[Paper Review] The angular size of dwarf stars and subgiants - Surface brightness relations calibrated by interferometry

P. Kervella, F. Thévenin+2 more|ArXiv.org|Apr 8, 2004

Adaptive optics and wavefront sensing230 citations

TL;DR

This paper calibrates empirical surface brightness relations for main-sequence dwarfs (A0–M2) and subgiants (A0–K0) using direct interferometric angular diameter measurements, enabling highly accurate predictions of limb-darkened angular diameters from broadband photometry (e.g., V–K or B–L colors) with intrinsic dispersions as low as 1%. The resulting relations achieve ±1% precision in angular diameter estimation, providing a robust, extinction-free method for selecting interferometric calibrators from standard photometry.

ABSTRACT

The availability of a number of new interferometric measurements of Main Sequence and subgiant stars makes it possible to calibrate the surface brightness relations of these stars using exclusively direct angular diameter measurements. These empirical laws allow to predict the limb darkened angular diameters theta_LD of dwarfs and subgiants using their dereddened Johnson magnitudes, or their effective temperature. The smallest intrinsic dispersions of sigma < 1% on theta_LD are obtained for the relations based on the K and L magnitudes, for instance log theta_LD = 0.0502 (B-L) + 0.5133 - 0.2 L or log theta_LD = 0.0755 (V-K) + 0.5170 - 0.2 K. Our calibrations are valid between the spectral types A0 and M2 for dwarf stars (with a possible extension to later types when using the effective temperature), and between A0 and K0 for subgiants. Such relations are particularly useful to estimate the angular size of calibrators for long baseline interferometry from readily available broadband photometry.

Motivation & Objective

• To establish accurate, empirically calibrated surface brightness relations for main-sequence stars and subgiants using direct interferometric measurements.
• To enable precise prediction of limb-darkened angular diameters (θ_LD) from readily available broadband photometry (e.g., V–K, B–L) to support long-baseline interferometry.
• To minimize intrinsic dispersion in angular diameter predictions, achieving σ ≤ 1% for the best-calibrated relations.
• To provide a reliable, extinction-free method for selecting interferometric calibrators, avoiding biases from multiplicity or circumstellar material.
• To validate the relations using well-known stars like 51 Pegasi A and HD 209458 A, comparing predictions with independent measurements.

Proposed method

• The study uses 16 new interferometric angular diameter measurements from the VLT Interferometer (VINCI) and 10 additional measurements from other interferometers (NII, Mk III, PTI, NPOI).
• It applies dereddened Johnson and infrared magnitudes (e.g., V, K, B, L) to derive empirical surface brightness (SB) relations linking color indices to limb-darkened angular diameter (θ_LD).
• The core method involves fitting linear relations of the form log θ_LD = a·(color) + b – 0.2·magnitude, calibrated using direct diameter measurements.
• The relations are derived using the expression F_λ = 4.2207 – 0.1·m_λ₀ – 0.5·log θ_LD, where F_λ is surface brightness, and inverting it to predict θ_LD from photometry.
• The calibration is validated using stars with independently measured radii (e.g., HD 209458 A), comparing predicted θ_LD with values derived from transit light curves and parallaxes.
• The method accounts for photometric errors and intrinsic dispersion, ensuring predictions are accurate to within ±1% for the best relations.

Experimental results

Research questions

• RQ1 Can surface brightness relations calibrated with direct interferometric measurements achieve sub-1% intrinsic dispersion in angular diameter predictions for main-sequence stars and subgiants?
• RQ2 To what extent can broadband photometry (e.g., V–K, B–L) predict limb-darkened angular diameters of dwarfs and subgiants with high precision?
• RQ3 How do the predicted angular diameters from these relations compare with independently measured values from astrophysical observations (e.g., transits, parallaxes)?
• RQ4 Can these relations be used to reliably select interferometric calibrators that are free from interstellar extinction, multiplicity, or circumstellar material biases?
• RQ5 Is there a detectable instrumental bias in the interferometric measurements used for calibration across different instruments (e.g., VLT, NPOI, PTI)?

Key findings

• The best surface brightness relations achieve an intrinsic dispersion of σ ≤ 1% in limb-darkened angular diameter predictions, with the K and L band relations being the most precise.
• The relation log θ_LD = 0.0755·(V–K) + 0.5170 – 0.2·K yields a predicted angular diameter of 0.689 ± 0.011 mas for 51 Pegasi A, consistent with its known radius of 1.138 ± 0.023 R☉.
• For HD 209458 A, the predicted θ_LD is 0.228 ± 0.004 mas, yielding a radius of 1.154 ± 0.059 R☉, in excellent agreement with the direct transit measurement of 1.146 ± 0.050 R☉.
• The relative uncertainty in θ_LD prediction is only ±2%, with the bulk of the error (±5%) arising from Hipparcos parallax uncertainty, not the SB relation itself.
• The relations are valid for dwarfs from A0 to M2 and subgiants from A0 to K0, and are particularly effective for stars fainter than m_V = 7, where direct interferometric measurement is impractical.
• No significant instrumental bias was detected across the five interferometric instruments used in the calibration, supporting the robustness of the derived relations.