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Information about stellar magnetic field topologies is obtained primarilyfrom high-resolution circular polarisation (Stokes $V$) observations. Due totheir generally complex morphologies, the stellar Stokes $V$ profiles areusually interpreted with elaborate inversion techniques such as Zeeman Dopplerimaging (ZDI). Here we further develop a new method of interpretation ofcircular polarisation signatures in spectral lines using cumulative Stokes $V$profiles (anti-derivative of Stokes $V$). This method is complimentary to ZDIand can be applied for validation of the inversion results or when theavailable observational data are insufficient for an inversion. Based on therigorous treatment of polarised line formation in the weak-field regime, weshow that, for rapidly rotating stars, the cumulative Stokes $V$ profilescontain information about the spatially resolved longitudinal magnetic fielddensity. Rotational modulation of these profiles can be employed for a simple,qualitative characterisation of the stellar magnetic field topologies. We applythis diagnostic method to the archival observations of the weak-line T Tauristar V410 Tau and Bp He-strong star HD 37776. We show that the magnetic fieldin V410 Tau is dominated by an azimuthal component, in agreement with the ZDImap that we recover from the same data set. For HD 37776 the cumulative Stokes$V$ profile variation indicates the presence of multiple regions of positiveand negative field polarity. This behaviour agrees with the ZDI results butcontradicts the popular hypothesis that the magnetic field of this star isdominated by an axisymmetric quadrupolar component.

Diagnostic of stellar magnetic fields with cumulative circular polarisation profiles