Context : One of the most enigmatic phenomena related to solar activity is the so-called Maunder minimum phase .
It consists of the lowest sunspot ’ s counting ever registered for the Sun , and never so far confirmed for other stars .
Since the spectroscopic observations of stellar activity at the Mount Wilson Observatory , the solar analog HD43587 has shown a very low and apparently invariant activity level , which makes it a Maunder minimum candidate .

Aims : We analyze the chromospheric activity evolution of HD43587 and its evolutive status , intending to unravel the reasons for this low and flat activity .

Methods : We use an activity measurements dataset available in the literature , and compute the activity S-index from HARPS and NARVAL spectra , to infer a cycle period .
Besides , we analyze the CoRoT light-curve of HD43587 , and apply gyrochronology and activity calibrations , to determine its rotation period .
Finally , based on an evolutionary model and the inferred rotation period , we use the EULAG-MHD code to perform global MHD simulations of HD43587 with the aim of getting some insights about its dynamo process .

Results : We confirm the almost flat activity profile , with a cycle period P _ { \mathrm { cyc } } = 10.44 \pm 3.03 yrs deduced from the S-index time series , and a long-term trend that might be a period larger than 50 yrs .
It was impossible to define a rotation period from the light-curve , however gyrochronology and activity calibrations allow to infer an indirect estimate of \overline { P } _ { \mathrm { rot } } = 22.6 \pm 1.9 d. Furthermore , the MHD simulations confirm an oscillatory dynamo with a cycle period in good agreement with the observations and a low level of surface magnetic activity .

Conclusions : We conclude that this object might be experiencing a ” natural ” decrease in magnetic activity as a consequence of its age .
Nevertheless , the possibility that HD43587 is in a Maunder minimum phase can not be ruled out .