Spectral energy distribution and generalized Wien's law for photons and cosmic string loops

Physical objects with energy $u_w(l) \sim l^{-3w}$ with $l$ characteristic length and $w$ a dimensionless constant, lead to an equation of state $p=w\rho$, with $p$ the pressure and $\rho$ the energy density. Special entities with thisbproperty are, for instance, photons ($u = hc/l$, with $l$ the wavelength) with $w = 1/3$, and some models of cosmic string loops ($u =(c^4/aG)l$, with $l$ the length of the loop and $a$ a numerical constant), with $w = -1/3$. Here, we discuss some features of the spectral energy distribution of these systems and the corresponding generalization of Wien's law, which in terms of $l$ has the form $Tl_{mp}^{3w}=constant$, being $l_{mp}$ the most probable size of the mentioned entities.