STELLAR MULTIPLICITY OF THE OPEN CLUSTER MELOTTE 111

Using our own speckle-interferometry observations and data taken from the literature, we have initiated a survey of binary stars and multiple systems in Galactic open clusters (Guerrero et al. 2014). This paper presents our investigation of stellar multiplicity by analyzing the open cluster Melotte 111. Our observations will be useful to have more precise statistics of the multiplicity fraction among open clusters, which is still an open question for star formation and stellar evolution (Riddle et al. 2015).

In the following section we describe the open cluster Melotte 111 and the data we collected from the literature. In Section 3 we describe our observations and data reduction procedure; in Section 4 we present the results of our observations. In Section 5 we estimate the completeness of our sample and the probable undetected systems and in Section 6 we discuss the binary frequency of Melotte 111 and the multiplicity frequency in the field around the cluster. Finally we discuss our results in Section 7 and present our conclusions in the last section.

The Melotte 111 star cluster (Coma Berenices) is a poorly populated cluster with a diameter of 8° that lies in the direction of the Coma Berenices constellation, about two times farther than the Hyades open cluster; its equatorial and galactic coordinates, taken from Kharchenko et al. (2005), are ${\alpha }_{2000}={12}^{{\rm h}}\;{22}^{{\rm m}}\;{30}^{{\rm s}}$, ${\delta }_{2000}\;=\;+25^\circ \;51^{\prime}$, and $l=222\buildrel{\circ}\over{.}43$, $b\;=\;+83\buildrel{\circ}\over{.}40$, respectively. It was first cataloged by Melotte (1915) and later revisited by Trumpler (1938); since then, Coma Ber has been the subject of several studies concerning all kinds of astrophysical topics. However, due to its large diameter, the sparse distribution of stars and their low average proper motion, ${\mu }_{\alpha }=-11.45$, ${\mu }_{\delta }=-8.98$ mas yr⁻¹ (Kharchenko et al. 2005), and the fact that the lower main sequence of Melotte 111 has very few stars, the membership selection has been a challenge for this cluster (see Casewell et al. 2014; Terrien et al. 2014). Melotte 111 is on the list of 520 open clusters identified by Kharchenko et al. (2005) in the All-sky Compiled Catalog of 2.5 Million Stars (ASCC-2.5,³ Kharchenko 2001) and, in order to use the same methodology as in our previous publication (Guerrero et al. 2014), we adopted the physical parameters that they reported: distance d = 87 pc, reddening $E(B-V)$ = 0.00 mag, distance modulus $V-{M}_{V}$ = 4.70 mag, log(t, years) = 8.78, core radius ${r}_{\mathrm{core}}=1,5^\circ$ and corona radius ${r}_{\mathrm{cl}}=4^\circ$, which are consistent with more recent publications (e.g., Silaj & Landstreet 2014). Gebran et al. (2008) reported a solar metallicity value for Melotte 111.

Kharchenko et al. (2005) analyzed 1524 stars in the direction of Melotte 111 and they established a membership selection procedure based on three criteria (Kharchenko et al. 2004): a kinematic constraint, P_kin, that takes into account proper motion; a photometric selection, P_phot, to exclude background co-moving stars; and a position factor P_s, equal to 1 within the cluster radius and zero elsewhere. Using such criteria, they defined the most probable members those stars for which P_kin and P_phot are not less than 61% ($1\sigma$-members); probable member stars for which both P_kin and P_phot are between 61% and 14% (2σ-members), and possible members all stars within a 3σ-deviation, i.e., P_kin and P_phot between 14% and 1%. Stars with both P_kin and P_phot less than 1% were considered as non-members. Given these criteria, the open cluster Melotte 111 has 38 most probable members, with 8 of these stars reported as binaries and 1 as a sextuple system; 52 probable members, 2 of them reported as binary and 2 as triples, and 78 possible members, with 4 of these stars previously known to be binaries. However, even using these selection criteria, it is probable that we included or rejected 1 or possibly more member stars of Melotte 111.

In total, we observed 168 stars among most probable, probable, and possible members of Melotte 111, over the $8^\circ$ diameter of the cluster. For comparison, we also observed 175 of the remaining stars that were considered as field stars, distributed within this sky area. Among these, 5 are reported as binary stars and 1 star as a multiple star consisting of seven stars. Important to note is that, for the remaining stars in our sample, we do not have prior knowledge of duplicity or multiplicity, so the conclusions derived from this study are reliable within the limits of our detections (see Section 5). We separated the previously known binary stars into two groups: binaries cataloged in the Washington Double Star (WDS) Catalog (Worley & Douglass 1997) and spectroscopic binaries. Table 1 summarizes the data available in the WDS Catalog: the first column contains the number of each star in the ASCC-2.5, the second column contains the epoch-2000 coordinates in the format used in the WDS Catalog; the third column gives the discoverer designation, adopted by the WDS Catalog. The three following columns contain the measured position angles given in degrees, the angular separation in arcseconds and the companion magnitude difference in magnitudes, respectively. The seventh column contains the value of the proper motion probability of being a cluster member and the last column the value of the photometric probability, both taken from Kharchenko et al. (2005). Table 2 gives the cross-references of some astronomical catalogs for the spectroscopic binaries reported in the literature; the first column contains the number of each star in the ASCC-2.5 and the three following columns the BD, HD and Hipparcos identifications, respectively. The fifth column contains information about the type of spectroscopic binary: SB1 for single lined spectroscopic binaries; SB2 for double lined spectroscopic binaries; SB for spectroscopic binaries without calculated orbit and SBO for spectroscopic binaries with orbital parameters calculated. The sixth column contains the value of the proper motion probability of being a cluster member and the seventh column the value of the photometric probability, as in Table 1. The last column contains a reference for the orbital parameters.

Table 1.  Known Stellar Multiplicity

ASCC	WDS	Disc.	P.A.	Sep.	Δm	Pkind	Pphotd
Number	($\alpha ,\delta$ J2000.0)	Name	(deg)	(arcsec)	(mag)
684431c	12073+2732	TDS8229	279	11.1	0.23	0.1572	0.0346
684735a	12207+2939	SDK 54	316	13.5	1.37	0.6415	0.8700
684740	12207+2703	STF1633	245	8.9	0.09	0.0000	0.3105
684743b	12208+2546	HJ 517	239	20.0	3.41	0.4291	1.0000
684781	12219+2833	LDS1300	99	62.2	7.73	0.0000	0.0429
684791c	12219+2909	HJ 518	328	25.3	0.8	0.1281	0.7627
684793a	12225+2551 AB	SHJ 143	57	36.7	6.94	0.9015	1.0000
684815a	12225+2551 AC	SHJ 143	168	58.9	4.04	0.7137	1.0000
684830a	12225+2551 AD	ARN 6	132	213.1	5.24	0.7680	1.0000
684853b	12244+2535 AB	STF1639	160	91.6	4.76	0.2225	1.0000
684853b	12244+2535 AC	STF1639	324	1.8	1.09	0.2225	1.0000
684967	12285+2953	ES 436	136	2.0	0.2	0.0000	0.0000
684977	12289+2555 BC	BU 1080	175	1.5	7.06	0.0000	1.0000
684977	12289+2556 BD	BU 1081	284	193.0	7.06	0.0000	1.0000
684982	12289+2555 AB	STFA 21	250	144.9	1.41	0.0000	1.0000
684982	12289+2555 AD	BU 1080	269	324.2	8.47	0.0000	1.0000
684982	12289+2555 AE	SLE 898	270	447.5	6.87	0.0000	1.0000
684982	12289+2555 AF	SLE 898	146	125.9	7.47	0.0000	1.0000
685146a	12349+2727	YSC 99	273	0.4	3.0	0.9608	1.0000
778532	12207+2255	STF1634	147	5.4	1.2	0.0000	0.3388
778605	12236+2326	STF1637	143	120.5	2.32	0.0000	1.0000
778618	12240+2447	SKF1582	249	96.1	1.5	0.0022	0.2889
778845c	12326+2414	SKF1015	302	28.0	0.2	0.0146	0.1103
778904	12349+2238	WRH 12	16	0.3	1.94	0.0000	0.0000

Notes. Stars without a mark are field stars.

^aMost probable member stars of the open cluster Melotte 111. ^bProbable member star of the open cluster Melotte 111. ^cPossible member star of the open cluster Melotte 111. ^dTaken from Kharchenko et al. (2005).

Download table as:  ASCIITypeset image

In Figure 1 we show the apparent magnitude distribution for the 343 stars that we observed, divided into field stars and cluster stars; Figure 2 represents the V versus $(B-V)$ diagram for our sample stars.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We obtained our speckle-interferometric data during one observing run at the 2.1 m telescope of the Observatorio Astronómico Nacional (OAN), México. The diffraction-limited resolution of the 2.1 m telescope is 007, for λ = 640 nm. We performed the observations using the EMCCD iXon 885 DU from Andor Technology. This is a low noise, high sensitive EMCCD camera. It is cooled thermoelectrically to −95°C which provides excellent elimination of EM-amplified dark current noise, even for short time exposures. This detector has more than 40% of quantum efficiency in the range of 400–800 nm and given its fast frame rate, it can be use for high resolution imaging. The CCD has 1004 × 1002 pixels of 8 μm. Speckle interferometry was introduced by Labeyrie (1970). This technique allows observations to reach a diffraction-limited resolution, using special methods for the reduction of short-exposure images. The main goal of this reduction is to remove the influence of the atmosphere from the observed data. Once we have the selected candidates to be observed, we take a set of 400 short-exposure images (20 ms) for each sample star. We also observe well-known visual double stars with very slow motion to calibrate our speckle data. The speckle data reduction is made in three steps. In the first step, we remove the sky background from each speckle image. In the second step, we calculate the square modulus of the complex visibility, Power Spectrum (PS), averaged over all the images, which is performed according to the standard Labeyrie (1970) procedure. The inverse Fourier transform of the PS gives us the Autocorrelation Function (ACF). We remove the atmospheric distortions from this spectrum using the Wiener Filtering. In the final step, we measure the angular separation between the stars (ρ) and the position angle (P.A.), which are given by the position of the secondary maximum of the ACF. Due to the fact that the ACF has central symmetry, the P.A. that we measured has a $180^\circ$ ambiguity, i.e., we can only say that the secondary star is at a position P.A. $\pm 180^\circ$, but this is different from the error in the measurement. We then use the Levenberg–Marquardt algorithm to calculate more accurate values of ρ and P.A., this algorithm gives us mean errors for these quantities. This reduction process is explained in detail by Tokovinin et al. (2010). During seven nights, from 2014 April 12 to 18, we used the $f/7.5$ secondary mirror, combined with a micro objective, which together provides a scale of 18.5 mas pixel⁻¹ after calibration, corresponding to a visual field of $16\buildrel{\prime\prime}\over{.}65\times 16\buildrel{\prime\prime}\over{.}65$ for the total area of the detector. We observed a total of 343 stars distributed over sky area with $8^\circ$ diameter of Melotte 111. We observed every object using the R Johnson–Cousins filter. For calibration we observed 30 known binaries with very slow orbital motions and some of them with known orbital parameters.

We estimated that the seeing was between 06 and 09 for the whole run and aberrations introduced by the telescope had similar values. As a result, long exposure images have a resolution of about 15 and the mean error in the companion separation is 0013 and $1^\circ$ in the position angle, modulo $180^\circ$.

For the whole sample, we were able to resolve systems as close as 035 and detect pairs as wide as 891 in some directions. We detected speckle-interferometric companions for nine of the stars in our sample. We astrometrically resolved four binary stars for the first time and we probably found a visual companion to the spectroscopic binary BD +27 2130 (see Section 6.1); we detected a new companion in one previously known binary star and confirmed three previously known binaries. We also detected a secondary star in the long exposure image of star ASCC 778453 (see Figure 3), however, the magnitude difference is so large that we could not detect it in the ACF. Nevertheless, we included it in our estimation of the multiplicity fraction of the field stars around Coma Ber (see Section 6.2). Table 3 contains the results of our measurements: the first column lists the number of each star in the ASCC-2.5, the second column gives the name of the star or the discoverer designation (only for stars previously known). The third column gives the epoch of the observation in fractional Besselian years and the fourth and fifth columns contain the measured position angles given in degrees and the angular distances in arcseconds. The sixth column contains the value of the proper motion probability of being a cluster member and the last column the value of the photometric probability, also taken from Kharchenko et al. (2005).

Zoom In Zoom Out Reset image size

During data processing, we noted that the data obtained using the EMCCD showed a good photometric stability. Photometric measurements were not the initial goal of this publication, so we did not observed standard stars. However, in the literature we found information about flux in the R band for 71 of our sample stars, excluding intrinsic variable stars, which allowed us to perform a flux calibration for our data. For relatively bright stars, $m\lt 9$, the mean error in magnitude is less than 1%. For weaker stars the errors increase up to 4%. We present the photometric results in Table 4, in which we excluded all binary stars; the first column lists the number of each star in the ASCC-2.5, the second and third columns contain the B and V magnitudes (respectively), taken from ASCC-2.5, and the fourth column contains the value of the R magnitude that we estimated. The fifth column contains the value of the proper motion probability and the last column the value of the photometric probability.

We should take into account the selection effect due to the brightness limit of the ASCC-2.5, about V = 14, and completeness limit of about V = 11.5 (Kharchenko et al. 2004), although, as we can see in Figure 1, the magnitudes of the majority of the stars in our sample lie within those limits. We know the distance for the member stars of Coma Ber but not for the field stars, so our sample might be biased toward intrinsically bright objects and nearby stars. As we mentioned in Guerrero et al. (2014), when using speckle-interferometry we have to consider the limits of our detections; if we have a binary star that has an elliptical orbit with semi-major axis a, then the expected observable separation is $1.4\rho$, with ρ the projected separation (Couteau 1960). Therefore, at a distance of 87 pc, we can expect separations around 0011, which is smaller than the diffraction limit of the 2.1 m telescope in the R band (see Section 3). The second effect is due to the dynamical range of the detector used to collect the data. The previous observations that we performed using the EMCCD iXon 885 DU allowed us to stablish the limits of our detections: ${\rm \Delta }m\leqslant 4$, $m\leqslant 13$ for the primary component of a binary system and a maximum field of view of $23^{\prime\prime}$. Therefore, we can detect every companion whose separation is larger than $1^{\prime\prime}$ (and less than $23^{\prime\prime}$) and ${\rm \Delta }m\leqslant 4$. For stars with $\rho \leqslant 1^{\prime\prime}$, there is a compromise between separation and magnitude-difference, we estimate that we cannot detect about 10% of stars in that range.

For these observations we also established a region of completeness in our cumulative distribution function of separations, by adjusting an Öpik distribution (Öpik 1924). Figure 4 shows the cumulative distribution $N(\mathrm{log}\rho )$ versus $\mathrm{log}\rho$ for the complete list of binaries and multiple stars in our sample (the ones reported in the literature and our own measurements). We also plot a Kolmogorov–Smirnov (K–S) test for cumulative distributions, in order to evaluate the largest reliably interval in which Öpik's distribution still represents the distribution of the angular separations of our sample. The coefficient of significance Q of the K–S test is plotted in the secondary axis. The test gives a value of Q = 0.99 in the interval $-0.46\lt \mathrm{log}\rho \lt 2.65$, which corresponds to $0.35\lt \rho (^{\prime\prime} )\lt 446.68$, i.e., in that interval, our sample still follows the Öpik's distribution. The y-intercept of the Öpik fit indicates the number of expected binaries between $1^{\prime\prime}$ ($\mathrm{log}\rho =0$) and the point where the fit intersects with the distribution function, about 08 or $\mathrm{log}\rho =-0.08$. In this case, we conclude that we are missing 3 or 4 binaries, i.e., between 0.8% and 1.1% in our total sample. We can say that, although our sample is not volume-complete, it does not shows a significant bias in the distribution of separations, which means that we do not have an important number of undetected companions.

Zoom In Zoom Out Reset image size

6.1. Binaries in Melotte 111

We included star ASCC 684901 (Tr 120) as a most probable member of Melotte 111 because, even though it does not satisfy the three membership criteria of Kharchenko et al. (2004), it was later confirmed to be a cluster member by Mermilliod et al. (2008), by means of radial velocities. This star is also known to be a spectroscopic binary and we found an interferometric binary system with a separation of $1\buildrel{\prime\prime}\over{.}11$ which, at the distance of Melotte 111, corresponds to a true semimajor axis of 48.28 AU. This is inconsistent with the expected separation for the spectroscopic binary, given the 294.78 days period reported by Terrien et al. (2014). If this system is not the spectroscopic binary astrometrically resolved, then it could be a triple star. We will continue to observe this system in order to establish the parameters of the visual orbit.

Apart from ASCC 684901, we did not find any new double stars among the most probable members of the open cluster Melotte 111. We were not able to resolve the secondary companion of star ASCC 685146, only reported by Horch et al. (2011), which should be well within the limits of our detections. Hence, for this open cluster the ratio of single to multiple stars is 29:9:0:0:0:1, corresponding to a multiplicity fraction of 25.6% ± 2%. In Figure 5 we can see the superficial distribution of multiple stars in Melotte 111: 58% of the multiple systems lie within the cluster's core and 42% are in the cluster's corona, so we can see that there is no evidence of any radial gradient in the superficial distribution of multiple stars in this open cluster.

Zoom In Zoom Out Reset image size

6.2. Stellar Multiplicity of the Field

6.3. BVR Photometry

We used our measurements of the R magnitudes (see Section 4) together with the B and V magnitudes obtained from the ASCC-2.5, in order to built color–magnitude diagrams for Melotte 111 and estimate its age, color excess, and distance modulus (see Figures 6 and 7). Assuming a value of Z = 0.015 (Gebran et al. 2008), we fitted Padova isochrones (Marigo et al. 2008), which are given in reddening-free, absolute magnitudes. Shifting the isochrones along the x-axis gives the color excess $E(V-R)$ and $E(B-R)$, which in this case are equal to zero in both cases. To estimate the distance modulus $\mathrm{DM}={V}_{0}-{M}_{V}$, we shifted the isochrones along the y-axis until we found the best fit to the observed main sequence. The precision of our determinations depends on the data scatter, arising from the photometric uncertainties and errors in the standard-system transformation; furthermore, our uncertainties have an additional error due to the manual fit of the isochrones. We plotted three isochrones varying in a range of log (t, years) = 8.65...8.85, to estimate an order of the uncertainties in our determination of $E(V-R)$, $E(B-R)$, log t, and DM. In Table 5 we summarized our findings and included the physical parameters estimated by other authors for comparison: the first column contains the respective color index, and the second column contains the respective color excess; the third column contains our estimation of the distance modulus; the fourth column the corresponding distance; the fifth column contains the estimated log t; and the last column the comparison references. As we can see in Table 5, the physical parameters that we estimated using BVR photometry are in good agreement with previous estimations. In Figures 6 and 7 we also included the binary stars among the most probable members of Melotte 111.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Table 5.  Physical Parameters of Melotte 111

Color	Color	$({V}_{0}-{M}_{V})$	d	log t	References
Index	Excess	(mag)	(pc)	(years)
$(V-R)$	0.00 ± 0.02	4.7 ± 0.2	87 ± 11	8.75 ± 0.15	this paper
$(B-R)$	0.00 ± 0.01	4.7 ± 0.1	87 ± 10	8.75 ± 0.10	this paper
mean	0.00 ± 0.01	4.7 ± 0.1	87 ± 10	8.75 ± 0.12	this paper
$(B-V)$	0.00	4.69	86.7	8.75	Silaj & Landstreet (2014)
$(B-V)$	0.00	4.70	87	8.78	Kharchenko et al. (2005)
$(B-V)$	0.013	5.063	102.94	8.652	Loktin et al. (2001)

Download table as:  ASCIITypeset image

It is very challenging to unequivocally establish the fraction of multiplicity of a particular population of stars, given the wide distribution of physical parameters among binary and multiple stars. However, that is the reason to study open clusters: we may assume they represent a homogeneous sample of stars with the same age, at the same distance, which are different only in mass. Speckle-interferometry has its own intrinsic limitations and we may have introduced a selection effect due to the fact that we are working with a magnitude-complete sample, which may be biased toward similar-mass companions. In this article, we studied the multiplicity fraction of the open cluster Melotte 111 and the multiplicity fraction of the surrounding field to compare with. For this cluster we found a binary fraction of 25.6% ± 2%, consistent with the fraction estimated by Helmut & Daryl (1999), Mermilliod et al. (2008) and Casewell et al. (2014): 25%, 22%, and 22%, respectively. The binary fractions slightly differ due to the number of most probable members taken into account for the calculation and the number of binary stars discovered at the respective time of analysis. However, we found that the multiplicity fraction of the surrounding field is 5.9% ± 3%, which is so much lower than that of the cluster. This result is contrary to the notion that many field stars are found to be binaries or high order multiplicity systems (see Goodwin 2010 and references therein). At least as a lower limit, we would expect a multiplicity fraction of ∼20% to be kept in the field stars, so we wonder if there has been a particular process undergone in that region of the sky or if we introduced a selection effect. In part, we can also attribute this result to the fact that Melotte 111 is a very extended open cluster, $8^\circ$, and the field in the direction of the cluster is more crowded than the stars that we were able to observe, due to the limited observing time.

Using speckle-interferometry we have initiated a survey of binary stars and multiple systems in Galactic open clusters. In this article, we continued our survey with the open cluster Melotte 111. In total, we detected speckle-interferometric companions for nine of the stars in our sample, with five of these detections being made for the first time. Combining our observations with data taken from the literature, we found a ratio of the number of single to multiple stars to be 29:8:0:0:0:1 for the the most probable members, so the multiplicity fraction for this cluster is 25.6% ± 2%. We also observed field stars around the cluster and estimated a ratio of multiplicities to be 286:17:1:0:0:0:1 (between one and seven companions), which is equivalent to a multiplicity fraction of 5.9% ± 3%. We attribute this difference to the fact that, due to limiting observing time, we were not able to observe every star in the surrounding field of Melotte 111. We concluded that there is no evidence of any radial gradient in the superficial distribution of multiple stars in this open cluster. We showed that the cumulative distribution of separations for the binary and multiple stars in our sample is in agreement with Öpik's law.

The speckle interferometry program at the OAN telescopes is supported by the Direccion General de Asuntos del Personal Académico (Universidad Nacional Autónoma de México) under the project IN102514.