1985AJ 90.2103S b) a) gap isprobablynotrealbecause of:(1)smallstatisticalfluc- recently analyzedtheVPsurvey, andconcludedthatthis lithium depletioninFandGdwarfs. could helptoexplainhisobservationsofHKemissionand activity. Duncan(1981)alsofoundthatsuchadiscontinuity the distributionatintermediatelevelsofchromospheric that time.Theysuggesteda“gap”mightbepresentin Currentaddress. BasedonobservationsobtainedatMount WilsonObservatory. HK emissionwith(B—V)amongthestarsobservedupto tion offewerstars.Intheir1980paper,VPshowedtherun ly completesample,comparedtoWilson’sdetailedexamina- VP surveyisasnapshotofchromosphericemissioninnear- hemisphere dwarfslaterthanaboutF5andwithin25pc.The 2103 Astron.1.90(10), October1985 0004-6256/85/102103-13S00.90 © 1985Am. Astron. Soc.2103 neighborhood dwarfs.VPsetouttoobserveallnorthern extended Wilson’sworktosurveyHKemissionamongsolar the absolutevisualmagnitudeofastar(WilsonandBappu activity cycles(Wilson1978),andthewell-knownWilson- Bappu relationbetweenthebreadthofHKemissionand mospheres. Thishasledto,forexample,thestudyofstellar dwarfs andgiantstoreconnoiterthebehaviorofstellarchro- then photoelectrically,hehasexaminedanumberofbright reversals oftheCanHandKlines.Firstphotographically, been seeninstellarspectraformanyyears,butWilson(1963) mospheres oflate-typestarsthroughobservingtheemission is primarilyresponsibleforthesystematicstudyofchro- 1957; Wilson1976). THE ASTRONOMICALJOURNALVOLUME90,NUMBER10OCTOBER1985 Hartmann etal.(1984a,hereafter referredtoasPaperI) Vaughan andPreston(1980,hereafterreferredtoasVP) Emission lineslikethoseofthesolarchromospherehave © American Astronomical Society • Provided by the NASA Astrophysics Data System A SURVEYOFCHROMOSPHERICEMISSIONANDROTATIONAMONGSOLAR-TYPESTARS depth. stars. Thedistributionof/2vs(i?—F)illustratestherapid,butsmooth,changeinrotationnearIS^q, regulating mechanism,andisinsensitivetothedetailsofastar’sstructuresuchasconvectivezone none haveflmass stars to II for the equations). R HK is shown against (B — K) in So- lose angular momentum during their main-sequence life- derblom (1983b) and in Paper I (although those diagrams times. This intimate relationship between rotation and chro- were made before the sample was screened as described be- mospheric emission means that understanding the evolution low). This conversion of 5 to R HK reverses the slope of the of a star’s outer atmosphere depends on knowing the star’s distribution, so that R HK tends to decrease with increasing angular momentum history. (B-V). Studying rotation in late-type dwarfs is difficult. Analysis The instrumental bandpasses admit some photospheric of high-resolution, high-signal-to-noise line profiles can light. All of the flux outside the Kj minima is assumed to be yield precise and accurate v sin/’s for solar-type stars (So- photospheric, even though there is some chromospheric derblom 1982), but such data are available only for bright emission in the inner wings of the H and K lines in very stars. There is an aspect dependence to v sin/’s, although this active stars. Conversely, all the flux between the Kj minima is unimportant for the mean of a sample of reasonable size. is assumed to come from the chromosphere. Linsky and Line profiles also contain information on other broadening Ayres (1978) argue that as much as 40% of this flux may be mechanisms, such as macroturbulence (Smith and Gray photospheric, but Noyes et al. present a full discussion in 1976). Paper II that justifies counting all of this flux as chromos- For dwarfs cooler than about G5, v sin/’s are very small pheric. This photospheric light is denoted Æphot> and is cal- (Soderblom 1981; Vogt, Soderblom, and Penrod 1983; Gray culated from the cubic relation in the Appendix to Paper II. _ 1984; Benz and Mayor 1985), partly because the stellar radi- This is then used to calculate Æ Hk = ^ hk ^Phot • Thus us decreases with mass, but mostly because these stars have R HK is the Ca n H and K flux, minus the photospheric con- long rotation periods (Vaughan et al. 1981). It is doubtful tamination, divided by the stellar bolometric luminosity. If that line-profile analyses will ever lead to an accurate picture .Rphot is plotted on the log Ä Hk (Æ — diagram, it paral- of rotation in very low-mass stars. lels the lower edge of the distribution, but is displaced below The most precise data on rotation in late-type dwarfs have it by about 0.2 dex (Paper I). Thus the correction for i£phot is come from the observations of rotational modulation of similar, but not identical, to the procedure of Wilson (1968), Ca II HK emission mentioned above. Although many obser- Skumanich and Eddy (1981), and Schrijver (1983), who sub- vations are needed to determine the period, this is a very tract the minimum HK flux seen at a given color from the powerful technique. The rotation period (or, equivalently, observed flux to get a residual flux representing the real the angular velocity) can be determined precisely, even for chromosphere. Herbig (1985) also uses such a procedure to stars that rotate very slowly. The result is the fundamental extract chromospheric Ha fluxes in solar-type stars. parameter that best describes the star’s rotation, free of any Linsky et al. (1979) define a quantity similar to Ä HK, but aspect of radius dependence. call it R . Their values of this quantity are reasonably close The properties of the Mount Wilson instrument limit HK to the R HK values of this paper for stars in common, given these modulation studies to stars whose HK emission is that their stars were observed with a different instrument at a strong relative to the continuum (Bahúnas et al. 1983). This different time. means that among the F dwarfs only young, chromospheri- cally active stars show detectable modulation, but that mo- dulation is detected in most K dwarfs. Old G dwarfs like the b) The Scope of the Survey and This Analysis Sun generally do not show enough modulation to make their rotation periods detectable. The VP survey was intended to include all stars meeting The well-determined rotation periods that exist are too five conditions: (1) definitely or probably on the main se- few to do more than suggest the trends of rotation on the quence; (2) later than F5; (3) within 25 pc; (4) in the northern lower main sequence, and obtaining such data for a large hemisphere; and, (5) not a known spectroscopic binary or sample is observationally impractical. In this paper, the em- close visual pair. This last condition was imposed because pirical relations of Paper II are used to obtain less precise but short-period binaries (P520d) show enhanced Can emis- more comprehensive rotation periods for stars of the solar sion (Wilson 1963), presumably due to tidally enforced rota- neighborhood. An examination of the distribution of the tion of the stars. A few spectroscopic binaries were retained normalized chromospheric emission is also made. if they have long periods and if the secondaries are too faint to contaminate the spectrum or photometry. II. THE VAUGHAN-PRESTON SURVEY This paper is concerned only with stars for which a) Analysis of the Survey 0.50<(i? - F)< 1.00, roughly F7 V to K2 V. There are too few stars with [B — F) < 0.50 within 25 pc to provide an ade- The instrument used to obtain these observations is the quate sample. The red limit is imposed because the HK ob- HK spectrophotometer of Vaughan, Preston, and Wilson servations are problematic for those stars. In particular, (1978), mounted on the Mount Wilson 1.5-m telescope. The VP’s instrumental color index, CRV, is ill behaved for solar neighborhood survey is described in Vaughan and (B-V)> 1.00 (see Fig. 3 of VP). Preston (1980). The instrument measures the flux through 1 Whenever possible, (B — F)’s from Nicolet (1978) were  bands centered on the H and K lines, and through 20 Á used; otherwise they are from Wooley et al. (1970). (B — V) bands centered at 3901 and 4001 Á (see Fig. 1 of Paper I). has been used as a temperature index here because it is avail- The ratio of the HK flux to the continuum flux is called S. able for virtually every star in the survey, even though This instrumental quantity (which is essentially an equiva- (V — R) or (V — I) would be superior. The equations that

© American Astronomical Society • Provided by the NASA Astrophysics Data System 2105 DAVID R. SODERBLOM: ROTATION AND Ca n EMISSION 2105 transform S to R HK and R HK implicitly assume a unique ^ Noyes > 1.004 + 0.087. The survey S values can also be color-temperature relation. compared to average S values that are computed from many VP's target list was compiled from the catalog of Wooley observations (typically 400). Note that these are computed etal. (1970). I reviewed the spectral types to ensure that only averages instead of the estimated averages of Paper II. For 32 main-sequence stars were included in this analysis (see Table stars, {S^y/S*vs ^ = 1*024 + 0.076. Again, the difference I for references). Most of the survey stars were always classi- is not significant. fied as dwarfs. Most stars for which Wooley et al. reported Thus, on the average, one or two observations of a star no luminosity class turned out to be giants with spurious yield an S value that’s within 8% of the long-term average. parallaxes, and so were deleted. Stars consistently classified Since R HK is proportional to S, it is similarly affected. The as subgiants were also weeded out, since they tend to be more uncertainty in S has a more complex effect on R HK that massive than dwarfs of the same spectral class/ Two stars depends on the star’s color and on S itself. For a star with a (HD 34411 and HD 37124) were sometimes classified as IV- weak chromosphere and [B —V) = 0.62, an 8% change in S V. These are probably just old, slightly evolved, main-se- produces about a 20% change in R HK. An active star at this quence stars, although they could be younger dwarfs of rela- color has R HK changed by about 12%. An inactive star at tively high metallicity that have a higher than average lumi- (B — K) = 0.90 is changed by 11%, while an active one nosity for their color. changes 9%. However, the blue, inactive stars show the least The Wooley catalog is not a complete sample of the stars variability (only 2%-3%; Wilson 1978), so that the observa- within 25 pc, but it is unbiased (Upgren and ArmandrofF tional error in S typically produces a 10% uncertainty (0.04 1981) for (i? — F)<1.00. In particular, there should be no dex) in R HK. selection effects that favor either young or old stars, as might be the case for very red stars (Soderblom 1983c). For those stars known to meet the above five criteria, the d) Deriving Rotation Rates from R Hk VP survey is at least 85% complete for this color range. A 1980 summary, made available by Drs. Vaughan and Dun- In Paper II, Noyes et al. (1984) show R HK is related to the r can, was used; this will soon be published as a catalog (Ba- Rossby number NK =PTOt/' c- The convective turnover húnas et al. 1985). A few stars were added that had been time rc was computed from an empirical fit to the models of observed at Mount Wilson since the summary was compiled, Gilman (1980) [see Eq. (4) of Paper II]. Gilman computed or if (B — F)’s had become available. those models for various stellar masses, and Noyes et al. The results of this screening process, 177 stars (including converted this to rc vs color by applying a standard main- the Sun), are listed in Table 1/ sequence mass-color relation. Such a mean relation ignores the range of masses that actually occur at any one color, due c) The Effect of Limited Sampling to observational error, evolutionary changes in the tempera- The stars in this sample have been observed an average of ture of a star, and abundance effects. The detailed properties about two times each. For comparison, the stars observed for of stellar convective zones are not well known in any case, rotational modulation (Paper II) were observed about 300 but these uncertainties must be recognized in interpreting times each. Does this limited sampling affect this analysis? what follows. Also, Gilman’s models produce a uniform rc These stars exhibit several kinds of variability: random fluc- for (R — F) ^ 0.90. This may or may not be physically rea- tuations from stellar activity; rotational modulation; the sonable, but is another reason for postponing discussion of star’s long-term activity cycle; and observational error. stars redward oi(B — F) = 1.00. The observational error is 5 2% (Vaughan, Preston, and A similar relation was fitted to R HK and Ar [Eq. (3) of Wilson 1978; Bahúnas et al. 1983), while the amplitude of Paper II]. That cubic is computationally convenient, but the the rotational modulation is rarely as much as 10% (Ba- data can be fitted just as well by an exponential: 5 húnas et al. 1983); the random fluctuations are also small. R HK = 6.40X10“ exp (-0.868 Ar). (1) The most serious problem is the stellar activity cycle, which can have an amplitude as large as 30%, although 10% is In both cases, cr^O.05. These two curves differ little for most values of R HK, and the resultant O ’s differ by only 2%-5%. more typical (Wilson 1978). In order to relate HK emission -5 to rotation, Noyes et al. in Paper II considered only those For R HK ^ 5 X 10 , the cubic produces more realistic rota- stars that were studied by Wilson (1978), so that the data tion rates than does the exponential (which would require spanned at least a decade, and the amplitude of variations in very small or negative AR values), and so the cubic fit has activity was known. An average S value was estimated for been used here to calculate Í2. Note that the R HK vs AR each star by drawing a visual mean through the data. relation was calculated using all the known rotation periods, Several of the stars in Paper II are also in this survey, so regardless of [B — V). one can see how well one or two observations indicate the The above relations have been applied to the Vaughan- Preston survey to produce column (10) of Table I. Prot has true mean level of HK emission. For the 33 stars in common < to the survey and Paper II (for which <«obs > = 1.7), <*S;urvey / been converted to /2* //20 using R0 = 25 ?4. As noted above, R HK is typically uncertain by about 10%. For an -5 inactive star (R HK ^ 1X10 ), this produces only a 5% un- 5 * The removal of giants and subgiants eliminated about 15% of the original certainty for Í2. For an active star (R int ^ 3 X 10~ ), chang- ing R by 10% changes Í2 by 15%. Even if these error sample. These stars were distributed at random through the original R HK vs HK {B — V) diagram of Paper I, so that their removal does not affect the conclu- estimates are too low, this procedure still yields Í2 ’s to higher sions of that paper. precision than has been obtained with v sin/’s, particularly ^ Table I has one omission: HD 84737 should also be named HR 3881. In for slow rotators (Soderblom 1982; Gray 1984), and the data previous papers (Soderblom 1982, 1983a), I misidentified this star as 15 are much more useful since no radius or aspect dependence is LMi. As Hoffleit (1979) points out, this star is in Ursa Major. present.

© American Astronomical Society • Provided by the NASA Astrophysics Data System o 00 C/} 2106 DAVIDR.SODERBLOM:ROTATIONANDCanEMISSION © American Astronomical Society

Table I. Ca n emission strengths and rotation rates of nearby solar-type stars. C? oo cmcn oo cnino zr in O UCOVO ooooo > o ooooo Ü TJluO in oovo o »-»-zrcm cn invoooo r- v-oocmin O' CM ooooo ooooo T- zrCM CM O t- 0OCMin r- VOCMO'zr «ägz > o vot-in O *dSdfed I CMt- vo in v- VOt—CM I I I no oO' VO 00O' »- ir>cn«- in vocn^-O' cm cno O CM00^ o' v—cn O TJ O CM«CO > 00VO «- oc\jon CM in vo zr invo vo oooin oo zrincm ooooo ooooo CM v-o-V-00 i I I i I cncmt- «< c< O' I CM I O' £ oo zrincm VO t—C- > N- »-•-<\jon cr> onO' O' invo invozrov- in or-voO' C3 OC5t»ä O'CO O'-=T<\J o «-cvjtv CM in oo«-cm zr vo»-O' zrcnvoinc^- o I- 00O'o O' inco«-on CM incmzro o zr>>in ooooo ooooo cm T-r- cm ooinvo cm vozrr- in vo ■o TJIt,<- sd ooin• i I I i I I ■»! I C3 O' g S ^ g°g Provided bythe NASA Astrophysics Data System 1— T>WO on T-»-•- in cn> o O' 0—OCOLfN CM OJ-h-CMt- zr t-ino VO OO' vo «-cncm ooooo o onzr t- coon O VOZ ooooo t- cnv-vo int-cncnv- Sd *« • socnooo t cnc - v-cmc I I i + 11+I t^oo zr ovot^v- vo goinco cn so•cmv- > oin t- o Sd T)O ooooo on ij-ztinO' vo I00O' cn O' N-COvo voo'izr+- v- oni•-cn o c-cn c- ioia. ooooo cm zri-CM in it- cm i if^ I i vo <-T-zr - »—CMCNJC\1 s 1 \m ooooo C3 bvibiChO > vo cnco O' JN CNO'^2 cm voint- c— inco cn zr cm zrocn in zrooO' o cmcn CM in ozrO'o' ooooo cm ent-r-( o» oor-vo« t- i«-cncm ooooo v- inO'cm ooooo in zrc Sd OCb > „t- I + I 0)A vo zr C- O'ooo O H +> D zr int--»-o zr t-zronzj- on •-»-r- oo ozrc—o' O' o t~- c--»-CM cnoo t-moo cninh-ot^ in onooc- cm cn CM VOt-vo cn ooO'zr ooooo r-^-t-cM»- O' ino'o ooooo v- CMcm»-T- e-- oozrc-vo ; cnvoco, i i I n < =r iA in voo zr cn “ =0«O S o int^c-c-T- OOOOO v- ooinzr o v- o zrcn ^ cmon zr inc-co zr cmcn cn o'o ovcncninr- in cm*-coo zr cnO' cn on oooztv-t- cn t—(MCM t- ovcmcn «- vozro >>>£>> > s O' o»-• o- CMO'v-t o bu:sd ooooo ooooo o» oo>oocn o cncm o r- onv-zr Û*vO >CM 3 HIO' ■ I ■ cm»—on ' VOo~o 'T-aronj» CM C i„ i Ki I “ - oo ocn co ooocn zr cmin o >f ooooo ^ §o5c ooooo on t-cm on vooCM eo cno'ino vOCMvOzr»— o zrin cn c-o O Sdoo >>ot«-> CM cmcn O' V-vCM O •OT3 ooooo ooooo cn v-zrt-m in cncmoo CM V- CM O'ocn cm o't-ino Xg g i I i o cnot- in vo 2106 00 O'! O CM o 00 LO C/} ^0 2107 DAVIDR.SODERBLOM:ROTATIONANDCanEMISSION © American Astronomical Society Table I. (continued) 8 ^ n — C? S a° S a t-min a envo coinai'-c- o cnain m voe-co oinc^c-c-- m sr¿t¿r in O'vo cm fainooi ooooo ooooo VO vo > t-I in cm »- aincmvo ooooo bd T3oI in oovo g C— voC-C' O >-CM cm acnvo O ■-voCM > ooooo M Obd g 7SÊ ë ¡oS i O' i a cmr-eno 00 T-CM cm avoin »- t-r-ovo ee^« VO C- fa Obd > ooooo cn «-av-cm t- ovcnc-a — voc^om VO COO'00o CO CM ooooo a-aioa-a- co mi~-o »- O'ain ocn^-cvjr- co cn ooooo r- CM>-O' O' CMO00 r- CMvoCO o •“ CO o ooooo ena •-cma o *- bd T)O CM intn«obd ooooo ooooo «- tna-cm a otj in voooo' I {o i I CMCO 5 0 a co O' vo ses Provided bytheNASA Astrophysics DataSystem in m O' O C—CMO' o vc—-»* a vov-o vo «-inooo bd -oTD en obd > in ooooo en v—acm 5 VOC-c~ a- cma’oo > oc ooooo s æ l <0VOvo c- coino' CO »—*—•— co COO't-irv O' covoin i :! I i I + > o S CQÍ oo cmcnini* in vou en oe CO O' CO VOo o O'CM > in VO V—COO'00 o fabdX) ooooo T-T-V-CMt- CM o c O' oco o avo o oo^inco > ooooo C\l r-T-r—1— O' VOt— in c-o.cmO' bd UO o i ¡ s æ« c- covoin ( i ! o ooooo ^ cot) > m£ oo coen^o cm incovo LTVNOVOVOI/N LOVOUNNOVOITN^ OO O<-oCO > in ooooo ooooo vo VOC-O' ac-ooo't- O bdT5 in voen ooooo •a- COC-OJO' m ina- cm mcou > a O C3T)bd V- »-«-CMVO co a•-cm- o m r r-«->-m i I O CM'-OOO'OOVO I ! a inu ov ov-■>-c a- a VO^-COO»“ eo t—covoa vo o'*-voc- cm <-t-en •o bdT3U bd avo t- en>o ooooo cn v-cmt- 0% ONOn «- voinenov o ovin ^-e^coooh- ooco ° nicm in a-t~-O'ooocm v- O'OC-00CMCO o v-bdcmt^mvo'-'- >t»o>> a> CO CMT- Ubd-ot^o -OCSUbdUi ooooo CM •—»—vO c- incovo co a-oin iode D VOE—OC i I I i i I t iI -oinenin cnmcmvo c~- incoc vo ooO'O CO vo o cmbd ooooo > en t-- invoen O C '— CMr-T bd uUoX) CM v— V—»—CM C-- c—V“o ooooo T- «-CM ooooo fMoooja i I I T— I i o, e"s ON CnOn O ONr- ooooo > U. C3 t- CM - mino 5 0 cvj inC"-m 2107 C/} o00 CM 2108 DAVID R. SODERBLOM: ROTATION AND Ca n EMISSION 2108 O'!O Notes to Table I

^0 Col. (1): number in catalog of Wooley et al. (1970). flux. R HK is the HK flux after subtracting the photospheric light admitted Col. (4): sources of spectral types: Jaschek, Conde, and de Sierra (1964); by the instrumental bandpasses, again normalized to the bolometric flux. Ú 00LO O'! Harlan (1969, 1974, 1981); Harlan and Taylor (1970); Kennedy and Bus- is the angular velocity calculated from R HK, divided by the solar rotation combe (1974); Buscombe (1977, 1980, 1981); Keenan and Pitts (1980); Hof- rate, using Pq = 25

e) The Uncertainty of the Rotation Rates curate. Recent independent determinations of v sin/’s in so- The ability of these relations to predict O accurately can lar-type stars (Gray 1984; Benz and Mayor 1985) also sub- be tested in two ways. First, these calculated Í2 ’s (using stantiate this conclusion. “snapshot” values of S from the Vaughan-Preston survey) can be compared to the true values of Paper II. This com- ß Metallicity Effects parison is shown in Fig. 1. The rms deviation from equality is No allowance has been made for abundance effects be- 0.087 dex, or about 20%. This is probably the best estimate cause they are largely unknown. The Hyades provide a pos- of the true errors in the calculated Í1 ’s. sible test of the effects of enhanced metallicity, since their These calculated Í2 ’s can also be compared to v sin/’s. For [Fe/H]~ -f 0.15 (Twarog 1981; Cayrel, Cayrel de Strobel, a large sample, one expects and Campbell 1985). Duncan et al. (1984) and Lockwood et v=((v sin/)/i;} = Galaxy. There are two separate questions The good agreement between measured v sin/’s and calcu- here: ( 1 ) Can a valid index of the strength of the HK emission lated Í2 ’s suggests that both procedures are fundamentally be calculated from these observations? (2) What does that sound since these two quantities are obtained in completely index mean? In particular, can the sameR HK vs WR relation different ways. This agreement also reinforces Soderblom’s be used as for solar-abundance stars to calculate il? (1982,1983a) conclusion that Smith’s (1978) v sin/’s are inac-

R'hk x io5

Fig. 2. Adopted polynomial relation between R HK and NK [Eq. (3) of Fig. 1. Comparison of calculated Í2 ’s (from Table I) to observed values Paper II], and observed points for Hyads and the Hyades Group mem- (Paper II). ber HD 1835.

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1985AJ 90.2103S 6 in in dash lineshowswhereP= r, andGray’s(1982)“logt been addedtoFig.6:thesolidline istheHyadeslineofFig.4, circles aretruerotationperiods forseveralHyads.Thedot- transformed toOwithequation (3)ofPaperII.Thelight have positiveslope. analogous toFigs.3and4.Some additionalinformationhas Æhk-SXIO“. appreciable scatteraboutthisline. stars thatareHVisroughlyconstantfor(B—F)>0.60. stars isalsoflatandofuniformbreadth.Thepercentage height. Ithasaflatlowerbound(exceptfortwostars)at ing sections.Anexaminationofthesediagramsindicates: as explainedbelow. tionary trackfortheSunisshown,assumingÆoct~ The dashedlinesjoinmembersofvisualbinaries.Anevolu- 1.11, 1.00,and0.92^q.These trackswerecomputedby the UrsaMajorGroup,andpositionofSunisshown. linear fittothosepoints.Thetrianglesrepresentmembersof sent individualHyads,andthesolidlineisaleast-squares with someadditionalinformation.Thelightcirclesrepre- rot c discriminating high-velocitystarsaregivenbelow(Sec.IVb). and halostars,denotedby“HV”inTableI.Thecriteriafor neighborhood. InFig.3,thelightcirclesrepresentolddisk for solar-typestars(roughlyF7VtoK2V)ofthesolar because theirchromospheresaresoweakrelativetoR. R hkvaluesofthesestarsareatorslightlybelowthosethe variability (Wilson1978). could bededuced,asdoneforsolar-abundancestarsby end, thehalostarsshowmuchscatterinRk>probably ages ofabout6-10Gyrifthet~lawisapplied.Atblue Noyes etal.(1984).However,thesestarsshowlittle,ifany, some interestinginformationontheirconvectivezones high-velocity starsinthissample(seeSec.IVb),indicating vey, theMountWilsongrouphasalsoobservedanumberof mine Rproperlyforthesestars. is overestimated.Afewhigh-dispersionspectracoulddeter- stars. However,Rmaybeunderestimated,sothat Thus Risprobablycomputedcorrectlyformetal-poor that thecontinuumfluxlevelnearHandKlinesis ence inmetallicityofthesetwopopulations,thissuggests stars asitisforyoungdiskstars.Giventheconsistentdiffer- color indexisrelatedto(2?—V)inthesamewayforolddisk HKf subdwarfs, someofwhicharetruehaloobjects.Themean same forallstarsofthe(B—V),regardless[Fe/H]. = 8.5”lineisalsoshown.Evolutionary tracksareshownfor phot H phot photHK HK 2109 DAVIDR.SODERBLOM:ROTATIONANDCanEMISSION Figures 5and6showthecalculatedO’sofTableIinaway (5) Thelinesjoiningmembersofvisualbinariesgenerally (4) TheHyadeslineisnearlyflat,butnotquite.There (3) NearlyallHVstarsareweakchromosphericemitters. Both ofthesefiguresarediscussedindetailthefollow- (2) ThedistributionofRforthehigh-velocity(HV) (1) TheRdistributionisroughlyflatandofuniform Figure 4showstheVaughan-Prestonsurveyreplotted Figures 3and4presentthedistributionofRwithcolor To addressthefirstquestion,InotethatVP’sC HK HK © American Astronomical Society • Provided by the NASA Astrophysics Data System If rotationperiodscanbedetectedinmetal-deficientstars, In additiontothehigh-velocity(olddisk)starsinsur- HK RV a) ChromosphericEmissionAmongSolar-TypeStars b) RotationAmongSolar-TypeStars III. RESULTS I1 -1/2 age andcomposition,whichhas beensuggestedbyGray single rotation-massrelationfor solar-typestarsofagiven (1982), Benz,Mayor,andMermilliod (1985),andDuncanet wood etal.estimate.TheseHyadesdataareconsistentwitha than the4%-5%errorsinrotationperiodsthatLock- voke ametallicity-dependentconvectivezonedepth. temperature relation.Inparticular,itisnotnecessarytoin- in Fig.2canbeattributedentirelytotheirdifferentcolor- served Í2’s.ThismeansthatthedisplacementofHyades 0.07 dex,whichisgreaterthantheratioofpredictedtoob- increases Rbyonlyabout0.01dex,butcanincreaseÍ2 by 0.i02[asisappropriatefortheHyades(Duncan1981)] Í2 is1.09,sothatthemeanRvsA^relationtendsto overestimate Í2(cf.Fig.2).ForagivenS',decreasing(B—V) these tenstars,theaverageratioofpredictedOtoobserved periods areknownfromcontinuumvariabilitystudies 0.45<(5 —F)<0.50 areadded,thisslopinglineisclearly the bestfit. (Lockwood etal.1984),andHD1835isagainshown.For figure, thelightcirclesrepresentHyadswhosetruerotation fitted wellbyahorizontalline.However, iftheadditionalHyadesdatafor (3) fromPaperII,isshownasasolidlineinFig.6.Inthat and meanchromosphericemission(cf.Duncanetal.). and compositionhavingaone-to-onerelationbetweenmass these Hyadesdataareconsistentwithstarsofaconstantage * Exceptforthepointsat{B—V)<0.55, theHyadesdatainFig.4couldbe can beaccountedforbyknowncauses,or,alternatively, activity cycles(Wilson1978).Thereisnogreaterscatterthan scatter expectedforagroupofstarsinvariousstagestheir HK HKR scatter isthencr=0.028dex(+6.6%).Thisaboutthe used tocalculateRand<7=0.022dex.Theresidual Duncan etal.listweightswiththeir(S)values,whichwere log Rhk=0.391(B—V)—4.725,with0.85issufficienttomakeÍ1 between RandiV. for higher/(/=angularmomentum).Rengarajan(1984) mechanism incorporatesfeedback,sothatdJ/dtishigher cubic transformationofthestraightlinehasaminimumat did, itscounterpartinFig.6wouldturnupwardbecausethe does notcontinuetoslopeupwardfor(B—V)>0.85.Ifit lower boundinFig.5,whichisanartifactoftherelation relation forstarsofagivenage.However,asexplainedbelow and Vaughan(1984)havesuggestedasimilarunique seems physicallyunreasonableaswell.HavingtheHyades conflicts withtheshapeofflvs(i?—V)distribution,and level offaswell. 2110 DAVIDR.SODERBLOM:ROTATIONANDCanEMISSION (B —V)~0.80.Suchanupturninftforthereddeststars (Sec. IVe),theirconclusionisbasedonthesharpnessof HKR Six ofthestarsinVaughan-Prestonsurveyaredefinite The straightlinefittoRvs(5—V)(Fig.4)probably © American Astronomical Society • Provided by the NASA Astrophysics Data System HK 0.50 0.600.700.80 2) TheUrsaMajorGroup (B-V) _1/2 1 R jjK^i(DuncanandSoderblom1985),givenagesof and woulddisappearifHD150706weredeleted.Removalof apparent excessHKemissionofHyadsalreadymentioned, 0.3 GyrforUMaG(vonHoerner1957;LevatoandAbt than theHyades.Adisplacementof0.15dexisexpectedif the UMaGmembersareabout0.05dexhigherinlogR agree wellwiththecalculatedvalues.Near(B—V)=0.60, True O’sareknownforjOriandÇBooA(PaperII);they HD 150706alsoreducesthescatterinRforUMaGtoa than Hyadsofthesamecolor,andtheyrotatefasteraswell. ber thatwasobservedaspartofthesurvey,butithasnot been includedbecauseit’saclosebinary(Bopp1980).HD HD 39587,41593,72905,115043,131156A,and150706 and 6.Theyare,onaverage,morechromosphericallyactive from theGroupmean. bership isuncertain:Ithasallthespectroscopicattributesof (Soderblom andJones1985).HD45088isanUMaGmem- an UMaGmember,butitsspacevelocitydifferssignificantly 1971; Patenaude1978).Thisdiscrepancyisdueinparttothe 1978; Giannuzzi1979),and0.6GyrfortheHyades(Maeder HK 131156A (£BooA)hasbeenretained,eventhoughitsmem- HK These sixUMaGstarsareshownastrianglesinFigs.4 0.90 1.00 1/2 Table I),i.e.,olddiskandPopu- lation II. sent high-velocitystars(“HV”in ty. TheSunisshownat{B—V) the stellarbolometricluminosi- mental bandpasses,dividedby ic contaminationintheinstru- of TableI.RistheCanH and Kflux,minusphotospher- as afunctionofcolorforthestars malized Cailemissionstrength Fig. 3.Distributionofthenor- for theSunisshown(withagesin dashed linesjoinmembersofvi- the solidlineisleast-squares Gyr), assumingRcct”. Group. Anevolutionarytrack are membersoftheUrsaMajor sual binaries,andthetriangles fit throughthosepoints.The served pointsfortheHyades,and in Fig.3.Thelightcirclesareob- tion. Thesmalldotsarethestars with someadditionalinforma- Fig. 4.Dataof3reshown HK = 0.656.Thelightcirclesrepre- HK 2110 1985AJ 90.2103S binaries. Sincesuchstarsarepresumablycoeval,lines in SoderblomandJones(1985). data ofAyresandLinsky(1980),whoshowthatchromos- than theprimary.Thiseffectisalsoseen,forinstance,in the coolercomponenttobemorechromosphericallyactive parallel totheHyadesline,althoughthereisatendencyfor should defineisochrones.Mostoftheselinesareroughly level similartothatoftheHyades.Thisisdiscussedfurther 2111 DAVIDR.SODERBLOM:ROTATIONANDCanEMISSION The dashedlinesinFigs.4and6joinmembersofvisual © American Astronomical Society • Provided by the NASA Astrophysics Data System 3)Binaries 21/- -1 bolometric flux.Additionalobservationsofbinariesare in aCenBthanA,afternormalizationtothestellar phere andtransitionregionlinesaretypically40%stronger needed todetermineifthiseffectisreal. increase ofstellarvelocitydispersionwithage(Widen1977; velocity components,takenfromWooleyetal.(1970).The velocity (“HV”)objectif(U+F)>65kms,or \W +101>30kms.U,VandWaretheGalacticspace f Following Oort(1926),astarwasjudgedtobehigh- b) High-VelocityStars in represent high-velocitystars. tion ofcolorforthestarsTable ities, relativetosolar,asafunc- I. AsinFig.3,thelightcircles Fig. 5.Calculatedangularveloc- The dashedlineshowswherethe true Hyadesrotationperiods. formed toHwithequation(3)of case, thesolidlineisfitto a mannersimilartoFig.4.Inthis Fig. 6.Dataof5reshownin 0.92 Af,forfloct~.The in thetext.Evolutionarytracks to thesecoordinatesasdescribed Rossby numberisunity Paper II.Thelightcirclesare Hyades pointsofFig.4,trans- are shownfor1.11,1.00,and dicate agesinGyr. numbers nexttothosetracksin- (P =r).AlsoshownisGray’s “log t=8.5”line,transformed 0 rotc 2111 2112 DAVID R. SODERBLOM: ROTATION AND Ca n EMISSION 2112

Twarog 1980) means that HV stars are generally old, and d) Chromospheric Emission in Field Stars consequently have low metallicities. Nearly all the HV stars have weak emission, as expected The removal of the photospheric contamination from for old stars. Four HV stars have relatively strong emission R hk> t° produce R HK, results in a flat distribution with a 5 lower bound at R k ~8x 10-6. (Note that both of the stars (R HK >2X 10~ ), but three of these have been observed H only once, so that confirming data are needed. The fourth that lie significantly below this limit have been observed only star, HD 152391, has been observed many times (Paper II), once each.) This lower bound probably does not represent and shows continuum variability (Radick etal. 1983), as well the chromospheric activity of a star in the absence of a driv- as strong HK emission. Although this star may be a subgiant ing force. All stars have some angular momentum which, (Harlan 1974), its parallax indicates that it’s on the main together with convection, will presumably lead to magnetic sequence. HD 152391 is an interesting star that deserves field generation through the dynamo mechanism, so that further observation, particularly to check for duplicity. even the oldest stars will exhibit some chromospheric activ- There may be old dwarfs with strong HK emission, which ity. A similar lower bound is seen in the Mg n h and k emis- would contradict an otherwise self-consistent picture of the sion fluxes for dwarfs [see Fig. 3 of Basri and Linsky (1979), loss of angular momentum and the concomitant weakening also Hartmann et al. (1984b)]. of the dynamo with age. The flatness and uniform breadth of the R HK distribution Except for these four stars, the distribution of HV’s in Fig. in Fig. 3 may seem, at first, unexpected because a greater 3 is flat and of uniform breadth, and there’s a constant per- range of stellar ages should be represented at the red end centage (^35%) of HV’s for (B — V) >0.60. These stars are than at the blue end. At (1? — V) — 0.50, TI/ÏÏIq ^ 1.25, and = fitted by log Æ hit 0.066 (B — V) — 5.041. The position of the main-sequence lifetime rMS —1/2 rMS(Q). At this line relative to the Hyades suggests that these HV’s are (B — V)= 1.00, -0.75, andrMS ^2rMS(©)- There- 1/2 fore the range of ages at the red end of the distribution could about 6-10 Gyr old, if Æ Hk r “ . These are reasonable ages since the very oldest stars have the highest velocities, be as much as four times that at the blue end. Yet the breadth and so tend to be missing from the solar neighborhood. of the distribution changes little with color, and the fraction The constant percentage of HV’s with color suggests that of high-velocity stars is nearly constant at all colors: there is the age distribution of this sample is also uniform with color not an abundance of old, red stars. since there is no reason to believe that the red HV’s are differ- The positive slope of the Hyades isochrone removes part ent than the blue ones. of this discrepancy by making red stars older than blue stars with the same R HK values. The constant fraction and flat c) The Sun Among the Stars distribution of high-velocity stars indicates that the age dis- tribution of those stars is roughly constant with color. Thus the R vs age relation is unlikely to change with color (or The Sun is shown at (B —V) = 0.656 (Campbell 1984), HK using the Ca n data in Paper II. Obtaining a reliable S value mass). The uniform breadth of the distribution results from a for the Sun is difficult because deep absorption lines are filled lack of very old stars at the blue end (because of rMS ), and a in a sky spectrum (Grainger and Ring 1962; Hunten 1970). modest deficiency of young stars at the red end. Only a few The solar S value in Paper II has not been reconciled with the young, red stars would be needed to make this apparent dis- observations of White and Livingston (1981), but the Í2 cal- crepancy disappear. culated from this S agrees well with the true value, even if the Subtracting RPh0t from R HK to produce R HK amplifies see the observational scatter. Among the old stars, there is two Sun is not used to calibrate iVR vs R hK ( Fig- 8 of Paper to three times as much scatter in R HK as there is in R HK (see II). The solar R HK in Table I is close to the same ratio for the “sky” that Linsky etal (1979) tabulate. Fig. 2 of Paper I). The position of the Sun in Fig. 3 indicates that it’s one of the older stars of the solar neighborhood. By comparison, e) Rotation in Field Stars Perrin et al. (1977) obtained ages for nearby solar-type stars The rotation rates of most solar-type stars fall within one by placing them on theoretical evolutionary tracks, and decade. Stars rotating faster than five times the solar rate are found the Sun to be a relatively young star. Other evidence rare because such stars are very young. The known rotation (Soderblom 1983a) also indicates that the age estimates of periods of very young, single stars, such as BY Draconis Perrin et al. are generally too large and that their technique variables (Bopp and Fekel 1977), agree with this upper does not work well for ^ ^ 1 . The Sun is 0.47 dex below bound. A few of these active stars could have strong HK the Hyades R HK line (Fig. 4), as expected for their relative emission and rapid rotation because of tidal effects in close ages, given a i ~1/2 law. binaries (Wilson 1963), but most such systems have been de- The Sun appears to have a normal rotation rate for a star tected as spectroscopic binaries because of their large radial- of its mass and age. Soderblom (1983a) drew this conclusion velocity variations. Moreover, the rapid rotators in this sam- from v sim’s; he found the Sun to be slightly below average ple show other signs of true youth: abundant lithium for old 1.0 stars, but by less than one standard deviation. (Duncan 1981; Soderblom 1983a; Soderblom and Jones The extent to which the Sun resembles other stars depends 1985) and low space velocities (Vaughan and Preston 1980). on the comparison sample. If (B — F)0 —0.63 (Olsen 1976; Thus there is no evidence that any of the rapid rotators are Chmeilewski 1981), then the Sun appears to rotate more old stars with excess angular momentum, as might be ex- slowly than other stars, but at the color plotted it’s a little pected if most of a star’s initial angular momentum were faster than average for old stars. If (2? — F)0 = 0.686 given to a planetary system. Unless low-mass stars always (Schmidt-Kaler 1984), the Sun would appear to rotate faster form planets, the Sun, and stars like it, have lost their natal than most old stars. Given these uncertainties, the safest angular momentum through their magnetic fields and conclusion is that the Sun is not significantly different from winds—which appear to be inevitable features of stars with other solar neighborhood stars of its mass and age. convective envelopes. The rotation rate of a solar-type star

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1985AJ 90.2103S 1 star (Soderblom1983a). probably offersnocluetothepresenceofplanetsaroundthat tion totheextentthatlongestperiodmeasuredfrom than halfthesolarrate.*Thisisalsoconsistentwithobserva- for tworeasons.First,rapproachesanasymptote low-mass (K7V),high-velocitystarthatisprobablyvery rotational modulationis50daysfor61CygniB(PaperII),a old.^ N ,whichisnotanisochrone,asshownbytheHyadesdata. The rvs(B—V)relationdependsona,theratioofmixing lar flatteninginFig.5becauseoftheRvsNrelation. transformed fromspectraltypetocolorusingPopper’s neighborhood (SoderblomandDuncan1985). real, butisinsteadduetoanexcessofyoungstarsinthesolar nism, theapparentgapindistributionatthispointisnot P )scaleforweakemitters,maskingrealstar-to-stardiffer- ferent 12’s,buttheavailabledata(PaperII)indicatethat length toscaleheight.Othervaluesofawouldproducedif- (B —V)^0.80(seeFig.5ofPaperII).Thisproducesasimi- iades andaPerseiclusters(vanLeeuwenAlphenaar rotators likesomelow-massstarsrecentlyfoundinthePle- systematically toolowfor(R—F)£0.70. between theoldestandyoungeststars.Althoughitistempt- R vsNrelation(Fig.2),whichcompressesthe(or this imposesalowerlimiton12. main sequence,rexceedstheageofGalacticdisk,and Gray’s lineisagoodapproximationattheblueend,but assuming anormalmain-sequencemass-radiusrelation (1980) correspondence,andconvertedfrom(vsin/)toÍ2by change inthenatureofconvectiondynamomecha- ing toassociatethechangefromPrwitha rate thatisprimarilyafunctionofmass.Thismayalsobe (Lacy 1977).Gray’slinecorrespondstoaofconstant intrinsic scatterinRor/2fortheseoldstars. true, butagaincannotbeinferredfromthepresentdata. bound toarguethatstarsreachadefiniteminimumrotation fitted wellbyP^2.3r.Thissharpnessisanartifactofthe Much morecarefulobervationsareneededtodeterminethe lowing Gray1982).Suchauniquemass-age-rotationrela- bound intheÍ2vs(B—V)diagramasevidenceforaunique ences. TheRdistribution(Fig.3)hasamuchmorerag- used asevidenceforit.Vaughan(1984)usesthissharplower tion mayturnouttobecorrect,butthisdiagramcannot rotational velocityforanystarofagivenmassandage(fol- ged edge.Rengarajan(1984)hasinterpretedthissharplower c 1982; Staufferetah1984,1985).ThestrongestHKemitters 2113 DAVIDR.SODERBLOM:ROTATIONANDCanEMISSION k c HKK TOt HKkK MS rotc HK rotc HK not in61CygA.ThepresenceofLi astarofsuchlowmasswouldbe high-signal-to-noise Reticonobservations bymyselfandB.F.Jonesatthe extraordinary, exceptforaTTauristar, andwouldindicateyouth.Recent even lowerthanat(2?—V)0.90. should beabout0.80,althoughatthat color,logRwouldbe—5.40, observed onlyonce.Moreover,itsdiscrepantCsuggeststhat{B—V) Lick 3-mcoudéshownoevidenceofLi ineitherstar,i.e.,W<5mÀ. * Bonsack(1960)claimedtodetectlithium (W~37mÁ)in61CygB,but HK RV A x Even theoldest,leastmassivestarsrotateatnoslower The flatteningofthelowerboundÍ2vs(B—V)occurs The onlyexceptionappearstobeHD175541,butthisstarhasbeen There arenofieldstarsinthissamplethatultrafast Also showninFig.6isGray’s(1982)“logt=8.5”line, The loweredgeofthedistributioninFig.5issharp,and Figure 6showsthelinewhereP=r,roughlymidway © American Astronomical Society • Provided by the NASA Astrophysics Data System TOtc is thebestchoice.Second,atsomepointonlower -1/2 -1 in in 1/2 justification forthe/law.AsR,thislaw blom andJones1985). in Fig.3,forinstance,allhavevsin/^20kms(Soder- tent withv. sion (Pallavicinietah1981)becausetherapidrotatorsare lated forsolar-typestars.Thismakesitdifficulttostudy, assumptions (e.g.,aconstantwindvelocity,magneticfield follows fromasimplemodelforangular-momentumloss indeed ispresenttosomeextentinthecalibrationofiV generally starsofhighermass.Thisproblemalsooccursin example, therotationaldependenceofcoronalx-rayemis- N isused[Eq.(1)],forsimplicity,thenRccexp(k/i2). strength proportionalto(2),sothatitcannotbetakenasa (Dumey 1976),butthattheorycontainsseveralunverifiable against R. studying chromosphericfluxes(Hartmannetah1984b),and rotation periodtotheconvective turnovertime).Strictlyem- ity, notthesurfacevelocity),butcanalsorequireaprodi- that therotation-agerelationisindependentofmassfor here. Benz,Mayor,andMermilliod(1984)alsoconcluded appears toholdfortheentiremassrangethatisrepresented tamination) andtheRossbynumber iV(theratioofthe pheric emissionflux(aftercorrection forphotosphericcon- mined relationshipbetweena star’s meanCanchromos- paper, thisdifficultywasavoided byutilizingthewell-deter- rotation periodssofarobtained isevidenceofthis.Inthis gious observationaleffort;the relativelysmallnumberof tions formagneticdynamosincorporatetheangularveloc- these solar-typestars,althoughtheyfeltthatthet~law nation andradius. cause oftheuncertaintyanindividualstar’sangleincli- these problems,vsin/’scanonlybetreatedstatisticallybe- tral resolutionandsignal-to-noiseareneeded.Evenwithout increasingly fainteratthesametimethatevergreaterspec- profiles arehardertofindasrdrops,andthestarsbecome With Í2insolarunitsandtGyr,theresultis tional (Fig.2).IftheexponentialrelationbetweenRand and Soderblom1985),giventhatRÍ2arenotpropor- did notapply. ening, goodmodelatmospheresarenotavailable,unblended but differentmasses,haveRossbynumbersN. HK Rotation contributesonlyslightlytotheoveralllinebroad- for 1.02^0.Thisrelationbreaksdown/50.3Gyr,butso form toconstantN.Inotherwords,starsofthesameage, the t~lawbylessthan0.1dex;suchsmalldeviations does equation(1).For¿>0.3Gyr,(2)differsfrom tially equivalenttothe/~relation. cannot bedetectedinthesedata.Thusequation(2)isessen- (Fig. 4)hasasmallpositiveslope,isochronesdonottrans- r R knK HK R eff HK HK K K 1/2l 12 RELATION BETWEENROTATIONANDCHROMOSPHERIC Finally, itisclearthatrotationandmassarehighlycorre- Observations ofthevsin/’ssolar-typestarsareconsis- At ~lawforÍ2isnotexpectedifÆk^t~(Duncan Rotation periodsaremoreintrinsicallyuseful(theequa- Í2 =- The vsin/’soflow-massstarsareverydifficulttomeasure. Because theHyadeslineinÆvs(i?—V)diagram H HK V. THEAGEDEPENDENCEOFROTATION,AND log i+0.82 1.48 cc t -1/2 VI. SUMMARY (Soderblom 1983a).Sucharelation EMISSION 2113 (2) 2114 DAVID R. SODERBLOM: ROTATION AND Ca n EMISSION 2114 pineal relations are used to transform the observed HK pendence suggests that the angular-momentum loss mecha- emission strength into the rotation rate Í2 = /2*//20 (Sec. nism is not sensitive to the details of a star’s structure. In this lid ). Even though the star’s HK emission strength is uncer- model, once a star has a convective envelope, magnetic field tain, these relations are capable of determining 12 to within generation and the resultant spindown and decline in chro- 20%, which is at least as good as most v sin/’s are deter- mospheric activity proceed in a predictable fashion, no mat- mined, particularly for the lowest masses (Sec. He). ter how deep that envelope is. A careful study of rotation These relations are applied to the Vaughan-Preston sur- versus age among the mid-F dwarfs, where the convective vey, a nearly complete snapshot of Ca n H and K emission envelopes are very thin, would help to determine if these among late-type dwarfs of the solar neighborhood. The sam- t—1/2 laws apply to higher masses. ple was reviewed to ensure that the original selection criteria Although these calculated Í2 ’s are valuable, there is one applied: northern hemisphere dwarfs later than —F5, not use to which they should not be put. Several people have part of spectroscopic or close visual binaries (Sec. I La). This recently suggested combining knowledge of a star’s v sim paper was restricted to 0.50 <(5 — F)< 1.00 (about F7 V to and Prot to calculate /, the angle of inclination of the rotation K2 V) for reasons explained in Sec. II. axis. In particular, stars with / —90° (equator-on) are sought The results of these transformations are shown in Figs. 3- for detecting planetary transits (Borucki and Summers 1984; 6, and described in Sec. III. An analysis of these data indicate Doyle, Wilcox, and Lorre 1984) or for radial-velocity vari- the following: Hyades data are fitted well by a straight line in ability studies (Campbell and Garrison 1985). Because the the log R hK vs (B — V) diagram (Fig. 4). The scatter about sine function changes slowly near 90°, unattainable precision this line can be attributed entirely to variability in the HK ( 5 1%) is needed for all the observables (Soderblom 1985a). flux and observational error (Sec. IVa). The transformation However, because the sine function changes rapidly near of this line to Í2 (Fig. 6) also corresponds well to true Hyades zero, it is possible to pick out stars that are likely to be seen rotation periods. Thus it appears that stars of the same com- pole-on, and thus favored for astrometric or direct planetary position and age have a one-to-one correspondence between searches (Soderblom 1985b). mass (color) and chromospheric activity or rotation rate. The high-velocity (HV) stars in this simple (mostly old disk objects) have weak chromospheric emission and low rotation rates (Sec. IVb ). The few exceptions to this rule need Part of this work was done while I was a Langley-Abbott further confirming observations. The Sun appears to have a fellow of the Smithsonian Institution; I thank Dr. A. K. Du- normal rotation rate for a star of its mass and age (Sec. IVc). pree for her hospitality. Drs. S. L. Bahúnas, D. K. Duncan, The rotation rates for stars below 1 fall within one and A. H. Vaughan were kind enough to permit use of their decade: half the solar rate up to 5/20 (Sec. IVc). These limits results in advance of publication. I thank them for their use- are consistent with known rotation periods. ful comments, as well as L. W. Hartmann, G. H. Herbig, R. 172 Both R HK and 12 appear to be related to age by a i “ law W. Noyes, and the referee. Ms. D. Schlogel has patiently and (Sec. V) for all the masses represented here. This mass inde- carefully prepared the manuscript.

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© American Astronomical Society • Provided by the NASA Astrophysics Data System 2115 DAVID R. SODERBLOM: ROTATION AND Ca n EMISSION 2115

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