Observing Stellar Magnetic Fields & Activity Magnetic Fields & Activity

Home , Stellar magnetic field

ASTR 7500: Solar and Stellar Magnetism Hale CGEP Solar & Space Physics Last time (Sarah Gibson) • Magnetic energy release and eruptions (solar magnetic activity!); flares & CMEs • Kink & Torus and other plasma instabilities • Magnetic reconnection • Observations of eruptions on the Sun, and possible links between coronal cavities and coronal mass ejections Ben Brown, Prof. Juri Toomre & friends Lecture 19 Tues 2 April 2013 http://zeus.colorado.edu/astr7500-toomre

This time: Observing stellar This time: Observing stellar magnetic fields & activity magnetic fields & activity

Question: • Signatures of magnetism in other stars •Based on what we’ve learned (spots, chromospheric & coronal heating) about the Sun, what signatures of • Mapping magnetic fields magnetism might we look for on • Following stellar cycles • Flares on other stars (M-dwarfs can have other stars? very large flares; 100x change in stellar flux!) NJIT: give me a non-time-varying signature Hawaii: give me a time-variable signature HAO: give me a direct spectral signature Next time: Simulations of stellar dynamos Others: have we missed any?

Solar magnetic signatures SDO: Solar magnetic signatures SDO: AR 1429: source of X5 flare Solar AR 1429: source of X5 flare Solar Dynamics Dynamics Observatory Observatory

Our Sun, March 7 2012 Our Sun, March 7 2012 (optical) (X-ray) SDO: SeptemberSDO 25,optical 2011 Solar Solar magnetic Dynamics Observatory signatures

Our Sun, March 7 2012 The Sun, (blend) past 8month

Corona is SDO X-ray The Solar Cycle at 304A dynamic

Flares and The Sun, SOHO continuous September 22-27, Long time-scale SOlar Heliospheric reconnection 2011 variability (11yr) Observatory

Sunspots & Solar Cycles 11-24 Solar Cycles 11-24

• Solar 11-year cycles fairly constant in period, variable in amplitude. ~400 years of data. • Occasional “grand minima” (Maunder)

(Hathaway, NASA) (Hathaway, NASA) Solar magnetism Starspots on other Suns The Astronomical Journal,141:20(8pp),2011January Basri et al. on many scales G-type M-type

Kepler photometry (Basri et al 2011 ApJ) (and see also results from MOST)

20 mmag variation -> 2% changes Doppler images in stellar flux. Huge! of “Speedy Mic” (BO Mic): F max = 10(∆m/2.5) This is not the Sun! Observations ofF Cool-Star Magnetic Fields 11 Swedish ST BBSO NST min (ESO press release)

to the magnetic field vector, both components are circularly polarized but in opposite directions. If the lineFigure of 5. Upper sight left: lightis perpendicular curves for clearly periodic (Gtransverse dwarfs (see the textfield) for a more toexact the description magnetic of stellar selection field, criteria). the Keplerσ-components IDs for these stars are: are 5302013, 9401951, 8367679, 11773022, 7200111, 4640983, 7037146, 12069336, 9269023. Upper right: Light curves for clearly periodic M dwarfs. KeplerIDsfor linearlythese polarized stars are: 11775907, in the 2424191, direction 4743351, 6382217, perpendicular 6420895, 8558589, 9573685,5950024, to the polarization 4554367. Lower left: of light the curvesπ for-component. weakly periodic G dwarfs. Note change of scale. Kepler IDs for these stars are: 9580212, 6125701, 8308260, 6837899, 10858832, 4366093, 4552939, 11598724, 3110216. Lower right: light curves It isfor important red giants. Kepler IDs to for realizethese stars are: that 12204548, measurements 3427850, 10666932, 12208273, of longitudinal 4772722, 4725874, 10937855, and 9783225, transerve 4271855. fields as seen in circular and linear polarization, and also field measurements from unpolarized light are usually the upper histogram). We also investigated whether the range of even when the signal looks very much like starspots. In many not identicalvariability to is athe function real of thesurface primary period.magnetic Generally, field shorter becausecases of itthe is more measuring likely to be the principles half-period; whendiscussed a star has here. 1388 PEVTSOV ET AL.For theperiods following, indicate more I will active speak stars (Pizzolato of longitudinal et al. 2003), and fields Vol.an if asymmetric 598 magnetic spot distribution fields are each derived face produces from a dip circular of a Proxies for Magnetic Activity these might be both moreHow obviously periodic do or show larger wedifferent measure depth so that there could be two major dips per rotation. polarization.amplitudes This of variation includes (unless the results activity were from too Stokes uniformly V magneticIf there is essentially maps, one activewhich location, combine or a continuous observational enough 33 experimentalinformation uncertaintiesdistributed). of longitudinal We see that for the faint, bulk fields of the cool, visible stars have coronal atVrng dialittlefferent plasmas.distribution epochs. around the star, two discrete dips may not appear 10 T Tauri Typical XBP temperaturesgreater than the active are Sun,T and there1magnetic:6MK. is modest evidence of and then flux? the periodogram will find the actual period. greater variability at shorter periods (the lowest Vrng are found ToproduceanactiveSunsampleforcomparison,20segments stars mostly at the long periods). Of course, by restricting this study of Solar and Heliospheric Observatory (SOHO)DIARAD G, K and M to stars rotating fast enough to show periodicity in two weeks, (Dewitte et al. 2004)datafrom2001wererecasttohavesimilar stars we have biased the result against the slower rotators (many of cadence and length as the Kepler data (as in Paper I). Periods which2.3. presumablySolar currently Active lie in ourRegions non-periodic sample). It are found between 10 and 50 days with a mean and median of 28 Sun: is known that activity saturates at short periods and that might about 20 days (and mean Pstr of 200). Of course, most of these 10 "knee" Fisher et al.be (1998) playing a role used here. Still, 333 it is vector perhaps a magnetogramslittle surprising periods of (even those matching the actual solar period) would -1 active that there is not a more obvious effect, especially since we are not be considered valid in our current analysis (since they are regions solar active regionssampling rotation observed periods up to with solar in the the case Haleakala of a half-period Stokesderived from 33 day data segments and we do not trust periods Sun: Polarimeter (Mickey(a)of two weeks. 1985) and cotemporal SXT imagesover 16 to(b) days). We composed a similar sample of quiet Sun

, erg s Xray bright We remind the reader that we did not analyze periods below data from 1996 SOHO measurements and actually obtained a x points Overall scaling showscompute the totaltwo days; unsigned there is indeed magnetic a population of short-period flux and cases total but similar X-ray period distribution with a mean Pstr of about 150. The L 23 1.15 radiance averagedwe expect over that those entire are not active due to rotation region (except areas. perhaps in Thehigh mag- significance of Pstr is primarily due to the very low noise 10 Lx Φ close binaries). It is important to note that one cannot assume in the SOHO data. We performed the additional experiment of Quiet Sun netic flux was determinedthat the dominant periodusing is thevertical rotation period (with of the respect star, removing to the a third-order fit from the quiet Sun data; this reduced across some∝ 12 orders Sun solar surface) magnetic field. In this paper, the SXT count of magnitude in both! 6 (Pevtsov et al 2003) rates were converted into spectral radiance by assuming a Coronal heating 18 10 coronalFigure temperature 2: Schematicspectra: of 3 view MK ofdirect Zeeman and integratingZeeman splitting. (a) splitting, aThe thermal upper level or in the example is split into three levels 16 18 20 22 24 26 28 ˚ 10 10 10 10 10 10 10 spectrumproducing over 2.8 three andspectropolarimetry: spectral 36.6 linesA,asdescribedearlier(Fisher that are separated. circular (b) Polarization polarization of the π [lineand σ components.of sight] & Magnetic flux, Mx et al. used a 1–300 A˚ integration range). linear polarization [transverse field] Magnetic Flux at photosphere (Φ) The LX values from Fisher et al. (1998) were reduced by a Fig. 1.—X-ray spectral radiance LX vs. total unsigned magnetic flux for factor of2.1.3 4 to correct The Stokes for an vectors incorrect conversion of Yohkoh solar and stellar objects. Dots:QuietSun.Squares:X-raybrightpoints. Pevtsov et al. 2003, “The relationship between X-ray radiance and magnetic flux” half-resolutionFor the characterization images to“Observations full of aresolution magnetic of cool-star field, in Fisher the magnetic measurement et fields,” al. ofAnsgar intensity Reiners, in different polarization Diamonds:Solaractiveregions.Pluses:Solardiskaverages.Crosses:G,K, (1998). This does not affecthttp://solarphysics.livingreviews.org/Articles/lrsp-2012-1/ any of the correlation studies and M dwarfs. Circles:TTauristars.Solid line:Power-lawapproximation states can be of great advantage. This is immediately clear from Figure 2bsincethedifferent 1:15 Zeeman components are polarized in a characteristic fashion. A commonly used system are the LX È of combined data set. reported in Fisher et al. (1998). / Stokes components I, Q, U, and V (Stokes, 1852) defined in the following sense: 2.4. Solar Disk AveragesI = + identified pairs of images observed in two different filters, ↔ We compute the total X-ray radianceQ and= unsigned Al.1 and AlMg, within 600 s of each other. The median U = −↔ number of pairs is 16 with a maximum of 55 for a given day. magnetic flux averaged over the visible solar hemisphere − for V = The Al.1/AlMg filter ratio is used to compute coronal the period from 1991 November 11–2001 December− 15. Magnetic fluxes are computed using NSO/KP daily plasma temperatures. We convert X-ray emission into spec- Stokes I is just the integrated (unpolarized) light. Stokes Q and U measure the two directions of magnetograms. The daily averaged X-ray fluxes are com- Magnetictral radiance by Activity integrating a thermal in spectrumOther over Suns the linear polarization,Magnetic and Stokes V measuresActivity circular polarization. in Other Note that Stokes Suns Q and U are 2.8–36.6 A˚ (0.3–4.4 keV) wavelength range, with the limits puted usingthe diYohkohfferences betweenSXL (soft two linearly X-ray polarizedhistogram beams log with files, perpendicular directions of polarization. corresponding to 1% of peak sensitivity through the Al.1 histogramsThe ofcomponents full-disk measured composite in Stokes images). U are rotated The bycoronal 45 with respect to the components measured temperaturesin Stokes have Q; been directions derived of Q using and U the are ratio not defined of two in SXT an absolute(Pizzolato sense et butal. 2003) require the definition filter at Yohkoh launch. For this and subsequent(Pizzolato et al. radiance2003) computations, we employ the spectral models of Mewe, filters, andof a the frame conversion of reference, between in which the polarization instrumental is measured. and For a very readable introduction to Gronenschild, & van den Oord (1985) and Mewe, Lemen, & physicalStokes units has vectors been and done alternative using the forms same the approachreader is referred as for to Tinbergen (1996). van den Oord (1986). The solar coronal abundances are the quiet Sun.Stokes Typical vectors solarare useful X-ray in astronomy disk temperatures because perpendicular are circular and linear polarization T 2:5MK.Toimprovethesignal-to-noiseratio,westates can be measured with relatively straightforward instrumentation. The representation of adapted from Meyer (1985). Modeling of the SXT response astronomical polarization measurements is usually done in terms of Stokes vectors. The problem to a multithermal coronal plasma has indicated that spectral excluded all pixels in the SXT frame beyond 1.1 solar radii. Furthermore,we are since concerned some with, X-ray however, radiation is under is associated what circumstances with the magnetic field of a star can be radiance for the SXT passband derived in this way, barring recovered from measurements of the Stokes vectors. If solar magnetic fields are a good example for unknown systematic errors, is accurate to about 10% the magneticother stellar field magneticat/behind fields, the we solar can expect limb, that we they compute often show up in groups of different polarity. solar rotation (27.2375 days) averages of the magnetic and (Acton, Weston, & BrunerRotation 1999). TheRate SXT fluxes were averaged over a given day and interpolated to magnetogram X-ray fluxes. The data set covers 127 solar rotations dates. There are 775 data points in this data set. beginning at Carrington rotation number 1849. F-, G-, K- Living Reviews in Solar Physics X-ray luminosityX-ray http://www.livingreviews.org/lrsp-2012-1 and M-type 2.5. Dwarfs and T Tauri Stars Magnetic Activity 2.2. X-Ray Bright Points Fisher et al. (1998) computed X-ray radiance and total Longcope et al. (2001) analyzed 285 X-ray bright points magnetic flux of 16 dwarf stars (types G, K, and M) using (XBPs) selected using the Extreme Ultraviolet Imaging X-ray surface flux, magnetic field strength, and magnetic Telescope (EIT; DelaboudiniereRotation etPeriod al. 1995) and the filling factor published by Saar (1996). The magneticRotation flux Period Michelson Doppler Imager (MDI; Scherrer et al. 1995) was computed from the field strength and the filling factor observations. For each XBP, they estimated the tempera- by multiplying these two parameters by estimated surface ture, T,andemissionmeasure,EM,usingtheratioofEUV area of each star. The X-ray spectral radiance was computed fluxes in two (171 and 195 A˚ )spectrallines.Thephoto- in the same way by multiplying the surface flux density by spheric magnetic fluxes of associated bipoles were derived estimated stellar surface area. The X-ray data are compo- using MDI longitudinal magnetograms. To achieve spectral sites of ROSAT (0.1–2.4 keV energy range), Einstein consistency, we use Yohkoh SXT data to measure soft X-ray Observatory (0.2–4.5 keV), and EXOSAT (0.04–4.5 keV) fluxes for 59 of the XBPs analyzed by Longcope et al. observations. Thus, the stellar and solar X-ray observations (2001), for which reliable correspondence to SXT measure- cover approximately the same energy range. A similar ments is possible. The SXT observations have been con- approach has been applied to the T Tauri stars observed by verted into spectral radiance using temperatures from the Johns-Krull & Valenti (2000; BP Tau, Hubble 4, and T Tau) EIT measurements of Longcope et al. (2001) rather than and Johns-Krull et al. (2000; DF Tau, TW Hya, and DK temperatures from the SXT filter ratios. Although the Tau). X-ray radiances for these stars are adopted from results from the two methods are within a factor of 3 on Walter & Kuhi (1981; DF Tau), Webb et al. (1999; average, there is substantially less scatter using the EIT tem- TW Hya), and Neuhaeuser et al. (1995; BP Tau, DK Tau, peratures. The SXT filter-ratio technique has relatively large Hubble 4, and T Tau). (Pizzolato (Pizzolato et al. 2003) Global dynamo link: Magnetic Activity CZ in Solar-like Stars differential rotation 64 S. H. Saar

Saturation regime Magnetic Activity

(Convective Magnetic Activity Envelope) Rotation Period Rotation Period Radiative Zone (RZ) No RZ!

CZ RZ RZ Scaling part of X-ray luminosity vs. CZ rotation-activity differential rotation M-type star relationship as inferred from CZ K-type star 0.3 M G-type star Magnetic Activity stellar active regions 0.5 M ~0.001 L 1 M 0.04 L Differential rotation (Ca H & K periods) Convection F-type star 1 L Zone (CZ) 1.5 M ~5 L F-M: all magnetically active (Saar 2009, 2011) A-type star 1.36 Figure 3. [Left]: LX /Lbol vs. normalized ∆Ω,showingtheﬁtLX /Lbol ∆Ω (solid) and SA level (dotted); symbols as in Fig. 1. [Right]: Normalized ∆Ω vs. age t (from∝ (Barnes & Kim 2010, Barnes & Kim 2010)). Symbols as in Fig. 1, with size scaling with stellar mass (1.15 to ANRV385-AA47-090.3M ARI;from(Barnes&Kim2010,Barnes&Kim2010)).Apowerlawﬁttothenon-SAstars 15 July 2009 0:23 ! 0.57 ∆Ω t− (solid) is also shown. ∝ Mapping Stellar Fields Magnetic activity at the bottom 0.5 notable similarityMean of the LSD pro power!les of τ Boo law (June with 13, 2006) the classic Skumanich (1972) v t− empirical of the main-sequence spindown law, together with the mass dependent start of the spindown, strongly∝ hint that c I /

V 1.1

DR hasan important role in controlling the rotational evolution of cool stars.Wewill explore this× further in an upcoming paper (Barnes & Saar 2010, in prep.) 1000

1.0 c I / I 3. Cycle0.9 Data and Analysis Circular polarization Armed Stokes withNull this polarization new check understanding of the Ω and mass dependence of DR in single Unpolarized line pro!le dwarfs, I now0.8 turn to the question of cycle properties. I adopt identical selection criteria as for the DR–40 sample,–20 and also 0 insist 20 vis. Saar 40 & Brandenburg (1999) that the cycle be –1 arelatively“clean”,highqualitydetection(thisisadmittedlysubjectiveinsomecases).Velocity (km s ) Higher Lower Figure 1 Weak signature (1/1000), so average over many thousands of lines mass mass LSDWe circular adopt polarizationto increase the (Stokes cycle signal-to-noiseV ) Zeeman sample signature (LSD of (red Saar = line Least), null (2009), Squares polarization withDeconvolution). check (dark some yellow recent line , additions (e.g., (Oláh et al. Here activity measured by H-alpha emission. both expanded byInverse 1000 and problem: shifted vertically deep by questions 1.06 for graphical about purposes) impact and of unpolarizedaveraging, (Stokes etc.I ) Fully convective stars are very active. profile2009; (blue line Fares) from the photosphericet al. 2009); lines of τ Boo, Milingo as derived fromet(Donati ESPaDOnSal. 2010,& Landstreet, data. these A clear 2009, Zeeman proceedings).ARA&A) A quick look at the signaturedata is detected reveals (with nothing no strong visible in the trend null polarization with check)Ω (as with a found full amplitude by, of about e.g., (Oláh et al. 2009). However, if 0.01% of the unpolarized continuum. The associated polarimetric sensitivity is 0.001%, i.e., 10 ppm. one separates the secondary (= weaker amplitude) cycle period Pcyc(2), present in many

instrumentmoderate-to-active (Donati et al. 1999) wasstars, installed on and the 2 insists m Telescope´ that Bernard they Lyot somehow (TBL) atop Pic be du in a relationship separate from ANRV385-AA47-09 ARI 15 July 2009 0:23 Midithe (southwest main France), stellar providing cycle the e.g, whole (Soon communityet with al. a wider1993; access Saar to spectropolarime- & Brandenburg 1999), a more complex, try. A new-generation high-resolution spectropolarimeter [called ESPaDOnS, Donati (2003)] multitiered patternAstron. emerges Nachr. / AN (2011) (Fig. 4). When cycle frequency ω867cyc is plotted against Ω, was installed in 2004 on the 3.6 m Canada-France-Hawaii Telescope (CFHT) atop Mauna Kea 1.1 (Hawaii),three and parallel was soon complemented tracks,2Instrumentalsetup,datareduction,and separated by a clone version by (NARVAL) a factor installed of at TBL.3.5, Both each instru- with ωcyc Ω .AtΩ 10Ω , Mappingab Stellar Fields with ZDI Mapping Stellarextraction of Zeeman signatures Fields with ZDI " ments are fully optimized for spectropolarimetry, perform a very achromatic∼ polarimetric analysis ∝ ≈0.6 Radial magnetic !eld very close to DR peakWe use data (Fig. from the NARVAL 1, spectropolarimeter(Auri`right),A. Morgenthaler theere relations et al.: reverse, Magnetic fieldshowing monitoringωcyc of ξ BootisΩ− A (Fig. ZDI: Zeeman 1 0.50 2003), installed at Telescope Bernard Lyot (Pic du Midi, µ 0 0.269 13.224 (using modifieda Fresnel more rhombs), solar-like and yield full coverage star of the optical domain (0.37 to 1 m) at ∝ Doppler Imaging 4). Only six of theFrance). 15 Thedouble instrumental setup cycle is strictly identical stars to the fail to have their Pcyc on separate branches. Br a spectral resolution of 65,000 andone with described a peak by Petit efficiency et al. (2008). The ofspectrograph about unit 15% of (telescope and detector 0.630 13.929 NARVAL benefits from a spectral resolution of 65 000 and 0.25 0.75 included).Thus Because the of DR their peak high throughput wouldcovers the whole and appear wavelength fringe-free domain to from polarimetric near-ultraviolet have left analysis, a mark ESPaDOnS in andωcyc as well. (370 nm) to near-infrared (1000 nm). Thanks to the polari- Make many, many 1.331 14.276 NARVAL can reach very high photon-noise-limited polarization accuracies (see Figure 1); their Key to this interpretationmetric module, NARVAL of can the provide cycle intensity, circularly data is the reality of the Pcyc(2) as true, separate, observations of a B or linearly polarized spectra. In the present study, we restrict 0.00 unprecedentedr sensitivity (as low as 0.1 G on bright narrow-lined cool stars) provides a fresh op- 1.683 14.628 the measurements to Stokes I and V . –2 by University of Wisconsin - Madison on 04/01/13. For personal use only. polarity-reversing cyclesThe circularly (rather polarized spectra allowthan the detection just of amplitude modulations of the main cycle). single star. Azimuthal magnetic !eld portunity to explore magnetic fields across most of the HR diagram and has already enabled the dis- G large-scale photospheric magnetic fields, thanks to the Zee- 0.50 7.960 15.683 400 coveryWhile of magnetic this fields is not in several known stellarman effect. classes to However, be not when true previouslyobserving incool dwarfs, general, known the sig- to be magneticthere is (see evidence below). supporting this idea. First, B nal-to-noise ratio of circularly polarized spectra produced 200 Use stellar rotation φ Annu. Rev. Astro. Astrophys. 2009.47:333-370. Downloaded from www.annualreviews.org With its polarimetric mode, FORS1by NARVAL on is thenot suf ESOficiently high Very to reach Large the detection Telescope (VLT) atop Cerro

(%) 8.303 16.382

c I threshold of typical Zeeman signatures (which amplitude / P (2) are generally short, and recent Zeeman Doppler imaging evidence demonstrates 0.25 0.75 cyc 1 0 V −4 velocity (Doppler) Paranal (Chile) can serve as a low-resolutiondoes not exceed (about10 Ic for 2,000) low-activity spectropolarimeter. stars, where Ic is With its 150 km s− 9.360 17.084 the continuum intensity). To solve this problem, we calcu- –200 Bφ to map features. resolutionthat element, at least it essentially some amounts shortlate from the to reducedcycles a Balmer spectrumdo a line single,reverse polarimetercross-correlated polarity for slow rotators (Fares (such et al. 2009; Petit et al. 2009, –4 –400 photospheric line profile using the Least-Squares-Decon- 0.00 9.709 17.440 as chemically peculiar stars), but provides an interesting opportunity for investigating large-scale Fares et al. 2009; Petitvolutionet (LSD) al. multi-line2009). technique (detailed Second, by Donati et the amplitudes of the primary and secondary Meridional magnetic !eld magnetic fields in very rapid rotatorsal. (Bagnulo 1997 and Kochukhov et al. 2002).et al. 2010). Its Thanks giant to the photon large collecting power makes Can infer some 10.405 17.786 1 0.50 number of available photospheric lines in cool stars (several it verycycles efficient show at exploring opposite magneticthousandstrends fields in in the distant spectral with domain stellarincreasing of NARVAL), clusters the andnoise in Ro studying− Moss how magneticet al. (2008), suggesting they have latitudinal information level is reduced by a factor of about 30 with respect to the Bθ 10.764 18.137 for long-lived features. fieldsdi canBfferent influence physical the evolution sources ofinitial early-type spectrum. B¨ As starsohm-Vitense an illustration, off the Fig. 1main shows the sequence result- (2007); (Bagnulo possibly et al. 2006). related to higher order dynamo 0.25 0.75 θ ing LSD signatures for successive observations of the Sun- –6 11.118 modes Petit et al. (2009).like star ξ Boo A. The amplitudes of many cycles vary in time though Oláh et al. Here: M-dwarf star, 3 Magnetic mapping and chromospheric 0.00 3.3.(2009), Parametric so Modeling assigning and aTomographic single amplitude Imaging of to Magnetic each Fieldscycle is likely too simplistic. color scale 400 G. –20 0 20 40 –20 0 20 40 emission ± Velocity (km s–1) Once a magnetic field is detected atThe the Stokes surfaceI and Stokes of aV star,LSD proonefilesusually allow the deriva- looks at whether the detected

Strong averageby University of Wisconsin - Madison on 04/01/13. For personal use only. fields! Figure 2 (Donati & Landstreet, 2009, ARA&A) Zeeman signatureshere ξ exhibitBoo, temporal 0.85tion variabilityM of various quantities, over60G to study timescales the temporal(Morgenthaler variations of days of and weeks.et al. 2011, In most 2012) cases, Magnetic imaging of the large-scale field of the early-M dwarf DT Vir using ZDI (a) from a time series of circular polarization the magnetic⊙field properties. Here we focus on the recon- (Stokes V ) Zeeman signatures covering the whole rotation cycle (b). The reconstructed magnetic topology includes a significant ± Fig. 1 (online colour at: www.an-journal.org) Normalized

Annu. Rev. Astro. Astrophys. 2009.47:333-370. Downloaded from www.annualreviews.org struction of the surface distribution of the magnetic vector Stokes V profiles of ξ Boo A for the summer of 2007, after correc- toroidal component (showing up as unipolar azimuthal fields over the visible hemisphere) and a mostly non-axisymmetric poloidal and on the computation of a chromospheric activity index. component, typical of F to early-M dwarfs. (a) The three components of the field in spherical coordinates are displayed (from top to tion of the mean radial velocity of the star. Black line represent the bottom) with magnetic fluxes labeled in G, with the star shown in flattened polar projection down to a latitude of 30 . Radial ticks www.annualreviews.org Magneticdata and Fields red lines of correspondNondegenerate to synthetic Stars profiles of 341our magnetic − ◦ • around each plot indicate phases of observations. (b) Observed Zeeman signatures are shown in black whereas the fit to the data is 3.1 Magnetic maps model. Successive profiles are shifted vertically for display clarity. shown in red. The rotational cycle and 3σ error bars of each observation are shown next to each profile (from Donati et al. 2008b). Rotational phases of observations are indicated in the right part of To reconstruct the surface magnetic geometry of the stars, the plot and errors bars are illustrated on the left of each profile. we use Zeeman-Doppler Imaging (ZDI). This tomographic By mapping Zeeman signatures over several successive rotation cycles, ZDI can also estimate inversion technique is based on the modelling of the rota- the amount of azimuthal shear (i.e., surface differential rotation) to which stellar magnetic topolo- tional modulation of the circularly polarized signal (Semel orientation of the magnetic vector in magnetic spots. The gies are subject. This method assumes a Sun-like surface rotation pattern with the rotation rate 1989). The time series of polarized signatures are iteratively 2 application of this technique to cool stars with low v sin i varying with latitude θ as #eq d# sin θ, where #eq is the angular rotation rate at the equator compared to artificial profiles corresponding to a synthetic − and moderate to low magnetic activity is described by Petit and d# the difference in angular rotation rate between the equator and the pole. By carrying out magnetic geometry, until a good fitisobtainedbetweenthe et al. (2008). In this case, ZDI is only sensitive to low-order magnetic reconstructions (at constant information content) for a range of #eq and d# values, one model and the observations (Donati & Brown 1997; Donati field components, contrary to the chromospheric flux which et al. 2006). Thus, ZDI enables to recover, to some extent, includes also the contribution of smaller scale magnetic el- www.annualreviews.org Magnetic Fields of Nondegenerate Stars 343 the location of magnetic regions, as well as the strength and • ements. 1 The Bernard Lyot Telescope is operated by the Institut National des Sciences de l’Univers of the Centre National de la Recherche Scientifique The resulting maps for the three stars presented here are of France. illustrated in Figs. 2, 3, and 4.

www.an-journal.org !c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Fig. 2. Magnetic maps of ξ Bootis A, derived from 2007.59, 2008.09, 2009.46, 2010.04, 2010.48, 2010.59, and 2011.07 observations (from left to right and top to bottom). For each data set, the three charts illustrate the field projection onto one axis of the spherical coordinate frame with, from top to bottom, the radial, azimuthal, and meridional field components. The magnetic field strength is expressed in Gauss.

fits, between modelled and observed LSD profiles, is noticed for One first limitation of this indirect imaging procedure is the values of "max greater than 5. roughness of the underlying stellar model, which, combined with Because each data set was collected over several weeks, we the sparse phase sampling and uneven S/N ratio, may be the assumed that the magnetic geometry might be distorted by lati- source of inaccuracies in the reconstructed magnetic geometry tudinal differential rotation over the timespan of the data collec- (see, e.g., Donati & Brown 1997). One other limitation of the tion. We therefore included a two-parameter differential rotation maximum-entropy algorithm is the absence of error bars on the law in our stellar model, with the form resulting maps. To limit the consequences of these two restric- tions as much as possible, we do not discuss here the finest de- Ω(l) = Ω dΩ sin2 l, (2) eq − tails of the magnetic topology (i.e., individual magnetic spots), where Ω(l)istherotationrateatlatitudel, Ωeq the rotation rate but rather concentrate on a set of quantities derived from the of the equator and dΩ the difference in rotation rate between the largest spatial scales of the field geometry (e.g., its low-order poles and equator. Following the method of Petit et al. (2002), a multipolar expansion), as listed in Table 1.Asanattemptto grid of magnetic inversions was calculated for a range of values evaluate the uncertainties on these global magnetic quantities, of the quantities Ωeq and dΩ.ThevalueslistedinTable1 corre- we then reproduce the approach of Petit et al. (2008)andcom- spond to the χ2 minimum in the parameter plane, whenever this pute several magnetic maps, each of which is calculated using minimum exists and is unique in the scanned Ωeq-dΩ area. different values of the input parameters of ZDI (within the error

A138, page 5 of 15 Observations of Cool-Star Magnetic Fields 53

for some stars, and this may be within the range of an observable net field of the Sun at a given moment. However, the information about field geometry from such a measurement alone would certainly be very limited. More information is available if a Doppler Image from a star with a stronger field can be obtained. Such an image takes into account all the net field snapshots visible at different rotational phases, which greatly enhances the detectability of tangled fields. An overview about the current picture of magnetic field geometries in low-mass stars, in particular among stars of spectral type M, was given by Donati and Landstreet (2009). The powerful methods of Least Squares Deconvolution and Zeeman Doppler Imaging have provided a wealth of Doppler Images showing very different pictures of stellar magnetic field geometries. A particularly interesting example are low-mass stars of spectral class M; not only are there many Doppler Images of M stars, this spectral range is also of particular interest for our understanding of the solar and stellar dynamos as pointed out earlier in this review.Mapping Stellar Fields with ZDI Mapping Stellar Cycles with ZDI P.Petitetal.:MagneticpolarityreversalofHD190771 L11 mean field: 20G not axisymmetric few G ± Br Lots of toroidal field 870 A. Morgenthaler et al.: Direct observation of magnetic cycles in Sun-like stars Bφ

Bθ ξ Boo Fig. 2. Magnetic maps of2007 HD 190771, derived from 2007, 2008, and2008 2009 observations in the left, middle2009, and right columns,respectively.The map on the left is plotted after P08. For each data set, the 3 charts illustrate the field projection onto one axis of the spherical coordinate frame with, •fromZDI top to bottommaps,theradial,azimuthal,andmeridionalfieldcomponents.ThemagneticfieldstrengthisexpressedinGaussandtherotational show magnetic reversal during a cycle Lots of phases of observation are indicated as vertical ticks above each epoch. CHROMOSPHERIC ACTIVITY IN G AND K STARS 487 poloidal field YZ CMi Tablein 2. rapidlyMagnetic quantities rotating derived from the set ofsolar-type magnetic maps. star. (Petit et al. 2009) TABLE 1 (flare star) (J.F. Donati 2011, Fractional year v B Pol. en. Dipole Quad. Oct. Axi. Ω dΩ log R • ZDI is a difficultr mean inverseBasic Data forproblem; Program Stars major hounds-eq HK! 1 1 1 and ongoing work by (km s− )(G)(%tot)(%pol)(%pol)(%pol)(%tot)(radd− )(radd− ) 2007.59 26.86 0.03 51 63414382022347330.71 0.01 0.12 0.03 –4.47 HR HD Spectral Type mV B V log TeA prot Pcyc Pcyc 2 log RHK0 log F(Ca ii)Sequence mean field: very axisymmetric Pascal Petit, Julien and-hares2008. 67 −26.72 ± exercises0.04 59 ± 339± 336 areÀ ± 818 ongoing± 219± 461 within± 30.71 ±the0.01 0.12Bcool± 0.03 –4.47 4437...... 2009. 47 −26 100180.48 ± 0.03 F7 58 V± 881 6.20± 223 0.57± 740 3.7746± 221 14± 236 12.9±12 3.6 0.66 ±4.9220.01 0.12 5.930± 0.02 –4.48 A Morin, Sandra À few kG 4983...... − 114710± F9 V± 4.26± 0.58± 3.7723± 12.35± 16.6± 9.6 ±4.745 6.097± A Notes:project we list the stellar using radial velocity modern (with its associated rms), stellar the mean unsigned dynamo magnetic field (Bmean simulations.), theÀ fraction of the large-scale magnetic Jeffers, Stephen 3625...... 78366 G0 V 5.93 0.60 3.7676 9.67 12.2 5.9 4.608 6.216 A energy reconstructed in the poloidal field component, the fraction of the poloidal magnetic energy in the dipolarÀ (! = 1), quadrupolar (! = 2), 7672...... 190406 G1 V 5.80 0.61 3.7653 13.94 16.9 2.6 4.797 6.018 A Marsden and other and octopolar (! = 3) components, and the fraction of energy stored in the axisymmetric component (m = 0).À We also list the differential rotation 88...... 1835 G3 V 6.39 0.66 3.7536 7.78 9.1 ... 4.433 6.335 A parameters Ωeq and dΩ.ThelastcolumncontainsthelogR! values derived from our sets of Stokes I spectra.À Values for 2007 are taken from P08, ZDI observations of other stars members of Bcool) 996...... • Also done 20630 for G5massive V 4.83HK 0.68 stars 3.7489 by 9.24 MiMeS 5.6 ... project.4.420 6.329 A except for the log R! value which was recalculated using a new calibration of NARVAL measurements againstÀ Mount Wilson estimates (Wright 3538...... HK 76151 G3 V 6.00 0.67 3.7512 15. ... 2.52 4.659 6.100 Ab? et al. 2004), involving 29 solar-type dwarfs. À 152391 G7 V 6.64 0.76 3.7302 11.43 10.9 ... 4.448 6.226 Ab À 3750...... 81809 K0 V 5.38 0.80 3.7208 40.2 8.2 ... 4.921 5.716 I À Figure 23: Properties of the large-scale magnetic geometries of cool stars (Donati, 2011) as a function 4550...... 103095 G8 V 6.45 0.75 3.7325 31 7.3 ... 4.896 5.788 I onto a spherical harmonics frame (Donati et al. 2006), where list several numerical quantitiesÀ derived from the spherical har- 115404 K1V 6.52 0.94 3.6880 18.47 12.4 ... 4.480 6.026 Ab, I of rotation period and stellar mass. Symbol size indicates magnetic densities with the smallest symbols À 6171...... the magnetic field geometry 149661 is divided K2 V between 5.75 a poloidal 0.84 and 3.7114monics 21.07 coefficients 16.2 defining 4.0 the4.583 magnetic geometries. 6.017 As Ab, in I P08, À corresponding to mean large-scale field strengths of 3 G and the largest symbols to 1.5 kG. Symbol shapes toroidal component (Chandrasekhar156026 K51961 V). As 6.34 in P08, 1.16 we limit 3.637errorbars 21 listed 21.0 in Table...2 are estimated4.662 by 5.638 reconstructing Ab, Ia set À 6752...... the spherical harmonics 165341 expansionK1 to ! V10, after 4.03 checking 0.86 that 3.7068of magnetic 19.9 maps 15.5 using 5.1 different4.548 input parameters 6.033 for Ab, the I in- depict different degrees of axisymmetry of the reconstructed magnetic field (from decagons for purely À 222...... increasing even more ! 4628does not provide K2 V≤ a superior 5.75 data 0.88 adjust- 3.7021version 38.5 code (with 8.6 individual... parameters4.852 being 5.710 varied over I the À axisymmetric fields to sharp stars for purely non-axisymmetric fields). Colors illustrate field configuration 493...... ment. We finally assume 10476 that thestar K1 V is not rotating 5.24as 0.84 a rigid 3.7114width 38.2 of their own 9.6 errorbars).... We4.912 note that 5.688the largest variations I À 160346 K3 V 6.52 0.96 3.6834 36.4 7.0 ... 4.795 5.692 I (dark blue for purely toroidal fields, dark red for purely poloidal fields, intermediate colors for intermediate body, but experiences a latitudinal shear that we simply model as in the output quantities are generallyÀ obtained by varying the 8085...... 2 201091 K5 V 5.21 1.17 3.6342 35.37 7.3 ... 4.964 5.327 I Ω(θ) = Ωeq dΩ. sin (θ), where θ is the stellar latitude, Ωeq is the stellar inclination, because ofÀ therelativelylargeuncertaintyin configurations). Full, dashed, and dash-dot lines trace lines of equal Rossby number Ro =1,0.1,and0.01, 8086...... − 201092 K7 V 6.03 1.37 3.5874 37.84 10.5 ... 4.891 5.212 I rotational rate of the equator and dΩ is the difference in rotation this specific parameter. À 166...... 3651 K0 V 5.87 0.85 3.7091 44. 14.6 ... 4.991 5.599 I Fig. 4respectively(online colour (from at: www.an-journal.org)Donati, 2011, reproduced Same as Fig. by 2 for permissionξ Bootis A, of for Cambridge 2007.59, 2008.09, University 2010.48, Press). and 2010.59 data sets rate between polar and equatorial regions. We use the new data À 753...... 16160 K3 V 5.82 0.98 3.6787 48.0 13.2 ... 4.958 5.510 I (from left to right and top to bottom). À 1325...... sets to obtain estimates 26965 of the diff K1erential V rotation 4.43 parameters 0.82 3.7161 43 10.1 ... 4.872 5.746 I 2.3. Temporal evolution in theÀ large-scale magnetic field Mapping Stellar Cycles 1614...... (Table 2), following the 32147 method described K5 V by Petit 6.22 et al. 1.06 (2002). 3.6560 48 11.1 ... 4.948 5.446 I 1 À 6806...... For 2008and2009,weCycles 166620 obtaina shear K2 level V of d 6.40Ωin= 0.12 0.87 radother d− 3.7044, 42.4 15.8stars:... 4.955 5.616 I Morin et al. (2010) summarized the results from Zeeman Doppler Imaging currently available Between 2007 and 2008, the mostÀ striking evolution in the mag- 8866...... in very good agreement 219834B with the value K2 V obtained ? by P08. 0.91 Values 3.6951 43 10.0 ... 4.944 5.590 I also observed in the chromospheric flux, with a sharp drop netic field distribution is a polarityÀ reversal of the large-scale in M-type stars. Including the results of Morin et al. (2010), Figure 23 shows properties of the derived for Ωeq are also in excellent agreement in 2007 and 2008 field. In the ZDI maps of Fig. 2,thischangeismostlyvisiblein of emission between the two epochs (Table 2). 1 large-scale magnetic geometries of cool stars from Donati (2011) in a visualization of magnetic (with Ωeq = 0.71 Mount0.01 rad d− ), but the measurement Wilson for 2009 the azimuthal project component of the magnetic vector. A more quanti- ± 1 The second• Now example found is visible in for the set several of observations andprovides also used us with by Lorente a different & Montesinos estimate (Ω (2005).eq = 0.66 The0 cycle.01 rad pe- d− ). tative way of estimating the details of this sign switch consists of field geometries as a function of mass and rotation period. Many of the stars follow the trend of ± collected during the summer of 2010, which we decided to riods,ThisP apparentcyc,aregiveninyears,andtherotationperiods, discrepancy may simply reflect the uncertaintiesprot, in tracking its origin in the evolution of the complex spherical har- days.in this For parameter. the Ca ii emission Errorbars line listed fluxes in Saar Table &2 Brandenburgare directly give derived monics coefficients α!,m, β!,m,andγ!,m (defined by Donati et al. split in two subsetsother (2010.48 stars, and 2010.59) spanning to take into ac- • 2 Monitor4 ~100 thefromRHK0 the Fχ(Camapii)/ inTe theA. ToΩeq obtain–dΩ theplaneF(Ca andii) wemight multiplied be underesti- the 2006). Because of the uncertainty in the stellar rotation period ¼ 4 “active branch” count the fast variations of the Zeeman signatures over this Rmated,0 with asT suggested,usingthe by PetitTeff (B et al.V (2002)relationusedbySaar&). that prevents us from comparing, at 1-year intervals, magnetic from F- to G-type at HK eAsolar-typeÀ stars short timespan. In the corresponding magnetic maps (bot- BrandenburgUsing this (1999). procedure, the spectropolarimetric data are ad- features that manifest themselves at specific rotation phases, we Living Reviews in Solar Physics justed at a reduced χ2 equal to 1.1 and 0.9, in 2008 and 2009, choose to limit our comparison to axisymmetric features (de- tom part of Fig. 4), the most striking evolution is a sharp 2 variety of rotation rates respectively2.2. Relation(F- (Fig. between1). through The Rotationχr value Periods for 2008 andK-), equals Cycle thatLeng obtainedths fined by modes with m = 0). We observe that all coefficients http://www.livingreviews.org/lrsp-2012-1 2 increase of the azimuthal magnetic field. These changes are one year earlier, andof the Stellar slightly Acti smallervity χr achieved in 2009 is α!,0, β!,0,orγ!,0 with a magnetic amplitude greater than 1 Gauss partly due to the higher relative noise in the data. The recon- (which only concerns modes with ! 4) have a different sign in taking place at(purple a roughly constant stars level in of chromosphericfig). In Figure 1every the lengths of thefew activity nights, cycles, P (in years), structed magnetic topologies are illustrated incyc Fig. 2,together both years, with the marginal exception≤ of γ .Anothernotice- are shown as a function of the rotation periods, p (in days). As 3,0 emission. with the magnetic map obtained in 2007 (P08).rot In Table 2,we able temporal evolution concerns the fraction of magnetic energy Not yet found for lower known from thefor Sun, the~30 cycle lengths years may vary from one cycle ξ Boo A is therefore submitted to fast and complex sur- to the next, see Baliunas & Vaughan (1985). The uncertainty in face changesmass that are different (late from G-, those ofK-type). the two previ- the cycle lengths may be up to 20%. Brandenburg• Measure et al. already found thatCa two sequencesH & areK in- ous stars, and reminiscent of the complex behaviour of other dicated, the active A sequence and the inactive I sequence. The rapid rotators observed in the past (e.g. Donati et al. 2003). steep sequenceas shows activity more scatter than proxy the flat one and may Fig. 5 (online colour at: www.an-journal.org) Rotation period actually consist of two subsequences, Aa and Ab. The Aa se- • The international Bcool projectversus mass foris the actively stellar sample. Pink symbols stand for stars quence contains four stars with B V values less than 0.63. They are indicated• byFound squares around cyclesÀ their symbols. Theyin cannot be 5 Discussion with at least one polarity switch. much older than the Sun, or they would not be on the main se- continuing this work for solar-type stars. quence. The presence~25 of twostars Hyades group(F7-K7) stars on the Aa se- “inactive branch” quence, indicated by an H, confirms the relative youth of these All stars of ourExpect sample show mapping variability over the magnetic four years cycles will be a major stars. Several of the A-sequence stars show two activity cycles. that active stars with masses below our lower mass bound- of our monitoring, but of different types. Stars which show Their secondary,• Dependence shorter cycles are shown by triangles. on The po- ary (in particular, mid-M dwarfs with masses just below the sition of the Sun is shown by a square with a dot inside. It is sit- at least one fistellareld reversal overmagnetism this timespan have focus in com- in next decade. fully convective limit) are reported to possess strong, simple uated betweenstellar the two primary parameters sequences. Clearly along each mon a fast rotation period (at least twice the solar one) and sequence the Pcyc increase with increasing prot. and stable surface magnetic fields (Morin et al. 2008a,b). Fig. 1.—Periods(Wilson of the activity 1968, cycles, PBaliunascyc in years, are plottedet al. as a1995, function masses equal or slightly larger than that of the Sun (Fig. 5). In Figure 2 the Pcyc are shown again as a function of prot,but of the rotation periods, prot , in days. The data follow two sequences, the rela- (Morgenthaler et al. 2011, 2012; Petit et al. 2012) this time in a doubleunclear logarithmic so plot. Thefar two Hyades group tively young, activeBohm-Vitense A sequence (dashed 2007) line)andthegenerallyolder,less In Fig. 5, we include τ Bootis, which is not part of our sam- τ Boo and HD 78366 were also observed at Mount Wil- stars are again indicated by an H. The position of the Sun is again active I sequences (dash-dotted line). The letter H indicates Hyades group stars, crosses indicate stars on the A sequence, and asterisks indicate stars on the I se- ple but which is reported to be affected by a short magnetic son as chromospherically active stars. For τ Boo, Baliunas shown by the square with a dot inside. The numbers give the quence. Squares around the crosses show stars with B V < 0:62. Triangles in- cycle of two years at most (Fares et al. 2009). We stress also et al. (1995) report a cycle of twelve years, versus two years B V values for the stars. Here the symbols for the stars with dicate secondary periods for some stars on the A sequence.À The solar point is secondaryÀ activity cycles are enclosed in squares. They include plotted as a square with a dot inside.

!c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.an-journal.org

The Astrophysical Journal Letters,763:L26(6pp),2013February1 Metcalfe et al.

Data: a Ca H & K cycle What we learned today Eridani (K2V) • We see signatures of magnetism on other stars The Astrophysical Journal Letters,763:L26(6pp),2013February1Ca H & K data: 1968-2012 MetcalfeLomb-Scargle et al. periodogram (peaks at ~3 and ~12 years) • Short-time-variable signatures include: photometry (spots; rotation period), ZDI magnetic maps (rotation period), flares (minutes-hours). • Long-time-variable signatures include: chromospheric emission (e.g., Ca H&K; H-alpha), coronal X-ray emission, total surface flux. Figure 1. Chromospheric activity measurements of the K2V star ! Eri. (a) Recent data from SMARTSFigure ( 2.),Lomb–Scargle Lowell Observatory periodograms (!), and ofthe CASLEO seasonal ( (top), along panel) with and nightly (bottom panel) mean S-index measurements from the MWO data 1968–1992 (dotted), previously published measurements from CPS ( ;Isaacson&Fischer2010) and HARPS ( + ; Anglada-Escudthe recent◦ datae´ & 1994–2012 Butler 2012 (dashed)). (b) Archival and the data full data from set× Mount 1968–2012 Wilson (solid). Significant variations are detected in the complete time series with periods near 3 years (1968–1992; Gray & Baliunas 1995) and the more# recent observations (gray points) with seasonal meansand 13 ( years,) and corresponding uncertainties toreflecting cycles on the the standard inactive deviationand active withinsequence respectively for a star with a rotation period near 11 days (Bohm-Vitense¨ 2007). each season. Mt Wilson project ended(A color in• version early of this figure 2000’s; is available in the Lowell online journal.) observatory continuing (A color version of this figure is available in the online journal.) • We see cycles on many other stars. Shortest is observations, some observationsproperties (Nelson et al.by2013 SMARTS). Of relevance to (2007-2012).! Eri, these of the quasi-biennial Hard, cycle. long Support for this interpretation has convection zone dynamos show both short-period and long- emerged recently from efforts to localize the source of the near 3 years, but they also show aterm weak signal monitoring near 7 years projectsin the MWOperiod databut variations appears very onlyin the innecessary global-scale the early observations, magnetism. for while understandingquasi-biennial variations,cycles. placing them firmly in the near-surface ~1.5 years; typical is ~10 years (similar to Sun). which corresponds to the orbital period of the exoplanet. This the 7-year artifact in the recent data is also transient and even regions of the Sun (Broomhall et al. 2012). 7-year period is present in the individual observations of the less prominent. Due to the limited4. timeDISCUSSION resolution of the wavelet If we assume that the 2.95-year/12.7-year cycles in ! Eri are longer time series measurements from both Lowell and CPS, analysis for longer periods, it is difficult to determine whether (Metcalfeanalogous to the et 2-year al./ 11-year2013) cycles in the Sun, then the lo- while the 3-year signal is present in each of the recent data sets the 2.95-yearThe and long-term 12.7-year behavior periods of coexist the magnetic simultaneously, activity cycles calization of the two signals has interesting consequences for individually. The longest time series from Lowell resolves the or if theyobserved alternate in instead.! Eri qualitatively If the 2.95-year resembles period the interaction actually of the the identification of the dynamos that are responsible for the 11-year solar cycle with the quasi-biennial ( 2year)variations active and inactive sequences as proposed by Bohm-Vitense¨ power between 3 and 5 years into multiple components, among disappeared during the broad activity minimum, it may∼ represent which the 3-year signal is the strongest. This is also reflected in the first observationanalyzed by of Fletcher another et star al.( entering2010,theirFigure1).Theamplitude (and later emerging (2007,p.492).Shesuggestedthat“differentialrotationnearthe the periodogram of the full data set (solid lines), which shows from) a Maunderof the shorter minimum-like (2.95 year) state cycle for in the! Eri short appears cycle. to be modulated surface mainly feeds [the A-sequence] dynamos,” while “interface dynamos in the stars with deep [outer convection zones] significant periodicities at 2.95 0.03 years and 12.7 0.3 It is strikingby the that longer! Eri (12.7 displays year) cycle.such short During magnetic the broad activity minimum of ± 6 ± the long cycle in 1985–1992 there is no evidence of the short- are the important ones for the I-sequence stars.” This is precisely years (both with false alarm probability <10− from the nightly cycles. Manyperiod models variations. of the Fletcher solar dynamo et al. documented favor a flux-transport similar behavior the opposite identification as that suggested by the helioseismic means) along with several weaker peaks between 3 and 7 years. paradigm,in and the typically Sun from the helioseismicslow meridional observations, circulations with set the the quasi- observations, which support a short cycle on the I-sequence Simulations of the two dominant periods reveal all of these cycle timescalebiennial for variations a dynamo almost operating disappearing in the during tachocline the minimum at localized in the near-surface regions and a long cycle on the peaks to be artifacts of the time sampling. An additional peak at the base ofof the the outer 11-year convection solar cycle zone but gradually (e.g., Dikpati returning & Gilmanduring the rise A-sequence attributed to an interface dynamo at the tachocline. longer periods of 20–35 years is present in both periodograms, 2006). Fromto solar three-dimensional maximum. They models attributed of stellar this behavior convection, to buoyant On the other hand, the Sun appears to be an outlier when com- but we exclude it from our analysis because it is correlated with we expectmagnetic that the meridional flux, generated circulations near the should tachocline be weaker during in periods pared to the A and I sequences established by observations of the length of the adopted data set. lower massof stars high and activity at faster in the rotation 11-year rates cycle, (Brown rising et through al. 2008 the; outer other stars. With the solar-like magnetic cycles observed in ! To investigate the strength of these periodic signals over Matt et al.convection2011;Augustsonetal. zone and episodically2012). In pumping Babcock–Leighton up the amplitude Eri, we are now in a better position to evaluate the specific time, we performed a wavelet analysis of the seasonal mean flux-transport models, this should lead to long activity cycles S-index measurements (Torrence & Compo 1998). Such an (Jouve et al. 2010). To test this assertion, we used the MESA 4 analysis essentially calculates a periodogram for overlapping code (Paxton et al. 2011)togenerateastellarstructuremodel subsets of the time series, where the length of the subset for ! Eri assuming a mass of 0.85 M and an age of 0.8 Gyr. % must be proportional to the periodicity under investigation. The radius, luminosity, and Teff of this model agree with the Consequently, there are regions of the wavelet spectrum (outside interferometric observations (Baines & Armstrong 2012), and of the so-called “cone of influence”) that suffer from edge the convective velocities vc are roughly half as fast as in the solar effects, where the signal is attenuated. The results are shown in convection zone. From angular momentum transport arguments 2 Figure 3,wheretheborderoftheconeofinfluenceisindicated (vm v /Ω), this suggests that the meridional flow speed ∼ c with a hatched region and the significance of the signal is shown vm might be as small as 10% of the solar value (or about 1 with a color scale going from the weakest (white and blue) 2–3 m s− at the photosphere), making ! Eri a challenging to the strongest (black and red). The 2.95-year and 12.7-year case for flux-transport dynamos. Recently, three-dimensional periods are indicated with dashed horizontal lines. The 2.95-year simulations of convectively-driven dynamos in rapidly rotating period maintains its strength through most of the duration of the stars have achieved large-scale organization and cyclic behavior time series, with the exception of the late 1980s to early 1990s in stellar convection zones (Brown et al. 2011). These dynamos through the broad activity minimum. During this interval, the do not rely on the slow meridional circulations, and can exhibit signal is dominated by the 12.7 year periodicity, which remains short cycles even in rapidly rotating lower mass stars, with the strong inside the cone of influence. The spurious 5-year signal cycle period determined by the rotation rate and the convective

3 Dynamo SSN cycle 24 predictions Questions of Solar and Global Dynamo$%&'(#)*#!!"#+,(-.&/012#34(21(''#)56)7# (Pesnell 2012, SoPhys) GGH"/'3" ?6.@A6@B',"?6*C>BD>>"0"E'*3F"D1 Stellar Magnetism GGH"/*I" Models current cycle 24 ;'+*:6<'2'"0";.:.<'=6><"D2 best estimate • How does the solar dynamo build organized 2D: Mean-field models magnetic fields that survive transiting the • !-" type 4*56*7*8"0"9'2:.3"D3 • interface dynamos &'()*+,"-./*"0"1'2/*3"D4 turbulent convection zone? • flux-transport and many variants (e.g. Babcock-Leighton) !" #!" $!!" $#!" %!!" • Why do the global solar fields cyclically Computationally inexpensive: simulate many cycles, try many!!"# ideas reverse polarity? In a position to try solar predictions (but parameterize convection) 3D: Convection, Rotation & Magnetism • What role does rotation play in the dynamo? • global-scale flows, magnetism, coupling from first principles • Is the Sun a typical magnetic star? • now achieving cyclic behavior, buoyant magnetic structures Next time: Simulations of stellar dynamos Computationally expensive Solar parameters well out of reach

Next time: Global simulations of stellar dynamos Learning more about stellar magnetic activity

“Observations of cool-star magnetic fields,” Ansgar Reiners, http://solarphysics.livingreviews.org/Articles/lrsp-2012-1/

“Magnetic fields of nongenerate stars,” J.F. Donati & J.D. Landstreet, 2009, Annual Reviews in Astronomy and Astrophysics

Convective ﬂows Large-scale B-ﬁelds

•Convection builds global-scale magnetic ﬁelds Next time: Simulations of stellar dynamos •Cyclic reversals of polarity now being found