Toward Ending the Polaris Parallax Debate: A Precise Distance to Our Nearest Cepheid from Gaia DR2

Polaris (α Ursae Minoris; F7 Ib–II; V = +1.99 mag) is one of the best known stars, serving as the North Pole Star for the last ∼500 years, and is the nearest Classical Cepheid (P = 3.974 days). Polaris serves as an important astrophysical laboratory for studying stellar pulsation, Cepheid properties (including calibration of the Leavitt period–luminosity-law) and probing the structure and evolution of these supergiant progenitors of core-collapse SNe Type-II.

Polaris' distance has remained uncertain and often contentious (see Table 1)—a major impediment in determining Polaris' fundamental properties and fully exploiting the star as a standard candle. Modern distance determinations of Polaris range from ∼100 to 160 pc (Turner et al. 2013—short-distance; Bond et al. 2018—long-distance). The direct Hipparcos parallax/distance of ${132.6}_{1.9}^{2.0}$ pc (van Leeuwen 2007) appears the most precise of these. In this note we utilize the recent Gaia DR2 (Gaia Collaboration 2018) results to determine the precise distance of Polaris and determine the star's physical properties and evolution-state.

Table 1.  Selected Distance Calculations of Polaris

Method	Parallax	Distance	Target	References
Photographic	4 ± 3	${250}_{107}^{750}$	Polaris A	van Altena et al. (1995)
Hipparcos	7.56 ± 0.48	${132.3}_{7.9}^{9.0}$	Polaris A	ESA (1997)
Hipparcos	7.54 ± 0.11	${132.6}_{1.9}^{2.0}$	Polaris A	van Leeuwen (2007)
Polaris B Photometry	10.10 ± 0.20	${99.0}_{1.9}^{2.0}$	Polaris B	Turner et al. (2013)
Spectroscopic Stellar Parameters	N/A	109.5	Polaris B	Usenko & Klochkova (2008)
HST/FGS	6.26 ± 0.24	${159.7}_{5.9}^{6.0}$	Polaris B	Bond et al. (2018)
Gaia DR2	7.292 ± 0.028	${137.14}_{0.52}^{0.53}$	Polaris B	This study; Gaia Collaboration (2018)

Gaia DR2 has recently returned remarkably precise parallax and proper motion measures of millions of stars. Unfortunately, Polaris is too bright for a direct parallax. However, Gaia DR2 returned an accurate parallax of Polaris B—the 8th mag (F3 V; V = 8.65 mag; B–V = 0.56) companion (∼18'' away) to the bright Cepheid (Evans et al. 2008; Usenko & Klochkova 2008). The Gaia DR2 parallax/distance of 7.292 ± 0.028 (${137.14}_{0.52}^{0.53}$  pc) of Polaris B agree well with the parallax/distance returned for Polaris itself by Hipparcos (van Leeuwen 2007) of π = 7.54 ± 0.11 mas (d = ${132.6}_{-1.9}^{+2.0}$  pc). Recent studies have found a possible small offset in the Gaia DR2 parallaxes of ∼−40 to −80 μas (see Stassun & Torres 2018; Zinn et al. 2018, and references therein). If applied, this results in a small distance decrease of ∼1 pc.

The "short-distances" (taken as <120 pc) published for Polaris yield a lower luminosity/smaller radius and imply a fundamental-mode, first-crossing Cepheid (see Turner et al. 2013). Bond et al. (2018) have recently determined a parallax/distance of π = 6.26 ± 0.24 mas (${159.7}_{5.9}^{6.0}$  pc) from high-precision astrometry of Polaris B made with the HST Fine Guidance Sensor (FGS). This "long" distance implies that Polaris may be a 2nd overtone, 3rd (or 5th) crossing Cepheid. However, adopting this HST/FGS distance, Anderson (2018) interprets Polaris as a ∼7 M_⊙, first-overtone Cepheid near the hot-boundary of the first instability strip crossing.

The Gaia parallax of Polaris B yields an absolute magnitude of M_V = +2.91 mag (using E_B − V = 0.013 and A_V = 0.04 mag from Polaris Kovtyukh et al. 2008). This M_V is about 0.5–0.7 mag brighter than expected for its F3V spectral type and young age of 60–100 Myr inferred from the Cepheid. Corresponding ∼F3 V stars in the Pleiades cluster have M_V = +3.6 ± 0.1 mag. This discrepancy seems best explained by Polaris B as a binary system, or as suggested by Bond et al. (2018), a merged binary. This higher luminosity of Polaris B has led to underestimates of the distance to Polaris B and thus Polaris.

Now with the high-precision Gaia parallax (in excellent agreement with the revised Hipparcos measure), Polaris' evolution-related properties can finally be resolved. Adopting the Gaia DR2 parallax of Polaris B as the Cepheid's distance, we compute the updated properties of Polaris. With $\langle V\rangle =+1.99$ mag and again adopting E_B−V = 0.013 ± 0.01 and A_V = 0.04, yields $\langle {M}_{V}\rangle =-3.74$ mag. Polaris' radius of R = 46.0 R_⊙ is calculated from its interferometric-angular diameter of α = 3.123 ± 0.008 mas (Mérand et al. 2006). Assuming additional quantities from Evans et al. (2008) that include its rather large period change of dP/dt ≈+4.5 sec yr⁻¹ (Neilson et al. 2012; Engle 2015) indicates that Polaris is most likely a first overtone, 1st crossing Cepheid. The results from previous studies based on the short distance, and more recently, the long distance should be reconsidered now that the star's distance is firmly determined. Evolutionary tracks including rotation effects (Ekström et al. 2012), as previously used by us (Sirorattanakul et al. 2017), give a preliminary fit for Polaris with revised properties: M ≈ 6.4–6.7 M_⊙, R ≈ 47–50 R_⊙, age ≈55–65 Myr.