  The classical radiation pressure instability has been a persistent
theoretical feature of thin, radiatively efficient accretion disks with
accretion rates 1 to 100 per cent of the Eddington rate. But there is only
limited evidence of its occurrence in nature: rapid heartbeat oscillations of a
few X-ray binaries and now, perhaps, the new class of hourly X-ray transients
called quasi-periodic eruptions (QPEs). The accretion disks formed in tidal
disruption events (TDEs) have been observed to peacefully trespass through the
range of unstable accretion rates without exhibiting any clear sign of the
instability. We try to explain the occurrence or otherwise of this instability
in these systems, by constructing steady state 1D models of thin magnetic
accretion disks. The local magnetic pressure in the disk is assumed to be
dominated by toroidal fields arising from a dynamo sourced by
magneto-rotational instability (MRI). We choose a physically motivated
criterion of MRI saturation, validated by recent magnetohydrodynamic
simulations, to determine the strength of magnetic pressure in the disk. The
resulting magnetic pressure support efficiently shrinks: (1) the parameter
space of unstable mass accretion rates, explaining the absence of instability
in systems such as TDEs and (2) the range of unstable radii in the inner
accretion disk, which can shorten the quasi-periods of instability limit-cycles
by more than three orders of magnitude, explaining the observed periods ( a few
hrs) of QPEs. In addition to examining stability properties of strongly
magnetized disks, we predict other observational signatures such as spectral
hardening factors and jet luminosities to test the compatibility of our disk
models with observations of apparently stable TDE disks.
