Accuracy

What about the accuracy of a home-made adjustable diffraction micrometer and what kind of factors will influence a result?

First of all, as with all double star measures, the better the seeing conditions the better the accuracy.

Trying to get results during poor seeing periods will end up in frustration. Good seeing allows high magnifications, which in turn produce large and easy-to-judge star configurations. Then, to obtain accurate results, a series of say 10-12 grating adjustments and readings should be made for a pair; and before the final mean values are determined, such series should even be repeated on consecutive nights. Most crucial for the accuracy of the result is certainly the precise judgement of square and right angle combinations between stars and satellites in the field of view. Equally bright pairs are obviously easier to judge and are thus likely to be more accurate than very unequal pairs.

Also the separation has an influence on accuracy; the closer a pair the higher the magnification needed for a clear interpretation of its satellite arrangement. But the higher the magnification the sooner the seeing can become a limiting factor with its potential negative influence on accuracy. Nevertheless, diffraction micrometer results are surprisingly reliable. Position angles can be obtained with mean errors of 1° and this is good enough to proceed to the next step, the separation measurement. Based on a large number of observations made during acceptable seeing, it can be concluded that for a typical double star the angular separation can be determined typically with a mean error of about ± 2%, but considerably more precise results have often been obtained. Indoor tests under perfect seeing conditions with artificial double stars have shown that still more can be expected from this instrument.

What this means numerically can be shown using two typical examples: for Castor's two bright components (magnitudes 1.9 and 2.9), which in the year 2000 were 3'.'8 apart, an accuracy of better than 0'.'1 was obtained. In the case of a faint and wide pair, such as STF 1529 in Leo, consisting of components of magnitude 6.6 and 7.4 and separation 9'.'5, the separation was determined with an error of less than 0'.'2.

Not only are the precision of the construction and careful tuning of star configurations important for the result's reliability, the assumed star wavelengths will also, as the formula predicts, directly influence the accuracy. Catalogues such as the Bright Star Catalogue can supply information about the spectral classes of brighter stars, of which Table 14.1 is a small subset. From Richardson's papers, these classes correspond approximately to the following visual wavelengths:

B0: 5620 A A0: 5640 A F0: 5660 A G0: 5680 A K0: 5710 A M0: 5760 A

The wavelengths between classes A-F, F-G or G-K do not differ considerably, each step being roughly 0.5%. Hence one might be tempted at first sight to ignore stars' spectral classes altogether, but why ignore useful information when these figures will help to improve the result's accuracy? And here comes a warning: initial diffraction micrometer results with these wavelength figures may perhaps show some strange systematic variations. These can be due to the observer's eye sensitivity or individual interpretation of the star and satellite configurations. Such variations can, as soon as enough experience has been accumulated, be eliminated by personal correction factors.

Is it possible to use the measuring method in reverse to try to calculate and determine the effective observed wavelengths of double stars when their separations and position angles are accurately known from catalogues? With a large database of catalogue data for PA and separations, double star wavelengths can be determined with similar accuracy to separation. Such wavelength

Table 14.1.

Pairs with known s

pectral

types near the

celestial equator

RA 2000 Dec

Pair

Epoch

PA°

Sep"

Sp. Types

Name

01137+0735

STF100

2000

63

23.2

5.21

6.44

A7IV

F7V

zeta Psc

01535+1918

STF180

1999

0

7.7

3.88

3.93

A1

B9V

gamma Ari

03543-0257

STF470

1991

348

6.9

4.46

5.65

G8III

A2V

32 Eri

05350-0600

STF747

1994

224

35.8

4.78

5.67

B0.5V

B1V

05351+0956

STF738

1997

44

4.3

3.39

5.35

O8

B0.5V

lambda Ori

05353-0523

STF748

1 995

96

21.4

4.98

6.71

O7

B0.5V

theta1 Ori

06090+0230

STF855

1991

1 14

29.2

5.70

6.93

A3V

A0V

06238+0436

STF900

1991

29

12.4

4.39

6.72

A5IV

F5V

epsilon Mon

08555-0758

STF1295

2000

4

4.1

6.07

6.32

A2

A7

17 Hya

12413-1301

STF1669

1 998

313

5.2

5.17

5.19

F5V

F5V

13134-1850

SHJ151

1991

33

5.4

6.26

6.76

A0V

A1 V

54 Vir

14226-0746

STF1833

1 995

1 74

6.1

6.82

6.84

G0V

G0V

14234+0827

STF1835

1 996

1 94

6.0

4.86

6.86

A0V

F2V

14241+1115

STF1838

1 997

336

9.4

6.76

6.94

F8V

G1 V

14514+1906

STF1888

2002

316

6.5

4.54

6.81

G8V

K5V

xi Boo

1 5075+091 4

STF1910

1 997

21 2

4.0

6.72

6.95

G2V

G3V

15387-0847

STF1962

1991

189

11.8

6.45

6.56

F8V

F8V

18562+0412

STF2417

1 993

1 03

22.6

4.62

4.98

A5V

A5V

theta Ser

19546-0814

STF2594

1991

1 70

35.6

5.70

6.49

B7Vn

B8V

57 Aql

20299-1 835

SHJ324

1991

239

21.9

5.94

6.74

A3Vn

A7V

o Cap

20467+1607

STF2727

2000

266

9.2

4.27

5.15

K1IV

F7V

gamma Del

23460-1841

H II 24

1993

135

6.8

5.28

6.28

A9IV

F2V

107 Aqr

determinations will reveal possible hardware weaknesses, and the overall accuracy can be improved accordingly.

The delicacy of spectral class distinction can also be demonstrated by observing a double star whose components have very different colours. A suitable example is STF 470, consisting of stars of spectral classes G8 and A2 stars and similar brightnesses (magnitudes 4.5 and 5.7). When the images are arranged in the standard "cross" configuration, slightly larger satellite distances for the yellow G8 primary, when compared with the white A2 secondary's satellites, are expected. But even when the two stars, as in this case differ by as much as two spectral classes, it is difficult to detect the slight difference of the first order distances because the two satellite separations still differ by only 1% or so. Hence, for calculating the separation of a double star with components of different spectral class, the mean wavelength of the two stars can safely be used.

Is the diffraction micrometer then even capable of earmarking individual spectral classes? For this purpose, an alternative method, which involves measuring the value of z directly by timing several transits of circumpolar stars can give values of z for a typical grating to an accuracy of about 0.3%. It is necessary to have an eyepiece fitted with a vertical crosswire in order to time the passage of the two first-order images across the centre of the field.1 Table 14.2 gives a short list of bright circumpolar stars with a range of spectral types which are suitable for this purpose.

Table 14.2.

A short list of bright

circumpolar stars suitable for determining

the value of z

Star

RA2000

Dec2000

V

B-V

Spectrum

HR 285

01 08 44.7

+86 15 25

4.25

1.21

K2II-III

alpha UMi

02 31 48.7

+89 15 51

2.02

0.60

F7:Ib-II

HR 2609

07 40 30.5

+87 01 12

5.07

1.63

M2IIIab

delta UMi

17 32 12.9

+86 35 11

4.36

0.02

A1Vn

HR 8546

22 13 10.6

+86 06 29

5.27

-0.03

B9.5Vn

HR 8748

22 54 24.8

+84 20 46

4.71

1.43

K4III

zeta Oct

08 56 41.1

-85 39 47

5.42

0.31

A8-9IV

iota Oct

12 54 58.6

-85 07 24

5.46

1.02

K0III

delta Oct

14 26 54.9

-83 40 04

4.32

1.31

K2III

chi Oct

18 54 46.9

-87 36 21

5.28

1.28

K3III

sigma Oct

21 08 46.2

-88 57 23

5.47

0.27

F0III

tau Oct

23 28 03.7

-87 28 56

5.49

1.27

K2III

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