Providing stringent star formation rate limits of z$\sim$2 QSO host   galaxies at high angular resolution
  We present integral field spectrograph (IFS) with laser guide star adaptive optics (LGS-AO) observations of z=2 quasi-stellar objects (QSOs) designed to resolve extended nebular line emission from the host galaxy. Our data was obtained with W. M. Keck and Gemini-North Observatories using OSIRIS and NIFS coupled with the LGS-AO systems. We have conducted a pilot survey of five QSOs, three observed with NIFS+AO and two observed with OSIRIS+AO at an average redshift of z=2.15. We demonstrate that the combination of AO and IFS provides the necessary spatial and spectral resolutions required to separate QSO emission from its host. We present our technique for generating a PSF from the broad-line region of the QSO and performing PSF subtraction of the QSO emission to detect the host galaxy. We detect H$\alpha$ and [NII] for two sources, SDSS J1029+6510 and SDSS J0925+06 that have both star formation and extended narrow-line emission. Assuming that the majority of narrow-line H$\alpha$ is from star formation, we infer a star formation rate for SDSS J1029+6510 of 78.4 M$_\odot$yr$^{-1}$ originating from a compact region that is kinematically offset by 290 - 350 km/s. For SDSS J0925+06 we infer a star formation rate of 29 M$_\odot$yr$^{-1}$ distributed over three clumps that are spatially offset by $\sim$ 7 kpc. The null detections on three of the QSOs are used to infer surface brightness limits and we find that at 1.4 kpc distance from the QSO that the un-reddened star formation limit is $<$ 0.3 M$_\odot$yr$^{-1}$kpc$^{-2}$. If we assume a typical extinction values for z=2 type-1 QSOs, the dereddened star formation rate for our null detections would be $<$ 0.6 M$_\odot$yr$^{-1}$kpc$^{-2}$. These IFS observations indicate that if star formation is present in the host it would have to occur diffusely with significant extinction and not in compact, clumpy regions. 
Andrey Vayner, Shelley A. Wright, Tuan Do, James E. Larkin, Lee Armus,   Sarah C. Gallagher
astro-ph.GA