Radial velocities and orbit

Radial velocities for AG Dor were determined from cross-correlations with spectra of the radial velocity standard star HR1829 ( $v_{\rm r} = -13.5$ kms$^{-1}$; Blumberg & Boksenberg [2000]), observed during the same night. The cross correlations were computed using IRAF's fxcor routine (see Fitzpatrick [1993]), which fits a Gaussian to the cross-correlation function to determine the central shift. Because the H$\alpha$ line can be severely affected by velocity fields originating from microflares or a stellar wind, the H$\alpha$ region was excluded from the cross correlations. However, the secondary of AG Dor shows up only as a weak emission line in H$\alpha$. Its radial velocities were measured from the residual spectra after subtraction of a reference spectrum (Sect. 3.2).

In case of UX For, FeI $\lambda$6546 Å is the only line that significantly contributes to the cross-correlation function besides the H$\alpha$ line. Consequently, the radial velocity of $\lambda$6546 was measured directly by fitting a double Gaussian to the primary and secondary line using IRAF's splot routine. In seven out of 37 cases, the primary and secondary lines were severely blended and no reliable radial velocities could be obtained. All other observations were given equal weight when calculating the orbit.

Orbital elements were derived with the differential-correction program of Barker et al. ([1967]), as modified and described by Fekel et al. ([1999]). Our final elements for both binaries converged at an eccentricity so close to zero that a formal zero-eccentricity solution was adopted (see Lucy & Sweeney [1971]). The standard error of an observation of unit weight is 4.62 kms$^{-1}$ for UX For, using all available measurements of the primary and secondary component. Some of Balona's ([1987]) O$-$C residuals are 12 kms$^{-1}$, and two of Balona's secondary O$-$C residuals are as large as 23 kms$^{-1}$. The standard error for the AG Dor primary was 0.41 kms$^{-1}$, and was calculated using all 38 cross-correlation measurements. The secondary-star orbit was computed independently from the primary star by using the radial velocities of the residual H$\alpha$ emission feature (see Sect. 4). H$\alpha$ is the only line that is detected from the secondary star and the accuracy of the secondary measurements is comparably poor. Its standard error of an observation of unit weight is 8.6 kms$^{-1}$.

Our revised elements agree very well with the preliminary orbit (from L. A. Balona [1987]; in Strassmeier et al. [1993]). Our best orbits with minimized O$-$C residuals were adopted as the final solution, are given in Table 3 and plotted in Fig. 2 and Fig. 3 for UX For and AG Dor, respectively.

Phases of all line profiles were computed using revised ephemerises. For UX For

$$\mathrm{HJD} = 2,448,945.2348 + 0.954812 \times E ,$$

and for AG Dor

$$\mathrm{HJD} = 2,448,945.496 + 2.5620 \times E .$$

The uncertainties of the zero point and the periods are such that we achieve a phase accuracy of 0001 for UX For and 0003 for AG Dor.

Figure: Observed and computed radial velocity curves for UX For. Dots are the measurements from this paper, crosses are from Balona ([1987]).

Figure: Observed and computed radial velocity curves for AG Dor. Filled circles are the cross-correlation measurements of the primary star, open circles are the values of the residual H$\alpha$ line of the secondary star.

Table 3: Double-lined orbital elements for UX For and AG Dor. The preliminary values were taken from Balona ([1987]). Note that for UX For the elements were solved for both companions simultaneously while for AG Dor the primary elements were solved seperately from the secondary elements.

	UX Fornacis			AG Doradus
Element	Prelim.	Final	Error	Prelim.	Final	Error	Unit
$P_{\mbox{\scriptsize orb}}$	0.95479	0.9548120	$5 10^{-7}$	2.562	2.5620	0.0027	days
$\gamma$	19.1	20.3	0.7	70.2	68.95	0.08	kms$^{-1}$
$K_1$	91.8	95.6	1.2	58.0	56.13	0.13	kms$^{-1}$
$K_2$	-	131.0	2.8	-	97.9	1.6	kms$^{-1}$
$e$	0	0	-	0.04	0	-
$T_0$	4000.512	8945.2348	0.002	4378.67	8945.496	0.002	244+HJD
$f(M)$	0.077	0.087	0.003	0.052	0.0470	0.0003	M$_{\odot}$
$M_1/M_2$	-	1.371	0.024	-	1.745	0.032
$M_1 \sin^3 i$	-	0.667	0.023	-	0.617	0.024	M$_{\odot}$
$M_2 \sin^3 i$	-	0.487	0.014	-	0.354	0.009	M$_{\odot}$
$a_1 \sin i$	1.21	1.255	0.015	2.04	1.977	0.005	$10^6$ km
$a_2 \sin i$	1.48	1.721	0.037	-	3.45	0.06	$10^6$ km
Standard error of an
observation of unit weight			4.62		0.41/8.6		kms$^{-1}$