4 Astrometry: Common proper motion pairs?

Because we have observed both HD 199143 and HD 358623 several times (Dec. 2000, July 2001, Dec. 2001), we can check whether the companion candidates share the proper motion with their respective primaries. In the case of HD 358623, we have detected the companion candidate at all three epochs, while in the case of HD 199143, the companion candidate is only marginally resolved in the two SofI images. We could compare our separations between HD 199143 A and B with those given in JB01, but that does not yield any significant conclusion, because the JB01 observations were obtained only one month before our SHARP-I images.

   

Table 3: Separations of the companion candidates ($\pm$$1 \sigma$ errors).

Pair	$\Delta \alpha [^{\prime \prime}]$	$\Delta \delta [^{\prime \prime}]$	sep. $[^{\prime \prime}]$	PA [$^{\circ}$]	epoch	Ref.
HD 199143 A & B	$0.619 \pm 0.016$	$0.884 \pm 0.015$	$1.079 \pm 0.009$	$325.0 \pm 0.7$	2001.4	JB01
HD 199143 A & B	$0.595 \pm 0.024$	$0.832 \pm 0.019$	$1.023 \pm 0.031$	$324.43 \pm 1.60$	2001.5	this work
HD 358623 A & B	$1.433 \pm 0.002$	$1.661 \pm 0.008$	$2.194 \pm 0.011$	$139.21 \pm 0.68$	2000.9	this work
HD 358623 A & B	$1.434 \pm 0.019$	$1.673 \pm 0.018$	$2.203 \pm 0.007$	$139.4 \pm 0.5$	2001.4	JB01
HD 358623 A & B	$1.426 \pm 0.013$	$1.640 \pm 0.015$	$2.178 \pm 0.007$	$138.99 \pm 1.02$	2001.5	this work
HD 358623 A & B	$1.433 \pm 0.011$	$1.725 \pm 0.010$	$2.243 \pm 0.021$	$140.28 \pm 0.88$	2001.9	this work

Figure 3: Measured separation (in arc sec, with $1 \sigma$ error bars) versus observing date (in years) between HD 358623 A and B with data points from Table 3. The solid line show the median separation. If the visual pair really is a bound pair, then the separation should not change (except for orbital motion, which is negligible for our relatively wide separation and small epoch difference). If the two stars were unrelated, then the separation should change according to the proper motions of the two stars, i.e. mainly the known proper motion of the primary star, assuming that the companion candidate is a non-moving background star; the changes in separation expected for that case are shown as dashed line. For the pair HD 358623 A and B, we have significant evidence for common proper motion: the companion is located SE of the star and the star is known to move to the SE, so that the observed separations should have decreased, if the pair would have been unbound; the last data point is $6 \sigma$ deviant from the background hypothesis, but less than $2 \sigma$ deviant from the companion hypothesis.

The separations are measured as differences between the photo-centers of the objects determined by a Gaussian centering with MIDAS, with the pixel scales mentioned above. The north-south alignment of SHARP-I during our observing nights was determined to be precise within less than half a degree using images of the galactic center and known bound binaries taken in the same nights. The separations in $\alpha$ and $\delta$ as well as the position angles PA given in Table 3 include an additional error of $\pm 0.5^{\circ}$ due to an uncertainty in the north-south alignment of the detectors, while the errors in total separation are independant of that uncertainty.

First, we have measured 18 other comparison stars in the HD 358623 field, in order to determine the precison of our astrometry. The separations between each pair of comparison stars did not change within the 10 to 20 mas errors. Hence, they are very likely non-moving background stars. HD 358623 moves relative to the comparison stars to the SE. From the difference in the separations between 18 comparison stars and HD 358623, we can measure its proper motion ($\sim$103 mas/yr), which is consistent with its known Tycho proper motion ($\sim$86 mas/yr) within less than 20 mas/yr. This shows how precise relative astrometry can be, even after only one year of epoch difference, due to (i) the small SofI pixels together with the small FWHM due to excellent seeing and active optics (hence small error in Gaussian centering), (ii) the relatively large SofI field-of-view even in the so-called small SofI field (hence many sufficiently bright comparison stars), (iii) and the stability of the telescope and instrument optics over the one year epoch difference.

If the close companion candidate would be an unrelated background object, it should also move relative to HD 358623 as the other very widely separated background objects, namely by almost $\sim$100 mas/yr according to the PA. The separations measured by us and by JB01 are given in Table 3. One can clearly see that the companion candidate HD 358623 B did not move relative HD 358623 A (see Fig. 3) from one epoch to any of the three other epochs, not within the measurement errors and certainly not with a motion as large as $\sim$100 mas/yr. In particular, the comparison between the Dec. 2000 SofI image and the Dec. 2001 SofI image is very significant, because they have been taken with the same instrument at the same airmass and also with exactly a full year epoch difference, so that there are no differential parallax nor refraction effects. Because the companion candidate is located SE of the primary and because the primary is known to move SE, the separation should have decreased by $\sim$100 mas, if the pair is not bound. This can be excluded with a significance of $6 \sigma$. Hence, the companion candidate is co-moving with the star. Therefore, it is very likely a truely bound companion of the young nearby star HD 358623. To confirm this conclusion, we have taken a spectrum of HD 358623 B.