Spectral type dependent rotational braking and strong magnetic flux in three components of the late-M multiple system LHS 1070
Ansgar Reiners, Andreas Seifahrt, Hans Ulrich Käufl, Ralf Siebenmorgen, Alain Smette
aa r X i v : . [ a s t r o - ph ] J u l Astronomy&Astrophysicsmanuscript no. LHS1070 c (cid:13)
ESO 2018October 30, 2018
Spectral type dependent rotational braking and strong magneticflux in three components of the late-M multiple system LHS 1070
A. Reiners ,⋆ , A. Seifahrt , , H.U. K¨aufl , R. Siebenmorgen , and A. Smette Universit¨at G¨ottingen, Institut f¨ur Astrophysik, Friedrich-Hund-Platz 1, D-37077 G¨ottingen, Germanye-mail:
[email protected] Universit¨at Jena, Astrophysikalisches Institut und Instituts-Sternwarte, Schillerg¨asschen 2, D-07745 Jena, Germany European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748 Garching, Germany European Southern Observatory, Alonso de C´ordova 3107, Casilla 19001, Santiago 19, ChileReceived 29 May 2007 / Accepted 14 June 2007
ABSTRACT
We show individual high resolution spectra of components A, B, and C of the nearby late-M type multiple system LHS 1070.Component A is a mid-M star, B and C are known to have masses at the threshold to brown dwarfs. From our spectra we measurerotation velocities and the mean magnetic field for all three components individually. We find magnetic flux on the order of severalkilo-Gauss in all components. The rotation velocities of the two late-M objects B and C are similar ( v sin i =
16 km s − ), the earlierA component is spinning only at about half that rate. This suggests weakening of net rotational braking at late-M spectral type, andthat the lack of slowly rotating late-M and L dwarfs is real. Furthermore, we found that magnetic flux in the B component is abouttwice as strong as in component C at similar rotation rate. This indicates that rotational braking is not proportional to magnetic fieldstrength in fully convective objects, and that a di ff erent field topology is the reason for the weak braking in low mass objects. Key words.
Stars: low-mass, brown dwarfs – Stars: magnetic fields – Stars: rotation – Stars: individual: LHS 1070
1. Introduction
The rotation of Sun-like stars is braked following an empiri-cally determined braking law with v ∝ t − . (Skumanich, 1972;Barnes, 2007). At several Gyr they have lost most of their an-gular momentum and become slow rotators like the Sun. Fullyconvective stars, however, are apparently not braked that much,and field dwarfs of spectral type late-M or L rotate more rapidlythan their higher mass siblings (Mohanty & Basri, 2003).Stars are believed to lose angular momentum due to a mag-netic stellar wind after the first phase of star formation. Angularmomentum loss critically depends on the star’s magnetic fieldand its geometry (Mestel, 1984; Kawaler, 1988; Chaboyer et al.,1995; Sills et al., 2000). The mechanism of magnetic field gener-ation is of crucial importance since it determines magnetic fieldstrength, hence braking, and how it reacts on angular velocitychanges. Since the mechanism of magnetic field generation isbelieved to change at the threshold to fully convective stars, itcan be expected that a change in the braking law appears as well.The lack of slowly rotating objects of spectral type later thanmid-M could be a consequence of a change in the net braking.These objects, however, are so faint that it is di ffi cult to probea sample that is unbiased to luminosity e ff ects, i.e. a luminositylimited sample will always contain more bright (hence youngand less braked) low mass objects than fainter ones.The close hierarchical system LHS 1070 (GJ 2005) is anideal probe for rotational evolution of late-M objects. Its indi-vidual components can be spatially resolved; the A componentis a mid-M star (M5.5) while the two fainter components B andC are cooler (around M9). Measuring the astrometric orbit of ⋆ Emmy Noether Fellow
B and C, Leinert et al. (2000) determined masses at the limit tobrown dwarfs.In this paper, we measure rotation velocities and magneticflux of LHS 1070 A, B, and C individually. Because all com-ponents are probably coeval, this gives direct insight in spectraltype dependent braking and magnetic field generation.
2. Data
In 2006, the three components LHS 1070 A, B, and C werenearly exactly lined up on the sky, a most suitable configurationfor simultaneous long-slit spectroscopy. We observed the triplein the night of October 09, 2006 during a science verificationrun (Prog.ID 60.A-9078) of the newly commissioned AO-fedhigh resolution NIR spectrograph CRIRES (K¨aufl et al., 2006)at Antu (UT1) of the VLT on Cerro Paranal.Separations of LHS 1070 AB and AC are about 1.35 ′′ and1.75 ′′ , respectively. The spectra are spatially well resolved withonly minimal overlap of the B and C components. Observationswere carried out in order 57 / / i with on-target AO, total expo-sure time of was 480s. We chose a slitwidth of 0.4 ′′ , i.e. a nomi-nal resolving power of 50 000. Data reduction followed the stan-dard procedure of dark subtraction and flatfielding. After properbackground subtraction to remove the OH airglow emission thespectra where extracted using an adaption of the optimal extrac-tion algorithm of Robertson (1986). The chosen spectral win-dow is clear of telluric lines on a 2% level. Thus we do not needto use a standard star for correction. Instead we determined theinstrument response from the flatfield spectra and removed theremaining tilt by minimal rectification of the pseudo-continuum.Wavelength calibration was performed using a ThAr spec-trum in comparison to an updated line list (Kerber, priv.comm.). A. Reiners et al.: Spectral type dependent rotational braking
Fig. 1.
A part of our CRIRES data in the three components LHS 1070 A, B, and C (from top to bottom), smoothed by a 3 pixelbox-car.Flux contamination of the B and C components was found to bemuch smaller than the intrinsic S / N ratio. Thus we do not see anyreason to doubt on the spectral purity of any of the componentsin LHS 1070 for the subsequent analysis. A part of our data isshown in Fig. 1, at 9920 Å the spectrum falls on a gap betweentwo of the four chips.
3. Analysis and Results
Our observations were carried out in the Wing-Ford bandof molecular FeH (starting at 9900 Å), which shows sharpabsorption features in mid- to late-M dwarfs. Some of thelines are strongly magnetically sensitive while some are not(Reiners & Basri, 2006b). This makes the region ideal for theanalysis of rotational broadening and the measurement of mag-netic fields in ultra-cool objects. Our analysis follows the strat-egy used by Reiners & Basri (2007a) and Reiners et al. (2007b).We use spectra of two template M-stars, one without anysigns of Zeeman broadening, and the other showing strong ef-fects of Zeeman broadening. First, the template spectra arescaled according to an optical depth scaling law to fit the target’sabsorption strength. Then, the two template spectra are artifi-cially broadened to match the targets rotation velocity. Finally,we search for the linear combination of the two template spectrathat simultaneously fits the magnetically sensitive and the mag-netically insensitive lines. From the interpolation parameter, wedetermine
B f , the product of the mean magnetic field and thefilling factor, assuming a linear relation between Zeeman broad-ening and
B f (see Reiners & Basri, 2006b, 2007a).As template spectra, we use data of GJ 1002 (M5.5) andGl 873 (M3.5) taken with HIRES at Keck observatory , bothstars have v sin i ≤ − . Because the template spectra weretaken at lower spectral resolving power ( R =
31 000), we applieda Gaussian broadening function to our data in order to match theresolution of the templates. This is a crucial step since it sets thezero-point for the calibration of rotational broadening. In orderto check our results, we carried out the analysis with a di ff erentset of templates observed at higher resolution. We used a spec-trum of GJ 1227 (M4.5, v sin i ≤ − ) for the field-free tem-plate, and a sunspot spectrum for the spectrum in the presence We thank G. Basri for providing the template spectra. of a magnetic field . The spectrum of GJ 1227 was also takenwith HIRES at Keck but at higher resolving power ( R ∼
80 000).The template spectra were degenerated in order to match the res-olution of our CRIRES data. We find that both strategies providehighly consistent results on the values of v sin i for all three com-ponents of LHS 1070, i.e. di ff erences are within 1 km s − . Forthe following, we rely on the low resolution set of templates be-cause they provide a much more consistent data set, and theirresolution is entirely su ffi cient for our purposes. We show our best fits over the 30 Å-wide region used for fit-ting as red lines in all three components of LHS 1070 in Fig. 2.Smoothing our spectra to match the lower resolution of thetemplate spectra strongly reduced the e ff ective noise level. S / Nratios per resolution element are now on the order of 70 forLHS 1070 A, 35 and 30 for LHS 1070 B and C, respectively.Di ff erences in projected rotation velocity can be distinguishedby eye for example at 9939 Å where two neighbored lines arejust separated in the A-component but already blended in com-ponents B and C. The two latter objects do not show any obviousdi ff erence in the width of individual lines.We derive projected rotation velocities of v sin i =
8, 16,and 16 km s − in LHS 1070 A, B, and C, respectively. The over-all fit quality is rather good particularly in the A-component ofthe system. In the two late-M components B and C, the fit hassome weaknesses which we attribute to the much stronger ab-sorption that may not be perfectly captured by the optical depthscaling. However, for our analysis of v sin i the quality is en-tirely su ffi cient. A formal χ analysis shows that the uncertaintyin v sin i is on the order of 1 km s − for the three objects. Theabsolute uncertainty is somewhat higher since the zero-point de-pends on the resolution we adopt for the template spectra andour target spectra. We estimate that absolute uncertainties are onthe order of 3 km s − , but that does not a ff ect the comparison ofrotation velocities between the three components of LHS 1070.Basri & Marcy (1995) have measured v sin i in a spatially unre-solved spectrum of LHS 1070. They find v sin i = ± − in excellent agreement with our result for LHS 1070 A, whichdominates the spatially unresolved spectrum. ftp://ftp.noao.edu . Reiners et al.: Spectral type dependent rotational braking 3 Fig. 2.
Data (black) and fit (red) in the entire region we used forthe fit in the three components LHS 1070, A, B, and C (from topto bottom). The data was degenerated in resolution to match theresolution of the template spectra ( R =
31 000).
Magnetic flux was determined by searching for a linear inter-polation between a field free template spectrum and a templatespectrum a ff ected by magnetic Zeeman broadening. For the lat-ter, we use a spectrum of Gl 873 and we adopt a magnetic fluxof B f = . ∼ ff ected byZeeman broadening, a di ff erence proportional to the magneticflux occurs. We show a representative region of our spectra atthe wavelength range 9946–9956 Å in Fig. 3. Here, we highlightthree absorption lines that are particularly sensitive to Zeemanbroadening. We plot the target spectra in black and overplot the(rotationally broadened) template spectra of GJ 1002 (no mag-netic flux) in blue, and the one of Gl 873 (strong flux) in red.The interpolation that best fits the data is overplotted in green.A very accurate fit is achieved in the spectrum ofLHS 1070 A, from which we derive a magnetic flux of 2.0 kG.The fit quality in the spectrum of LHS 1070 B is not as ac-curate. However, it appears that the two sensitive absorptionlines at 9948 Å and 9954 Å are strongly smeared out, possi-bly even more than in the template spectrum of Gl 873. Thisindicates very strong magnetic flux, and we adopt a value of B f ∼ Fig. 3.
Portion of the spectral range that shows the e ff ect of mag-netic flux. Green bars mark magnetically most sensitive lines.Top to bottom: LHS 1070 A, B, and C. Black lines are the targetspectra, red lines mark spectra a ff ected by strong magnetic flux(Gl 873), blue lines spectra without magnetic flux (GJ 1002).Green lines are our best fits. Note that in the B component thered line is covered by the green one. Table 1.
Parameter of the three components LHS 1070 A, B, andC. Spectral types are from Leinert et al. (2000).
Component SpType
V J v sin i B f [km / s − ] [kG]LHS 1070 A M 5.5 15.42 9.25 8 2.0LHS 1070 B M 8.5 16 4.0LHS 1070 C M 9.0 16 2.0 molecule causes the main uncertainty in the determination ofmagnetic flux using this molecule as a tracer. On an absolutescale, we estimate our uncertainties in magnetic flux on the orderof a kilo-Gauss. However, the main result of our magnetic fluxanalysis is already seen in a rough comparison of the three spec-tra: All three components show a substantial e ff ect of magneticflux on the spectral lines, and the magnetic flux in LHS 1070 Bis stronger than the flux in LHS 1070 A and LHS 1070 C.
4. Summary and Conclusions
We have isolated high-resolution spectra of the three compo-nents of the multiple M-object system LHS 1070. From eachspectrum, we have determined the projected rotation velocity v sin and the mean magnetic field over the entire star. The resultsof our analysis are summarized in Table 1. We find a projectedrotational velocity of v sin i = − in the hottest component,LHS 1070 A, while rotation in LHS 1070 B and C is about twiceas rapid. Under the reasonable assumption that the entire systemLHS 1070 was formed at the same time, we are facing three dif-ferent objects that have evolved from the same initial conditions.Disc orientations in pre-main sequence stars (Monin et al., 2006)and orbit orientations in multiple systems (Sterzik & Tokovinin, A. Reiners et al.: Spectral type dependent rotational braking
Fig. 4.
Projected rotation velocities of LHS 1070 A, B, andC. We overplot rotation velocities according to a modifiedSkumanich braking law at 1, 2, 5, and and 10 Gyr (top to bot-tom).2002) are partially correlated, and Bate et al. (2000) find thatstrong misalignments are unlikely in binaries with separations ≤
100 AU. Thus, we may assume that the inclination angles i of LHS 1070 A, B and C are comparable (see also Leinert et al.,2001). As long as they su ff er the same rotational braking, wewould expect comparable rotation velocities in all components.We observe comparable rotation rates in the components B andC, which are of very similar spectral type. However, the rotationvelocity in LHS 1070 A is about a factor of two smaller. Thiscan probably be attributed to a di ff erence in the rotational brak-ing during their evolution.Mohanty & Basri (2003) showed that in the field the frac-tion of slow rotators ( v sin i < − ) later than spectral typeM6 is much smaller than among early-M dwarfs, which gener-ally rotate very slowly (Delfosse et al., 1998). However, the sam-ple of Mohanty & Basri (2003) could be biased to bright (henceyoung) objects that are still more rapidly rotating than theirolder (hence fainter) siblings. Reiners & Basri (2006a) foundslow rotation in a mid / late-M subdwarf, and very rapid rotation( v sin i =
65 km s − ) in a late-L subdwarf. Since late-type sub-dwarfs are probably the oldest relics of the early galaxy havingspun down for several Gyr, this is another argument for less e ffi -cient rotational braking at later spectral type.In LHS 1070, we see three objects of di ff erent spectral typethat are probably of same age. We plot the projected rotationvelocities of LHS 1070 A, B, and C in Fig. 4. As stated above,the two later objects show higher rotation rates than the earlierA-component. One explanation may be a di ff erence in the ini-tial conditions, but together with Mohanty & Basri (2003) thiswould suggest that later objects in general start o ff rotating morerapidly, which is unlikely. On the other hand, the rotation activ-ity connection seems to vanish around late-M spectral type. Thisis likely connected to a modified wind-law and consequently todi ff erent rotational braking.Detailed simulations of rotational braking were performedby Chaboyer et al. (1995); Sills et al. (2000). They give a pre-scription for a wind-braking law in stars at given angular veloc-ity, and they show that the braking law in fully convective starsrequires di ff erent treatment (to fit observations in the Hyadesthey had to tune their value of ω crit ; Sills et al., 2000). In thiswork, we do not intend to give a full description of the brakinglaw in fully convective objects. Instead, we assume that the net braking law in LHS 1070 A is still Skumanich-type ( v ∝ t − . ,Skumanich, 1972), and that the exponent of the braking law isgradually decreasing towards lower temperatures.For this purpose, we calculate the rotational evolution start-ing at an age of 10 Myr and an initial rotation velocity of70 km s − . For our spectral type dependent braking law, we chose v ∝ t − α with gradually decreasing α = . ff erence in rotation velocities as measuredin LHS 1070, and at the same time generate the rise in mini-mum rotational velocities consistent to measurements in late-Mstars (Mohanty & Basri, 2003). We thus conclude that brakingin late-M stars is spectral-type dependent, and that the lack ofslowly rotating late-M dwarfs is not a selection e ff ect due to abias towards young rapid rotators.The age estimated from our approach is on the order of 1 Gyr.Basri & Marcy (1995) found a high velocity component perpen-dicular to the galactic plane that suggests higher age. We thinkthat this point deserves further attention. Although age estimatesfrom space velocity are rather uncertain, this may hint to an ab-solute scale of the braking law di ff erent to the one used here.All three components of LHS 1070 show strong magneticflux suggesting that in fully convective objects, the field strengthdoes not strongly depend on rotation. Leinert et al. (2000) foundsigns of magnetic activity in components A and B, but not inC. This is consistent with our results in the sense that the mag-netic flux in LHS 1070 B is much stronger than the one inLHS 1070 C. Nevertheless, one expects that the C componentalso exhibits H α emission, which may still be below the detec-tion limit of Leinert et al. (2000).Interestingly, the di ff erence in magnetic flux betweenLHS 1070 B and C does apparently not influence rotational brak-ing. It is generally believed that angular momentum loss de-pends on magnetic field strength with an exponent given bythe field geometry (Mestel, 1984). This coupling, however, de-pends on the field generation mechanism (Kawaler, 1988), andangular momentum loss becomes saturated at a certain level(Chaboyer et al., 1995). According to Chabrier & K¨uker (2006),large scale magnetic fields of equipartition strength (a few kG)can be generated by an α dynamo. These authors predict thefield topology to di ff er from an organized dipole field, whichcould explain our result that rotational braking does not growwith magnetic field strength. It would imply that field geometryis the reason for lower rotational braking in low mass objects. Acknowledgements.
We like to thank the CRIRES science verification team,for their work on CRIRES and for the execution of the observations, andthe referee, Subu Mohanty, for a very constructive report. AR acknowledgesfinancial support through an Emmy Noether Fellowship from the DeutscheForschungsgemeinschaft under DFG RE 1664 / References
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