\(\mathit{uvby}\beta \) - photometry and effective surface temperature of stars B0-4V-III AND \(\beta \) Cephei variables

Using \(\mathit{uvby}\beta \)-photometry, the Eddington pulsation constant can be determined for \(\beta \) Cephei variables, which are mostly stars B0.5-2V-III. Therefore, the known relations between the effective surface temperature and the indexes of \(\mathit{uvby}\beta \)-photometry are analyzed for B-stars. These relations were determined using the empirical data from small numbers of stars. Therefore, the representative calibration sample is formed from 104 stars B0-4V-III, for which the effective surface temperature and the indexes of \(\mathit{uvby}\beta \)-photometry (\(c_{1}\), \((b- y)\), \(m_{1}\), \(\beta \)) are known. Using this sample, for stars B0-4 the relations between \(c_{0}\), \((b- y)_{0}\), \(m_{0}\), \(\beta \) and the effective surface temperature are determined in luminosity classes V, IV and III. It is established new indexes of \((b- y)_{0} '\), \(m_{0} '\) and \(\beta '\) that are \(((b- y)_{0} - (b- y)_{0(\mathrm{V}+\mathrm{IV})})/ ((b- y)_{0(\mathrm{V}+\mathrm{IV})} - (b- y)_{0(\mathrm{III})})\), \((m_{0} - m_{0(\mathrm{IV}+\mathrm{V})})/(m_{0(\mathrm{IV}+\mathrm{V})} - m_{0(\mathrm{III})})\) and \((\beta - \beta _{(\mathrm{IV}+\mathrm{V})})/(\beta _{(\mathrm{IV}+\mathrm{V})}- \beta _{\mathrm{III}})\), respectively. Using the condition of \((b- y)_{0} ' = m_{0} ' = \beta '\) at a constant metallicity, the accurate relations between \(c_{0}\), \((b- y)_{0}\), \(m_{0}\), \(\beta \), \(\beta '\) and the surface effective temperature are determined for stars B0-4V-III. It is found that in \(\mathit{uvby}\beta \)-photometry for stars B0-4V-III the known temperature calibrations have average errors of (4 – 9)%. The new accurate temperature calibration has an error of about 1%. It is found that the Eddington pulsation constant depends very loosely on the pulsation period for \(\beta \) Cephei variables.