High-resolution spectroscopy of the intermediate polar EX Hydrae

II. The inner disk radius^⋆,⋆⋆

Institut für Astrophysik und Geophysik, Georg-August-Universität, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
e-mail: k.beuermann@t-online.de

Received: 11 July 2022
Accepted: 25 January 2024

Abstract

EX Hya is one of the best studied, but still enigmatic intermediate polars. We present phase-resolved blue VLT/UVES high-resolution (λ/Δλ ≃ 16.000) spectra of EX Hya taken in January 2004. Our analysis involves a unique decomposition of the Balmer line profiles into the spin-modulated line wings that represent streaming motions in the magnetosphere and the orbital-phase modulated line core that represents the accretion disk. Spectral analysis and tomography show that the division line between the two is solidly located at ∣υ_rad ∣   ≃  1200 km s⁻¹, defining the inner edge of the accretion disk at r_in ≃ 7  ×  10⁹ cm or ∼10R₁ (WD radii). This large central hole allows an unimpeded view of the tall accretion curtain at the lower pole with a shock height up to h_sh ∼ 1R₁ that is required by X-ray and optical observations. Our results contradict models that advocate a small magnetosphere and a small inner disk hole. Equating r_in with the magnetospheric radius in the orbital plane allows us to derive a magnetic moment of the WD of μ₁ ≃ 1.3  ×  10³² G cm³ and a surface field strength B₁ ∼ 0.35 MG. Given a polar field strength B_p ≲ 1.0 MG, optical circular polarization is not expected. With an accretion rate Ṁ = 3.9 × 10⁻¹¹ M_⊙ yr⁻¹, the accretion torque is G_acc ≃ 2.2  ×  10³³ g cm² s⁻². The magnetostatic torque is of similar magnitude, suggesting that EX Hya is not far from being synchronized. We measured the orbital radial-velocity amplitude of the WD, K₁ = 58.7 ± 3.9 km s⁻¹, and found a spin-dependent velocity modulation as well. The former is in perfect agreement with the mean velocity amplitude obtained by other researchers, confirming the published component masses M₁ ≃ 0.79 M_⊙ and M₂ ≃ 0.11 M_⊙.