V440 Per: the longest period overtone Cepheid
  V440 Per is a Population I Cepheid with the period of 7.57 day and low
amplitude, almost sinusoidal light and radial velocity curves. With no reliable
data on the 1st harmonic, its pulsation mode identification remained
controversial. We obtained a radial velocity curve of V440 Per with our new
high precision and high throughput Poznan Spectroscopic Telescope. Our data
reach the accuracy of 130 m/s per individual measurement and yield a secure
detection of the 1st harmonic with the amplitude of A_2= 140+/- 15 m/s. The
velocity Fourier phase \phi_21 of V440 Per is inconsistent at the 7.25 \sigma
level with those of the fundamental mode Cepheids, implying that the star must
be an overtone Cepheid, as originally proposed by Kienzle et al.(1999). Thus,
V440 Per becomes the longest period Cepheid with the securely established
overtone pulsations. We show, that the convective nonlinear pulsation hydrocode
can reproduce the Fourier parameters of V440 Per very well. Requirement to
match the observed properties of V440 Per constrains free parameters of the
dynamical convection model used in the pulsation calculations, in particular
the radiative losses parameter.
