Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/preprints/488.pdf Äàòà èçìåíåíèÿ: Tue Aug 22 15:54:50 2006 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 22:00:43 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: coronal hole

ROTATIONAL MODULATION OF THE RADIO EMISSION FROM THE M9 DWARF TVLM 513-46546: BROADBAND COHERENT EMISSION AT THE SUBSTELLAR BOUNDARY?
G. Hallinan1 , A. Antonova2 , J.G. Doyle2 , S. Bourke1 , W. F. Brisken3 and A. Golden ABSTRACT The Very Large Array was used to observe the ultraco ol rapidly rotating M9 dwarf TVLM 513-46546 simultaneously at 4.88 GHz and 8.44 GHz. The radio emission was determined to b e p ersistent, variable and p erio dic at b oth frequencies with a p erio d of 2 hours. This p erio dicity is in excellent agreement with the estimated p erio d of rotation of the dwarf based on its v sin i of 60 km s-1 . This rotational mo dulation places strong constraints on the source size of the radio emitting region and hence the brightness temp erature of the asso ciated emission. We find the resulting high brightness temp erature, together with the inherent directivity of the rotationally mo dulated comp onent of the emission, difficult to reconcile with incoherent gyrosynchrotron radiation. We conclude that a more likely source is coherent, electron cyclotron maser emission from the low density regions ab ove the magnetic p oles. This mo del requires the magnetic field of TVLM 513-46546 to take the form of a large-scale, stable, dip ole or multip ole with surface field strengths up to at least 3kG. We discuss a mechanism by which broadband, p ersistent electron cyclotron maser emission can b e sustained in the low density regions of the magnetospheres of ultraco ol dwarfs. A second nonvarying, unp olarized comp onent of the emission may b e due to dep olarization of the coherent electron cyclotron maser emission or alternatively, incoherent gyrosynchrotron or synchrotron radiation from a p opulation of electrons trapp ed in the large-scale magnetic field. Subject headings: radio continuum: stars ­ stars: low-mass, brown dwarfs ­ stars: activity ­ stars: magnetic fields ­ stars: rotation ­ radiation mechanisms: non-thermal
Computational Astrophysics Laboratory, I.T. Building, National University of Ireland, Galway, Ireland; gregg@it.nuigalway.ie, stephen@it.nuigalway.ie, agolden@it.nuigalway.ie.
2 2 1

1

Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland; tan@arm.ac.uk, jgd@arm.ac.uk. National Radio Astronomy Observatory, P.O. Box O, Socorro, NM 87801; wbrisken@nrao.edu.


­2­ 1. INTRODUCTION

Magnetic activity in co ol main sequence stars is usually diagnosed through the detection of coronal X-ray and radio emission, and via the emission from sp ectral lines such as chromospheric H. In the Sun's case, it is accepted that such magnetic activity is p owered by magnetic fields generated by a so-called dynamo at the base of the convective layer where differential rotation is strongest (Parker 1975). This dynamo mechanism is also thought to op erate in a wide sp ectral range of co ol stars from F-typ e to early M-typ e dwarfs and is particularly successful in accounting for the well-established rotation-activity relationship observed over this sp ectral range (Pallavicini et al. 1981; Noyes et al. 1984). For low mass stars with sp ectral typ e M3, the nature of magnetic activity is less well understo o d. Here lies the b oundary at which low mass stars b ecome fully convective, no longer p ossessing the radiative layer necessary to sustain the dynamo. However, M dwarf flare stars, very often with sp ectral typ e later than M3, are asso ciated with intense levels of magnetic activity and are also characterized by large magnetic filling factors, with kG magnetic fields covering a large prop ortion of the stellar disk (Saar 1994; Johns-Krull & Valenti 1996). Indeed, the fraction of ob jects exhibiting emission asso ciated with magnetic activity, particularly high levels of quiescent H emission, is seen to increase steadily for sp ectral typ es M 3 reaching 70% by ab out sp ectral typ e M8 (Gizis et al. 2000; West et al. 2004). Recently, magnetic mapping of the stellar surface of an M4 dwarf has directly confirmed the presence of large-scale, axisymmetric, p oloidal fields, including a strong dip olar comp onent, despite the absence of surface differential rotation (Donati et al. 2006). Clearly an extremely efficient alternative dynamo op erates in low mass, fully convective stars. Beyond sp ectral typ e M8, the realm of ultraco ol stars and brown dwarfs, a sharp drop o ccurs in the levels of quiescent H and X-ray emission observed, along with a complete breakdown of the activity-rotation relationship, with many fast rotators (v sin i > 15 km s-1 ) showing no evidence of quiescent H or X-ray emission (Neuh¨ aser et al. 1999; Gizis et al. 2000; Mohanty & Basri 2003; Fleming et al. 2003; West et al. 2004). This reduction in activity may b e due to the reduced ionization levels in the atmospheres of these co oler dwarfs (Mohanty et al. 2002). Magnetic fields b ecome decoupled from the surrounding atmosphere and are no longer able to generate the necessary magnetic stress required for the dissipation of heat to sustain a chromosphere and corona. However, this do es not preclude the efficient op eration of a dynamo or the generation of large-scale kG magnetic fields on ultraco ol dwarfs. In fact, despite the reduction in the levels of quiescent emission, there have b een detections of H and X-ray flares from a numb er of ultraco ol dwarfs (Reid et al. 1999; Gizis et al. 2000; Rutledge et al. 2000; Lieb ert et al. 2003; Fuhrmeister & Schmitt 2004; Stelzer 2004; Ro ckenfeller et al. 2006a) including a T dwarf (Burgasser et al. 2000) which


­3­ p oint to the presence of strong magnetic fields. Ro ckenfeller et al. (2006b) have recently used multiband photometric monitoring to confirm a p erio dicity of 3.65 ±0.1 hours in observations of the M9V dwarf 2M1707+64. Moreover, these authors asso ciate this p erio dicity with the rotational p erio d of the dwarf and rule out the presence of dust clouds as a source of this variability. Instead, they attribute this p erio dicity to the presence of magnetically induced co ol sp ots on the surface of the star, further evidence for the presence of strong surface magnetic fields on ultraco ol dwarfs. Based on the sharp drop in quiescent H and X-ray emission and the empirical relationships established b etween the observed X-ray and radio emission for a wide sp ectral range of low mass, main sequence stars (Gudel & Benz 1993; Benz & Gudel 1994), it was exp ected ¨ ¨ that any radio emission from ultraco ol stars and brown dwarfs would b e b elow the sensitivity of the current generation of radio telescop es. Nonetheless, Berger et al. (2001) unexp ectedly detected p ersistent, highly variable radio emission from the M9 field brown dwarf LP 944-20 at levels which, based on the lower limit for the quiescent X-ray flux established by the Chandra observation of Rutledge et al. (2000), violated the Gudel-Benz relations by more ¨ than 4 orders of magnitude. Follow up VLA observations by Berger (2002, hereafter B02) yielded three further candidates. All detected sources with measured rotation rates were fast rotators, with confirmed v sin i ranging up to 60 km s-1 , despite quiescent levels of H and X-ray emission b eing absent, greatly suppressed, or not yet observed. B02 p ostulated that the rotation-activity relationship may hold for radio emission in ultraco ol stars and brown dwarfs despite breaking down in other wavelength regimes. Burgasser & Putman (2005) also conducted a survey of southern late M and L dwarfs using the Australia Telescop e Compact Array (ATCA) and confirmed two detected sources. One of these sources, DENIS 1048-3956, was seen to emit an extremely bright ( 20 mJy), narrow bandwidth, 100% circularly p olarized flare, with the inferred brightness temp erature 1013 K requiring a coherent emission mechanism, most likely an electron cyclotron maser which would require the presence of kG magnetic fields. Berger et al. (2005, hereafter B05) have also confirmed a p erio dicity of 3 hours in the radio emission from the L3.5 candidate brown dwarf 2MASS J00361617+1821104 (hereafter 2M 0036+18) in observations separated by three years, citing three p ossible sources of the p erio dicity, (1) orbital motion of a companion (2) rotation of 2M 0036+18 or (3) weak p erio dic flaring. Finally, a large scale survey of late M, L and T dwarfs has yielded three more confirmed radio detections and highlights the trend that Lrad /Lbol increases with later sp ectral typ e, contrary to what is observed at H and X-ray wavelengths (Berger 2006). Observations thus far have established that p ersistent radio emission at the b ottom of the main sequence is a reality, despite the sharp drop in activity observed in X-ray and H emission and confirming the probable existence of large-scale, stable magnetic fields on


­4­ ultraco ol stars and brown dwarfs. In this pap er we rep ort on VLA observations of a previously detected M9 dwarf, TVLM 513-46546 (hereafter TVLM 513), undertaken to further investigate the mechanism resp onsible for this anomalous radio emission. These observations provide insights into the nature, top ology and strength of the asso ciated magnetic fields and more fundamentally, the dynamo mechanism resp onsible for their generation.

2.

TVLM 513

TVLM 513 is a young disk M9 dwarf lo cated at a distance of 10.5 p c with a surface temp erature of 2200 K and a b olometric magnitude of log Lbol /L -3.65 (Tinney et al. 1993, 1995; Leggett et al. 2001). The absence of lithium in the sp ectrum of TVLM 513 requires its mass to b e > 0.6 M (Reid et al. 2002). We further lo osely constrain its mass to b e < 0.8 M for an age < 10 Gyr, based on correlation of its determined prop erties with the evolutionary mo dels put forward by Baraffe et al (1998) and Chabrier et al. (2000). This places TVLM 513 right at the substellar b oundary, b eing either a high mass brown dwarf or an older, very low mass star. It is one of the most rapidly rotating ultraco ol dwarfs thus far detected with a measured v sin i of 60 km s-1 (Basri 2001). Despite this rapid rotation it displays only weak H emission, with equivalent width measurements of 1.7-3.5 ° (Mart´ et al. 1994; Reid et al. 2001; Mohanty & Basri 2003), and there are A in no rep orted X-ray detections in the literature. Although H activity is suppressed, it has b een strongly detected at radio frequencies. B02 used the VLA to detect p ersistent, variable emission at 8.46 GHz which included a strongly right circularly p olarized ( 65%) flare which reached a flux intensity of 1100µJy. More recently, Osten et al. (2006) conducted a multifrequency VLA observation of TVLM 513 at 8.4 GHz, 4.8 GHz and 1.4 GHz, using a strategy that involved time-sharing a single 10 ten hour observation b etween the various frequency bands. TVLM 513 was detected at each frequency band with only marginal confirmation of variability and no detection of flares or strong circular p olarization, p ossibly due to the absence of continuous coverage at any one frequency band.

3.

RADIO OBSERVATIONS

The radio observations of TVLM513 were conducted with the NRAO Very Large Array (VLA) 1 , for a duration of 4.74 hours on 2005 January 13 and 4.74 hours on 2005 January
The VLA is operated by the National Radio Astronomy Observatory, a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.
1


­5­ 14, simultaneously in C (4.88 GHz) and X (8.44 GHz) band. This was achieved by splitting the VLA into two subarrays, with 14 and 11 antennas used for C and X band resp ectively on January 13, and 13 and 12 antennas used for C and X band resp ectively on January 14. 3C286 was used for flux calibration and 1513+236 was used for phase calibration with a time on source in a single scan of 12 minutes b efore moving to the phase calibrator for 2 minutes for b oth bands. Reduction of the data was carried out using the AIPS software package. After applying the standard pro cedures of calibrating and editing the data, the background sources were removed from the visibility data. This was achieved by using the task IMAGR to CLEAN the region around each source, and then the task UVSUB to subtract the resulting mo dels of the background sources from the map. The task UVFIX was used to shift the tangent p oint co ordinates of the target source to coincide with the phase centre. Light curves were generated by plotting the real part of the complex visibilities at the p osition of TVLM 513 as a function of time.

4.

PROPERTIES OF THE RADIO EMISSION

TVLM 513 was detected as a variable source at b oth 4.88 GHz and 8.44 GHz (Figure 1). The average flux received was 405 ± 18 µJy at 4.88 GHz and 396 ± 16 µJy at 8.44 GHz, with the corresp onding sp ectral index of = 0.0 ± 0.2 consistent with observations of earlier sp ectral typ e M dwarfs (Gudel & Benz 1996). There was significant variability around these ¨ average flux levels, as highlighted in Figure 1, which plots the total intensity (Stokes I) radio light curves received at each frequency for b oth observations with a time resolution of 15 minutes. In order to quantify this variability we assumed a constant source and determined the reduced chi-square values, 2 , for Stokes I radio light curves derived from the data at r each frequency with a range of time resolutions from 5-60 minutes. The resulting 2 values r range from 1.2 - 4.0 for the 4.88 GHz light curves and 1.4 - 4.8 for the 8.44 GHz light curves. The higher 2 values are generally derived from the light curves with lower time resolution, r due to reduced error in the data p oints as a result of lower rms noise in the corresp onding longer integration images. Based on the maximum 2 values attained, the 4.88 GHz data r agree at the 4.63% level with a constant source while the 8.44 GHz data agree at the 2.9% level with a constant source. The upp er limit (3 ) on the net degree of circular p olarization is rc 13% at 4.88 GHz and rc 12% at 8.44 GHz. However, in higher time resolution light curves there are significant (> 3 ) detections of b oth left and right circularly p olarized emission at b oth frequencies. Also, as mentioned ab ove, B02 rep orted on a 65% right circularly p olarized flare at 8.44 GHz. As we will discuss further b elow, we p ostulate that there may b e comp onents of b oth left and right circularly p olarized emission from TVLM 513 which may add destructively to give a much reduced net circular p olarization.


­6­ The radio emission from TVLM 513 is also p erio dic at b oth frequencies with a p erio d of 2 hours. This is particularly clear in Figure 2 which correlates the Stokes I radio flux received at 4.88 GHz on January 13th and 14th 2005. To investigate this p erio dicity we p erformed a Lomb-Scargle p erio dogram analysis (Lomb 1976; Scargle 1982; Press & Rybicki 1989) of the 4.88 GHz and 8.44 GHz Stokes I radio light curves for a wide range of time resolutions. The significance of the p eaks derived from this analysis was dep endent on the choice of time resolution, with the strength of the p erio dic signal reduced for more coarsely sampled data. With this in mind, the highest time resolution available of 10 seconds is used for b oth the 4.88 GHz (Figure 3) and 8.44 GHz (Figure 4) p erio dograms. Two clear p eaks are present in b oth p erio dograms at frequencies of 0.5 hr-1 and 1 hr-1 with the p eak at 0.5 hr-1 corresp onding to the fundamental 2 hour p erio d. The secondary harmonic p eak at 1 hr-1 is accounted for by the presence of two main p eaks in the emission p er 2 hour p erio d (Figure 1). The manifestation of b oth p eaks as a group of multiple p eaks (sp ectral leakage) is due to the large gap ( 17 hours) in the observation. We used a program provided by Harry Lehto (private communication) which used a 1-dimensional CLEAN algorithm (Rob erts et al 1987) to iteratively remove the sp ectral window function from the raw data and confirm the presence of b oth p eaks. To further assert that this p erio dicity is not an artifact of the observation, we conducted a Lomb-Scargle p erio dogram analysis of the 4.88 GHz and 8.44 GHz Stokes I light curves of a field source detected in the observation of TVLM 513. A time resolution of 10 seconds was used and the field source data have the same sp ectral window function as the TVLM 513 data. No significant p eaks were present in the p erio dogram of the field source data. In order to determine the significance of the detected p erio dicity in the radio emission from TVLM 513 we conducted Monte Carlo simulations pro ducing Lomb-Scargle p erio dograms of 60,000 randomized versions of the data at b oth frequencies. For all randomized datasets the same sp ectral window function as the original data was also maintained. The resulting false alarm probabilities are shown in Figure 3 and Figure 4. Both p eaks are present with 99% probability in the 4.88 GHz data and > 99.9% probability in the 8.44 GHz data. We also include the p erio dogram of the data from the single observation at 8.44 GHz on January 14 2005 (Figure 5). Once again, the p eaks at 0.5 hr-1 and 1 hr-1 are present with > 99.9% probability. It is also notable that the sp ectral leakage observed in the p erio dograms in Figure 3 and Figure 4 is absent in this p erio dogram which is derived from a single observation and do es not contain a large gap in the data. Interestingly, there are also further significant p eaks present in the p erio dogram at the frequencies of 2 hr-1 , 3 hr-1 and 5 hr-1 , harmonics of the fundamental 0.5 hr-1 frequency. This may b e evidence of further structure in the p erio dic emission from TVLM 513, in particular the p erio dic light curve may b e non-sinusoidal in nature. Similar harmonic p eaks were not detected in


­7­ the p erio dograms of the other individual datasets and further observations are required to investigate this p ossibility. The data were ep o ch folded to generate a high signal to noise light curve of the p erio dic radio emission from TVLM 513. We initially folded the data for a range of p ossible p erio ds at or near two hours and analysed the 2 values of the resulting light curves in an attempt r to detect a p eak in variance. A clear p eak was observed at approximately 1.96 hours and this value was used as the putative p erio d for ep o ch folding the data. Phase bins of 6, 7 and 8 minutes were used with the resulting light curves plotting the total intensity (Stokes I) and circular p olarization (Stokes V) of the data shown in Figure 6 (4.88 GHz) and Figure 7 (8.44 GHz). For each figure two phases of the ep o ch folded light curve are shown for clarity. At b oth frequencies the emission is shown to vary in a non-sinusoidal manner with p erio dic sharp increases in intensity characterized by high levels of either left or right circular p olarization. At 8.44 GHz there is a short p erio dic right circularly p olarized burst where total intensity levels exceed 1000 µJy and circular p olarization levels reach 40%. It is worth noting that a similar burst was observed in a previous 1.83 hour, 8.44 GHz observation of TVLM 513 (B02). At 4.88 GHz a broad p eak in emission observed at phase 0.3 is seen to consist of two adjacent but separate p eaks, the first showing strong left circular p olarization and the second showing right circular p olarization. This amounts to a p erio dic reversal in the p olarization of the emission. To investigate the variation in circular p olarization with frequency we also correlate high time resolution light curves of the Stokes V, 4.88 GHz and 8.44 GHz data, shown in Figure 8. The large p erio dic p eak in left circular p olarization observed in the 4.88 GHz data has no corresp onding counterpart in the 8.44 GHz data, p ossibly indicating a p olarization reversal from low to high frequencies. Another p ossibility is that different regions pro ducing emission with opp osite p olarities are contributing to the emission and different regions dominate at different frequencies. The presence of various regions pro ducing either left or right circularly p olarized emission would also account for the p erio dic reversals in the p olarization of the emission at 4.88 GHz. We can therefore assert that the radio emission from TVLM 513 is characterised by p erio dic bursts of b oth left and right circularly p olarized emission. It is noteworthy, however, that the flux intensity do es not drop b elow 200µJy at either frequency and circular p olarization is absent for much of the ep o ch folded light curve. This indicates that the radio emission from TVLM 513 consists of two comp onents, a highly circularly p olarized p erio dically varying comp onent and a non-varying, unp olarized comp onent. Perio dicity was not detected previously by B02, as the corresp onding 1.83 hour observation was shorter than the estimated p erio d of 2 hours. Similarly, the observation conducted by Osten et al. (2006) involved time-sharing b etween 3 frequency bands with


­8­ the coarseness of the resulting time-series probably inhibiting the detection of the p erio dic signal.

5.

SOURCE OF THE PERIODICITY

The most plausible explanation for the p erio dicity of the radio emission from TVLM 513 is its p erio d of rotation. The maximum p erio d of rotation can b e constrained using the measured v sin i of 60 km s-1 and an estimated radius, the latter b eing a strong function of b oth mass and age. Based on a Teff of 2200 K, the inferred age is greater than 400 Myr, which together with a mass estimate of 0.6 M - 0.8 M yields a radius of 0.1 ± 0.01 R (Chabrier et al. 2000), which is in agreement with the estimated radius for TVLM 513 of Dahn et al. (2002). The resulting maximum p erio d of rotation is 2.0 ± 0.2 hours. This is in excellent agreement with the observed p erio dicity of the radio emission from TVLM 513 and infers a high inclination angle i 65 , i.e., the equatorial plane is very close to our line of sight. Considering the striking similarities in the prop erties of the radio emission from TVLM 513 and the L3.5 dwarf 2M J0036+18 (B02; B05), which include p erio dicity, a high degree of variability and the p erio dic presence of high levels of circular p olarization, it seems probable that the same emission mechanism is resp onsible in b oth cases. Although, B05 cited 3 p ossible sources for the 3 hour p erio dicity in the radio emission from 2M 0036+18, rotation of the dwarf would seem the most likely candidate in light of the probable rotational mo dulation of the radio emission from TVLM 513. Based on the v sin i of 15 ± 5 km s-1 measured for 2M J0036+18 by Schweitzer et al. (2001), this would require a low inclination angle i 24 ± 8 of the axis of rotation, i.e. almost p ole-on. However, Zapatero Osorio et al. (2006) have recently rep orted on a revised measurement of 36 ± 2.7 km s -1 , in close agreement with the equatorial velo city derived from a 3 hour p erio d of rotation. This would require a much larger inclination angle b etween the axis of rotation and our line of sight 66 , similar to what is found for TVLM 513. Any viable mo del for the radio emission from these two ultraco ol dwarfs must account for the rotational mo dulation, which coupled with the high degree of variability, place strong constraints on the length scale of the emitting regions and therefore the brightness temp erature of the asso ciated radio emission.


­9­ 6. RADIO EMISSION MECHANISMS

To date, the radio emission from TVLM 513, and other detected ultraco ol stars and brown dwarfs, has b een attributed to incoherent gyrosynchrotron emission from a nonthermal p opulation of mildly relativistic electrons (B02; Burgasser & Putman 2005; B05; Osten et al. 2006), with the exception of the highly p olarized flare detected from DENIS 1048-3956 (Burgasser & Putman 2005). Such a p opulation of electrons is thought to follow a p ower law distribution, n(E ) E - , with 2 - 4 typically invoked for low mass stars (Gudel 2002). The resulting radio emission is broadly p eaked p erp endicular to the field ¨ ( sin -0.43+0.65 , Dulk & Marsh 1982), which, if applicable to the p erio dic comp onent of the radio emission from TVLM 513, requires o ccultation of emitting active regions by the stellar disc to account for the variability and p erio dicity. Indeed, the high degree of variability of the radio emission, characterized by three-fold variations in flux over short timescales 0.5 hours (Figure 6 & Figure 7), requires the distribution of the emitting active regions to b e non-uniform and confines their length scale, L, to b e much less than the size of the stellar disc. The brightness temp erature asso ciated with an incoherent radiation pro cess is limited to 1012 K by inverse Compton co oling (Kellerman & Pauliny-Toth 1969; Readhead 1994). However, this limiting value applies to synchrotron emission from ultra-relativistic electrons in very weak magnetic fields 1 G, as observed from extragalactic sources, whereas here we are interested in gyrosynchrotron emission from mildly relativistic electrons and the corresp onding higher strength stellar magnetic fields. In this case, the emission is emitted at a frequency, , where = sc , s 10 - 100 and the electron cyclotron frequency c 2.8 â 106 B Hz. Dulk & Marsh (1982) have shown that the effective temp erature of gyrosynchrotron emission, Teff , from an isotropic distribution of electrons with a p ower-law index 2 7 and a low energy cut-off of 10 keV is T 2.2 â 109 10
-0.31

eff

(sin )

-0.36-0.06

(

) c

0.50+0.085

K

(1)

and is limited to a few times 109 K. The brightness temp erature for all incoherent emission is also limited by TB Teff (Dulk 1985), consequently TB is thus limited to a few times 109 K for gyrosynchrotron emission. The brightness temp erature of the radio emission from TVLM 513 is given by TB = 2 â 109 (f /mJ y )( /GH z )-2 (d/pc)2 (L/R )-2 K (2)

Jup


­ 10 ­ Assuming a radius R 0.1 R RJup infers a TB 3.7 â 109 (L/RJup )-2 , based on the average flux received at 4.88 GHz of 405 µJy. Even assuming a length scale L of the order of the size of the stellar disk would yield a brightness temp erature 1 â 109 K. Indeed, this source was also detected at 1.4 GHz by Osten et al. (2006) with a brightness temp erature of TB = 2.9 â 1010 (L/RJup )-2 . If gyrosynchrotron emission is applicable, such a high brightness temp erature requires a source size of the order of the stellar disk or greater. Contrary to this, the characteristics of the p erio dic light curve require highly directive emission from compact regions much less than the size of the stellar disk with a corresp onding much higher brightness temp erature. In particular, the highly circularly p olarized bursts at b oth frequencies (Figure 7 & Figure 8) have very narrow duty cycles ( 0.15 phase) o ccurring over timescales much less than that required for an emitting region to rotate in an out of view, thus confirming the directivity of the emission. Moreover, the p erio dic reversal of the sense of p olarization of the emission at 4.88 GHz confirms the presence of more than one such active region. It seems unlikely, therefore, that the high brightness temp erature and high directivity of the rotationally mo dulated comp onent of the radio emission from TVLM 513 is compatible with isotropic gyrosynchrotron emission from a large extended corona, although it cannot b e ruled out as a p ossible source of the non-varying, unp olarized comp onent. Other incoherent emission pro cesses such as synchrotron emission from a p opulation of ultra relativistic electrons can b e highly b eamed p erp endicular to the lo cal magnetic field, accounting for the variability and rotational mo dulation of the radio emission, and can reach higher brightness temp eratures than gyrosynchrotron emission. Indeed, synchrotron radiation has b een previously prop osed as a source of rotationally mo dulated stellar radio emission (Lim et al. 1992, 1994). However, the detection of significant levels of circular p olarization is incompatible with synchrotron emission. Alternatively, a coherent emission pro cess may b e applicable with the p ossibility of much higher brightness temp eratures b eing invoked. One such coherent pro cess is plasma radiation, which is generated at the plasma frequency, 1/2 p 9000ne Hz where ne is the plasma electron density. However, plasma radiation is more dominant at lower frequencies ( 1 GHz) due to increasing free-free absorption with increasing (and hence ne ) (Gudel 2002). It has b een sp eculated that the degree of absorption ¨ may b e relaxed for a higher temp erature, dense, coronal plasma enabling the generation of plasma radiation at higher frequencies (White & Franciosini 1995; Osten & Bastian 2006). However, such conditions are at o dds with those exp ected for the increasingly co oler and more neutral atmospheres of ultraco ol dwarfs as highlighted by the reduced levels of X-ray and H emission. Another p ossible coherent emission pro cess is electron cyclotron maser emission which, as discussed in §7, can account for the prop erties of the rotationally mo dulated emission


­ 11 ­ from b oth TVLM 513 and 2M 0036+18, particularly if the magnetosphere takes the form of a large-scale, stable, dip ole or multip ole, with kG field strengths at the surface, such as that confirmed for earlier typ e M dwarfs by Donati et al. (2006).

7.

ELECTRON CYCLOTRON MASER EMISSION

The electron cyclotron maser (hereafter referred to as maser) is a particle-wave plasma instability caused by the resonance b etween the gyrating electrons in an externally generated magnetic field and the electric field of electromagnetic waves at frequencies near the electron cyclotron frequency and p erhaps its low harmonics. It has b een prop osed as a p ossible generation mechanism for a wide range of astrophysical radio emission including planetary radiation from all of the magnetized planets, solar microwave bursts as well as certain emissions from dMe stars, T Tauri stars, RS CVn binaries, Algol-like binaries and magnetic chemically p eculiar stars. To date, masering has b een overlo oked as a p ossible source of the radio emission from TVLM 513 and 2M 0036+18 due to the broadband, p ersistent nature of the detected emission from b oth candidates (B05, Osten et al. 2006), whereas maser emission is exp ected to b e confined to short timescales and narrow bands around the fundamental or second harmonic of the electron cyclotron frequency of the emitting source region. However, the emission is only narrow-banded if the masering is confined to a region with very little variation in the lo cal magnetic field strength and hence, the electron cyclotron frequency. This may b e exp ected if the anisotropic electron distribution resp onsible for the maser instability solely takes the form of a loss-cone, a mo del applied to terrestrial auroral kilometric radiation by Wu & Lee (1979). In this mo del, electrons trapp ed in a magnetic field mirror at the surface, developing a loss-cone distribution due to the precipitation of electrons with small pitch angles. This results in an excess in the p erp endicular comp onent of the electron velo city distribution p erp endicular to the magnetic field such that f / > 0, providing the free energy to p ower the maser. This mo del was further develop ed and suggested as a source of certain solar and stellar bursts by Melrose & Dulk (1982), who prop osed that mirroring electrons trapp ed in coronal lo ops may form a loss-cone at the lo op fo otp oints. In the case of maser emission p owered by a loss-cone, the instability is often confined to regions close to the stellar or planetary surface limiting the range in magnetic field strength and hence the bandwidth of the emission. It is also sub ject to saturation of the wave growth as the radiative pro cess removes the loss-cone anisotropy from the electron distribution. However, work by Pritchett (1984a,b), Pritchett & Strangeway (1985) and Winglee & Pritchett (1986) highlighted an alternative mechanism by which the electron distribution


­ 12 ­ can also achieve the necessary anisotropy required for maser emission. Electrons accelerated along magnetic field lines into regions of higher field strength conserve magnetic momentum by evolving adiabatically to higher pitch angles, generating the necessary excess in the p erp endicular comp onent of the electron velo city distribution p erp endicular to the magnetic field, . This "shell distribution" of electrons was subsequently determined to b e more dominant in the generation of terrestrial auroral kilometric radiation than the loss-cone distribution (Ergun et al. 2000, and references therein). Interestingly, maser emission from a shell distribution of electrons is not confined to regions close to the stellar or planetary surface, but can o ccur from source regions at any height where conditions are suitable for the op eration of the maser. Also, the saturation conditions which limit the growth and continuous generation of maser emission from a loss-cone distribution do not apply to the shell maser, which can sustain steady-state, high brightness temp erature emission as long as electron acceleration in the source region is maintained (Pritchett et al. 1999). The conditions in the source region must b e such that (a ) the magnetic field strength is relatively high and the plasma electron density is low such that the electron cyclotron frequency c is much 1/2 greater than the plasma frequency p , where c 2.8 â 106 B Hz and p 9000ne Hz, and (b ) electrons are continuously accelerated in the source region and can adiabatically evolve to form the shell distribution required to p ower the maser. If these conditions were present over a large range of heights ab ove the surface of ultraco ol dwarfs, with a corresp onding wide range of magnetic field strengths, maser emission could viably b e continuously generated at a wide range of frequencies resulting in broadband, p ersistent radio emission. This mo del, if applicable to ultraco ol dwarfs, is a significant departure from the mo del generally applied to co ol stars, which attributes the bulk of broadband, p ersistent radio emission from such stars to incoherent, gyrosynchrotron radiation. In fact, the coherent radio emission observed from all of the magnetized planets in our solar system (Zarka 1998, and references therein), attributed to the electron cyclotron maser instability, is of more relevance to this discussion. In particular, we highlight the coherent radio emission from the quasi-dip olar magnetosphere of Jupiter, which originates in the low density, high magnetic latitude regions and from the magnetic flux tub e of the volcanic mo on Io. This radio emission is emitted in a numb er of comp onents at a range of heights ab ove the planetary surface, with frequencies ranging up to a maximum of approximately 40 MHz which corresp onds to the electron cyclotron frequency at the regions of strongest magnetic field strength at Jupiter's surface (approx 14 G). The low cutoff frequency corresp onds to the electron cyclotron frequency at the height where c /p falls b elow a critical value, typically b etween 2.5 and 10, thereby quenching the instability (Zarka et al. 2001). The emission propagates, for the most part, in the supraluminous X mo de, resulting in 100% circularly or elliptically p olarized emission highly b eamed p erp endicular to the lo cal magnetic field, that can reach


­ 13 ­ brightness temp eratures up to 1020 K. This X mo de emission has an inherent right-handed circular p olarization relative to the lo cal magnetic field, resulting in the detection of right circularly p olarized emission from Jupiter's northern hemisphere and left circularly emission from Jupiter's southern hemisphere. Certain comp onents of this radio emission, such as the decametric emission ( 10 to 40 MHz) from the high magnetic latitudes, referred to as nonIo DAM, can b e broadband ( ), non-varying for timescales of the order of minutes, and show strong rotational mo dulation. By comparison, we now consider this maser emission pro cess in the context of the radio emission prop erties and magnetospheric conditions on ultraco ol dwarfs such as TVLM 513 and 2M 0036+18. It has b een established that the magnetic fields are large-scale and stable due to the presence of p erio dicity in radio observations of 2M 0036+18 separated by two years (B05). If this large scale, stable magnetosphere takes the form of a dip ole or multip ole, with kG fields present at the surface there may b e a large prop ortion of the magnetosphere where source conditions are suitable for the generation of maser emission. In particular, considering the atmospheres of dwarf stars b ecome increasingly neutral b eyond ab out sp ectral typ e M7 (Mohanty et al. 2002) it is reasonable to assume that the average plasma electron density also drops significantly. This assumption is supp orted by the sharp drop in detectable levels of H and X-ray emission for late M and L dwarfs. Moreover, if the magnetosphere takes the form of a dip ole or multip ole, the plasma density would not b e homogeneous throughout the magnetosphere. For example, in the case of a dip ole, any plasma injected into the magnetosphere would remain trapp ed mirroring in the closed field lines and p ossibly form "radiation b elts" analogous to Earth's Van Allen b elts. However, in regions over the p oles, plasma would rapidly escap e along op en field lines leading to the formation of density cavities in the plasma. In this scenario, the plasma density would b e much higher in the radiation b elts than in the "coronal holes" ab ove the magnetic p oles. The rapid rotation of the dwarf might also further aid the trapping of particles at lower latitudes. It is feasible that the plasma density in these density cavities is such that p c for a wide range of heights ab ove the stellar surface. Assuming emission at the fundamental of the electron cyclotron frequency, the upp er cutoff frequency of emission would probably corresp ond to the electron cyclotron frequency at the stellar surface while the lower cutoff frequency of emission would corresp ond to the electron cyclotron frequency at the height ab ove the surface where c /p is insufficient and the instability quenches. In the case of TVLM 513 and 2M 0036+18, with simultaneous detections at frequencies of 4.9 GHz and 8.5 GHz, this would require a range of magnetic field strength in the density cavity ranging from 1.7 - 3 kG with a plasma electron density 3 â 1011 cm-3 . As discussed in §1 the probable detection of an electron cyclotron maser flare at a frequency of 8.5 GHz from the M8.5 dwarf DENIS 1048-3956 (Burgasser & Putman 2005) would indicate that kG field


­ 14 ­ strengths may b e present on ultraco ol dwarfs. A dip olar magnetic field can b e mo delled by Rs R
3

BB

s

(3)

where Bs and Rs are the surface magnetic field strength and radius resp ectively. Considering that the radius of an evolved ultraco ol dwarf is approximately the same as that of Jupiter, the length scale of the emitting region pro ducing simultaneous emission at 4.9 GHz and 8.5 GHz on TVLM 513 and 2M J0036+18 would b e smaller than that pro ducing broadband decametric emission in the frequency range 10 - 40 MHz from Jupiter's p olar regions, alb eit with much stronger kG fields in the source region. An electron density of 3 â 1011 cm-3 in the low density regions ab ove the magnetic p oles of an ultraco ol dwarf is extremely likely, and may b e many orders of magnitude less than this value, considering coronal electron density estimates for more massive, hotter, X-ray emitting stars range from 108 cm-3 - 1013 cm-3 (Gudel 2004). If by some mechanism, a comp onent of the p opulation of trapp ed ¨ mirroring electrons was continuously accelerated into these low density plasma cavities due to the presence of magnetic field-aligned electric fields, these regions could b e the source of p ersistent, broadband, coherent emission. The generation of such quasi-stable, long-lived, electric fields would have to b e inherent to the nature of the large-scale, stable magnetosphere. One p ossible source of electric p otential drops may b e the formation of electrostatic double layers b etween the p opulations of trapp ed ions and electrons. Ions and electrons mirroring at different lo cations could p ossibly form a strong magnetic field-aligned p otential drop, which may b e a source of the continuous particle acceleration necessary for steady-state maser emission. The resulting radiation is exp ected to b e highly b eamed p erp endicular to the magnetic field, explaining the rotational mo dulation of the emission from b oth TVLM 513 and 2M J0036+18. For 2M J0036+18 the emission shows strong net left circularly p olarization indicating that the emission from one hemisphere is dominant. Indeed, Figures 3 & 4 in B05 would seem to indicate that this circular p olarization reaches almost 100% once p er p erio d of emission. In the case of TVLM 513, efficient masering from b oth hemispheres is required to account for the prop erties of the radio emission, with detections of b oth left and right circularly p olarized emission. This is unsurprising considering the rotational axis is almost p erp endicular to our line of sight. The presence of two strong p eaks p er p erio d of emission separated by 0.5 phase also strongly argues for the presence of a dip olar comp onent to the magnetosphere. The broad p eaks in emission o ccur when the magnetic axis of the dip olar field is p erp endicular to our line of sight, which o ccurs twice p er rotational p erio d. However, the fact that there is no net circular p olarization for much of its rotational phase requires a rather contrived geometrical coincidence if the emission is generated solely in the density


­ 15 ­ cavities asso ciated with a dip olar field. The presence of a multip olar comp onent to the magnetic field, with the corresp onding asso ciated density cavities also pro ducing coherent radio emission, may account for this low net p olarization. It is also p ossible that mo de conversion or dep olarization of the X mo de emission o ccurs in the density cavity. Mo de conversion of terrestrial auroral kilometric radiation from X mo de to R mo de in the emitting density cavity is prop osed by Ergun et al. (2000) as an efficient metho d by which the maser emission can escap e without reabsorption at higher harmonics of the emission frequency. Similarly, mo de conversion from X mo de to O mo de has also b een considered as a p ossible source of the elliptical p olarization of the Jovian decametric emission (Zarka 1998, and references therein). Alternatively, the non-varying unp olarized comp onent may b e incoherent gyrosynchrotron or synchrotron radiation. Indeed, if the magnetic field takes the form of a large-scale, stable dip ole or multip ole, the p opulation of electrons mirroring in closed field lines may contribute to the radio emission. As discussed ab ove, this p opulation of electrons would have an anisotropic distribution which, for gyrosynchrotron emission, can result in higher intensity emission than that pro duced by an isotropic p opulation (Fleishman & Melnikov 2003). It is also p ossible that such a p opulation of electrons may b e continuously accelerated by radial diffusion to extremely high ultrarelativistic energies conducive to the generation of synchrotron emission. Such emission is generated at decimetric wavelengths from the radiation b elts of Jupiter and may b e a contributing comp onent to the emission from b oth TVLM 513 and 2M J0036+18.

8.

DISCUSSION AND CONCLUSIONS

We rep ort on VLA observations showing rotational mo dulation of the radio emission from the M9 dwarf TVLM 513, which places strong constraints on the source size of the emitting region, and hence brightness temp erature of the emission. The resulting high brightness temp eratures along with the implicit directivity of the rotationally mo dulated comp onent of the radio emission are difficult to reconcile with incoherent gyrosynchrotron radiation from a p opulation of mildly relativistic electrons. We discuss a new mo del for the radio emission from ultraco ol dwarfs based on the assumption that the magnetic field on these ob jects takes the form of a large scale dip ole or multip ole p owered with kG strength fields at the surface. In regions over the magnetic p oles, plasma can escap e along op en field lines forming density cavities where the electron cyclotron frequency is much greater than the plasma frequency. If a comp onent of the p opulation of trapp ed electrons was continuously accelerated into such density cavities by magnetic field-aligned electric fields,


­ 16 ­ p ossibly due to the presence of electrostatic double layers, such density cavities may b e the source of steady-state, broadband electron cyclotron maser emission. We also discuss the p ossible presence of a non-varying, unp olarized comp onent of the radio emission, which may b e due to dep olarization or mo de conversion of the maser emission in the density cavity. Alternatively, this comp onent of the radio emission may b e incoherent gyrosynchrotron or synchrotron radiation. In particular, trapp ed particles mirroring on closed field lines in the large scale magnetic field can form high density radiation b elts where electrons can b e accelerated to ultrarelativistic energies emitting synchrotron radiation. Coherent maser emission can account for the presence of high levels of circular p olarization and the high brightness temp eratures of the radio emission from ultraco ol dwarfs. The p erio dicity and high degree of variability from b oth TVLM 513 and 2M J0036+18 can b e attributed to the inherent directivity of the radio emission coupled with the rapid rotation of the dwarf. We differentiate b etween this broadband, p ersistent maser emission and the extremely bright 100% circularly p olarized flare observed from the M8.5 dwarf DENIS 10483956 (Burgasser & Putman 2005), typical of flares observed from earlier typ e M dwarfs. Such flares are almost always narrow-banded, 100% circularly p olarized and can display structure over very short millisecond timescales. We sp eculate that b oth the broadband, quiescent emission and narrowband, flare emission are generated in the same source regions by the same mechanism, the electron cyclotron maser, alb eit with fundamental differences in the nature by which the emission is generated. For example, the smo oth broadband emission may b e asso ciated with constant particle acceleration due to quasi-stable electric fields across the source region, whereas the narrowband flaring may b e due to more impulsive acceleration events. This is analogous, once again, to Jupiter's decametric emission, which is characterized by smo oth, broadband bursts with (referred to as L bursts), and more impulsive, narrowbanded bursts with , which can reach much higher brightness temp eratures (referred to as S bursts) (Zarka 1998). The configuration of the magnetosphere may also b e a contributing factor to the ubiquitous rapid rotation of ultraco ol dwarfs. It is unlikely that such a large-scale stable magnetic field would undergo reconnection events in the increasingly neutral atmospheric plasma of ultraco ol dwarfs, minimizing momentum loss due to dissipation of magnetic energy, and thus leading to much longer spin down times than observed on earlier typ e dwarfs. This mo del for the radio emission from ultraco ol dwarfs can also account for the fact that Lrad /Lbol is maintained, and even seen to increase for late M and L typ e dwarfs, despite the sharp drop in magnetic activity detected at other frequencies. The lower plasma density with later sp ectral typ e which inhibits the generation of H and X-ray emission, leads to conditions where more efficient generation of radio emission by the electron cyclotron maser instability can o ccur.


­ 17 ­ The mechanism by which H and X-ray flares are generated on ultraco ol dwarfs is still unclear. Chabrier & Kuker (2006) p ostulate that the magnetic stresses necessary for ¨ such flares are generated in the higher temp erature conductive layers of the star and rise to the surface, dissipating magnetic energy in the upp er atmospheric layers. Such a mo del is supp orted by the observations of Fuhrmeister & Schmitt (2004) who rep ort on a H flare from the M8.5 dwarf DENIS 1048-3956, the source of the large coherent radio flare discussed in §1. They interpret broadening on the blue side of the sp ectral line during the flare as p ossible evidence that the flare was asso ciated with a rising cloud of emission ejected from the dwarf. Such ejections may also b e the source of the trapp ed plasma mirroring in the large-scale magnetic field resp onsible for the generation of the radio emission. The generation of coherent emission in density cavities asso ciated with large scale dip olar or multip olar fields should b e considered as a p ossible source of b oth quiescent and flaring radio emission in a wide range of astrophysical ob jects, including T Tauri stars (Smith et al. 2003), RS CVn binaries (Osten et al. 2004), Algol-typ e binaries (Mutel et al. 1998) and chemically p eculiar stars (Trigilio et al. 2000). Moreover, the absence of high levels of circular p olarization and narrowband structure do es not preclude the p ossibility that such emission may b e coherent. The recent confirmation of a strong, large-scale axisymmetric field on a rapidly rotating M4 dwarf, with a strong dip olar comp onent (Donati et al. 2006), highlights the p ossibility that electron cyclotron maser emission from p olar density cavities may b e a viable source of radio emission from dMe stars. Indeed, Bingham et al. (2001) have suggested maser emission from a shell distribution of electrons as a p ossible source of the 100% circularly p olarized emission from UV Ceti. Considering the ubiquity of highly p olarized, narrowband, coherent bursts from such ob jects, it is quite p ossible that broadband, slowly varying maser emission from the same source regions resp onsible for the flares may also contribute to the quiescent comp onent of the emission. Indeed, such ob jects have much longer p erio ds of rotation than later sp ectral typ e dwarfs such as TVLM 513 and 2M J0036+18 resulting in much slower rotational mo dulation of the highly b eamed emission, and hence lower variability. An imp ortant factor in the determination of the emission mechanism in dMe stars has b een the direct measurement of the extent of stellar radio coronae, and hence constraint of the brightness temp erature of the asso ciated emission, afforded by very long baseline interferometry (VLBI). Some VLBI observations of single dMe stars have revealed large extended radio coronae up to a few stellar radii in diameter, with brightness temp eratures and degrees of circular p olarization in line with incoherent emission such as gyrosynchrotron or synchrotron radiation (Alef et al. 1997; Benz et al. 1998; Pestalozzi et al. 2000). However, other observations of single dMe stars have revealed unresolved flaring and quiescent emission with brightness temp eratures, TB > 1010 K, and very high degrees of circular p olarization


­ 18 ­ (Benz & Alef 1991; Benz et al. 1995). In these cases a coherent emission mechanism such as electron cyclotron maser is the more plausible candidate. Further VLBI observations may clarify the degree to which b oth coherent and incoherent mechanisms contribute to the radio emission from dMe stars, and whether the prevalence of an individual mechanism is frequency dep endent, activity dep endent or related to the magnetospheric conditions on each individual star. Further high sensitivity observations of ultraco ol dwarfs previously detected at radio frequencies should b e undertaken to investigate the presence of p erio dicity and to confirm if this p erio dicity is indeed due to the rotation of the dwarf. Direct detection of the magnetic fields on these ob jects may also b e feasible. Assuming a gyrosynchrotron source would imply a magnetic field strengths of the order of a few hundred gauss to 1kG, however, the coherent pro cess, requires considerably higher field strengths of several kilo-gauss which could p otentially b e detectable using the FeH band around 1µm (Reiners & Basri 2006). Although this technique is still in its infancy, the ab ove authors show that that are sufficient FeH lines available even for the faster rotators whose observation and mo delling could have an imp ortant b earing on the question of which radio pro cess is at work in these ultraco ol dwarfs. Confirmation of the generation of broadband coherent emission from ultraco ol dwarfs would have immense implications for our understanding of stellar magnetic activity and the nature of the dynamo mechanism resp onsible for the generation of the magnetic fields driving this activity. It would also highlight the p ossibility that a similar mechanism for the generation of coherent radio emission from large-scale dip olar or multip olar fields may b e a op erating in a wide range of astrophysical ob jects, ranging from planets to brown dwarfs and co ol stars. Comparison with more exotic phenomena such as coherent pulsar radio emission is also comp elling. The authors gratefully acknowledge the supp ort of the HEA funded Cosmogrid pro ject and Enterprise Ireland under the grant award SC/2001/0322. The authors also wish to acknowledge the SFI/HEA Irish Centre for High-End Computing (ICHEC) for the provision of computational facilities and supp ort. Armagh Observatory is grant-aided by the N. Ireland Dept. of Culture, Arts & Leisure. We are very grateful to Harry Lehto for the use of his CLEAN algorithm and co de and the informative comments on the results pro duced and to Jerome Sheahan for helpful discussions on certain asp ects of this manuscript. Finally, we would like to thank the referee, Rachel Osten, for valuable input and suggestions on how to improve this manuscript.


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A This preprint was prepared with the AAS L TEX macros v5.2.


­ 23 ­

800 Flux (µJy) Flux (µJy) 600 400 200 0 12 4.88 GHz 13 14 15 16 2005 January 13 UT 17

800 600 400 200 0 12 4.88 GHz 13 14 15 16 2005 January 14 UT 17

800 Flux (µJy) 600 400 200 0 12 8.44 GHz 13 14 15 16 2005 January 13 UT 17 Flux (µJy)

800 600 400 200 0 12 8.44 GHz 13 14 15 16 2005 January 14 UT 17

Fig. 1.-- Light curves for the Stokes I radio flux received from TVLM 513 at 4.88 GHz (top ) and 8.44 GHz (bottom ) on 2005 January 13 and 2005 January 14. The time resolution used is 15 minutes for all light curves.


­ 24 ­

800 600 Flux (µJy) 400 200 0 0 1 2 3 hours 4 5 6

Fig. 2.-- Light curves for the Stokes I radio flux received from TVLM 513 at 4.88 GHz on 2005 January 13 (solid line ) and 2005 January 14 (dashed-dotted line ). The two light curves have b een aligned to highlight the close correlation and p erio dicity.


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1 0.5 0 18 16 14 12 Power 10 8 6 4 2 0 0 1 2 3 Frequency (hr-1) 4 5 6
0.05 0.1 0.5 0.001 0.005 0.01

Fig. 3.-- Lomb-Scargle p erio dogram of the 4.88 GHz Stokes I radio emission from TVLM 513 with a time resolution of 10 seconds. Clear p eaks are present at 0.5 hr-1 and 1 hr-1 , corresp onding to the two p eaks in emission p er 2 hour p erio d. The sp ectral leakage present for each p eak is due to the sp ectral window function (shown on top) which is a result of the 17 hour gap b etween the two observations. The small p eak in the sp ectral window function at 4 hr-1 is due to the phase calibration every 15 minutes. The dashed-dotted lines represent the false alarm probabilities of the significance of the p eaks based on 60,000 Monte-Carlo simulations of randomised versions of the light curve with the same sp ectral window function as the original data. The solid lines on the right hand side of the graph represent the false alarm probabilities of the significance of the p eaks as calculated by the Lomb-Scargle algorithm.


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1 0.5 0 18 16 14 12 Power 10 8 6 4 2 0 0 1 2 3 -1 Frequency (hr ) 4 5 6
0.001 0.005 0.01 0.05 0.1 0.5

Fig. 4.-- Same as Figure 3 for the 8.44 GHz Stokes I radio emission from TVLM 513 with a time resolution of 10 seconds. Once again, two clear p eaks at 0.5 hr-1 and 1 hr-1 are present.


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1 0.5 0 12
0.001

10 8

0.005 0.01 0.05

Power

6 4 2 0 0 1 2 3 -1 Frequency (hr ) 4 5

0.1

0.5

6

Fig. 5.-- Lomb-Scargle p erio dogram of the 8.44 GHz Stokes I radio emission from the single observation of TVLM 513 on 2005 January 14, with a time resolution of 10 seconds. There is no sp ectral leakage due to the absence of a large gap in the data. The single p eak in the sp ectral window function at 4 hr-1 is due to the phase calibration every 15 minutes. Once again, the two clear p eaks at 0.5 hr-1 and 1 hr-1 are present. Significant p eaks at the frequencies of 2 hr-1 , 3 hr-1 and 5 hr-1 , harmonics of the fundamental 0.5 hr-1 frequency, are also present. This highlights the p ossible presence of further structure in the p erio dic radio light curve of TVLM 513, in particular the p erio dic light curve may b e non-sinusoidal in nature.


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800 Stokes I 600 Flux (µJy) 400 200 0 0 0.5 1 Phase 1.5 2

Stokes V 200 Flux (µJy) 0 -200 -400 0 0.5 1 Phase 1.5 2

Fig. 6.-- Ep o ch folded light curves derived from the 4.88 GHz Stokes I (top ) and Stokes V (bottom ) radio data from TVLM 513 with phase bins of 6, 7 & 8 minutes. Two p erio ds of the same ep o ch folded light curve are shown for clarity. Positive values for Stokes V indicate right circular p olarization while negative values indicate left circular p olarization. The main p eak at phase 0.3 is resolved to consist of two adjacent p eaks, the first one showing strong left circular p olarization with the second showing right circular p olarization. These highly p olarized emissions add destructively over the course of one p erio d of emission resulting in much lower net circular p olarization.


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1200 1000 Flux (µJy) 800 600 400 200 0 0 0.5 1 Phase 1.5

Stokes I

2

600 400 Flux (µJy) 200 0 -200 -400 0 0.5 1 Phase 1.5

Stokes V

2

Fig. 7.-- Ep o ch folded light curves derived from the 8.44 GHz Stokes I (top ) and Stokes V (bottom ) radio data from TVLM 513 with phase bins of 6, 7 & 8 minutes. Two p erio ds of the same ep o ch folded light curve are shown for clarity. Positive values for Stokes V indicate right circular p olarization while negative values indicate left circular p olarization. The presence of p erio ds of right circular p olarization is clear while evidence for left circular p olarization is marginal at b est. Of particular interest is the short p eak of right circularly p olarized emission where Stokes I flux levels exceed 1000 µJy. The presence of such short duration p erio dic p eaks implies that the emission is inherently directive or b eamed in nature.


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200 Flux (µJy) 0 -200 -400 0 0.5 1 Phase 1.5

4.88 GHz

2

400 Flux (µJy) 200 0 -200 0 0.5 1 Phase 1.5

8.44 GHz

2

Fig. 8.-- Ep o ch folded light curves derived for the 4.88 GHz (top ) and 8.44 GHz (bottom ) Stokes V radio data from TVLM 513 with higher time resolutions of 6, 7 & 8 minutes. Two p erio ds of the same ep o ch folded light curve are shown for clarity. The large p erio dic p eak in left circular p olarization observed in the 4.88 GHz data has no corresp onding counterpart in the 8.44 GHz data. In fact, the emission is mildly right circular p olarized suggesting a reversal in p olarization with frequency.