Keck/MOSFIRE Spectroscopy of z=7-8 Galaxies: Lyα\alpha Emission from a Galaxy at z=7.66

We report the results from some of the deepest Keck/Multi-Object Spectrometer For Infra-Red Exploration data yet obtained for candidate $z \gtrsim 7$ galaxies. Our data show one significant line detection with 6.5$\sigma$ significance in our combined 10 hr of integration which is independently detected on more than one night, thus ruling out the possibility that the detection is spurious. The asymmetric line profile and non-detection in the optical bands strongly imply that the detected line is Ly$\alpha$ emission from a galaxy at $z$(Ly$\alpha)=7.6637 \pm 0.0011$, making it the fourth spectroscopically confirmed galaxy via Ly$\alpha$ at $z>7.5$. This galaxy is bright in the rest-frame ultraviolet (UV; $M_{\rm UV} \sim -21.2$) with a moderately blue UV slope ($\beta=-2.2^{+0.3}_{-0.2}$), and exhibits a rest-frame Ly$\alpha$ equivalent width of EW(Ly$\alpha$) $\sim 15.6^{+5.9}_{-3.6}$ \AA. The non-detection of the 11 other $z \sim$ 7-8 galaxies in our long 10 hr integration, reaching a median 5$\sigma$ sensitivity of 28 \AA\ in the rest-frame EW(Ly$\alpha$), implies a 1.3$\sigma$ deviation from the null hypothesis of a non-evolving distribution in the rest-frame EW(Ly$\alpha$) between $3<z<6$ and $z=$ 7-8. Our results are consistent with previous studies finding a decline in Ly$\alpha$ emission at $z>6.5$, which may signal the evolving neutral fraction in the intergalactic medium at the end of the reionization epoch, although our weak evidence suggests the need for a larger statistical sample to allow for a more robust conclusion.Comment: 10 pages, 4 figures, ApJ, in pres

On the determination of constitutive parametersin a hyperelastic model for a soft tissue

The aim of this paper is to study a model of hyperelastic materials and itsapplications into soft tissue mechanics. In particular, we first determine an unbounded domain of the constitutive parameters of the model making our smoothstrain energy function to be polyconvex and hence satisfying the Legendre–Hadamard condition. Thus, physically reasonable material behaviour are described by our model with these parameters and a plently of tissues can betreated. Furthermore, we localize bounded subsets of constitutive parameters in fixed physical and very general bounds and then introduce a family of descrete stress–strain curves. Whence, various classes of tissues are characterized. Ourgeneral approach is based on a detailed analytical study of the first Piola–Kirchhoff stress tensor through its dependence on the invariants and on the constitutive parameters. The uniqueness of parameters for one tissue is discussed by introducing the notion of manifold of constitutive parameters, whichis locally represented by possibly different physical quantities. The advantage of our study is that we show a possible way to improve of the usual approachesshown in the literature which are mainly based on the minimization of a costfunction as the difference between experimental and model results