THE ANOMALOUS EXTINCTION LAW II. The Effect of Changing the Lower Size Cutoff of the Particle Size Distribution H. STEENMAN Academic Computing Services Amsterdam, Amsterdam, The Netherlands and P. S. THI~ Astronomical Institute "Anton Pannekoek', University of Amsterdam, Amsterdam, The Netherlands (Received 13 November, 1990) Abstract. In this paper we present further results of the calculation of anomalous extinction laws following Steenman and Th6 (1989). The extinction laws in this article are calculated by enlarging the lower size cutoff of the particle size distribution, as opposed to the laws in the previous paper, which were obtained by making the upper size cutoff larger. The extinction laws we have derived have three important properties: (1)the change in the infrared is similar as in the case of changing the upper size cutoff; the difference increases as the value of R becomes larger, (2) in the ultraviolet the 2200 A, bump disappears gradually as the lower size cutoffis made larger, (3) in the far-UV the extinction curves become more and more flat. The ultraviolet extinction laws in the direction of the stars HD 200775 and HD 259431 are lower than the Savage and Mathis (1979) galactic interstellar extinction law. 1. Introduction In Steenman and Th6 (1989, hereafter referred to as Paper I) we have described the calculation of anomalous extinction laws by enlarging the upper size cutoffof the particle size distribution. These calculations are based on the Mie theorie for spherical particles. The extinction efficiency, derived by applying the Mie theorie, is integrated over the size distribution of the particles which results in an extinction cross-section as function of wavelength (Equations (1) and (2), Paper I). In above mentioned paper we have published the values of Ax/A v as function of effective wavelengths of currently used photometric systems. Another result of our calculation in Paper I is, that, when the value of R = AJE(B - V) is made larger the deviations of the extinction laws in the UV around the 2200 ,~ bump are relatively small. This is shown tridimensionally in Figure 1. In order to visualize how these deviations actually are, we plot in Figure 2 the values [E(mo.22 - V)] R - [E(mo.22 - V)]3.1 versus R. We see that the differences first are positive, then approaching zero, and afterwards become positive again as R is made larger. From observational studies of the extinction law of several Herbig Ae/Be stars in the spectral region from the UV to the IR, it was found that, when the value of R becomes larger than 3.1, the UV extinction law of these type of stars, around the 2200 ,~ bump becomes significantly flatter than that of the normal extinction law (Th6 et al., 1981, Astrophysics and Space Science 184: 9-30, 1991. 1991 Kluwer Academic Publishers. Printed in Belgium.
Transcript
T H E A N O M A L O U S E X T I N C T I O N L A W
II. The Effect of Changing the Lower Size Cutoff of the Particle Size Distribution
H. S T E E N M A N
Academic Computing Services Amsterdam, Amsterdam, The Netherlands
and
P. S. THI~
Astronomical Institute "Anton Pannekoek', University of Amsterdam, Amsterdam, The Netherlands
(Received 13 November, 1990)
Abstract. In this paper we present further results of the calculation of anomalous extinction laws following Steenman and Th6 (1989). The extinction laws in this article are calculated by enlarging the lower size cutoff of the particle size distribution, as opposed to the laws in the previous paper, which were obtained by making the upper size cutoff larger. The extinction laws we have derived have three important properties: (1) the change in the infrared is similar as in the case of changing the upper size cutoff; the difference increases as the value of R becomes larger, (2) in the ultraviolet the 2200 A, bump disappears gradually as the lower size cutoffis made larger, (3) in the far-UV the extinction curves become more and more flat. The ultraviolet extinction laws in the direction of the stars HD 200775 and HD 259431 are lower than the Savage and Mathis (1979) galactic interstellar extinction law.
1. Introduction
In Steenman and Th6 (1989, hereafter referred to as Paper I) we have described the calculation of anomalous extinction laws by enlarging the upper size cutoffof the particle size distribution. These calculations are based on the Mie theorie for spherical particles. The extinction efficiency, derived by applying the Mie theorie, is integrated over the size distribution of the particles which results in an extinction cross-section as function of wavelength (Equations (1) and (2), Paper I). In above mentioned paper we have published the values of Ax/A v as function of effective wavelengths of currently used photometric systems.
Another result of our calculation in Paper I is, that, when the value of R = A J E ( B - V) is made larger the deviations of the extinction laws in the UV around the 2200 ,~ bump are relatively small. This is shown tridimensionally in Figure 1. In order to visualize how these deviations actually are, we plot in Figure 2 the values
[ E ( m o . 2 2 - V)] R - [ E ( m o . 2 2 - V)]3.1 versus R. We see that the differences first are positive, then approaching zero, and afterwards become positive again as R is made larger.
From observational studies of the extinction law of several Herbig Ae/Be stars in the spectral region from the UV to the IR, it was found that, when the value of R becomes larger than 3.1, the UV extinction law of these type of stars, around the 2200 ,~ bump becomes significantly flatter than that of the normal extinction law (Th6 et al., 1981,
Astrophysics and Space Science 184: 9-30, 1991. �9 1991 Kluwer Academic Publishers. Printed in Belgium.
l 0 H. S T E E N M A N A N D P, S THF"
1985; Sitko et al. , 1981 ; Hecht et al., 1984). In order to understand this behaviour we have tried to find out the effect of enlarging the lower size cutoff of the particle size distribution on the shape of the anomalous extinction curve. By doing this we in fact
Fig. 1. The tridimensional plot of the ratio E ( m o . 2 z - V ) / E ( B - V ) as function of2 1 for several R values in case the upper size cutoff a+ is enlarged. The circles indicate several points of the observed normal
extinction law of Savage and Mathis (1979).
Fig. 2.
Ii 0.8
>, 0.6
~' 0.4
0.2 >,
0.0
0
0 0
0 0
0
O 0
0 0 000
0 0
i I i
3 .0 4 .0 5.0
R The difference [ g ( m o . 2 2 - V ) ] R - [ E ( m o . 2 2 - V)]3 . l plotted versus R.
not only enlarged the average particle size, but, at the same time we also take away the influence of the very small particles (say about 0.01 gm) on the extinction law in the UV.
In the present paper we will show the results of the calculations of the extinction law when the lower size cutoff of the particle size distribution is enlarged from 0.005 pm
THE ANOMALOUS EXTINCTION LAW, II 11
upward. The upper size cutoff is held constant at 0.22 gm. These results will be compared (1) with those of Paper I, and (2) qualitatively with the observed extinction laws obtained using ANS data and/or IUE spectra, and published visual and near-IR photometric observations of two Herbig Ae/Be stars.
2. Derivation of the Anomalous Extinction Laws
The theoretical extinction laws are derived using exactly the same procedure as described in Paper I, except that it is now the lower size cutoff that will be enlarged. Again we use the dielectric functions for both graphite and silicate published by Draine (1985). Following Mathis et aL (1977, hereafter referred to as MRN) the size distribu- tion for both particle specimen will be taken as n(a) ~ a -35. Similar as in Paper I we will study the case in which the lower size cutoff for both materials is changed. Application of the standard Mie theory (Equation (1), Paper I) results in the extinction efficiency Qext(a, 2). Averaging this quantity over the particle size distribution we obtain the mean cross-section for extinction Ce• ) (Equation (2), Paper I) to be given by
Cext()~) = ( Qex t ( a , }0rca2> =
a +
~.i f Q~xt(a, 2)rca2n,(a) da a
a+
i f ni(a ) da a _
(1)
where a+ and a represent the upper and lower size cutoff of the particle size distribu- tion, respectively. The extinction in magnitudes for a certain wavelength 2 can then be written as
A m z = 1 .086Cext(J~ ) (2 )
(Spitzer, 1978). We will give the extinction laws either as Ax/A v or as E(ma - V)/E(B - V) for effective wavelengths of currently used photometric systems. In terms of the extinction cross-section these quantities can be written as
A~_ Cext (m,0
A~ C~xt(V ) (3)
o r a s
E(m z - V ) _ C c = ( m ~ ) - Cext(V)
E(B - V) C~dB) -Co~(V) (4)
In Table I the extinction laws Aa/A v are given for different R-values. For comparison with observational results published by other authors a presentation of the anomalous
12 H. STEENMAN AND P, S. THI ~
TABLE I
Extinction laws A,~/Av for different R values, calculated by changing the lower size cutoff. The upper size cutoff is held constant at 0.22 ~tm.
is larger than that for the upper size cutoff (filled circles). This is understandable from the adopted form of the size distribution function: n(a) ~ a - 3.5. There are more small
particles than large ones. In Figure 4 we show the relation between R = E ( V - m2ooo)/E(B - V ) and the lower
size cutoff of the particle size distributon. As can be seen up to a particle size of about 0.1 gm (20 times the initial value of 0.005 ~tm) R is continuously increasing.
In Figure 5 we s h o w the re la t ion b e t w e e n E(mo.22 - V ) / E ( B - V ) a n d the lower size
cutoff. W e can clearly see tha t the 2200 ~ b u m p gradua l ly v a n i s h e s wi th inc reas ing a .
In F igure 6 a s a m p l e o f the ca lcu la ted ex t inc t ion laws for 3.04 _< R < 6.0 is s h o w n .
T h e s e laws are p r e s e n t e d as E ( m x - V ) / E ( B - V ) as func t ion o f 2 - 1. Severa l o f the
ex t inc t ion l aws are s h o w n en la rged for only the 2200 ]~ region in F igure 7. Severa l curves
are labeled wi th the e m p l o y e d value o f R. N o t e tha t the f la t tening o f the 2200 ~_ b u m p
18 H. STEENMAN AND P, S. THFz
Fig. 3.
:L
A
V
0.i0
0.08
0.06
0.04
0.02
0
0
0
0 0
0
O O O
O
I i
3.8 4.6 R
The results for the average values ( a ) plotted against the corresponding R values.
Fig. 4.
>
C~
g
i
>
7.0
6.0
5.0
4.0
3.0
I I I L I
I I 1 I I
0.02 0.04 0.06 0.08 0.10
a am
The relation between the ratio R = E(V- m 2 o o o ) / E ( B - V) versus the lower-size cutoff a .
occurs already at very small changes of a_ . Figure 8 shows the infrared part of the
extinction curves in terms ofE(V - rnx)/E(B - V) as function of 2 - t, for 3.1 -< R < 6.0. Comparing the results obtained by changing the lower size cutoff of the particle size
distribution with the ones obtained by changing that of the upper size cutoff, we plotted
in Figure 9 the difference between the laws in the near- and far-infrared part of the energy spectrum for laws with values ofR = 3.3, 3.5, and 4.1, respectively. As can be seen the
difference increases with increasing R. This can be explained by the change in shape
of the theoretical laws.obtained by enlarging the upper size cutoff (see Paper I).
T H E A N O M A L O U S E X T I N C T I O N L A W , I1 19
Fig. 5.
6.0 >
I
5.0
>. 4.0 �88
3.0
2.0
I I 1
I I I
0.02 0.04 0.06
a p,m
The relation between the ratio E ( m o . 2 2 - V ) / E ( B - V ) and lower size cutoff a .
4. Comparison with Observations
I t is o f in teres t to c o m p a r e our theore t ica l ex t inc t ion laws for R = 3.1 wi th tha t ob t a ined
by S a v a g e and M a t h i s (1979), which is ind ica ted by circles in F igures 6, 7, and 8, T h e
ag reemen t in the inf rared is quite good. Dev i a t i ons begin to appea r at wave leng ths
I L I L 1 1 I
6 .0
4-,0
, .0
I< 0.0
--4-.0
! , !
1 2 3 ~- 5 6 7
Fig. 6. The relation ofE(V - m~,) /E(B - V ) as function of 2- ~ for different values of the lower size cutoff 3.04 _< R < 6.0. As can be seen the shape of the theoretical extinction laws change over the whole wavelength range. The circles indicate several points of the observed normal extinction law of Savage m~d Mathis
(1979).
20 H. STEENMAN AND P. S. THt~
Fig. 7.
I I i i I I I I
| /5-,:3~ b /L\ff--a"
5.0
4-.0
3.0
3 3.5 a- 4-.5 5 5.5 6 ~-1 /zm-1
The same as in Figure 6, but now only for the '2200 A. bump' region shown enlarged. Several curves are labeled with the employed value of R.
shorter than the effective wavelength of the B pass-band, in the sense that the theoretical extinction is larger than observed. The same deviations also appear in the case of the
theoretical extinction laws obtained by increasing only the upper size cutoff of the
particle size distribution (see Paper I). Furthermore, the maximum of the bump is
situated at a wavelength somewhat shorter than 2175 A. Note, however, that the fit with the 2200 A bump as observed by Savage and Mathis (1979) is much better for a
theoretical curve obtained by a small change in the lower size cutoff, 0.007 instead of 0.005 gm. The R-value of this curve is 3.12. What remains is the discrepancy at 2 . 5 < 2 - 1 < 4 . 0 .
In the study of the UV extinction law, normalization is often not taken at the
effective wavelength of the V pass-band, but at a wavelength more towards the UV, for instance at 0.286 ~tm (2- 1 = 3.5) (Boggs and B6hm-Vitense, 1989). In Figure 10
we show the calculated UV extinction curves normalized at 2 = 0.286 rtm, as
E ( m x - mo.286)/E(B- V) versus 2-1. From this figure it is clear that due to this normalization the galactic extinction law (R = 3.1) as derived by Savage and Mathis (1979) apparently agrees between 3.5 < Z 1 < 4.3 with the calculated one, but deviates much fo r2 1>4 .5 .
A direct comparison with observations can also be obtained by checking the obser- vational relation between R and the ratio of the colour excesses E(V - K) and E(B - V)
R = 1 . I E ( V - K ) / E ( B - V)) (6)
(Whittet et al., 1976; Vrba and Rydgren, 1984). In this relation K is the near-infrared pass-band at 2.2 gm. In Figure 11 above relation is shown by the line, and the theoretical
THE -~NOMALOUS EXTINCTION LAW, I[ 21
4..5
4..0
3.5
3.0 I
~.5 I
2.0
1.5
1.0
0.5
Fig. 8.
2 . 3 2.1 1.~ 1.7 1.s 1.3 1.1 o . g 0.7 o . 5 0.~ X -1 ~ r n -~
The same as in Figure 6, but now only the infrared part , of the extinction curve~ are shown for
2.1 <_R<6.0.
one by the open circles. The agreement between the theoretical and the observational results is very good. This is not the case with the extinction laws obtained by increasing the upper size cutoff of the particle size distribution (see Paper I, Figure 5).
We have also compared our theoretical calculations with observational results by Th6 and Groot (1983) and Chini (t981). As is shown in Figures 12(a-c) for R = 3.6, 4.1, and 4.4, respectively, the agreements are quite good, considering the observational errors.
5. Comparison with the Observed UV Extinction
As is mentioned in the Introduction, the main purpose of this study is to explain qualitatively the abnormal behaviour of the observed extinction laws of Herbig Ae/Be stars, especially in the ultraviolet region of the energy spectrum. First we will show the observed spectral energy distribution (SED) of the programme stars from the UV up to the infrared, and the extinction free SED corrected for normal extinction (R = 3.1) using the data of Savage and Mathis (1979). The latter is then compared to the
2 2 H , S T E E N M A N A N D P , S . T H I ~
~<
0.06
0.04
0.02
0.00
I, A A
A A A
A
$ DDD �9 D �9 3: l~ A 5 A
~ l 0 0 0 0 0 0 0 0 0 BD o o 3.3 o
o
L I I
0.5 1.0 1.5
k 1 am-i
I 2.0
Fig. 9. The difference A ( A a / A ~ ) for the extinction laws o fR = 3.3, 3.5, and 4,1, obtained by changing the lower size cutoff and those calculated by enlarging the upper size cutoff of the particle size distribution.
Fig. 10.
I [ 1 I 1 I I
4-.0
3.0 ? o 2.0
0.0
3.5 4- 4-.5 5 5,5 6
k -1/_zm -1
The calculated UV extinction law normalised at 2 = 0.286 pm (2 l = 3.5), expressed as E ( m a - mo.2~6) /E(B - V ) , plotted versus )~- 1.
theoretical Kurucz (1979) model for the same Tea and log g as those of the star. In case the extinction law in the direction of the star is normal, good agreement will be the result. However, when this law is anomalous, the extinction-fi'ee SED will deviate from the Kurucz model, more or less, according to the amount of abnormality.
The extinction law in the UV is derived by direct comparison of the UV data
THE ANOMAf_OLJS EXTINCTION LAW, U 23
6.0
I I I
5.0
4.0
3.0
3.5 4.5 5.5
E(V- K)/E(B-V)
Fig. 11. The relation of R as function ofE(V - K)/E(B - V) derived from our theoretical extinction curves. The line represents the empirical relation 0fR = 1.1E(V - K)/E(B - V). K is the near-infrared pass-band
at 2.2 gin.
(spectroscopic and/or photometric) of the star to the Kurucz model. The result is then plotted over the theoretically calculated UV extinction laws, in the same figure. From
this figure we can see qualitatively the amount of abnormality of the UV extinction law in the direction of the star.
The observational data in the UV are taken from the IUE data-bank and/or the ANS
catalogue (Wesselius et al. , 1982). The far-IR data are taken from the I R A S P o i n t Source
Catalogue , whereas the data in between come from different sources in the literature. Below we will describe the results of our study for two Herbig Ae/Be stars.
5.1. H D 200775 = MWC 361
This star has been observed in the visual by many authors. The earliest by Racine (1968)
and the latest by Bergner et al. (1985). The V magnitude varies from 7'7.39 in 1968 to
7'7.53 in 1984, although Pogodin (1985) obtained V = 7~3 for this star in 1982. Since H D 200775 is a Herbig Be star of spectral type B5e (Racine, 1968) we do not, indeed, expect large variations in the V magnitude (Bibo and Th+, 1991). Johnson R and I
magnitudes were observed by Bergner et al. (1985). Near-infrared magnitudes were obtained by several authors: Milkey and Dyck (1973), Allen (1973), Altamore e t a l .
(1980), Lorenzetti et al. (1983), Bergner et al. (1985); Pogodin (1985), and Berrilli et al.
(1987). In the ultraviolet IUE spectra are also available (we have used LWR 5178 and SWP 5967). Furthermore, H D 200775 was observed by IRAS in the far-infrared spectral region.
In Figure 13(a) we have plotted the observed SED of H D 200775 based on the available data in the literature. In the same figure we have shown the extinction free SED corrected with a ratio of total to selective extinction R = 3.10 and E ( B - V) = 0~63.
24
>
1.2
0.8
0.4
H. STEENMAN AND P. S. THI~
R=3.6
1.0 2.0
)-1 gm.1
1,2
0.8 .<
0.4
R=4.1
1.0 2.0
~-i gm.1
R= 4.4
1.2
-~ 0,s <
0.4
L0 2,0
k -I grn-1
Fig. 12. Comparison of the theoretical extinction laws for different R values with observational ones: (a) with that of Th6 and Groot (1983) for R = 3.6, (b)with that of the same authors and of Chini (1981)
for R = 4.1, and (c)with that of Th6 and Groot (1983) for R = 4.4.
The corresponding galactic extinction law for this R-value is taken from Savage and
Mathis (1979). A Kurucz (1979)theoret ical SED for Tee ~ = 20 000 K and log g = 4.0 is
fitted to the visual region of the spectrum. It is immediately clear that there is an
over-correct ion of the extinction free SED in the UV spectral region a round 2200 A.
In order to suppress the overcorrect ion we have to apply an extinction law
character ized by a larger R-value (R = 3.2). The extinction values for R = 3.2 are
T H E A N O M A L O U S E X t i N C T I O N L A W , I[ 25
-7.70
-&40
-9~0
-9.80
-10.50
- 1 1 . 2 0
- 1 L I t O
- I ? . 6 0
-L .%30
i i i 1 J i 1 i i t
- , I - [ D 2 0 0 ' 7 7 5
P T r I i r I i I I
-0.8 --0.4 0.0 (14- 0.8
k~g X (~m)
r i l l
~ ~ 0
Fig. 13a_ The spectral energy distribution (SED) of liD 200775. The lower plot gives the observed SED, the upper one the extinction-free SED corrected with R = 3.10 and E(B - V) = 0m63. The last mentioned plot is compared with a Kurucz theoretical model with Tel r = 20000 K and logg = 4.0. Note the over-
correction in the neighbourhood of the 2200 h bump.
theoretically calculated and given in Table I. We have chosen this R-value so that the
extinction free SED of HD 200775 fits the Kurucz theoretical model as well as possible
over the whole spectral range from the ultraviolet to the J pass-band in the near IR (see Figure 13(b)).
By demanding that the fit of the extinction-free SED and the theoretical Kurucz SED
must be almost perfect, we can derive the UV extinction law in the direction of
HD 200775. Such an extinction law can be compared with the calculated laws as
described in this paper. This comparison is shown in Figure 14. In this figure the circles represent the average galactic UV extinction law published by Savage and Mathis
(1979). It is clear that the observed extinction law for HD 200775 is lower than that of
Savage and Mathis, which means that in the direction of this Herbig Be star there is
a depletion of very small particles (about 0.01 gm) especially of graphite (see also Sitko et al., 1981).
5.2. HD 259431 = MWC 147
This Herbig Be star (Sp. T. B6pe; V ~ 8~!~7) has also been observed by many authors.
As can be seen from the literature this star does not show large visual magnitude changes
from 1971 to 1985. Since the star is of spectral type earlier than A0 this is to be expected from the study of the variability of Herbig Ae/Be stars made by Bibo and Th6 (1991).
26 H. STEENMAN AND P. S. THI~
Fig. 13b.
I I i 1 I 5 1 ~ 1 1
-~~ I4Z)200775
-&.CO
- 9 1 0
-i0.50
~'< -11.20
-11.90
-i~.50 ~
-13-30
i I i I I i I F I l
-43.8 . --0.4 0.0 0.4- 0/3
log x 0zm)
I t I I
12 1-6 ZO
The same as in Figure 13(a), except that the R-value is taken to be 3.20. In this case the extinction-free SED agrees at the 2200 ,~ bump quite well with the Kurucz model.
I I l I
3 . 5 - H I )200775
3 -
>.
2 .5 - ..< %.
2 -
1.5
i [ T i
3 4 5 6
k -1 / / , in -J-
Fig. 14. A comparison of the extinction law observed in the direction of HD 200775, with the theoretical laws studied in the present paper. The circles represent the Savage and Mathis (1979) galactic interstellar
extinction taw. The observed extinction law for HD 200775 is lower than that of the galactic law.
T H E A N O M A L O U S E X T I N C T I O N L A W , I I 27
In the visual and near-IR HD 259431 has been observed by Strom etal . (1972), Kilkenny et aL (1985), Herbst et al. (1982), Giltett and Stein (t97 t), Allen (1973), Berrilli et al. (1987). In the UV, observations by ANS and IUE (LWR 5629) are available. Also IRAS has observed this star in the far-IR spectral region.
In Figure 15(a) we show a plot of the observed SED of HD 259431 based on data available in the literature. We show in this figure also the extinction-free SED calculated
- 8 . 6
- 9 2 ,
- 9 + 8
-10.4
-21,0
y -1s
-12B
- l & 4
HD259431
+ I I + P , + r r I u T P r
--0.4 0+0 0.4 O~ 12 1+8 2-0
logX ( ~
Fig. 15a. The same as in Figure 13(a), but now for HD 259431. The extinction-free SED for this star is
obtained with R = 3.10 and E(B - V) = 0. m51. In this case we also observe an over-correction at the 2200
bump.
using the average galactic extinction of Savage and Mathis (1979), R = 3.1 and E ( B - V) = 0.51, and fits this SED in the visual to a Kurucz (1979) theoretical SED for Tel r = 20000 K and logg -- 4.0. Like in the case of HD 200775, here there is also an overcorrection of the UV SED in the neighbourhood of the 2200 }i bump. To obtain a best fit to the Kumcz model, the observed SED of HD 259431 should be corrected with an extinction law characterized by R = 3.25 taken from Table I (see Figure 15(b)).
If the UV SED of HD 259431 should completely fit the Kurucz model, then we can calculate an extinction law as shown in Figure 16, and compare it to the theoretical
extinction laws. Again, there is most probably a depletion of very small particles (about 0.01 gin) in the direction of HD 259431. This conclusion has also been drawn by Sitko et al. (1981) in their ultraviolet study of hot stars with circumstellar dust. These authors have also suggested several mechanisms which are possibly causing this depletion.
28 H. STEENMAN AND P. S. THE
Fig. 15b.
--8.8
-92
-9/3
~'~ -10.4
--~ -110
~O ~ -11.6
-122
-12.8
-18.4
HDE59431 I
I
I l i I p r r I I
-0.4 0.0 0.4 0-8
logx (urn) p i r I P
1.2 1.8 2.0
The same as in Figure 15(a) except that the R-value is taken to be 3.25. The extinction-free SED then agrees well with the Kurucz model.
Fig. 16.
I I I I
HD259431 3 .5 -
3 -
I>
2 .5 - ~ A
2 -
1.5
X
I I 1 I
3 4- 5 6
>-1/zm-t The same as in Figure 14 for the star HD 259431. The same conclusion can also be drawn. The
triangles represent ANS observations.
THE ANOMALOUS EXTINCTION LAW, I1 29
6. Conclusions
In this paper we show: (1) That the change of the extinction law in the infrared by enlarging the lower size
cutoff of the size distribution of the particles is similar as in the case of changing the upper size cutoff. The difference increases as the value of R becomes larger.
(2) That anomalous extinction in the IR and UV region of the energy spectrum can simultaneously be caused by a depletion of very small particles, especially graphite, of about 0.01 gm in diameter. The reason is that such a depletion not only enlarge the average size of the dust particles, but, at the same time also takes away the influence of very small particles on the extinction law in the UV.
(3) That the anomalous extinction mentioned above is characterized by a larger value of the ratio of total to selective extinction in the infrared and a disappearance of the 2200 ~ bump in the ultraviolet. Furthermore, in the far-UV region of the spectrum the extinction law becomes more and more fiat.
(4) This result has been compared with observations in the near-IR and in the UV. From this comparison the conclusion is drawn that qualitatively our theoretical results do not disagree with observations.
It should be stressed here that the agreement in the UV between theory and observa- tions is only qualitatively. It is planned to study the UV extinction law in the direction of Herbig Ae/Be stars more extensively by considering also the variation in the abun- dances of the different constituents which are responsible for the UV extinction.
References
Allen, D. A.: 1973, Monthly Notices Roy. Astron. Soc. 161, 145. Altamore, A., Baratta, G. B., Cassatella, A., Grasdalen, G. L., Persi, P., and Viotti, R.: 1980, Astron.
Astrophys. 90, 290. Bergner, Yu. K., Miroshnichenko, A. S., Yudin, R. V., Yutanov, N. Yu., Kuratov, K. S., and Mukanov, D.
B.: 1985, Astron. Tsirk. 1396, 1. Berrilli, F., Lorenzetti, D , Saraceno, P., and Strafella, F.: 1987, Monthly Notices Roy. Astron. Soc. 228, 833. Bibo, E. and Thr, P. S.: 1990, Astron. Astrophys. Suppl. Ser. (in press). Boggs, D. and Brhm-Vitense, E.: 1989, Astrophys. J. 339, 209. Chini, R.: 1981, Astron. Astrophys. 99, 346. Draine, B. T.: 1985, Astrophys. J. Suppl. Ser. 57, 587. Gillett, F. C. and Stein, W. A.: 1971, Astrophys. J. 164, 77. Hecht, J. H., Hohn, A. V., Ake III, T. B., and Imhoff, C. L.: 1984, Future of Ultraviolet Astronomy Based on
Six Years of lUE Research, NASA Conference Publication 2349, p. 318. Herbst, W., Miller, D. P., Warner, J. W., and Herzog, A.: 1982, Astron. J. 87, 98. Kilkenny, D., Whittet, D. C. B., Davies, J. K., Evans, A., Bode, M. F., Robson, E. I., and Banfield, R. M.:
1985, South African Astron. Obs. Circ. 1, 55. Kurucz, R. L: 1979, Astrophys. J. Suppl. Ser. 40, l. Lerenzetti, D., Saraceno, P., and Strafella, F.: 1983, Astrophys. J. 264, 554. Mathis, J. S., Rumpl, W., and Nordsieck, K. H.: 1977, Astrophys. J. 217, 425. Milkey, R. W. and Dyck, H. M.: 1973, Astrophys. J. 181, 833. Pogodin, M. A.: 1985, Soviet Astron. 29, 531. Racine, R.: 1968, Astron. J. 73, 233. Savage, B. D. and Ma_this, J. S.: 1979, Ann. Rev. Astron. Astrophys. 17, 73. Sitko, M. L., Savage, B. D., and Maeder, M. R.: 1981, Astrophys. J. 246, 161.
30 H. STEENMAN AND P, S. -FHE
Spitzer, L.: 1978, Physical Processes in the Interstellar Medium, John Wiley, New York. Steenman, H. and The, P. S.: 1989, Astrophys. Space Sci. 159, 189. Strom, S. E., Strom, K. M., and Yost, J.: 1972, Astrophys. J. 173, 353. Th6, P. S. and Groot, M.: 1983, Astron. Astrophys. 125, 75. Th6, P. S., Felenbok, P., Cuypers, H., and Tjin A Djie, H. R. E.: 1985, Astron. Astrophys. 149, 429. Th6, P. S., Tjin A Djie, H. R. E., Bakker, R., Bastiaansen, P. A., Burger, M., Cassatella, A., Fredga, K.
Gahm, G., Liseau, R., Smyth, M. J., Viotti, R., Wamsteker, W., and Zeuge, W.: 1981, Astron. Astrophys. Suppl. Ser. 44, 451.
Vrba, F. J. and Rydgren, A. E.: 1984, Astrophys. J. 283, 123. Wesselius, P. R., van Duinen, R. J., de Jonge, A. R. W., Aalders, J. W. G., Luinge, W., and Wildeman, K.
J.: 1982, Astron. Astrophys. Suppl. Ser. 49, 427. Whittet, D. C. B., van Breda, I, G., and Glass, I. S.: 1976, Monthly Notices Roy. Astron. Soc. 177, 625.
