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Magnetic fields in red giant stars remain a poorly understood topic,particularly in what concerns their intensity in regions far below the surface.In this work, we propose that gravity-dominated mixed modes of high absoluteradial order and low angular degree can be used to probe the magnetic field intheir radiative cores. Using two poloidal, axisymmetric configurations for thefield in the core and the classical perturbative approach, we derive ananalytical expression for the magnetic frequency splitting of these oscillationmodes. Considering three distinct red giant models, with masses of1.3$M_\odot$, 1.6$M_\odot$ and 2.0$M_\odot$, we find that a fieldstrength of $10^5$ G is necessary in the core of these stars to induce afrequency splitting of the order of a $\mu$Hz in dipole and quadrupoleoscillation modes. Moreover, taking into account observational limits, weestimate that magnetic fields in the cores of red giants that do not presentobservable magnetic splittings cannot exceed $10^4$ G. Given the generalabsence of observable splittings in the oscillation spectra of these stars, andassuming that present mode suppression mechanisms are not biased towardscertain azimuthal orders and retain all peaks in each multiplet, our resultslead us to conclude that internal fields with the considered configurations andstrengths above $10^4$ G are not prevalent in red giants.

Core magnetic field imprint in the non-radial oscillations of red giant stars