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r 1

LYMAN A1,1 1 11A INITIA' I-M b'INDS IN LATK-TYPE STARS ^^I

B. tt. Hainch, ` .1. L. 1.111sky *1and K. A. van der Nucht

Joint Institute for Laboratory Antrophysics, Univer;;ity of Colorado and National. Bureau of Standards, 11nul.der, Col.orsdo 50309 1

Abstract r ^' One of the first major results of the WE survey of late-type stars was the discovery of a sharp division in the 1111 diagram he- tween stars with solar type spectra (chromosphere and transition ` q^ ('I region lines) and those with non-solar ti1 )e sp. salsa t (oil chroma-y o sphere Lines). 7ais result is especially interesting in view of

I M Ln observational evidence for mass loss from C and K giants and super-

Co giants discussed recently by both Reimers and Stencel. We have cal- x ^ a , culatcd models of. both hot coronae and cool wind flows using stellar model. chromospheres as starting points for stellar wind calculations G in order to investigate the possibility of having a "supersonic transition locus" in the HR diagram dividing hot coronae from cool m N ° winds. We conclude from these models that the La flux may play an P 44 important role in determining the Location of a stellar wind critical P4 tn u PC +J 0 point. We investigate in detail the interaction of La radiation pres- H m H 0; sure with Alfven waves in producing; strong, low temperature stellar H +J N winds in the star Arcturus. qo

t^ O I. INTRODUCTION W Gr a An important result of"the first survey of late-type stars by the International Ultraviolet Explorer (1UE) was the discovery by N N Linsky and Haisch (1979) of a sharp division in the HR diagram be-

r tween stars which do or do not have outer atmospheres similar to the Sun. The short wavelength (1175-2000 A) spectra of the solar type N EH 4 group contain ehromospheric emission lines (La, C I, 0 I, Si II) in- 1 N 4J U H of 5000-10,000 K plasma and emission lines of He II, C 11- 0C E IV, Si III-1V, N V indicative 0^ 20,000-250,000 K plasma analogous to rn A . the solar transition region. The non-solar type group has spectra 4 H A0 M04 v containing the chromospheric lines, but none of the hotter lines.

* Guest Observer, with the International Ultraviolet Explorer satellite. t Staff Mcinber, Quantum Physyics Division, National Bureau of Standards. A g -384-

1

I. T spectra of these two groups are shown in figure. 1. 11tts dis- is covery is especia lly interesting in light of o nszrvational evidence, r^ in the visible spectrumfor extensive mass loss from G and k giants , And superglants presented by Reimers (1977) and by Stencel (1978). .r Their results also indicate a division into two fairly distinct a groups in about the same place in the 11R diagram, a division charac-

s tc:rized by the onset of large stellar winds.

The observations of Reimers (1977) and Stencel ( 1978) were used by Mullan ( 1978) to derive a "supersonic transition locus" ( STQ in

a U M io u J0 C r Pi U U b u1 tI N I I 1 0 , i t^ it I 1

0800 r , t p I I I 1 I II ) I I I I !I I I I I ^ 4 I I! I I I , X J i I, I I I LL esc0 f ^ I I I I I I I 1 1 I II I t ti! it I 1 1 I I I . 1 GJ W a Ser i ( ( it I II I 1 i I I I d ' j I I I n ^ !! I I

a On j I II ^rywy9^ I 1 4 i j F I I II I I I I II I I ( I p 1 I I II I I

I I II I I i! I t l i t s 1000 1200 1400 1600 1800 2000 1200 1400 1600 1800 2000 X 141

Fig. 1. Calibrated WE spectra of the solar-type stars R Dra (G2 II), u Vel (G5 III), a Aur (G5 III+GO III), ^ Cet (K1 III), and a And (G8 III-IV). Also included for reference is the quiet Sun spectrum of Rottman (1978), which is degraded to the In-' spectral resolution. Important spectral features are noted. (b) Cal grated IUi: spectra of the non-solar type stars ac'vri U42 lab), a UNa (K0 II-I11), a Boo (K2 III), a Sco (K2 III-IV), and a r ur (K2 III). Dashed lines, spectral Lines absent in the data. t{ L' ;I I;

.A L . _...^ ^^ f -385- {fit

Y1 t; t ^, t t N^ `i Lite lilt di;t t;cow. In Mu11.1 ,1'r: ptettirk. , wind flowt, ar y expected to becomo vopersonic Ott Lilt, t?ttsa (If the c01-0710 :,lung; a 10 CUS of point", w ir, the 11H dinrrnm correiponding Lo 1,be observed mass-loss; division.

Mullan's STL is also in rough agreement with the dividing; line i. between solar type and non-solar type :spectra in the Hit diagram drawl) ii by Linsky and llaisch (1979). A plausible phycieal connection between these two ideas is that when a strong wind develops it dominates the z energy balance such that the major portion of the available nonra-

diative heating above r l ,e chromosphere goes iito driving; the mass flow rather than into he.'iting a corona.. Thus late-type stars either A

have a chromosphere and a hot corona, or they have a chromosphere and t+^ S a large wind. Although this simple Picture is appealing, there are ► sore serious problems. The minimum flux corona theory that forms the basis of Mullah'S arguments incorporates various simplifications and I^f approximations which moy tint be valid, especially in the limiting II case used by Mullan (see Antiokos :iud Underwood 1978 and Vaiana and Rosner 1978 for di.snussions of the pros and cons of nie minimum :flux corona theory debate). Another serious difficulty is that one cannot simply push material through a critical point. A proper matching; of

densities, tempeL,: Inures, and velocities is required to get through the "throat: of the nozzle" (see Brandt 1970, pp. 72-75), and the

addition of new material into the existing steady-state flow would I^ 1 change the nature of the temperature and velocity structure and upset the balance that defines the critical point in the first place. We have investigated in detail various possible stellar wind models for one of the 1UC non-solar type stars, Arcturus (a Boo, K2111p), which has been observed to have a variable chromospheric

outflow (Chia et al. 1977; van der liucht' et al. 1979) and which has a

chromospheric model (Ayres and Unsky 1975; tiaisch et al. 1977) that can be used as a starting point for stellar wind calculations. Our first models attempted to take into account the energy balance of mass flux, conductive flux, radiative cooling;, and various forms of mechanical energ; dissipation, but these models were found to have 6 high temperature•coronne (T > 3x10 tt). Other models having various ^1 t

It pre-specilled temperature distributions with Tm4x < 20,000 K yielded `^ t analytical solutions for the mass flow based on the mass and momentum F conservation equations alone which resulted in very low wind veloci- t ties near the stellar surface and very low mass loss rates. Models i including; divergence of the wind Clow also failed by several orders •terO-" .._ i I ► ^ —3lRG- i x

^ e of r.Yr, F;nituel to ncco►►nt for the outflow rates stol m, times si.-rn to Arcturus by Ghiu et al. (1977) of near conic velocities in the upper chromosphere. We conclude., therefore, thnt cool stellar Winds which R

. I become supersonic in or near the chromosphere require a source of womentum input to the mass flow. k Radiation pressure on dust grains has been suggested as a pos -

sible source of momentum input in M—type superpiants ( Jennings 1973;

Kwok 1975; Hagan 1978), but K — type giants and supergiant .,; do not usually exhibit, infrared excesses or polarization indicative of dusty circumstellar envelopes. We decided to look elsewhere. for an.ade - i quate source of radiation pressure on the gas, and were surprised to GINA.L 01P P discover that the scattering of to photons in an optically thin enve- Is i i QvI lope could provide a large force locally comparable to gravity. A ,r ! closer examination of a detailed chromospheric model for the to flux Indicates that the radiation pressure gradient exceeds gravity by as

1 ' I much as a factor of 4 in the upper chromosphere, and provides a sig-

e ^` nificant "push" at line center optical depths greater than -r = 200.

y Y Although locally large, the force due to the to flux is only signifi -

^' Y r , r cant over a limited region in the upper chromosphere, and thus by itself could not provide sufficient momentum to drive a wind. The n . nature of any stellar wind, however, must be strongly affected by the t t presence of the steep radiative pressure gradient, and the interac- tion of this effect with other sources of momentinn input, such as A Alfven waves or acoustic waves, may bring about a multiple critical

i point topology possibly involving a stationary shock front. Thus the presence of a strong Lot force, although insufficient by itself to t bring►, about a large mass loss, could be viewed as a necessary condi - tion for a stellar wind driven primarily by some other mechanism or i mechanisms, since even a small outflow at some point in the atmo- sphere by continuity requires an outflow everywhere. This in turn may be possible only in conjunction with a much larger stellar wind. We examine the to flux radiation pressure, Atfven wave pressure, and the formation of a stationary shock in a possible cool wind model for Y Arcturus. Our results should be viewed as an exploratory attempt to delimit some of the constraints on cool wind flows. Lastly, we ex - trapolate conditions in Arcturus to other G, K and M stars to delin - .t eate in which region of the HR diagram cool winds may be important..

f x :

7 1­ -3Ei7- r1

^. lie 11`1114 WIND 'll$11 f1'1," 9 Y- Wo chow A VCLur%is n.a our It protutypo model for cool stellar vinals In late - type Guar;: for several rowsoiis: the star 1100 gust Lo tike right of the Linsky -llaaisch division In the lilt diagram, it has booll observed to have a variable chromocpherle ouLflow oil the order of 10- 20 Vin s-1 , and it has a well-inodelecl chromosphere. It is much enoler , 9 to evaluate the importance of various terms in the flow equations ! when the stellar parameters are well, specified, and only a detaatled model atmosphere can provide the La flutes needed for an examination of the radiative force in the upper chromosphere. K t We assume a maximum temperature Tmaax r, 20,000 in the chroino^ sphere or extended wind region, and we take as fundaaaental parar+,eters R* - 1.9 x 10 12 cm (27.3 Ito ) and g - 50 cm/s 2 (Ayres and Linsky 1975). We extend the Ayres-Linrlty model chromosphere to include ar 20,000 1'.plateau. In this model R ('1'=20,000 K) = 2.017 x 10 12 em (1.06 It * ) and n ('r-20,000 K) = 2 x 10 8 c11143• More than 987 of the hydrogen is ionized at this point, and thus n p me n n. We assume a ff , mean particle weight u - 0.7, and for simplicity of notation we let 2 Umll = ra = 2.33 x 10_24 g, i.e. p = ama. We now ask the question, "llow much radial wind flow can be generated by the thermal energy of the gns alone, with and without passible temperature gradients?" 111e equaLions of mass and momentum conservation are

nvr2 np vroo , (1)

V dv 4kT(r) - GMm _ dT i m _ 2kT(r) 2k (2) dr r 2 dr} 2 r v We have used the perfect gas law, P = 2nkT, to replace the pressure gradient, and for simplicity bypass energy balance considerations by specifying a priori a temperature structure. We have analyzed solutions of (2) For four possible models a) T - 20,000 K for all r > R*. b) rc (critical point) = R * , T(r c ) = 20,000 K, dT/dr < 0 for r > rc. c) T = 20,000 K for R* < r < rc , dT/dr < 0 for r > rc , v(r) - vc fat s for r > r c , T(r) + 0 at -. fi, e d) T = 20,000 K fox , * R < r < rc , d'1'/dr < 0 for r > r c , v(r) = V l for r > r c , T(r) + 0 at R, where It is deLe aimed by Inter- ! stellar pressure conditions.

-388- 4 it

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)w ror all of theste models the irman, loses rater: are extremely small, <10-17 M a ©/yr.. Clearly a spherically symmetric evaporative wind model is not feasible for temperatures lest; than 20,000 K.

l 1f It is probable that Arcturus, like the -Sun, has an lnhomoge- t t^ neous chromosphere such that mass loss involves inhomoCeneous flows. x The possible existence of giant convective cells has been disc:unv d t by Schwarzschild (1975) and by Chiu at al, (1977) in connection with lv their observations that the Ca 11 K line profiles are variable. An excellent discussion of the effects of diverging geometr.es on solar

t. and stellar winds is given by Holzer (1977). Assuming as before variou• , given temperature structures with the constraint that Ts,tnx C 20,000 K, we investigate the effect of divergence in the flow by as-

i suning the miss and momentun conservation equations may be written as a^ nvA novoAo r (3) A dv 2kT(r) dA Mm dT1 2kT v ..[ -2k (4) A(r) dr - 2 dr J 2^ dr r v The flow takes the form of diverging cones in, ,this first order ap-

r proximation. We parametrize the cross section A(r) of the flow as

a

A(r) r2w(r) (5)

where the expansion factor w(r) is allowed to have various assumed functional fortis, and w(r o ) p 1, thus normalizing the flow to a rate per steradian. We again analyze solutions of the equation of motion (1) for several possible configurations allowing for divergence of the flow. No reasonable combination of expansion factors w(r) or temperature gradients will produce a stellar wind involving large mass loss. A crude calculation of the effects of La resonance scattering is an optically thin envelope showed that a substantial radiative force could result. We therefore chose a model chromosphere based on the Ayres and Linsky (1975) modeling of the Ca 11 11 and K lines,

^ ly and ran a five-level ionization equilibrium-non-LTI: radiative trans- fer program for hydrogen to calculate La fluxes in the upper chromo- sphere. The model is shown in figure 2. We found that at optical w depths as high as T w 200, the radiative force exceeds. gravity. For Y a spherically symmetric outflow the equation of momenttmi conserva- tion, including the effect of radiation pressure, is i r

-389- )I i( i^

Fig. 2. Distribu- tions of total den- sity, temperature, and fractional, J ^tl IN neutral hydrogen lx ) PACE in the 20,000 K pla- ^00 " teau model ehromo- ` ^► sphet,: for ArcCurus. 1 The scale for x is fib linear with 100% at the top and 0% at the bottom.

Heigh► obove R R (1010 cm) dv 4kT(r) _ CMm dT 1 dpR 2kT2(r) vdr^[ r `' ["1- , (6) r 2-2kdr-n(r) rlr I ^ where d n(r) dxr = x(r) c (0.011)Fv(r) (7) 01 Fv is the mean la flux near line center, and x the fraction of neu- tral hydrogen. The numerator of (6) goes through zero at the top of the chromosphere due to the sudden onset of the radiative force. We

call this the critical point, r c , and c?►oose v(rc ) so that the de- nominator also goes through zero. (6) may be solved for v(r. < rc) throughout the model chromosphere using the known temperature-density structure. This results in v(r) consistent with the prespecified n(r), i.e. nvr 2 " constant for a mass loss rate of -10-9 Mo/yr-l. Above re , however, the radiative force soon diminishes, and the wind finds itself with a supersonic velocity, but no means of main- taining that velocity. The multiple critical point topologies of If Holzer (1977) allow for a wind flow passing through an innermost

critical point close to a star's surface, around a second critical IR^ " point, and out through an outermost critical point presumably at a y Tarf;e distanr.c: from the star. Such a topology may involve a shock 'o discontinuity. We therefore let our wind model, shock above rco 1 -3J0-

evnNnt,? the E2,° ► nhtne-llugonlot r0ations; fn( , the poet-chock cundl- tl(, as, and examine the wind flaw fn the rejo,:Ie o1'' the seconrl ,end third arf tical poii► ts. We find that the thermal energy of the gat; is insuff'icicnt to maintain the flow. x ^r► To satisfy a clear need for an additional source of momentm Input, we choose among several potential sources the pressure due to outwardly propagating Alfven waves. Alfven waves have been identi-

E fied in the solar wind and are observed to be associated with, and are perhaps responsible for, solar active regions (11ollweg 1973). We incorporate an Alfven wave pressure gradient term into the equa- tion of motion while limiting ourselves to regimes where heating is negligible,

2tcT ) dv 1 r 4kT(r) _ GMm` _ 2k dT _ 1 d , (d) ^m _ v2 ^r`" - v r r2 dr T_( _r) dr Sir r 1^

where <6B2> is the fluctuating part of the magnetic field. If we rake certain simplifying assumptions, such as a radial magnetic r 'N 2 field, <6B and Alfven velocities v >> vflow, (8) may be > << B2 , A E # solved for various magnetic field strengths. 'We re-examine the wind flow in our model chromosphere at the critical point due to the 1A force (which involves adding the term -[1/n(r)j(dP R/dr) to (8) in the upper chromosphere), and in a shock and post-shock regime. One such solution is shown schematically in figure 3. At present we do not have a completely consistent solution for such a wind flow. Somewhat higher magnetic field strengths are re - a quired to maintain the mass flow in the outer regimes of the Holzer ,, multiple critical point topologies than are consistent with mass flux conservation in the model chromosphere. However we feel that the in- teraction of a strong La force with other sources of momentum input will point to some significant new configurations for stellar wind models in late type stars.

VII. IMPLICATIONS FOR OTlirR LATE-TYPE STARS The role of the La flux is to define a condition which in turn can only be satisfied by the existence of a certain stellar wind. If we accept that the La force exceeds gravity somewhere in a stellar chromosphere, then'mass loss and a transition through a singular { point in the mua►cnttm► equation both must occur. If we also require that the maximum temperature not exceed a certain value determined 4. observntionally, then the constraints on possible wind models

r;

6 Y t t^

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Fig. 3. A schematic ' 1 representation of a r' Y wind model for

batic ex pansi on and a

FOSS Oft IERIOROLOGICS ► ^.,,r shock transition. He to :s the critical point and possible Holzer ,Y topologies are i.n_. dicated.

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X WIND '3r } POSSIOLE WIND Oil X 0 NO WIND Fig. 4. An 11R diagram with our predictions of -t which stars have La 1 -4 1 initiated cool. winds. The dashed line indi- L t cates the Linsky-11aisch s 0 DfoX; X e Gom 1^ empirical division be- r ` + • You ^i tween stars with hot ^ l M6 of o Aur'F 1 X X Cc•P a Do* coronae (to the left) 0 -- 80,60 and stars with no evi- 1) Oro 0 CA 'I Gain dence of material : l •ne hotter than 20,000 K S (to the right). I

4 Y 0 Sun

0,1 Irl 1 1 c 0.4 06 0.1 1.0 11 14 1.6 I" Iv -R1

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. I , fulfilling those conditions are quite st.vere. Wc: linve here. pre- steeled only one ichematic wind model; one Oat relles on n com- I bontion of several different re ggimes in which one or the other ie I ty I r r t of mechanism dominates the solution. Other modals must cartniall be t A, possible, for example, with acoustic wave pressure instead of Altven wave pressure (see Ulmschneider 1979). t t We extrapolate our results to other late-type stars by assuni.ng I similar ionization and temperature conditions, and derive a La i "supersonic transition locus" by comparing La fluxes and stellar i gravities. Figure 44 shows an IIR diagram with our predictions of large cool winds based on a comparison of Let fluxes to stellar Y r gravities for some representative C, K and ht stars. The dashed line is the division between stars with hot coronae (to the left) and those with cool winds (to the right) determined observationally by Linsky and Haisch (1979). We suggest that the onset of Let initiated i winds is responsible for this division by providing a large sink for the nonradiative heating which would otherwise produce a hot corona. 1 I This work is supported by NASA under grants NAS5 - 23274 and NCL- i

a a 06-003-057 to the University of Colorado. We wish to thank Drs. Tom Holzer and Dimitri Mihalas for their comments, and Dr. John Castor for his critical reading of this paper and insights regarding stel-

; = A lar winds.

E ' r t^ ,.A REFERENCES x r

A Antiokos, S. K. and Underwood, J. 11. 1978, Astr. Ap., 68, L19• Ayres, T. R. and Linsky, J. L. 1975, Ap. J., 200, 660. :P r • Brandt, J. C. 1970, Introduction to the Solar Wind ( San Francisco: r ) Freeman). 1^ a Chiu, H.-Y., Adams, P. J., Linsky, J. L., Basri, C. S., Miran, S. P. .x and Hobbs, R. W. 1977, Ap. J., 211, 453. Hagan, W.' 1978, Ap. J. Suppl. , 38, 1. Haisch, B. M., Linsky, J. L., Weinstein, A. and Shine, R. A. 19770 Ap. J., 214, 785. Hollweg, J. V. 1973, Ap. J. 181, 547. Holzer, T. E. 1977, J. Geophys. Ros. , 82, 23. v. d. Hucht, K., Stencel, R. E., Haisch, B. M. and Kondo, Y. 1979, Astr. Ap. Suppl. , in press. Jennings, M. C. 1973, Ap. J., 1.85, :97.

Kwok, S. 1975, Ap. J., 220, 962. Linsky, J. L. and Ilaisch, B. M. 1979, Ap. J. (betters), 229, L27.

} ,t Mullan, D. J. 1978, Ap. J., 226, 151.

4 r^

E . 1

1

R{elmar;, V. 1:977 1 A I; tr. A(^- , 57, 395. 1975, it) 7lic Interaction or Viri} i+ire . t;M. wait Anir

^'nvironnont 1 I.,kU Colloquituo No, 42, +! do, R-ipj) ^ttlt i n, }^• ^ ^.ikv, J. and Strohmoicro W. (DoNrooistt Roidel), p, 559. E Rottman, G. J. 1978, private comtmtnicntion.

Schwarzschild, M. 1975, Ap.J., 195, 137. i

Stencel., R. E. 1978, A . J. (Letters), ?.23; 1,37. l Ill Ulmschneider, 1". 1979 1 Sp Sci. Rev., submitted. Vatana, C. S. and Rosner, R. 1978, Anil. Rev. Astr. Ap., 16, 393,

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