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is important to consider any other solutions which the data may permit. Consequently attempts were made to f i t other gaussians to both the A and F star data, the Cramer Von Mises Goodness of F it test being used at the 95% confidence level to determine whether or not such fits were compatible with the data.

I t was found that , although the gaussians given above

produced by far the best fit s , there were alternatives. The 1 results of these tests may be summarised as follows: For the

A stars, with the mean taken at -6.4kms , the allowable

—1

the mean taken at -4.1kms , the allowable dispersions lay in the range lU.9j^3kms\ By holding the dispersions constant

- 3. —"7

at ll.Ukms and lU.9kms respectively the allowable ranges

—Î i

i n the means were for the A stars and +ikms for the F stars. (From the nature of a gaussian i t is to be expected that only a small range in the mean would be acceptable.) These small ranges in acceptable means are comparable with the errors in the means of the observed distributions.

The allowable variations in the dispersions are of most significance here, and the effect of such variation must be considered. For a distribution with constant dispersion,

Kz = w^£_(ln (v/vo)^) dz

where the subscripted variables refer to the ith mass component of the Galactic system being considered. From this Kz, the system force law, is found, and the local mass

density is obtained by inserting solar neighbourhood values i nto,

(fisr + Kr + (Rz = -4rtGjp

W ~ W ~ ^

In the solar neighbourhood, since w^^ is constant in the case considerdd)

d[Kz = W'^A, A = [(f^ (In (v/vo): )]o

dz dzF

and [dkz]o >> [ dKr + Kr]e

%

Thus pg = w^A , where A is a constant. | I f the dispersion of the appropriate sub-system is

' I - i

-llkms , a variation of +lkms in this dispersion w ill change the resultant mass density by -2ü%. ( cf H ill et al, 1979, who found, using a modified model due to Camm { 1950, 1952 ), that a change of +^lkmi. in the dispersion of th eir PI F star sample would require a change of ^25-30% in the mass density. However, such a change in dispersion, was not allowed by th eir data. A similar dependence of mass density on dispersion is shown in Bahcall (1984), where a different model is applied to the H ill et al data.) For the combined NGP and SGP data used here a dispersion change of j4kms^ would a lte r by ^100%.

I t is apparent from the above that the current velocity data is too ambiguous to be used in the determination of po, as i t cannot be demonstrated that the adopted velocity distributions are unique, and small uncertainties in the adopted dispersions produce significant uncertainties in p^. 5.7.2 The Existence of Contaminants

The presence of 'contaminants' in the observed PI velocity distributions has been discussed in Chapter 1, with reference to both the apparent velocity dispersion increase

I

'i

•

of apparently normal PI stars at large distances from the

1

with z distance found by H ill et al (1979), and the presence jÿ

i

I

available data, attempts were made to impose lim its on the | possible proportions of such contaminants in the data | samples, the Cramer Von Mises Goodness of F it test being

used at the 95% level to test i f these fits were compatible with the observed distributions.

Two possible contaminants were considered, the fir s t having a dispersion of 30kms.^, comparable with that for the 'classical' PII stars, and the second a dispersion of

6Ukms.\ comparable with that found for the PI A stars | at large z distances by, for example. Pier (1983). The

former case is of particular interest as Bahcall (1984) has managed to obtain a good f i t to the F star density distribution of H ill et al (1979) out to 500pc. by adding a 5% contaminant with this dispersion to the 'normal' PI distribution.

For the f ir s t case (dispersion 30kms ), i t is found that the A star data w ill allow a contaminant of up to 35%, and the F star data permits a contaminant of up to 25%. For the second case (dispersion 6ükms") the A star data permits a contaminant of up to 25%, and the F star data up to 20%.

(64% jL

The implications of these results are that the available velocity data do not permit the identification of small gaussian contaminants with the quoted dispersions. In fact, as found in the preceding section, the data do not define a unique gaussian distribution, but can be quite well fitte d by a number of different gaussians and sums of gaussians. Thus these contaminants may well exist, but the present data can not identify their presence.

5.8. Space Density Distribution and Galaxy Models