Deep Thermal Infrared Imaging of HR 8799 bcde: New Atmospheric Constraints and Limits on a Fifth Planet

We present new $L^\prime$ (3.8 $\mu m$) and Br-$\alpha$ (4.05 $\mu m$) data and reprocessed archival $L^\prime$ data for the young, planet-hosting star HR 8799 obtained with Keck/NIRC2, VLT/NaCo and Subaru/IRCS. We detect all four HR 8799 planets in each dataset at a moderate to high signal-to-noise (SNR $\gtrsim$ 6-15). We fail to identify a fifth planet, "HR 8799 f", at $r$ $<$ 15 $AU$ at a 5-$\sigma$ confidence level: one suggestive, marginally significant residual at 0.2" is most likely a PSF artifact. Assuming companion ages of 30 $Myr$ and the Baraffe (Spiegel \& Burrows) planet cooling models, we rule out an HR 8799 f with mass of 5 $M_{J}$ (7 $M_{J}$), 7 $M_{J}$ (10 $M_{J}$), and 12 $M_{J}$ (13 $M_{J}$) at $r_{proj}$ $\sim$ 12 $AU$, 9 $AU$, and 5 $AU$, respectively. All four HR 8799 planets have red early T dwarf-like $L^\prime$ - [4.05] colors, suggesting that their SEDs peak in between the $L^\prime$ and $M^\prime$ broadband filters. We find no statistically significant difference in HR 8799 cde's colors. Atmosphere models assuming thick, patchy clouds appear to better match HR 8799 bcde's photometry than models assuming a uniform cloud layer. While non-equilibrium carbon chemistry is required to explain HR 8799 bc's photometry/spectra, evidence for it from HR 8799 de's photometry is weaker. Future, deep IR spectroscopy/spectrophotometry with the Gemini Planet Imager, SCExAO/CHARIS, and other facilities may clarify whether the planets are chemically similar or heterogeneous.