t
70-26,253
BOTTEMILLER, Robert Leland, 1942- A STUDY OF INTRINSIC POLARIZATION IN Be STARS.
The Ohio State University, Ph.D., 1970 Astronomy
University Microfilms, A XEROX Company, Ann Arbor, Michigani
TWTR nTRRFBTATTnW HAS PFFN MTrRnTTT.MFn FVAfTT-Y AS RFTIFTVFT1 A STUDY OF INTRINSIC POLARIZATION
IN Be STARS
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By
Robert Leland Bottemiller, B.S., B.S.
A A * A A A
The Ohio State University 1970
Approved by
lfff.tr *a 'f K ' — I Adviser Department of Astronomy ACKNOWLEDGMENTS
Gratitude is extended to Dr. George W. Collins, II, who suggested this research problem and who contributed many beneficial ideas throughout the pursuit of this work.
Thanks also go to Drs. Robert F. Wing and Terry P. Roark who made a number of suggestions which increased the clar
ity and accuracy of this dissertation.
All observations were made using the Perkins reflector of the Ohio Wesleyan and Ohio State Universities at Lowell
Observatory. The author is indebted to these institutions
for the use of their facilities, and special thanks go to
Dr. John S. Hall, Director of Lowell Observatory, for the
use of his polarimeter and for hospitality extended to the
author during his visits to Lowell Observatory. The Com puter Center of The Ohio State University is also to be
thanked for the allotment of machine time necessary for
data reduction. This work was initiated while the author
held a Traineeship from the National Science Foundation
whose support is appreciated.
Last mentioned, but foremost, is the love and grati
tude felt for the author's wife for her encouragement
through several years of study and for her perseverance
through several months of thesis preparation and typing.
i i VITA
August 14, 1942 . . . Born - Portland, Oregon
1964 ...... B.S. (Mathematics), University of Portland, Portland, Oregon
1965 ...... B.S. (Physics), University of Portland, Portland, Oregon
1966-1967 ...... Teaching Assistant, Department of Astronomy, The Ohio State University, Columbus, Ohio
1967-1968 ...... Research Assistant, Department of Astronomy, The Ohio State University, Columbus, Ohio
1968-1969 ...... National Science Foundation Trainee
PUBLICATIONS
"HD 191980 A Peculiar B-Type Star," P. C. Keenan, A. Slettebak, and R. L. Bottemiller, Astrophysical Letters, Vol. 3, page 55, 1969.
FIELDS OF STUDY
Major Field: Astronomy
Studies in Late Type Stars. Professor Philip C. Keenan
Studies in Radiative Transfer. Associate Professors George W. Collins, II, and Eugene R. Capriotti
Studies in Molecular Dissociation Equilibria. Assistant Professor Robert F. Wing TABLE OF CONTENTS Page ACKNOWLEDGMENTS ...... ii
VITA ...... i ii
LIST OF T A B L E S ...... v
LIST OF F I G U R E S ...... vii
Chapt er
I. INTRODUCTION ...... 1
II. OBSERVATIONAL PRELIMINARIES ...... 9
Program Systems Single and Double Standard Stars Equipment
III. DATA REDUCTION AND ERROR ANALYSIS OF OBSERVATIONS ...... 22
Data Reduction Error Analysis Intrinsic Polarization
IV. OBSERVATIONAL RESULTS: STANDARD STARS . . . 38
V. OBSERVATIONAL RESULTS: PROGRAM STARS .... 60
VI. INTERPRETATION OF RESULTS ...... 90
APPENDIX
A ...... 101
B ...... 109
BIBLIOGRAPHY ...... 115
iv LIST OF TABLES
Double Star Systems ...... 12
Standard Single Stars ...... 15
Standard Double Star Systems ...... 15
Comparison with Other Observers ...... 59
Standard Stars with Published Stokes Parameters ...... 47
Estimate of Instrumental Polarization . . . 48
Polarization Data: Standard Single Stars . 56
Calculated Intrinsic Polarization: Standard Double Stars ...... 58
23 Orionis: U ...... 61
23 Orionis: B ...... 61
23 Orionis: V ...... * . . 62
HD 4 599 5: U ...... 66
HD 45995: B...... 66
HD 45995: V ...... 67
59 Cygni ...... 68
e Capricorni ...... 69
8 Lacertae: U ...... 71
8 Lacertae: B ...... 71
8 Lacertae: V...... 72
v LIST OF TABLES--Continued
Table Page
20. 8 M o n ...... 74
21. 8 Mon: Intrinsic Polarizations...... 76
22. Summary of Polarimetric D a t a ...... 78
23. Fractional Breakup Velocities for Program Stars ...... 85
vi LIST OF ILLUSTRATIONS
Figure Page
1 . Idealized Scan Records of a Typical Program Double System and g M o n ...... 24
2 . Summary of Observational Data for Standard HD 154445 43
3. The Deviation of Individual Polarization Observations from the Mean Quantity Versus Night of Observation ...... 51
4 . Observed Stokes Parameters (U Filter) of Low Polarization Objects ...... 52
5. Observed Stokes Parameters (B Filter) of Low Polarization Objects ...... 53
6 . Observed Stokes Parameters (V Filter) of Low Polarization Objects ...... 54
7. Summary of Results for Single Star Standards...... 57
8 . Results for e Cap A and Comparison with Other Observers...... 70
9. Derived Intrinsic Polarizations for the Seven Program S t a r s ...... 79
10. Derived Intrinsic Polarization Against the Ratio of V sin (i) to Theoretical Breakup Velocity for U Filter Observations ...... 86
11. Derived Intrinsic Polarization Against the Ratio of V sin (i) to Theoretical Breakup Velocity for B Filter Observations ...... 87
12. Derived Intrinsic Polarization Against the Ratio of V sin (i) to Theoretical Breakup Velocity for V Filter Observations ...... 88
vi i LIST OF ILLUSTRATIONS--Continued
Figure Page
13. Average Normalized Polarization from Coyne and Kruszewski (1969) and the Same for Derived Intrinsic Polarization from This Research Versus Inverse Wavelength...... 94
vi i i I. INTRODUCTION
The possibility that early type stars may exhibit intrinsic polarization is an idea that, for much of its
24-year history, has been neglected in favor of the pheno menon of interstellar polarization discovered so serendi- pitously by researchers looking for intrinsic polarization.
Chandrasekhar (1946) first demonstrated the possible existence of the effect. He calculated the transport of radiation for a semi - infinite, p 1ane-paral1 el atmosphere where such transport is governed solely by the scattering due to free electrons. By allowing for the polarizing effect of the scattering process on the radiation field, he was able to derive a polarization for the emergent light at the stellar limb of some 11 per cent.
Since electron scattering plays an important role in the opacity of early type stars, Chandrasekhar suggested the observation of eclipsing binaries with such primaries near the time of deepest minimum as a test of his results.
The first subsequent attempts at this were made photo graphically with ambiguous results of low accuracy (Janssen,
1946; Hiltner, 1947). Much better accuracy was deemed necessary since masking effects by the eclipsing star 2 reduced the predicted polarization, in the example of RY
Persei, from 11 per cent to 1.2 per cent (Hiltner, 1949).
During this period, Hall (1949) had been building a photoelectric polarimeter at Amherst College and made contact with Hiltner which led to initial observations at the 82-inch telescope of the McDonald Observatory of the
University of Texas in the summer of 1947.
Although there were "no dependable results" (Hiltner,
1949), at least some evidence of polarization in the light of the Wolf-Rayet eclipsing binary CQ Cephei was obtained
(Hall, 1949). Improvements in Hall's apparatus made polarization easily measurable in CQ Cephei the following summer at Amherst and no dependence on the light curve phase was discernible. He soon moved to the United States
Naval Observatory, and observations made with the 40-inch telescope in Washington from November, 1948, to January,
1949, culminated in Hall's 1949 results for nearly thirty stars.
By the summer of 1948, Hiltner's own photoelectric polarimeter was complete and observations were underway.
Data obtained at the McDonald and Lick Observatories also showed measurable polarization for CQ Cephei, independent of phase, and for other stars as well.
The unexpected conclusion was that the polarization was introduced not in the stellar atmosphere but during the photons' traversal of the interstellar medium 3
(Hiltner, 1949). Hall's report also showed a rough corre lation with color excess.
This discovery raised many questions yet to be fully answered and at the same time opened an entirely new means of probing the characteristics of the interstellar medium.
One question that was seemingly laid to rest was that of
Chandrasekhar's original prediction. The total lack of time variation in the polarization of the observed binaries meant that the phenomenon, if it existed, was much smaller than originally thought.
A major difference between Chandrasekhar's computa tion and the actual situation in early type stars is that the opacity is due to absorption as well as scattering.
Code (1950) reformulated the transfer problem to allow for both pure absorption and pure scattering. One of his results was that the amount of polarization at the limb dropped nearly linearly from 11 per cent to nothing as the scattering component of the opacity was varied from
100 per cent to zero. For equal amounts of scattering and absorption, the degree of polarization is 4.8 per cent.
The net polarization of the integrated light from an evenly illuminated, symmetrical stellar disk would be zero and, in the case of eclipsing systems, the masking effect mentioned by Hiltner would seem to preclude the observation of any intrinsic polarization. 4
Over the next few years, theoretical work in this area centered on the physics of the interstellar medium while observers amassed more data on this new phenomenon.
Hall and Mikesell (1950) published the results of obser vations of 551 stars. Hiltner (1951) soon thereafter
reported data on 841 objects, 228 of which were common
to Hall and Mikesell. More extensive catalogs were pro duced by Hiltner (1956), including UBV colors and spectral types as well as polarimetric information on 1,259 stars, and by Hall (1958). The latter includes 1,455 stars observed by Hall plus data from Hiltner and Smith (1956)
for a total of 2,592 objects.
These compilations, together with Behr’s (1959)
catalog of observations of about 500 nearby stars, make up the most extensive set of observational material
available at the present time.
A number of other observers have conducted polariza
tion programs with various specific aims in mind, for
example, Schmidt’s (1958) data on 31 Cepheids, Loden's
surveys in several Kapteyn Selected Areas (1961a, b), and
the lengthy series begun in 1960 on the wavelength depen
dence of polarization, primarily by Coyne and Gehrels.
Behr (1959) remarked, in a footnote to the tabulation
of data, that there was a suspicion of variability in his
observations of y Cas (BOIV e). This was the first public
notice that variable polarization did perhaps actually 5
exist. Soon thereafter, Shakhovskoi (1962) reported
observations of variable polarization for x Oph (B2III pe).
Since these groundbreaking results, several more emission-
line B stars have been observed to have varying polariza
tion (Coyne and Gehrels, 1967 ; Serkowski , 1968 ; Kruszewski
and Coyne, 1969).
It should be noted that of the numerous observations
of 0 and B stars, only those with some specific peculiar
ities have indicated time variations or an unusual wave
length dependence of polarization (Serkowski, 1968). For
example, Y Cas is a Be star, x Ophiuchi is a nova-like variable, B Lyrae (Appenzeller and Hiltner, 1967) is an
eclipsing binary with a B8 supergiant primary, T Pyxidis
is a recurrent nova (Eggen, et al, 1967) -- the latter
two showing unusual wavelength dependence rather than time
variation -- and several other cases refer to B super
giants (Ha in emission) and Be stars.
A common property of these objects is evidence of
considerable material above the stellar atmosphere due
to eruptions, binary tidal forces, or rapid rotation.
Of the ten stars listed by Coyne and Kruszewski (1969)
as either definite or suspected polarization variables,
seven have V sin (i)'s between 210 and 560 km/sec. The
other three include X Oph, mentioned above, u Sagitarii,
a hydrogen-poor eclipsing binary (Sahade, 1969) exhibiting
large-scale atmospheric motions (Huang and Struve, 1960), and "Aquarii which shows double emission lines of varying
intensity.
Also of considerable interest is the fact that a number of late type supergiants have shown non-constant polarization (see, for example, Kruszewski and Gehrels,
1968, and Dyck, 1968). These are objects in which
scattering may also play a large role in the overall opacity; in this case Rayleigh scattering by molecules or perhaps by graphite particles (Harrington, 1969).
In a series of papers (Collins, 1963, 1965; Collins
and Harrington, 1966) investigating the effect of rapid
rotation on the atmospheres of B stars, Harrington and
Collins (1968) extended Chandrasekhar's pure scattering, plane-parallel formulation to include the effects of
gravity darkening, limb darkening, rotational distortion,
and aspect on the observed stellar flux. The lack of
spherical symmetry and the presence of gravitationally
darkened equatorial regions lead to non-zero polarization
for the integrated light of the star. The amount depends
on the angle of inclination to the line of sight as well
as how close to the breakup velocity the star is rotating
but a maximum figure of 1.7 per cent was computed.
In defining observational tests of intrinsic polar
ization, one is faced with the interference of the irregu
lar but nearly universal, interstellar polarization.
Harrington and Collins put forth several possible tests, 7 one of which is the motivation and basis for this disser tation. It entails the observation of visual binary systems with one member a Be star of high V sin (i) and the other just about any other type as long as it is a sharp-lined object, i.e., of low V sin (i). The com panion provides a measure of any interstellar polarization arising along the line of sight from the observer to the stellar system. Since this component of the polarization affects the light of both pair members identically, the amount present in the companion's beam may be subtracted vectorially from the primary yielding the amount and position angle of the intrinsic polarization.
In considering which Be types are most likely to exhibit polarization, Harrington and Collins argue that the addition of a pure absorption component to the opacity would maximize the probability of polarization in the earlier types, BO to B3. The B0e-83e group exhibits the largest observed V sin (i)'s and the smallest difference between this figure and the predicted equatorial breakup velocities. Also in the range B0-B3 lies the greatest percentage of B stars showing emission lines (Slettebak,
1966) .
This project was undertaken by the author in the fall of 1968 with a view towards examining the presence, magni tude and, in a limited way, the wavelength dependence of polarization in rapidly rotating Be stars. Observations 8 of visual binaries with high V sin (i) Be primaries were made in November, 1968, and June, 1969.
More recently, Collins (1970) has investigated in detail the effect on the net polarization of an absorption component in the total opacity. He found that the polar ization at optical wavelengths was reduced to a level far below the current limits of detectability. Since obser vations of variable polarization cited already and preliminary results of this work both supported the reality of intrinsic polarization, Collins' result did not affect the course of this research. It does, however, have implications for explanations of the origin of any established cases of intrinsic polarization.
The following chapters report the stars observed, the equipment used, the observational technique and data reduction methods, and present the results and conclusions obtained therefrom. II. OBSERVATIONAL PRELIMINARIES
Program Systems
The criteria employed in the selection of double star systems to be observed are derived from two basic considerations, theoretical necessity and observational expediency. That is, the primary should have those characteristics thought to maximize the probability that it be intrinsically polarized while the secondary, the control object, should possess as few of those characteristics as possible. In addition, systems with large magnitude differences and small pair separations should be avoided.
Then, from the discussion in the previous chapter, binaries are sought with a BOe to B3e primary of high
V sin (i) and a sharp-lined companion. The companion itself may be an emission line B star but with low V sin
(i) it is being seen nearly pole-on and, hence, should exhibit no intrinsic polarization.
The search for program systems primarily consisted of perusing the 0 and B star lists of Merrill and Burwell
(1933, 1943, and 1949) while simultaneously cross-checking early B emission line objects for inclusion in the Lick
9 10
Index Catalog of Visual Double Stars (Jeffers, et al.,
1963). For stars meeting these criteria, Boyarchuk and
Kopylov's (1964) compilation of rotational velocities was then consulted.
At this point, observational requirements and limi tations must be considered.
The equipment used is of the area-scanning type (see below, this chapter). Up to a certain limit of separation both objects of a pair may be scanned simultaneously.
Using the fainter star as the determinant of integration time, one gains an observation of the brighter star almost
Mat no extra cost." However, as the magnitude difference becomes greater, several drawbacks make their appearance.
First, the time spent on a separate observation of the primary becomes a smaller percentage of the total
time spent observing the pair, lessening the advantage on that count. Secondly, prescalers that may have been
introduced to avoid saturation of the pulse counting
electronics, due to the brightness of the primary, may
be superfluous or undesirable in the case of the secon
dary. Thirdly, if the prescalers are removed, the inte
gration time dictated by the fainter pair member may, if
no saturation in count rate occurs, result in an overflow
of the cells accumulating counts for the primary.
All these ills may be avoided by separate observa
tions of the pair members except in the case of small 11 separations, say 10" or less. In this instance light scattered from the beam of one star into the other also becomes a consideration and more so with greater Am’s.
Some desirable systems were dismissed from further consideration due to small separations listed in the Lick catalog. An example of this misfortune is HD 208682. It
is of spectral type B2e with a V sin (i) of 350 km/sec and a tolerable Am of 2.2 magnitudes but a separation of only 1.5 seconds of arc.
On the other hand, 6 Mon B and C are separated by only 3 seconds of arc but, with Am = 0*1*5, are usefully recorded with a sufficiently narrow slit on the scanning head.
Further considerations, such as most southerly acces sible declination, led to a final observing list of ten objects available for observation in the two runs at
Lowell Observatory in November, 1968, and June, 1969.
Ultimately, six systems were observed.
The six program systems are listed below in Table 1
together with some pertinent data. The spectral types
and rotational velocities are from Meisel (1968) with the
exception of those for 8 Lacertae. For this object the
classification of Murphy (1969) is listed along with the
V sin (i) given by Boyarchuk and Kopylov (1964). Meisel*s
data agree well with available comparisons except for the
A8III classification of 59 Cyg B, given by Murphy as A3V, TABLE 1
DOUBLE STAR SYSTEMS
HD Name ADS Sp V sin (i) my 4m Sep.
35149 23 Ori A 3962 A BllVnn 350+50 5.0 35148 B B B3Vnn 370+10 2.1 3271
45725 11 (6) Mon A 5107 A B4IV:nne 350+50 4.6 45726 B B B2V 130+10 (AB) 0.5 7.3 45727 C C B4IV:nne 370+50 (BC) 0.4 2.8
45995 4 * 5153 A B3IV:nne 320+20 6.1 • * * * B B8Ve 220+10 2.9 16.3
200120 59 Cyg A 14526 A B1IV:nne 420+50 4.6
■ - B B A8III 100±30 4.4 20.3
205637 39 (e) Cap A * » B5V:nnesh 370+30 4.6 * • B K1III-IV <. 50 4.0 68.1
214168 8 Lac A 16095 BlVe 327 5.7 214167 B B2V 30 0.7 22.4 13 and the 370 km/sec rotational velocity of 23 Ori B, listed as 300 km/sec by Berger (1962). The visual magnitudes of the primaries are from the Yale Catalogue of Bright Stars
(Hoffleit, 1964) and the separations are from the Lick double star compilation.
It should be noted that two program companions, 23
Ori B and HD 45995 B, have appreciable rotational veloci ties. There are no V sin (i)'s listed for these objects in Boyarchuk and Kopylov, and they were deemed suitable companions on the basis of the Am's and the spectral types in the Bright Star Catalogue -- "A" and "AS," respectively. After observations were made in November,
1968, it was found that V sin (i)'s for these objects had been published and were of significant size. Although it is no longer possible to assume that the interstellar polarization is the only contributor to polarization in the light of either companion, both systems have been retained for discussion purposes.
Single and Double Standard Stars
The purpose of observing already well observed stars
is, of course, to obtain checks on the performance of the telescope-polarimeter system in several respects.
One of these checks is with regard to the results of other observers and their equipment. Of specific inter est is the performance with stars of low polarization 14 because a lack of sensitivity here is indicative of some polarization being introduced by the system itself. If some systemic polarization exists, it does not necessarily affect the derivation of intrinsic polarization. Inter stellar polarization is supposed to be present in the light of both pair members in the same amounts and some systemically introduced polarization may be as well. The vector subtraction of the companion's observed polariza tion from the primary's would then, ideally, compensate for some instrumental effects.
Differential effects, due to the non-identical optical paths taken by the two stellar images may not be compensated for, however. Also as the polarimeter head is moved to various position angles, the images of the primary mirror rotate on the surface of the photo multiplier tubes with the attendant possibility of non- uniform cathode sensitivity and non-uniform stresses in the glass envelope of the tube window.
In addition to instrumental sensitivity and possible bias, repeated standard star observations provide a gauge of the night - to-night stability of the telescope-polari- meter system.
With the potential problem of differential effects in mind, three double systems of sufficient normality to rule out the existence of intrinsic polarization were chosen for observation. If true binary objects, then 15 the interstellar light paths should be essentially the same for both members and any differential polarization detected would have its origin in the equipment. Tables
2 and 3 list the eight single and the three double star standards observed. The results are discussed in Chapter
4.
TABLE 2
STANDARD SINGLE STARS
HD Name BS Sp. my
2905 15 (k ) Cas 130 Blla 4.15 34578 19 Aur 1740 A5II 5.03 126660 23 (e) Boo 5404 F7V 4.06 154445 • * 6353 B1V 5.62 164852 96 Her 6738 B3V 5.10 188512 60 (6) Aql 7602 G8IV 3.71 198478 5 5 Cyg 7977 B3Ia 4 . 83 210027 24 ( O Peg 8430 F5V 3. 76
TABLE 3
STANDARD DOUBLE STAR SYSTEMS
HD Name ADS Sp. my Am Sep.
166045 100 Her A 11089 A A3 5, 86 166046 B B A3 5,90 0 . 0 1472
175638 63 (O1] Ser 11853 A A5V 4.59 175639 (e2) Ser B A5n 4. 99 0.4 2272
178911 A ft ft 12101 A dGl 6.43
B • 4 B G5 • * 1. 3 1674 16
Equipment
All data was collected at Flagstaff, Arizona, with the 72-inch Perkins reflector of Ohio Wesleyan and The
Ohio State University at Lowell Observatory, The polari- meter, mounted at the Cassegrain focus, is of the dual beam type with an area-scanning entrance slit (Hall,
1968) .
The scanning head (consisting of the focal-plane aperture, the drive motor, and viewing optics) is mechani cally independent of the prism, filters, and photomulti plier tubes below and may be set at any position angle from 0 to 180 degrees. In observing double stars, this allows scanning along the line of centers of the two images giving maximum separation of objects in the output record.
When operated in the scanning mode, a synchronous motor rotates a cam at one revolution every 1.042 seconds which in turn drives the entrance slit carriage. The aperture moves through its range of motion in one direc tion in one second with constant velocity. At this point a shutter blocks the slit and the carriage is returned to
its initial position. This "flyback" operation takes the remaining fraction of the period so that only 42 milli seconds, or 4 per cent, are lost out of each cycle.
The scan distance may be altered by the choice of one of four interchangeable cams. With amplitudes of 17 three, six, nine, and twelve millimeters and a scale of
6.7 seconds of arc per millimeter, the cams give scan amplitudes of 20, 40, 60, and 80 seconds of arc. The entrance slit carriage accepts a variety of fixed-size circular and rectangular apertures plus one in which both the slit width and height are adjustable.
The apertures are all centrally located in highly polished metal plates, 25 x 40 millimeters, which ride in the carriage at a 79-degree angle from the optical axis.
Thus, a field of about 2.8 x 4.4 minutes of arc (except for that portion passing through the slit) is diverted from the optical axis at an angle of 22 degrees and into an eyepiece with movable crosswires permitting visual monitoring of the scanning process and image location.
Light passing through the aperture enters a chamber containing the calcite Wollaston prism, the filters, and various beam-controlling mirrors and lenses. This and the two cold boxes housing the photomultiplier tubes may be rotated as a unit, independently of the scanning head, through 360 degrees with detent stops at 45-degree inter vals .
For parallel incident light, the ordinary and extra ordinary rays emerging from the three-element prism are separated by 16.8 and 14.3 degrees at 3600A and 9000A, respectively. Immediately following the prism is a quartz lens through which both beams pass and, after further 18 separation, proceed through individual Fabry lenses. The latter elements focus the ordinary and extraordinary images of the primary reflector via a pair of mirrors onto the cathodes which face each other on a line per pendicular to the optical axis of the telescope. The multipliers are both EMI type 9526A (S-13 spectral response) with 22-millimeter diameter photocathodes.
Filter slides are located between the mirrors and phototubes. Schott glass filters UG1, BG12, and 0G5 were used for the UBV observations, respectively, with the addition of a Wratten 2B to the BG12 filter to eliminate the ultraviolet. The scale of colors exceeds the standard
U-B baseline by about S per cent and the B-V baseline by
10 per cent. The spectral intervals are well separated except for a small overlap near 4000A. The effective wavelengths for the UBV filters are 3760A, 4460A, and
5740A, respectively. The associated effective wave num bers are 2.66, 2.24, and 1.74 cm'^ (Elvius and Hall,
1966), while those for the standard UBV system are 2.89,
2.29, and 1.83 (Code, 1960).
The response of each photomultiplier is fed through a coaxial cable to an equipment cabinet which houses the recording and output apparatus. The output of each photo multiplier is amplified by a 100 MHz pulse amplifier, then passed through a discriminator and on to a multi channel analyzer either directly or through prescalers. 19
Each cell of the analyzer (or "computer of average
transients," "CAT" for short) accumulates counts cor
responding to a specific point in the scan. A proper
correlation between each of the CAT cells and aperture position is maintained by a magnetic sensor on the
scanning head. It is triggered at the beginning of each
sweep and causes the return of the distribution of counts
to the first cell. The connections are arranged so that
the odd channels accumulate the counts from one phototube while the even cells record that of the other.
In actuality two complete sets of counting electronics,
totaling 400 channels, were available, but the output of
only one CAT was retained since most objects observed were
bright and no significant decrease in the errors was ex
pected from the additional counts.
The CAT can handle count rates up to about 20,000
per second before saturation becomes significant. How
ever, before non-linearity is approached, one may insert
one or two prescalers between the discriminator and the
analyzer. Each introduces a sixteen-to - one reduction in
the count rate for a maximum factor of 256 to one. At
no time was the use of more than one prescaler necessary.
Additional components control the integration time
by allowing one to preset the number of sweeps and the
punching of data on paper tape. When the data is recorded
on tape, a sequence number displayed on the cabinet is 20 automatically punched first and incremented by one, fol lowed by the contents of those cells corresponding to one photomultiplier, then by the remaining cells.
The controls also permit the interruption of count accumulation at any time and the resumption of the inte gration without any loss of data. When not integrating, a plot of the counts versus cell location may be displayed on a cathode ray tube.
A punchout of 200 CAT channels requires 22 seconds, and 50 such dumps may be made on a single reel of tape.
The 100 channels associated with one phototube are punched in sequence followed by the 100 alternate cells which accumulated counts from the other phototube. Thus, the ordinary and extraordinary images of the area scanned are each represented by a record consisting of the number of counts registered for each of the 100 intervals of the scan distance. For scans of double stars, the slit width is narrowed only enough to adequately resolve the indivi dual components. For all systems except 6 Mon, this results in a count distribution consisting of two flat- topped plateaus with an emphatic dip between them. The
shoulders are steep and they are flanked by low-level noise made up of sky background and photomultiplier dark
current. The reduction of data and the special case of
8 Mon is discussed in the next chapter. 21
In practice an "observation" consists of four inte grations at polarimeter settings of 0, 45, 90, and 135 degrees. Usually the readings were immediately repeated in reverse order. If an object were so observed in three colors with a one-minute integration time and thirty seconds for data punchout and changing the polarimeter position angle, then the total time involved would be 36 minutes. Rarely was this efficiency achieved due to peripheral activities such as changing tape reels, taking notes, etc.
For ease in subsequent reduction schemes, the binary data on paper tape was converted to the base ten and punched on cards by means of an IBM 1130 computer. The conversion program and computer time were both generously provided by Lowell Observatory.
The reduction methods described in the next chapter were implemented on the IBM S/360 Model 75 computer of The
Ohio State University Computer Center. Ill. DATA REDUCTION AND ERROR ANALYSIS OF OBSERVATIONS
Data Reduction
By convention the position angle of polarized light detected •'in celestial bodies is measured in the same manner as is the relative position of a companion star to its primary in visual binary observations, i.e., measured eastward from a north-south baseline. Due to the 180-degree ambiguity in the position angle of linearly polarized light, this angle is conventionally placed in the appropriate quadrant between 0 and 180 degrees.
If the light coming from a star is partially polar ized, it can be considered as two beams of intensities
Imax and Im in » vibrating at right angles. These corres pond to the semi-major and semi-minor axes of the
"polarization ellipse." If Imax lies at an angle $ with respect to the defined baseline and the analyzer is at position o then, except for some reflection and trans mission losses, the received intensity in one image formed by the Wollaston prism is
= Imax cos2 [ 2 (<{< ~ 9) ] + Ijnin sin [2(
= 1/2 [(Imax + ^min) + (Imax ‘ *min) cos 2 ( = */2 Hmax + W n H 1 + P cos 2(* - ©)] = 1/2 1(1 + P cos 2(<* - 0)) , (!) 22 23 where the following definitions have been used ^max + Imin “ I » (Imax The intensity in the other image will be I 'Q = 1/2 1(1 - P cos 2 ( Linear polarization is sometimes discussed in terms of the Stokes' parameters I ,Q and U. In terms of quanti ties used in this development, the Stokes* parameter I is defined as above while Q and U are defined as follows Q * d m a x !min) cos 2 C - 0) , u " (Imax Imin) sin 2 (* ’ * In relation to the observations, Ie and I*0 corres pond to the responses of the two photomultiplier tubes at four position angles 01 = 0, ©2 = 45, ©3 = 90, and 04 *= 135 degrees. The numerical value of the response is derived from the scan record as follows. In all cases except that of 0 Mon, discussed below, a stellar scan is represented by a rather level plateau of counts some distance above the background noise (see Figure 1). The record is searched to determine the cell containing the largest number of counts. The boundary of the plateau is fixed by finding a point on either side of this cell which is the outer most such point to have no less than 95 per cent of the maximum counts. Inspection of the scan record and com parison with boundaries determined as above confirmed i. -Ielzd cn eod o aTpcl rga Double Program Typical a of Records Scan 1--Idealized Fig. Number of Counts (Arbitrary Scale) ytm Aoe ad Mn (Below). e Mon and (Above) System 20 40 ll e C 60 60 100 24 25 that this technique works reliably to establish outer limits to the flattest part of the stellar scan. The response for a given filter and polarimeter position an gle, uncorrected for background, was taken to be the mean counts per cell averaged within the two boundary points. The background was considered to begin at the first cells exterior to the plateau boundary which con tained a certain specified fraction of the maximum counts. The initial guess at the background level was 0.5 per cent. If no cells were found with a fractional total this low, the level was increased by steps of 0.5 per cent until such cells were found. The average background was calculated for the scan intervals located thusly and subtracted from the mean response. Only a very few observations had noise levels above 0.5 per cent. Fail ure to subtract the background in the low-noise cases changed the derived polarization only in the third or fourth significant figure, an amount less than the observational errors. In observing the triple system g Mon, a much narrower slit than normally used was needed to resolve components B and C. The resulting scans are decidedly peaked, and no clear-cut boundaries are able to be defined as above (see Figure 1). In this case, a functional representation of the scan profile was obtained by fitting gaussians to the three components. The expressions are of the form 26 yi = r^exp[-(x - m i)2/2s2), where and are the scale factors and central abscissae for the three components, respectively, and s is the dis persion -- determined only by the slit width and, hence, constant for all three components. The primary is suffi ciently distant from B and C so that it may be attacked separately. A function of the above form was fitted to the data points of component A by the least squares tech nique. Since the dispersion derived for B Mon A was also used for B and C, there are four parameters remaining to be determined, rj* r 3, m 2, and m 3. Companions B and C are blended so it was necessary to fit a sum of two gaus- sians to the entire B-C profile. The normal equations developed in both cases, i.e., the least squares fit to component A alone and the com bined B-C fit, are non-linear and must be solved by an iterative technique. Initial estimates of the seven parameters were made by examining the individual profiles. This method of curve fitting was tested by manufacturing "data points" from a sum of three gaussians of appropriate height, separation, and dispersion and was found to be successful. The response of the system to each component is taken to be the area under the individual, fitted functions and may be written I * /Trf sr for gaussians integrated from minus to plus infinity. This range of the variable of integration, x, is not strictly correct 27 but the contributions to the integral at large distances from the mean, m, are negligible. It may be shown that 1, as used above, is equal to one-half the sum of the • To compensate for possible inequalities in tube response, this is formed for each channel. Taking the difference of equations (1) and (2), one gets If) I ' n i - i = P cos 2(0 - 6 i) I I* = P(cos 20 cos 20^ + sin 2 Let = P sin 20 » a2 - P cos 20 , x ^ = sin 20^ , x ^2 = cos 20^ , so that fj = alx il + a2x i2 ’ I = I» 4 * (4) The and x^2 are known precisely from the setting of the polarimeter and the f^ are derived from the obser vational data. The primary reduction process is a least squares fit of the parameters ai and a2• With these obtained, the desired quantities P and 0 are given by 28 the relations 2 P * » 1/2 arctan The signs of ai and a2 determine the trigonometrically correct quadrant for . A standard error was derived for each I and I* 0 * on the basis of the error expected to arise in those quantities due to random fluctuations in the count rate. Employing the usual error propagation analysis techniques, an error was computed for each f^ and a weight assigned to each equal to the inverse of the error. With weighted data points the form of equation (4) becomes (5) A "best" fit, in the least squares sense, has been obtained when a.1 and a2 have those values such that the sum of the deviations squared is a minimum. Letting S be the sum of the deviations squared we have (6) i = 1 Then (7) (8) 29 are the two relations to be evaluated and solved for ai and a 2 . Written in more detail, equations (7) and (8) are, with the sum understood to run from i « 1 to i ■ 4, l y>i xi l ti - a, I w ^ x i ,2 - a 2 I wj x ^ x ^ - 0, (9) I w i2x i2fi - a i I K i*x iix i2 - a 2 I w i ^ x i 22 ’ Recalling the definitions of x- and x, and the 6 1 1 1 2 values of the e., we have the following relations i X 11 = X 31 “ X 2 2 “ X *» 2 * °* x21 = X 12 = 1 * X 32 — Xi+l - “1, so that the terms in equations (9) and (10) are as follows r 2 _ 2 - 2 ) W. X. f. * w f - w fh ** 1 1 1 1 2 2 U „ 2 2 2 y W. X. f. ■ W f - W f u 1 12 1 1 1 3 3 i W i2x ilX i2 " ° ’ r 2 2 2 I Wi Xil ' W2 + W. „ 2 2 2 2 £ w i X 12 w i + w 3 Solving for aj and a2 after substitution of the above terms yields zation to the case of a single observation. /wixn wixi2\ / 0 w 2 0 __ W * X - 1 11 112 jX12... WAX r Jwi2xil2 I" i2jtllxi2^ B=X’X= ,I«i2xiixi2 I«i2xi22 j : •** i ‘ j det B - (Zwi2xil2)(^wi2xi22) - (IwiJx ilx i2)‘ = (w22 + W tt2) (Wj 2 ♦ w^2) -Tw.2x ■ x • f Iwi2xi2 i 1 A 1 I 1X 2 det I - 2X i tx Iwi2Xi, w, * + w \ W 2 2 * Wt, 2 / In the same context a ; and a2 correspond to the third and second Stokes parameters, respectively, normalized by the factor 1/1, or max a2 = P cos 2$ max I . max m m aj = P sin 2 The same analysis can easily be extended to more than one observation as when deriving a night average for an object. If there are k observations, then the summation runs from i = 1 to i = 4k and there is a one- to-one correlation between x and x between 1,1 4k + 1,1* Error Analysis The errors in a 1 and a2 fall out rather directly from the results of the least squares computations but will be more conveniently discussed if the normal equa tions (9) and (10) are recast in vector notation. The necessary definitions are given below, first in general, then immediately followed by their particulari- 31 zat ion to the case of a single observation. W X \ / 0 w /w lxll 1 1 2 \ A • t W 2 0 X = • ■ •« 0 - w \w ix il WiXi2/ l -W4 0 I / WjXj j ... Kl X i l ' 0 w 0 -w. 2 X' = w ix i2 * * * w ix i2 \W1 0 -W 3 2+W 2 0 (l*i2Xil2 ^W i2xilX i2^ (w 2 4 B=X'X= \ l w i 2x i l x i2 l v i 2*i22 j W 12+W3 2 det B “ (£w i2x ii2) d w i2xi22) - (Iwi2XiiXi2)2 = (w22 + W 42^(W l2 + W 42^ Iwi2x i2 -Iw i Xi1112 ,x i det B yw .2x . 2 - I * ! 2x i lx i 2 A n y ( ^ r W 1 2 + w 32 \12 + W l142 / 32 / w i £1 > F = w' f. ) V 1 1J 2 \ f 2 2 iw i x u f i i w 2 £2 • w 4 f4 Y = X 1F = W 2f - W 2f i Iw i x i2 ^i j W 1 1 1 3 r 3 ra A - With these definitions, the normal equations may be expressed as X'F = X'XA, or (13) Y = BA, with the solution A = X* F(X'X)" 1 => YB' 1 . (14) Adopting the results of regression analysis, of which the least squares technique may be considered a subset, the standard error squared of the a^ may be written 2 - 1 2 o (a*) ~ b . . o v y • (15) j n Y ’x i The term b.. is the jth diagonal element of the 2 B-matrix and x is the variance of the fit, or regres sion. The latter may be written as follows 33 °v,x2 - • (15) where k is the number of observations, N is the number of variables, always two in this problem, and the are the residual differences between the observed points Yi = wifi , (17) and those predicted by the parameters ai and a2 , y* i = + a2xi2) . (18) Thus, we have that I£i2 = Z Cy i - y*i) = I y i + l y * i - 2^yiy*i . (19) But since data taken at the various position angles are independent, the errors accrue orthogonally in the vector space of observations (see, for example, Hildebrand, 1956) and the following also holds 2 _ 2 2 I£i = ZCyi- y*i ), or Iy*i2 3 lYi - 5>i2 • (2°) Putting this into equation (19) yields the resultant expression for , Ici2 = f r i * ‘ h i Y * i 2 2 “ Iw i £i * Iwifiw i(a ixii + a2xi2), (21) 34 or in the vector notation developed above £ e i 2 = F'F - F ’XA . (22) Returning to equation (15) and considering only one observation 2 Iw i fi 'a l (w2 £2'w^ f j - a 2(w1 fr w 3 f3) p a (aO= ------2 2 2 2 » 2(w 2 +w 4 )(w 3 +w 3 ) 1 1-> (23) or, specifically 2 2 2 2 2 2 2 , , _ ^ f2-«^ f,-w f ) a (_aij ------— 3------(24) 2 2 . 2 (w1 +w3 ) 2 2 o (a2) =■ a (a.) WI * w 3 . (2S) w 22 * w„2 With the a(aj) known, an error propogation analysis can be performed relating the errors in the aj to those in P and 2 2 2 2 o (ai) sin 2 o (P) - . 2 _ T ~ C26) sin 2 2 2 2 2 2 , „ o (a2) sin 2 The estimated standard errors are then SE(P) = 100 o(P), per cent polarization, (28) (P)/.4605, magnitudes polarization, (29) 35 SE( It should probably be noted how polarizatiun, ex pressed in magnitudes, is defined. The amount of polarization, P, has been defined as I - I . p = max min 2maxI + I 1min By convention, in order to always have positive numbers, polarization in magnitudes is defined Am = t 2.5 c ilog V■j---- a x 1min But P may be rewritten as Imax _ 1 + P Ijnin 1 ' P so that Am is (Hall, 1958) Am = (2.5) (.4343) loge \ +_ p 3 5 2 = 2.1717(P + + ...), P < 1. If P is small then terms to the third power or higher may be neglected and, hence, P(magnitudes) = P(amount)/.4605 = P(per cent)/46.05. Intrinsic Polarization Double star scans lead to observed polarizations and position angles both for the primary (Pq » ^q ) and 36 the companion (Pj> A detailed consideration of the alteration of the Stokes parameters of a beam traversing a polarizing medium leads to expressions for the intrinsic polariza tion of the initial beam in terms of the net observed polarization and the purely interstellar component- If the intrinsic quantities are PA and 4>q, and ^ are defined as above, then the following rela tions hold (van de Hulst, 1957), 2 2 2 + Pj2 - 2PqPj cos 26 - Pq Pj sin 2 6 P 1 - PqPj cos 26 6 = If both PQ and Pj are small, then higher order terms may be neglected yielding (31) sin 2 6 = 1/2 arctan cos 26 1 P j / P q (32) 37 Equations (31) and (32) in slightly altered form are those derived by Treanor (1962) to correct for instru mental polarization. The errors in and may be found as follows, where g ^ — Pq t g2 ' Pj, and g ^ — 5. (33) (34) In the above, the standard errors in Pq and P^ are computed in amount (per cent * 100) and 6, in radians. Conversion to per cent, magnitudes, and degrees follows the form of equations (28) through (30). IV. OBSERVATIONAL RESULTS: STANDARD STARS Observations of standard stars were made in order to evaluate the telescope-polarimeter performance with regard to night-to-night repeatability and the possi bility of large or small scale systematic bias. Treanor (1963) distinguishes between these two types of bias as scale and instrumental error, respectively. The former is stated to be present in "most observations of high polarization" but decreasing in importance with decreasing polarization and, in any case, independent of position angle. This is probably best thought of as arising from an improperly calibrated scale of deflec tions when the variation of such deflections are fitted for polarization and position angle. The point is that its origin is in the method of measurement and data reduction rather than in any instrumentally-induced polarization. The dual-beam differential method employed in this study minimizes any tendency for large deviations due to an improper scale. Table 4 lists the data available in three colors for the eight standard single stars. While there are not enough stars for a meaningful statistical analysis, 38 39 TABLE 4 COMPARISON WITH OTHER OBSERVERS HD Reference pu 290S • a a 1. 28% 86° .• . a a a 1 24% 86° 1. 40 86 1. 51% 83° b • • • 1. 52 84 * a a a e ■ p * * * p a 1.47 83 f 0 73 96 0 .28 90 0.84 81 RLB° 34578 * 1 . 20 174 * * p a a * m # 1 . 34 175 a * a a e 1 15 165 0.73 177 0 . 80 171 RLB 126660 * p a 0.06 70 • • a a a * • a 0.00 a * a * a a e * • • 0.02 11 0.17 105 i • * a • a a * 0.03 23 k 0 76 111 0.28 59 0.05 99 RLB 154445 2 87 89 3.42 86 3.68 89 b 2 88 90 3. 29 90 3. 56 91 d * p * 3.32 88 • p a e 3 5 85 3.1 90 4 . 0 92 h • • a 3.04 89 3. 64 89 i • • * m , , * 3. 54 m , 1 * * 3. 29 90 3.16 93 n 3 21 96 3.25 88 3. 39 88 RLB 164852 a • • 0.91 171 a * • a a a • * 0.97 176 a a a a e 0 7 171 0.8 170 0.8 170 h 0 49 129 0.87 174 0.90 176 RLB 188512 a • a 0.02 106 a a a a a • * a , * # , 0. 04 146 g a a • 0.08 92 0. 08 100 i * • p m m * « 0.01 64 m 0 30 116 0.45 4 0.17 51 RLB 198478 a * p 2.86 2 a a a a a 2 33 1 2.68 1 2.89 2 b a • p 3.13 4 a a a a e a a a p * * a 2 .81 5 f a • a 2.16 171 2.49 3 g 2 6 0 2.7 3 3.0 2 h 40 TABLE 4 --Continued HD Referei pu *U PB *B pv V 198478 (Cont.) • • ■ 4 2.40% 3 ° 2 .67% 3° i 2.48% » * 2. 68 • • 2.85 p p j ■ * • • * * * * 2.81 3 k 2. 56 177° 2. 59 5 2.42 5 n 1. 56 171 2. 68 0 2. 33 2 RLB 210027 • * * p 0. 06 111 • p p • a • * * « 0.10 49 0.04 1 i • * * « p * m m 0 .002 45 m 0.85 102 0.52 164 0.29 98 RLB References: aBehr, 1959 L Coyne and Gehrels, 1966 cCoyne and Kruszewski, 1969 ^Coyne and Wickramasinghe, 1969 eHal1, 1958 ^Hiltner, 1956 ^Kruszewski, 1962 ^Martel and Martel, 1964 *Serkowski, 1965 ^Serkowski, 1968 u Serkowski and Chojnacki, 1969 1Smith, 1956 mWalborn, 1968 nTreanor, 1963 °This research 41 it appears that the polarizations derived in this inves tigation tend to be slightly lower than those of other observers. Agreement in position angle is generally satisfactory except for low-polarization objects, in which the position angle is less well defined. HD 2905 (k Cas) is definitely low in comparison to previous observations as is HD 34578 (19 Aur) although the latter was observed only once. In the B and V bands, HD 198478 (55 Cyg) is quite in line with other reports but deviates significantly downwards in U as does HD 164852 (96 Her). However, the overall U average for the latter object includes some of the least self-consistent data of all the standard stars and is hardly a well determined number. HD 154445 shows good agreement in all colors. The question might be raised here just what is meant by "good agreement with other observers." In the case of 55 Cyg, polarization in the V region varies from 2.42 to 3.0 per cent with a mean for eight observers of 2.74 per cent. The spread for HD 154445 is from 3.16 to 4.0 per cent with a 3.58 per cent average for six ob servers. These are fairly generous limits to meet in order to have good agreement with other observers. Some of the spread may be attributed to slight dif ferences in effective wavelength from the system of one observer to another. However, there still can be 42 considerable variation between observations made by the same persons using essentially the same telescope and polarimeter at different times. Figure 2 is a plot of the data in print for HD 154445. Error bars are not plotted but range from ±.05 per cent (Coyne and Gehrels, 1966) to +.5 per cent (Martel and Martel, 1964, at 1/A = 2.89). The most extensive wavelength baseline has been used by G. V. Coyne, et al . , at the University of Arizona. Information published by Coyne and Gehrels is represented by the filled circles, while open circles are points reported in 1969 by Coyne and Wickramasinghe. The only difference in equipment is an additional filter at 1/A = 1.56 y 1 and effective wavelength changes in four of the remaining five filters of less than 0.0 2 y \ Agreement between the two observations is good at short wavelengths where one might expect to find larger than average errors. However, from 1/A = 2.8 to 1.4 y agreement deteriorates steadily to a maximum of about 0.6 per cent. To be fair, the 1.39 y 1 value was based on a single observation although immediately adjacent points were not. The main point is not that the current results are no worse than those of other researchers but that standard stars in the polarimetric sense are far from fulfilling a role analogous to their function in photometry. There 4.0 .oe 3.0 Magnitudes Polarization .0 7 3.0 .0 6 2.0 Fig. 2--Summary of Observational Data for HD 154445. The References in Table 4 are Associated with the Symbols Used Above as Follows: Closed Circles --Reference b, Open Circles--d, Open Triangles--e , Crosses--h, X's--if Closed Triangles--1, Open Squares--n, Asterisks--RLB. 44 are, of course, no standard observing systems as defined for photometry. However, an existing moderate-to-wide band, multicolor photometric system could easily be adopted for polarimetric purposes and would indeed be useful. Agreement in band width as well as band place ment is necessary since in some regions of the spectrum, particularly longward of about 6000A, interstellar polarization changes rapidly. Little additional stan dardization would be necessary since most observers are using the dual-beam type of design similar to that out lined in the previous chapter. The scatter in various observers' data about the mean mentioned above may be partly a result of such "scale" effects as different filter band widths but is surely due in part to instrumental and accidental error as well. That is to say, accuracy is finite under the best of conditions and inevitable equipment flaws will further reduce this. Behr has estimated (1960) that the dual-beam design is capable of accuracy of O^OOOZ (about 0.01 per cent) in polarization measurements. His observations with a 34 cm. astrograph had errors of the order of 0.03 per cent while few reflectors have been quoted as having errors smaller than 0.1 per cent. Contributions to instrumental error in either a reflector or refractor may come from the non-uniformity 45 of the photocathode surface, different sensitivity dis tributions for the two cells in the dual-beam type of instrument, and telescope flexure leading to movement of the objective image. Reflectors also may suffer from flaws in the aluminum coating. Linear deviations of the response of one phototube from the other are compensated for rather well in the reduction technique employed. However, non-linear factors or a poorly aluminized surface will lead to some instrumental bias. A particularly serious example of instrumental polarization is given by Behr. In January of I960, the McDonald 36-inch reflector of the University of Texas was examined by him for polarization originating in the primary mirror. It was found to be present in a patchy, color-dependent manner. In the U band it varied from 0.95 to 1.64 per cent and decreased to a range of from 0.07 to 0.44 per cent in the V. Treanor (1963) pointed out, however, that after care ful re-aluminizing, observations of nearby stars indi cated instrumental polarization was less than 0.05 per cent with a total error of about the same size. It is important to note that all polarization effects behind the Wollaston prism have no influence on the mea surements because the orientation of any such polarization is always the same relative to the phototubes. Only 46 polarization effects in front of the rotating polarimeter head can influence the result. This fact has led to the use of telescopes with fully rotatable tubes for polarization measurements -- notably the 24-inch instruments at Siding Springs Obser vatory in Australia and at Yerkes Observatory. Walborn (1968) has used the latter telescope to observe 26 nearby stars with unusually small errors. The object was to aid in establishing a set of standard objects of accurately known, very low polarization. Two of the three low polarization stars included in this research were observed by Walborn. His quoted errors in polarization are O^OOOll for 8 Aql and 0*P00013 for i Peg, or roughly, 0.006 per cent. Table 5 lists in magnitudes all published Stokes parameters relating to three low polarization stars. Px and Py are the normal ized parameters Q/I and U/I, respectively. The references are numbered the same as in Table 4. Walborn does not state what, if any, filter was used. The results listed in Table 5 for this research are the unweighted means of the observed Stokes parameters for a given star. A number of parameters were rejected as being unreliable and not included in the average. To be specific, 64 observations of the low polarization objects yielded 128 Stokes parameters; of these, nine were not included in the average because they deviated 47 TABLE 5 STANDARD STARS WITH PUBLISHED STOKES PARAMETERS Name Reference Px (mag) Py(mag) Xeff 6 Boo +.0005 +.0002 4400 i -.0032 - . 0018 5500 i +.0004 +.0004 5800 k -.0084 - . 0049 3760 RLB +.0035 +.0049 4460 RLB -.0016 - . 0016 5740 RLB 8 Aql - .0018 -.0001 4400 i - .0017 - .0006 5500 i +.00016 -.00020 * a m - .0003 -.0056 3760 RLB +.0087 +.0012 4460 RLB - .0017 +.0023 5740 RLB i Peg - .0003 +.0021 4400 i +.0008 +.0001 5500 i +.0008 +.0004 5800 k +.00000 +.00005 • a m -.0120 -.0046 3760 RLB +.00006 +.0063 4460 RLB - .0051 -.0022 5740 RLB so markedly from the mean given by the remaining Stokes parameters for that star and filter. In the case of Q Boo, twelve observations in the U bandpass gave mean Stokes parameters of Px = -70129 and Py = -70117. When the three observations yielding extreme numbers were excluded from consideration, the mean for Px dropped to -70084 and for Py, -70049. This may seem to artificially lower the indicated instrumental polarization, but this is not so in all cases. The V observations of 0 Boo give gross means of Px = +70004 and P = -70005. When one 48 exceptionally deviant observation is deleted, the averages increase to P = P = -'Pooib. y A comparison of Walborn's and other data with the results of these observations clearly indicates the pre sence of instrumental polarization and in generally increasing amounts towards the ultraviolet. If an aver age of the Stokes parameters over all three stars, in each bandpass, is an adequate representation of the instrumental polarization, then Table 6, below, shows the wavelength dependence of this polarization. TABLE 6 ESTIMATE OF INSTRUMENTAL POLARIZATION Filter P U 0.38% 109° B 0.28 20 V 0.10 97 If the instrumental polarization is known accurately, observations may be corrected for its effect by using the equations developed in the previous chapter for removing the interstellar component of the light of an intrinsi cally polarized star. In the case at hand, Pq is taken to be the observed polarization of a star, .] is the amount of instrumental polarization, while 4>q and The mediocre success in correcting the amount of polari zation and serious departures from other observers' results after applying position angle corrections indi cates that a blanket correction for instrumental polari zation is not advisable. One may also ask how the application of instrumental corrections to double stars modifies the subsequent calculation of intrinsic polarization. At first glance one might expect that no difference should arise between intrinsic polarization calculations made from corrected and uncorrected results. That is to say, the derivation of intrinsic polarization is essentially a differential process so that if the same correction is applied to the results for both pair members then the subsequent vector subtraction should yield an unchanged intrinsic value. In order to check this, all U and B filter observations of program stars were corrected as indicated above and the intrinsic polarization was rederived. In no case was a 50 result obtained that differed from the "uncorrected" one by more than the round-off error of the calculation. From the above results, it appears that the esti mates of instrumental polarization are perhaps fairly close in amount but the position angles are doubtful. Since no self-consistent corrections are available, none are applied. Night-to-night consistency is examined in Figure 3. The mean result for each star, in three filters, is used to normalize the nightly color averages. These numbers are then plotted against the date -- June, 1969, except for k Cas which was observed in November, 1968. Filled symbols denote objects with at least moderate polariza tion while unfilled symbols stand for the three low polarization stars. The main conclusion to be drawn from Figure 3 is not too surprising, namely, that for moderate to high polarizations observations on three nights are quite sufficient for a good determination of polarization, two nights are probably satisfactory, but one night's data might be treated with suspicion. In order to investigate the possibility of telescope flexure being a source of systematic errors, the Stokes parameters of low polarization objects are plotted against the hour angle of the observation for the three filters in Figures 4, 5, and 6. Although the distribution 51 3.0 r U 10 3 .0 r K e.o - it... rB i.o 3 .0 A 8.0 “ rV 1 .0 13 14 15 16 19 8 0 81 88 83 Dot* Fig. 3--The deviation of individual polarization observations from the mean quantity is plotted versus night of observation. Deviations greater than 3.0 have vertical arrows attached to the associated symbol. Date refers to June, 1969, except for one object which was observed in November, 1968. Open symbols refer to low polarization stars, filled symbols to moderate to high polarization. Polarization Objects Plotted Versus Hour Angle. Hour Versus Plotted Low of Objects Filter) (U Polarization Parameters Stokes 4--Observed Fig. CJ Normalized Stoke* Poramotors, X 10 2 E 0 76 7 100 E 125 U/I /Z Q 25 0 5 or Angle Hour 25 0 l mW 5 l2 100 5 7 0 5 53 .6 O o .2 o w o % o E o 55 - . 2 o E - . 4 -.6 O - - 0 / I • - U / I _1_____ XX XX _l l25m E 100 75 50 25 0 25 50 76 100 !2 5 mW Hour Anglo Fig. 5--0bserved Stokes Parameters (B Filter) of Low Polarization Objects Plotted Versus Hour Angle. Normoliztd Stokos Parometoro, X I02 4 . - -.6 oaiain bet PotdVru Hu Angle. Hour Versus Plotted Objects Polarization Fig, 0 .6 25mE 0 75 7 100 E m 5 l2 ~U/I / U ~ • I / Q — O - 6 -Observed Stokes Parameters Parameters Stokes -Observed 552 0 or Anglo Hour 0 * O 25 (V (V 0 l W m 5 l2 100 5 7 0 5 Filter) of Low of Filter) 54 55 of points varies from filter to filter, what would indi cate flexure problems would be a dependence of the vertical point spread on hour angle within a given plot and this is not in evidence. Thus, it is concluded that telescope flexure is not a contributor to any systematic errors. The plots do reflect the general features of the instrumental polarization estimated in Table 6. Going from U to V there is a tendency for increased central concentration of the points and the centroid is nearer zero. Also the mean value alternates in sign. It is negative in U, positive in B, and negative again in V; this is in line with the alternation in quadrant of the position angle -- 109, 20, and 97 degrees for U, B, and V, respectively. The overall averages of the eight individual stan dards together with errors in P and <|> are compiled in Table 7. Polarization is listed in per cent and the last column indicates the number of observations -- usually twice the number of nights the object was observed. The results are plotted in Figure 7. Typically, the interstellar polarization is slowly varying in this wavelength region, at least out to about 6000A. This is borne out by these stars with the possible exceptions of 55 Cyg, in going from U to B, and k Cas. A complete journal of individual observations is contained in Appendix A. 56 TABLE 7 POLARIZATION DATA: STANDARD SINGLE STARS Name Filter P £ n P * e 4> k Cas U 0. 73% 0.12% 96 0 5° 8 B 0 . 28 0 . 04 90 4 8 V 0.84 0.05 81 2 8 19 Aur u 1.15 0.17 165 4 2 B 0.73 0.04 177 2 2 V 0. 80 0.06 171 2 1 0 Boo U 0.76 0.14 111 5 12 B 0.28 0.15 59 16 12 V 0. 05 0.07 99 40 12 HD 15445 u 3.21 0.32 96 3 8 B 3.25 0 . 13 88 1 8 V 3. 39 0.08 88 1 8 96 Her u 0. 49 0.23 129 14 6 B 0. 87 0. 09 174 3 6 V 0.90 0.09 176 3 6 6 Aql U 0 . 30 0.16 116 15 6 B 0.45 0.06 4 4 6 V 0.17 0.09 51 16 6 55 Cyg u 1. 56 0 . 23 171 4 4 B 2. 68 0.15 0 2 4 V 2.33 0. 08 2 1 4 i Peg u 0.85 0.15 102 5 4 B 0.52 0.22 164 12 4 V 0. 29 0.16 98 16 4 The three "standard" double systems 100 Her, 63 Ser, and HD 178911 were observed as planned. The polarization of the secondary was subtracted vectorially from the pri mary as part of an examination for differential effects. Par Cant Polarization .0 3 e.o 2 0 i.e i.o 1.4 i. -Smay f eut*fr ige tr Standards Results* Star of Single for 7--Summary Fig. 0 0 0 4 0 0 5 4 0 0 0 5 HO 154445 t Po® ' Caa 0 0 5 5 ■# .01 .03 .07 9 0 58 The results for each object and color are collected in Table 8. Numbers have the same units as in Table 6. TABLE 8 CALCULATED INTRINSIC POLARIZATION: STANDARD DOUBLE STARS System Filter P 100 Her U 0.57% 0.65% 44° 38° 4 B 0.39 0. 36 44 50 4 V 0.74 0.54 104 19 4 63 Ser U 0.51 0.37 75 17 4 B 0.29 0.16 117 18 4 V 0.36 0.12 49 57 4 HD 178911 U 0.49 1.15 59 66 2 B 0.19 0.27 8 55 2 V 0.35 0.23 109 16 2 The consistently striking features of these measure ments is that they indicate such high differential effects and that they are of such low quality. It is my opinion that it is primarily the latter that gives the impression of the former. An examination of the individual observations and nightly averages (Appendix B) shows a considerable scat ter in quality. The standard error in the position angle is a particularly good indicator of poor data and is generally quite large for these observations. In addi tion, poorly defined position angles that would otherwise be nearly equal result in artifically swollen "intrinsic" 59 or instrumental polarization. Most observations of program doubles had less error both in amount of polari zation and in position angle. It is not clear why these systems, particularly 100 Her, were observed with markedly inferior accuracy especially since all were picked partially because of observational convenience with regard to Am and separa tion. For the above reasons, it is felt by this researcher that if any differential effects exist, they are probably smaller than the largest indicated by Table 8. It may be prudent to beware of possible effects of about the size indicated in Table 6 but, fortunately, these have a minimal effect on the intrinsic polarization. V. OBSERVATIONAL RESULTS: PROGRAM STARS It was concluded in the preceding chapter that a solution for instrumental or intrinsic polarization based on an average of rather poor observational material leads to ambiguous, ill-defined results -- or, bad data breeds bad answers. Thus, because of their importance and limited numbers, all observations of program systems are presented here for the closest scrutiny -- star by star, color by color. HD 35149, 23 O r i , was observed two nights in Novem ber, 1968. The three color results are listed in Tables 9, 10, and 11, and discussed below. Observations of the primary in U were slightly less worthy on the 21st than on the first night; however, each night has one rather good measurement. Fairly large errors in position angle are to be expected due to the rather low measured polarization. The companion also suffers from one exceptionally bad observation on the second night. The resultant average polarization would be probably better expressed as a few hundredths higher but this is still well within the error of the current value. The calculated intrinsic polarization is self- 60 61 TABLE 9 23 ORIONIS: U Date Obs. Object P 18 1 Pr imary 0.43% 0.21% 48° 17° 2 0.55 0.09 44 4 Ave . 0.48 0.10 45 6 21 1 0.58 0.37 11 16 2 0. 56 0.13 25 10 Ave. 0.56 0.18 18 7 Average 0.45 0.10 34 7 18 1 Compan ion 0.85 0.13 98 3 2 1. 24 0 . 06 86 1 Ave. 1.06 0.14 91 3 21 1 1. 06 0 . 16 132 5 2 0. 86 0, 50 89 15 Ave. 0.73 1, 38 112 50 Average 0.87 0,20 98 6 18 1 Intrins ic 1.01 0.27 102 7 2 1. 30 0.10 102 2 Ave. 1.18 0.17 102 3 21 1 1.44 0. 38 80 7 2 1. 29 0.52 100 8 Ave. 1.28 1 .39 88 22 Average 1. 20 0.22 99 3 TABLE 10 23 ORIONIS: B Date Obs. Obj ect P £P E* 18 1 Primary 0.17% 0 .07% 16° 13° 2 0.47 0 . 56 62 23 Ave. 0.24 0 . 23 53 25 21 1 0 . 34 0.05 32 5 2 0.48 0.01 58 1 Ave . 0 .37 0. 08 48 6 Average 0. 30 0.12 51 11 62 TABLE 10'-Continued Date Obs. Obj ect P eP * e 18 1 Companion 0.30% 0. 26% 135° 27° 2 0.47 0.11 46 6 Ave. 0. 04 0 . 20 50 90 21 1 0.59 0 .27 106 9 2 0.10 0. 24 177 65 Ave. 0. 24 0.32 112 22 Average 0 . 09 0.14 107 40 18 1 Intrins ic 0. 41 0. 28 80 12 2 0.27 0.40 53 60 Ave. 0. 20 0.31 4 90 1 0 . 89 0. 27 96 4 2 0. 54 0.23 65 58 Ave. 0 .55 0. 30 106 17 Average 0.34 0.18 117 36 TABLE 11 23 ORIONIS : V Date Obs . Object P 18 1 Primary 0.50% 0. 24% 36° 13° 2 0.46 0 .03 60 2 Ave. 0.44 0.13 47 8 21 1 0.37 0.19 75 19 2 0.59 0.12 69 2 Ave. 0.48 0.10 71 7 Average 0.42 0. 09 57 6 18 1 Companion 0 . 12 0.07 170 16 2 0. 23 0.26 98 29 Ave. 0.07 0.10 115 60 21 1 0. 34 0.78 157 60 2 0.41 0. 39 146 32 Ave. 0. 38 0.21 151 15 Ave rage 0.16 0.11 145 21 63 TABLE 11 --Continued Date Obs. Object P * £P e 4> 18 1 Intrinsic 0.53% 0.25% 54° 20° 2 0.46 0.23 128 30 Ave . 0. 49 0.17 109 53 1 0.70 0.80 94 33 2 0 . 97 0.41 97 19 Ave. 0.85 0.23 95 9 Average 0 . 58 0.14 91 16 consistent on the 18th but is affected in position angle by the error in the first observation of the primary on November 21. In view of the fact that the most difficulty with differential effects is expected to occur in U, the over all average intrinsic polarization is perhaps no more accurate than ±0.3 per cent. However, this is still only one-fourth of the calculated amount so intrinsic polari zation apparently has been measured. In the B filter, the primary has one very sub standard observation while data for the secondary are decidedly mediocre. Again, the scatter in position angles, and the size of their errors, are partly due to the low amount of the polarization and partly to the error in it. Despite these difficulties, the resultant position angles are consistent with those derived for the U filter, 64 with the primary having the largest deviation. This dif ference is 17 degrees, roughly the size of the combined errors in and so not completely contradictory. Hall's observation of 23 Ori at Aeff = 4500A showed Pfi = 0.37 per cent at 74 degrees. The mean intrinsic polarization is much less well established than in U but its position angle is consistent with those results. Observations appear satisfactory for the primary in V but, as before, less than ideal for the companion. The observation of the latter object with the smallest error in P is quite close to the final average. With an even smaller polarization, the position angle is more ambi guous in this filter than the others. On the other hand, the resultant computed intrinsic values become more strongly dependent on the observed characteristics of the primary and the deduced position angle is consistent with the earlier values. It should be recalled that 23 Orionis B was found by Meisel to have a larger observed rotational velocity (370 km/sec) than the primary (350 km/sec). Although the calculated intrinsic polarizations in B and V are the lowest of any program systems, the figure in U is quite large and demands further discussion. After all observa tional results are presented for the remaining stars, the rest of this chapter will be concerned with some general 65 questions of the validity of the observations, among them the problem of the U filter results for 23 Orionis. In the case of HD 45995, an inconsistency in posi tion angle reduces the worth of the U and B data. Hall's figure of 150 degrees supports these results in B and V for the primary (146 and 138 degrees) but the U value of 61 degrees (e^ = 13) is contradictory. One might be tempted to suggest that perhaps something was changed in the connection of the phototubes to the electronics. Exchanging leads to the two photomultipliers gives a position angle difference of precisely 90 degrees. How ever, examination of the companion data shows that the best agreement in position angle is between U and V (56 and 72 degrees). The B figure is 178 degrees. Further confusion results from noting that the fit is fairly good in V and even better in B -- the latter observed on one night only. Poorer results in U are reflected in the large uncertainty in intrinsic polari zation. The B results are more accurate but still in doubt. The data for HD 45995 is summarized in Tables 12, 13, and 14, below. HD 200120 (59 Cyg), the first of the June data, poses the greatest observational difficulties with a separation of 20.3 seconds of arc and Am = 4.5. It was observed twice in U and only once each in B and V. 66 TABLE 12 HD 45995: U Date Obs. Obj ect P £P 4 e4 20 1 Primary 1.83% 0. 04% 80° 1° 2 0, 20 0.09 167 12 Ave. 0. 88 0.41 82 14 22 1 0 . 57 0.29 176 15 2 1 .60 0.30 51 5 Ave. 0 . 83 0.42 43 14 Average 0.67 0.32 61 13 20 1 Companion 0 .77 2.02 63 44 2 0. 21 0. 98 80 133 Ave. 0. 50 2.51 67 128 22 1 0.83 0. 09 50 3 2 3. 39 0. 76 56 7 Ave. 2. 21 0. 61 55 9 Average 1.41 0. 53 56 11 20 1 Intrinsic 1. 26 1.54 27 70 2 0.41 0.98 88 65 Ave. 0 .51 2.35 30 90 22 1 1.16 0. 31 104 7 2 1 .84 0.82 94 8 Ave. 1. 50 0. 74 97 9 Average 0.76 0.62 86 15 TABLE 13 HD 45995 : B Date Obs. Obj ect P £P 4 e«t> 20 1 Primary 0.36% 0. 20% 150° 17° 2 1. 59 0.16 145 3 Average 0.92 0. 27 146 9 20 1 Companion 1.42 0.05 175 1 2 1. 25 0. 06 3 2 Average 1. 33 0. 09 178 2 20 1 Intrinsic 1. 22 0.21 97 5 2 1. 79 0.17 120 3 Average 1. 25 0. 29 111 6 67 TABLI5 14 HD 45995: V Date Obs. Object P * EP e4 20 1 Primary 0.45% 0.25% 167 * 19° 2 0.39 0. 02 91 1 Ave. 0.10 0.21 140 54 22 1 0.77 0.06 130 2 2 0. 26 0. 07 157 13 Ave. 0.45 0.14 138 9 Average 0. 32 0.12 138 11 20 1 Companion 1.35 0.15 81 4 2 0.65 0. 29 150 10 Ave. 0.50 0 . 39 93 25 22 1 0.86 0 . 04 41 2 2 0.37 0.44 90 35 Ave. 0.44 0.27 58 19 Average 0.40 0.23 72 17 20 1 Intrinsic 1. 79 0. 29 89 5 2 0. 89 0. 28 101 5 Ave. 0. 52 0.44 84 13 22 1 1.63 0. 07 89 1 2 0.59 0.45 81 16 Ave. 0.88 0. 30 85 11 Average 0.65 0. 26 79 10 Consequently, little confidence should be placed in the results. One piece of support is Hall's (1958) observa tion of P = 0.37 per cent, $ = 106 degrees, which com pares with the 0.38 per cent and 69 degrees found in this study. Results for 59 Cyg are summarized in Table 15. HD 205637 (e Cap) was observed only twice in each color but the results are more subject to verification since Serkowski (1968) and Coyne and Kruszewski (1969) have also made multicolor observations. 68 TABLE 15 59 CYGNI Date Filter Obj ect P ♦ £P s 14 U Primary 1. 091 0.38% 78° 10° 18 1. 28 0.12 92 3 Average 1.17 0.19 86 5 14 U Companion 0.67 1. 22 68 54 18 0. 37 0.15 52 12 Average 0.46 0.17 63 5 14 U Int r ins ic 0.52 1.30 24 90 18 1. 26 0.19 48 12 Average 0.92 0.22 34 10 14 B Primary 0. 38 0.10 69 6 Companion 1.40 0.41 8 9 Intrinsic 1.63 0.42 84 3 14 V Primary 0.30 0.27 86 26 Companion 0.40 0. 03 23 2 Intrins ic 0.62 0.27 79 13 Table 16 presents data collected in this research, and Figure 8 compares the results with the other observa tions. Each of two observations at every wavelength by Coyne and Kruszewski is represented by open circles. The primary's polarization in B is rather low but U and V compare well. The position angle of the com panion's polarization is roughly 120 odd degrees away from the primary's, so the interstellar polarization is almost a simple addition. This means that the calculated intrinsic polarization cannot be much smaller than its estimated figure in Table 16 or there would have to be a 69 TABLE 16 e CAPRICORNI Date Obs. Filter Obj ect P eP e 22 1 U Primary 1.12% 0.62% 133° 16° 2 0.95 0.13 166 4 Average 0. 88 0.35 148 11 22 1 U Compan ion 1 . 90 1.60 35 27 2 1 . 10 0 . 20 140 5 Average 0. 54 0.48 23 72 22 1 U Intrinsic 2.99 1.72 93 12 2 0.90 0.23 62 7 Average 1.17 1 .08 113 50 22 1 B Primary 0.79 0.12 150 4 2 0.86 0.30 166 10 Average 0.79 0 .16 158 6 22 1 B Companion 1.15 1.02 32 27 2 0.37 0. 27 34 21 Average 0.76 0.47 33 18 22 1 B Intrinsic 1.73 1. 04 101 12 2 0.97 0.40 121 21 Average 1.27 0.50 108 12 22 1 V Primary 1. 29 0.32 166 7 2 1.48 0. 34 170 7 Average 1.39 0.20 168 4 22 1 V Companion 0.31 0.24 25 23 2 0.17 0.05 75 8 Average 0.16 0.12 42 22 22 1 V Intrinsic 1.27 0.40 134 24 2 1.65 0. 34 95 9 Average 1.44 0.23 123 22 very much larger error in the position angle of the com panion. P*r Cant Polarization 1.0 1.4 1.6 bevr. Smos ee,t Tbe a Flos Open Follows: as 4 ‘Symbols Refer, Table to Observers. ice-j Asterisks--RLB. Circles--j, ice-Rfrne Coe Tinls-» Closed Triangles--e» t Closed c Circles--Reference i. -Rsls o e a A n Cmaio wt Other with Comparison and A e Cap for 8--Results Fig. 1,75 l/A( 2 3 70 X)l .02 .03 The results for Ml) 21411> 8 (8 Lac) are compiled in Tables 17, 18, and 19. TABLE 17 8 LACERTAE: U Date Obs. Obj ect P * "P L 4 19 1 Primary 0.57: 0.031 94° 7 © 2 0. 34 0 .08 81 7 Ave. 0.45 0.07 89 5 20 1 0. SS 0.22 95 1 1 ? 0. 2S 0 .05 68 6 Ave. 0. 36 0.13 87 10 Average 0.40 0.07 89 5 19 1 Companion 0. 97 0.05 138 7 7 1 . 05 0.01 144 1 Ave. 1. 00 0 .05 141 i 20 1 0. 50 0. 04 129 i 2 0.47 0.01 175 1 Ave. 0. 33 0.15 1S1 12 Average 0. 6b 0. 12 143 5 19 1 Intrinsic 1. 09 0.06 106 1 2 1. 28 0.08 96 2 Ave . 1. 18 0.09 101 2 20 1 0. 58 0.22 120 11 2 0.69 0.05 84 2 Ave. 0.62 0. 20 104 9 Average 0. 88 0.14 103 3 TABLE 18 8 LACERTAE: B Date Obs. Object P 4 EP e ♦ 19 1 Primary 0.41% 0.43% 84° 29° 2 0.83 0.08 13 3 Ave. 0. 29 0. 26 26 33 20 1 0.45 0.06 32 4 2 0.44 0.04 26 3 Ave. 0.44 0.03 29 2 Average 0.37 0.13 28 11 72 TABLE 18--Continued Date Obs. Obj ect P £ 4 P e4 19 1 Compan ion 1.14% 0.12% 105° 3° 2 0. 30 0. 36 113 28 Ave. 0.71 0.23 107 9 20 1 0.15 0. 38 159 52 2 0.18 0. 33 21 44 Ave. 0.12 0.19 3 44 Ave rage 0. 29 0.18 110 17 19 1 Intrinsic 0.88 0.43 99 14 2 1.11 0. 36 82 21 Ave. 0.98 0.35 93 10 20 1 0.52 0 . 31 61 47 i 0.26 0 .32 9 75 Ave. 0. 38 0 .19 34 51 Ave rage 0.65 0 . 22 95 12 TABLE 19 8 LACERTAE: V Date Obs . Object P 4 £P e 4 19 1 Pr iraary 0.48% 0 . 50% 150° 27° 2 0. 78 0.10 23 2 Ave. 0.42 0.28 8 20 20 1 0.41 0 .32 36 22 2 0.35 0. 59 46 48 Ave. 0.37 0. 28 41 21 Average 0. 33 0. 20 25 16 19 1 Companion 0.51 0.44 106 23 2 0. 38 0.01 78 1 Ave. 0. 39 0. 20 94 14 20 1 0 . 57 0.25 109 12 2 0 . 87 0. 09 98 3 Ave. 0 .72 0.13 102 5 Average 0.56 0.12 100 6 72 TABLE 18--Continued Date Obs. Obj ect P £ 4> P £ 19 1 Companion 1.14% 0.12% 105° 3° 2 0. 30 0. 36 113 28 Ave. 0.71 0 . 23 107 9 20 1 0.15 0 . 38 159 52 2 0.18 0. 33 21 44 Ave . 0.12 0.19 3 44 Average 0.29 0.18 110 17 19 1 Intrinsic 0.88 0.43 99 14 2 1.11 0 . 36 82 21 Ave. 0.98 0 . 35 93 10 20 1 0.52 0. 31 61 47 2 0. 26 0 . 32 9 75 Ave. 0. 38 0 . 19 34 51 Average 0.65 0 . 22 95 12 TABLE 19 8 LACERTAE: V Date Obs . Object P £P ♦ 19 1 Primary 0.48% 0 . 50% 150° 27° 2 0.78 0 . 10 23 2 Ave. 0.42 0 . 28 8 20 20 1 0.41 0 . 32 36 22 2 0.35 0. 59 46 48 Ave. 0. 37 0. 28 41 21 Average 0. 33 0 . 20 25 16 19 1 Companion 0.51 0.44 106 23 2 0. 38 0.01 78 1 Ave. 0. 39 0. 20 94 14 20 1 0.57 0 .25 109 12 2 0. 87 0.09 98 3 Ave. 0.72 0.13 102 S Average 0. 56 0 .12 100 6 73 TABLE 19--Continued Date O b s . Obj ect P 4 CP e4 19 1 Intrins ic 0. 69% 0.64% 68° 26° 2 0 . 97 0. 09 114 2 A v e . 0 .81 0. 34 92 13 1 0 . 94 0.40 97 11 2 1 .02 0. 59 100 17 A v e . 0.97 0. 31 99 8 Average 0 . 86 0. 23 96 7 Observations of 8 Lac have unusually low polariza tion errors in U and somewhat larger ones in B and V. However, the position angles in U deviate from the more self-consistent values in B and V by more than the com bined errors in either case. The multiple star system 8 Mon was observed twice on each of two nights in November, 1968. The reduction procedure outlined on pages 25 through 27 was followed and yielded satisfactory results from the viewpoint of error size and self-consistency except for the first nights' B and V data on components A and B. The observed polarizations and position angles for components A, B, and C are listed in Table 20, not including the rejected B and V data. Of the three components, B is by far the slowest rotator. Its polarization is taken to be purely inter stellar for the purposes of calculating the derived ! TABLE 20 6 MON Date Obs. Filter Obj ect P 4> e EP 17 1 U A 0 . 85% 0. 55% 20° 9 2 0.87 0. 22 2 8 Ave . 0 . 84 0. 22 11 8 23 1 0.66 0. 00 22 0 2 0 . 18 0. 26 2 38 A v e . 0.42 0.14 17 10 Average 0. 75 0.15 12 6 17 1 U B 1. 62 0,01 72 1 2 0. 64 0. 27 90 13 A v e . 1. 03 0. 26 76 7 23 1 0. 12 0.18 142 38 2 0. 27 0, 23 89 24 Ave . 0.11 0, 13 104 34 Average 0. 83 0,19 77 7 17 1 U C 2.63 0.45 124 6 2 1. 10 0. 56 123 12 A v e . 1. 91 0 . 42 125 7 23 1 0. 57 0. 22 89 12 2 1,25 0 .37 122 10 A v e . 0.81 0.53 113 12 Average 1. 67 0. 29 124 5 23 1 B A 1. 00 0. 24 11 6 2 1, 10 0 . 01 14 1 Average 1. 05 0 . 09 13 3 23 1 B B 0 . 49 0. 28 87 14 2 0,31 0. 30 96 29 Ave rage 0. 38 0, 17 90 13 17 1 B C 0.85 0.32 150 13 2 0, 97 0. 22 149 6 A v e . 0,92 0.16 149 6 23 1 0.74 0. 38 88 13 2 0. 68 0. 24 108 12 A v e . 0. 66 0. 20 98 9 Average 0.72 0.17 144 7 75 TABLE 20--Continued Date Obs . Filter Obj ect P 4 £P 23 1 V A 0.91% 0.13% 13° 5° 2 0.45 0.15 14 10 Average 0.70 0.12 13 5 23 1 V B 0.63 0.15 79 8 2 0. 54 0.05 70 2 Average 0. 59 0. 08 75 4 17 1 V C 1. 94 0.01 130 1 2 0.70 0.17 128 8 A v e . 1.33 0. 26 130 7 23 1 0. 57 0.12 78 7 2 0.68 0.06 165 3 A v e . 0 .06 0. 27 121 90 Average 1.15 0. 21 130 6 intrinsic polarization of components A and C. The results are presented in Table 21. It should be noted that the calculated intrinsic polarizations for individual B and V observations of component C on November 17 reflect the poor data on com ponent B. Final results, denoted by "Average" in the first column of Table 21, are computed from the averaged observed polarizations for the appropriate stars and do not represent an average of the computed intrinsic polarizations. Comparison of this "final average" with the computed quantity for individual observations indi cates that the intrinsic polarization of component C may be too high by several tenths of a per cent in the U and V bands. The standard errors in both amount and position 76 TABLE 21 B MON: INTRINSIC POLARIZATIONS Date Obs . Filter Obj ect P ♦ e £P 17 1 U A 2. 01% 0. 40% 102° 7 2 1. 51 0.35 91 9 Ave . 1.70 0.35 101 5 23 1 0. 73 0.17 64 34 2 0.45 0.35 91 18 A v e . 0.53 0. 19 92 28 Average 1.43 0. 24 102 5 17 1 U C 3.40 0.48 66 5 2 1.02 0.60 50 20 Av e . 2. 28 0. 50 62 8 23 1 0.61 0.27 122 37 2 1.16 0.44 39 27 Av e . 0.70 0. 54 11 42 Average 1.91 0.35 60 7 23 1 B A 1.46 0. 37 99 11 2 1.40 0.30 97 23 Average 1.40 0. 20 99 10 17 1 B C 0. 55 0.38 33 25 2 0.77 0.25 50 10 A v e . 0.67 0. 20 45 10 23 1 0.25 0.47 S 57 2 0.42 0. 39 21 50 A v e . 0.31 0. 27 17 32 Average 0.91 0 . 24 66 20 23 1 V A 1.41 0. 20 105 6 2 0. 81 0. 16 106 6 Average 1. 13 0.15 106 4 17 1 VC 1.07 0. 01 171 1 2 1.03 0.19 111 5 A v e . 0.99 0. 37 140 14 23 1 0.07 0. 20 100 88 2 1. 21 0.08 93 2 Ave . 0.60 0. 27 87 13 Average 1.72 0.38 83 5 77 angle of the calculated polarization are larger for com ponent C than for A, as might be expected. The only other polarimetric observation of the system known to this writer is reported by Hall (1958). He lists a polarization for g Mon A of .031 magnitudes, or about 1.4 per cent -- about double that found here. The position angle given by Hall is two degrees, comparing fairly well with the current result of 13 degrees. For convenience, the final polarimetric results for all program systems are tabulated in Table 22. The observed quantities for the primary, the secondary, and the derived intrinsic polarization for the primary are listed by rows for each system while the columns delineate data in the three filters. The intrinsic polarizations are displayed in Figure 9 as a function of wavelength; open circles denote stand ard errors of at least 0.3 per cent while filled circles indicate errors less than this amount. The spread in intrinsic polarizations is about the same in each filter but with a considerable variety of wavelength dependences. The difference between the largest and smallest calculated polarizations is 1.15 per cent in U, 1.29 in B, and 1.14 in V. However, 23 Ori, 8 Lac, and g Mon C are decidedly concave downward, 59 Cyg and HD 45995 markedly so upward, while e Cap A and 6 Mon A are nearly linear -- but with slopes of opposite sign. TABLE 2 2 SUMMARY OF POLARIMETRIC DATA Star P ♦ P ♦ P ♦ £P 23 Ori-A 0.45% 0.10% 34° 7° 0.30% 0.12% 51° 11° 0.42% 0.09% 57° 6 -B 0.87 0.20 98 6 0.09 0.14 107 40 0.16 0.11 145 21 1.20 0.22 99 3 0.34 117 36 0.58 0.14 91 16 AI 0.18 HD 45995-A 0.67 0.32 61 13 0.92 0.27 146 9 0.32 0.12 138 11 -B 1.41 0.53 56 11 1.33 0.09 178 2 0.40 0.23 72 17 AI 0.76 0.62 86 15 1.25 0.29 111 6 0.65 0.26 79 10 59 Cyg-A 1.17 0.19 86 5 0.38 0.10 69 6 0.30 0.27 86 26 -B 0.46 0.17 63 5 1.40 0.41 8 9 0.40 0.03 23 2 AI 0.92 0. 22 34 10 1.63 0.42 84 3 0.62 0.27 79 13 e Cap-A 0.88 0.35 148 11 0.79 0.16 158 6 1,39 0,20 168 4 -B 0.54 0.48 23 72 0.76 0.47 33 18 0.16 0.12 42 22 A i 1.17 1.08 113 50 1.27 0.50 108 12 1.44 0.23 123 22 8 Lac-A 0.40 0.07 89 5 0.37 0.13 28 11 0.33 0.20 25 16 -B 0.66 0.12 143 5 0.29 0.18 110 17 0. 56 0.12 100 6 A i 0.88 0.14 103 3 0.65 0.22 95 12 0.86 0.23 96 7 6 Mon-A 0.75 0.15 12 6 1.05 0.09 13 3 0.70 0.12 13 5 -B 0.83 0.19 77 7 0.38 0.17 90 13 0.59 0.08 75 4 -c 1.67 0.29 124 5 0.72 0.17 144 7 1.15 0.21 130 6 Ai 1.43 0.24 102 5 1.40 0. 20 99 10 1.13 0.15 106 4 CI 1.91 0.35 60 7 0.91 0.24 66 20 1.72 0.38 83 5 00 79 59 Cyg 1.6 « Cop $ Mon-A u o HO 45995 8 L«C .O l 23 Orf u 6 V Fig. 9--Derived Intrinsic Polarizations for the Seven Program Stars. Open Circles Denote Numbers with a Standard Error >_ 0.31; Filled Circles, Standard Errors < 0.31. 80 One point in favor of the program star observations, insofar as they indicate the presence of intrinsic polari zation, is that the position angles of the components are generally well differentiated. With the "standard" double stars, the difference between the position angles of the pair members is less than the sum of their standard errors in eight of nine cases. However, with the program stars there is only one example where the position angle difference is less than the combined standard errors. The validity of the results for intrinsic polariza tion may also be partially judged by another consideration of the results for the standard double stars. The calcu lated "intrinsic" polarization for these objects was found to be surprisingly high and was ascribed to inferior observations. For discussion purposes, assume, instead, that these results represent the threshhold of sensitivity of the apparatus for the detection of intrinsic polariza tion. Taking the maximum figures derived for each band pass from Table 8, the assumed sensitivity levels are .57, .39, and .75 per cent for U, B, and V, respectively. Applying this hypothesis to Figure 9, it is seen that the three lowest intrinsic polarizations in V (those of 23 O r i , 59 Cyg, and HD 45995} fall below the threshhold, while the next lowest points, representing 8 Lac and 6 Mon A, lie above it by .12 and .38 per cent, respec tively. In the B region, only 23 Ori lies below the 81 hypothetical level while none do in the U filter results. By this test, most of the intrinsic polarizations derived in the B bandpass are the most securely established by reason of their distance above the assumed threshhold. In U, all are above it but by a smaller margin on the average. In V, three results are below the criterion of acceptability set by this rather extieme test. At this point, the difficulties must be faced that are presented by the significantly high V sin (i) of 23 Ori B and, to a lesser degree, of HD 45995 B. The quantity plotted in Figure 9 is actually the differential polariza tion between two objects. It can be called fully intrinsic within the errors of observation only if all the polariza tion in the light of one object arises in the interstellar medium and if differential instrumental polarization is not bothersome; the latter was indicated to be so in Chapter 4. In the case of 23 Ori, both components have V sin (ij’s and spectral types that do not allow the presence of intrinsic polarization to be ruled out. In fact, 23 Ori B is rotating more rapidly than the primary. Since the derived intrinsic polarization is unaltered by interchanging Pq and Pj in Equation 31, Chapter 3, it could just as well be ascribed to 23 Ori B, Viewed as differential, rather than intrinsic, polarization the B and V results are understandably low but in U a consider ably higher figure was derived. If valid, and the U 82 observations do appear to be fairly good, then a different wavelength dependence of polarization is implied. In any case, the results cannot be directly compared with those more reliably called wholly intrinsic and, thus, should not be quoted as supporting a correlation between frac tional breakup velocity and intrinsic polarization. HD 45995 B poses somewhat less of a problem since it is rotating more slowly than the primary and H6 only "appears to be in emission" on a fogged spectrogram (Meisel, 1968). It is probably correct to regard the HD 45995 results as more "purely" intrinsic than those of 23 Ori but not quite as much so as the results of the rest of the program systems. All things considered, it seems that the most well established examples of intrinsic polarization are 6 Mon A, e Cap A, 59 Cyg A, and 8 Lac A. Less well determined are 6 Mon C and HD 45995 A while the 23 Orionis system is not open to unambiguous discussion. Another consideration is that of variability. Shakhovskoi’s (1962) observations of x Oph indicated a change in polarization of as much as .36 per cent in four days. Data collected over a 13-day span, however, varied by only .09 per cent. Two multicolor observations of e Cap A by Coyne and Kruszewski (1969) separated by two months showed polarization differences of from .19 to .42 per cent, depending on wavelength. The same star noted 83 by Behr to be a possible polarization variable, y Cas, has been observed by Hutchings (1967) to display significant changes in emission line intensity on a time scale of several minutes. Unfortunately, the observations made in the course of this work do not allow a positive state ment to be made with regard to variability on any of these time scales. Several minutes are required to perform a single observation so that time resolution is insufficient with regard to the shortest time scale. Observations were made no further apart than six days and usually less than four days so that a base line was never established to detect changes in an interval of the order of two months. Considering a time scale of a few days, no indication of variability is evident other than scatter in the program star observations of the same order of magnitude as in the data for single star polarization standards. At the undertaking of this research, it was thought that any intrinsic polarization had its origin in the rotationally darkened and distorted atmosphere of a rapidly spinning Be star. Accordingly, there should be a strong correlation between intrinsic polarization and V sin (i) for a given spectral type; that is to say, between intrinsic polarization and the fraction of equa torial breakup velocity at which the star is rotating (Vj,) . It is assumed that the program Be stars are being seen nearly equator-on. Although Collins' (1970) latest 84 work indicates that the atmosphere is not the place of origin of intrinsic polarization, it is still to be asso ciated with the Be phenomenon and that is fundamentally a rotational phenomenon. Thus, it appears worthwhile to compare the derived intrinsic polarizations with each object's rotational velocity normalized to the theoreti cal breakup velocity for that spectral type. For the latter quantities, the results of Faulkner, Roxburgh, and Strittmatter (1968) is adopted. Their calculated breakup velocities are tabulated only for one, two, and five solar masses -- the latter two figures corresponding to main sequence stars of spectral types about AO and Bl, respectively. Values for intermediate B types were inter polated linearly between the AO and Bl points. Table 23 summarizes the relevant data. The luminosity class in column 2 is IV or V unless otherwise indicated. It should be kept in mind that the observed V sin (i)'s may be in error by as much as 50 km/sec and that other, systematic, errors may be present. Also, the models used yield break up velocities lower than those of other theoretical workers. In Figures 10, 11, and 12 the calculated intrinsic polarizations are plotted as a function of the ratio of V sin (i) to theoretical breakup velocity, as listed in Table 23, for each filter. Correlation coefficients were calculated between P* and log (V sin (i)/V^) for the U, B, and V filters and were 0.41, 0.47, and 0.36, respectively. 85 TABLE 2 3 FRACTIONAL BREAKUP VELOCITIES FOR PROGRAM STARS Obj ect Sp. Type vb V sin (i) V sin (i)/Vb 23 Ori-A Bl 404 km/sec 350 km/sec 0. 87 -B B3 393 370 0.94 6 Mon-A B4 386 350 0.91 -B B 2 399 130 0. 33 -C B4 386 370 0.96 HD 4 599 5 - A B3 393 320 0.81 -B B8 357 220 0.62 59 Cyg-A Bl 404 420 1.04 -B A8III « » 100 * * e Cap-A B5 380 370 0.97 -B K1III-IV « • 50 • * 8 Lac-A Bl 404 327 0.81 -B B 2 399 30 0. 08 For a sample size of seven, this means that a zero corre lation can be excluded only at significance levels of 20 per cent in U and B and of 25 per cent in V. Similar cor relation calculations, only linear in the fractional breakup velocity were all lower. It would appear that only a weak correlation exists, if any, but a stronger interdependence could be masked by errors. Comments with regard to group properties, such as above, are rather limited in force not only because of the non-trivial observational errors but also due to the small sample size. Unfortunately, no large increase in the sample size can be made due to the limited number of binary systems fulfilling the research requirements. Oorivtd Intrinsic Polarization, Psr Csnt 2.0 1.0 gis te ai o sn i t Tertcl Breakup Theoretical to (i) sin V of Ratio the Against 1.5 Velocity for U Filter Observations. Filter U for Velocity i. 0-eie Itisc oaiain s Plotted Is Polarization Intrinsic 10--Derived Fig. vsini/ 1.0 04 .0 .02 03 .0 86 gis te ai o V i () o hoeia Breakup Theoretical (i) to sin V of Ratio the Against Ocrivtd Intrinsic Polarization, P*r Cent Velocity for B Filter Observations. Filter B for Velocity i.e i. 1-Drvd nrni Plrzto Is Plotted Polarization Fig. ,11--Derived Intrinsic 1.7 1.0 005 0 .0 .01 .02 X>3 p t Ob Derived Intrinsic PoJarizotion, Per Csnt 2.0 1.0 gis te ai o sn i t Tertcl Breakup Observations. Filter V Theoretical to (i) for sin V Velocity of Ratio the Against 1.9 i. 2-eie Itisc oaiain s Plotted Is Polarization Intrinsic 12--Derived Fig. i / V / isin v 1.0 .03 04 .0 88 89 As a study of intrinsic polarization, this research has provided some new information. Even with allowance for observational errors and uncertain instrumental polar ization, particularly at shorter wavelengths, it has been fairly well established that intrinsic polarization of over one per cent has been observed. It appears that there is not only a local polarization to be associated with the primary of several of the observed systems but also a difference in wavelength dependence between systems. This dependence ranges from a strong maximum in the B filter to more nearly linear curves, but oppositely sloped, and to curves with a minimum in B but with some increased uncertainty and ambiguity. In the final chapter the results will be discussed with regard to possible origins of the local polarization, and recommendations for further observational work will be m a d e . VI. INTERPRETATION OF RESULTS The double star results reported here and the time variation and peculiar wavelength dependence noted by other observers establish the existence of intrinsic polarization in Be stars with a rather high degree of certainty. Although much observational work remains to be done, some comments about the nature of the phenomenon may be made at this time. Harrington and Collins (1968) and Collins (1970) have examined in detail the influence of the relevant photospheric parameters on the intrinsic polarization of early type stars, and Harrington (1969) has begun an analysis of the problem for late type stars. The most detailed calculations on the atmospheres of rapidly rotating early type stars (Collins, 1970) indicate that negligible intrinsic polarization is to be expected at optical wavelengths. The only apparent alternative is to direct attention to the circumstellar shell as the source of the local polarization. However, since no investiga tions have been made of the effect of a circumstellar envelope on the transport and polarization of light emerging from such an atmosphere, the following discussion will be more qualitative than quantitative. 90 91 The critical requirements for there to be intrinsic polarization are a scattering component in the opacity to produce polarization on the microscopic level and a suffi cient lack of symmetry to preclude self-cancellation of the effect in the integrated light of the object. In Be stars the precise mechanism of material ejection is not known but it may be argued that, whatever the imme diate photospheric cause, it is bound to be more effective in the equatorial regions due to the much reduced effective gravity. This would lead to a "shell" that is more disk like than spherical. In fact, Hutchings’ (1968) analysis of the BOIV shell star y Cas led him to conclude that the observed double-peaked emission lines could only be achieved by a shell much thinner and flatter than a spherical one. With regard to intrinsic polarization in late type giants, there is no ready-made mechanism for an asymmetrical distribution of matter above the photo sphere. In such objects the surface gravity itself is already several orders of magnitude smaller than that of B stars and mass loss is well established (Deutsch, 1960) so that an ejection mechanism of unequal distribution across the stellar surface, in analogy to solar promi nences, may be sufficient for asymmetry. On the other hand, gross mass asymmetry may not be required (see Harrington, 1969). In the case of late type supergiants, the temperature is sufficiently low so that the formation 92 of molecules and, perhaps, graphite and other particulate matter is promoted. All are strong scattering agents. There may also be reason to expect scattering to play a role in the transfer of radiation out through the material around Be stars. Marlborough (1969) has esti mated that electron scattering is important in the broadening of the wings of Hct. Due to the sharpness of the core of the line, however, significant scattering must be restricted to the inner regions of the envelope, which, in Marlborough's models, corresponds to distances of a half-dozen or so stellar radii. Coyne and Kruszewski (1969) have discussed the character of the observed wavelength dependence of polari zation for Be stars in relation to the properties of circumstellar shells. Although individual graphs of polarization versus wavelength differ markedly from star to star, the mean plot is, in a rough fashion, inversely related to the continuous absorption coefficient of hydrogen. That is to say, for increased H absorption the normalized mean polarization of various emission line objects is lower. The interpretation is that for condi tions appropriate to Be shells electron scattering is an important, yet frequency-independent, polarizing agent; however, in wavelength regions of increased absorption by hydrogen the radiation due to recombination is redis tributed randomly with regard to the orientation of the 93 plane of vibration and, hence, there is a depolarization effect. If the data represented in Figure 9 are averaged, excluding 23 Ori and e Mon C, then the mean intrinsic polarization as a function of wavelength is Py = 1.03, Pg = 1.24, and Py = 0.95 per cent. Normalized to Pg we have then .83, 1,00, and .77 in the U, B, and V filters, respectively. Figure 13 reproduces these numbers (filled circles) along with Coyne and Kruszewski's plot of norma lized polarization averaged over eight Be stars (open circles). Since both sets of data are normalized to the B bandpass, agreement there is built-in. The agreement is also excellent in U , but there is a considerable dif ference in V. Mean polarizations are to be taken with a grain of salt since radical departures from the average may be found in the sample from which the mean was derived. If the mean relation is used to make a case for a specific mechanism, it may be that individual examples are contra dictory. In this research, the objects 8 Lac A, e Cap A, and £ Mon A provide the best established counter-examples to Coyne and Kruszewski's electron scattering model. Some other program systems show a polarization minimum in the B filter and, hence, are also contrary cases but with a lesser degree of observational reliability. It should be pointed out that a unique wavelength variation of the intrinsic or "local" polarization is not Avaroga Normalized Polarization 100' 0 9 80 0 6 0 5 TO pn ice, n te ae o Itisc oaiain Ti Rsac, lsd ^ Closed Research, This Polarization, Intrinsic for Same the and Circles, Open ice, lte ess nes Wvlnt. ^ Wavelength. Inverse Versus Plotted Circles, i. *-Aeae omlzd oaiain rmCye n Kuzwk (1969), Kruszewski and Coyne from Polarization 1*3--Average Normalized Fig. 2 ' 3 i 9 5 implied by the combination electron scattering and contin uous absorption picture presented by Coyne and Kruszewski. They state that their mean polarization curve may be achieved with an average electron density of 1012 cm"3 through a thin circumstellar disk approximately three stellar radii in extent and with an electron temperature of 10U°K. These values are consistent with the current knowledge of the conditions in such objects and agree roughly with Marlborough's (1969) recent models of Be star envelopes. A flatter curve than that in Figure 13 can result if the neutral hydrogen density is lowered while maintaining a constant electron density, i.e., a higher degree of ionization. Under these conditions a photon traversing the circumstellar envelope has the same probability of being scattered but a smaller likelihood of ionizing a neutral H atom. This would also result in a higher net polarization. If the opposite prevailed, that is, the same electron density but more neutral atoms, then a stronger frequency dependence and a lower intrinsic polar ization would be expected. While a certain variety of polarization-versus-wavelength curves may arise from the above model, it does not allow a variation of the position of minima and maxima. If the counter-examples mentioned above are observationally sound, then an electron scatter ing model of the circumstellar shell cannot be the sole 96 origin of intrinsic polarization. In view of the above difficulties, one may be moti vated to search for alternate scattering agents. A rather ubiquitous agent that should come under scrutiny is par ticulate matter, the same material responsible for inter stellar polarization. At first glance, it would seem that the conditions in the immediate vicinity of early type stars, i.e., a much higher radiation field, would tend to disrupt the alignment of particles necessary to produce polarization and, in the case of some types of grains, would foster the evaporation of the particle itself. However, this may not be so. In the Pleiades, with some stars as early as B 6 , nebular polarization is observed to occur in a manner implying it is done by non-spherical particles non-randomly oriented (Johnson, 1968) , Additional evidence of the possibility of a solid constituent in the circumstellar shells of Be stars is the infrared excess noted by Johnson (1967). In a survey of some 85 0 and B stars, he reported a considerable infrared excess in several shell stars. Some additional early type objects in Orion show similar excesses but these may be due, in part, to peculiar reddening laws. This overabundance of long wavelength radiation in Be stirs may be interpreted as emission from a possible granular component of circumstellar shells. The presence 97 of a local concentration of small particulate material could also influence the amount and wavelength dependence of intrinsic polarization. If there is a considerable infrared excess around Be stars, there may also be some differential extinction between such a primary and its companion in a double system. If accurate photometry is available for both pair members and they are known to be B stars, Johnson and Morgan*s Q-method (1953) may be applied to derive the reddening. The reddening, and hence the method, is slightly dependent on spectral type (Johnson, 1958) so that this information is also necessary for the best results. Unfortunately, only one of the program systems, 8 Lac, meets these requirements. Adopting the colors for 8 Lac from Johnson and Morgan and applying the Q- method yields a difference in B-V color excess of Efi-v = If the ratio of total-to-selective absorp tion is taken to be 3.0, then the differential absorption is only 0.09 magnitudes and is probably not too signifi cant a number. Somewhat less accurate photometry is available for 3 Mon A and C (Mendoza, 1958). No photometry is avail able for 6 Mon B, but the polarization measurements do allow differential colors to be derived. The sum of the responses at all position angles for a given photomulti plier tube represents a polarization-independent "intensity" for the star in question. Division of this quantity by the summed responses for the second object yields a Am for that observation. The same procedure may be followed for the results from the second photo tube and, since only ratios of stellar responses are calculated, this is a second, simultaneous observation. The resultant set of ratios may be averaged over all observations and a mean Am derived. The magnitude dif ference between components A and C, derived as above, agrees with Mendoza's colors to within a tenth of a magnitude or better in all three filters. Using the same ratio of total-to-selective absorption, there is somewhat better evidence of differential absorption in this system. The derived absorptions for components A, B, and C are 0.25, 0.05, and 0.13 magnitudes, respective Suppressing the spectral type dependence of the reddening, that is, following Johnson and Morgan (1953), the Q-method implies spectral types slightly earlier for 6 Mon A and somewhat later for B and C relative to Meisel's classification. Good agreement is for the published types of 8 Lac A and B. Similar results for the differential reddening in both systems are obtained using the 1953 version of the Q-method. No current theory attempting to describe the nature of the solid component of interstellar matter is without its weaknesses. With regard to polarization, one at 99 least requires a maximum somewhere in the visible wave- ’?ngth region and a certain flexibility in the exact placement of this maximum. From Greenberg's (1968) sum mary, it appears that neither metallic grains, pure graphite flakes, nor free radicals pass this test. Particle models consisting of a metallic or graphite core with a dielectric mantle have been calculated to satisfactorily reproduce the interstellar extinction curve shortward of about 2600A. However, the scattering theory required to obtain the wavelength dependence of polarization is not fully developed, and only qualitative results have been obtained. The properties of dielectric grains, or "dirty ice," have been more thoroughly ana lyzed and can yield an adequate representation of the interstellar wavelength dependence of polarization with a distribution of particle radii. For a single size radius of 0.25p and an index of refraction equal to that of ice, a double-peaked dependence results and is similar to the curve in Figure 13. The minimum between peaks seems to be too shallow, particularly for a highly dis ordered array of grains, but would act in conjunction with the electron scattering-H absorption mechanism if the latter were also active. There are abundant quantities of work remaining to be done in this area, both of a theoretical and observa tional nature. The program stars observed here, and a 100 few additional systems, merit further careful multicolor observation. The double systems and other Be stars need consistent monitoring over a time span of several weeks to acquire adequate documentation of time variations in polarization. It would also be useful to do polarimetry through an Ha interference filter to help determine the mechanism giving rise to the local polarization and the shell structure. Theoretical investigations are called for to do the problem of the transfer of continuous radia tion through a circumstellar shell while allowing for its polarization both by electron and granular scattering agents. With regard to the latter, an analysis of the factors governing the growth and destruction of various grain types in this environment is needed. APPENDIX A OBSERVATIONS OF STANDARD SINGLE STARS Object Date Obs. Filter ♦ < Gas N o v , 1 U 0. 59% 0.01% 101° 1 B 0.18 0.02 96 4 V 0.65 0.08 89 4 2 U 1.10 0. 20 96 5 B 0. 50 0.09 101 5 V 1.02 0.02 ' 81 1 A v e . u 0. 83 0.14 98 4 B 0. 34 0. 08 100 7 V 0. 84 0.10 84 3 N o v , 1 U 0.46 0.14 67 2 B 0. 31 0.01 85 1 V 0. 67 0. 09 79 4 2 u 1.72 0. 08 102 2 B 0. 33 0.13 85 10 V 0. 80 0 .08 83 3 A v e . U 0. 94 0.32 95 11 B 0. 32 0. 06 85 5 V 0.73 0.06 81 2 Nov, 1 U 0.39 0 . 01 74 1 B 0. 33 0 . 04 72 4 V 1.01 0.10 76 3 2 u 0.48 0.03 66 2 B 0.37 0.02 74 2 V 0.82 0.12 75 5 A v e . u 0.43 0. 03 70 2 B 0.35 0.02 73 2 V 0.91 0.08 76 3 101 102 APPENDIX A--Continued Object Date Ob s. Filter P cp <)> « Cas Nov. 23 1 u 1. 04% 0 .38% 106° 11 B 0.33 0.12 131 10 V 0.92 0. 14 87 4 2 U 0.87 0.40 106 14 B 0. 33 0.13 85 10 V 0. 94 0.20 84 6 Ave. U 0. 96 0.23 106 7 B 0 . 21 0.13 107 15 V 0. 93 0.10 85 3 K Cas Average U 0.73 0.12 96 5 B 0. 28 0.04 90 4 V 0, 84 0.05 81 2 19 Aur Nov. 20 1 u 1.48 0. 20 167 4 B 0.77 0.08 179 3 2 U 0. 84 0.15 163 6 B 0 . 68 0.01 175 1 V 0. 80 0.06 171 2 19 Aur Average U 1.15 0.17 165 4 B 0.73 0.04 177 2 V 0.80 0.06 171 2 0 Boo Nov. 13 1 U 0. 44 0.42 159 28 B 0.44 0.07 50 5 V 0.44 0.03 63 2 2 u 0.92 0.05 106 1 B 0. 49 0.13 70 9 V 0. 27 0. 08 120 8 Ave. u 0. 42 0. 28 124 20 B 0 . 44 0.09 61 6 V 0. 20 0.13 81 18 Nov. 14 1 U 1 .71 0.16 101 3 B 2.9 7 1.19 S 0 1 3 V 1.17 0.30 14 *7 103 APPENDIX A--Continued Object Date Obs. Filter P ep 0 Boo Nov. 14 2 u 0,711 0. 18% 105° 8 B 0. 78 0. 25 73 9 V 0.41 0 . 66 141 53 Ave . U 1 . 19 0. 23 102 6 B 1 . 89 0 .69 84 11 V 0.63 0.42 5 18 Nov. 18 1 U 0. 72 0 . 39 115 17 B 0 . 27 0.02 7 2 V 0. 24 0 . 07 96 8 2 U 0.81 0 . 25 68 22 B 0.23 0 . 04 15 6 V 0 . 13 0 . 07 108 16 Ave . u 0. 53 0 . 35 87 19 B 0.25 0 . 03 11 3 V 0.18 0 . 05 100 8 Nov. 19 1 U 2.12 0. 24 117 3 B 0 .42 0. 04 12 3 V 0 . 07 0.27 164 122 2 u 0 . 39 0.11 102 8 B 0 . 37 0 . 05 12 4 V 0 . 09 0 . 01 101 2 A v e . U 1 . 23 0. 38 115 9 B 0. 39 0.03 12 2 V 0. 04 0 . 12 124 88 Nov. 20 1 u 0. 91 0. 13 108 4 B 0.44 0.13 10 9 V 0.09 0.13 94 38 2 u 0.22 0 . 3 3 30 44 B 0. 72 0. 34 15 13 V 0.12 0. 23 122 55 A v e . u 0 . 36 0. 28 105 21 B 0 . 57 0.16 13 8 V 0.09 0 .13 111 29 104 APPENDIX A--Continued Object Date Obs. Liter P ♦ e P 0 Boo Nov. 21 1 U 2.21% 0.16% 124° 2 B 0.57 0. 09 114 3 V 0.16 0.01 113 2 2 U 0.57 0.09 114 3 B 0.57 0.16 23 4 V 0.12 0.13 131 31 A v e . U 1 . 39 0.35 122 7 B 0.35 0.12 13 10 V 0. 13 0. 06 121 12 0 Boo Average U 0. 76 0. 14 111 5 B 0 . 28 0.15 59 16 V 0 . 05 0 . 07 99 40 HD 154445 Nov. 13 1 u 2.76 0 . 19 92 2 B 3.18 0.05 89 1 V 3.5 2 0.21 88 2 L.■y u 3 . 68 0 . 09 92 1 B 3 . 28 0 . 26 88 2 V 3. 67 0.21 87 2 Ave . U 3 . 23 0 . 21 92 2 B 3 . 23 0.11 88 1 V 3. 59 0 . 13 88 1 Nov. 15 1 U 3. 26 0 . 75 101 7 B 2.75 0 . 08 90 1 V 3.40 0 . 20 86 2 2 u 3 . 09 0 . 29 92 3 B 2. 72 0 . 20 86 2 V 3. 19 0. 19 91 2 A v e . u 3. 14 0. 38 97 4 B 2. 73 0.11 88 1 V 3.28 0.17 88 2 Nov. 19 1 U 3.81 0. 13 93 1 B 3.37 0.12 89 1 V 3.48 0 . 28 89 2 105 APPENDIX A--Continued Object Date Obs. Filter P 4 £ £P HD 154445 Nov. 19 2 U 3 . 59% 0.12% 93° 1 B 3 .03 0 .11 87 1 V 3.21 0.30 89 Ave. u 3 . 70 0.09 93 1 B 3. 20 0.11 88 1 V 3 . 34 0.18 89 Nov. 2 2 1 u 5. 56 0. 08 95 1 B 3 .05 0.01 88 1 V 3. 16 0. 37 89 3 2 u 3.34 1.46 146 12 B 4. 89 0.75 89 5 V 3.12 0.22 88 2 Ave. u 2 . 94 1.44 111 16 B 3. 98 0.49 89 4 V 3.14 0.18 89 2 HD 154445 Average u 3.21 0.32 96 3 B 3.25 0.13 88 1 V 3. 39 0.08 88 1 96 Her Nov. 18 1 u 1. 43 0.75 113 19 B 0. 90 0.08 170 3 V 1 . 01 0.21 176 6 2 u 0.65 0. 28 173 12 p 1 1 1. 27 0. 26 179 6 V 0.88 0. 10 172 3 Ave, u 0.63 0.53 127 24 B 1 . 07 0.15 175 4 V t 0.94 0. 10 174 3 Nov. 20 1 U 0.44 0.46 133 30 B 0. 59 0. 22 171 1 1 V 0.65 0.42 178 18 2 U 0.65 0.21 10 9 B 0. 76 0.29 4 11 V 0. 53 0.31 178 17 106 APPENDIX A--Continued Object Date Obs. Filter P ♦ E £P 96 Her Nov. 20 Ave. U 0. 30 0 . 28 170 26 B 0. 66 0.17 178 7 V 0. 59 0.21 178 11 Nov. 21 1 u 1.14 0.77 121 19 B 0.88 0.07 162 2 V 1.16 0.16 176 4 2 u 0.44 0.35 117 23 B 0. 86 0.05 1 2 V 1.17 0.15 176 4 Ave. U 0. 80 0 . 38 120 13 B 0.83 0.12 171 4 V 1.16 0 .09 176 2 96 Her Average u 0.49 0 . 23 129 14 B 0.87 0 .09 174 3 V 0.90 0.09 176 3 P Aql Nov. 13 1 u 0.31 0.41 176 37 B 0.59 0.19 7 10 V 0.41 0.35 32 25 2 U 0 . 52 0.02 106 1 B 0.68 0.18 3 7 V 0.47 0. 23 37 14 Ave. U 0.17 0. 23 123 40 B 0.64 0.11 5 5 V 0.44 0.17 35 12 Nov. 18 1 u 1. 20 0.78 98 18 B 0.32 0.16 3 14 V 0.33 0.01 87 1 ~ i u 0.09 0.13 1 b6 44 B 0 . 35 0.01 8 1 V 0.35 0.02 92 2 Ave . U 0. 56 0.40 100 20 B 0.34 0.06 5 6 V 0. 34 0.01 90 1 107 APPENDIX A--Continued Object Obs. Filter P 6 Aql Nov. 20 .1 nl - U ' " 0.70% -0.37% . 138° 14° B 0. 18 0.03 167 * * 5 ^ V 0.22 0.05 114 6 2 U 0 . 26 0 . 37 127 39 B 0 . 34 0,14 7 12 V 0.07 0, 09 161 37 A v e . U 0. 46 0. 23 135 14 B 0. 24 0.08 1 9 V 0. 11 0. 06 122 16 B Aql Average U 0. 30 0. 16 116 15 B 0.45 0. 06 4 4 V 0.17 0.09 51 16 5 5 Cyg Nov. 20 1 U 1. 18 0.43 163 10 B 2 . 62 0.05 3 1 V 2.31 0. 25 2 3 2 u 2 . 02 0. 11 1 2 B 2 . 85 0. 52 174 5 V 2 .40 0 . 25 2 3 Ave . u 1. 53 0.32 174 6 B 2. 70 0. 28 178 3 V 2 . 36 0. 14 2 2 Nov. 21 1 u 1. 44 0.42 153 8 B 2. 52 0.07 1 1 V 2 . 41 0.10 2 1 2 u 2, 08 0.04 178 1 B 2. 84 0.14 4 1 V 2.19 0.17 2 2 Ave . u 1. 60 0 .37 168 7 B 2. 67 0.11 3 1 V 2. 30 0 . 09 2 1 55 Cyg Average u 1, 56 0. 23 171 4 B 2.68 0.15 1 2 V 2. 33 0. 08 2 1 108 APPENDIX A--Continued Object Date Obs. Filter P ♦ EP E 2 U 0.39 0.08 106 6 B 0.62 0.02 3 1 V 0. 39 0.08 106 6 Ave. u 0. 60 0. 23 104 11 B 0.62 0.01 3 1 V 0.35 0.11 125 9 Nov. 2 2 1 u 0. 59 0.24 93 12 B 1.36 0.69 153 15 V 0.12 0 . 54 90 130 2 u 1.41 0.08 104 2 B 0 .07 0.04 69 14 V 0 . 60 0 . 25 86 12 Ave . u 0.99 0.21 101 6 B 0. 58 0.40 152 20 V 0. 36 0. 26 87 21 t Peg Average u 0.85 0.15 102 5 B 0.52 0.22 164 12 V 0. 29 0.16 98 16 APPENDIX B OBSERVATIONS OF STANDARD DOUBLE STARS Date Obs. Filter Obj ect P eP 4 June 12 1 U 100 Her A 1 . 14% 1.01% 104° 25° B 2. 34 0. 70 99 9 Intrins ic 1 . 24 1.22 85 24 BA 0 . 68 0.11 1 0 1 5 B 0.49 0.08 81 10 Intrins ic 0.43 0. 21 43 18 VA 1. 60 0. 51 95 9 B 0.87 0. 34 83 12 Intrins ic 0. 88 0.62 24 27 2 U A 2.13 0.74 115 9 B 2.47 0. 96 93 12 Intrins ic 1. 71 1. 20 61 19 B A 1.42 0. 56 102 11 B 1. 09 0.45 93 12 Intrinsic 0 .51 0.71 30 45 VA 1 . 85 0. 61 95 10 B 2. 31 0. 30 92 4 Intrinsic 0. 50 0.68 79 38 Ave * U A 1 . 58 0. 56 111 10 B 2.39 0.49 96 6 Intrinsic 1.27 0. 74 71 15 BA 1 . 04 0.28 1 0 1 7 B 0 . 7 h 0.24 sy 9 Intrins i c 0.47 0 . 36 34 26 V A 1 . 73 0.33 95 S B 1 . 57 0 . 36 90 7 Intrinsic 0 . 34 0 . 50 34 44 109 110 APPENDIX B - -Cont inued Date Obs . Filter Obj ect P E £P ♦ June 14 1 U 100 Her A 0.52% 0.21% 141° 12 B 1 . 40 0 .69 6 15 Intrinsic 1. 490.73 100 6 B A 0.65 0.23 127 10 B 1. 32 0 . 25 108 5 Intrins ic 0.87 0. 33 77 8 VA 1. 98 0.39 4 6 B 0. 65 0. 35 111 14 Intrins i c 2 . 54 0.52 77 12 2 u A 1.17 0 .67 154 18 B 1.02 0 . 34 122 10 Intrins ic 1.15 0 . 80 58 20 B A 0. 71 0 . 29 174 13 B 0.72 0. 48 9 21 Intrins ic 0.37 0.61 127 43 V A 1.12 0.52 33 12 B 1 .11 0.50 45 12 Intrins ic 0.47 0.67 130 44 A v e . u A 0 .82 0.32 150 12 B 0. 66 0. 54 168 24 Intrins ic 0.49 0 . 66 135 44 BA 0.49 0 . 27 151 14 B 0.29 0. 43 174 45 Intrinsic 0. 35 0 . 52 139 65 VA 1 .27 0.41 17 10 B 0.32 0.39 79 35 Intrinsic 1 . 47 0. 56 113 32 Average u A 0 . 93 0.36 124 11 B 0 . 73 0.51 105 21 Intrinsic 0! 57 0.65 44 38 B A 0.44 0.24 124 15 B 0.19 0.27 93 42 Intrinsic 0.39 0.36 44 50 Ill APPENDIX B--Continued Date Obs. Filter Object P ep ^ ^ Average V 100 Her A 0. 34% 0.47% 40° 39 B 0.65 0.29 86 13 Intrins ic 0. 74 0. 54 104 19 June 19 1 u 63 Ser A 0. 61 0 .07 121 3 B 0.77 0.38 99 14 Intrins ic 0. 54 0 . 38 64 16 B A 0. 30 0 . 08 54 8 B 0.15 0 . 06 134 12 Intrins ic 0.44 0.10 97 10 V A 0.17 0 .14 82 25 B 0. 26 0 . 16 57 17 Intrins ic 0.20 0.22 70 26 2 U A 1.51 0. 53 105 10 B 1.66 0. 66 97 11 Intrinsic 0.48 0 . 86 58 48 B A 0.28 0.03 97 3 B 0.42 0.17 125 11 Intrinsic 0.35 0.17 110 10 V A 0.04 0. 02 91 11 B 0.19 0.10 77 14 Intrinsic 0.15 0.10 87 5 A v e . U A 1.02 0.31 110 9 B 1. 21 0. 36 97 8 Intrins ic 0. 51 0.47 62 24 B A 0. 21 0 . 09 74 12 B 0 . 28 0 . 09 128 10 Intrins ic 0. 39 0.13 105 8 V A 0.10 0.07 84 18 B 0. 21 0.08 66 11 Intrinsic 0.14 0.11 77 16 June 22 1 U A 0. 66 0. 76 98 33 B 1.28 0.67 100 15 Intrinsic 0.63 1.01 92 37 112 APPENDIX B--Continued Date Obs. Filter Obj ect P 4 EP e June 22 1 B 63 Ser A 0.52% 0.48% 93° 27° B 0.32 0 . 09 104 8 Intrinsic 0. 26 0.49 154 57 V A 0.60 0 .08 70 5 B 0.11 0. 26 164 74 * Intrinsic 0.72 0.28 87 62 2 U A 0.10 0 . 34 161 92 B 0. 56 0 . 70 76 39 Intrinsic 0.66 0.78 89 16 B A 0.21 0 . 29 40 39 B 0. 26 0 . 08 8 9 Intrinsi c 0.25 0 . 30 66 34 V A 0.56 0.09 67 4 B 0.27 0.18 170 19 Intrinsic 0.81 0 . 20 81 1 3 Ave. U A 0. 30 0.37 102 3 5 B 0. 84 0.45 93 1 5 Intrins i c 0. 57 0 . 58 85 20 B A 0.25 0 . 26 82 30 B 0.05 0.13 120 7b Intrinsic 0.25 0 . 29 136 84 V A 0. 58 0.05 69 3 B 0.19 0.14 168 21 Intrinsic 0.76 0. 14 83 17 Average u A 0.62 0.25 108 11 B 1.00 0 .27 95 8 Intrinsic 0.51 0 . 37 75 17 B A 0. 23 0 . 13 79 16 B 0. IS 0. 08 126 15 Intrinsic 0. 29 0.15 117 18 V A 0. 35 0.07 71 6 B 0.05 0 .09 26 57 Intrinsic 0. 36 0 .12 49 57 113 APPENDIX B--Continued Date Obs Filter Obj ect P E EP ♦ June 18 U HD 178 911 A 2.59% 1. 18% 32° 13 B 3. 28 1.06 33 8 Intrinsic 0 . 70 1. 59 93 57 BA 0 . 68 0 . 25 101 11 B 0.75 0 .25 96 9 Intrinsic 0 . 13 0.36 63 74 VA 0 . 54 0 . 37 56 20 B 0 .67 0.16 88 7 Intrinsic 0 .65 0.41 114 18 U A 1 .80 0. 20 83 3 B 1.10 0. 58 74 17 Intrinsic 0 . 84 0 . 65 22 37 BA 0.61 0.01 66 1 B 0 . 34 0 . 08 46 6 Int rinsic 0.42 0 . 08 36 9 VA 0.22 0.13 84 18 B 0.41 0 . 21 79 15 Intrinsic 0 . 20 0 . 25 85 25 Ave U A 1 . 36 0. 83 55 18 B 1. 51 0.82 46 15 Intrinsic 0.49 1.15 59 66 BA 0 . 53 0.18 83 10 B 0 .35 0. 20 80 16 Intrins ic 0.19 0.27 8 55 VA 0 . 34 0 . 18 64 16 B 0 . 53 0.13 84 7 Intrinsic 0. 35 0 . 23 109 16 Average U A 1. 36 0 . 83 55 18 B 1 . 51 0.82 46 15 Intrins ic 0.49 1.15 59 66 BA 0 . 53 0.18 83 10 B 0. 35 0. 20 80 16 Intrins ic 0.19 0.27 8 55 114 APPENDIX B--Continued Date Obs. Filter Obj ect P EP Average V HD 178911 A 0 . 34% 0.18% 64° 16° B 0 . 53 0.13 84 7 Intrinsic 0.35 0.23 109 16 BIBLIOGRAPHY Appenzeller, I., and Hiltner, W. A. 1967, Ap.J., 149, 353. Behr, A. 1959 , Veroff. Gott. , No. 126. ______. 1960, Lowell Obs. Bull., 292. Berger, J. 1962 , Ann. d'ap., 25^, 1. Boyarchuk, A. A., and Kopylov, I. M. 1964, Pub. Crimean Ap. Obs . , 3_1_, 4 4 . Chandrasekhar, S. 1946, Ap.J., 103, 352. Code, A. D. 1950, Ap.J., 112, 22. ______. 1960, Stellar Atmospheres, ed. J. Greenstein (Chicago! University of GTiicago Press), p. 58. Collins, G. W . , II. 1963, Ap.J., 138, 1134. ______. 1965, ibid., 142^ 265. ______. 1970 , ibid., 15£, 583. Collins, G. W . , II, and Harrington, J. P. 1966, ibid., 146, 152. Coyne, G. V., and Gehrels, T. 1967, A.J., 7_2 , 887. Coyne, G. V., and Kruszewski, A. 1969, ibid., 7^4 , 528. Coyne, G. V., and Wickramasinghe, N. C. 1969, ibid., 74, 1179. Deutsch, A. J. 1960, Stellar Atmospheres, ed. J. Greenstein (Chicago: University of Chicago Press), pp. 543-568. Dyck, H. M. 1968, A.J., 7J5 , 688 . Eggen, 0. J., Mathewson, D. S., and Serkowski, K. 1967, Nature, 213, 1216. 115 116 Elvius, A., and Hall, J. S. 1966, Lowell Obs. Bull., 6, 257. Faulkner, J., Rosburgh, I. W., and Strittmatter, P. A. 19 68, Ap.J. , 151, 20 5. Greenberg, J. M. 1968, Nebuand Interstellar Matter, ed. B, M. Middlehurst and L. H. Aller (Chicago: University of Chicago Press), pp. 221-361. Hall, J. S. 1949, Science, 109, 166. 1958, Publ. U. S. Naval Obs., Ser. II, 17, part V I . 1968, Lowell Obs. Bull., 7, 61. Hall, J. S . , and Mikesell, A. H. 1950, Publ, U. S. Naval Obs., Ser. II, V7_, part I. Harrington, J. P., and Collins, G. W., II. 1968, Ap.J., 151, 1051. Harrington, J. P. 1969 , A p . Letters, 3_, 165. Hildebrand, F. B. 1956 , Int roduc t i on to Nume rical Analysis (New York! MeGraw-HT11)^ pp. ?58-269. Hiltner, W. A. 1947, Ap.J., 106, 231. 1949, Science, 109, 165. 1951, Ap .J. , 114, 241. 19 56, Ap.J. Supp., 2, 389. Hoffleit, D. 1964, Yale Catalogue of Bright Stars (New Haven: Yale University Observatory), Huang, S .-S . , and Struve, 0 . 1960, Stel1ar Atmospheres, ed. J. Greenstein (Chicago: University of Chicago Press), p. 332. Hulst, H. C. van d e . 1957, Light Scattering by Small Particles (New York: John Wiley and Sons) , p p . 4 2-46. Hutchings, J. B. 1967, Observatory, 8_7 , 289. ______. 1968, M.N.R.A.S., 141, 329. * 117 Janssen, E. M. 1946, Ap.J., 105 , 352. Jeffers, H. M . , van den Bos, W. H., and Greeby, F. M. 1963, Publ. Lick Obs., No. 20. Johnson, H. L. 1958, Lowell Obs. Bull., 4_, 47. ______. 1967, Ap.J., 1 5 0 , L39. Johnson, H. L., and Morgan, W, W. 1953, Ap.J,, 117, 313. Johnson, H. M. 1968, Nebulae and Intersteliar Matter, ed. B. M. Middlehurst and L. FT Aller [Chicago: University of Chicago Press), p. 80, Kruszewski, A. 1962 , Acta A., 12_, 234. Kruszewski, A., Gehrels, T., and Serkowski, K. 1968, A . J . , 7_3 , 67 7. Loden, L. 0. 1961a, Stockholm Obs, Ann., _21L, No. 7. ______. 1961b, ibid., 2 2, No. 1. Marlborough, J. M, 1969, Ap.J., 156, 135. Martel, L., and Martel, M.-Th. 19b4 , Publ. Obs. Haute- Provence, 7_, No. 28. Meisel, D, D. 1968, 7_3, 350. Mendoza, L. E. 1958 , Ap.J. , 1 28 , 207. Merrill, P., and Burwell, C. G. 1933, Ap.J., 7jS, 87. ______. 1943, ibid., 98^, 153. ______. 1949 , ibid., 110 , 387. Sahade, J. 1960, Stellar Atmospheres, ed. J. Greenstein (Chicago: University of Chicago Press), p. 494. t > Schmidt, T. 1958, Veroff. Gott., No. 121. Serkowski, K. 1965, Acta A., 1^, 79. ______. 1968, Ap.J., 154, 115. Serkowski, K. , and Chojnacki, tf. 1969 , A. and Ap., 1^, 442. 118 Shakhovskoi, N. M. 1962, A. Tsircular, No. 228, 16. Slettebak, A. 1966, Ap.J., 14 5, 126. Smith, E. van P. 1956, ibid., 124 , 45. Treanor, P. J. 1962, Astronomical Techniques, ed. W. A. Hiltner (Chicago: University of Chicago Press), pp. 2 54-255, . 1963, A.J., 68, 185. Walborn, N. R. 1968, Publ. A.S.P., 80 , 162.