What does "hard tail" mean in the context of astronomical spectra? I am currently reading about neutron stars and came across this sentence:
"Often the radius is underestimated because only a hot spot emits or the spectrum contains a hard tail."
I can find a lot of other articles commenting on hard tails in spectra, but no explanation what it actually means.
Any help would be appreciated!
 A: Choose cutoff vertical line in such chart :

so that curve areas from cutoff line to the left side and to the right side would be equal. Then curve part to the right would be "long tail" or "hard tail". In the context of neutron star jet EM emission spectral distribution, left part of distribution can be modelled by black body or some other law and right part (or hard-tail) of spectrum where high-energies dominates can be modelled by some power law. I.E. "hard tail" concept arises due to the need of different distribution laws applied to different parts of curve.
A: Found this

"It is generally accepted that the X-ray spectral continuum of BHXB [black hole X-ray binaries] and NSXB [neutron star X-ray binaries] results from the sum of two main components: one thermal component which follows a blackbody distribution and another non-thermal component that is best described as a power law. The thermal component dominates at lower energies, hence it is referred to as the soft component, while the power-law component extends up to a few hundred keV and it is often known as the “hard tail” (Barret 2004; McClintock & Remillard 2006; Lin et al. 2007; Done et al. 2007; Church et al. 2012)."
[bracketed remarks by me], emphasis by me

in
P. Reig & N. Kylafis, 2016, The origin of the hard X-ray tail in neutron-star X-ray binaries, A&A, 591, A24
(Open Access - full HTML)
Looks like the naming is based on the soft X-ray vs hard X-ray distinction.

Note for clarity:
The "tail" is a feature of the spectrum (essentially, a feature of the graph of a statistical  distribution), not a physical structure (although it is, of course, generated by the physics of the phenomena under observation).

(Simulated spectra from the same paper - Fig. 1 (modified))
A: Roughly speaking, you can estimate the apparent radius of a neutron star by assuming the emission is a blackbody (or thermal emission from the surface at least). Thus application of Stefan's law
$$ R \simeq  \left(\frac{L}{4\pi \sigma T^4}\right)^{1/2}\, ,$$
where the temperature $T$ would also come from modelling the spectrum.
However, if there is non-thermal emission, associated for example with accelerated charged particles in the magnetosphere, then this can result in a overestimation of the thermal luminosity, but also an overestimation of the thermal temperature because the non-thermal emission would usually make a disproportionately large contribution at higher energies. This is the "hard tail" - the nomenclature referring to hard X-rays at higher energies than soft X-rays that might be more characteristic of the the thermal emission. An overestimated temperature leads to an underestimated radius.
Here is an example - the spectrum above 5 keV energies is dominated by a hard, non-thermal component, whilst a thermal component dominates at low energies. Of course if you have good enough spectral data across a broad enough energy range, you can in principle separate these things out as has been attempted in this plot.

