4 Results and discussion

The list of observed targets (cf. Sect. 4.1/Table 2) displays mainly three types:

• eclipsing binaries with a close companion, most of which were discovered by Hipparcos and for which the existing information is insufficient;
• visual double stars with an angular separation smaller than 1 $^{\prime\prime}$ which require new observations to better constrain the speckle orbits;
• "astrometric standards" chosen among visual double stars with an angular separation larger than 1 $^{\prime\prime}$ and thought to have a stable configuration useful to determine the scale of the instrument.

Two additional objects were selected because they are suspected binaries by Hipparcos: both components of the very wide system CCDM 19282-0932 (HIP 95724/95726) carry a variability flag "D'' in the catalogue meaning variability induced by duplicity; however we could not resolve these objects.

  

Table 3: Astrometric calibration: comparison with measurements made at ESO with a CCD camera (Epoch 1991.797, Cuypers & Seggewiss 1999)

The following convention was used to assign a type to each programme star:

• (a) an "astrometric standard'';
• (b) a close companion was discovered by Hipparcos;
• (e) a known eclipsing binary;
• (h) a new eclipsing binary discovered by Hipparcos;
• (o) binary with a known orbit;
• (u) a new unsolved Hipparcos variable: variable star entry in the Hipparcos Variability Annex without a period determination (Part 2).

In our list HIP 6287, 22050, 25252, 93867, 96840, 101236 belong to the OHP programme for the determination of the radial velocity curves in order to fully understand the dynamics of these systems. All of them have been resolved by these observations which will then provide useful data for the orbit determination of the visual companion.

Some objects of the list were not resolved. This may be the consequence of a particularly poor FWHM seeing. Several objects may also present a configuration of close periastron passage: e.g., for HIP 98234, McAlister et al. (1987) gives an angular separation less than 0.038 $^{\prime\prime}$ which is beyond our detection limit.

Among the four objects of our list discovered to be double by Hipparcos, we confirm the binarity for HIP 16083 and 27309, but we have not been able to do the same for HIP 14542 and 116167.

   
4.1 Astrometric measurements

The astrometric measurements are presented in Table 2. The position angle $\theta$ (relative to the North and increasing to the East) was generally measured on the auto-correlation function which leaves a 180$^\circ$ ambiguity (cf. Sect. 3.4). An asterisk following the value of $\theta$ indicates that the absolute angle could be determined by using a complementary processing: Aristidi's triple correlation technique for HIP 1447, 10280, 54061, 58112, 97091 and 101769, and a full image restoration with a bispectrum method for HIP 23699 and 101236.

When this ambiguity could not be solved, we chose the value between 0 and 180$^\circ$, or, when available, we selected a value compatible with previous data sources (Hartkopf et al. 1998; ESA 1997) for the following stars: HIP 981, 4065, 15627, 16083, 19201, 22050, 25252, 27309, 96840, 103505, 107162, 111805 and 116164.

In the case of HIP 93867, Hartkopf et al. (1998) list position angles between 140$^\circ$ and 121$^\circ$ for the period 1987-1993, whereas Hipparcos and micrometric observations (Heintz 1996b) give respectively $\theta=305^\circ$ and 305.6$^\circ$. It seems there is simply a problem of 180$^\circ$ ambiguity with the speckle measurements. To keep quadrant consistency with the visual observations, we chose $\theta=289.3^\circ$.

When two or more measurements were available, we determined the best value using the following procedure:

-

if available, we adopted the value with the magnification scale of 10 mm since the accuracy was larger than with the 20 mm scale and there were less artefacts near the centre;

-

else we computed the mean value and the corresponding error by taking the signal-to-noise ratio of the data into account (measurement in brackets).

This value, coded "Best'' in Table 2, was used for the comparison with other sources (cf. next sections).

   

Table 4: Hipparcos data and comparison with our measurements; (1) Hip number; (2) source of the multiplicity data in the Hipparcos Catalogue: I = Input Catalogue, M = known as double although not mentioned as double in the Input Catalogue, H = Hipparcos discovery; (3) solution quality; (4) component identifiers; (5) Hipparcos position angle; (6) Hipparcos angular separation; (7) Hipparcos sigma of separation; (8) difference of magnitude $H_{\rm p}$; (9) total V (Johnson) magnitude; (10) trigonometric parallax; difference (PISCO-Hipparcos) for the position angle (11), the angular separation (12), and distance (13). Bottom part: systems with a known orbit

HIPPARCOS										PISCO-HIP
Number	Notes			$\theta$	$\rho$	$\sigma_\rho$	$\Delta H_{\rm p}$	V	$\pi$	$\Delta \theta$		$\Delta \rho$		$\Delta$pos
HIP	S	Q	Comp.	$^\circ$	''	''	mag	mag	mas	$^\circ$		''		''
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)		(12)		(13)
1447-1446	I	A	AB	210.54	11.83	-	0.83	9.16	4.17	0.36		-0.06		0.095
4065	I	A	AB	352	2.240	0.003	0.65	8.41	9.61	-0.60	*	0.013	*	0.027
6287	I	A	AB	90	0.381	0.005	1.89	7.10	1.63	0.31	*	-0.003	*	0.004
10280	I	A	AB	70	3.920	0.004	1.50	4.94	10.68	-0.50		0.021		0.040
15627	I	A	AB	227	0.809	0.014	2.81	5.27	7.06	-1.90	*	0.009	*	0.028
16083	H	A	AB	315	0.628	0.017	3.81	3.73	14.68	26.91		-0.169		0.302
19201	I	A	AB	226	0.803	0.008	1.81	6.70	3.89	1.30	*	-0.016	*	0.024
22050	M	A	AB	194	0.206	0.010	0.85	8.31	5.12	13.85		-0.011		0.050
23699	I	A	AB	152	0.355	0.003	1.48	6.69	4.02	-1.00	*	0.003	*	0.007
25252	I	A	AB	227	0.230	0.013	0.94	8.34	-0.11	2.01	*	0.024	*	0.025
25930	I	A	AD	140	0.267	0.003	1.35	2.25	3.56	-4.00		0.038		0.043
27309	H	A	AB	219	0.580	0.012	0.96	9.70	5.70	-2.10	*	0.007	*	0.023
93867	M	A	AB	305	0.310	0.004	0.95	5.07	6.43	-15.70		0.007		0.086
97091	I	A	AB	283	0.336	0.003	1.20	6.27	0.75	0.60	*	0.013	*	0.013
101236	I	B	AB	69	1.802	0.012	0.28	8.77	22.53	2.50		-0.040		0.087
103505	M	A	AB	309	1.212	0.038	1.67	9.99	9.25	-0.10	*	-0.043	*	0.043
981	I	A	AB	278	0.172	0.007	1.21	6.87	9.42	17.1		0.096		0.110
10952	I	A	AS	305	0.196	0.006	0.28	8.79	16.36	57.18		0.111		0.260
11318	I	A	AB	56	0.360	0.003	0.44	7.00	4.43	7.11		0.032		0.057
54061	I	A	AB	270	0.672	0.006	2.92	1.81	26.38	-62.4		-0.245		0.607
96840	I	A	AS	311	0.189	0.002	0.06	5.98	1.98	-0.50		0.012		0.012
101769	I	A	AB	205	0.240	0.006	0.91	3.64	33.49	128.9		0.203		0.622
107162	I	A	AB	355	0.189	0.003	0.39	5.73	8.76	-99.2		-0.088		0.228
111805	I	A	AB	337	0.214	0.003	0.51	6.82	26.33	-169.7		-0.051		0.376
116164	I	A	AB	261	0.157	0.012	0.46	6.60	13.00	68.0		0.044		0.203

   
4.2 Comparison with Hipparcos measurements: visual binaries without known orbits

In addition to some information retrieved from the Hipparcos Main Catalogue (ESA 1997) we list the differences in $\theta$, $\rho$ and in relative position in the sense (PISCO - HIP) in Table 4. Sometimes, as in the case of the double entry HIP 1447/1446, we refer to the Double and Multiple Star Annex (ESA 1997).

The bottom part of Table 4 contains the systems with a known orbit that will not be considered here, since we shall compare more adequately the Hipparcos measurements with the ephemerides computed for epoch 1991.25 in Sect. 4.3.

To evaluate possible systematic differences, we have selected from the upper part of Table 4 all the objects which did not show any relative motion according to the observational data available in the literature (asterisked in Cols. 11 and 12 in Table 4). The derived mean differences between PISCO and Hipparcos measurements for these systems are $\langle \Delta \theta \rangle = -0.16^\circ$ and $\langle \Delta \rho \rangle = +0.001$''. Note that the typical error values for PISCO measurements of $\sim 0.8^\circ$ in $\theta$ and $\sim 0.01$'' in $\rho$ are actually lower limits for the error estimates for $\langle \Delta \theta \rangle$ and $\langle \Delta \rho \rangle$ respectively, if we do not take into consideration Hipparcos errors. As the derived mean differences are much smaller than their estimated errors, one can state that no significant systematic difference is present between these measurements.

With the same selection of the asterisked objects, we obtained an estimate of the standard error: $\sigma_{\theta}$= 0.99$^\circ$, and $\sigma_\rho$= 0.014''. Applying a 3-$\sigma$ level criterion and checking the value of $\Delta$pos allowed us to point some objects as possible candidates for orbital motion: HIP 16083, 22050, 93867 and 101236.

HIP 16083 is an interesting case. We resolved it, whereas five unresolved observations are listed in Hartkopf et al. (1998), probably due to a large magnitude difference of the two components: $\Delta m = 3.8$ mag. As mentioned in Mason et al. (1999), the CHARA team found one previous measurement among their archival data of 1983. They suggested that the change in relative position between their and the Hipparcos data might be due to rapid orbital motion. From our measurements we deduce a mean motion of 3.6$^\circ$/yr (cf. Table 5 and Kurpinska & Oblak 2000a). Assuming a circular motion, the period would then be of order 100-150 yrs.

 

 

Table 5: Evidence of rapid motion for HIP 16083

Epoch	$\theta$	$\rho$	Source	Derived motion
	$^\circ$	''
1983.713	297.8	0.689	Mason et al. 1999
1991.25	315	0.628	Hipparcos	2.3$^\circ$/yr; -8.09 mas/yr
1998.688	341.9	0.459	PISCO	3.6$^\circ$/yr; -22.7 mas/yr

HIP 22050, 93867 and 101236 are known to be visual binaries showing small changes in measured positions over the last 20 years, but it is still too early to decide about their orbital motion. Only for one of them, HIP 93867, is there a suggestion of orbital motion from the photometric data which shows drastic changes in the depth of the minima during the last 100 years, as probably due to the effect of a large-scale secular decrease in the inclination of its orbit, caused by a third, close visual component on a non-coplanar orbit. Note that HIP 22050 and 101236 were discovered as eclipsing binaries by Hipparcos.

   
4.3 Comparison with Hipparcos measurements: visual binaries with a known orbit

   

Table 6: Comparison of Hipparcos measurements (Hip) with ephemerides (C) computed for epoch 1991.25 for the visual binaries with orbits (bottom part of Table 4)

Identifiers		$\rho_{\rm C}$	$\theta_{\rm C}$	$\rho_{\rm Hip}$	$\theta_{\rm Hip}$	$\Delta\rho_{\rm Hip-C}$	$\Delta\theta_{\rm Hip-C}$	$\Delta \hbox{pos}_{\rm Hip-C}$	$\rho_{\rm Hip}$/ $\rho_{\rm C}$	Period	Source
HIP	CCDM	''	$^\circ$	''	$^\circ$	''	$^\circ$	''		yr
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
981	00121+5337	0.171	276.11	0.172	278.	0.001	1.89	0.006	1.006	66.8	(Hartkopf & McA. 1996)
10952	02211+4246	0.192	311.84	0.196	305.	0.004	-6.82	0.023	1.021	299.	(Ruymaekers 1999)
"	"	0.203	304.68	0.196	305.	-0.007	0.32	0.007	0.966	277.	(Couteau 1991)
"	"	0.192	314.40	0.196	305.	0.004	-9.40	0.032	1.021	300.	(Heintz 1996a)
11318	02257+6133	0.363	58.04	0.360	55.6	-0.003	-2.44	0.016	0.992	530.	(Ruymaekers 1999)
"	"	0.366	54.18	0.360	55.6	-0.006	1.42	0.011	0.984	836.	(Zaera de Toledo 1985)
54061	11037+6145	0.681	271.48	0.672	269.6	-0.009	-1.88	0.024	0.987	44.6	(Aristidi et al. 1999)
"	"	0.675	269.66	0.672	269.6	-0.003	-0.06	0.003	0.997	44.5	(Söderhjelm 1999)
96840	19411+1349	0.190	310.77	0.189	311.	-0.001	0.23	0.001	0.995	68.21	(Docobo & Ling 2000)
101769	20375+1436	0.267	201.57	0.240	205.	-0.027	3.43	0.031	0.899	26.55	(Ruymaekers 1999)
"	"	0.284	191.83	0.240	205.	-0.044	13.17	0.074	0.845	26.60	(Hartkopf et al. 1989)
107162	21424+4105	0.193	354.89	0.189	355.	-0.004	0.04	0.004	0.979	26.54	(Ruymaekers 1999)
"	"	0.194	354.94	0.189	355.	-0.005	0.11	0.005	0.974	26.51	(Hartkopf et al. 1989)
111805	22388+4419	0.216	338.83	0.214	337.	-0.002	-1.83	0.007	0.991	29.74	(Ruymaekers 1999)
"	"	0.214	337.49	0.214	337.	0.000	-0.49	0.002	1.000	29.89	(Hartkopf & McA. 1996)
116164	23322+0705	0.132	251.46	0.157	261.	0.025	9.54	0.035	1.189	30.80	(Ruymaekers 1999)
"	"	0.132	261.48	0.157	261.	0.025	-0.48	0.025	1.189	30.53	(Cester 1963)

Ephemerides for epoch 1991.25 were computed based on the best known orbit, either a speckle orbit (Hartkopf et al. 1989; Hartkopf & McAlister 1996) or else a combined speckle-visual orbit (Ruymaekers & Cuypers 2000, in preparation) for the pairs with a known orbit not discussed previously. We have considered the relative error criterion

$$Q=\frac{\sigma(a^3/P^2)}{(a^3/P^2)} \;< 0.1$$

(where a is the semi major axis and P the orbital period, and $\sigma(a^3/P^2)$ the rms error on (a³/P²)), which is an indication of the quality of the orbital parameters that are important for a useful determination of the sum of the masses (provided an accurate parallax is also available). This criterion is however not applicable for HIP 10952 (Q=0.24) and HIP 54061 for which an orbit was determined based on both ground-based and Hipparcos Transit data (Söderhjelm 1999).

In Table 6 we see that the overall smallest differences in relative position for each system (Col. 9) are of the order of 0.01-0.02 $^{\prime\prime}$ (which is similar to the standard error in separation from Sect. 4.2) and the corresponding differences in position angle rarely exceed 1$^\circ$, therefore matching our estimated error in orientation. We can thus state that the agreement between the ephemerides and the Hipparcos measurements is generally good to very good. One exception is HIP 101769 for which the orbit proposed by Hartkopf et al. (1989) leads to a difference of 0.074'' in position on the sky. Let us now look to individual cases in more detail.

For HIP 10952, the orbit derived by (Couteau 1991) matches better than more recent orbit determinations, indicating a clear need for more data. For HIP 11318 the correspondence is good for both orbits even though the periods are very different (resp. 830 or 530 yrs). Two cases show large discrepancies: there is no good match for HIP 101769 (best concordance with Ruymaekers (1999) nor for HIP 116164 (best concordance with Cester 1963) - both have periods of about 30 yrs - although the orbits have high-quality (relative error $Q < 8\%$). This supports the conclusion that the Hipparcos relative position at epoch 1991.25 is not useful for orbit determination when the orbital period is of order 30 yrs or less. For the other cases with a longer orbital period such as HIP 981 ($P\sim 67$ yrs), HIP 10952 ($P\sim 300$ yrs), HIP 11318 (P>500 yrs), we do not expect nor find evidence for a systematic effect in the Hipparcos relative position.

Note that for HIP 58112, this comparison was not possible, because the speckle orbits and our observations refer to the close pair (AB), whereas Hipparcos measured the wide pair (AB-C).

   
4.4 Comparison with ephemerides from known orbits

Our goal was to confront three types of orbits:
- an orbit based on speckle data mainly (e.g. as derived by the CHARA group (Hartkopf et al. 1989; Hartkopf & McAlister 1996), with a quite recent date);
- an orbit based on mostly visual non-speckle data (from the literature, rarely very recent) and;
- a combined orbit taken from a new catalogue of orbits of visual binaries (Ruymaekers 1999). When the solution of the combined orbit was such that the associated relative error Q was larger than 1, no combined orbit was given since such a solution was not retained in the catalogue (for reasons of insufficient quality). This was the case for HIP 54061 and HIP 98416.

Most of the binaries that we have observed have periods smaller than 50 yrs (cf. Table 6). An exception was made for HIP 11318 and 96840 which belong to the programme of eclipsing systems, HIP 10952, a spectroscopic-visual binary for which - partly thanks to the additional data - new masses have been derived lately by Pourbaix (2000), and HIP 54061 and 58112 for which Aristidi et al. (1999) have computed a new orbit. We have re-observed them to check their orbits. The residuals are still quite large for HIP 54061: it is indeed the first time that it is observed at periastron. Speckle observations are presently particularly valuable since they will considerably constrain the orbit.

The case of HIP 98416 is peculiar. Due to a quadrant ambiguity of the relative positions two orbits can be derived for this binary: an orbit with period 9.8 yrs and small eccentricity or an orbit with half the period and high eccentricity. The first one is proposed by Baize (1990) and also by Hartkopf & McAlister (1996). However, radial velocities confirm the period of $\sim$4.9 yrs (Duquennoy & Mayor 1991; Pourbaix 2000), but with errors still too large to be useful at present. With the available observations, the objective function of the least-square minimization has a lot of local minima that cannot be distinguished. More observations are clearly needed.

In Table 7, we present ephemerides based on the best orbits obtained from ground-based observations for the sample of binaries observed with PISCO for which an orbit was known (i.e. objects with the mention "o'' in Table 2). We list the residuals in $\rho$, $\theta$ and in relative position in the sense (observed minus computed values). The last column gives the reference code of the published orbit.

The residuals are of the order of 20 milliarcsec on average. There are no systematic errors as shown in Fig. 2, which illustrates the quality of the calibration.

Figure 2: Residuals of our measurements with orbits ephemerides for the position angle $\theta$ and the angular separation $\rho$ (cf. Table 7)

The large scatter in this figure shows the level of inaccuracy that still exists for the orbits under discussion and the need for more speckle observations.

   
4.5 Relative photometry of HIP 101769

A full set of B, V, R photometric differential magnitudes (cf. Table 8) was obtained for the nearby object HIP 101769 ($\beta$ Del) using the probability imaging technique described by Carbillet et al. (1998). When computing the average values of the colour differences one finds a small colour trend in the sense that the differences increase towards the redder wavelengths: $\Delta B = 0.72 \pm 0.15$, $\Delta V = 0.83 \pm 0.15$, $\Delta R = 0.87 \pm 0.15$ and $\Delta I = 1.0 \pm 0.1$ mag.

   

Table 7: Comparison of PISCO measurements (P) with ephemerides (C) of known orbits

Identifiers		Epoch	$\rho_{\rm C}$	$\theta_{\rm C}$	$\Delta\rho_{\rm (P-C)}$	$\Delta\theta_{\rm (P-C)}$	$\Delta \hbox{pos}_{\rm (P-C)}$	$\rho_{\rm P}/\rho_{\rm C}$	Source
HIP	CCDM		''	$^\circ$	''	$^\circ$	''
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
981(v1)	00121+5337	1998.665	0.259	293.45	.010	1.65	.012	1.037	(Ruymaekers 1999)
"	"	"	0.242	291.91	.025	3.19	.029	1.105	(Baize 1983)
"	"	"	0.274	297.02	-.006	-1.92	.011	0.979	(Hartkopf & McA. 1996)
10952	02211+4246	1998.687	0.311	241.11	-.004	6.69	.036	0.988	(Ruymaekers 1999)
"	"	"	0.321	244.83	-.014	2.97	.022	0.956	(Couteau1991)
"	"	"	0.299	245.29	.008	2.51	.015	1.027	(Heintz 1996a)
11318	02257+6133	1998.687	0.396	65.84	-.004	-2.74	.019	0.991	(Ruymaekers 1999)
"	"	"	0.400	61.21	-.008	1.89	.015	0.980	(Zaera de Toledo 1985)
54061	11037+6145	1998.430	0.365	188.55	.062	19.05	.145	1.171	(Symms 1969)
"	"	"	0.329	199.25	.098	8.35	.112	1.298	(Aristidi et al. 1999)
58112	11551+4629	1998.430	0.111	291.95	.009	-.012	.015	1.077	(Ruymaekers 1999)
"	"	"	0.114	315.12	.006	-29.12	.059	1.050	(Baize 1989)
"	"	"	0.120	283.77	.000	2.23	.005	1.000	(Aristidi et al. 1999)
96840	19411+1349	1998.689	0.194	312.85	.007	-2.35	.011	1.036	(Docobo & Ling 2000)
101769	20375+1436	1998.430	0.471	335.10	-.028	-1.20	.030	0.940	(Ruymaekers 1999)
"	"	"	0.422	332.92	.021	0.98	.022	1.049	(Hartkopf et al. 1989)
"	"	"	0.462	334.83	-.019	-0.93	.020	0.959	(Couteau 1962)
107162	21424+4105	1993.602	0.170	336.86	-.004	-1.36	.006	0.977	(Ruymaekers 1999)
"	"	"	0.167	334.79	-.001	.002	.710	0.994	(Baize 1984)
"	"	"	0.173	338.05	-.007	-2.55	.010	0.960	(Hartkopf et al. 1989)
107162	21424+4105	1998.690	0.112	266.05	-.011	-10.25	.022	0.899	(Ruymaekers 1999)
"	"	"	0.110	265.93	-.009	-10.13	.021	0.918	(Baize 1984)
"	"	"	0.105	269.37	-.004	-13.57	.025	0.961	(Hartkopf et al. 1989)
111805	22388+4419	1998.690	0.152	147.81	.011	-1.11	.011	1.072	(Ruymaekers 1999)
"	"	"	0.137	148.03	.027	-1.33	.027	1.194	(Hartkopf & McA. 1996)
"	"	"	0.149	140.24	.014	6.46	.022	1.093	(Cester 1962)
116164	23322+0705	1998.690	0.225	328.98	-.024	0.02	.024	0.892	(Ruymaekers 1999)
"	"	"	0.240	334.08	-.039	-5.08	.044	0.836	(Cester 1963)
"	"	"	0.235	328.75	-.034	0.25	.034	0.854	(Muller 1955)

Using the mass-luminosity relations based on the new Hipparcos parallaxes (Lampens et al. 1997; 1999), these measurements can lead to an estimation of the component masses for this object which is highly desirable since there is no spectroscopic mass ratio available (the system is a single-lined spectroscopic binary). The mass ratio can be derived from the difference in bolometric magnitude, $\Delta$ $M_{\rm bol}$ using:

$$q = 10^{-\Delta M_{\rm Bol} /(2.5 \,K)},$$

where the coefficient K is the slope of the used mass-luminosity relation. From the photoelectric UBV data of the combined system $V_{\rm AB}$=3.63, $(B-V)_{\rm AB}$=+0.44 (Mermilliod et al. 1996) and our measurements of $\Delta \rm B$ and $\Delta V$ one can derive the colours of both components: $(B-V)_{\rm A}$=+0.48 and $(B-V)_{\rm B}$=+0.37. The corresponding temperatures and bolometric corrections are $T_{\rm eff,A}=6400$ K, $BC_{\rm A}=-0.004$ and $T_{\rm eff,B}=6900$ K, ${\rm BC}_{\rm B} = +0.026$ (Flower 1996), which leads to: $\Delta {\rm BC} = +0.03$. Since $\Delta M_{\rm bol} = \Delta {V} + \Delta {\rm BC}$ we obtain $\Delta M_{\rm bol}=0.86\pm0.15$. With $K=3.82\pm0.07$ (Lampens et al. 1997) we derive a mass ratio $q=0.81\pm0.03$. Note that this determination of the bolometric magnitude difference is in agreement with the value $\Delta H_{\rm p} = 0.91 \pm 0.05$ (ESA 1997), which is a good estimation for $\Delta M_{\rm Bol}$ due to the broadness of the $H_{\rm p}$ passband since the difference in bolometric correction between the two components is small (they have very similar spectral types of F5III and F5IV). However, we caution these spectral classifications as they are simply based on a global spectral type designation and a not very precise visual estimate of the magnitude difference (Christy & Walker 1969). With this approach, a precision of $\sim$3-5 subclasses on the secondary spectral class is obtained for a magnitude difference smaller than 1.3 mag.

In the Hipparcos photometric system the slope of the mass-luminosity relation is $K=4.45\pm 0.08$ (Ruymaekers 1999) and leads to $q=0.83\pm 0.01$, which is consistent with the first determination. Adopting the mean value $q=0.82\pm 0.02$ and using for the sum of the masses the value of $3.66\pm 0.31~{\cal M}_{\odot}$ derived by Ruymaekers (1999), we obtain the following estimation for the component masses: ${\cal M}_{\rm A}=2.01\pm 0.17$ and ${\cal M}_{\rm B}=1.65\pm 0.17~{\cal M}_{\odot}$.

   

Table 8: Photometric measurements for HIP 101769 ($\beta$ Del) with PISCO.

Date	Filter	$\Delta m$	Error	Source
		mag	mag
11/09/1994	R$^\prime$	0.88	0.06	Aristidi et al., 1997b
25/07/1997	B	0.8	0.2	Aristidi et al., 1999
"	V	1.0	0.2	Aristidi et al., 1999
"	R	1.0	0.1	Aristidi et al., 1999
"	RL	1.0	0.1	Aristidi et al., 1999
"	I	1.1	0.1	Aristidi et al., 1999
07/06/1998	B	0.63	0.18	This work
"	V	0.65	0.14	This work
"	R	0.74	0.19	This work