Lyman alpha Luminosity Functions at Redshift z = 4.5

We present a spectroscopically confirmed sample of Lyman alpha emitting galaxies (LAEs) at z ~ 4.5 in the Extended Chandra Deep Field South (ECDFS), which we combine with a sample of z ~ 4.5 LAEs from the Large Area Lyman Alpha (LALA) survey to build a unified Lya luminosity function (LF). We spectroscopically observed 64 candidate LAEs in the ECDFS, confirming 46 objects as z~4.5 LAEs. We did not detect significant flux from neither C_iv 1549\AA\ nor the He_ii 1640\AA\ emission in individual LAE spectra, even with a coadded spectrum. With the coadded line ratio of He_ii to Lya constraining the Population III star formation rate (SFR) to be <0.3% of the total SFR, and <1.25% of the observed SFR (both at the 2-$\sigma$ level). Only one LAE was detected in both the X-ray and radio, while the other objects remained undetected, even when stacked. The Lya LF in our two deepest narrowband filters in the ECDFS differ at >2$\sigma$ significance, and the product $L^*\Phi^*$ differs by a factor of >3. Similar LF differences have been used to infer evolution in the neutral gas fraction in the intergalactic medium at z>6, yet here the difference is likely due to cosmic variance, given that the two samples are from adjoining line-of-sight volumes. Combining our new sample of LAEs with those from previous LALA narrowband surveys at z = 4.5, we obtain one of the best measured Lya LFs to date of L* = 42.83 $\pm$ 0.06 and $\Phi^*$ = -3.48 $\pm$ 0.09. We compare our new LF to others from the literature to study the evolution of the Lya luminosity density at 0 < z < 7. We find tentative evidence for evolution in the product $L^* \Phi^*$, which approximately tracks the cosmic SFR density, but since field-to-field and survey-to-survey variations are in some cases as large as the possible evolution, some caution is needed in interpreting this trend.