  The FIR distribution at high Galactic latitudes, observed with Planck, is
filamentary with coherent structures in polarization. These structures are also
closely related to HI filaments with coherent velocity structures. There is a
long-standing debate about the physical nature of these structures. They are
considered either as velocity caustics, fluctuations engraved by the turbulent
velocity field or as cold three-dimensional density structures in the
interstellar medium (ISM). We discuss different approaches to data analysis and
interpretation in order to work out the differences. We considered mathematical
preliminaries for the derivation of caustics that characterize filamentary
structures in the ISM. Using the Hessian operator, we traced individual FIR
filamentary structures in HI from channel maps as observed and alternatively
from data that are provided by the velocity decomposition algorithm (VDA). VDA
is claimed to separate velocity caustics from density effects. Based on the
strict mathematical definition, the so-called velocity caustics are not
actually caustics. These VDA data products may contain caustics in the same way
as the original HI observations. Caustics derived by a Hessian analysis of both
databases are nearly identical with a correlation coefficient of 98%. However,
the VDA algorithm leads to a 30% increase in the alignment uncertainties when
fitting FIR/HI orientation angles. We used HI absorption data to constrain the
physical nature of FIR/HI filaments and determine spin temperatures and volume
densities of FIR/HI filaments. HI filaments exist as CNM structures; outside
the filaments no CNM absorption is detectable. The CNM in the diffuse ISM is
exclusively located in filaments with FIR counterparts. These filaments at high
Galactic latitudes exist as cold density structures; velocity crowding effects
are negligible.
