We report the discovery of type-I X-ray bursts from the low-mass X-ray binary 4U 1708-40 during the 100 ks observation performed by BeppoSAX on 1999 August 15-16. Six X-ray bursts have been observed. The unabsorbed 2-10 keV fluxes of the bursts range from ~ (3-9)x10^(-10) erg cm^(-2)s^(-1). A correlation between peak flux and fluence of the bursts is found, in agreement with the behaviour observed in other similar sources. There is a trend of the burst flux to increase with the time interval from the previous burst. From the value of the persistent flux we infer a mass accretion rate Mdot~7x10^(-11) Msun/yr, that may correspond to the mixed hydrogen/helium burning regime triggered by thermally unstable hydrogen. We have also analysed a BeppoSAX observation performed on 2001 August 22 and previous RXTE observations of 4U 1708-40, where no bursts have been observed; we found persistent fluxes of more than a factor of 7 higher than the persistent flux observed during the BeppoSAX observation showing X-ray bursts.
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