[Paper Review] Mean Angular Diameters and Angular Diameter Amplitudes of Bright Cepheids

P. Moskalik, N. A. Gorynya|arXiv (Cornell University)|Jul 4, 2005

Astronomy and Astrophysical Research3 citations

TL;DR

This paper predicts mean angular diameters and angular diameter amplitudes for 79 bright, monoperiodic Population I Cepheids with ⟨V⟩ ≤ 8.0 mag using period–luminosity and period–radius relations, combined with radial velocity integration via a fixed projection factor. The key result is a prioritized list of 13 Cepheids with detectable angular diameter variations (Δθ > 0.15 mas), ideal for interferometric distance measurements via the geometric Baade-Wesselink method, significantly enhancing P-L relation calibration prospects.

ABSTRACT

We predict mean angular diameters and amplitudes of angular diameter variations for all monoperiodic Pop.I Cepheids brighter than = 8.0mag. The catalog is intended to aid selecting most promising Cepheid targets for future interferometric observations.

Motivation & Objective

• To identify the most promising Cepheid targets for long-baseline interferometry by estimating their mean angular diameters and angular diameter amplitudes.
• To support the calibration of the Cepheid period–luminosity (P-L) relation by providing a catalog of expected interferometric observables.
• To enable geometric distance measurements via the Baade-Wesselink method using future interferometers like VLTI/AMBER and CHARA.
• To extend the sample of Cepheids accessible to interferometric study beyond the current five observed stars.
• To support surface brightness-colour relation calibration by providing a range of Cepheids with diverse effective temperatures.

Proposed method

• Calculated distances using the Fouqué et al. (2003) P-L relation in the V band, with zero point calibrated via infrared surface brightness method.
• Estimated mean linear radii using the Gieren et al. (1998) P-R relation, with first-overtone pulsators converted to fundamental-mode periods using Eq. (2).
• Computed radius variations by integrating observed radial velocity curves with a fixed projection factor p = 1.36.
• Derived mean angular diameters (⟨θ⟩) and angular diameter amplitudes (Δθ) using the formula ⟨θ⟩ = 9.305 × ⟨R⟩ / d, where R is in solar radii and d in parsecs.
• Assessed uncertainties by combining intrinsic dispersions of the P-L (0.157 mag) and P-R (1.6%) relations, leading to ~7.2% uncertainty in Δθ and ~7.2% in d.
• Used a theoretical framework based on period–mass–radius and mass–luminosity relations to estimate systematic uncertainties in radius and angular diameter estimates.

Experimental results

Research questions

• RQ1 Which bright Cepheids have angular diameter variations large enough to be resolved by current and near-future interferometers?
• RQ2 How accurately can mean angular diameters be predicted for Cepheids with ⟨V⟩ ≤ 8.0 mag using standard P-L and P-R relations?
• RQ3 What is the expected distribution of detectable angular diameter amplitudes across the Cepheid period range?
• RQ4 How many Cepheids in the sample can be used for geometric distance determination via the Baade-Wesselink method with existing or upcoming interferometers?
• RQ5 To what extent can this catalog improve the calibration of the Cepheid P-L relation and surface brightness-colour relations?

Key findings

• Thirteen Cepheids have angular diameter amplitudes exceeding 0.15 mas, making them detectable with current interferometers like VINCI/VLTI and PTI.
• Of these 13, seven have no prior interferometric observations, and for the eighth (δ Cep), only the mean angular diameter has been measured.
• The mean angular diameter can be measured to 1% precision in over 50 Cepheids and to 2% precision in all 79 stars in the sample.
• The VLTI/AMBER interferometer (baseline 202 m) and the CHARA array (baseline 330 m) are expected to increase the number of resolvable Cepheids with detectable pulsations to approximately 30.
• The catalog includes four Cepheids (SV Vul, U Car, RS Pup, FF Aql) not yet observed interferometrically, highlighting them as high-priority targets.
• The method achieves ~7.2% uncertainty in angular diameter amplitudes due to intrinsic dispersion in the P-L relation and ~7.2% in distances, with additional 1.6% uncertainty in mean radius estimates.