Reflection nebulae and the nature of interstellar grains

Reflection Nebulae and the Nature of Interstellar Grains VLADIMi~ VA:N~SEK Astronomical Institute, Faculty of Mathematics and Physics, Charles University, Prague SUm~RY In the following paper the results of recent studies on reflection nebulae are discussed. An accurate photoelectric method, applied to measurements of brightness, colour and polarization of galactic nebulae, can now be used for the exploration of the physical nature of interstellar grains. The fitting of several theoretical models of interstellar grain-clouds to the observed colour distributions in bright reflection nebulae shows that the presence of dielectric grains in such objects is more probable than the presence of small particles with other physical properties.

1. INTRODUCTION Interstellar m a t t e r consists of gas and dust components. I n principle, the physical state and chemical composition of the gaseous component are known. The temperature, density and abundance of individual elements in the interstellar gas can be derived with some accuracy, particularly from spectroscopic and radio-astronomical data. On the other hand, the solution of the problem of the dust component is not yet satisfactory. The dust- or smoke-component of interstellar m a t t e r does not exceed 1 to 2 % of the total m a t t e r dispersed between the stars; however, its role in the processes taking place in interstellar space evidently is so important t h a t the knowledge of its physical nature is essential for further progress in m a n y other fields of astrophysics. Clouds of solid interstellar particles the g r a i n s - - a p p e a r in the Milky W a y as "zones of avoidance", which show such an extremely high concentration t h a t the obscuring matter creates dark patches. Apart from this general absorption of light also selective interstellar extinction has been found, as well as polarization of the light from distant stars due to solid particles (grains). A positive correlation between the amount of interstellar absorption and the degree of polarization has proved t h a t the polarization of the star-light is caused by the dust component of the interstellar matter. F r o m the point of view of the study of interstellar matter, the effects of interstellar absorption and polarization offer undoubtedly the most important basis for observation, especially recently, when the necessary data have been extended to the infrared and ultraviolet regions of the spectrum. Finally, one should not neglect the study of the reflection nebulae which m a y be considered as rather small areas of higher concentration of interstellar particles, exposed to the illumination of a not too distant star of relatively high luminosity. The reflection nebulae are suitable objects for studying the physical nature of interstellar grains. Unfortunately, there exist only a few sufficiently bright objects, particularly NGC 7023, NGC 2068, the nebula around the stars Merope in the Pleiades and Alcyone, and comet-like objects, such as for instance Hubble's variable nebula 2261 in Monoceros. Recently, Dorsehner and Giirtler (1966) identified on the Palomar Observatory Sky Survey 189

190

Reflection Nebulae and the Nature of Interstellar Grains

Charts 192 objects which may with certainty or high probability be described as reflection nebulae. Some of them are situated in such a way that they may be better observed from the southern hemisphere; this is the very reason why there are only so few observational data available. From the physical description of the process of light scattering on particles, the dimensions of which are comparable with the wavelength of light, it may rightly be expected that from the observed distribution of the brightness of the nebula, the difference in colour between the star and the nebula, and the polarization measurements it would be possible to derive the physical properties of the particles which form these objects. The application of the observation of reflection nebulae to the study of the physical properties of interstellar particles is not quite new. The best-known and the oldest interpretation of observational results, as far as reflection nebulae are concerned, is the derivation of the relation between the apparent magnitude of the central star and the size of the nebula, which was used for the first time by Hubble (1922) for the determination of the albedo of t h e particles. If m is apparent magnitude, a' the maximum determinable distance from the edge of the nebula with an area mF, Hubble's relation is m + 5 log a '

--

m F

~ - 16,

where the constant k essentially depends, apart from the geometrical configuration, on the albedo and the phase function of the particle. If the albedo is 1, and the distance a' (in minutes of are, then there is k ---- --11.6. The value of k may be determined by statistical treatment of data from a large number of objects, tIubble's relation has been revised several times. The treatment of more than 190 objects by Dorsehner and Giirtler (1966) verifies the previous result of Cederblad (1946) that the albedo of reflection nebulae is close to the possible maximum value. Other important papers are those of H e n y e y (1936), and H e n y e y and Greenstein (1938, 1940), who formulated the general relation for the distribution of intensity in a nebula by interpreting Eddington's solution of the radiation transfer. As in the previous case, Schal~n (1945, 1953) later examined the theoretical values of the intensities in the plane-parallel layer; he integrated with respect to the change of the phase angle, and used an approximate formula expressing the phase function by means of simple parameters. Schal~n's geometrical formulation of the problem was quite recently used by Greenberg and Roark (1966), and by Roark (1966), but with the use of the rigorous definition of the phase function as it follows from Mie's theory. Several solutions have been given for the spherical shape of nebulae. Of importance in this respect are the papers by Sobolev (1960), Minin (1962), Kaplan (1955) and Rozhkovsky (1960, 1961a, 1961b), as well as that by van ttouten (1961). These works are devoted particularly to the theory of the brightness-distribution in nebulae. Sobolev used arbitrary phase-functions and his method was then applied by Minin (1962) to the analysis of observations of the reflection nebulae IC 431 and IC 435. With the exception of Roark (1966) most of the authors did not use fast computers, and this is why the observations are usually only roughly compared with the theory. Fast computers, however, enable the calculation not only of the actual phase-functions of particles or clouds of particles, but also make it possible to construct certain models of nebulae, which may then be fitted to the observed parameters of real objects. The recent photoelectric methods of determining the surface brightness of nebulae enables us to determine with a relatively high degree of precision the brightness distribution in the nebula in selected spectral regions. This makes it possible to find easily also the differences in the energy distribution in the spectrum; this with non-selective scattering in

V. VA~'S~.K

191

an optically sufficiently thin nebula, should be equivalent to the energy distribution in the spectrum of the illuminating star. I n other words, it is thus possible to determine colour differences between the star and a given point in the nebula. I t appears, in general, t h a t most reflection nebulae are bluer t h a n the illuminating stars. However, at closer examination it m a y be found t h a t the increase in blue colour is limited to a close region around the star, while in greater distances the eolour of the nebula resembles the colour of the star. I n an optically thin nebula, after correction for instrumental scattering of the star-light, and for the case of non-selective isotropic scattering, the eolour of the star and of the nebula would be identical. Only as a consequence of the optical thickness would it be possible to observe a reddening towards the edge of the nebula. However, careful corrections for the instrumental scattering of light do not remove the increase of blue eolour of the nebula in the vicinity of the star; the changes in the colour of its surface towards the edge cannot, therefore, be caused only by "internal reddening". The increase in the blue colour of nebulae, extending to a certain distance from the illuminating star, m a y only p a r t l y be due to instrumental scattering of the star-light. However, the residual blue colour, and i t s " r e t u r n " to the colour of the star in the area near the edge of the nebula, is caused b y the intrinsic nature of nebular grains. This fact indicates t h a t the scattering on the particles is strongly anisotropic. I t is therefore essential to find the rate of anisotropic scattering in the nebula and, by a suitable method, to ascertain satisfactory sizes of the scattering particles. The study of the distribution of the surface brightness of the nebula, or rather the change in colour, is certainly not in itself a satisfactory source for obtaining observational data. Of definite importance are also polarization effects which, however, depend on the geometrical configuration of the object more t h a n on the intensity- and colour-distribution. Average and m a x i m u m values of the observed polarization m a y exclude a number of unsuitable particle-models, as well as the dependence between polarization and wavelength. Unfortunately, there is a scarcity of these observational data. The following chapters deal in more detail with the problem of reflection nebulae from the point of view of their utilization for examining the properties of interstellar particles. 2. LIGHT SCATTERING IN A REFLECTION N E B U L A As a simplified solution has been used, it is necessary to assume that the reflection nebula is optically thin enough to prevent the multifold scattering on small particles to be of any substantial importance. This assumption is in a number of cases nearly fulfilled. Thus, it is possible to use a much simpler theory, involving the assumption of the simple first-order scattering on particles which do not eclipse each other. On the other hand, in the ease of multifold scattering it would be necessary to use the theory of the radiation transfer. Another simplifying assumption is t h a t the scattering occurs on spherical particles in homogeneous regions. Let us consider a flux of the intensity I(2), which falls on a particle situated at a distance zl from the observer. (The total flux o/radiation, which is scattered and absorbed, ]alls on the

area defined by scattering and absorbing cross-sections o/the particle. I / o n l y scattering crosssection is considered, then A = 1). The observed intensity ID(a, ~) will then be 22 IB(a,o) = AI(,~) ~ [S~ + S~](o) A -2, (1) where A is the albedo of the particle; S x is a complex function of the amplitude of the component of the polarized light scattered in the direction 0 (which is the phase angle contained

192

Reflection Nebulae and the Nature of Interstellar Grains

N

Fro. 1. Beam of light coming fxom a star ~ which is the source of illumination in the nebula Zr. The beam is scattered on a particle situated a t the point C. The direction to the observer is indicated b y an arrow. Phase-angle ~ = ~z - - #', the size z of the nebula, and the distances r and A are here considered Z << r <
/ FIG. 2. The geometry of a spherical model of a reflection nebula. The direction to the observer is indicated by an arrow.

...~::~:.'..::."/~!~:..;:-:.."..."~-..:.~.:=::~ ~:i.:.'/-:..j/!

FIO. 3. The geometry of a large plane-parallel nebula. The illuminating star is situated in front of the nebula. The direction to the observer is indicated by an arrow. The (x, y)-plane is perpendicular to the line of sight.

V . VANYSEK

193

between the direction of the incident beam and the particle-observer direction). Introducing further the Mie coefficients il, equalling S~ (which are functions of the radius of the par. ticle a, the angle v~, the wavelength 2, and the refractive index m), then it is possible to write : Ir(~,~) -----I(2) 2 - ~ [il + i~] (v~, x, m) A -2,

(2)

2re where x = ka; k is the wave number or k = -~--. Denoting with ~0(v~,x, m) the function of scattering ~0(~, x, m) = ~

1

[i 1 + i2] (v~, x, ra),

(3)

then we have for the intensity of the light scattered in the direction of the phase angle v~ :

dI(2, ~) = 1(2) Acf(~, x, m) N(a) d V da.

(4)

Here, d V is the elementary volume of the nebula and N(a) the number of particles per unit volume. The intensity of the incident light is

1(4) = Is(k) Wr -~ e-~1",

(5)

where n is the absorption coefficient and l1 the length of the p a t h traversed by the beam in the nebula from the star to the particle. The dilution factor is approximated as Wr -~, where W = ¼ R *. The observed intensity, neglecting extinction outside the nebula, is given b y z araax

ID(~)

Is(2) WA d p / 0

/

~

N(a)exp [-- u(l x -~/~)] dz da~(va),

(6)

amln

when dp dz = dV; dp is the surface of the base of the cylinder, whose axis lies on the line connecting the points CBD. The distances (see Fig. 1) z] >> r are considerably greater t h a n the dimensions of a nebular cloud z = BD, and therefore also the paths of the beam l 1 = AC and 12 = BC. The direction CBD lies in the direction of the line of sight from the observer, with respect to which the integration is done. If the density of the nebula is the same at each point it is: dr u = - - ---- const,

dli and thus the geometrical size of the nebula m a y be substituted b y the standard optical thickness T0. Certain limitations m a y be admitted as to the size-distribution function. According to Oort and van de Hulst (1950) this function is determined b y the ratio of growth and destruction of grains. I t m a y be expressed, for example, b y N(a) = 570 exp [--nla"~ ]. According to Greenberg (1964) we have n I = 5 and n, = 3; the function is near the Oort-van de Hulst size-distribution function. Optically, the most effective size of the particles follows from the m a x i m u m cross-section corrected for the distribution function. The scattering cross-section is given b y C~c~ -~ Q(a) ga 2, (7) where Q(a) is an efficiency factor which has for dielectric particles m a x i m u m values between x = 2 and x = 6. The efficiency of the particles, i.e. their contribution towards the total

194

Reflection Nebulae and the Nature of Interstellar Grains

intensity of the cloud, will be given b y the dependence of the n u m b e r of particles on their diameters and cross-sections; this means t h a t the efficiency function is given b y

U(a) = N O/(a) Q(a) ga S,

(8)

where /(a) is the distribution function. Figure 4 shows the behaviour of the efficiency function for grains with refraction index m = 1.50, 2.00, and 1.33, respectively, assuming -5(~) 3 the Oort-van de Hulst distribution-function in Greenberg's approximation f(a) = e a, +

°

0.5

0.2p '

'

O. 4" p

a'

FI(L 4. The optical efficiency U, i.e. the contribution to the radiation of a reflection nebula, of grains is given (in arbitrary units) for dielectric spheres with refractive indices m ----1.33, 1"50 and 2.00. The Oort-van de Hulst size-distribution hmction is adopted. The size is given in microns. where a o ~ 0.5 ~. A sharp m a x i m u m appears in particles of m ~ 2 a r o u n d 0.2 F, i.e. for x -~ - ~ - a = 2.2, if ~ ---- 0.55 {z. I t is therefore evident t h a t the optical properties of a nebula in which the size of the grains is distributed according to the above distribution function, are determined b y particles of 0.25 to 0-35/~. The distribution function of t y p e /(a) ---- e -a for dielectric particles of refraction index m --~ 1 leads to an average efficiency factor Q(a) -- 2 for particles greater t h a n 0.25 - 0-4 ~; it decreases sharply for a ---- 0.2 F. Consequently, particles smaller t h a n 0.2 [z appear of little importance for nebular radiation. The same applies for other simple distribution fune1 tions of the types ](a) -~--~ (a ~ 1), ](a) ~ 0 (a :~ 1), ](a) = 1 (a ~ 1); the limitation of the scattering cross-section of grains is even more pronounced in these cases. I t is thus possible to determine easily the lower limit of integration with respect to the particle diameter. Using the distribution function, whose shape m u s t be assumed, unfortunately does n o t represent a close approximation of the calculated models to reality. Models, in which a single size of the particles is considered, m a y therefore be used in certain cases for an estimate of the effective scattering cross-section. If we consider, e.g., models with a refractive index m = 2, there is a sharp m a x i m u m for x ---- 2, i.e. we are dealing with particles of radius a ~ 0.18 ~. More i m p o r t a n t still is the problem of the distribution function in the case of polarization studies as mentioned in Section 5.

V. VAI~'YSEK

195

3. GEOMETRY OF A MODEL ~EBULA The basic formula described in the preceding section must be modified according to the geometry and size of the model nebula. In order to obtain a reasonable number of variants of models, usually two simple forms of nebular clouds are used: a spherical, or a semispherical cloud in which stars are situated at the points of symmetry and an infinite or semi-infinite layer tilted to the line of sight by an arbitrary angle. The spherical-cloud model was used by many authors, e.g. by Rozhkovsky (1960), Fesenkov (1955), van Houten (1961), Minin (1962), Sobolev (1960), Svato~ and Van~sek (1964), while the infinite layer form has been computed by Schal6n (1940), Greenberg and Roark (1965), Roark (1966) and also by van Houten (1961). I t should be pointed out that no preference of any geometrical properties of cloud models exists. The spherical shape of the reflection nebula can be supposed to exist in NGC 7023, while the well-known nebulosity in the Pleiades is a thin parallel-layer nebula. The adopted geometrical properties approximate more or less the complicated structure of the real shape of reflection nebulae. From the computation point of view the spherical homogeneous cloud is the most convenient case. Let 3o be the adopted optical thickness of the cloud sphere with stars at the centre S. Then l 1 ----1: cosec v~ (9) 12 =

V ( 3 o2 -

3 ~) -

3 cot ~.

If dp is the unit cross-section of column BD, dV is seen from the point S under the solid angle co, according to the definition of v, and from Fig. 2, it follows dv---- 1 deo r The modified Eq. (6) for the unit distance A and a uniform size of particles is

dI(2, v~) : Is().) WA l e x p r

[-- ~/(3~ -- 32) -- 3 (cosec ~ -- cot v~)]~(v~) d0.

(10)

The relative surface brightness of the nebula at the projected distance Q : r sin v~, between the boundaries v~ and ~ -

v~, expressed in (arc sin ~ o ) a n d ( ~ • sin

~-arc

arc sin T-~To ) is:

T ~o

1 exp [-- ~/(v~ -- T~)] /

exp [-- v (cosec v~ -- cot v~)]~(v~) dye.

arc sin

(11)

v "go

I t is evident that

dB(q) q do

(12)

in a given area of the nebula, especially when the optical thickness To < 1, depends above all on the phase function q)(0). For the semi-spherical model holds b

B(0) = -~1 exp[-- I/(~ -- T2)].fexp[-- 3 (cosec v~ -- cot 0)] ~0(v~) d0. G

(131

196

Reflection Nebulae and the Nature of Interstellar Grains

I n the case of the illuminating star in front of the nebula it can easily be found t h a t 1 a =-~, T

b = 7t -- arc sin - - , 30

and for the afar behind the nebula 27

a = arc s i n - -

3o

b =~ 1 The plane-parallel models have been treated b y Schal6n and more recently v e r y extensively b y R o a r k (1966) and Greenberg and R o a r k (1965). Similarly as in the previous section, the position of the illuminating star determines the basic geometrical formulation of the problem in the following cases: (a) star in front of plane-parallel nebula; (b) star behind the nebula; (c) star inside the nebula. The xy plane of the nebula generally is tilted b y an angle fl (Fig. 3). F o r the case thag the star is in front of a plane-parallel nebula the p a t h of the light inside the nebula is:

11 = vo(\ 21 - - z I sec 7,

(14)

/

where 7 = O' y=o¢

if

fl = 90 °

+ v ~ if

/3<90 °

7=0'--°¢ 7=~--v

if

/3>90 °

and

~
~ if

/~<90 °

and

~>vq

As the distances r 1 and r 2 of the points P and P ' are negligible with respect to the distance of observer there is ~ - 90 ° -- fl, and the phase angle becomes t~ = 180 ° -- v~'. The other p a r t of the p a t h is l~ = 30( 2

-- z)see ~;

(15)

if we consider t h a t the nebula is geometrically as well as optically thin, and t h a t fl is near to 90 °, l S can be replaced b y a constant term. Thus the intensity of such a nebula depends strongly on the m i n i m u m distance of the star, z > ½30, and on the phase-angle function ~0(vq). W h e n z* = ½30 and the star is on the front side of the nebula, then the optical thickness along the p a t h l 1 becomes a more i m p o r t a n t parameter which determines the intensity- a n d colour-distribution. If ~:z* < ~:½vo then the star is embedded in the surface of the plane-parallel layer and l~ = 3o V[x~ + (z -

z*)2],

l~ = ~0(~ - z)sec ,.

(16)

The phase function determines the intensity and colour distribution in the close vicinity of the star only.

V. VAt'SEE

197

When x ~ ½T0, t h a t is larger t h a n the geometrical thickness, the phase-function effect is affected b y the extinction in the nebula, even if the optical thickness is small.. For the third case, i.e. for stars behind the nebula it is easily found t h a t l 1 ----- T O " ~ +

Z see

(17) 12

=

To

z sec v~.

--

Since the coordinate z of the scattering volume is the variable of integration, the phase angle must be expressed in terms of z; this is not complicated from the geometrical point of view, particularly when some simplification is adopted. The optical thickness of the nebula, v0, is decisive for the "internal reddening". I n a spherical model, for instance, it considerably weakens the back-scattering contribution, and also has a certain effect on the depolarization of the light in the nebula. Generally, it m a y be assumed t h a t the densities of particles in interstellar space, a,, and in the nebula, an, will be in the ratio O'n

~¢1t

- -

=

O's

_ _

~

10 a.

~s

Thus, if we adopt for general absorption in the visual region of the spectrum A v - I m kpc -z, then the absorption in the nebula for the same region will be 1.0 to 1.5 m kpc -1. Another acceptable assumption is to consider absorption as inversely proportional to the wavelength; thus, for the ratio between total visual absorption and selective absorption a standard relation m a y be used Av 3.0. E (B- V) For stars in the nebula or behind it, provided the geometrical thickness of the nebula is greater t h a n 1 pc, the colour excess (B -- V) should not be greater t h a n 0-5. The value E(B-V) ~ 0.6 is valid for the star H D 200775 which is inside the nebula 51GC 7023. I n the same way, certain weak stars, which are evidently behind the nebula in the Pleiades, have E(B-V) ~--0"4. On the other hand, however, the illuminating star near NGC 2068 has E(B-V) = 1"5, and thus a total absorption A ;~ ~ 4.5 pc-L Since this case is rather an exception, A v ---- 1.2 m p c -1 m a y be adopted as an acceptable value. The Asymmetry Factor The relatively complicated scattering function ~(v~) m a y be replaced by the function (0), which contains the a s y m m e t r y factor. This factor is defined as g ~ cos iS, w h e r e ~ is the phase angle at which the average intensity of scattered radiation is emitted. Thus it holds +1

g = -~

cos v~~(v~) d(eos v~)

(18)

-1

The a s y m m e t r y factor itself is dependent, in view of ¢(v~), of the particle diameter and the refraction index.

198

Reflection Nebulae and the Nature of Interstellar Grains

Tables of g values, or cos v~ for different x and m m a y be found in a n u m b e r of papers, especially Irvine (1964); v a n de Hulst (1957); Chu, Leaeock, Chen and Churchill (1962}; and Chu, Clark and Churchill (1957). I f the angle t~ is a deviation from the forward scattering direction, then the phase func. tion ~g(v~), according to H e n y e y and Greenstein (1941), is 1

1 - - g2

~og(~) = 4re (1 -t- g~ -- 2geosv~) 8/2"

(19)

W i t h the knowledge of the efficiency factor for scattering, Qsca, it is possible to substitute ~g(v~) into (10) as a phase function, because it holds 1 /

gOsca = x-~-F] [il(v~) ~- i2(v~)] cos v~ sin v~ dr%

(20)

0

B y means of this factor it is possible to calculate b o t h the intensity distribution and the eolour difference in the interstellar dust cloud. Several examples of the behaviour of the colour differences and of I(~) ~, calculated for a spherical model with phase function ~(v~), are shown in Fig. 5 for optically very thin nebula (v0 ~ 0.1) a n d for g ---- 0.0, 0.5, 0.75 and 0.95. A n a d v a n t a g e of the phase function ~0~(t?), resulting from the a s y m m e t r y function, is its easy adaptability to calculation a n d the saving of time when using medium-size computers. The smooth r u n of the function ~ ( v~) with phase angle does not, of course, correspond to the 2~a real behaviour of ~(~), which is more complicated, particularly for large values of x --

g=O

rn o ,II

I

2

J

3+L0g "t.T/"'o

•

3

FIG. 5. The dependence of normalized surface brightness B = ](Q) Q (in arbitrary units) on the distance from the centre in a spherical model of a reflection nebula. Curve g = 0 is for the isotropical scattering, while g = 0.95 is for strong forward throwing scattering.

V. VAlc~s~x

199

This is why there must exist certain differences in the theoretical behaviour of the surface brightness of the nebula, if integrated with respect to ~g(Vq), or ~(vq). According to computations by Van~sek (1966),

dI(r)r -~r

is systematically lower for a spherical model, if the asym-

metry factor (or ~g(0)) rather than the rigorous phase function ~(v~) is used for the calculation. This systematic difference is essentially caused by the numerical handling of the problem, i.e. mainly by the number of integration operations. One of the most suitable objects for the study of the optical properties of interstellar grains in reflection nebulae is the nebula in the Pleiades. The small reddening effect observed for the stars Maia and Merope shows t h a t these illuminating stars are situated in front of the nebula.

4. CERTAIN PROPERTIES OF THE CALCULATEDMODELS Only a limited number of models of reflection nebula have recently been calculated by means of fast computers, so that their general properties may be determined only very roughly. Roark presents in his Dissertation (1966) the calculation of some 280 models of plane-parallel nebulae with dielectric and conductive particles. Van~sek and Svato§ had at their disposal, in 1963, t h i r t y models of a spherical nebula for particle refraction-indices 1.33, 1.50 and 2.00 respectively, obtained by photographic methods. This article gives comparison for 680 models of spherical nebulae these were calculated by Vanysek on the computers Gier and EUiott 4100. As for the physical properties of the particles, two different types have been used : (1) the particles are assumed to be dielectric with refractive indices from 1.33; to 2.00, and with a high albedo; (2) the particles are assumed to be conductive, metallic, with refraction indices m - 1.4 - 1-5i, for 2 ~- 5100 A, or graphite with m - 2.45 - 1.45i, i.e. with a low albedo. The size of the particles could be limited by the assumption that their photometrically effective diameter will be hardly greater than about 0.5 ~. The simplified assumption t h a t the particles are spherical has been adopted in all cases. Models have been calculated both for particles of a single size, and for the Oort-van de ttulst distribution function in Greenberg's formulation. The trial and error method, which makes it necessary to compare the calculated models with observations, is very effective when the theoretical and observed values of the colour difference or of the polarization are charted graphically. In using current computation techniques it is therefore not possible to avoid a certain amount of labourious work in the fitting of even tentatively chosen models. Nevertheless, certain general properties of the models may limit in advance their choice for further treatment. From the observed properties of reflection nebulae it follows that models m a y be found suitable in which the colour of the nebula differs markedly with increasing distance from the illuminating star. This is the property of all models with dielectric particles which have been calculated up to now. On the other hand, as has been shown by the work of Greenberg and Roark (1966), models with graphite and iron particles do no comply with this requirement. Such models show an extreme increase in the blue colour of the nebula, but without any pronounced changes taking place with increasing distance from the star. A characteristic feature of models with a plane-parallel layer is their considerable sensitiveness with regard to the geometry of the entire situation, i.e. to the distance of the star

200

Reflection Nebulae and the Nature of Interstellar Grains

FIG. 6. This photograph of the Pleiades was taken by A. Mrkos at the Czechoslovakian Lomnick~ Stlt Observatory, using an Agfa-Astro special plate at the primary focus of the 50 cm reflector; the exposure time was 80 minutes.

8' X 8" 30' × 19' 39' x 30' 2!5 x 1.t3 8' x 6'

B10

IC 405

Ced. 44 NGC 2261 M78

Antares IC 1287

7

8

10 11

12 13 126' x 78' 44' x 34'

30" x 30'

Merope

6

9

20' X 16'

Electra

30' x 30"

10' x 10'

23.7 23.2

21.2 21.4 20.9 20-7 24.2 22.3 22.4 22.6 23.5 20.0 20-6

23~2 25"6 23"3 21.4 21.5

18' x 18'

NGC 7023 NGC 1333 IG 348 Maia 9' x 5"

V/"

Dimensions

Nebula

5

No.

TABLE 1A

4.°5E I°E

I°N l°S I°N

12'S 3"E

I°N

6"NNW 3"SW Nob 1{25E

15"E + W

3°S

3°S

3°S

I°N l°S 20'N

Centre (sky)

3'E

3'N 3'S 3'W Neb. 3'N

3'E

3'W

3"E

3'N 6'N 3'N 3'S

Centre (nebula)

+0.78 --0.42

+0.65 --0.25

--0"67 --0.42 --0-40 --0.28 --0.90 --1.31 --1.41 --1.17 --0.82 --0.30 --0.35

--1.ml0 --1"27 --0"55 --0"60 --0"70

+O.m14 +0"96 --0"02 --0"62 --0"42 --0.30 --0.16 --0.13 --0.21 +0.67 --0"21 --0.31 --0.28 --0.72 +0.52 +0-25

U -- B

B -- V

GENERAL AND COLORIMETRICDATA FOR NEBULAE

--1.19 --0.52

-o.98(0)

--0.37(A)

--0"59

--0.19 --0.10 --0.07 --0.15

--0.70 --0"55 --0.35

--0~31

--0.32(A) --0.71(C) --0.52 --0.05

+0.08

+0.03 +0.15

--0"26 +0.01

--0"56 --0"20 --0"30

--0.m62

(B--V)n--(B--V)s (B--V)n--(B--V),

.<

12 13

8 9 10 ll

No.

200 775 + 3 0 ° 549 +31 ° 643 Maia Electra Merope DD Tau CZ Tau AE Aur H R 1763 R Mon + 0 ° 1177(A) + 0 ° 1177(C) Antares H R 6946(A) H R 6946(B)

Star dB3ne B8-Bgp B5 V B7 I I I B6 I I I B6 IVnn dK6e dM2e 09.5 V B1 V A-Fpe (B5) B1 M1 Ib B2 V dB9

Sp.

TABLE 1 ~

-0-90 --0.03 +0.36 +1.30 --0.37

+0"62 +1-23 ÷1.84 +0-27

10-49 10-73 0.92 5.91

+0.01 --0.40 --0-41 --0.43

+0.68 --0.07 --0.11 --0"06

8"53 3"86 3"69 4.16

--0-13

--0.m48

+0.m45

7"32

5.78

U -- B

B -- V

V

11.3-13.8

14"5-15-5 15.8-17"3 5"4-- 6.1

10"9

mpq

0"018

0"036 0"025

0"017

0"011 0"002 0.004 0"007

0-007

p

d

168

0 99

66

6O 71 26 47

179 °

DATAFOR STARS ASSOCIATED WITH NEBULAE (ACCORDING TO JOHI~SON, 1960).

71 ° 127 128 134 134 135 137 137 140 163 172 173 173 320 349

1

1

--13 --13 +14 --2

+3

--14

--

--13° --19 --17 --22 --23 --23 --14 --14

b

tO

V. VAN~SEK

203

from the nebula, the thickness of the layer, and the tilt of the plane of the layer relative to the observer. The position of the star and the tilt of the layer determine the range of the phase angle over which the integration is to be done. On the other hand, it is evident t h a t the properties of a spherical model are primarily determined by physical parameters of the particles, once the geometry of the problem is given. Figures 7 and 8 show the behaviour of the colour-ehanges in certain selected models. The models for the plane-parallel layer are taken from the work of Roark (1966), and the spherical ones from the work by Van~sek (1967). As for the values of m a x i m u m colour in these models, it is interesting t h a t none of the models for dielectric particles shouts a greater increase, in the blue colour of the nebula, as compared with the illuminating star, t h a n --0.60 m in (B -- V); this also corresponds to the current m a x i m u m observations of colour differences. The influence of the distribution function on the behaviour of the colour difference in models is very interesting. If the distribution of the colour is calculated for a single size of the particles, the maxima and minima of the phase function are very pronounced. However, the integration with respect to the distribution function of the particle diameter has smoothing effect, especially on the secondary m a x i m a and minima. A more difficult problem is the question of the distribution function in treating polarization effects. The polarization in models of optically thin nebulae is generally calculated from the relation

fi,(~) dO -- j'i,(O) dO P = fil(O) dO + fi~(O) dO"

(21)

27ta

Since in the case of small values x z - - ~ the polarization reaches a m a x i m u m for 0 ~ 90 °, the distribution function has the greatest effect at great distances from the star, for instance for polarization at the edge of the nebula, where i1(90) - - i~(90) P = i1(90) ~- i~(90)

(22)

Therefore, for models calculated for a unified diameter of particles, we have p ~ 1, i.e. 100%. The introduction of the distribution function considerably lowers the values of extreme polarization and has, therefore, a "depolarization" effect. As polarization on dust particles is an important criterion for a more precise limitation of suitable nebular models, it will be necessary to devote more attention to this problem and, especially, t r y to solve it with the use of fast computers. 5. OBSERVATIONALPROCEDURES

Measurements of the distribution of the light intensity, or of colour and polarization, in reflection nebulae are carried out either photographically or photoelectrically. The first extensive measurements of intensity and colour of the light in I~GC 7023 were obtained by Collins (1936) and by Keenan (1938). I n recent times the problem was tackled b y Kachiklan (1960), Rozhkovski and Fesenkov (1955) and Kaehikian and Parsamian {1966). Photoelectric measurements were made b y Martel (1958), Johnson (1960), Van#sek and Svatog (1964), Roark (1966) and Hall and Elvius (1966). These mainly concern bright objects. Quite recently, photometric studies in the region of the continuum, with regard to scattered radiation on solid particles, were extended by O'Dell (1965) and O'Dell and H u b b a r d (1965) to a typically mixed dust-gaseous nebula in Orion. 14.

204

Reflection Nebulae and the Nature of Interstellar Grains

No a t t e m p t has been made so far to combine the photographic and photoelectric methods. However, this would very probably enable us, in certain cases, to study the detailed distribution of the luminous intensity and perhaps even uncover the fine-structure of certain objects. The technique of measurement mainly requires t h a t the observer measures certain selected regions in the nebula, usually limited b y a circular diaphragm with a diameter of a few tenths of a second. An exception are the photoelectric measurements used in the work by Van:~sek and Svato~, where NGC 7023 was measured along three sections across the object in the direction of hour angle. I t seems, however, t h a t the difference in measuring technique is rather unimportant as long as the surface brightness is sufficiently high. In regions of low surface brightness it is necessary to use the quanta-integration method. I n t h a t case it is essential to carry out measurements in isolated regions selected in advance and, as far as possible, with a background free of stars. A very important problem is the influence of light scattering in the instrument and in the atmosphere close to bright stars. If the surface brightness of a nebula at a given wavelength with regard to the illuminating star is studied, it is necessary to obtain measurements at different distances from the star. Unfortunately, a number of investigations does not consider this influence of light scattering of the central star both in the atmosphere and in the optics of the instrument. The light scattering in the instrument is not negligible and depends on the state of its optics. J. S. Hall and A. Elvius studied this effect on two nearly identical instruments--the 69-in. and the 72-in. reflectors of the Lowell Observatory. An important conclusion m a y be quoted from their observations: " T h e scattered light increased substantially toward the shorter wavelengths and varied from night to night. Furthermore, it was ten or twenty times greater for the 69-in. optics t h a n for the new, freshly-aluminized 72-in. mirrors. The 69-in was last aluminized in 1960. Parts of this mirror have become noticeably etched during resilvering operations since it was polished 34 years ago." R o a r k (1966) arrives in principle at the same conclusion. The dependence of the flux of the scattered light on the distance from the central star m a y be expressed b y / = aF~-b. The coefficient a depends on the instrument and expresses the quantity of scattered light in the unit distance from the star. This coefficient depends primarily on the quality of the optics. For instance, from the measurements b y Hall and Elvins on the 69-in. reflector follows a ~ 10 -1"8 for the effective wavelength 3800 A, and 10 -a'2 for the wavelength 5750 A (p ~ 1" is the unit diameter of the diaphragm). On the other hand, in the 72-in. telescope the value 10 -4 is practically valid for all wavelengths. Roark's measurements have given the value a ---- 10 -a. The change in instrumental scattering expressed b y exponent b is about 2. If therefore the surface brightness of the nebula in the vicinity of the star is about 21TMin V per square-second then (for instance in the nebula NGC 7023, where the brightness of the central star is 7"5m) the scattered light in the instrument is comparable with the surface brightness of the actual nebula. Only at greater distances, or when the value of a is smaller t h a n 10 -7 , it is possible to neglect in principle this effect. Instrumental scattering m a y have a certain effect also on measurements in emission lines, as long as they occur in reflection nebulae (NGC 7023 shows traces of emission H~), and it naturally has a considerable effect if the central star shows emission lines of the Balmer series. If the intensity of scattered light in the instrument follows the )l-4 law, then the logarithm or ratio Ho,/H ~ will be --0.52, as against the theoretical value (with assumed electron temperature 9000°K) of 40"45.

V. VA~'SEK

205

Instrumental scattering evidently influences also the photographic measurements where the scattering of the light of illuminating stars in the emulsion considerably affects the already delicate photographic measuring of the surface brightness of diffuse objects. Naturally also the measurement of polarization is strongly affected by instrumental factors. Polarization and depolarization effects of light scattering in the instrument, and the uneven distribution of sensitivity lower the photographic plate, or on the photo-emissive cathode of the photomultiplier, may be responsible for a considerable distortion of the results. In using photographic methods for the measurement of polarization, the effects of apparent polarization (or depolarization) caused by different sensitivity of the emulsion are hard to control. Therefore, the accuracy of photograph polarization measurements is not more than (p ~ 5)%. 6. DEFINITION OP COLOUR DIFFERENCES AND THE DEGREE O1~ POLARIZATION OF NEBULAR LIGHT

In colorimetric measurements of reflection nebulae it is important to elucidate the definition of colour difference.This is to be defined by the difference in colour between the central or illuminating star, and a given place in the nebula. If we denote the flux of the central star as F, and the flux from this point of the nebula a s / - - in the same range of wavelength, we obtain for the colour difference between ;to and ;tl: D(1, 0) = log J(~l) F(2o) /(;to) $'(;L~)

(23) "

I t is evident that this colour difference, expressed in stellar magnitudes, becomes: Din(l, 0) ---- --2.5D(1, 0). The wavelengths 2o and 21 are in photoelectric measurements the effective wavelengths determined by Q(2), which involves the sensitivity of the multiplier, the transmission of the filters, and the optics of the instrument. The flux from the star $'(4), or from the nebula / (;t), for the wavelength 2 is given by the energy distribution in the spectrum. The effective wavelength ~ is, therefore, for the maximum of the recorded flux $'(~) -----f $'(2) Q(2) d2, (24) which is integrated over the entire interval/12 of the theoretical sensitivity of the receiver. Let us further assume that Yx ---- --2.5 log/(21), and Y1 = --2.5 log $'(;tl), where Yl, or Y1, are magnitudes in the colour of an arbitrary colour system for the effective wavelength 21. For the colour difference, not corrected for atmospheric extinction and not converted into an international system, we then have Dm (1, 0) ---- (y~ -- Y0) -- ( r l -- r0).

(25)

For conversion into the selected international colour system we have C(1, O) = A~ H- A~(yl -- Yo),

(26)

and therefore D,(1, O) : D m

(1, 0) A S,

(27)

206

Reflection Nebulae and the Nature of Interstellar Grains

where A 1 and A 2 are the appropriate experimentally determined conversion coefficients. Atmospheric extinction m a y be neglected under certain circumstances. The star's magnitude outside the E a r t h ' s atmosphere is given by the well-known relation Y0 =

Y -

k~

-

k'(c)~,

where 9~ is the air mass. I t holds further k----a+b

- - 2 -4 ,

where a is the " g r e y - t e r m " of atmospheric extinction, while b is the "colour-term". The " g r e y - t e r m " has values around 0El but differs from night to night by about 30 %. The "colour-term", on the other hand, shows variations of about 10 % and has a value of 0T01. The atmospheric coefficient of absorption, k, which is dependent on the colour of the star, has values from +0.03 to --0.01, and m a y be neglected in case of differential measurements when the nebula and the star have approximately the same sec z (since with a difference of about one magnitude the error would not be more t h a n 3 %). The same applies to the coefficient k'; if the required quantity is only the colour difference D, we need not know the intensity of the central star, nor the measured place within the nebula. Polarization in the nebula is defined by the general relation p =- (11 - - I , ) / ( I 1 + I , ) ,

where 11 is the intensity of the ordinary ray and 12 t h a t of the extraordinary ray. The polarization angle, or rather the angle of the polarization plane, is defined in such a way t h a t 0 ° is in the North-South direction. I n stellar magnitudes we have therefore, mp ----2.5 log p, or for low percentages of polarization m v ----2.1717p. 7. I N T E N S I T Y D I S T R I B U T I O N IN I ~ E B U L A E

Recent studies devoted to the distribution of the light intensity in reflection nebulae m a y be divided into three basic groups: (a) determining the intensity distribution in the nebula; (b) determining the colour difference; (c) determining the degree and orientation of polarization. The first group of studies, of which the papers by Rozhkovsky (1955), Martel (1957) and Grygar (1959) should be mentioned especially, deals mainly with the general structure of certain reflection nebulae. Apart from this, they give a general picture of the distribution of the intensity from the illuminating star out to the edge of the nebula. I n isotropic light-scattering in a spherical nebula is dm'*(e----~) - -

2.5,

d log where m~ (~) denotes the surface brightness of unit area of the nebula, expressed in stellar magnitudes at the distance 0 from the star. The nebula NGC 7023 seems to correspond best to the spherical nebular model, and the average values of the ratio of m (Q) and log might therefore be suitable quantities for a preliminary qualitative judgement as to the extent to which the condition of isotropy, or anisotropy, of the scattering function has been fulfilled.

V. VANYSEK

207

Table 2 compares the values

dm,(~)/d log @---- - - 7 for photoelectric and photographic measurements in different wavelengths. TABLE 2. MEAN GRADIENT OF INTENSITY IN ~N~GC7023

eft. ~ 395 390 410 440 550 641

pe 2.7 i 0.1

ph(g)

ph(k)

2.3 2.14

2.2 :t: 0.1 3.0 -}- 0.1

(6.6--7.4)

7.0 ~- 0.3

2.4 -4- 0.05 2.3 -4- 0.05

dmo(~) ~ - d log @ p~ determined from photoelectric measurements. ph(a) ph(k)

-----determined from photographic measurements by Grygar (1959). determined from photographic measurements by Keenan (1936).

As it appears from the value of the brightness gradient in the nebula NGC 7023, especially from photoelectric determinations for various wavelengths, the light-scattering is not isotropic and a considerable a s y m m e t r y of the scattering function is evident from the low gradient in the short-wave region of the spectrum. The extremely high ~ value in the 6410/k region is caused by the emission of H , near the star, and the high gradient in the red part of the spectrum is therefore not due to selec. tive properties of grains in the nebula. From isophotes obtained photographically it is only possible to determine the approximate colour distribution in the nebula. This information, however, can be furnished much better b y photoelectric measurements. Earlier photographic measurements have already demonstrated beyond doubt t h a t almost all reflection nebulae show a negative excess in comparison with the colour of the illuminating star. This conclusion has been verified photoelectrically b y Johnson (1960), who found t h a t in the B -- V system the average difference between the colour of the star and t h a t of a nebula is --0.2 . Although these facts have been known for a long time, the distribution of the colour excesses in the nebulae themselves has been studied very intensively only in recent years. 8. ]~)ISTRIBUTION OF THE COLOUR DIFFERENCE IN NEBULAE

The largest number of measurements has been obtained b y various authors in the study of two objects, of NGC 7023 and of the nebula in the Pleiades, especially in the vicinity of Merope (73 Tau). Very detailed photoelectric measurements in various parts of NGC 7023, of polarization and colour m a y be found in the paper b y Martel (1958), while photographic measurements of this kind b y Keenan date back to 1936. Older photographic measurements, in which the zero point of the entire colour-system is evidently shifted b y an unknown value, m a y hardly be compared with new photographic measurements. The nebula NGC 7023 has been measured b y Martel at some 8 different points. Quite recently Van~sek and Svato~, as well as Elvius and Hall, and also Roark, have provided

208

Reflection Nebulae and the Nature oI Interstellar Grains

data from more than ten different places around the illuminating star, in which the precision of the colour determination is probably not less than 4-0.05 in (B -- V). All measurements show that this nebula, especially in the vicinity of the illuminating star, is bluer than the star itself. The following Table 3 gives a survey of all the more important measurements mentioned. I t can be seen that the colour difference between the nebula and the star is on the average D(B, v) ---- ( B - - V ) , - - ( B - - V) s = --0-25 m. I t is also evident that the TABLE 3. THe. COLOURDIFFEREI~CES IN NGC 7023

Observer [(eenan

~ollins )Iartel ~ohneon tran~sek Ivato~i $1vius and Hall [~oark

Colour

Colour differences in (B-V)

Year

Method

1936 1937 1958 1960 1964

photogr. photogr. photoclectr. photoelectr. photoelectr. photoelectr.

~-0.23; --0.23 Ph, Pv --0.30 Ph, Pv --0.01; --0.41 Ph, Pv --0.31 B, V ~0.21; --0.50 B,V --0.25 U, B, g

1966 1966

photoelectr. photoelectr.

U, B, V U, B, V

system

--0.02; --0.67;

--0.62 ~-0.70

Number of points 8 points 3 points 6 points 1 point 3' N 3 tracings to 4-4' 1 point 1' S 12 points 14 points, all in the N direction

maximum value of the negative excess lies south-east of the central star, in the direction of the position angle 190-200 °, and thus even in places where Martel found maximum polarization. If we compare the total colour excess of NGC 7023 with the colour excesses of other nebulae of the reflection type, we see that it does not differ very much from these. For example, Johnson (1960) gives for 10 different objects the colour differences D(B, I1) ---- --0.20 m in the (B -- V) system. On the other hand, it should be noted that the northern part of the nebula has a low colour excess, on the average about 0, according to the measurements of Martel and Van~sek and Svato~. I n the position 40" north-west of the central star, Keenan found places with a positive excess, i.e. regions where the nebula should be redder than the star itself. Although there is a large error of zero point in the photographic data of Keenan, it is obvious that the high positive colour difference in his measurements is certainly outside this error limit. I t is not without interest that Roark found 2' North of the illuminating star the value D(B, v) -~ +0.27. A considerable decrease in the negative value of the colour difference in the north and north-west of the central star follows also from measurements of the other above mentioned authors. Martel finds a zero colour-difference 0.8' North of the central star; the same found Van~sek and Svato§, whose measurements show a slight excess of the eolour difference towards positive values D(B ' v) -~ -~-0.2 in the eastern direction. By comparing the results of U B V measurements in NGC 7023 by Elvius and Hall with those by Van~sek and Svato§, one finds at once a difference in the general trend of the change of eolour. The measurements by Van~sek and Svato~, which have been obtained during three scans across the nebula (in an east-west direction), show a general increase in colour as one scans away from the star, with the maximum negative eolour excess to the south.east. On the other hand, the colour differences measured b y Elvius and Hall show a certain increase up to D(B, V) -~ --0.62 at a point 4' East of the illuminating star. Here, too, the nebula has a very low surface brightness, and the measurements involve great errors.

V. VA~r~s~x

209

TABLE4. DISTRIBUTIONOF COLOURDIFFERENCESIN NEBULANGC 7023 (UNITOr (B-V)neb -- (B-V)star IN 0"01TM) Martel (1958) E 1'.6 0'.8 N O'.8 0'.0 S O'8

W 0'.0

0'.8

1'.6

--07

--34

--01 --34

--41 --28

Van~sek and Svato~ (1964) E N S

1!2 0~0 1~2

W

4'

3'

2'

1'

0!0

---20 --

+16 --33 --10

+05 --44 --50

--03 --08 --32

--02 ---18

1' --21 --41 --18

2'

3'

--13 --50 --15

4'

+27 ---40 --20 -}-14 - -

ElviusandHall(1966 E 4'

3'

W 2'

1'

0!0

--52

--40 --36 --52

--02 --24 --21" --24 --38

1s

N 2' O' 1" S 2'

--62

--52

1'

2'

3'

4'

--61

The comparison of results between different individual authors is v e r y difficult. E a c h observer uses a relatively wide spectral pass-band for determining the intensity in colour. I n view of t h e fact t h a t one m a y assume t h a t the nebular particles m a y also show reflections of the emission lines H , and H~, originating in the star, small differences in the spectral sensitivity of the receiver m a y affect the d a t a in a n y otherwise well-defined colour system. Since according to all current measurements the colour of the nebula changes sharply from place to place, it would be desirable to compare only measurements carried out with the same diameters of diaphragms. The emission from the nebula NGC 7023 itself m a y also be of importance in this respect. Greenstein and Aller (1957) have dealt with the nebular emissions in H~ and H~. The measurements of J o h n s o n (1960), using interference filters, have also shown an excess of intensity in the neighbourhood of H r. However, Greenstein points out t h a t this is the reflection of the emission lines of the star within the nebula. Unfortunately, we do not possess suitable spectrophotometric d a t a which m i g h t definitely decide this question. Shain, Gaze and Pikelner (1954) classified this nebula as a gaseous- and dust-nebula, b u t this can be explained b y the reflection of the conspicuous emission lines H , and H~ in the illuminating star. Nevertheless, the decrease in brightness in the H~ region of this nebula is v e r y steep, and the isophotometric measurements show that, particularly in the immediate neighbourhood of the star, the a n o m a l y in the red spectral region is significant. As long as there exists an H~-emission in the nebula itself, it contributes to the total intensity of the continuous spectrum, except for regions v e r y far f r o m the illuminating star. * Measured by a special method around the illuminating star.

210

Reflection Nebulae and the Nature of Interstellar Grains

Although the comparison of measurements b y different authors is difficult, all recent measurements indicate t h a t the structure of the nebula is evidently very complicated and t h a t there m a y exist a considerably denser region north-east of the central star, which is responsible for the change in the general character of the star-nebula colour-difference. The nebula in the Pleiades is a much more rewarding object in this respect. Recent measurements by the already above mentioned authors Elvius and Hall (1966), furthermore by O'Dell (1965), and Roark (1966), are available. Figure 7 shows observations of these authors, which compare very satisfactorily, and show a systematic positive colourincrease in the direction from the central star, which in this case is Merope (73 Tau). The general character of the changes in colour-difference in the direction to the illuminating star corresponds to the changes found by Van~sek and Svato~ in NGC 7023, and by Hall (1965) who measured NGC 2261.

+.2 or) ii1

o

v 0

++

80

÷

o

ov v

.0 v

¢9-.2 Z

I

U.l It

i

v

°o

O,,o+

oo

u_ .0 °2~" -.2

0_.1- . 4 0

0-.6

0~. ~'0

CB-v) (B-Vl s

, e"

oo,,

%

'0,

i'0'

Distance from

1o' Merope

Fie. 7. Colour differences in (U-B) and (B-V) colours measured in the nebula around Merope (73 Tau) in the Pleiades. Open circles indicate measurements by Elvius and Hall (1966), crosses those by O'Dell (1965) and v-marks those by Roark (1966). The exceptionally favourable comparison of measurements b y different authors in the region of the nebula in the Pleiades indicates t h a t this object m a y have a simple structure ; this is also confirmed b y the co]our excess of the illuminating star, which is directly connected with the internal absorption in the nebula. I t shows t h a t the optical thickness of the layer between the star and the nebula is about at least three times smaller than the optical thickness of the nebula NGC 7023, and by about one order smaller t h a n t h a t of NGC 2068. The illuminating star is therefore most probably in front of the nebula and the irregularities in the Pleiades nebula are not important; this m a y explain the uniform colour change without a n y discontinuities, in the direction to the star.

9. COMPARISON ]~ETWEEN OBSERVATIONS AND MODELS

A sufficient number of various nebular models, when compared with observed properties of reflection nebulae, permits to exclude those models which are evidently not realized in actual celestial objects. A first simple comparison rejects practically all models with graphite or iron particles ~ 0.05 ~z in diameter. The colour differences of these models are very negative, without any significant dependence of colour on the distance from the star; on the other hand, the change of colour is the most typical feature of reflection nebulae.

V. VAN~-SEK

211

However, the change in colour difference is very pronounced in those cases were the model nebula is constituted by dielectric particles. Very instructive results of such comparisons between such dielectric models and reflection nebulae are presented in Fig. 8. The curves (a), (b) and (c) represent the colour differences in a plane-parallel layer, according to Roark's computation. The model is computed for ice grains with refractive index m ---- 1.33, the Oort-van de Hulst size-distribution function, and a diameter a 0 ~ 0.5 ~. The plane of the layer is perpendicular to the line of sight, the curve (a) is for the star situated in front and the curve (c) for the star behind the nebula. The curve (b) is for the case of an illuminating star embedded in the nebular matter. The hatched area in Fig. 8 denotes the region of She observed colour differences in the Pleiades nebula around Merope.

,.6 +./o ÷.~ C le- -.~

-.~ -.6 I

0'

I

I

I0" 20" Distance from Merope

:FIG. 8. A comparison of the theoretical colour-distribution in plane-parallel models (according to Roark), and the colour differences measured in the Pleiades. Parameters are: refractive index m ~ 1-33; the Oort-van de Hulst size distribution; a0 ~ 0.5~ ; distance of the nebula 160 pc; thickness of the nebula 1 pc; internal absorption 1.20mpc-1. Curves: (a) star in front; (b) star inside; (c) star behind the nebula. All curves are smoothed. The observed colour-difference distribution is schematically represented by the hatched area. Quite a good agreement with observations seems to exist for curve (b). However, this is not the only model which agrees rather well with observations. The behaviour of the colourdifferences in a spherical model as computed by Van:~sek (1967) for dielectric grains (refractive index 1.33, and size a ~ 0.2 ~), is represente din Fig. 9. The curve (c) has obviously the same trend as the Pleiades nebula. Similar results have been found for :NGC 7023 and NGC 2261. The spherical model is very sensitive to the adopted dimensions of the nebula. Van~sek's and Svato~'s results for the model with m ~ 2 coincide with measurements in NGC 7023, if the apparent diameter of the nebula is smaller than 18'. Nevertheless, the model with m = 1.33 is quite good if the diameter of the nebula is assumed to be larger than 25'. Thus, the interpretation of particles with a refractive index 1.3 requires the assumption t h a t the nebula has larger dimensions than follows from the observed apparent radius. Another question is : would a solution be achieved by models filled with semi-conducting heterogeneous particles? The latter have been considered b y Hoyle and Wickramasinghe (1962) and b y Wickramasinghe (1962)for the problem of interstellar absorption. His calculations for carbon particles show a substantial increase of the albedo in the blue region of the visible spectrum for particles of 0.03-0.05 ~ diameter. As the author shows, carbon particles could not explain the relatively high albedo wich interstellar grains very probably have. He thus considers another model, where the carbon particle is covered by a relatively

212

Reflection l~ebul~e and the Nature of Interstellar Grains

thick layer of ice, and thus arrives at complicated ratios when calculating the scatteringf u n c t i o n - - ( i n his case, of course, he only computes the ratio of the scattering and the extinction cross-section i.e. the albedo of the particle). Particles having a diameter of 0.24 would best satisfy the dependence of the interstellar absorption on the wavelength, if the ratio of the radius of the carbon nucleus to the total dimension of the particle were 1 : 3. I n such a case the albedo of the particles is v e r y high, about 0.8.

>

Ic i

-2

-4

0

O.5

P

FIG. 9. Colour differences in two models of spherical, homogeneous nebulae computed by Van~sek (1967). Parameters of dielectric grains are: refractive index 1.33, a = 0.18 be (curve a) and a = 0.22 (curve b); optical thickness 30 ----1. Gehrels (1966) concludes from his measurements of NGC 7023 t h a t the albcdo is not t o o high (about 0.5) and proposes two alternatives for t h e properties of the grains. The grains m a y be homogeneous with a m e a n size of 0.3 ~ and a refractive index between (1.2 -- 8i) a n d (1.6 -- 8i), with the imaginary component between 0.1i a n d 0.4/. Alternatively, the grains m a y be heterogeneous with a condensation nucleus of 0"05 in diameter, a n d an outer shell consisting of " d i r t y " ices. The refractive index in such a case m a y be m ~-- 1.3-0.1i.

+6

sd"

+./-4 +.2 '

~

.d

lb"

2bb

_FIG.10. Schematic smoothed colour differences computed for the plane-parallel layer models of reflection nebulae (according to Roark). Curve (g) is for graphite clouds, with single size of grains 0-05 be, and stars situated in front of the nebula, while (g') is for stars behind the nebular layer. The same curves have been found for iron particles a = 0.05 be, indicated by i or i', respectively. Other parameters see legend to Fig. 7. The model of a nebula containing dielectric particles with the Oort-van de Hulst distribution-function and a o ----0.5 beproduced the curves (d), stars in front, and (d'), stars behind. The hatched area illustrates schematically the whole region of measured values of colonr di~erencee in reflection nebulae.

V. VANYSEK

213

At it appears, colorimetrie measurements of reflection nebulae outline only approximately the physical properties of interstellar grains. The refractive indices of the models are between 1.33 and 2. I t may not be forgotten, however, that the properties of the models do not change proportionally with increasing refractive index. Irrespective of the considered refractive index, the most probable particle diameters are about 0.3 ~. Colorimetric measurements may be confronted with polarization data. Important photographic measurements of polarization in reflection nebulae have been published b y Martel (1958); photoelectric ones have been carried out by Elvius and Hall (1966), and there are also available a few measurements by Johnson (1960) and Gehrels (1960). Older measurements of this kind, mainly in the nebula NGC 7023, are due to Gliese and Walter (1951), who worked photographically. Apart from this, there exists a study by Weston (1952); Kachikian (1958) and Kachikian and Parsamian (1965) also published several series of polarization measurements b y photographic methods. Of great importance are the photoelectric measurements by Elvins and Hall in the Pleiades, NGC 7023, and NGC 2068. According to the orientation of the plane of polarization, one can divide the reflection nebulae into two groups: (a) the "random-oriented t y p e " , where the planes of polarization are all perpendicular to the radius vector from the star to the selected point in the nebula. This, in general, corresponds to the theoretical assumption of scattering and polarization on more or less spherical particles, or on particles which are not spherical, but have a random orientation.

2' N

to o

I

2"

0

I

2" W ~

FIG. 11. A "random" type of orientation of the electric vector of polarized light in NGC 7023 (Elvius and Hall, 1966). (b) the "parallel t y p e " , where the polarization planes are more or less parallel, and are either perpendicular to, or parallel with an existing filamentary structure of the nebula. A typical example of this is the nebula in the Pleiades. This fact was first mentioned by Hall (1955), who expressed the idea that the particles have a nonspherical shape and are oriented under the influence of an outside magnetic field, similarly to the behaviour of interstellar grains in the Galaxy. If the nebula has a simple structure and is optically not too thick, one may logically assume an increase of the polarization in the direction away from the illuminating star. This follows from the very fact that, especially in particles in which x does not exceed the value 3 to 4, the degree of polarization is strongly dependent on the phase angle v~ and increases towards v~ ~ 90 °. Such an assumption is again very well supported by the nebulae in the Pleiades, especially in the neighbourhood of Merope. Elvius and Hall have found that the degree of polarization rises from the relatively low value of 2 to 5 % at a distance of 4', to

214

Reflection Nebulae and the Nature of Interstellar Grains

15 % at a distance of 20', while at a distance of about 12' the polarization attains a maximum and from then on changes only very little. Van:~sek (1967) carried out computations of the polarization for nebulae with particles of refractive indices 1.33 and 1.50. I t should be noted, however, that in these computations no consideration was given to the depolarization effect of multiple scattering, which may, in the case of greater optical thicknesses, reduce the calculated value of polarization by about 1 to 2 %. Nevertheless, these results show that it is possible to exclude particles for instance with refractive index 1-5 and size x = 10-15, in which the polarization in certain

~

*/c N

'

V B

1'o,

'

2'0'

FIe. 12. Dependenoe of the polarization on the distance from the star in the Pleiades, measured in two colours by Elvius and Hall (1966). P % 20

NGC 7023 _

S

, , ~ /

/

/i x /

15 //

10

67"

133" 3Y'

/

x o...

//J ~133"S ,'/... ,.o [ 73"E

186"v~,;-" / 67' " ~ UG1

~ j

_ BG12

® Star 1~L55 OG5 1/>,

FIG. 13. The strong variation of polarization with wavelength follows from the measurements by Elvius and Hall (1966). This figure is taken from their original paper. parts of the nebula would exceed 70 %. Also models with particles, in which x = 2.5 and the refractive index 1.5 show polarization effects greater than 50%. Measurements narrow down the choice to grains with refractive index 1.33 and x ---- 6, or to particles with the refractive index 1-5 and x = 4-5. The degree of polarization increases proportionally with the wavelength, and is very pronounced, for instance, in NGC 7023. This fact indicates that very small particles---of the type considered by Platt (1960), i.e. with a maximum diameter of several hundred angstroms--must be excluded from further considerations.

V. VA~ffS~K

215

10. COI~'CLUSIONS I n this article only the most important recent studies of reflection nebulae have been discussed. The present results show beyond doubt t h a t purely conductive particles with a large imaginary part in the refractive index must be excluded from further considerations of the physical composition of reflection nebulae. Grains with a diameter of about 0.3 ix and refractive index m ~ 1.33-1.5 appear to be most suitable. These data, however, must be considered only as a rough approximation to the real properties of interstellar particles. The refractive index, on which further studies of the physical structure of interstellar grains depend, is so far the most uncertain quantity. The small imaginary component in the refractive index need not very much affect the results as far as the particle size is concerned, but is of basic importance for ideas concerning the structure and chemical composition of interstellar grains. Thus it cannot yet be stated t h a t interstellar particles, and particles in reflection or "dust-and-gas"-nebulae are similar with respect to size and physical structure. Therefore, we should say t h a t the exploration of reflection nebulae is only at the initial stage, and t h a t recent progress in p h o t o m e t r y and in computation technique has not yet been used adequately. I t is essential t h a t special measurements of the surface brightness of reflection nebulae should be extended to a larger number of objects. Much greater attention should be paid to photoelectric work in narrow spectral regions, combined with polarization measurements. Theoretical interpretation of the results requires especially the numerical solution of models; this can be done b y the use of fast computers. Thus, it would be possible to a t t e m p t the solution of the problem b y the method of radiation transfer, in which multiple scattering would be included, as indicated b y Sobolev (1960) and his associates. As similar studies are very topical, both for observers and theoretical workers, it is to be hoped t h a t our actual knowledge in this field will grow considerably in the course of the next few years. I t has been the purpose of this article to contribute to this growing interest of astrophysicists in the study of reflection nebulae.

REFERENCES

CEDERBLAD,S. (1946) L u ~ Obs. Me~d., Ser. II, No. 119. CHU, C. M., CLARK,G. C. and CHURCHILL,S. W. (1957) Tables o] An~]ar Distribution Coe]flcients ]or ~ght Scattering by Spheres, Univ. Michigan, Engineering Research Inst., Ann Arbor. CHU, C. M., LEACOC•, S. A., CHEN, J. C. and CHURCHILL,S. W. (1962) Proc. Interdisciplinary Con/erenee on Electromagnetic Scattering, Potsdam, New York. COLLn~S,O. C. (1937) Astrophys. J. 86, 529. DORSCH~ER,J. and GiiRTLER,J. (1966) A.Zr. 289, 51. ELVIUS,A. and HALL,J. S. (1966} .Lowell Obs. Bull. 6, 257. F]:s•Nxov, V. G. (1955) Astr. J. U.S.S.R. 82, 97. G~.HRELS,T. (1960) Lowell Obs. Bull. 4, 300. GEHRELS,T. (1966) Proe. I A U Symposium on Interstellar Grains, August 1965, at Rensselaer Polytechnic Institute, Troy, New York. GLIES~,W. and WALTER,K. (1951) Z/A 29, 300. GREE~BERG,J.M. (1964) IAU-Symposium 1~o.24, Spectral Classification and Multicolcur Photometry, p. 291. GREE~BERG,J. M. and ROARK,T. P. (1966) Proc. I A U Symposium ,m Interstellar Grains, August 1965, at Rensselaer Polytechnic Institute, Troy, New York. GREENSTEII~,J. L. (1938) Astrophys. J. 87, 581.

216

Reflection Nebulae and the Nature of Interstellar Grains

GREENSTEIN,J. L. and ALLER,L. H. (1957) P.A.S.P. 59, 139. GR~.~NSTEI~,J. L. and H~.NYEY,L. G. (1939) Astrolghys. J. 89, 647. GRYGAR,J. (1959) Aeta Univ. Carol. Set..Math. et Phys., 1. HALL, J. S. (1955) M~moires Li~e, ser. 4, 1~, 453. HALL, R. C. (1965) P.A.S.P. 77, 158. HE~rr~Y, L. G. (1936) Astrophys. J. 84, 609. H~.NYEY, L. G. and GEEENSTEIN,J. L. (1938) Astrophys. J. 88, 580. HENYv.y, L. G. and GREENST~I~,J. L. (1940) .Ann. d'Aph. 8, 117. HOYLV.,F. and WICX~MASING~, N. C. (1962) M.N. 124, 417. HOUTEN, VAN,C. J. (1961) B.A.N. 16, 509. HUBBLE, E. P. (1922) Astrophys. J. 56, 162, 400. HULST, VAN DE, H. C. (1957) Light Scattering on Small Parlivles, New York, John Wiley. IEVn~E, M. W. (1964) B.A.N. 17, 176. Jom~soN, H. M. (1960) P.A.S.P. 72, 10. KACm~TA~,E. (1957) Izve~iya A.N. Arm. SSR X, No. 5. KACHrKIAN,E. and P ~ s ~ , E. S. (1965) Soobsh. Byurakan 41, 38. KAPLAN,S. A. (1952) Astr. J. U.S.S.R. 19, 326. K~.ENAN, P. C. (1936) Astrot~hys. J. 84, 600. MARTEL,M. T. (1951) Publ. Obs. Haute-Provenee 2, 17. MARTEL,M. T. (1958) Ann. d'Aph. Suppl. No. 7. MINI~, I. N. (1962) Soviet Astr. A.J. 5, 487. 0'DELL, C. R. (1965) Astrol~hys. J. 142, 604. O'DELL, C. R. and HVBBARD,W. B. (1965) Astrophys. J. 142, 591. 0ORT, J. H. and HULST, VAN D~,, H. C. (1946) B.A.N. 1O, 187. P~RSAMIAN,E. S. (1962) Soobsh. Byuralcan 80, 57. PLATT, J. (1956) A~rol~hys. J. 128, 486. ROARK, T. P. (1966) Thesis, Rensselaer Polytechnic Institute, Troy, New York. ROZHKOVSKYI,D. A. (1960) Izv. Astr. Inst. Kaz. SSR 1O. ROZHKOVSKYLD. A. (1961a) Astr. J. U.S.S.R. 88, 278. ROZHXOVSKYI,D. A. (1961b) Izv. AsSr. lnst. Kaz. S.S.R. 18. SKAte, G. A., P~K~LN~R,S. B. and GAZe,B. F. (1954) Izv. Krym Ob. 1~. SCHAL~N,C. (1945) Ul~psata AsSr. Obs. Ann. 1, No. 9. SCHAL~ C. (1953) Uppsala AsSt. Obs. Ann. 8, No. 9. SOBOL~.V,V. V. (1960) Soviet Astr. A.J. 4, 1. VA~SEK, V. (1967) in print. VA~SEK, V. and SVATO~,J. (1964) Ac,ta Univ. Carol. Set. MaSh. et Phys. 1, 1. W~,STON,E. B. (1952) A . J . ~7, 28. W~CKR~M~Sn~GH:~,N. C. (1963) M.N. 126, 99.

Note. In addition, reference should be made to two recent relevant publications. The first of these is a discussion of the problem "dielectric versus metallic particles" by J. M. Greenberg and T. P. Roark (Ap. J. 147, 917, 1967). Some results of this investigation are already quoted in the present paper (Roark's Thesis). - The second publication here to be mentioned is due to K. S. Krishna-Swamy and C. R. O'Dell (Ap. J. 147, 937, 1967). Here, the normalized back scattering croes-sectinn (which is proportional to ~(~) for 180°) of various grain models is compared with the extrapolated colour differences for ~ ~ 180° in the Merope nebula. Good agreement is found for grains with a graphite core of 0.056 p and an ice-mantle of radius 0.19. This co-called "radar scattering" method must of course be interpreted with caution because of the serious problem involved in using extrapolations up to ~ = 180°, and the dependence of scattering c~oss-sections on the shape of the particles.