Rotational Modulation of M/L Dwarfs due to Magnetic Spots
C. Lane, G. Hallinan, R. T. Zavala, R. F. Butler, R. P. Boyle, S. Bourke, A. Antonova, J. G. Doyle, F. J. Vrba, A. Golden
aa r X i v : . [ a s t r o - ph ] S e p Rotational Modulation of M/L Dwarfs due to Magnetic Spots
C. Lane , G. Hallinan , R. T. Zavala , R. F. Butler , R. P. Boyle , S. Bourke ,A. Antonova , J. G. Doyle , F. J. Vrba andA. Golden ABSTRACT
We find periodic I-band variability in two ultracool dwarfs, TVLM 513-46546and 2MASS J00361617+1821104, on either side of the M/L dwarf boundary.Both of these targets are short-period radio transients, with the detected I-bandperiods matching those found at radio wavelengths (P=1.96 hr for TVLM 513-46546, and P=3 hr for 2MASS J00361617+1821104). We attribute the detectedI-band periodicities to the periods of rotation of the dwarfs, supported by radiusestimates and measured v sin i values for the objects. Based on the detected pe-riod of rotation of TVLM 513-46546 (M9) in the I-band, along with confirmationof strong magnetic fields from recent radio observations, we argue for magneti-cally induced spots as the cause of this periodic variability. The I-band rotationalmodulation of L3.5 dwarf 2MASS J00361617+1821104 appeared to vary in ampli-tude with time. We conclude that the most likely cause of the I-band variabilityfor this object is magnetic spots, possibly coupled with time-evolving featuressuch as dust clouds. Subject headings: stars: low-mass, brown dwarfs — stars: rotation — stars: spots— stars: variables: general Centre for Astronomy, National University of Ireland, Galway, Ireland; [email protected],[email protected], [email protected], [email protected], [email protected] United States Naval Observatory, Flagstaff Station, 10391 West Naval Observatory Road, Flagstaff, AZ86001; [email protected], [email protected] Vatican Observatory Research Group, Steward Observatory, University of Arizona, Tucson, AZ 85721;[email protected] Armagh Observatory, College Hill, Armagh BT619DG, N. Ireland; [email protected], [email protected]
1. Introduction
The term ultracool dwarf encompasses very low mass stars and brown dwarfs, coveringspectral types late-M, L and T. As the temperature decreases, spectral type moves from Mto L, with the characteristic TiO and VO bands of M dwarf spectra becoming replaced bybroad neutral alkali and iron hydride lines in L dwarfs at roughly 2000 K (Kirkpatrick etal., 2000). Although the change in spectral features in progressing between spectral typesM and L is well characterised, the processes occurring in their cool, neutral atmospheresare not fully understood. Also uncharacterised are any differences in the physical nature orextent of surface features.One of the main reasons for photometric variability studies of late-M and L dwarfs isto probe the physical nature of their atmospheres. Ultracool dwarf variability is generallyattributed to two sources: the presence of magnetic spots, or dust clouds (Mart´ın et al., 2001;Gelino, 2002 (G02); Rockenfeller et al., 2006 (R06)). Surface features such as magnetic spotsor dust clouds may cause optical modulation as the object rotates, and in certain cases allowa measurement of the period of rotation of a dwarf. For either of these scenarios to beaccepted as the dominant source of photometric variability for a particular ultracool dwarf,they must explain the type of variability observed, whether it is aperiodic or periodic. It issometimes possible to constrain the probable cause of variability for an object, by comparingmultiwavelength photometry to photometric signatures generated using atmospheric modelssuch as those of Allard et al. (2001). This method has recently been used to indicatemagnetically induced cool spots as the most likely cause of periodic variability (P=3.65 + − ∼
80% (G02).Another characteristic of L dwarf photometric variability is a lack of stability in bothperiodicity and amplitude. Aperiodic variability is the dominant type of L dwarf variabilityfound in the surveys by BJM01 and G02. Two of the seven variables in the latter sur-vey, 2MASS 0746+20AB and 2MASS 1300+19, displayed significant peaks in a CLEANperiodogram (Roberts et al., 1987), but did not display persistent periodicity throughoutthe dataset. Koen (2006) reported a 2.4 hr periodicity for 2MASS 0605-22342, which per-sisted over 3 days, but decreased significantly in amplitude throughout the observations. 3 –This apparent paucity of stable periodic variability may be linked to spectral type, althoughthere has been no long-timescale monitoring of ultracool dwarf variability to establish thisstatistically.It has been suggested that rapid evolution of atmospheric features such as dust cloudsis the most likely cause of observed aperiodic variability in L dwarfs (G02). However, it maybe possible that magnetic spots on L dwarfs also produce significant periodic modulation,but that evolving features such as dust obscure the underlying period. One theory whichmay explain the characteristics of L dwarf variability is the masking hypothesis, proposedby BJM01, which suggests that if the time scale of evolving surface features is shorterthan the period of rotation of an object, the periodic modulation of its lightcurve will beinhibited. In order to assess the validity of such theories of variability for a particularobject, constraints on the value of its period of rotation from v sin i measurements andradius estimates are extremely useful. Limits on the period of rotation determine whethera period detected in photometric timeseries is rotational, and allow an evaluation of thestability of the photometric periodicity in relation to it.Recent Very Large Array (VLA) observations of the M9 dwarf TVLM 513-46546 (here-after TVLM 513) provided evidence of a 1.96 hr stable periodicity (Hallinan et al., 2006,2007 (H06 & H07)). This periodicity was found to be consistent with a coherent radiationmechanism generated via the electron cyclotron maser instability operating in the low plasmadensity regions above the magnetic poles of the dwarf, requiring TVLM 513 to possess ex-tremely strong ( ∼ kG) magnetic fields. Such strong fields were later confirmed for otherultracool dwarfs by Reiners and Basri (2007). H06 also argues that the L3.5 dwarf 2MASSJ00361617+1821104 (hereafter 2MASS J0036+18) requires the same mechanism to explainthe properties of its radio emission (Berger, 2005 (B05)), which are almost identical to thoseof TVLM 513.The extremely strong magnetic fields of TVLM 513, and most likely for 2MASS J0036+18,might be expected to produce the necessary temperature gradient to create magnetic spots,thus causing photometric modulation. Consequently, we decided to photometrically monitorthese dwarfs on either side of the M/L boundary for I-band variability.
2. Data Acquisition & Observations2.1. Supporting Radio Data
The supporting radio observations discussed in this paper involve ∼
10 hours of VLAobservations of TVLM 513 at a frequency of 8.4 GHz on 2006 May 20th and ∼
10 hours at a 4 –frequency of 4.9 GHz on 2006 May 21st. These observations and the accompanying resultsare detailed in H07. The 4.9 GHz radio data of 2MASS J0036+18 is that of B05, and wasobtained from the VLA archives (project AB1052).
Choices made with regard to the optical observations are as follows: (1) the TVLM513 observations were chosen to coincide with the nights of additional VLA observations(H07), (2) due to the very red optical colours of these dwarfs, the I-band was chosen tomonitor these objects for variability, (3) high time-sampling was performed for sensitivity tothe rotational modulation of these rapid rotators.
The four-night photometric campaign of TVLM 513 ( m I ∼ .
09) was carried out be-tween 2006 May 18th and 21st, UT. Observations were performed on the United States NavalObservatory (USNO) 1m reflector, Flagstaff, Arizona from May 18th - 20th. A Tektronix2048 × ′′ /pixel giving a field of view of 23 ′ × ′ .An imaging cadence of ∼ ∼ ×
512 pixel frame (field of view=1.7 ′ × ′ ) to reducereadout time. This CCD showed evidence of fringing above the sky noise level in the I-band,so frames were dithered to allow removal of fringing during the data reduction. An imagingcadence of ∼ Photometric observations of 2MASS J0036+18 ( m I ∼ .
05) were carried out on 2006September 19th UT, using the USNO 1.55m reflector at Flagstaff, Arizona. The detectorused was the Tek2K CCD, providing an image scale of 0.33 ′′ /pixel and an 11 ′ × ′ fieldof view. Over the ∼ ∼
3. Data Reduction3.1. Basic Reduction
Science frames of TVLM 513 and 2MASS J0036+18 were processed using standardIRAF /PyRAF data reduction techniques and the USNO on-site reduction pipeline. Biassubtraction and flat-fielding were carried out on all frames. The 2MASS J0036+18 data werealso linearized using the Tek2K linearity curve. The fringing pattern of the VATT CCD wasfound to be stable, and its removal was carried out by producing a fringe-correction framefrom the median of a large number of dithered, reduced science frames. I -band Differential Photometry Differential photometry was carried out on all datasets in order to achieve photomet-ric precision of the order of milli-magnitudes through the reduction of atmospheric effects.Aperture photometry was carried out on the targets and a selection of reference stars, chosenon the basis of their stability, linearity, isolation on the frame, and having a similar mag-nitude to the target. Apertures were chosen to provide the highest signal to noise for thetarget. Standard differential photometry techniques were used, similar to those outlined inBJM01, and summarized below. Time series of relative magnitudes ( m rel ) were calculatedas follows: If F i is the instrumental flux for reference star i, with range of reference starsi=1...M, then the relative flux of the r th frame (F r ) is: F r = 1 M M X i F i (1)The m rel values were calculated as follows, from corresponding target and relative mag-nitudes, m t and m r , where F t is the measured flux of the target: m rel = m t − m r =2 . log ( F r /F t ). Image Reduction and Analysis Facility.
Assuming the reference stars were well selected, the standard deviations of their non-variable differential lightcurves may be used to make an empirical estimate of the totalphotometric errors for a target of a certain magnitude (BJM01). This approach may be usedto estimate both formal and “informal” errors, such as those from flat-fielding and fringing,which may be difficult to evaluate accurately. The advantage of this strategy is that it modelsthe expected error in a target due to noise alone, which may be difficult to otherwise isolatein a target with intrinsic variability. The photometric errors in the individual reference starlightcurves were calculated by plotting their formal photometric errors from IRAF ( σ IRAF )against the standard deviations of their lightcurves ( σ rms ). The free parameters of the firstorder polynomial fit to this plot ( a and b ) were then used to give the errors in the i th referencestar lightcurve ( δm i ): δm i = a + b · σ IRAF . The error in the relative magnitude ( δm rel ) wasthen calculated using the magnitude errors in the target δm t , and the i th reference star, δm i (i=1...M), as demonstrated by BJM01:( δm rel ) = ( δm t ) + ( 1 M F r ) M X i F i ( δm i ) (2) Periodograms or power spectra were used to search for periodic variability. The Lomb-Scargle Periodogram (Lomb, 1976; Scargle, 1982) was calculated for the I-band data ofTVLM 513 and 2MASS J0036+18. The power spectra or periodograms were searched forsignificant peaks, which signify periodic variability. When a significant peak was found,the data were phase folded to this period. These phase folded lightcurves were then visuallyinspected as a final test - the scatter of the lightcurves were found to be lowest when folded tothe periods detected in the periodograms, and began to show increased scatter when foldedat other periods. The measure of variability amplitude used is σ rel , the standard deviationof the target lightcurve. However, the significance of variability in a lightcurve is not simplythe ratio σ rel / δm rel , as for a large number of points, statistically significant variability maybe detected even if σ rel is only slightly larger than δm rel (see BJM01). 7 –
4. Results
Low amplitude, quasi-sinusoidal variability was detected in the I-band photometry forboth objects, with periods identical to those found at radio wavelengths (P=1.96 hr forTVLM 513, and P=3 hr for 2MASS J0036+18); see Fig 1 of this paper and Fig 2 of H07.These periods were used with radius estimates (Dahn et al., 2002) to calculate rotationalvelocities of ∼
60 km s − for TVLM 513 and ∼
37 km s − for 2MASS J0036+18. Thecalculated velocities are consistent with v sin i measurements of ∼
60 km s − for TVLM 513(Basri, 2001) and 36 + − − for 2MASS J0036+18 (Zapaterio Osorio, 2006), indicatinga high inclination angle, i . Based on these results, we attribute the I-band periods to theperiods of rotation, with rotation axes perpendicular to the line of sight.The detected rotational modulation in the TVLM 513 I-band data ( σ rel =0.0076, δm rel =0.0054),along with confirmation of strong magnetic fields in the radio data suggests that magneticspots are the most probable cause of variability. Additionally, this periodic modulation ap-peared to be sustained over the four nights of the observing campaign, being detected inperiodograms of the optical data on all nights between May 18th and 20th (USNO) and inthe May 21st data (VATT). There is a high degree of correlation in the lightcurves fromboth telescopes, despite instrumental differences (see Fig 2).The rotational modulation found for 2MASS J0036+18 is interesting ( σ rel =0.015, δm rel =0.0089),as the amplitude of the modulation apparently changes within the timescale of the observa-tion, a phenomenon which is not reflected in the lightcurves of reference stars or of a fieldstar of similar magnitude (see Fig 2). Just less than three cycles are visible in the 2MASSJ0036+18 lightcurve, with the amplitude of the first ‘peak’ most closely matching the third(Fig 2). Due to the short observation, the Lomb Scargle periodogram assumes that thisbehaviour will repeat ad infinitum, and thus a second peak is produced in the periodogramat a frequency of half the fundamental (Fig 1). As the 3 hr periodicity provides a rotationalvelocity consistent with v sin i measurements, and there is no physical reason for the 6 hrperiodicity, the variation in the peak to peak amplitude is most likely due to some underlyingaperiodic variability. If this object is indeed an analogue of TVLM 513 as argued by H06, itmust have strong magnetic fields. Therefore, we suggest that magnetic spots are the mostlikely source of the 3 hr rotational modulation, while rapidly evolving features may causethe apparent change in amplitude of the variability. Such features might include dust cloudsor magnetic spots which are changing in size or temperature. 8 –
5. Discussion & Conclusions
We have detected periodic modulation in the I-band photometry of TVLM 513 and2MASS J0036+18, which we have determined to be rotational using radius estimates and v sin i measurements. Radio observations have provided confirmation of strong magneticfields for TVLM 513 and there is evidence for their existence on 2MASS J0036+18. Basedon the optical and radio results, we argue that magnetic spots are the cause of the variabilityof both these objects.In the case of 2MASS J0036+18 (L3.5), this is contrary to expectations that dust isthe cause of all L dwarf variability. It has been suggested that the fractional ionization ofthe photospheric and atmospheric plasma of ultracool dwarfs is too low to sustain magneticspot structures (G02, Mohanty et al., 2002). However, if the magnetic field is large-scale, ashas been confirmed to be the case for TVLM 513 (H07), it may produce magnetic spots. Aplausible explanation for the 2MASS J0036+18 result is that the amplitude of the underlyingrotational signal due to magnetic spots is itself modulated by evolving features such as dustclouds. However, long-timescale observations are necessary to rule out random noise effectsand to investigate the possible influence of evolving features.It should be noted that our observations were designed to be sensitive to the rotationalmodulation of rapid rotators, with high temporal resolution photometry obtained for bothobjects. This strategy was found to be successful, and our next challenge is to monitor2MASS J0036+18 to investigate timescales for possible evolving features by isolating theireffects from the underlying rotational modulation.This work is supported by Science Foundation Ireland under its Research FrontiersProgramme, the Higher Education Authority’s Programme for Research in Third Level In-stitutions, and the Irish Research Council for Science, Engineering and Technology. ArmaghObservatory is grant-aided by the N. Ireland Dept. of Culture, Arts & Leisure. We alsothank Hugh Harris and our referee for their suggestions, which have greatly improved themanuscript. REFERENCES
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This preprint was prepared with the AAS L A TEX macros v5.2.
10 – −1 ) P o w e r Berger (2005) USNO I BandField Star
Fig. 1.— Lomb-Scargle Periodograms of raw radio and optical data. I-band photometryof 2MASS J0036+18 and a field star of similar magnitude, obtained on USNO 1.55m, Sept19th, 2006 and 4.9 GHz total intensity radio emission, B05. 11 – −0.04−0.020 0.02 0.04 ∆ m ∆ m Fig. 2.— I-band lightcurves of 2MASS J0036+18 and TVLM 513 (a) USNO 1.55m raw2MASS J0036+18 lightcurve, September 19th UT, 2006, measured using 9 reference stars.(b) USNO 1.55m raw lightcurve of a field star of similar magnitude to 2MASS J0036+18,using same reference stars. (c) Binned, phase-folded lightcurves of TVLM 513 data, obtainedat VATT 1.8m, May 21 2006 (black) and USNO 1m, May 18 2006 (grey), both measuredusing two reference stars. The error bars are taken as δm relrel