HARPS-N high spectral resolution observations of Cepheids

II. The impact of the surface-brightness color relation on the Baade-Wesselink projection factor of η Aql

¹ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229 06304 Nice Cedex 4, France
e-mail: Nicolas.Nardetto@oca.eu
² Universidad de Concepción, Departamento de Astronomía, Casilla 160-C, Concepción, Chile
³ Millenium Institute of Astrophysics, Avenue Libertador Bernardo O’Higgins 340, Casa Central, Santiago, Chile
⁴ Leibniz Institute for Astrophysics, An der Sternwarte 16, 14482 Potsdam, Germany
⁵ Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, PL-00-716 Warszawa, Poland
⁶ LESIA (UMR 8109), Observatoire de Paris, PSL, CNRS, UPMC, Univ. Paris-Diderot, 5 place Jules Janssen, 92195 Meudon, France
⁷ European Southern Observatory, Alonso de Córdova 3107, Casilla 19001, Santiago 19, Chile
⁸ Unidad Mixta Internacional Franco-Chilena de Astronomía (CNRS UMI 3386), Departamento de Astronomía, Universidad de Chile, Camino El Observatorio 1515, Las Condes, Santiago, Chile
⁹ INAF – Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807 Merate (LC), Italy

Received: 26 October 2022
Accepted: 12 January 2023

Abstract

Context. The Baade-Wesselink (BW) method of distance determination of Cepheids is used to calibrate the distance scale. Various versions of this method are mainly based on interferometry and/or the surface-brightness color relation (SBCR).

Aims. We quantify the impact of the SBCR, its slope, and its zero point on the projection factor. This quantity is used to convert the pulsation velocity into the radial velocity in the BW method. We also study the impact of extinction and of a potential circumstellar environment on the projection factor.

Methods. We analyzed HARPS-N spectra of η Aql to derive its radial velocity curve using different methods. We then applied the inverse BW method using various SBCRs in the literature in order to derive the BW projection factor.

Results. We find that the choice of the SBCR is critical: a scatter of about 8% is found in the projection factor for different SBCRs in the literature. The uncertainty on the coefficients of the SBCR affects the statistical precision of the projection factor only little (1–2%). Confirming previous studies, we find that the method with which the radial velocity curve is derived is also critical, with a potential difference on the projection factor of 9%. An increase of 0.1 in E(B − V) translates into a decrease in the projection factor of 3%. A 0.1 mag effect of a circumstellar envelope (CSE) in the visible domain is rather small on the projection factor, about 1.5%. However, we find that a 0.1 mag infrared excess in the K band due to a CSE can increase the projection factor by about 6%.

Conclusions. The impact of the surface-brightness color relation on the BW projection factor is found to be critical. Efforts should be devoted in the future to improve the SBCR of Cepheids empirically, but also theoretically, taking their CSE into account as well.