We study the Spectral Energy Distribution (SED) and the power spectrum of Galactic cirrus emission observed in the 14 deg^2 Science Demonstration Phase field of the Herschel-ATLAS using Herschel and IRAS data from 100 to 500 um. We compare the SPIRE 250, 350 and 500um maps with IRAS 100um emission, binned in 6 pixels. We assume a modified black-body SED with dust emissivity parameter beta (F ~ lambda^(-beta)) and a single dust temperature T_d, and find that the dust temperature and emissivity index varies over the science demonstration field as 10< T_rm < 25 K and 1 < beta< 4. The latter values are somewhat higher than the range of beta often quoted in the literature (1< beta< 2). We estimate the mean values of these parameters to be T_d=19.0 +/- 2.4 K and beta = 1.4 +/- 0.4. In regions of bright cirrus emission, we find that the dust has similar temperatures with T_d = 18.0 +/- 2.5 K, and similar values of beta, ranging from 1.4 +- 0.5 to 1.9+/- 0.5. We show that T_d and beta associated with diffuse cirrus emission are anti-correlated and can be described by the relationship: beta(T_d) = NT_d^alpha with [N=116+/-38, alpha=-1.4+/1 0.1]. The strong correlation found in this analysis is not just limited to high density clumps of cirrus emission as seen in previous studies, but is also seen in diffuse cirrus in low density regions. To provide an independent measure of $T_{rm d}$ and $beta$, we obtain the angular power spectrum of the cirrus emission in the {it IRAS} and SPIRE maps, which is consistent with a power spectrum of the form P(k)=P_0(k/k_0)^gamma where gamma = ^a H R2.6+/-m 0.2 for scales of 50-200 in the SPIRE maps. The cirrus rms fluctuation amplitude at angular scales of 100 is consistent with a modified blackbody SED with T_d = 20.1+/- 0.9 K and beta = 1.3+/- 0.2, in agreement with the values obtained above.
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