THE DYNAMICAL STATE OF THE ATMOSPHERE OF THE SUPERGIANT ALPHA CYGNI (A2 Iae) DERIVED FROM HIGH-RESOLUTION ULTRAVIOLET SPECTRA

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THE DYNAMICAL STATE OF THE ATMOSPHERE OF THE SUPERGIANT ALPHA CYGNI (A2 Iae)

DERIVED FROM HIGH-RESOLUTION ULTRAVIOLET SPECTRA

B. Boer, C. de Jager, H. Nieuwenhuijzen

To cite this version:

B. Boer, C. de Jager, H. Nieuwenhuijzen. THE DYNAMICAL STATE OF THE ATMOSPHERE OF THE SUPERGIANT ALPHA CYGNI (A2 Iae) DERIVED FROM HIGH-RESOLUTION ULTRAVIOLET SPECTRA. Journal de Physique Colloques, 1988, 49 (C1), pp.C1-383-C1-386.

�10.1051/jphyscol:1988184�. �jpa-00227598�

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JOURNAL DE PHYSIQUE

Colloque C1, Suppl6ment au n 0 3 , Tome 49, Mars 1988

THE DYNAMICAL STATE OF THE ATMOSPHERE OF THE SUPERGIANT ALPHA CYGNI

( A 2 Iae) DERIVED FROM HIGH-RESOLUTION ULTRAVIOLET SPECTRA

B. BOER, C. de JAGER and H. NIEUWENHUIJZEN

Astronomical Observatory and Laboratory for Space Research, Beneluxlaan 21, NL-3527 HS Utrecht, The Netherlands

Sommaire: Des spectres 2 haute r6solution ( A / A A = 8x104) de la super- g'eante Alpha Cygni, obtenus & l'aide du BIJSS (Balloon-borne Ultravio- let Stellar Spectrometer) ont 6t6 utilis6s pour 6tudier les causes de ltinstabilit6 de 11atmosph6re. On trouve qu'h une profondeur optique 75 = 0.1 la vitesse microturbulente est 6gale h la vitesse du son.

~'acc616ration turbulente d6riv6e de ces resultats augmente vers l1ext6rieur, en atteignant 2 T 5 = 0.01 la moiti6 de l'acc616ration effective. Le profil de la distribution des vitesses macroturbulentes aontre deux maxima h 14 km s-1 (positive et negative). Nous sugg6rons que ces mouvements sont des pulsations stochastiques des grands elements: un diambtre moyen d'environ 30 x 106 km

B

6t6 trouv6.

Abstract: In order to study the apparent near instability of supergiant atmospheres high-resolution ( X / A X = 8x1 04 ) BUSS ( ~alloon-borne Ultraviolet Stellar Spectrometer) spectra of the supergiant Alpha Cyg have been investigated. Equivalent widths of lines yield the variation of the line-of-sight microturbulent velocity component C,, with optical depth T . We find at T 5 = 0.1:

c,,

equal to the velocity of sound. The consequent turbulent acceleration is directed outward. It increases outward and is about half the effective acceleration at T g = 0.01. The macroturbulent velocity profile is double peaked with up- and downward velocities of 14 km s-1. We suggest that these motions are stochastic pulsations of large elements. At any time there are 30 to 40 such elements on the visible disk.

1. Introduction. A series of investigations of super- and hypergiants is at present underway at the Utrecht Laboratory for Space Research and the Astronomical Observatofy, to study the near-instability of the atmospheres of stars close to the upper limit of stellar existence, the so-called Humphreys-Davidson limit. One of us ( 1 ) has forwarded the hypothesis that this limit is determined by the approximate equa- lity between the gravitational acceleration and the outward accelera- tions due to radiation pressure and turbulent pressure:

If the last term is neglected, eq. (1 ) reduces to the classical Eddington criterion. Lamers (2) has shown that the Eddington critericn applies to hot stars (Teff

>

¹⁰⁴^{K )}

.

For cooler stars, however, radiation pressure is not efficient as a driver of the outer stellar layers (except in the case o f dust-driven winds: this applies to supergiants with Teff

<

3000 K )

.

In this paper we will show that turbulent acceleration tends to com- pensate gravitation in the atmospheres of cool super- and hypergiants.

The present study is based on high-resolution spectra of the supergiant Aloha Cvqni ( A 2 Iae) obtained with the TJtrecht Balloon-borne

!~ltraviolet Stellar Spectrometer (r3USS). The spectrograph of BUSS has a spectral resolution of X / A X = 8x104, which is about 3 times better than IUE. Such high-resolution spectra allow one to determine the detailed motion field in the stellar atmosphere, as will be shown.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988184

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C1-384 JOURNAL DE PHYSIQUE

2. Microturbulence and the gravitational acceleration

If the model and the chemical composition of a stellar atmosphere are known, the measured equivalent widths of spectral lines allow for a determination of the microturbulent line-of-sight velocity component CV of the atmosphere. Since spectral lines with different equivalent wldths are in general formed at different optical depths T, the study of a large number of spectral lines yields the depth-variation 5 0).

The model-parameters Teff and geff of Alpha Cyg were taken from a previous investigation ( 3 ) , in which it was also found that the abun- dances were solar. From the present data we derived the variation Cp/s (where s is the local velocity of sound) shown in Figure 1 (upper curve). It appears that this ratio varies from about 0.8 at ~5 = 1 to 1.2 at T5 = 0.001. Here, T5 is the monochromatic optical depth at 5000 A.

Ffg. 1. Upper curve and right side ordinate: the ratio $/s as a func- tlon of the o p t i c a p r curve and left side ordinate: the turbulent acceleration gt (cm-).

-

Turbulent pressure arises through momentu~n transfer in a stochastic motion field, and the consequent turbulent acceleration is

1 dPt

9 t = _P _dZ (2)

where

For the dimensionless constant a we usually take 0.5, assuming a Gaus- sian distribution of turbulent velocities. The depth-variation gt(r5) thus derived is shown as the lower curve in Figure 1. It varies from about 2 cm se2 at T5 = 1 to 7 cm s-2 at ~5 = 0.001. The gravitational acceleration 9grav = 26 cm s-2 and is hence counteracted for nearly one-third at T5 = 0.001. Obviously, Alpha Cygni has still a stable, albeit very extended atmosphere: this is in line with the fact that this star is not an extreme supergiant: its absolute luminosity is still by a factor ten smaller than the luminosity at the HO-limit.

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3. Rotational velocity and macroturbulence We define the following wavelength-profiles:

e(m): the line-profile emitted by an atmosphere with a known depth variation of microturbulence;

P(R): the rotational profile for a given projected velocity component

V R sin i;

P(A): the instrumental (apparatus) profile;

P(M): the distribution function of macroscopic velocities expressed in wavelength units.

Then, the observed line profile P(O) is the result of a convolution (symbol: * ) :

The profiles P(A) and ~ ( m ) are known or can be calculated. Hence, for an assumed rotational velocity VR sin i the P(M) profile can be obtained from a deconvolution of P(0) with the convolved profile P(m)*P(R)*P(A).

We assumed several values of V R sin i. For each of them the deconvolution yields a P(%) profile, and the quality of the determination is given by a resulting chi-squared value. A comparison of the different determinations of P(M) showed that chi-squared reached a distinct minimum value for V R sin i = 8 km s-l. This is therefore the 'best' rotational velocity value; it is considerably smaller than values found in literature which ranqe up to 45 km s-1, but it should be remembered that current literature values are for the greater part determined from visual inspection of plates or of line profiles.

The macroturbulent velocity distribution corresponding to this rotational velocity appears to be double-peaked or at least flat-topped for

all ( 1 7 ) lines investigated, with peaks at plus and minus 14 km s-1

(Figure 2 ) . This result suqqests the existence of large-scale stronq

Fig. 2. Lower curve: the profile P(m)*P(A)*P(R) for V R sin i = 8 kn s-1. Upper curve: macroturbulent velocity profile, showing peaks at 14

km s-1. The little peaks at about half height have no physical signi-

ficance.

3.a

1.1

I

1.4

1.1

1 . 0

i.1

l . B

L.4

1.1

1.0

0..

0 . 1

0.4

0 . 1

0 . 0

-

- microturb II aep r r o t

- vrot (km/sl

-

^8.0

-

macroturb. (from deconv.)

-

chi-sqaure

-

^0.0378

-

- -

-

- - - - - -

- - -

, , I . 1 . , . , . , * , . l

-,.o -0.1 -,.I *.. -,.1 0.s 0 . 2 a + < 0.. 0 . 1 1.0

wav?Itnqtn Llngstrosl

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C 1-386 JOURNAL DE PHYSIQUE

up- and downward motions with an average velocity difference of 28 km s-1. The interpretation is difficult: convection is not expected for stars as hot as Alpha Cyg, and one wonders if these notions are a nanifestation of non-radial or stochastic pulsations.

4. The size of the large-scale elements on Alpha Cygni

There is a simple way to estimate the size of the elements responsible for these lmacro-turbulentl motions. Lucy (4) has studied a large sample of radial velocity measurements of ~ l p h a Cygni obtained in the thirties, and by Fourier-analysis found a dozen discrete periods, ranging from 10 to 100 days with amplitudes of a few km s-l. The average radial velocity is <vrad2,' = 2.3 km Realizing that the time needed for an element to move through the atmosphere with 14 km s-l is of the same order as the periods found by Lucy, the question arises whether his average radial velocity is the net result of the existence of a large number of up- and downward moving elements, each moving with 14 Itm s-1. For an infinite number oE elements the net resulting Vrad would be zero, but < Vrad2>" = 2.3 km s-1 demands 30 to 40 elements on the disc. Ydith the given radius of Alpha Cyg (140

Rd

one finds that these elements have diameters of z 3 0 x 106 km.

5. Conclusions and comparison with other data

There is evidence that the large-scale motion field of a Cyg should be described by stochastic, rather than by non-linear pulsations. The size of supergiants (the radius of Alpha Cyg is 140 Rg) com~ared with the velocity of sound in their atmos~heres (10 km/s in Alpha Cyg) excludes coherent and coordinated motions of the stellar atmosphere a s a whole and rather points to stochastic pulsations, in which parts of the atmosphere pulsate independent of other parts. Convection would be another possibility, but current theories exclude convection in stars as hot as Alpha Cyg.

The average diameter of the elements is about 30x106 km. These large- scale notions drive motions with shorter and shorter scales down to scales smaller than the photosphere's thickness: the observed microturbulence. By momentum transfer from this motion field an outward acceleration, the turbulent acceleration counteracts the gravitational acceleration, and thus contributes to increasing the atmospheric instability. For Alpha Cyg, which is a bright but not an extreme supergiant, gturb is in the outer atmosphere one third of the gravitational acceleration. For a more extreme supergiant YR8752 (Piters et al., submitted to Astron. Astrophys.) a larger value has been found.

This suggests that atmospheric instability of cool supergiants is due to the near-equal ity

thus adding support to eq. ( 1 ) , advanced in the introduction of this paper.

References

1. De Jager, C.: 1984, Astron. Astrophys.

138,

245.

2. Laflers, H.J.G.L.M.: 1984, Astron. Astrophys.

3. Oe Jager, C., Yulder, P., Yondo, Y.: 1984, Astron. Astrophys.

141,

304.

4. Lucy, L . 5 . : 1976, Astrophys. J.

205,

^449.