NEW EVIDENCE SUPPORTING CLUSTER MEMBERSHIP FOR THE KEYSTONE CALIBRATOR DELTA CEPHEI

In their comprehensive study, de Zeeuw et al. (1999) discovered that δ Cep was a member of a group subsequently denoted as Cep OB6 (see also Hoogerwerf et al. 1997). Twenty stars identified by de Zeeuw et al. (1999) as Cep OB6 members are highlighted in Table 1. Stars exhibiting spectral types inconsistent with cluster membership based on their UBVJHK_s color–color and color–magnitude positions were flagged as non-members. For example, HIP 110459 was previously assigned a membership probability of 100% (Table 1), yet the star exhibits JHK_s photometry and a late-type temperature class (K5; Skiff 2010) indicative of a field red clump giant (Figure 2). UBVJHK_s photometry was obtained from Mermilliod (1991) and Two Micron All Sky Survey (2MASS; Cutri et al. 2003). Spectral types were assigned to stars featured in the Catalogue of Stellar Spectral Classifications (Skiff 2010).

Revised HIP parallaxes (van Leeuwen 2007) were tabulated for 15 stars in Table 1 which were identified as probable cluster members. The revised HIP parallaxes exhibit a ∼30% reduction in uncertainties relative to existing data (Perryman & ESA 1997), and the parallaxes for δ Cep and HD 213307 (r ∼ 07) were increased from π = 3.32  ±  0.58:3.43  ±  0.64 to π = 3.77  ±  0.16:3.69  ±  0.46 mas. A mean distance for the revised cluster sample outlined in Table 1 is $d=271\,{\pm}\, 11(\sigma _{\bar{x}})\,{\pm}\, 42(\sigma)$ pc (see also de Zeeuw et al. 1999, and their Appendix B).

UBVJHK_s color–color analyses permit an assessment of the sample's extinction properties. UBV data are particularly efficient at identifying early-type stars owing to the U-band's sensitivity to the Balmer decrement (e.g., Turner 1989; Carraro et al. 2006).

Cluster members featuring UBV photometry (Mermilliod 1991) are offset from the intrinsic UBV color–color relation by E(B − V) = 0.077 ± 0.016(σ) (Table 1 and Figure 1). The findings support the field reddening determined for δ Cep by Benedict et al. (2002) and are consistent with those established from spectroscopic and JHK_s observations. However, uncertainties associated with the latter hamper a precise assessment. The minimal spread, E(B − V) ∼ 0.06–0.10 (Table 1), may be indicative of marginal differential reddening, rotation, binarity, or photometric uncertainties.

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UBVJHK_s color–color analyses imply a cluster turnoff near B5–B7 (M_*/M_☉ ∼ 5), according to intrinsic relations (Padova models; Straižys & Lazauskaitė 2009; Turner 1976, 1989, 2011). A cluster age of log τ = 7.9 ± 0.1 was inferred from the turnoff determined (Figure 1 and Table 1), and since the corresponding Padova evolutionary track (Figure 2) matches bluer and redder evolved members (δ and ζ Cep). The result agrees with the Cepheid's predicted age (Turner 1996; Bono et al. 2005). The temporal match is pertinent evidence in support of cluster membership for δ Cep.

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A precise distance may be established since two of four principal parameters associated with isochrone fitting were constrained by the UBVJHK_s color–color and spectroscopic analyses, namely, the reddening and age (spectral type at the turnoff). δ Cep exhibits solar abundances, and hence the remaining parameter is the shift required in magnitude space to overlay the intrinsic relation upon the data. The resulting distance is d = 277 ± 15 pc (Figure 2). The zero point is tied to seven benchmark open clusters (d < 250 pc) which exhibit matching JHK_s and revised Hipparcos distances (the Hyades, α Per, Praesepe, Coma Ber, IC 2391, IC 2609, and NGC 2451; van Leeuwen 2009; Majaess et al. 2011a). A redetermination of the HST parallax for the Hyades supports that scale (McArthur et al. 2011). Isochrones, models, and the distance scale should be anchored (and evaluated) using clusters where consensus exists, rather than the discrepant case (i.e., the Pleiades). A ratio of total to selective extinction R_J was adopted from Majaess et al. (2011b; see also Bonatto et al. 2004), whereas a value for R_V was adopted from Turner (1976). An advantage of employing JHK_s observations is that the cluster reddening is negligible in that part of the spectrum (E_{J − H} ∼ 0.3 × E_{B − V}, Majaess et al. 2008; Bonatto et al. 2004, and references therein), which consequently mitigates the impact of uncertainties in R_λ (J₀ = J − E_{J − H} × R_J).

The distance derived from the cluster color–magnitude diagrams (Figure 2) is tied to additional potential cluster members identified using NOMAD (Zacharias et al. 2004). That database was queried for stars exhibiting μ_α = 11–19 and μ_δ = 2–7 mas yr⁻¹ (Table 1). Stars fainter than J ∼ 9.2 were culled from the resulting sample to reduce field contamination. Proper motions may be less reliable for such stars, and spectroscopic and UBV observations are typically unavailable. Stars redder than J − H ∼ 0.4 were likewise removed to mitigate contamination from field red clump giants. In addition, stars featuring anomalous positions in the multiband color–color and color–magnitude diagrams were removed. The remaining stars double the number of existing potential cluster members and are highlighted in Table 2. The stars in Tables 1 and 2 are potential members pending further evidence. The NOMAD proper motions are consistent with estimates from the PPMXL catalog (Table 2). UBVJHK_s photometry was sought from Mermilliod (1991), 2MASS (Cutri et al. 2003), and pertinent resources. For example, new observations acquired from the Bright Star Monitor, which is part of the AAVSO's robotic telescope network, provided BV photometry for HD 239949: V = 10.013 ± 0.031 and B − V = 0.392 ± 0.048. The cluster reddening was redetermined (E_{B − V} = 0.073 ± 0.018(σ)) after including four earlier type stars highlighted in Table 2 which possess UBV photometry.

Cluster members appear to aggregate near J2000 coordinates of $22^{\rm h} 22\mbox{$.\!\!^{\mathrm m}$}5 +56\mbox{$^\circ $}34\mbox{$^\prime $}$ (Figure 3). δ Cep lies at the periphery of the density enhancement, and within the confines of the cluster since the corona extends further (Kholopov 1969; Turner 1985). The Cepheid is r ∼ 2° from the aforementioned coordinates, which is equivalent to a linear projected separation of ∼9 pc. The revised HIP and HST parallaxes for δ Cep and HD 213307 (r ∼ 07 from δ Cep), in tandem with their apparent positions, suggest that the distance to the cluster center and Cepheid is analogous to within the uncertainties.

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The mean HIP parallax for the cluster (Section 2.1) agrees with the HIP parallax for δ Cep (π = 3.77 ± 0.16 mas), the HST parallax for δ Cep (π = 3.66 ± 0.15 mas; Benedict et al. 2002), and the distance inferred for the host cluster from UBVJHK_s and spectroscopic observations (Figures 1 and 2). Assigning equal weight to each method, the mean of the four distances for δ Cep is: $d=272\pm 3(\sigma _{\bar{x}}) \pm 5 (\sigma)$ pc. That result agrees with the Storm et al. (2011) determination from the infrared surface brightness technique (IRSB; Fouque & Gieren 1997). The associated standard error and deviation provide a realistic estimate for the systematic uncertainty, which is often difficult to characterize.

The resulting VI_c Wesenheit magnitude for δ Cep is $W_{VI_c,0}=-5.12$ ($R_{VI_c}=2.55$). That is consistent with results established for classical Cepheids displaying similar pulsation periods: CV Mon, V Cen, Y Sgr, and CS Vel (Benedict et al. 2007; Turner 2010; Majaess et al. 2011b).