4 New PMS binaries

4.1 The visual binary Cru-1

The near-IR imaging shows that the star Cru-1 is a close visual pair. Unfortunately, the binary is only marginally resolved in the J and H bands, while it can just be resolved in the K band with a separation of about 0.25 arcsec and a position angle of about 76$^{\circ }$ (cf. Fig. 3). The flux ratio of the components in the K band is about 1.8, the East component being brighter than the West component.

Some evidence of a variable radial velocity was found from the cross-correlation analysis. Therefore, one cannot exclude that Cru-1 may also be a spectroscopic binary.

Figure 3: The visual binary Cru-1 in the K band. The image scale is 50 mas/pix. The separation of the components is about 0.25 arcsec and the position angle is about 76$^{\circ }$. The flux ratio of the components in this band is about 1.8.

4.2 The spectroscopic binary Cru-3

The double-lined spectroscopic binary nature of Cru-3 was revealed in the course of our observing run with CASPEC in February 1999. Since then, the system was systematically observed during several observing runs conducted with CORALIE and FEROS, on La Silla (Chile). The observations were performed in different epochs during 1999, 2000 and 2001. The radial velocities of the system were determined applying cross-correlation techniques as explained in Sect. 3.1. All the radial velocity measurements for Cru-3 are listed in Table 4.

 

 

Table 4: Radial velocity measurements, in km s^-1, for the SB2 components of Cru-3.

HJD-2400000	RVa	RVb	Instr.
51216.765407	48.210	-20.370	CORALIE
51253.768142	-8.092	38.534	CORALIE
51260.784077	10.555	19.182	CORALIE
51274.686200	48.000	-21.500	FEROS
51275.683360	47.500	-21.000	FEROS
51311.568220	-9.050	39.480	CORALIE
51312.735649	-6.530	36.930	CORALIE
51313.731979	-4.080	34.570	CORALIE
51314.735635	-1.530	32.120	CORALIE
51315.176678	0.400	28.400	CORALIE
51315.670575	0.680	29.410	CORALIE
51315.680420	1.000	29.500	FEROS
51316.216678	3.400	25.200	CORALIE
51316.580283	3.020	26.830	CORALIE
51316.720410	3.500	27.500	FEROS
51317.226979	7.200	21.400	CORALIE
51317.662823	6.210	23.600	CORALIE
51317.730690	6.500	24.000	FEROS
51318.144826	14.000	14.000	CORALIE
51318.634322	8.910	20.540	CORALIE
51318.648520	15.000	15.000	FEROS
51319.180359	14.000	14.000	CORALIE
51319.684030	15.000	15.000	FEROS
51320.647870	15.000	15.000	FEROS
51321.146088	14.800	14.800	CORALIE
51321.616683	14.720	14.720	CORALIE
51321.649730	15.000	15.000	FEROS
51328.678780	41.350	-10.110	CORALIE
51364.500093	-15.520	46.090	CORALIE
51365.506992	-14.860	45.340	CORALIE
51366.500928	-13.850	44.400	CORALIE
51368.489771	-11.250	41.810	CORALIE
51526.853957	1.190	26.790	CORALIE
51527.825863	-1.410	30.770	CORALIE
51528.801809	-4.200	33.590	CORALIE
51529.841162	-6.780	36.270	CORALIE
51530.852991	-9.270	38.610	CORALIE
51533.833932	-14.320	43.740	CORALIE
51667.717920	5.700	20.300	FEROS
51672.591324	20.210	2.190	CORALIE
51674.726350	27.800	-4.400	FEROS
51682.717875	44.550	-23.810	CORALIE
51684.647100	45.200	-23.700	FEROS
51686.662950	44.500	-22.500	FEROS
51687.617595	43.090	-22.730	CORALIE
51918.849790	35.500	-33.000	FEROS
51923.850610	29.000	-25.000	FEROS
52019.604800	4.500	4.500	FEROS
52026.612060	26.000	-19.000	FEROS
52031.598260	37.000	-29.200	FEROS

A first, preliminary orbital solution for Cru-3 was obtained early in June 1999, using all FEROS and CORALIE data available at that moment. The solution of the spectroscopic orbit was obtained using standard non-linear least squares techniques (e.g., Press et al. 1992) on all data points, except those where the two components were seen in blend. From this, the following orbital elements were determined: the orbital period, $P_{\rm orb}$, the radial velocity of the center of mass, $\gamma$, the semi-amplitudes of the radial velocity curves of each component, K₁ and K₂, the eccentricity, e, the longitude of periastron, $\omega$, and the time of periastron passage, T. Other derived quantities include the projected semi-major axes, $a_1\sin{i}$ and $a_2\sin{i}$, the minimum masses of the components, $M_1\sin^3{i}$ and $M_2\sin^3{i}$, and, of course, the mass ratio, q.

Since, by that time, only half of the radial velocity curve was satisfactorily covered by the observations, we continued collecting data in order to achieve a better coverage of the entire curve but, surprisingly, the dispersion around the orbital solution was found to increase continuously with the addition of new data. We also noticed, however, that the radial velocities observed for both components in January 2001 with FEROS appeared shifted some 10 km s^-1 with respect to the first orbital solution obtained in 1999, although the relative radial velocity between the two components was in good agreement with the predictions from the former orbital solution. Such a shift in the radial velocity of both components strongly suggests that the barycentric velocity of the binary system is changing due to the presence of a third body and therefore, any attempt to fit new and old data sets simultaneously, while keeping the $\gamma$ parameter fixed, failed.

Hence, we adopted a different approach in order to find out whether a barycentric velocity variation was really occurring in this system. We chose the observations obtained with CORALIE during May 1999 as a reference, since it was in this run that a longer series of consecutive observations were collected, allowing a good orbital solution with the data of this run alone. The orbital solution found by using only the CORALIE data of May 1999 is hereafter referred to as the reference solution. Then we imposed the orbital parameters from the reference solution for the other blocks of observations obtained in other epochs allowing only the barycentric velocity to vary freely. As shown in Fig. 4, a marked trend in the $\gamma$ velocity (varying from about 15 down to about 3 km s^-1) is present, confirming our suspicious of a changing barycentric velocity and hence the presence of a third body.

Figure 4: Barycentric velocity, $\gamma$, of the SB2 system Cru-3 as a function of time. Each data point corresponds to the average barycentric velocity derived for each observing run versus the mean Heliocentric Julian Date for that run. Circles and triangles represent CORALIE and FEROS runs, respectively.

The final orbital solution, obtained combining all available data points from both FEROS and CORALIE, was found as follows: for a given run, R_i, with CORALIE (FEROS), the observed radial velocities, $V_{\rm r,obs}$, were corrected by a constant k_i such as: $V_{\rm r,cor}=V_{\rm r,obs}+k_{i}$, where $k_{i}=\gamma_{\rm May99}-\gamma_{i}$, with $\gamma_{\rm May99}$ the barycentric velocity of the CORALIE (FEROS) orbital solution obtained with the data of May 1999 and $\gamma_{i}$ the barycentric velocity derived from the data obtained in the considered run. At this point, the radial velocity data collected with each of the two instruments are reported to the same reference frame of May 1999, using the $\gamma$ values reported in Table 5. A final correction still remains to be made, namely, tie the FEROS data to the reference frame of CORALIE. This is done by adding another constant k' to the already corrected (as above) FEROS data, where $k'=\gamma_{\rm May/99,CORALIE}-\gamma_{\rm May99,FEROS}$. The final orbital solution was then found by using all corrected data with all orbital parameters allowed to vary. Figure 5 shows the corrected radial velocity curve of Cru-3 SB2 components and the corresponding best fit, whereas Fig. 4 shows the systemic radial velocity, $\gamma$, as a function of time. The results of the orbital solution are reported in Table 6. As one can see from the spectrum shown in Fig. 1, the components of this double-lined spectroscopic binary are very similar and, in fact, from the orbital solution it turns out that the mass ratio is about 0.95.

Figure 5: Radial velocity curve of Cru-3. The data points for the primary and secondary components are represented by filled and open symbols, respectively, and the corresponding orbital fit, as solid lines. The circles and triangles represent the CORALIE and FEROS points respectively.

 

 

Table 5: Barycentric velocity, $\gamma$, for each CORALIE and FEROS observing runs. $<{\rm HJD}>$ corresponds to the mean Heliocentric Julian Date (-2400000) for each run. The barycentric velocity is given in km s^-1.

Run	$<{\rm HJD}>$	$\gamma$
CORALIE
Feb./99	51243.7725	14.715
May/99	51315.1649	14.757
Aug./99	51366.2494	14.675
Dec./99	51529.6682	14.164
May/00	51680.9756	11.064
Jan./01	51922.2441	3.429
FEROS
Apr./99	51275.1848	13.949
May/99	51316.7105	15.101
May/00	51678.4386	12.009
Jan./01	51921.3502	2.241
Apr./01	52025.9384	4.354

Figure 6: Preliminary orbit of the center of mass of the spectroscopic binary. The error bars represent the standard deviation from the mean RV in each observing period.

   

Table 6: Orbital parameters for the SB2 components of Cru-3

Parameter	Value/error
$P_{\rm orb}$ (d)	58.2748 $\pm$ 0.0055
T (HJD-240000)a	51048.65 $\pm$ 0.36
e	0.0675 $\pm$ 0.0016
$\gamma_{\rm May/99}$ (km s-1)	14.722 $\pm$ 0.032
$\omega$ (deg)	34.61 $\pm$ 1.93
K1 (km s-1)	32.380 $\pm$ 0.063
K2 (km s-1)	33.955 $\pm$ 0.063
$a_1\sin{i}$ (Gm)	25.888 $\pm$ 0.051
$a_2\sin{i}$ (Gm)	27.147 $\pm$ 0.051
M2/M1	0.954 $\pm$ 0.004
$M_1\sin^3{i}$ ($M_\odot$)	0.8980 $\pm$ 0.0038
$M_2\sin^3{i}$ ($M_\odot$)	0.8564 $\pm$ 0.0037
No. of meas.b	42 (50)
rms1 (km s-1)	0.292
rms2 (km s-1)	0.292
Time span (days)	815

Notes to Table: ^a Time of passage to periastron. ^b Number of measurements used
for the orbital solution and, in parenthesis, total number of observations.

Figures 4 and 5 clearly show that Cru-3 is in fact a hierarchical triple system, i.e., a long period binary system in which one of the components is itself a binary. From Fig. 4, one can clearly see that the spectroscopic binary, Cru-3AB, has not yet completed an entire orbital revolution around the center of mass of the system Cru-3AB+Cru-3C. However, since the value of the barycentric velocity from the most recent FEROS observations of April 2001 suggests that the barycentric velocity has started increasing again, we can hypothesize that Cru-3AB has already covered approximately half of the orbit, in which case the orbital period of the binary Cru-3AB+Cru-3C would be around 1500 days. Using this value as an initial guess for the orbital period, we find the orbital solution reported in Fig. 6 with the corresponding orbital parameters given in Table 7. From Table 7 one can see that the barycentric velocity of the system Cru-3AB+Cru-3C is quite consistent with the radial velocity of the other members of the Crux group, which suggests that the actual orbit might indeed be not very far from the one shown in Fig. 6. Assuming that Cru-3AB is composed by two solar-mass stars and using the mass function given in Table 7, we estimate that the mass of Cru-3C might be about 0.5-0.6 $M_\odot$. More data are obviously needed in order to check the validity of this preliminary orbit and improve the tertiary mass estimate made here.

Statistically it appears that spectroscopic sub-systems are frequent in visual or wide spectroscopic binaries (Tokovinin & Smekhov 2001). The fact that the eccentricity of the inner SB2 of Cru-3 is small (almost circular), and the outer is moderately high is consistent with recent results by Tokovinin & Smekhov (2001). Also the "long'' to "short'' period ratio of about 29 for Cru-3 points towards dynamical stability of the triple: empirically, triples with period ratios $P_{\rm long}/P_{\rm short}~>$ 10 are viewed upon as stable (Tokovinin 2000).

 

 

Table 7: Orbital parameters for the system Cru-3AB+Cru3C.

$P_{\rm orb}$ (days)	1688.15
$T_0-2\,400\,000$ (HJD)	50152.6914
e	0.41
$\gamma$ (km s-1)	10.616
$K_{\rm a}$ (km s-1)	5.941
$a_{\rm a}\sin i$ (109 m)	125.6742
f1(m) ($M_\odot$)	0.278 $\times~10^{-1}$
$\sigma$(O-C) (km s-1)	0.540
Number of measur.	11