and i denote the stel-lar radius and the inclination of its rotation axis to theline of sight. By comparing the luminosity-derived radiusto that from the stellar rotation, we derive that i is equalto ◦ + − , in excellent agreement with that found using ourtomographic modelling (see Section 4). Using the evolution-ary models of Siess et al. (2000) (assuming solar metallicityand including convective overshooting), we find that TWA 6has a mass of . ± . M (cid:12) , with an age of ± Myr(see the H-R diagram in Figure 1, with evolutionary tracksand corresponding isochrones). Similarly, using the evolu-tionary models of Baraffe et al. (2015), we obtain a mass of . ± . M (cid:12) and an age of ± Myr.For TWA 8A, our spectral fitting code yields a best-fit at T eff = ± K and log g = . ± . , however, this T eff is in the regime where the Kurucz synthetic spectra areconsidered unreliable in terms of temperature. To addressthis issue, we are currently working on a more advancedspectral classification tool based on PHOENIX model at-mospheres and synthetic spectra (see Allard 2014). In themean time for the work presented here, we determined T eff for TWA 8A from the observed B − V value and the rela- MNRAS000
Journal of ESPaDOnS observations of TWA 6 (first22 rows) and TWA 8A (last 15 rows), each consisting of a se-quence of 4 subexposures lasting 406 s and 1115 s for TWA 6and TWA 8A, respectively. Columns 1–4 list (i) the UT date ofthe observation, (ii) the corresponding UT time at mid exposure,(iii) the Barycentric Julian Date (BJD), and (iv) the peak signal-to-noise ratio (per 2.6 kms − velocity bin) of each observation.Columns 5 and 6 respectively list the S/N in Stokes I LSD pro-files (per 1.8 kms − velocity bin), and the rms noise level (relativeto the unpolarized continuum level I c and per 1.8 kms − velocitybin) in the Stokes V LSD profiles. Column 6 indicates the rota-tional cycle associated with each exposure, using the ephemeridesgiven in Equation 1.Date UT BJD S/N S/N lsd σ lsd Cycle(2014) (hh:mm:ss) (2456693.9+) (0.01%)Feb 04 11:15:00 0.07239 160 1796 5.6 0.151Feb 04 12:17:52 0.11605 184 2260 4.5 0.232Feb 07 10:28:34 3.04027 134 1619 6.2 5.638Feb 07 11:30:04 3.08299 131 1559 6.4 5.717Feb 07 13:04:25 3.14851 158 1849 5.4 5.838Feb 09 09:27:53 4.99822 168 1990 5.1 9.258Feb 09 10:46:58 5.05313 169 1973 5.1 9.359Feb 09 11:48:45 5.09605 132 1639 6.1 9.439Feb 10 11:08:25 6.06807 163 1914 5.3 11.236Feb 10 12:10:38 6.11128 178 2126 4.7 11.316Feb 11 09:37:38 7.00507 183 2273 4.4 12.968Feb 11 11:05:43 7.06624 197 2461 4.1 13.081Feb 11 11:54:04 7.09981 169 1922 5.2 13.143Feb 12 09:21:45 7.99407 164 1933 5.2 14.797Feb 12 11:22:19 8.07780 159 1869 5.4 14.951Feb 12 12:49:30 8.13834 160 1855 5.4 15.063Feb 13 10:35:31 9.04533 111 1514 6.6 16.740Feb 13 13:06:11 9.14997 180 2094 4.8 16.934Feb 19 09:23:25 14.99545 160 1847 5.4 27.741Feb 19 10:51:16 15.05645 181 2223 4.5 27.853Feb 19 12:29:16 15.12451 192 2387 4.2 27.979Feb 20 12:06:25 16.10867 137 1345 7.5 29.799(2015) (2457107.9+)Mar 25 11:43:05 0.06756 338 3847 2.6 0.020Mar 26 11:04:43 1.04090 343 3812 2.6 0.230Mar 27 11:40:03 2.06545 340 3863 2.6 0.451Mar 28 11:30:18 3.05868 341 3841 2.6 0.665Mar 29 12:16:00 4.09040 302 3348 3.0 0.887Mar 30 11:49:48 5.07220 369 4244 2.4 1.099Mar 31 08:28:33 5.93245 357 4071 2.5 1.285Apr 01 08:26:55 6.93130 349 3960 2.5 1.500Apr 03 11:25:50 9.05552 253 2670 3.8 1.958Apr 04 11:34:15 10.06136 355 4091 2.5 2.175Apr 05 08:42:10 10.94184 332 3764 2.7 2.365Apr 06 08:30:36 11.93379 353 4013 2.5 2.579Apr 08 09:13:10 13.97061 202 1754 5.7 3.018Apr 09 07:18:42 14.90036 253 2819 3.6 3.218Apr 09 08:45:35 14.95143 309 3621 2.8 3.229 in Equation 1) are computed from Barycentric Julian Dates(BJDs) according to the (arbitrary) ephemerides:BJD (d) = . + . E (for TWA 6)BJD (d) = . + . E (for TWA 8A) (1) To determine the T eff and log g of our target stars, we ap-plied our automatic spectral classification tool (discussed inDonati et al. 2012) to several of the highest S/N spectra forboth stars. We fit the observed spectrum using multiple win-dows in the wavelength ranges 515–520 nm and 600–620 nm(using Kurucz model atmospheres, Kurucz 1993), in a sim-ilar way to the method of Valenti & Fischer (2005). Thisprocess yields estimates of T eff and log g , where the opti-mum parameters are those that minimize χ , with errorsbars determined from the curvature of the χ landscape atthe derived minimum.For TWA 6, we find that T eff = ± K and log g = . ± . (with g in cgs units). While two-temperaturemodelling such as that carried out by Gully-Santiago et al.(2017) would provide a better estimate of T eff and the frac-tional spot coverage, for our purposes, a homogeneous modelis sufficient. For TWA 6, we adopt the V and B magnitudesof . ± . and . ± . from (Messina et al. 2010),and assuming a spot coverage of the visible stellar hemi-sphere of ∼ per cent (typical for such active stars, seeSection 4), we derive an unspotted V magnitude of . ± . .We note that assuming a different spot coverage (such as 0or 50 per cent) places our derived parameters within ourquoted error bars. Using the relation from Pecaut & Ma-majek (2013), the expected visual bolometric correction forTWA 6 is BC v = − . ± . , and as there is no evidenceof extinction to TWA members (e.g. Stelzer et al. 2013), weadopt A v = . Combining V , BC v , A v and the trigonomet-ric parallax distance found by Gaia of . ± . pc (cor-responding to a distance modulus of . ± . , Gaia Col-laboration et al. 2016, 2018, in excellent agreement with the . ± . pc of Donaldson et al. 2016), we obtain an absolutebolometric magnitude of . ± . , or equivalently, a loga-rithmic luminosity relative to the Sun of − . ± . . Whencombined with the photospheric temperature obtained pre-viously, we obtain a radius of . ± . R (cid:12) .Coupling P rot (see Equation 1) with the measured v sin i of . ± . kms − (see Section 4), we can infer that R (cid:63) sin i is equal to . ± . R (cid:12) , where R (cid:63) and i denote the stel-lar radius and the inclination of its rotation axis to theline of sight. By comparing the luminosity-derived radiusto that from the stellar rotation, we derive that i is equalto ◦ + − , in excellent agreement with that found using ourtomographic modelling (see Section 4). Using the evolution-ary models of Siess et al. (2000) (assuming solar metallicityand including convective overshooting), we find that TWA 6has a mass of . ± . M (cid:12) , with an age of ± Myr(see the H-R diagram in Figure 1, with evolutionary tracksand corresponding isochrones). Similarly, using the evolu-tionary models of Baraffe et al. (2015), we obtain a mass of . ± . M (cid:12) and an age of ± Myr.For TWA 8A, our spectral fitting code yields a best-fit at T eff = ± K and log g = . ± . , however, this T eff is in the regime where the Kurucz synthetic spectra areconsidered unreliable in terms of temperature. To addressthis issue, we are currently working on a more advancedspectral classification tool based on PHOENIX model at-mospheres and synthetic spectra (see Allard 2014). In themean time for the work presented here, we determined T eff for TWA 8A from the observed B − V value and the rela- MNRAS000 , 1–27 (2018)
C. A. Hill et al. tion between T eff and B − V for young stars from Pecaut& Mamajek (2013) (and by assuming A v = ). We adopt V = . ± . and B = . ± . from Henden et al.(2016), with B − V = . ± . . Using this B − V withthe relation between intrinsic colour and T eff for young starsfound by Pecaut & Mamajek (2013), and assuming A v = ,we derive T eff = ± K. Combining the observed V magnitude with the expected BC v for TWA 8A of − . ± . (Pecaut & Mamajek 2013) with the trigonometric parallaxdistance of . ± . pc as found by Gaia (Gaia Col-laboration et al. 2016, 2018, corresponding to a distancemodulus of . ± . , in excellent agreement with the . ± . pc of Donaldson et al. 2016 and . + . − . pc ofRiedel et al. 2014), we obtain an absolute bolometric mag-nitude of . ± . , or equivalently, a logarithmic luminosityrelative to the Sun of − . ± . . When combined with thephotospheric temperature obtained previously, we obtain aradius of . ± . R (cid:12) . Combining this radius with the massderived below (from Baraffe et al. 2015 evolutionary mod-els), we estimate log g = . ± . .Combining P rot (see Equation 1) with the v sin i of . ± . kms − (see Section 5), we find R (cid:63) sin i = . ± . R (cid:12) ,yielding i = ◦ + − , in good agreement with our tomographicmodelling (see Section 4). Using Siess et al. (2000) modelswe find M = . ± . M (cid:12) , with an age of ± Myr.Using the evolutionary models of Baraffe et al. (2015), wefind M= . ± . M (cid:12) , with an age of ± Myr.We note that we do not consider the formal error barson the derived masses and ages to be representative of thetrue uncertainties, given the inherent limitations of theseevolutionary models. Furthermore, we note that for internalconsistency with previous MaPP and MaTYSSE results, thevalues from the Siess et al. (2000) models should be refer-enced. We note that the ages derived here are consistent withthe age of the young TWA moving group (of ± Myr, Bellet al. 2015), and that both evolutionary models suggest thatTWA 6 has a mostly radiative interior, where as TWA 8Ais mostly (or fully) convective.The temperatures measured here are hotter than ex-pected from spectral types estimated from red-optical spec-tra that cover TiO and other molecular bands (White &Hillenbrand 2004; Stelzer et al. 2013; Herczeg & Hillenbrand2014). This discrepancy is consistent with past wavelength-dependent differences in photospheric temperatures fromyoung stars, which may be introduced by spots (e.g. Bouvier& Appenzeller 1992; Debes et al. 2013; Gully-Santiago et al.2017). The interpretation of these differences is not yet un-derstood. Use of the lower temperatures that are measuredat longer wavelengths from molecular bands would lead tolower masses and younger ages. Our temperatures are accu-rate measurements of the photospheric emission from 5000–6000 ˚A and are consistent with all temperature measure-ments for stars in the MaTYSSE program.
Spectral Energy Distributions (SEDs) of TWA 6 andTWA 8A were constructed using photometry sourced fromthe DENIS survey (DENIS Consortium 2005), the AAVSOPhotometric All Sky Survey (APASS, Henden et al. 2015),the GALEX all-sky imaging survey (Bianchi et al. 2011), the T eff (K) log(L/L fl ) TWA 6TWA 8A
Figure 1.
H-R diagram showing the stellar evolutionary tracksprovided by Siess et al. (2000, blue solid lines) and Baraffe et al.(2015, black solid lines) for masses of 0.3, 0.4, 0.5, 0.9 and 1.0 M (cid:12) .Blue dashed lines show the corresponding isochrones for ages 5,10 & 20 Myr, and blue dotted lines mark the 0 and 50 per centfractional radius for the bottom of the convective envelope, bothfor for Siess et al. (2000) models.
TYCHO-2 catalogue (Høg et al. 2000), the WISE, Spitzerand Gaia catalogues (Wright et al. 2010; Werner et al. 2004;Gaia Collaboration et al. 2016, 2018), and Torres et al.(2006). We note that deep, sensitive sub-mm and mm pho-tometry are not currently available for our targets. Com-paring the SEDs (shown in Fig. 2) to PHOENIX-BT-Settlsynthetic spectra (Allard 2014), we find that neither TWA 6nor TWA 8A have an infrared excess up to 23.675 µ m, indi-cating that both objects have dissipated their circumstellardiscs. Given that the SEDs of TWA 6 and TWA 8A show noevidence of an infra-red excess, both stars are likely disc-lessand are not accreting (also see e.g., Weinberger et al. 2004;Low et al. 2005). However, for completeness, in Appendix Bwe present several metrics that determine the accretion ratesfrom emission lines (if accretion were present), with our anal-ysis showing that chromospheric emission likely dominatesthe line formation for both targets, confirming their classi-fication as wTTSs. We find that TWA 6 shows core Ca ii infrared triplet (IRT)emission (see Fig. A1) with a mean equivalent width (EW)of around 0.3 ˚A (10.7 kms − ), similar to what is expectedfrom chromospheric emission for such PMS stars (e.g. In-gleby et al. 2011), and lower than that for accreting cTTSs(e.g. Donati et al. 2007). The core Ca ii IRT emission is some-what variable, with both red and blue-shifted peaks (wherethe red-shifted emission is generally larger), and where theemission is significantly higher at cycles 9.258, 9.359, 14.951and 15.063. We note that there are some differences in theStokes V line profiles of the Ca ii IRT, that are likely due totheir different atmospheric formation heights. We note thatno significant Zeeman signatures are detected in Ca ii H&K,Ca ii IRT or He i α and MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A ( m) -15 -14 -13 -12 F (W/m²) ( m) -15 -14 -13 -12 F (W/m²)
Figure 2.
Spectral energy distributions (SEDs) of TWA 6 (top)and TWA 8A (bottom), where the photometric data (see text)are shown as black dots, and where PHOENIX-BT-Settl modelspectra (Allard 2014) are shown as a red line. For the model spec-tra we adopt T eff = K and 3700 K for TWA 6 and TWA 8Arespectively, and log g = . for both stars, as well as the otherparameters given in Table 2, adopting the extinction relation ofCardelli et al. (1989). Furthermore, we assume that both starshave a 30 per cent surface coverage of cool starspots (see Sec-tion 4.1), and so the displayed spectra have a 30 per cent contri-bution from a spectrum that is 1000 K cooler. H β emission that displays relatively little variability overthe ∼ rotation cycles (see Fig. A1). For H α , significantlyhigher flux is seen in cycles 9.258, 9.359 and 9.439, withthe extra emission arising in a predominantly red-shiftedcomponent. Moreover, cycle 14.797 displays a significantlyhigher flux that is symmetric about zero velocity. This higherflux is also seen in H β , with larger emission for cycles 9.258and 9.359 (both asymmetric, red-shifted), 14.797 (symmet-ric) and 14.951 (asymmetric, red-shifted). Given that theseemission features occur at similar phases in Ca ii IRT, H α and H β , and are also short lived, they likely stem from thesame formation mechanism in the form of stellar promi-nences that are rotating away from the observer. This con-clusion is also supported by the mapped magnetic topology,as we see closed magnetic loops off the stellar limb, alongwhich prominence material may flow. To better determinethe nature of the emission and its variability, one can cal- culate variance profiles and autocorrelation matrices, as de-scribed in Johns & Basri (1995) and given by: V λ = (cid:205) ni = (cid:16) I λ, i − I λ (cid:17) n − (2)Fig. A4 shows that the H α emission varies from around -200 kms − to +300 kms − (similar to that found previouslyfor TWA 6 by Skelly et al. 2008), well beyond the v sin i of72.6 kms − , and with most of the variability in a red-shiftedcomponent. Furthermore, the autocorrelation matrix showsstrong correlation of the low-velocity components, indicatinga common origin. We find that H β and He i D3 show negli-gible variability, with a relatively low spectral S/N limitingthe analysis.In the case of TWA 8A, core Ca ii IRT emission ispresent with a mean EW of around 0.37 ˚A (11.9 kms − , seeFig. A2). This emission is mostly non-variable, with only cy-cle 1.958 showing significantly higher (symmetric) emission.Furthermore, the Zeeman signatures in the Stokes V lineprofiles (see Fig. A3) have the same sign as those of the ab-sorption lines (see Fig. 3), and so are of photospheric origin.TWA 8A also displays double-peaked H α and H β emission,with a peak separation of around 40 kms − . This separa-tion lies well within the co-rotation radius, and is only a fewtimes larger than the v sin i of 4.82 kms − , indicating that thesource of the emission is chromospheric. The lines are some-what variable, with a significant increase in emission (forboth H α and H β ) at cycles 1.958, 2.579 and 3.018. Fig. A5shows the variance profiles and autocorrelation matrices ofH α , H β and He i D3, Here we see that for H α , the variabil-ity concentrates in two peaks centred around -50 kms − and+75 kms − (ranging ± kms − ), with variability in H β likewise occurring in two peaks centred around -75 kms − and +65 kms − (ranging ± kms − ), with both autocor-relation matrices showing the low-velocity components tobe highly correlated. For He i D3 we find that the variabil-ity is single peaked, centred around zero velocity, with onlylow-velocity components showing significant correlation. Wealso note that the H α emission of TWA 8A shows strongZeeman signatures (see Fig. A3) that are opposite in signto those of the absorption lines (see Fig. 5), as expected forchromospheric emission. In order to map both the surface brightness and magneticfield topology of TWA 6 and TWA 8A, we have appliedour dedicated stellar-surface tomographic-imaging packageto the data sets described in Section 2. In doing this, weassumed that the observed variability is dominated by ro-tational modulation (and optionally differential rotation).Our imaging code simultaneously inverts the time series ofStokes I and Stokes V profiles into brightness maps (featur-ing both cool spots and warm plages) and magnetic maps(with poloidal and toroidal components, using a sphericalharmonic decomposition). For brightness imaging, a copyof a local line profile is assigned to each pixel on a spher-ical grid, and the total line profile is found by summing MNRAS000
Spectral energy distributions (SEDs) of TWA 6 (top)and TWA 8A (bottom), where the photometric data (see text)are shown as black dots, and where PHOENIX-BT-Settl modelspectra (Allard 2014) are shown as a red line. For the model spec-tra we adopt T eff = K and 3700 K for TWA 6 and TWA 8Arespectively, and log g = . for both stars, as well as the otherparameters given in Table 2, adopting the extinction relation ofCardelli et al. (1989). Furthermore, we assume that both starshave a 30 per cent surface coverage of cool starspots (see Sec-tion 4.1), and so the displayed spectra have a 30 per cent contri-bution from a spectrum that is 1000 K cooler. H β emission that displays relatively little variability overthe ∼ rotation cycles (see Fig. A1). For H α , significantlyhigher flux is seen in cycles 9.258, 9.359 and 9.439, withthe extra emission arising in a predominantly red-shiftedcomponent. Moreover, cycle 14.797 displays a significantlyhigher flux that is symmetric about zero velocity. This higherflux is also seen in H β , with larger emission for cycles 9.258and 9.359 (both asymmetric, red-shifted), 14.797 (symmet-ric) and 14.951 (asymmetric, red-shifted). Given that theseemission features occur at similar phases in Ca ii IRT, H α and H β , and are also short lived, they likely stem from thesame formation mechanism in the form of stellar promi-nences that are rotating away from the observer. This con-clusion is also supported by the mapped magnetic topology,as we see closed magnetic loops off the stellar limb, alongwhich prominence material may flow. To better determinethe nature of the emission and its variability, one can cal- culate variance profiles and autocorrelation matrices, as de-scribed in Johns & Basri (1995) and given by: V λ = (cid:205) ni = (cid:16) I λ, i − I λ (cid:17) n − (2)Fig. A4 shows that the H α emission varies from around -200 kms − to +300 kms − (similar to that found previouslyfor TWA 6 by Skelly et al. 2008), well beyond the v sin i of72.6 kms − , and with most of the variability in a red-shiftedcomponent. Furthermore, the autocorrelation matrix showsstrong correlation of the low-velocity components, indicatinga common origin. We find that H β and He i D3 show negli-gible variability, with a relatively low spectral S/N limitingthe analysis.In the case of TWA 8A, core Ca ii IRT emission ispresent with a mean EW of around 0.37 ˚A (11.9 kms − , seeFig. A2). This emission is mostly non-variable, with only cy-cle 1.958 showing significantly higher (symmetric) emission.Furthermore, the Zeeman signatures in the Stokes V lineprofiles (see Fig. A3) have the same sign as those of the ab-sorption lines (see Fig. 3), and so are of photospheric origin.TWA 8A also displays double-peaked H α and H β emission,with a peak separation of around 40 kms − . This separa-tion lies well within the co-rotation radius, and is only a fewtimes larger than the v sin i of 4.82 kms − , indicating that thesource of the emission is chromospheric. The lines are some-what variable, with a significant increase in emission (forboth H α and H β ) at cycles 1.958, 2.579 and 3.018. Fig. A5shows the variance profiles and autocorrelation matrices ofH α , H β and He i D3, Here we see that for H α , the variabil-ity concentrates in two peaks centred around -50 kms − and+75 kms − (ranging ± kms − ), with variability in H β likewise occurring in two peaks centred around -75 kms − and +65 kms − (ranging ± kms − ), with both autocor-relation matrices showing the low-velocity components tobe highly correlated. For He i D3 we find that the variabil-ity is single peaked, centred around zero velocity, with onlylow-velocity components showing significant correlation. Wealso note that the H α emission of TWA 8A shows strongZeeman signatures (see Fig. A3) that are opposite in signto those of the absorption lines (see Fig. 5), as expected forchromospheric emission. In order to map both the surface brightness and magneticfield topology of TWA 6 and TWA 8A, we have appliedour dedicated stellar-surface tomographic-imaging packageto the data sets described in Section 2. In doing this, weassumed that the observed variability is dominated by ro-tational modulation (and optionally differential rotation).Our imaging code simultaneously inverts the time series ofStokes I and Stokes V profiles into brightness maps (featur-ing both cool spots and warm plages) and magnetic maps(with poloidal and toroidal components, using a sphericalharmonic decomposition). For brightness imaging, a copyof a local line profile is assigned to each pixel on a spher-ical grid, and the total line profile is found by summing MNRAS000 , 1–27 (2018)
C. A. Hill et al. over all visible pixels (at a given phase), where the pixelintensities are scaled iteratively to fit the observed data.For magnetic imaging, the Zeeman signatures are fit using aspherical-harmonic decomposition of potential and toroidalfield components, where the weighting of the harmonics arescaled iteratively (Donati 2001). The data are fit to an aim χ , with the optimal fit determined using the maximum-entropy routine of Skilling & Bryan (1984), and where thechosen map is that which contains least information (whereentropy is maximized) required to fit the data. For furtherdetails about the specific application of our code to wTTSs,we refer the reader to previous papers in the series (e.g.,Donati et al. 2010, 2014, 2015).As with previous studies of wTTSs, we applied the tech-nique of Least-Squares Deconvolution (LSD, Donati et al.1997) to all of our spectra. Given that relative noise levelsare around − in a typical spectrum (for a single line),with Zeeman signatures exhibiting relative amplitudes of ∼ . per cent, the use of LSD allows us to create a single‘mean’ line profile with a dramatically enhanced S/N, withaccurate error bars for the Zeeman signatures. LSD involvescross-correlating the observed spectrum with a stellar line-list, and for this work, stellar line lists were sourced fromthe Vienna Atomic Line Database (VALD, Ryabchikovaet al. 2015), computed for T eff = K and log g = . (incgs units) for TWA 6, and T eff = K and log g = . forTWA 8A (the closest available to our derived spectral-types,see Section 3.1). Only moderate to strong atomic spectrallines were included (with line-to-continuum core depressionslarger than 40 per cent prior to all non-thermal broadening).Furthermore, spectral regions containing strong lines mostlyformed outside the photosphere (e.g. Balmer, He, Ca ii H&Kand Ca ii IRT lines) and regions heavily crowded with tel-luric lines were discarded (see e.g. Donati et al. 2010 for moredetails), leaving 6088 and 5953 spectral lines for use in LSD,for TWA 6 and TWA 8A, respectively. Expressed in units ofthe unpolarized continuum level I c (and per 1.8 kms − ve-locity bin), the average noise level of the resulting Stokes V signatures range from 4.1–7.5 × − (median of . × − )for TWA 6, and 2.4–5.7 × − (median of . × − ) forTWA 8A.The disc-integrated average photospheric LSD profilesare computed by first synthesizing the local Stokes I and V profiles using the Unno-Rachkovsky analytical solutionto the polarized radiative transfer equations in a Milne-Eddington model atmosphere, taking into account the lo-cal brightness and magnetic field. Then, these local lineprofiles are integrated over the visible hemisphere (includ-ing linear limb darkening, with a coefficient of 0.75, as ob-served young stars, e.g. Donati & Collier Cameron 1997)to produce synthetic profiles for comparison with observa-tions. This method provides a reliable description of howline profiles are distorted due to magnetic fields (includingmagneto-optical effects, e.g., Landi Degl’Innocenti & Lan-dolfi 2004). The main parameters of the local line profilesare similar to those used in our previous studies; the wave-length, Doppler width, equivalent width and Land´e factorbeing set to 670 nm, 1.8 kms − , 3.9 kms − and 1.2, respec-tively.We note that while Zeeman signatures are detected atall times in Stokes V LSD profiles for both stars (see Fig-ure 3 for an example), TWA 8A exhibits much larger longi-
150 100 50 0 50 100 150
Velocity (km/s)
Stokes I/I c × V/I c
50 0 50
Velocity (km/s)
Stokes I/I c × V/I c Figure 3.
LSD circularly-polarized (Stokes V , top/red curve)and unpolarized (Stokes I , bottom/blue curve) profiles of TWA 6(top, collected on 19-02-2014, cycle 27.979) and TWA 8A (bot-tom, collected on 26-03-2015, cycle 0.223). Clear Zeeman signa-tures are detected in both LSD Stokes V profiles in conjunctionwith the unpolarized line profiles. The mean polarization profilesare expanded by a factor of 10 shifted upwards by 0.04 for displaypurposes. tudinal field strengths ( B l ), similar to those of e.g. mid Mdwarfs (see Morin et al. 2008), with values shown in Fig. 4,as calculated from the LSD profiles. Here we clearly see theperiodicity in field strength, with the maximum B l aroundphase 0.37, coincident with the phase of the aligned dipoleof the magnetic field (see Fig. 7) being viewed along the lineof sight, with the minimum B l seen around half a rotationlater. TWA 8A also exhibits significant Zeeman broadeningin the Stokes I profiles that we model in Section 5, withalmost no distortions due to brightness inhomogeneities onthe surface.As part of the imaging process we obtain accurate es-timates for v rad (the RV the star would have if unspotted),equal to . ± . kms − and . ± . kms − , the incli-nation i of the rotation axis to the line of sight, equal to ◦ ± ◦ and ◦ ± ◦ , for TWA 6 and TWA 8A, respec-tively, and for TWA 6 the v sin i equal to . ± . kms − (seeTable 2, in excellent agreement with the values derived in MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A Rotation phase B l (G) Figure 4.
The longitudional field strengths (cid:104) B l (cid:105) for TWA 8A,as measured from the LSD profiles. Table 2.
Main parameters of TWA 6 and TWA 8A as derivedfrom our study, with v rad noting the RV that the star would haveif unspotted, the equatorial rotation rate Ω eq and the differencebetween equatorial and polar rotation rates d Ω (as inferred fromthe modelling of Section 4). Note, the stellar masses and ages arethose determined from Siess et al. (2000) models, with values fromBaraffe et al. (2015) given in parenthesis. The log g for TWA 8Ais estimated from its mass (using Baraffe et al. (2015) models)and R (cid:63) . TWA 6 TWA 8A M (cid:63) (M (cid:12) ) . ± . ( . ± . ) . ± . ( . ± . ) R (cid:63) (R (cid:12) ) . ± . . ± . Age (Myr) ± ( ± ) ± ( ± ) log g (cgs units) . ± . . ± . T eff (K) ±
50 3690 ± log( L (cid:63) /L (cid:12) ) − . ± . − . ± . P rot (d) . ± . . ± . v sin i (kms − ) . ± . . ± . v rad (kms − ) . ± . . ± . i ( ◦ ) ±
10 42 ± Distance (pc) . ± . a . ± . a Ω eq (rad d − ) . ± . - d Ω (rad d − ) . ± . - References : (a) Gaia Collaboration et al. 2016, 2018.
Section 3.1). For TWA 8A, we fixed the v sin i to 4.82 kms − ,as this was determined by direct spectral fitting in Section 5and is more accurate than that derived from ZDI. The observed LSD profiles for TWA 6 and TWA 8A, as wellas our fits to data, are shown in Fig. 5. For TWA 6, we obtaina reduced chi-squared χ r fit equal to 1 (where the number offitted data points is equal to 4312, with simultaneous fittingof both Stokes I and Stokes V line profiles). For TWA 8A,the low v sin i means that there is little modulation of theStokes I line profiles, with the strong magnetic fields caus-ing significant Zeeman broadening of the lines. Indeed, weare able to model the Stokes I line profiles sufficiently wellusing a stellar model with a homogeneous surface brightness,with our fits to the Stokes V line profiles yielding χ r = . (for 930 fitted data points). We note that, given the sub-stantially larger v sin i of TWA 6 as compared to TWA 8A,combined with more complete phase coverage, the recon-structed maps of TWA 6 have an effective resolution around10 times higher.The brightness map of TWA 6 includes both cool spotsand warm plages (see Fig. 6), with no true polar spot, butrather a large spotted region centred around ◦ latitude(centred around phase 0.6), with the majority of plages at asimilar latitude on the opposing hemisphere. These featuresintroduce significant distortions to the Stokes I profiles (seeFig. 5), introducing large RV variations (with maximum am-plitude 6.0 kms − , see Section 6). Overall, we find a spot andplage coverage of (cid:39) per cent (10 and 7 per cent for spotsand plages, respectively), similar to that found for V819 Tau,V830 Tau (Donati et al. 2015), and Par 2244 (Hill et al.2017).Note that the estimates of spot and plage coverageshould be considered as lower limits only, as Doppler imag-ing is mostly insensitive to small-scale structures that areevenly distributed over the stellar surface (hence the largerminimal spot coverage assumed in Section 3.1 to derive thelocation of the stars in the H-R diagram). Using our imaging code, we have reconstructed the magneticfields of our target stars using both poloidal and toroidalfields, each expressed using a spherical-harmonic (SH) ex-pansion, with (cid:96) and m denoting the mode and order of the SH(Donati et al. 2006). For a given set of complex coefficients α (cid:96), m , β (cid:96), m and γ (cid:96), m (where α (cid:96), m characterizes the radial fieldcomponent, β (cid:96), m the azimuthal and meridional componentsof the poloidal field term, and γ (cid:96), m the azimuthal and merid-ional components of the toroidal field term), one can con-struct an associated magnetic image at the surface of thestar, and thus derive the corresponding Stokes V data set.Here, we carry out the inverse, where we reconstruct the setof coefficients that fit the observed data.For TWA 6, our reconstructed fields presented in Fig. 7are limited to SH expansions with terms (cid:96) ≤ . Given thehigh v sin i of TWA 6 (combined with good phase coverage),we are able to resolve smaller-scale magnetic fields, and in-deed such a large number of modes are required to fit the ob-served Stokes V signatures. We note, however, that includ-ing higher-order terms ( > ) only marginally improves ourfit. Such high-degree modes indicate that the magnetic fieldsin TWA 6 concentrate on smaller, more compact spatial-scales. In contrast, our fits to the Stokes V observations ofTWA 8A only require terms up to (cid:96) ≤ , with higher orderterms providing only a marginal improvement. Hence, themagnetic field of TWA 8A is concentrated at larger spatialscales.The reconstructed magnetic field for TWA 6 is splitalmost evenly between poloidal and toroidal components (53and 47 per cent, respectively), with a total magnetic energy (cid:104) B (cid:105) = G, where (cid:104) B (cid:105) is given by (cid:104) B (cid:105) = ∯ θ,φ (cid:16) B α + B β + B γ (cid:17) / d θ d φ (3)The poloidal field is mostly axisymmetric (49 per cent), with MNRAS000
Section 3.1). For TWA 8A, we fixed the v sin i to 4.82 kms − ,as this was determined by direct spectral fitting in Section 5and is more accurate than that derived from ZDI. The observed LSD profiles for TWA 6 and TWA 8A, as wellas our fits to data, are shown in Fig. 5. For TWA 6, we obtaina reduced chi-squared χ r fit equal to 1 (where the number offitted data points is equal to 4312, with simultaneous fittingof both Stokes I and Stokes V line profiles). For TWA 8A,the low v sin i means that there is little modulation of theStokes I line profiles, with the strong magnetic fields caus-ing significant Zeeman broadening of the lines. Indeed, weare able to model the Stokes I line profiles sufficiently wellusing a stellar model with a homogeneous surface brightness,with our fits to the Stokes V line profiles yielding χ r = . (for 930 fitted data points). We note that, given the sub-stantially larger v sin i of TWA 6 as compared to TWA 8A,combined with more complete phase coverage, the recon-structed maps of TWA 6 have an effective resolution around10 times higher.The brightness map of TWA 6 includes both cool spotsand warm plages (see Fig. 6), with no true polar spot, butrather a large spotted region centred around ◦ latitude(centred around phase 0.6), with the majority of plages at asimilar latitude on the opposing hemisphere. These featuresintroduce significant distortions to the Stokes I profiles (seeFig. 5), introducing large RV variations (with maximum am-plitude 6.0 kms − , see Section 6). Overall, we find a spot andplage coverage of (cid:39) per cent (10 and 7 per cent for spotsand plages, respectively), similar to that found for V819 Tau,V830 Tau (Donati et al. 2015), and Par 2244 (Hill et al.2017).Note that the estimates of spot and plage coverageshould be considered as lower limits only, as Doppler imag-ing is mostly insensitive to small-scale structures that areevenly distributed over the stellar surface (hence the largerminimal spot coverage assumed in Section 3.1 to derive thelocation of the stars in the H-R diagram). Using our imaging code, we have reconstructed the magneticfields of our target stars using both poloidal and toroidalfields, each expressed using a spherical-harmonic (SH) ex-pansion, with (cid:96) and m denoting the mode and order of the SH(Donati et al. 2006). For a given set of complex coefficients α (cid:96), m , β (cid:96), m and γ (cid:96), m (where α (cid:96), m characterizes the radial fieldcomponent, β (cid:96), m the azimuthal and meridional componentsof the poloidal field term, and γ (cid:96), m the azimuthal and merid-ional components of the toroidal field term), one can con-struct an associated magnetic image at the surface of thestar, and thus derive the corresponding Stokes V data set.Here, we carry out the inverse, where we reconstruct the setof coefficients that fit the observed data.For TWA 6, our reconstructed fields presented in Fig. 7are limited to SH expansions with terms (cid:96) ≤ . Given thehigh v sin i of TWA 6 (combined with good phase coverage),we are able to resolve smaller-scale magnetic fields, and in-deed such a large number of modes are required to fit the ob-served Stokes V signatures. We note, however, that includ-ing higher-order terms ( > ) only marginally improves ourfit. Such high-degree modes indicate that the magnetic fieldsin TWA 6 concentrate on smaller, more compact spatial-scales. In contrast, our fits to the Stokes V observations ofTWA 8A only require terms up to (cid:96) ≤ , with higher orderterms providing only a marginal improvement. Hence, themagnetic field of TWA 8A is concentrated at larger spatialscales.The reconstructed magnetic field for TWA 6 is splitalmost evenly between poloidal and toroidal components (53and 47 per cent, respectively), with a total magnetic energy (cid:104) B (cid:105) = G, where (cid:104) B (cid:105) is given by (cid:104) B (cid:105) = ∯ θ,φ (cid:16) B α + B β + B γ (cid:17) / d θ d φ (3)The poloidal field is mostly axisymmetric (49 per cent), with MNRAS000 , 1–27 (2018)
C. A. Hill et al.
Figure 5.
Maximum-entropy fit (thin red line) to the observed (thick black line) Stokes I (first and third panels) and Stokes V (secondand fourth panels) LSD photospheric profiles of TWA 6 (first two panels) and TWA 8A (last two panels). Note that for TWA 8A thevelocity scales are different. Rotational cycles are shown next to each profile. This figure is best viewed in colour. Figure 6.
Map of the logarithmic brightness (relative to the quiet photosphere) at the surface of TWA 6. The star is shown in flattenedpolar projection down to latitudes of − ◦ , with the equator depicted as a bold circle, and 30 ◦ and 60 ◦ parallels as dashed circles. Radialticks indicate the phases of observation. This figure is best viewed in colour. the largest fraction of energy (58 per cent) in modes with (cid:96) > , and with 30 per cent of energy in the dipole mode( (cid:96) = , with a field strength of 550 G). On large scales,the poloidal component is tilted at ◦ from the rotationaxis (towards phase 0.34). The toroidal component is alsomostly axisymmetric, with the largest fraction of energy(68 per cent) in modes with (cid:96) > , and with 17 per centof energy in the octupole ( (cid:96) = ) mode. These componentscombine to generate an intense field of ≥ kG at ◦ lat- itude around phase 0.50–0.75 and 0.20–0.35, as well as anoff-pole 2 kG spot at phase 0.75. We note that the largespotted region reconstructed in the brightness map (around ◦ latitude at phase 0.6, see Fig. 6) aligns well with theseintense fields, suggesting that they are related.In the case of TWA 8A, the reconstructed field is71 per cent poloidal and 29 per cent toroidal, with a totalunsigned flux of 1.4 kG, and with a magnetic filling factorof f v = . (where f v is equal to the fraction of the stellar MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A surface that is covered by the mapped magnetic field usingStokes V data). The poloidal field is mostly axisymmetric(70 per cent), with 16 per cent of the energy in the dipole( (cid:96) = , with a field strength of 0.72 kG), 21 per cent in thequadrupole ( (cid:96) = ), 18 per cent in the octupole ( (cid:96) = ), andwith the remaining 44 per cent of energy in modes with (cid:96) > .On large scales (several radii from the star), the poloidalcomponent may be approximated by an B = . kG aligned-dipole tilted at ◦ from the rotation axis (towards phase0.37). The toroidal component is mostly non-axisymmetric,with the majority of energy (55 per cent) in modes with (cid:96) > , and with 21, 6 and 18 per cent in modes with (cid:96) = , & . These components combine to generate intense fields inexcess of 2 kG in around phases 0.08, 0.42 and 0.75 on thestellar surface, centred around ◦ latitude in the radial fieldcomponent and around ◦ in the meridional field compo-nent. Given the filling factor of f v = . , this suggests thatsurface magnetic fields can locally reach over 10 kG. More-over, the high fraction of energy in high-order modes sug-gests that there are a large number of small-scale magneticfeatures, a conclusion also supported by the direct spectralfitting in Section 5.5.In Figure 8 we use the a potential field approximation(e.g., Jardine et al. 2002) to extrapolate the large-scale fieldtopologies of TWA 6 and TWA 8A. These topologies are de-rived solely from the reconstructed radial field components,and represent the lowest possible states of magnetic energy,providing a reliable description of the magnetic field wellwithin the Alfv´en radius (Jardine et al. 2013). The level of surface differential rotation of TWA 6 was de-termined in a similar manner as that carried out for otherwTTSs (e.g., Skelly et al. 2008, 2010; Donati et al. 2014,2015). Assuming that the rotation rate at the surface of thestar varies with latitude θ as Ω eq − d Ω sin θ (where Ω eq isthe rotation rate at the equator and d Ω is the difference inrotation rate between the equator and the pole), we recon-struct brightness and magnetic maps at a fixed informationcontent for many pairs of Ω eq and d Ω and determine thecorresponding reduced chi-squared χ r of our fit to the obser-vations. The resulting χ r surface usually has a well definedminimum to which we fit a parabola, allowing an estimateof both Ω eq and d Ω (and their corresponding error bars).Fig. 9 shows the χ r surface we obtain (as a functionof Ω eq and d Ω ) for both Stokes I and V , for TWA 6. Wefind a clear minimum at Ω eq = . ± . rad d − and d Ω = . ± . rad d − for Stokes I data (cor-responding to rotation periods of . ± . d atthe equator and . ± . d at the poles; see leftpanel of Figure 9), with the fits to the Stokes V data of Ω eq = . ± . rad d − and d Ω = . ± . rad d − showing consistent estimates, though with larger error bars(right panel of Figure 9). We note that both these periodsare in excellent agreement with those found previously bySkelly et al. (2008) and Kiraga (2012).For TWA 8A, we were able to constrain the rota-tional period to . ± . d (corresponding to Ω eq = . ± . rad d − ), in good agreement with the photo-metric period of 4.638 d found by Kiraga (2012). However, given that the observations span only ∼ rotation cycles, therecurrence of profile distortions across different latitudes isseverely limited, and so we were unable to constrain surfaceshear. Hence, for our fits with ZDI we have assumed solidbody rotation. TWA 8A has a very strong photospheric magnetic field thatcan be detected in some individual lines, allowing directspectral fitting to derive the strength of the magnetic field.As this is not the case for TWA 6, it is not included in thefollowing analysis. For TWA 8A, Stokes V signatures arevisible in over 20 lines, mostly redwards of 8000 ˚A wherethe S/N is largest. Of particular interest are a set of elevenstrong Ti i lines between 9674 and 9834 ˚A ten of which aredetected in Stokes V , and one which has a Land´e factor ofzero (9743.6 ˚A, see Fig. 10). These atomic lines have mini-mal blending from molecular lines, and while there is a someblending from telluric lines, it can be corrected. These lineshave the added advantage that all but two of them are fromthe same multiplet, which mitigates the impact of some sys-tematic errors (e.g., errors in T eff ) on our measurements ofthe magnetic field. A detailed description of these lines isgiven in Table C1. Before a detailed analysis of the Stokes I spectra may becarried out, we must first correct for the large number oftelluric water lines present between 9670–9840 ˚A. Telluriclines are not expected to produce circular polarisation, andwe see no indication of them in Stokes V , hence we concludethat their impact on the Stokes V spectrum is negligible.As we did not expect to detect magnetic fields in indi-vidual telluric blended lines, we did not observe a hot starfor telluric calibration. Fortuitously, on some nights, otherprograms with ESPaDOnS at the CFHT observed the hotstars HD 63401 (PI J.D. Landstreet) and HD 121743 (PIG.A. Wade). HD 63401 is a 13500 K Bp star (e.g., Bailey2014) and HD 121743 is a 21000 K B star (e.g., Alecian et al.2014), with both stars having virtually no photospheric linesin the wavelength range of interest, apart from Paschen lines.Our observations of TWA 8A on the nights of March 25 toApril 1, as well as April 5 and 6, had suitable telluric ref-erence observations that were sufficiently close in time andobtained under sufficiently similar conditions.The telluric reference spectra were first continuum nor-malised by fitting low order polynomials through carefullyselected continuum regions, then dividing by those polyno-mials, independently for each spectral order. The telluricreference spectra were then scaled in the form I a , where I isthe continuum normalised spectrum and a the scaling factor.The scaling factor a and the radial velocity shift for the tel-luric lines were determined by fitting the modified referencespectrum to telluric lines of the science spectrum through χ minimisation. Telluric lines around the photospheric lines ofinterest ( ∼ MNRAS000
Map of the logarithmic brightness (relative to the quiet photosphere) at the surface of TWA 6. The star is shown in flattenedpolar projection down to latitudes of − ◦ , with the equator depicted as a bold circle, and 30 ◦ and 60 ◦ parallels as dashed circles. Radialticks indicate the phases of observation. This figure is best viewed in colour. the largest fraction of energy (58 per cent) in modes with (cid:96) > , and with 30 per cent of energy in the dipole mode( (cid:96) = , with a field strength of 550 G). On large scales,the poloidal component is tilted at ◦ from the rotationaxis (towards phase 0.34). The toroidal component is alsomostly axisymmetric, with the largest fraction of energy(68 per cent) in modes with (cid:96) > , and with 17 per centof energy in the octupole ( (cid:96) = ) mode. These componentscombine to generate an intense field of ≥ kG at ◦ lat- itude around phase 0.50–0.75 and 0.20–0.35, as well as anoff-pole 2 kG spot at phase 0.75. We note that the largespotted region reconstructed in the brightness map (around ◦ latitude at phase 0.6, see Fig. 6) aligns well with theseintense fields, suggesting that they are related.In the case of TWA 8A, the reconstructed field is71 per cent poloidal and 29 per cent toroidal, with a totalunsigned flux of 1.4 kG, and with a magnetic filling factorof f v = . (where f v is equal to the fraction of the stellar MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A surface that is covered by the mapped magnetic field usingStokes V data). The poloidal field is mostly axisymmetric(70 per cent), with 16 per cent of the energy in the dipole( (cid:96) = , with a field strength of 0.72 kG), 21 per cent in thequadrupole ( (cid:96) = ), 18 per cent in the octupole ( (cid:96) = ), andwith the remaining 44 per cent of energy in modes with (cid:96) > .On large scales (several radii from the star), the poloidalcomponent may be approximated by an B = . kG aligned-dipole tilted at ◦ from the rotation axis (towards phase0.37). The toroidal component is mostly non-axisymmetric,with the majority of energy (55 per cent) in modes with (cid:96) > , and with 21, 6 and 18 per cent in modes with (cid:96) = , & . These components combine to generate intense fields inexcess of 2 kG in around phases 0.08, 0.42 and 0.75 on thestellar surface, centred around ◦ latitude in the radial fieldcomponent and around ◦ in the meridional field compo-nent. Given the filling factor of f v = . , this suggests thatsurface magnetic fields can locally reach over 10 kG. More-over, the high fraction of energy in high-order modes sug-gests that there are a large number of small-scale magneticfeatures, a conclusion also supported by the direct spectralfitting in Section 5.5.In Figure 8 we use the a potential field approximation(e.g., Jardine et al. 2002) to extrapolate the large-scale fieldtopologies of TWA 6 and TWA 8A. These topologies are de-rived solely from the reconstructed radial field components,and represent the lowest possible states of magnetic energy,providing a reliable description of the magnetic field wellwithin the Alfv´en radius (Jardine et al. 2013). The level of surface differential rotation of TWA 6 was de-termined in a similar manner as that carried out for otherwTTSs (e.g., Skelly et al. 2008, 2010; Donati et al. 2014,2015). Assuming that the rotation rate at the surface of thestar varies with latitude θ as Ω eq − d Ω sin θ (where Ω eq isthe rotation rate at the equator and d Ω is the difference inrotation rate between the equator and the pole), we recon-struct brightness and magnetic maps at a fixed informationcontent for many pairs of Ω eq and d Ω and determine thecorresponding reduced chi-squared χ r of our fit to the obser-vations. The resulting χ r surface usually has a well definedminimum to which we fit a parabola, allowing an estimateof both Ω eq and d Ω (and their corresponding error bars).Fig. 9 shows the χ r surface we obtain (as a functionof Ω eq and d Ω ) for both Stokes I and V , for TWA 6. Wefind a clear minimum at Ω eq = . ± . rad d − and d Ω = . ± . rad d − for Stokes I data (cor-responding to rotation periods of . ± . d atthe equator and . ± . d at the poles; see leftpanel of Figure 9), with the fits to the Stokes V data of Ω eq = . ± . rad d − and d Ω = . ± . rad d − showing consistent estimates, though with larger error bars(right panel of Figure 9). We note that both these periodsare in excellent agreement with those found previously bySkelly et al. (2008) and Kiraga (2012).For TWA 8A, we were able to constrain the rota-tional period to . ± . d (corresponding to Ω eq = . ± . rad d − ), in good agreement with the photo-metric period of 4.638 d found by Kiraga (2012). However, given that the observations span only ∼ rotation cycles, therecurrence of profile distortions across different latitudes isseverely limited, and so we were unable to constrain surfaceshear. Hence, for our fits with ZDI we have assumed solidbody rotation. TWA 8A has a very strong photospheric magnetic field thatcan be detected in some individual lines, allowing directspectral fitting to derive the strength of the magnetic field.As this is not the case for TWA 6, it is not included in thefollowing analysis. For TWA 8A, Stokes V signatures arevisible in over 20 lines, mostly redwards of 8000 ˚A wherethe S/N is largest. Of particular interest are a set of elevenstrong Ti i lines between 9674 and 9834 ˚A ten of which aredetected in Stokes V , and one which has a Land´e factor ofzero (9743.6 ˚A, see Fig. 10). These atomic lines have mini-mal blending from molecular lines, and while there is a someblending from telluric lines, it can be corrected. These lineshave the added advantage that all but two of them are fromthe same multiplet, which mitigates the impact of some sys-tematic errors (e.g., errors in T eff ) on our measurements ofthe magnetic field. A detailed description of these lines isgiven in Table C1. Before a detailed analysis of the Stokes I spectra may becarried out, we must first correct for the large number oftelluric water lines present between 9670–9840 ˚A. Telluriclines are not expected to produce circular polarisation, andwe see no indication of them in Stokes V , hence we concludethat their impact on the Stokes V spectrum is negligible.As we did not expect to detect magnetic fields in indi-vidual telluric blended lines, we did not observe a hot starfor telluric calibration. Fortuitously, on some nights, otherprograms with ESPaDOnS at the CFHT observed the hotstars HD 63401 (PI J.D. Landstreet) and HD 121743 (PIG.A. Wade). HD 63401 is a 13500 K Bp star (e.g., Bailey2014) and HD 121743 is a 21000 K B star (e.g., Alecian et al.2014), with both stars having virtually no photospheric linesin the wavelength range of interest, apart from Paschen lines.Our observations of TWA 8A on the nights of March 25 toApril 1, as well as April 5 and 6, had suitable telluric ref-erence observations that were sufficiently close in time andobtained under sufficiently similar conditions.The telluric reference spectra were first continuum nor-malised by fitting low order polynomials through carefullyselected continuum regions, then dividing by those polyno-mials, independently for each spectral order. The telluricreference spectra were then scaled in the form I a , where I isthe continuum normalised spectrum and a the scaling factor.The scaling factor a and the radial velocity shift for the tel-luric lines were determined by fitting the modified referencespectrum to telluric lines of the science spectrum through χ minimisation. Telluric lines around the photospheric lines ofinterest ( ∼ MNRAS000 , 1–27 (2018) C. A. Hill et al.
Figure 7.
Map of the radial (left), azimuthal (middle) and meridional (right) components of the magnetic field B at the surface ofTWA 6 (top) and TWA 8A (bottom). Magnetic fluxes in the colourbar are expressed in G. Note that the magnetic filling factor forTWA 8A is f v = . . The star is shown in flattened polar projection as in Figure 6. This figure is best viewed in colour. Figure 8.
Potential field extrapolations of the radial magnetic field reconstructed for TWA 6 (left) and TWA 8A (right), viewed atphases 0.95 and 0.70, with inclinations of . ◦ and ◦ , respectively. Open and closed field lines are shown in blue and white, respectively,whereas colours at the stellar surface depict the local values of the radial field (as shown in the left panels of Figure 7). The sourcesurfaces at which the field becomes radial are set at distances of 2.6 R (cid:63) for TWA 6 and 10.7 R (cid:63) for TWA 8A, as these are close to theco-rotation radii (where the Keplerian orbital period equals the stellar rotation period, and beyond which the field lines tend to openunder the effect of centrifugal forces, Jardine 2004), and are smaller than or similar to the Alfv´en radii of > R (cid:63) (R´eville et al. 2016).This figure is best viewed in colour. Full animations may be found for both TWA 6 and TWA 8A at https://imgur.com/hSkhYLT andhttps://imgur.com/AdKptUx. MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A Ω eq (rad d − ) d Ω (rad d − ) Stokes IStokes V
Figure 9.
Variations of χ r as a function of Ω eq and d Ω forTWA 6, derived from modelling of our Stokes I (red) and Stokes V (blue) LSD profiles at a constant information content. For bothStokes I and Stokes V , a clear and well defined parabola is ob-served, shown by the 1, 2 and σ ellipses (depicting 68.3, 95.5and 99.7 per cent confidence levels, respectively), with the σ contour tracing the 5.5 per cent increase in χ r (or equivalently a χ increase of 11.8 for 2156 fitted data points). This figure is bestviewed in colour. divided by the scaled shifted telluric spectrum. A exam-ple spectrum before and after telluric correction is shownin Fig. 10. To constrain the strength of the photospheric magneticfield, we have modelled individual lines in the Stokes I andStokes V spectra of TWA 8A. Furthermore, as one of the Ti i lines has a Land´e factor of zero, and is narrower in Stokes I as compared to the other Ti i lines, the magnetic field canalso be strongly constrained by the Stokes I spectrum.To generate synthetic spectra, we used the Zeeman spectrum synthesis program (Landstreet 1998; Wade et al.2001; Folsom et al. 2012). This program includes the Zeemaneffect and performs polarized radiative transfer in Stokes
IQUV . The code uses plane-parallel model atmospheres andassumes LTE, and produces disk-integrated spectra.
Zee-man includes quadratic Stark, radiative, and van der Waalsbroadening, as well as optional microturbulence ( v mic ) andradial-tangential macroturbulence. A limitation of the codefor use in very cool stars is that it does not include molecu-lar lines, or calculations of molecular reactions in the abun-dances for atomic species. The Ti i lines in the 9674–9834˚A region are blended with a few very weak molecular lines,and so Zeeman can produce accurate spectra for this re-gion, however most of the spectral region bluewards of thisis problematic.For input to the code we used MARCS model atmo-spheres (Gustafsson et al. 2008) and atomic data taken fromVALD (Ryabchikova et al. 2015) (see Table C1 for the prop-erties of the atomic lines). VALD data for these particularTi i lines were also used by Kochukhov & Lavail (2017) fora similar analysis, and were deemed reliable. Additionally,we can reproduce these Ti lines with near-solar abundances, implying that the oscillator strengths are likely close to cor-rect.To model the magnetic field of TWA 8A, we adopteda uniform radial magnetic field. While this is an unrealis-tically simple magnetic geometry, the ZDI analysis foundthe magnetic geometry to be more complex than a simpledipole. Therefore we leave the geometric analysis to ZDIand adopt the simplest possible geometry here to avoid ad-ditional weakly constrained geometric parameters. Further-more, since this analysis is applied to individual observa-tions, a full magnetic geometry cannot be reliably derived.The model we implement here includes a combination ofmagnetic field strengths B , each with their own filling factor f , with the sum of the filling factors (including a region ofzero field) equal to unity.We fit synthetic spectra using a Levenberg-Marquardt χ minimisation routine (similar to Folsom et al. 2012,2016), with the radial magnetic field strengths and fillingfactors as optional additional free parameters. The code wasupdated to allow fitting observed Stokes I spectra, V spectra,or I and V simultaneously, with wavelength ranges carefullyset around the lines of interest. In order to place uncertain-ties on the fitting parameters, we use the square root ofthe diagonal of the covariance matrix, as is commonly done.This is then scaled by the square root of the reduced χ , tovery approximately account for systematic errors. These for-mal uncertainties may still be underestimates, and a furtherconsideration of uncertainties is discussed in Sect. 5.5. I spectrum Our initial fits were carried out with the observation onMarch 27 since the Stokes V LSD profile for this night hasone of the simplest shapes, indicating a more uniform mag-netic field in the visible hemisphere.Measurements of magnetic fields in Stokes I spectra areconstrained by both the width and the desaturation of lineswith different Land´e factors. Fitting the Stokes I spectrumto determine magnetic field strengths requires constraints onseveral other stellar parameters which influence line widthand depth. Here, we adopt the T eff and log g values derived inSection 3 (see Table 2). Since our choice of lines is dominatedby one multiplet, adopting these values is a small source ofuncertainty. We note that these lines are not well adaptedto constraining T eff and log g spectroscopically. We include v sin i and v mic as free parameters in the fit, since they canplay an important role in line shape and strength, and canonly be determined spectroscopically. v mic is constrained bydesaturation of strong (on the curve of growth) lines and,given the lack of weak lines in our spectral range, is de-termined with only a modest accuracy by different degreesof desaturation of different strong lines. Macroturbulence isassumed to be zero, since it is likely much smaller than the v sin i of ∼ − . Ti abundance is included as a free pa-rameter, however, we caution the reader that this may notprovide reliable results, as the code neglects the fraction ofTi bound in molecules. Nevertheless, this free parameter isnecessary to avoid the code fitting line strength entirely byvarying magnetic field and v mic .When fitting the spectra of TWA 8A we adopted threemain models, each of increasing complexity, to better con-strain the nature of the magnetic field. These three mod- MNRAS000
Zee-man includes quadratic Stark, radiative, and van der Waalsbroadening, as well as optional microturbulence ( v mic ) andradial-tangential macroturbulence. A limitation of the codefor use in very cool stars is that it does not include molecu-lar lines, or calculations of molecular reactions in the abun-dances for atomic species. The Ti i lines in the 9674–9834˚A region are blended with a few very weak molecular lines,and so Zeeman can produce accurate spectra for this re-gion, however most of the spectral region bluewards of thisis problematic.For input to the code we used MARCS model atmo-spheres (Gustafsson et al. 2008) and atomic data taken fromVALD (Ryabchikova et al. 2015) (see Table C1 for the prop-erties of the atomic lines). VALD data for these particularTi i lines were also used by Kochukhov & Lavail (2017) fora similar analysis, and were deemed reliable. Additionally,we can reproduce these Ti lines with near-solar abundances, implying that the oscillator strengths are likely close to cor-rect.To model the magnetic field of TWA 8A, we adopteda uniform radial magnetic field. While this is an unrealis-tically simple magnetic geometry, the ZDI analysis foundthe magnetic geometry to be more complex than a simpledipole. Therefore we leave the geometric analysis to ZDIand adopt the simplest possible geometry here to avoid ad-ditional weakly constrained geometric parameters. Further-more, since this analysis is applied to individual observa-tions, a full magnetic geometry cannot be reliably derived.The model we implement here includes a combination ofmagnetic field strengths B , each with their own filling factor f , with the sum of the filling factors (including a region ofzero field) equal to unity.We fit synthetic spectra using a Levenberg-Marquardt χ minimisation routine (similar to Folsom et al. 2012,2016), with the radial magnetic field strengths and fillingfactors as optional additional free parameters. The code wasupdated to allow fitting observed Stokes I spectra, V spectra,or I and V simultaneously, with wavelength ranges carefullyset around the lines of interest. In order to place uncertain-ties on the fitting parameters, we use the square root ofthe diagonal of the covariance matrix, as is commonly done.This is then scaled by the square root of the reduced χ , tovery approximately account for systematic errors. These for-mal uncertainties may still be underestimates, and a furtherconsideration of uncertainties is discussed in Sect. 5.5. I spectrum Our initial fits were carried out with the observation onMarch 27 since the Stokes V LSD profile for this night hasone of the simplest shapes, indicating a more uniform mag-netic field in the visible hemisphere.Measurements of magnetic fields in Stokes I spectra areconstrained by both the width and the desaturation of lineswith different Land´e factors. Fitting the Stokes I spectrumto determine magnetic field strengths requires constraints onseveral other stellar parameters which influence line widthand depth. Here, we adopt the T eff and log g values derived inSection 3 (see Table 2). Since our choice of lines is dominatedby one multiplet, adopting these values is a small source ofuncertainty. We note that these lines are not well adaptedto constraining T eff and log g spectroscopically. We include v sin i and v mic as free parameters in the fit, since they canplay an important role in line shape and strength, and canonly be determined spectroscopically. v mic is constrained bydesaturation of strong (on the curve of growth) lines and,given the lack of weak lines in our spectral range, is de-termined with only a modest accuracy by different degreesof desaturation of different strong lines. Macroturbulence isassumed to be zero, since it is likely much smaller than the v sin i of ∼ − . Ti abundance is included as a free pa-rameter, however, we caution the reader that this may notprovide reliable results, as the code neglects the fraction ofTi bound in molecules. Nevertheless, this free parameter isnecessary to avoid the code fitting line strength entirely byvarying magnetic field and v mic .When fitting the spectra of TWA 8A we adopted threemain models, each of increasing complexity, to better con-strain the nature of the magnetic field. These three mod- MNRAS000 , 1–27 (2018) C. A. Hill et al.
Ti 1 I / I c Ca 1Ti 1 Ti 1 Ti 1 Ti 1 Ti 1 Cr 1 V / I c Ti 1 I / I c Ti 1 Ti 1Ti 1 Ti 1Ti 1 Ti 1 Ti 1 V / I c Figure 10.
Detections of Zeeman broadening in the observation of TWA 8A on March 27. The panels show the Stokes I spectrum atthe top and the corresponding Stokes V spectrum below for the full set of lines used in our fits (see Table C1). Dashed lines show theobservation before telluric correction and solid lines show the spectrum after telluric correction. Over-plotted in a red solid line is ourbest fit using our third model to fit both Stokes I and Stokes V simultaneously. els (described below) are used to fit Stokes I spectra only,Stokes V only, and both Stokes I and V simultaneously.Our first model consists of fitting the Stokes I spectrumusing just one magnetic region with a corresponding fillingfactor, yielding a best-fit magnetic field strength of B = . ± . kG with a filling factor f = . ± . , but ata reduced χ of 19.6. Fits with f fixed to 1 consistently failto reproduce the line shape, with a core that is far too wideand with wings that are too narrow, implying that only afraction of the star is covered by very strong magnetic fields.Our second model increases the number of free pa-rameters by including two magnetic regions and filling fac-tors, achieving a visibly much better fit with a reduced χ of 12.9, and with field strengths of B = . ± . kGwith f = . ± . , and B = . ± . kG with f = . ± . . This second model does a better job of si-multaneously reproducing the narrow core and broad wingsof the magnetically sensitive lines, although the high fieldstrength region produces a sharper change in the shape ofthe wings than seen in the observation, implying that thestar has a more continuous distribution of magnetic fieldstrengths than our model.Our third model again increases the number of free pa- rameters to improve the fit. However, rather than add ad-ditional sets of magnetic field strengths and filling factors,which may become more poorly conditioned or not convergewell, we instead adopt a grid of fixed magnetic field strengthswith filling factors as free parameters (in a similar way toe.g. Johns-Krull et al. 1999, 2004). This provides an approx-imate distribution of magnetic field strengths on the visiblehemisphere of the star. Using our third model for fittingStokes I only, we use bins of 0, 2, 5, 10, 15 and 20 kG.Bins of ∼ kG allow for smooth model line profiles, and sosmaller bins (that would be less well constrained) are notnecessary. Adding bins above 20 kG improves the χ fit bya small but formally significant amount. However, the im-pact on the synthetic line is small and only affects the farwings of the line in Stokes I . Small changes in the far wingsof the line are most vulnerable to systematic errors, suchas weak lines that are not accounted for, errors in the tel-luric correction, errors in continuum normalisation, or veryweak fringing, all of which could approach the strength ofthe line this far into the wing. Thus we limit the magneticfield to 20 kG, and caution that even for this bin the fillingfactor may be overestimated. The resulting best fit parame- MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A
20 15 10 5 2 0 2 5 10 15 20
Magnetic field strength (kG)
Fraction of total
Magnetic field strength (kG)
Fraction of total
Figure 11.
The distribution of surface magnetic field strengthsfor TWA 8A, as determined from ZDI and direct spectral fittingof Ti i lines. Blue bars show the fraction of the total mappedmagnetic field strength from ZDI, for fields of a given bin. Toppanel: Comparison between the magnetic field strengths deter-mined from fitting Stokes I data. Red circles show the mean fillingfactors for each field strength using our third model to simulta-neously fit Stokes I and V spectra (see Section 5.5). Black circlesshow the combined filling factors for both the positive and neg-ative fields. Thus, one can directly compare the recovered fieldstrengths for Stokes I data from ZDI and direct spectral fittingby comparing the blue bars and the black circles, respectively.One can see that a significantly larger fraction of higher-strengthfields are recovered by direct spectral fitting, as compared to thatfrom ZDI (see discussion in Section 5.5). Bottom panel: Compar-ison between the magnetic field strengths determined from fittingStokes V data. Black circles show the resulting filling factors aftersubtracting the contributions of the negative fields from those ofthe positive fields. As Stokes V profiles are sensitive to the sign ofthe line-of-sight component of B , significant cancellation of fieldsmay occur, and so we must compare our fits with ZDI to Stokes V profiles, to these black circles. In this case, we see that ZDI recov-ers a similar fraction of field strengths for the 5 and 10 kG bins,but significantly more for the 2 kG bin, and significantly less forthe 15 and 20 kG bins (see discussion in Section 5.5). ters for Stokes I only for March 27 using our third model ispresented in Table 3, with a reduced χ of 10.6.Yang et al. (2008) studied TWA 8A and derived somemagnetic quantities based on Stokes I observations in theIR. They adopted literature values for the stellar parame-ters of T eff = K, log g = . and v sin i = . kms − . Their“Model 1” corresponds to our first model with one filling fac- tor and magnetic field strength. They report only the prod-uct of their filling factor and magnetic field strength as 2.3kG, which is close to our value for March 27 of . ± . kG,although not within uncertainty. Their “Model 2” corre-sponds to our second model with two filling factors andmagnetic field strengths. They report the quantity (cid:104)| B f |(cid:105) = . kG, which is comparable but again not consistent withour value of . ± . kG. The “Model 3” of Yang et al.(2008) is closest to our third model with a grid of filling fac-tors, although they only fit filling factors for field strengthsof 2, 4 and 6 kG. They report (cid:104)| B f |(cid:105) = (cid:205) i B i f i of 3.3 kG.The equivalent value from our fit is (cid:104)| B f |(cid:105) = . ± . kG,which is again inconsistent. We note that, if we perform ourfit using the three bins of 2, 4, and 6 kG used by Yang et al.(2008), we find (cid:104)| B f |(cid:105) = . ± . kG. While this is muchcloser to their “Model 3” results, we find that the fit to ourdata is much worse in the wings of the lines, so we considerthis model to be less accurate for our spectra. The IR spec-tra of Yang et al. (2008) had a much lower S/N than ourobservations, and so the wings of the lines may not havebeen detected as clearly as in our spectra. Indeed, the verystrong magnetic field with a very small filling factor neces-sary to fit the wings of our magnetically sensitive lines islikely the cause of the difference between our results, as wellas intrinsic variability of the field. V spectrum In order to fit the Stokes V spectrum we adopt the bestfit v sin i , v mic and Ti abundance from fitting Stokes I withour third model, since these parameters cannot be well con-strained from V spectra (see Table 3).When directly fitting the Stokes V spectrum, it be-comes immediately apparent that a filling factor (much lessthan unity) is necessary. To produce Stokes V profiles withthe widths of the observed lines, a very strong magneticfield is necessary. However, to reproduce the amplitudes ofthe Stokes V profiles, a weaker field is necessary, or a verystrong field covering a small portion of the star. This can beeasily seen by comparing the widths of the observed Stokes I and V profiles (see Fig. 5) and noting that the V profiles re-main stronger in the far wings compared to the I profiles.Fitting the Stokes V profiles with our first model yieldsa best fit of B = . ± . kG and f = . ± . , with areduced χ of 2.27. However, this provides a poor fit to theline profiles, in particular the outer and inner parts of theline cannot be well fit simultaneously. We find a much betterfit when using our second model, with a reduced χ of 1.58,and field strengths and filling factors of B = . ± . kGwith f = . ± . , and B = . ± . kG with f = . ± . , implying (cid:104)| B f |(cid:105) = . ± . kG. The fillingfactors and (cid:104)| B f |(cid:105) derived here are much smaller than thosederived from Stokes I . Stokes V is sensitive to the sign of theline-of-sight component of B , while Stokes I is sensitive tothe magnitude of B . The difference in filling factors is likelydue to cancelation in V of nearby regions with opposite sign.We also fit the Stokes V spectra with our third model,where our use of positive fields is still appropriate as the discintegrated field is positive for March 27, and indeed at allother phases. Our fit yields a reduced χ of 1.56, where theparameters are summarised in Table 3. The improvement inthe fit using our third model is modest compared to the first MNRAS , 1–27 (2018) C. A. Hill et al. and second models, but it is clearly better visually, witha formally significant improvement of nearly σ . We notethat the distribution of filling factors is quite different fromthat of the Stokes I fit, with most of the surface having nomagnetic field detected in Stokes V , and the remaining fieldlying more in the 5 and 15 kG bins.Using our fits to approximate the longitudinal magneticfield ( B l ), we have taken the line of sight component ofthe model magnetic field, averaged over the stellar disc andweighted by the brightness of the continuum, i.e. B l , syn = (cid:213) i ∫ I c f i B i cos ( θ ) d Ω ∫ I c d Ω (4)where f i is the filling factor for component i , B i is the purelyradial magnetic field for that component, θ is the angle be-tween the line of sight and the radial field. I c is the contin-uum brightness at for a point on the disc (accounting forlimb darkening), and the integral of d Ω is over the visibledisk.From Eqn. 4 we derive B l , syn = . ± . kG and . ± . kG for our second and third models, respectively.These values agree to within their uncertainties, and arecomparable to (but roughly 1.7 times larger than) the ac-tual observed B l values for this phase, as calculated fromthe LSD profiles (see Fig. 4). Indeed, if we calculate an ob-served B l from just the Ti i . ± . kG for March 27. Moreover, the behaviour of thisTi i line with rotational phase is consistent with the LSDprofile, except that it shows a higher field strength. This im-plies that the signal in the Stokes V LSD profiles may notbe adding perfectly coherently, producing a lower amplitude V profile. This is not surprising as, due to the very largefield strength, Zeeman splitting patterns of individual linesbegin to matter for the line profile shapes. Thus, simply scal-ing amplitudes by effective Land´e factors is a less effectiveapproximation for such strong fields. I and V As we detect magnetic fields in both Stokes I and V observa-tions, our model should be able to reproduce these signaturessimultaneously. This requires us to allow a combination ofpositive and negative magnetic fields, resulting in a cancel-lation of much of the signal in Stokes V while allowing fora large unsigned magnetic flux in Stokes I . This is evidentfrom the much smaller filling factor in our fits of Stokes V compared to our fits to Stokes I .Firstly, we performed simultaneous fits to Stokes I and V using a simple model with three magnetic regions - twowith positive fields and one with a negative field. A modelwith one positive field and one negative field is insufficientto reproduce the shapes of the Stokes I or V line profiles. Forthis simple model, the best fit magnetic parameters are B =+ . ± . kG with f = . ± . , B = − . ± . kGwith f = . ± . , and B = + . ± . kG with f = . ± . (with v sin i = . ± . kms − , v mic = . ± . kms − and [Ti/H] = − . ± . ). This fit givesa reduced χ of 7.94, and fits the I spectrum similarly wellto our best model from fitting Stokes I only (see above),although it is too strong in the wings of V , implying that there should be additional cancellation. This model impliesa total (cid:104)| B f |(cid:105) of 4.70 kG, and a synthetic B l , syn (allowing forcancellation) of 1.28 kG, although (as noted) this is likelytoo large.Using our third model (with a grid of magnetic fieldstrengths and filling factors, see above), we again requireboth negative and positive magnetic fields. As with fittingonly Stokes I or Stokes V , we use bins of 0 G, ± kG, ± kG, ± kG, ± kG, and ± kG, for a total of 11 bins. The re-sults of our fit with this model, with 11 filling factors as wellas v sin i , v mic and [Ti/H], are presented in Table C2, witha reduced χ of 6.33 - clearly an improvement over the sim-ple three magnetic-region model. Our fit to the observationtaken on March 27 is shown in Fig. 10, showing a good fit toboth Stokes I and V spectra, including matching the widthof the magnetically-insensitive line with a Land´e factor ofzero.A summation of the filling factors for bins with the same | B | yields a very similar distribution to that for the fit toStokes I only, with differences much smaller than the formaluncertainties. This can be understood as Stokes I is sensitiveto the total magnetic field strength but not the orientationof the magnetic field. Similarly, the difference between fillingfactors for bins with the same | B | but opposite sign producesa distribution very similar to that of the fit to Stokes V only. This can also be understood since Stokes V is sensitiveto the line-of-sight component of the magnetic field only,with the spatially unresolved (within the same model pixel)components of opposite orientation cancelling out. For ourobservation on March 27, we find a total (cid:104)| B f |(cid:105) = . ± . kG and B l , syn = . ± . kG. This (cid:104)| B f |(cid:105) is consistentwith our fit of only Stokes I with our third model, and B l , syn is consistent with our fit of only Stokes V .Over the rotation of TWA 8A, this set of results shows B l , syn to range from ± to ± G, with (cid:104)| B f |(cid:105) rang-ing from . ± . to . ± . kG, and varying coherentlywith rotation phase.Given the high S/N of our observations, the results wepresent here may be limited by systematic errors, and ouruncertainties may be underestimated. To investigate the im-pact of uncertainties in T eff and log g , we re-fit the obser-vation on March 27 with these two parameters changed by ± σ . The change in T eff produces at most a change of . σ inthe other parameters, and often smaller changes than that,and so we conclude that the uncertainty on T eff has a mi-nor contribution to the total uncertainty. Changing log g by σ has a large impact on v sin i and [Ti/H] (4–5 σ ) and on v mic ( σ ), although it has a much smaller impact on themagnetic filling factors of only ∼ σ , rising to σ for the2 kG and 5 kG bins when log g is decreased by σ . In thatcase, the filling factor shifts from the 2 kG bin into the 0 and5 kG bins, underscoring the uncertainty of the 2 kG bin. Therelatively large uncertainty in log g changes the line broad-ening, but does so independently of Land´e factor, and so v sin i and v mic are more sensitive to log g than filling fac-tors. It is possible that our v mic is an over-estimate, sincetypical v mic values for PMS M-dwarfs are not well known.To estimate an upper limit on this uncertainty, we re-ranthe fit with v mic = , finding that the best fitting v sin i de-creases by 1 kms − , that [Ti/H] increases by 0.1 dex, andthat filling factors generally change by less than σ (exceptfor the 10 kG bin which decreases by σ ). From these tests MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A we conclude that our formal uncertainties may be underes-timated by a factor (cid:46) , mostly due to the large uncertaintyin log g and the (potentially) larger systematic errors on thefilling factors for the 2 and 20 kG bins.Having established an analysis method for the observa-tion of March 27 using our third model to fit both Stokes I and V , we performed this analysis on all observations forwhich we could perform reliable telluric correction, provid-ing us with ten sets of results, shown in Table C2. Taking anaverage over all 10 observations, we find a mean magneticfield strength of (cid:104)| B f |(cid:105) = . ± . kG, where the amountof magnetic energy in each bin is shown in Table 3. Thestandard deviation of these results is close to the mean un-certainty for all parameters, suggesting that our formal un-certainties account well for random errors, with the largerstandard deviation likely due to the rotational modulation.In Fig. 11 we compare the magnetic field strength dis-tribution on TWA 8A as determined by our ZDI maps inSection 4.2, to our direct spectral fitting here. As our ZDImap has a continuous distribution of field strengths, we havecreated histograms using the same bins as that for the directspectral fitting, allowing for a direct comparison of recov-ered field strengths. For Stokes I , we find that 75 per centof the field strength recovered by ZDI is in the 2 kG bin,with a 15 per cent in the 5 kG bin, and 9 per cent at higherfield strengths. In comparison, direct spectral fitting yields32 per cent of the magnetic field to be 2 kG, with almost46 per cent in the 5 kG bin, and with 22 per cent of fields inthe 10, 15 and 20 kG bins. For Stokes V , the line profiles aresensitive to the sign of the line-of-sight component of B , andso there is likely significant cancellation of fields of oppositepolarity. Hence, our fits to Stokes V LSD profiles with ZDIrecover only the uncanceled magnetic fields. Therefore, forcomparison to direct spectra fitting, we must subtract thefilling factors determined for the negative fields from thepositive fields, yielding the fraction of uncanceled fields thatcould be fit with ZDI. For ZDI we find that 80 per cent ofthe surface has a 0 G field, with 15 per cent of the field inthe 2 kG bin, 3 per cent in the 5 kG bin, 1 per cent in the10 kG bin, and with 1 per cent at higher field strengths.In comparison, for direct spectral fitting we find that lessthan 1 per cent of the field is 2 kG, with 3.6 per cent of thefield at 5 kG, 1.4 per cent at 10 kG, and with 4.5 per centat higher field strengths. Thus, with ZDI we recover mostof the magnetic flux up to 10 kG, but are not as sensitiveto fields higher than this. Moreover, our results demonstratethat we underestimate the fraction of high field strengths us-ing the ZDI technique with LSD profiles Stokes V spectra.As mentioned previously, this may be due to the signal inthe Stokes V LSD profiles not adding perfectly coherently,as variations in line splitting patterns cause variations in lineshapes, and so scaling amplitudes by effective Land´e factorsis less accurate. Moreover, there may be significant cancel-lation in Stokes V profiles as it is sensitive to the sign of theline-of-sight component of B . The recovery of small-scale,high-field-strength features would likely be improved if lin-ear polarization spectra (Stokes Q and U ) were included inthe ZDI modelling, and would likely increase the recoveredtotal magnetic field energy (see Ros´en et al. 2015). Table 3.
Best fit parameters from direct spectral fitting ofTWA 8A. The first and second columns respectively give the re-sults of fitting Stokes I and V separately (using our third model)for the spectrum taken on 27 Mar 2015. Parameters with no er-ror bars for the V fit were held fixed. The third column showsthe results of fitting Stokes I and V simultaneously, where wepresent the mean over the 10 nights that could be reliably telluric-corrected, with error bars given as the standard deviations. Valuesfor fits to individual nights are presented in Table C2.Stokes I only Stokes V only Stokes I and V
27 Mar 2015 27 Mar 2015 mean v sin i (kms − ) . ± . . ± . v mic (kms − ) . ± . . ± . [ Ti/H ] − . ± . -7.01 − . ± . . ± .
084 0 . ± .
014 0 . ± . +2 kG . ± .
067 0 . ± .
010 0 . ± . +5 kG . ± .
044 0 . ± .
007 0 . ± . +10 kG . ± .
020 0 . ± .
005 0 . ± . +15 kG . ± .
013 0 . ± .
005 0 . ± . +20 kG . ± .
011 0 . ± .
004 0 . ± . -2 kG - - . ± . -5 kG - - . ± . -10 kG - - . ± . -15 kG - - . ± . -20 kG - - . ± . (cid:104)| B f |(cid:105) (kG) . ± . . ± . . ± . As well as characterizing magnetic fields of wTTSs, theMaTYSSE program also aims to detect close-in giant plan-ets (called hot Jupiters, hJs) to test planetary formationand migration mechanisms. In particular, characterizing thenumber and position of hJs will allow us to quantiatively as-sess the likelihood of the disc migration scenario, where giantplanets form in the outer accretion disc and then migrateinward until they reach the central magnetospheric gaps ofcTTSs (see e.g., Lin et al. 1996; Romanova & Lovelace 2006).Given that we map the surface brightness of the host star,we are able to use our fits to the observed data to filter outthe activity-related jitter from the RV curves (where the RVis measured as the first-order moment of the LSD profile;see Donati et al. 2014, 2015). After subtraction of the RVjitter, we may look for periodic signals in the RV residualsto reveal the presence of hJs. Indeed, this method has sofar yielded two detections of hJs in the MaTYSSE sample,around both V830 Tau (Donati et al. 2015, 2016, 2017) andTAP 26 (Yu et al. 2017).For TWA 6, the unfiltered RVs have an rms disper-sion of 3.8 kms − . The predicted RV due to stellar activityand the filtered RVs are shown in Fig. 12. We find that RVresiduals exhibit an rms dispersion of ∼ . kms − , with amaximum amplitude of 0.51 kms − . This is well above the in-trinsic RV precision of ESPaDOnS (around 0.03 kms − , e.g.Moutou et al. 2007; Donati et al. 2008), however, given thehigh v sin i , the accuracy of the filtering process is somewhatreduced, with an intrinsic uncertainty of around 0.1 kms − .Indeed, we find no significant peaks in a periodogram anal-ysis, and so we find that TWA 6 is unlikely to host a hJwith an orbital period in the range of what we can detect(i.e. not too close to the stellar rotation period or its firstharmonics; see Donati et al. 2014). We find a σ error bar on MNRAS000
004 0 . ± . -2 kG - - . ± . -5 kG - - . ± . -10 kG - - . ± . -15 kG - - . ± . -20 kG - - . ± . (cid:104)| B f |(cid:105) (kG) . ± . . ± . . ± . As well as characterizing magnetic fields of wTTSs, theMaTYSSE program also aims to detect close-in giant plan-ets (called hot Jupiters, hJs) to test planetary formationand migration mechanisms. In particular, characterizing thenumber and position of hJs will allow us to quantiatively as-sess the likelihood of the disc migration scenario, where giantplanets form in the outer accretion disc and then migrateinward until they reach the central magnetospheric gaps ofcTTSs (see e.g., Lin et al. 1996; Romanova & Lovelace 2006).Given that we map the surface brightness of the host star,we are able to use our fits to the observed data to filter outthe activity-related jitter from the RV curves (where the RVis measured as the first-order moment of the LSD profile;see Donati et al. 2014, 2015). After subtraction of the RVjitter, we may look for periodic signals in the RV residualsto reveal the presence of hJs. Indeed, this method has sofar yielded two detections of hJs in the MaTYSSE sample,around both V830 Tau (Donati et al. 2015, 2016, 2017) andTAP 26 (Yu et al. 2017).For TWA 6, the unfiltered RVs have an rms disper-sion of 3.8 kms − . The predicted RV due to stellar activityand the filtered RVs are shown in Fig. 12. We find that RVresiduals exhibit an rms dispersion of ∼ . kms − , with amaximum amplitude of 0.51 kms − . This is well above the in-trinsic RV precision of ESPaDOnS (around 0.03 kms − , e.g.Moutou et al. 2007; Donati et al. 2008), however, given thehigh v sin i , the accuracy of the filtering process is somewhatreduced, with an intrinsic uncertainty of around 0.1 kms − .Indeed, we find no significant peaks in a periodogram anal-ysis, and so we find that TWA 6 is unlikely to host a hJwith an orbital period in the range of what we can detect(i.e. not too close to the stellar rotation period or its firstharmonics; see Donati et al. 2014). We find a σ error bar on MNRAS000 , 1–27 (2018) C. A. Hill et al. the semi-amplitude of the RV residuals equal to 0.19 kms − ,translating into a planet mass of (cid:39) . M Jup orbiting at (cid:39) . au (assuming a circular orbit in the equatorial planeof the star; see Figure 13).For TWA 8A, the unfiltered RVs have an rms dispersionof 0.13 kms − . Given that the surface brightness of TWA 8Ais compatible with that of a homogeneous star, we were un-able to filter the RVs in the same manner. However, themeasured RVs (shown in Fig. 12) do display a clear periodicsignal that is equal to the stellar rotation period, imply-ing that there are starspots on the surface, even though themodulation of the line profiles is minimal. We report the results of our spectropolarimetric observa-tions collected with ESPaDOnS at CFHT of two wTTSs,namely TWA 6 and TWA 8A, in the framework of the in-ternational MaTYSSE Large Program. Our spectral analysisreveals that the two stars have quite different atmosphericproperties, with photospheric temperatures of ± Kand ± K and logarithmic gravities (in cgs units) of . ± . and . ± . . The stars are significantly different inmass, with TWA 6 being . ± . M (cid:12) and TWA 8A beingaround half that at . ± . M (cid:12) . Likewise, the radii arealso different with . ± . R (cid:12) for TWA 6 and . ± . R (cid:12) for TWA 8A, viewed at inclinations of ◦ ± ◦ and ◦ ± ◦ .Using the Siess et al. (2000) evolutionary models (for directcomparison to other MaTYSSE and MaPP results), we esti-mate their ages to be ± Myr and ± Myr, with TWA 6being mostly radiative, and TWA 8A being fully convective.We note that these masses, ages and internal structures de-pend strongly on the adopted temperatures.With a rotation period of . ± . d, TWA 6 isthe most rapidly rotating wTTS yet mapped with ZDI, andone of the fastest rotators in TWA (see de la Reza & Pinz´on2004). By contrast, TWA 8A has a much slower period of . ± . d, which is very similar to the median period of4.7 d of the TWA 1–13 group (Lawson & Crause 2005), andalso more similar to that of other wTTSs such as V819 Tau( P rot = . d, Donati et al. 2015), as well as Par 1379( P rot = . d, Hill et al. 2017).We find that neither TWA 6 nor TWA 8A have an in-frared excess up to 23.675 µ m. Hence, both stars have likelydissipated their circumstellar accretion discs, with either noaccretion taking place, or with accretion occurring at an un-detectable level, given that standard accretion-rate metricsbased on the equivalent widths of H α , H β and He i D arestrongly affected by chromospheric emission.The H α , H β and Ca ii IRT emission for both stars ismostly non-variable, with only a few spectra showing ex-cess emission that is attributable to flaring events or promi-nences. In particular, TWA 6 shows excess red-shifted emis-sion in the H α , H β and Ca ii IRT lines in three spectra, how-ever, these features are not long lasting and are not periodic.Indeed, the magnetic topology at these phases is such thatexcess emission could be due to off-limb prominence materialthat is rotating away from the observer in closed magneticloops.Using Zeeman Doppler Imaging, we have derived a sur-face brightness map of TWA 6, and the magnetic topologies of both stars. We find that TWA 6 has many cool spotsand warm plages on its surface, with a total coverage ofaround 17 per cent. We detect no significant modulationof the Stokes I lines profiles for TWA 8A, and so find itssurface to be compatible with a uniformly bright star. Thereconstructed magnetic fields for TWA 6 and TWA 8A aresomewhat different in strength, and dramatically differentin topology. TWA 6 has a field that is split equally betweenpoloidal and toroidal components, with the largest fractionof energy in higher order modes (with (cid:96) > ), with a totalunsigned flux of (cid:104) B (cid:105) = G and where the large-scale mag-netosphere is tilted at ◦ from the rotation axis. On theother hand, TWA 8A has a highly poloidal field, with mostof the energy in the high order modes with (cid:96) > . The fieldstrength is sufficiently large that the Stokes I lines profilesare significantly Zeeman broadened, with Zeeman signaturesclearly detected in individual Stokes V spectral lines. Wederive a total unsigned flux of (cid:104) B (cid:105) = . kG, using a mag-netic filling factor f equal to 0.2 (meaning that 20 per centof the surface was covered with the mapped magnetic fea-tures), where on large scales the magnetosphere is tilted at ◦ from the rotation axis.For TWA 8A, our simultaneous fits to both Stokes I and V spectra yields a mean magnetic field strength of (cid:104)| B f |(cid:105) = . ± . kG, with a significant fraction of energyin high-strength fields ( > kG). Given that we recover alarger fraction of high magnetic field strengths from our di-rect modelling of Stokes I profiles, with those fields havingsmall filling factors, a significant proportion of magnetic en-ergy likely lies in small-scale fields that are unresolved byZDI. The difference between direct spectral fitting and ZDIis likely due to several factors; Firstly, by the cancellationof near-by regions of different sign in Stokes V (providingmost of the difference between Stokes I and V in single lines);Secondly, by the signal in Stokes V LSD profiles not addingperfectly coherently due to the non-self similarity of differ-ent lines in Stokes V , with scaling amplitudes by effectiveLand´e factors yielding a less accurate line profile (most ofthe difference between single lines and LSD profiles). Hence,small-scale high-strength magnetic fields are not recoveredwith LSD, and are thus not reconstructed with ZDI.Compared to Tap 26, another wTTS that has a similarmass, age and rotation rate (Yu et al. 2017), TWA 6 has alarger toroidal field component (50 per cent for TWA 6 ver-sus 30 per cent for Tap 26), with a total field strength thatis around twice as large. Likewise, the field of TWA 6 is alsoaround twice as strong as those of the slower rotating (butsimilarly massive) wTTSs, V819 Tau and V830 Tau (Donatiet al. 2015). In the case of TWA 8A, we find that is has aweaker (poloidal) dipole field (of B = . kG) comparedto LkCa 4 (with B = . kG), a wTTSs with a similar rota-tion rate and a slightly higher mass ( P rot = . d, 0.8 M (cid:12) ).Moreover, compared to main-sequence M dwarfs with a sim-ilar mass and period, namely EV Lac ( (cid:104) B (cid:105) = . kG) andGJ 182 ( (cid:104) B (cid:105) = G), we see that TWA 8A has a slightlystronger magnetic field.In Fig. 14 we compare the magnetic field topologies ofall cTTSs and wTTSs so far mapped with ZDI in an H-Rdiagram. Fig. 14 also indicates the fraction of the field thatis poloidal, the axisymmetry of the poloidal component, andshows PMS evolutionary tracks from Siess et al. (2000). Incontrast to cTTSs of the MaPP project, the wTTSs that
MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A Rotation cycle
RVs & x4 residuals (km/s)
Rotation phase
Rotation cycle
RV (km/s)
Figure 12.
Top left panel: RV variations (in the stellar rest frame) of TWA 6 a function of rotation phase, as measured from ourobservations (open blue circles) and predicted by the tomographic brightness map of Figure 6 (green line). RV residuals are also shown(red crosses, with values and error bars scaled by a factor of 4 for clarity), and exhibit a rms dispersion equal to 0.20 kms − . RVs areestimated as the first order moment of the Stokes I LSD profiles rather than through Gaussian fits, due to their asymmetric and oftenirregular shape. Top right panel: The same as the top left panel after phase-folding the data and model. Note that the model shows littlevariation over the ∼ rotation cycles, showing the very low level of differential rotation. Bottom panel: The measured RVs of TWA 8Aas a function of rotation phase. Note that the filtered RVs are not shown for TWA 8A as the line profiles are compatible with a starof uniform brightness. The unfiltered RVs show a period signal that is equal to the stellar rotation period. This figure is best viewed incolour. Orbital distance (AU)
Mass (M
Jup ) TWA 6 σ TWA 6 σ Figure 13.
The σ and σ upper limits (solid and dashed lines,respectively) on the recovered planet mass as a function of orbitaldistance, using the RVs shown in Fig. 12 for TWA 6. This figureis best viewed in colour. have been analysed (so far) in the MaTYSSE sample do notappear to show many obvious trends with internal struc-ture. The magnetic field strength does not appear to changesignificantly after the star becomes mostly radiative, with the largely convective V830 Tau, V819 Tau and V410 Tauhosting a similarly strong dipole field to the mostly radiativeTAP 26, and with the largely convective Par 2244 hostinga similarly strong field mostly radiative TWA 6. Moreover,the percentage of poloidal field does not appear to changefrom when the star is fully convective to when it is mostlyradiative (e.g., V410 Tau and TWA 6 are both around50 per cent poloidal). However, the degree of axisymmetryof the poloidal field appears to correlate with the strengthof the magnetic field, given that LkCa 4 and TWA 8A (twostars with significantly stronger fields of 1.2 kG and 1.4 kG,respectively) are mostly axisymmetric ( (cid:38) per cent). Con-sidering both cTTSs and wTTSs as a whole, it appears thatstars are mostly poloidal and axisymmetric when they aremostly convective and cooler than ∼ K. Moreover, starshotter than ∼ K appear to be less axisymmetric and lesspoloidal, regardless of their internal structure. We note thatthe wTTSs studied thus far clearly show a wider range offield topologies compared to those of cTTSs, with large scalefields that can be more toroidal and non-axisymmetric, con-sistent with the fact that most of them are largely radiativeor are higher mass. We also note that a more complete anal-ysis will be possible once the remainder of the MaTYSSEsample has been analysed.Through our tomographic modelling, we were able to
MNRAS000
MNRAS000 , 1–27 (2018) C. A. Hill et al. T eff (K)1.02.03.04.05.06.0 L ( L (cid:12) ) LkCa 4V830 TauV410 TauV819 TauPar 1379Par 2244TWA 6 TWA 8ATAP 26TWA 9A A x i s y mm e t r y ( s h a p e ) / P o l o i d a l ( c o l o u r) < B > ( G ) Figure 14.
H-R diagram showing the MaTYSSE wTTSs (black line border and labelled) and the MaPP cTTSs (no border). Thesize of the symbols represents the surface-averaged magnetic field strength (with a larger symbol meaning a stronger field), the colourof the symbol represents the fraction of the field that is poloidal (with red being completely poloidal), and the shape of the symbolsrepresents the axisymmetry of the poloidal field component (with higher axisymmetry shown as a more circular symbol). Also shown areevolutionary tracks from Siess et al. (2000) (black dashed lines, ranging from 0.3–1.9M (cid:12) ), with corresponding isochrones (black dottedlines, for ages of 0.5, 1, 3, 5 & 10 Myr), and lines showing 100% and 50% convective interior by radius (blue dashed). determine that TWA 6 has a non-zero surface latitudinal-shear at a confidence level of over 99.99 per cent for thebrightness map, and 90 per cent for the magnetic map, asmeasured over the 16 nights of observation. Its shear rateis around 56 times smaller than the Sun, with an equator-pole lap time of + − d. Given the lack of variability inthe lines profiles and the small number of observed rotations( ∼ cycles), we were unable to measure the shear rate forTWA 8A. Out measured shear rate for TWA 6 is similar tothat found for V410 Tau, V819 Tau, V830 Tau and LkCa 4(Skelly et al. 2010; Donati et al. 2014, 2015), which are allof similar mass.Finally, the brightness map of TWA 6 was used to pre-dict the activity related RV jitter due to stellar activity,allowing us to filter the measured RVs in the search forpotential hJs (in the same manner as Donati et al. 2014,2015). Here, the activity jitter was filtered down to a rmsRV precision of ∼ . kms − (from an initial unfilteredrms of 3.8 kms − ). While this is well above the RV preci-sion of ESPaDOnS, the high v sin i decreases the accuracy ofthe filtering process, with an intrinsic uncertainty of around0.1 kms − . We find no significant peaks in a periodogramanalysis, and find that TWA 6 is unlikely to host a hJ withan orbital period in the range of what we can detect, with a σ error bar on the semi-amplitude of the RV residuals equal to 0.19 kms − , translating into a planet mass of (cid:39) . M Jup orbiting at (cid:39) . au. ACKNOWLEDGEMENTS
This paper is based on observations obtained at the CFHT,operated by the National Research Council of Canada, theInstitut National des Sciences de l’Univers of the Centre Na-tional de la Recherche Scientifique (INSU/CNRS) of Franceand the University of Hawaii. We thank the CFHT QSOteam for its great work and effort at collecting the high-quality MaTYSSE data presented in this paper. MaTYSSEis an international collaborative research programme involv-ing experts from more than 10 different countries (France,Canada, Brazil, Taiwan, UK, Russia, Chile, USA, Switzer-land, Portugal, China and Italy). Observations of TWA 8Aare supported by the contribution to the MaTYSSE LargeProject on CFHT obtained through the Telescope AccessProgram (TAP), which has been funded by the“the StrategicPriority Research Program - The Emergence of Cosmologi-cal Structures” of the Chinese Academy of Sciences (GrantNo.11 XDB09000000) and the Special Fund for Astronomyfrom the Ministry of Finance. GJH is supported by generalgrants 11473005 and 11773002 awarded by the National Sci-ence Foundation of China. We also thank the IDEX initia-tive at Universit´e F´ed´erale Toulouse Midi-Pyr´en´ees (UFT-
MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A MiP) for funding the STEPS collaboration program be-tween IRAP/OMP and ESO and for allocating a ‘Chaired’Attractivit´e’ to GAJH. JFD acknowledges funding fromthe European Research Council (ERC) under the H2020 re-search & innovation programme (grant agreement
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APPENDIX A: LINE PROFILES OF CA iiINFRARED TRIPLET, H α , AND H β , FORTWA 6 AND TWA 8A Line profiles of the Ca ii infrared triplet, H α and H β areshown in Fig. A1 and Fig. A2 for TWA 6 and TWA 8A,respectively. APPENDIX B: ACCRETION STATUS OF TWA6 AND TWA 8A
The SEDs of TWA 6 and TWA 8A show no evidence of aninfra-red excess (see Fig. 2), suggesting that both stars aredisc-less. Nevertheless, we may use our high-quality spec-tra of both targets to determine their accretion status usingseveral metrics.Following our previous studies (e.g., Hill et al. 2017),one may estimate the level of surface accretion in TTSs byadopting the relations between line luminosity L line and theaccretion luminosity L acc of Alcal´a et al. (2017). For thispurpose we determined L line by assuming blackbody scal-ing using the stellar radius R (cid:63) and T eff given in Table 2.Then, the mass accretion rate (cid:219) M acc was calculated using therelationship (cid:219) M acc = L acc R (cid:63) GM (cid:63) ( − R (cid:63) R in ) (B1)where R in denotes the truncation radius of the disc, and istaken to be R (cid:63) (Gullbring et al. 1998).For TWA 6, we detect weak He i D emission withan EW of around 0.03 ˚A (1.6 kms − ), corresponding to log (cid:219) M acc (cid:39) − . M (cid:12) yr − . We find the H β emission (seeFig. A1) to have an EW ranging between 0.69–1.44 ˚A(average of 0.96 ˚A, equivalent to 59.5 kms − , correspond-ing to log (cid:219) M acc (cid:39) − . M (cid:12) yr − ), and the H α emissionto have an EW ranging between 2.26–4.03 ˚A (average of 2.85 ˚A, equivalent to 130.2 kms − , corresponding to log (cid:219) M acc (cid:39) − . M (cid:12) yr − ).For TWA 8A, we detect moderate He i D emissionwith an EW of around 0.3 ˚A (17.4 kms − ), correspond-ing to log (cid:219) M acc (cid:39) − . M (cid:12) yr − . We find the H β emis-sion (see Fig. A2) to have an EW ranging between 3.1–6.8 ˚A (average of 3.9 ˚A, equivalent to 238.0 kms − , cor-responding to log (cid:219) M acc (cid:39) − . M (cid:12) yr − ), and the H α emis-sion to have an EW ranging between 5.9–10.9 ˚A (aver-age of 7.2 ˚A, equivalent to 326.9 kms − , corresponding to log (cid:219) M acc (cid:39) − . M (cid:12) yr − ).These accretion rates would suggest that both stars areweakly accreting, however, as discussed in Hill et al. (2017),chromospheric activity in TTS becomes a significant influ-ence on the strength and width of emission lines in the lowaccretion regime. Pertinently, the large convective turnovertimes of TTSs (Gilliland 1986) combined with their rapidrotation means they possess a low Rossby number, placingthem well within the saturated activity regime (e.g., Reinerset al. 2014). Indeed, the H α line luminosity is observed tosaturate in young stars at around log [ L ( H α )/ L bol ] = − . orlower (Barrado y Navascu´es & Mart´ın 2003), and as bothour target stars show line luminosities that are similar to(or below) this level, with log [ L ( H α )/ L bol ] equal to − . for TWA 6 and − . for TWA 8A, any estimate of accre-tion rates based on line luminosities (especially H α , and toa lesser extent H β ) must be considered to be significantlyinfluenced or even dominated by chromospheric activity.The distinction between emission due to accretion andthat due to chromospheric activity has been characterized byseveral authors, yielding a distinct threshold between theseregimes. Using the empirical spectral-type-dependant rela-tionship between the EW(H α ) and the accretion rate of Bar-rado y Navascu´es & Mart´ın (2003), the defining thresholdof an accreting TTS is EW(H α ) equal to 5.1 ˚A and 12.2 ˚Afor K5 and M3 spectral types, respectively (appropriate forTWA 6 and TWA 8A, see Section 3.1). Given that the max-imum EW(H α ) of TWA 6 and TWA 8A are equal to 4.0 ˚Aand 10.9 ˚A , both stars lie below these limits and fall intothe non-accreting regime (where line broadening is domi-nated by chromospheric activity).Elsewhere, Manara et al. (2017) derived an empiricalrelationship between a star’s spectral-type and the point atwhich line emission may be dominated by chromospheric ac-tivity (termed chromospheric accretion ‘noise’). In the caseof TWA 6, this threshold is at log ( L acc,noise / L star ) = − . ± . . Given that the average line luminosities log ( L acc / L star ) for H α , H β and He i D are respectively equal to − . ± . , − . ± . and − . ± . , the luminosity of all threeemission lines are significantly below the threshold of chro-mospheric noise. Likewise for TWA 8A, this threshold isestimated as log ( L acc,noise / L star ) = − . ± . . Here, theaverage line luminosities for H α , H β and He i D are respec-tively equal to − . ± . , − . ± . and − . ± . ,where again, all emission is well below the threshold whereone can distinguish between accretion and chromosphericemission.Thus, the accretion rates determined above for TWA 6and TWA 8A must be taken to be upper limits, given thatchromospheric emission is likely the dominant broadeningmechanism. Hence, our target stars are likely not accreting(or are doing so at an undetectable level), thus confirming MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A
150 0 15001234
I/I Ca II 8498.02
150 0 150
Velocity (km/s)
Ca II 8542.09
150 0 150 0.1510.2325.6385.7175.8389.2589.3599.43911.23611.31612.96813.08113.14314.79714.95115.06316.74016.93427.74127.85327.97929.799
Ca II 8662.14
200 0 200024681012141618
I/I H
200 0 200 0.1510.2325.6385.7175.8389.2589.3599.43911.23611.31612.96813.08113.14314.79714.95115.06316.74016.93427.74127.85327.97929.799 H Velocity (km/s)
Figure A1.
For TWA 6. Left panel: The Ca ii infrared triplet, with line profiles of the 8498.0.2 ˚A 8542.09 ˚A and 8662.14 ˚A componentsshown (left to right) as black solid lines, where the mean line profile is shown in red, with the cycle number displayed on the right of theprofiles. Right panel: H α and H β line profiles, shown in the same manner, additionally showing the co-rotation radius as a dashed blueline. their classification as wTTSs - a result consistent with pastwork by White & Hillenbrand (e.g. 2004); Kastner et al. (e.g.2016). APPENDIX C: MAGNETIC FIELDS FROMDIRECT SPECTRAL FITTING
MNRAS000
MNRAS000 , 1–27 (2018) C. A. Hill et al.
100 0 10010123456789101112131415
I/I Ca II 8498.02
100 0 100
Velocity (km/s)
Ca II 8542.09
100 0 100 0.0200.2300.4510.6650.8871.0991.2851.5001.9582.1752.3652.5793.0183.2183.229
Ca II 8662.14
200 0 200051015202530354045505560657075
I/I H
200 0 200 0.0200.2300.4510.6650.8871.0991.2851.5001.9582.1752.3652.5793.0183.2183.229 H Velocity (km/s)
Figure A2.
Same as Fig. A1 but for TWA 8A, with the left panel showing the Ca ii infrared triplet, and the right panel showing H α and H β line profiles. MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A
100 0 1000.00.20.40.6
V/I (%) Ca II 8498.02
100 0 100
Velocity (km/s)
Ca II 8542.09
100 0 100 0.0200.2300.4510.6650.8871.0991.2851.5001.9582.1752.3652.5793.0183.2183.229
Ca II 8662.14
100 0 100
Velocity (km/s)
V/I (%) H Figure A3.
Stokes V line profiles of TWA 8A with the Ca ii IRT shown in the left panel, and H α shown in the right panel. σ errorbarsare shown in red on the left side of the line profiles.MNRAS000
Stokes V line profiles of TWA 8A with the Ca ii IRT shown in the left panel, and H α shown in the right panel. σ errorbarsare shown in red on the left side of the line profiles.MNRAS000 , 1–27 (2018) C. A. Hill et al.
600 300 0 300 600
Velocity (km/s)
Normalized variance -300 0 300
Velocity (km/s) -3000300
Velocity (km/s) -1.0-0.50.00.51.0
Figure A4.
Left panel: The normalized variance profile of H α for TWA 6. There is variance from around -200 kms − up to around+300 kms − . Right panel: The autocorrelation matrix for H α , where black means perfect correlation and white means perfect anticorre-lation. MNRAS , 1–27 (2018) he weak-line T Tauri stars TWA 6 and TWA 8A
200 100 0 100 200
Velocity (km/s)
Normalized variance
200 100 0 100 200
Velocity (km/s)
Normalized variance
200 100 0 100 200
Velocity (km/s)
Normalized variance -100 0 100
Velocity (km/s) -1000100
Velocity (km/s) -1.0-0.50.00.51.0 -100 0 100
Velocity (km/s) -1000100
Velocity (km/s) -1.0-0.50.00.51.0 -100 0 100
Velocity (km/s) -1000100
Velocity (km/s) -1.0-0.50.00.51.0
Figure A5.
Same as Fig. A4 but for TWA 8A. The top row shows normalized variance profiles for H α , H β and He i D3 (left to right),with the bottom row showing the corresponding autocorrelation matrices.MNRAS000
Same as Fig. A4 but for TWA 8A. The top row shows normalized variance profiles for H α , H β and He i D3 (left to right),with the bottom row showing the corresponding autocorrelation matrices.MNRAS000 , 1–27 (2018) C . A . H i ll e t a l . Table C1.
Atomic data used in the direct spectrum fitting, from VALD, for the major lines. Additional much weaker lines were included in the spectrum synthesis for completeness,but are omitted here for brevity. The quantities low and high refer to the lower and upper level of the transition, respectively. Term symbols are provided to identify lines of the samemultiplet. Species Wavelength (˚A) log gf E low (Ev) J low J high Land´e g low Land´e g high Multiplet termsTi i F – z F ◦ Ti i F – z F ◦ Ti i F – z F ◦ Ti i G – z F ◦ Ti i F – z F ◦ Ti i F – z F ◦ Ti i F – z F ◦ Ti i F – z F ◦ Ti i F – z F ◦ Ti i F – z F ◦ Ti i G – y F ◦ Table C2.
Best fit parameters from direct spectral fitting of TWA 8A, using our third model that fits Stokes I and V simutaneously, for observations that could be adequatelytelluric-corrected. Each column gives the fitted parameters for the spectrum obtained on the date given at the top. Mean values are presented in Table 3.2015-03-25 2015-03-26 2015-03-27 2015-03-28 2015-03-29 2015-03-30 2015-03-31 2015-04-01 2015-04-05 2015-04-06 v sin i (kms − ) . ± .
19 4 . ± .
17 4 . ± .
18 5 . ± .
17 4 . ± .
18 4 . ± .
16 4 . ± .
16 4 . ± .
17 4 . ± .
17 5 . ± . v mic (kms − ) . ± .
07 1 . ± .
06 1 . ± .
06 1 . ± .
06 1 . ± .
06 1 . ± .
05 1 . ± .
06 1 . ± .
06 1 . ± .
06 1 . ± . [ Ti/H ] − . ± . − . ± . − . ± . − . ± . − . ± .
012 6 . ± . − . ± . − . ± . − . ± . − . ± . +2 kG . ± .
023 0 . ± .
017 0 . ± .
018 0 . ± .
018 0 . ± .
018 0 . ± .
016 0 . ± .
016 0 . ± .
018 0 . ± .
019 0 . ± . +5 kG . ± .
010 0 . ± .
009 0 . ± .
010 0 . ± .
010 0 . ± .
010 0 . ± .
009 0 . ± .
009 0 . ± .
010 0 . ± .
010 0 . ± . +10 kG . ± .
008 0 . ± .
006 0 . ± .
007 0 . ± .
007 0 . ± .
006 0 . ± .
006 0 . ± .
006 0 . ± .
006 0 . ± .
006 0 . ± . +15 kG . ± .
007 0 . ± .
006 0 . ± .
006 0 . ± .
006 0 . ± .
006 0 . ± .
005 0 . ± .
005 0 . ± .
006 0 . ± .
006 0 . ± . +20 kG . ± .
005 0 . ± .
004 0 . ± .
005 0 . ± .
005 0 . ± .
005 0 . ± .
004 0 . ± .
004 0 . ± .
005 0 . ± .
004 0 . ± . -2 kG . ± .
023 0 . ± .
017 0 . ± .
018 0 . ± .
018 0 . ± .
018 0 . ± .
016 0 . ± .
016 0 . ± .
018 0 . ± .
019 0 . ± . -5 kG . ± .
010 0 . ± .
009 0 . ± .
010 0 . ± .
010 0 . ± .
010 0 . ± .
009 0 . ± .
009 0 . ± .
010 0 . ± .
010 0 . ± . -10 kG . ± .
008 0 . ± .
006 0 . ± .
007 0 . ± .
007 0 . ± .
006 0 . ± .
006 0 . ± .
006 0 . ± .
006 0 . ± .
006 0 . ± . -15 kG . ± .
006 0 . ± .
006 0 . ± .
006 0 . ± .
006 0 . ± .
006 0 . ± .
005 0 . ± .
005 0 . ± .
006 0 . ± .
006 0 . ± . -20 kG . ± .
005 0 . ± .
004 0 . ± .
005 0 . ± .
005 0 . ± .
005 0 . ± .
004 0 . ± .
004 0 . ± .
005 0 . ± .
004 0 . ± . . ± .
039 0 . ± .
031 0 . ± .
033 0 . ± .
033 0 . ± .
032 0 . ± .
029 0 . ± .
029 0 . ± .
032 0 . ± .
033 0 . ± . M N R A S , ( ) he weak-line T Tauri stars TWA 6 and TWA 8A This paper has been typeset from a TEX/L A TEX file prepared bythe author.MNRAS000