PROVIDING STRINGENT STAR FORMATION RATE LIMITS OF z ∼ 2 QSO HOST GALAXIES AT HIGH ANGULAR RESOLUTION

We selected these QSOs from the fifth edition of the SDSS quasar catalog based on the seventh data release (Schneider et al. 2010). For this pilot survey we selected sources that would have optimal AO performance to aid in the PSF subtraction. Criteria for the Keck and Gemini North observations were: (1) all objects must be observable with the ALTAIR and Keck AO systems based on tip/tilt magnitude and separations (R mag <16.5 within 25'' for ALTAIR system and R mag <18.5 within 45'' for Keck-AO), and (2) objects must have redshift between 2.016 and 2.427 where Hα falls in the prime K-band wavelength regime (<2.2 μm). Using these constraints at the K-band allowed only ∼30 observable QSOs. We made our final selection based on available tip/tilt stars that are bright and close in separation: one with on-axis tip-tilt source correction (R = 16.4 mag), and four for off-axis tip-tilt correction. Table 1 contains all the information on the tip/tilt stars. All of our selected sources are Type 1 radio-quiet QSOs with 1.4 GHz flux <0.15 mJy (Becker et al. 1995) with no availible near-IR spectroscopy, making our sample less biased towards QSO hosts with high SFRs. Host galaxies with high SFRs presented in Alexander et al. (2010), Cano-Díaz et al. (2012) were pre-selected based on long slit spectra of the [O iii]5007 Å line or far-IR observations.

For multi-wavelength analysis of our objects we include archival observations on our sources. Table 2 contains optical to near-infrared archival photometric information on our QSO sample, encompassing archival data from the SDSS for the optical magnitudes and 2MASS for near-infrared. As of Data Release 10, SDSS has incorporated WISE and 2MASS photometric data into their catalog, made available in web format on the object explorer website that can be accessed through sdss3.org. In Table 3 we present photometry for the four WISE bands at 3.4, 4.6, 12, and 22 μm. All five sources are detected in the 3.4–12 μm bands however only three sources have reliable photometry, where the other two suffer from confusion of flux from the bright nearby tip/tilt stars. Three sources are detected in the 22 μm band, one is undetected and one does not have reliable photometry due to confusion; please see Table 3 for details on the individual sources. Two of our sources, SDSS J1029+651 and SDSS J2123-005 were observed with the Herschel Space Telescope's SPIRE instrument⁸ in the 250, 350, and 500 μm bands. We downloaded the fully reduced level 2 maps from the Herschel data archive (http://irsa.ipac.caltech.edu/applications/Herschel/), we converted the maps from Jy beam⁻¹ to Jy pixel⁻¹ by dividing the maps by the beam size found in the SPIRE Handbook, available at herschel.esac.esa.int and applied standard aperture photometry over the beam size (176, 239, 352) of the telescope in each of the bands at the optical location of the QSOs from Table 1. The two sources are undetected in all of the bands and we provide the 3σ limits in Table 3.

The OSIRIS observations were reduced using the publicly available OSIRIS data reduction pipeline.⁹ Dark frames were median-combined to produce a master dark frame using the OSIRIS pipeline routine "combine frames." Each science and calibration frame then had the master dark subtracted from it and the following pipeline routines were performed: "adjust channel levels," "remove crosstalk," "clean cosmic rays," "extract spectra," "assemble data cube," "correct dispersion." For sky subtraction, each science frame had the nearest in time sky frame subtracted using the "scaled sky subtraction" routine that accounts for the temporal variability of the OH sky lines (Davies 2007). The science and telluric frames were stacked together using a 3σ mean clip algorithm in the "mosaic frames" routine to remove large bad pixels that occur from the "extract spectra" routine. A 1D telluric spectrum was then extracted from the highest signal-to-noise spaxels in the telluric cube using the "extract star" routine. Strong hydrogen absorption lines were masked using the "remove hydrogen lines" routine, and the blackbody of the star was subtracted using the "divide blackbody" routine. The spectra were normalized and used to correct for atmospheric absorption and the instrumental footprint in the mosaiced science frame. The final science data was flux calibrated using standard star observations that were taken closest in time, at similar air mass and were reduced in the same manner as described above.

The NIFS observations were reduced using the Gemini NIFS IRAF reduction pipeline that operates within Pyraf.¹⁰ Some modifications were applied to the standard pipeline and additional routines were written to match our science goals. For each night we reduced the Xe, Ar lamp observations to establish the wavelength solution for each of the targets using the Gemini NIFS Pyraf baseline calibration routine. Dark frames for the science observations were median-combined and subtracted from each of the science and sky frames. The science, telluric, and sky frames were then reduced using the NIFS science reduction routine. The end result is a data cube which has been flat fielded, bad pixel masked, and reformatted into a 3D cube, which was spatially re-sampled from the native spatial sampling of 0.1 × 004 to square pixels with a size of 005. The science and telluric frames had the nearest sky frame in time subtracted, with OH emission line scaling between the sky and science frames. The centroids of the QSO and telluric stars were obtained through a 2D Gaussian fit to a spectrally collapsed image, and the dithered observations were shifted and stacked using a 3σ mean clipped algorithm. The 1D telluric star spectrum was extracted by averaging spatially over the highest signal-to-noise spaxels, its blackbody was subtracted, and the strong hydrogen absorption lines were masked. The 1D telluric spectrum was then divided into the science cube to correct for atmospheric and instrumental absorption features.

The broad Hα emission originates from gas located in a compact disk within the central few parsecs, making this emission essentially point-like in our observations. We use spectral channels that confine the broad line emission for PSF construction. Our algorithm finds the highest signal-to-noise spectral channels that do not coincide with OH emission lines to be combined to create a master PSF image. Generally the selected PSF regions are 2.5–3 nm (10–15 spectral channels) in size and tend to sit near the peak of the broad Hα line. We hypothesized that the majority of the extended narrow line emission will be within 400 km s⁻¹ from the QSO's redshift, where the PSF has the highest signal to noise and the greatest potential for contamination from the NLR, so we also select spectral regions that are offset from the peak of the broad emission line (not including OH sky lines), that should have minimal contribution from extended narrow-line emission. We combine all spectral regions using a 3σ clipping routine, to mitigate contamination from the extended narrow-line emission. This way spaxels that do contain narrow emission would be weighted less since spectral channels offsets by 2000–3000 km s⁻¹ are less likely to contain NLR. The end result is a 2D image of our observed PSF that gets normalized to the flux at the peak pixel. We then go through individual channels in our data cube, scale the image to the maximum value of the PSF at the particular channel and subtract the image. This routine provided the best residuals post PSF subtraction. Some studies have additional steps with PSF construction, by initially fitting and subtracting the nuclear continuum with a low order polynomial (Inskip et al. 2011). The purpose of the linear fit is to remove any continuum emission from the host galaxy. In our work, extensive studies of the final PSF subtracted cube using both methods do not reveal a continuum emission from the host galaxy at the 3σ level (average K mag >20.9), hence we decided not to include this additional step in our QSO PSF construction routine since it adds at least 1.2 times more noise in the PSF subtracted cubes.

To test the quality of our PSF subtraction, we constructed radial profiles at different wavelength channels, before and after PSF subtraction, to verify whether the final cube had the central core and seeing halo successfully removed. Figure 2 shows the results of these tests for two of our targets. The green and blue radial profile curves are constructed from a spectrally-summed image that contains both broad and narrow Hα emission (Δλ = 2.5 nm or Δv = 1142 km s⁻¹). The green curve is constructed from the data cube before PSF subtraction, the blue curve is after the PSF is removed, and the red curve is constructed from just the PSF image ($\sim {\rm{\Delta }}\lambda =2.5\;{\rm{nm}}$, spectrally offset 1–5 nm). The points are constructed by taking an average in an annulus with Δr = 01 at a range of separations from the centroid of the QSO. The radial profiles in the post PSF subtracted data cube (blue curves) have little slope and significantly less flux, and do not strongly correlate with the general shape of the green and red curves. This demonstrates that the PSF subtracted data has a significant portion of the QSO flux removed, with only the inner 02 being strongly dominated by noise from PSF subtraction. Averaging over the data cube along the spectral axis, we find that generally within 02 the QSO still contributes to about 10%–20% of the total data counts, while only 2%–5% outside 02. As expected, observations with the smallest PSF FWHM showed the best post PSF subtraction data cubes producing the best contrast. However, it should be noted that leftover QSO continuum/BLR light does not affect measured values derived from narrow line emission, since they are derived by fitting the line and any underline continuum left over from PSF subtraction simultaneously, at which stage the continuum contamination can be calculated.

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Figure 3 (panel I) shows the K-band image of the SDSS J1029+6510 QSO from the collapsed data cube (1.99–2.4 μm). Figure 3 (panel II) and Figure 3 (panel III) show the 2D kinematics of the extended narrow line emission relative to the broad Hα emission and the spectra of the individual components.

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The PSF subtracted data cube reveals three extended narrow line emission regions, labeled A, B, and C in Figure 3 (panel II). These emission-line regions have a blueshifted velocity offset of 10–500 km s⁻¹ with respect to broad Hα emission, and a maximum projected separation of ∼06 (4.2 kpc) from the QSO. We bin the individual spaxels in regions A and C to detect a hint of Hα emission at a signal-to-noise of 3.1 and 2.1, respectively. Individual spaxels in region B reach a signal-to-noise of ≳2, with the central 3 pixels reaching a signal to noise ≳7. In Table 6 we present the extracted emission-line properties of the individual regions. Using [N ii] and Hα we adopt the the line ratio separation between star formation and AGN to be at log([N ii]/Hα) = −0.5 in the H ii diagnostic or "BPT" (Baldwin et al. 1981) diagram (Figure 7). The majority of the objects in the region log([N ii]/Hα) < −0.5 are star-forming galaxies (Kewley et al. 2001; Kauffmann et al. 2003; Groves et al. 2006). While low metallicity regions ionized by an AGN can be a contaminant at these line ratios, all of the QSOs in our sample (particularly SDSS J1029+6510) show strong UV emission lines in C iv, S iv+O iv and Mg ii (Figure 1) that are typical of solar to super-solar metallicity QSOs; hence for this particular system we are not concerned about low metallicity contamination in the region log([N ii]/Hα) < −0.5. Our limits allow us to discard shock contributions to the emission for regions A and B; line ratios of emission due to shocks tend to reside in log([N ii]/Hα) > −0.4 on the BPT diagram (Allen et al. 2008) from a gas that is moving at the recorded velocities of our extended emission. Based on the ratio of log([N ii]/Hα) for A, this region can reside in the transition zone between AGN/SF; assuming no extinction, the SFR limit for Hα flux in region A is 11.0 ± 2.3 M_⊙ yr⁻¹ using the Schmidt–Kennicutt law (${\mathrm{SFR}}_{{\rm{H}}\alpha }=\tfrac{{L}_{{\rm{H}}\alpha }}{1.26\times {10}^{41}}$, Kennicutt 1998), this is a limit because AGN photo ionization contribution will increase the observed flux, hence the SFR is lower than what is quoted. Region B is located well in the star formation position on the BPT (log([N ii]/Hα) < −1.5) diagram with a SFR limit of 67.4 ± 5.7 M_⊙ yr⁻¹. Region C resides well inside the AGN component of the diagram, and therefore is likely narrow line emission from the QSO, at a projected radial distance of ∼2.8 kpc.

Figure 4 (panel I) is a K-band image of the QSO constructed by summing the flux across the entire data cube (1.99–2.4 μm). Figure 4 (panels II and III) shows the 2D kinematics of the extended narrow line emission relative to the redshift of the broad Hα emission and the spectra of the individual components, respectively. The post-PSF subtracted data cube reveals resolved narrow Hα emission originating from three distinct regions (A, B, and C), that are both spatially offset (05–1'') and redshifted (80–250 km s⁻¹) from the QSO; see Table 7 for extracted parameters on individual regions. We bin by 025 × 025 for each of these regions to increase the signal-to-noise for kinematic analysis. Using the ([N ii] and Hα) ratio diagnostic, we put the separation between star formation and AGN at log([N ii]/Hα) = −0.5, with star formation being the dominant photoionization mechanism in log([N ii]/Hα) < −0.5 (see, Section 5.1 for further discussion). Limits on the log([N ii]/Hα) ratio places regions A, B, and C inside the star formation region on the BPT diagram. Our limits allow us to discard shock contributions to the emission for regions A, B, and C; line ratios of emission due to shocks tend to reside in log([N ii]/Hα) > −0.4 on the BPT diagram (Allen et al. 2008) from a gas that is moving at the recorded velocities of our extended emission. Using the Schmidt–Kennicutt law (Kennicutt 1998) we obtain un-reddened upper limit SFRs of 13 ± 2.3, 12.0 ± 0.5, 4.0 ± 0.4 M_⊙ yr⁻¹ for regions A, B, and C, respectively. Assuming these three clumps have virialized we obtain dynamical masses of 8.7, 1.0, 0.3 × 10⁹ M_⊙. (Table 7 using the standard virial mass equation ${M}_{\mathrm{virial}}\approx \tfrac{5R{\sigma }_{r}^{2}}{G}$.)

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The remaining three targets reveal no narrow-line Hα emission offset spatially or spectrally from the QSO. Null detections may be due to two possibilities: (1) these sources have heavy extinction azimuthally around the QSO ≳1 kpc; and/or (2) these sources have sufficiently low SFRs that reside below the sensitivity limit of these observations.

We perform a Monte-Carlo simulation in which we generate star-forming regions with narrow-line Hα emission surrounding the QSO at various spatial separations. The purpose of this simulation is to find the limiting flux (and unreddened SFR limits) of our observations and determine how our PSF removal techniques affect our sensitivity versus distance from these QSOs. For our simulations, individual star-forming regions occupy 02 × 02 in the OSIRIS data cube and 025 × 025 in the NIFS data cube, with each spaxel containing a spectrum consisting of an emission line resembling narrow Hα with a fixed full width at half maximum of 80 km s⁻¹ (not convolved with an instrumental profile). We select a FWHM of 80 km s⁻¹ to match the widths of some of our detected extended narrow line emission, to further test their validity. In a given data cube the star-forming regions have a spatially uniform flux, the integrated flux over all the simulated regions vary between cubes. We insert these regions uniformly surrounding the QSO in a cross shape to resemble resolved extended structure, which ranges from 01 to 15 in separation from the QSO in the NIFS data cubes and 01–07 in the OSIRIS cubes. The star-forming regions are always centered on the quasar whose position we obtain by fitting a 2D Gaussian to an image of a collapsed data cube along the spectral axis. The spacing between the star-forming regions is 01 to allow signal-to-noise estimates surrounding each individual region. We vary the SFRs from 0.5 to 40 M_⊙ yr⁻¹ in each of the narrow-line emission regions. For the OSIRIS data, we insert the simulated star-forming regions into a data cube that is created by running the extract spectra routine that simply transforms the two dimensional data into a 3D cube. For the Gemini data we run the standard iraf reduction pipeline that extracts the 2D spectra and constructs the 3D data cubes, into which we insert the star-forming regions. We then process the data cubes through the rest of the reduction pipeline as described in Section 3. Finally we run our PSF subtraction routine on the reduced data cubes as described in Section 4. We attempt to recover each of the narrow-line Hα emission regions that were artificially inserted. Just as for the real data, emission must be detected with a minimum of 3σ confidence, and emission lines must have a FWMH greater than the instrumental width.

Recovered star-forming regions with minimum SFRs at various angular separations are presented in Figures 5 and 6, and fluxes of Hα from SDSS J0925+0655 and SDSS J1029+6510 regions A, B, and C are overplotted for comparison. In general we find that our data reduction procedure is not the main factor for missing narrow Hα flux; the dominant effect is the sensitivity of the detector and PSF removal within 02 from the QSO. At separations >02, limiting SFRs are an average of 1.4 M_⊙ yr⁻¹ (0.7 × 10⁻¹⁷ erg s⁻¹ cm⁻²) integrated over a star-forming region for the NIFS instrument and 1.5 M_⊙ yr⁻¹ for OSIRIS. This translates to 0.32 and 0.53 M_⊙ yr⁻¹ kpc⁻² in the NIFS and OSIRIS data cubes respectively.

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For SDSS J1029+6510, we show the integrated flux of region B as well as its individual components in Figure 5, and find they are detected without binning. These simulations and the limiting fluxes for both of these sources indicate low Hα flux at near and far angular separations from the QSO. For SDSS J0925+0655, fluxes of the observed components sit well above the star formation distribution (Figure 6), and in principle we are able to detect fainter emission at smaller separations. The other three QSOs do not show any signs of Hα narrow-line emission.

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We use the bolometric luminosities of our sources to make estimates of dust extinction. The Bolometric luminosities of our sample all sit near 1 × 10⁴⁷ erg s⁻¹ cm⁻²; the maximum value for a z ∼ 2 QSO is around 1 × 10⁴⁸ erg s⁻¹ cm⁻² as has been found by studies such as Croom et al. (2009). This limit only allows us to correct for 2.5 magnitudes of extinction at 1450 Å, so the limiting SFRs get as large as 2.03 M_⊙ yr⁻¹ (0.5 M_⊙ yr⁻¹ kpc⁻²) or 2.2 M_⊙ yr⁻¹ (0.8 M_⊙ yr⁻¹ kpc⁻², using a Small Magellanic Cloud (SMC) extinction curve from Gordon et al. 2003) for NIFS and OSIRIS respectively (see Sections 6.1 and 6.2). Note that for SDSS J0925+0655 the limits may be higher, as the QSO is intrinsically redder than the rest of our sample (see Section 6.2). We acknowledge that the dust in these scenarios is uniformly distributed, hence the same dust properties that we find along the line of sight to the QSO are elsewhere in the galaxy. Most studies that quote SFRs give them integrated over some angular scale, typically the beam size of their instrument if the sources they are referencing are not resolved. At the angular resolution of our observations we are capable of resolving a typical z ∼ 2 galaxy with an angular scale of ∼1''. Integrating these limits over a 1'' box we obtain for NIFS: 22 M_⊙ yr⁻¹ (33 M_⊙ yr⁻¹ with maximum dust extinction), OSIRIS: 37 M_⊙ yr⁻¹ (54 M_⊙ yr⁻¹ with maximum dust extinction). These limits are a sum of the lowest flux that we detected around the QSOs in a 1''² box in our simulations with the addition of possible dust obscuration. We believe these are hard limits on the upper value of the SFR in these host galaxies. Derived SFR limits include contamination from dust in the AGN. There is a possibly that most of the dust is surrounding the nuclear region rather than distributed in the host galaxy. Archival WISE photometry of our sources (Table 3) shows that three of our sources are detected at 22 μm (rest frame ∼7 μm), all of the sources are detected in the other three WISE bands that range from 1 to 3.75 μm at an average redshift of z = 2.2; however, only three sources have reliable photometry due to confusion of flux from the nearby bright tip/tilt stars. For the sources that were detected at an observed wavelength of 22 μm we find that the average flux density is 16.8 mJy, indicating that the dust is AGN heated (Rowan-Robinson 1995). Limits closer to the value with minimum dust (22 M_⊙ yr⁻¹ for NIFS and 37 M_⊙ yr⁻¹ for OSIRIS) may be more realistic, as some previous studies of dust in type-1 luminous QSOs near z ∼ 2 have found a number of sources with very little (A_V < 0.01) to no extinction (see, Fynbo et al. 2013).

Examining QSO spectra extracted over the PSF halo (Figure 1, right side) we do not detect any unresolved narrow line region emission in any of our sources. We find that generally the spectra are well fitted with a single Gaussian profile and the inclusion of narrow emission is only required for the case of SDSS J1029+65 due to narrow Hα emission associated with star formation within 02 of the QSO. We place a flux limit of 3–4 × 10⁻¹⁷ erg s⁻¹ cm⁻² which converts to 1–1.5 × 10⁴² erg s⁻¹, assuming the NLR emission line has a FWHM of 80 km s⁻¹.

The host galaxy of this object shows compact vigorous star formation within 2 kpc from the QSO. The rest of the galaxy seems to show no narrow Hα, which we attribute to low SFRs. SDSS J1029+6510 is the second most powerful QSO in our sample with a bolometric luminosity of 1.39 ± 0.06 × 10⁴⁷ erg s⁻¹(Table 1), in addition to the second longest observation time in our sample. Note that some of the emission in individual spaxels of region B are at the 3σ level, near the limit of our observations. The ratio of log([N ii]/Hα)  < −1.5 is located in the H ii star formation portion of the diagram (Figure 7) for region B making it a strong candidate for star formation with a formation rate of 67.4 ± 5.7 M_⊙ yr⁻¹. This indicates rapid star formation within 2 kpc of the QSO.

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For region C, a ratio of 0.57 ± 0.3 for log([N ii]/Hα) puts this source partly in the AGN ionization region of the diagram (Figure 7), and detection of [N ii] emission with higher signal to noise than Hα suggests this emission is due to the AGN. Lastly for region A, the measured ratio of log([N ii]/Hα) = −0.6 places it partially inside the star formation region on the diagram.

This source has a lack of extended star-forming regions, with 90% of the star formation activity within 2 kpc from the QSO. This is in stark contrast to other resolved host galaxies in Inskip et al. (2011), Cano-Díaz et al. (2012), and Alexander et al. (2010), which have extended star-forming regions over several kiloparsecs with SFRs of ∼100 M_⊙ yr⁻¹. Our limiting flux simulations indicate that we should detect SFRs as low as 1.4 M_⊙ yr⁻¹ or down to a flux level of 0.6–0.8 × 10⁻¹⁷ erg s⁻¹ cm⁻², at separations >02 from the QSO. Instead, we detect two "streams" (region B at SNR >3) of narrow Hα and nothing else significant around it (regions A and C are ∼3σ). This indicates that the surrounding (>2 kpc) regions have narrow Hα flux that is below the sensitivity of the instrument.

Dust can cause extinction of Hα flux by re-radiating it at longer wavelength. QSOs in early stages of evolution are thought to be heavily obscured. After the AGN inputs energy/momentum during the "blow out" phase, gas, and dust can get pushed out allowing the AGN and galaxy to be detected in the optical, which otherwise would be obscured. Observations at other wavelengths can provide clues about the level of obscuration. A strong detection in the far-IR can indicate dust heating due to UV radiation from recent birth of massive stars. This would indicate that some portion of the UV radiation is absorbed (suppressed) and re-emitted at longer wavelength. QSOs that show reddening in their rest-frame UV spectra are good candidates for systems with a considerable level of obscuration, including a number of systems with indicators of outflows through blueshifted broad absorption lines in their rest-frame UV spectra, or broad blueshifted components in the 500.7 nm [O iii] emission line, indicating that some of these systems might be in the "blow-out" stage (Farrah et al. 2012; Urrutia et al. 2012).

For the case of SDSS J1029+6510 we are able to put some constraints on the level of obscuration from both far-IR photometry and rest-frame UV-spectrum. This QSO was observed as part of a program with the Herschel space telescope to target some of the brightest optical QSOs with the SPIRE instrument. Examining the archival data we find that at the optical position of the QSO nothing is detected above the 3σ level in the 250, 350, and 500 μm bands. The flux density limits are (∼10 mJy, see Table 3), indicating that this QSO's host galaxy is not in a star-burst phase (L_ir < 10¹³ L_⊙). The rest frame UV spectrum obtained from SDSS shows (Figure 1) a continuum slope typical of a type 1 un-obscured QSO (steep blue continuum), and a bolometric luminosity of 1.39 × 10⁴⁷ erg s⁻¹ (Table 4), which is about an order of magnitude above the average QSO bolometric luminosity. Any correction for dust will start pushing the bolometric luminosity beyond the typical value for bright QSOs at z ∼ 2 (∼10⁴⁸ erg s⁻¹). Assuming we need to correct an order of magnitude of flux at rest frame wavelength of 1450 Å due to dust we would only push the limiting SFR to 0.7 M_⊙ yr⁻¹ kpc⁻² (using a SMC extinction curve from Gordon et al. 2003), not sufficient to explain the lack of Hα flux. We therefore favor the low SFR model as the main explanation for the observed Hα flux in the case of SDSS J1029+6510 at separations greater than 2 kpc.

The extended Hα emission surrounding SDSS J0925+0655 is a strong candidate for active star formation. The ratio of log([N ii]/Hα) for region A is within the star formation region on the diagram (Figure 7) while our limits on regions B and C place them near the ambiguous regions between star formation and AGN. The total flux from all these implies an integrated SFR of 29 ± 2.4 M_⊙ yr⁻¹. The detected narrow Hα emission regions are compact (∼2kpc) and we only detect narrow Hα in these three regions. In other regions of the data cube we are able to reach a sensitivity limit of 0.8 × 10⁻¹⁷ erg s⁻¹ or a SFR of 1.4 M_⊙ yr⁻¹ at separations ≳02 from the QSO. All of the detected regions are at separations ≳05 (4 kpc). This implies that the narrow Hα flux sits below the sensitivity of the detector at separations between 1.4 and 4 kpc. We propose that the primary reason for lack of Hα flux is either from star formation halting, or from obscuration due to dust in the host galaxy (as introduced in the Section 6.1). The bolometric luminosity (5.9 × 10⁴⁵ erg s⁻¹) of this QSO as calculated from the 1450 Å continuum is about an order of magnitude below the average value of a QSO at this redshift, due to the continuum being heavily reddened. However, the broad Hα emission of this source agrees with the rest of the objects in our sample (similar equivalent width and luminosity, see Table 4) that do not show any signs of reddening in their rest-frame UV spectra (see Figure 1 and Table 5). The average bolometric luminosity of our sample is 1.24 × 10⁴⁷ erg s⁻¹ (see Table 4). The agreement between broad line Hα properties (velocity dispersion and intensity) hints that the bolometric luminosity should be consistent with other members of our sample. As found in Fynbo et al. (2013) most reddened QSOs are red due to dust in their host galaxies rather than the intergalactic medium or dust inside the Milky Way. For this source we estimate the amount of reddening by invoking the condition that the bolometric luminosity should be at the average value for a QSO with such a strong broad Hα emission (at least ∼3 × 10⁴⁶ erg s⁻¹). This implies that the flux at 1450 Å needs to be boosted by 10^0.94, implying that A₁₄₅₀ = 2.35. Using the extinction curve from Gordon et al. (2003) assuming SMC like extinction (R_v = 2.74) we obtain ${A}_{{{\rm{H}}}_{\alpha }}=0.38$. This implies that the flux at Hα needs to be corrected by at least 10^0.15, yielding a de-reddened SFR limit of 0.45 M_⊙ yr⁻¹ kpc⁻², and the combined de-reddened SFR on A, B, and C of 41 M_⊙ yr⁻¹ . This implies that dust attenuation only removes 0.1 M_⊙ yr⁻¹ kpc⁻² if we only correct the bolometric luminosity such that it sits at the average. Overall this level of dust obscuration is not enough to be the primary reason for low Hα flux.

Even assuming an extreme case where the bolometric luminosity is near the maximum value for a type-1 QSO at z ∼ 2 (∼10⁴⁸) would only imply a limit of 0.9 M_⊙ yr⁻¹ kpc⁻². This could imply that there is a low SFR in the host galaxy, where the star formation has been nearly shut off within 02–05 (1.4–4 kpc) from the QSO. These distant regions (A, B, and C) are still forming stars at rates that are detectable. Our observations indicate that the host could be in a process of transitioning from a star-forming into a quiescent galaxy. However, the less unlikely possibility is that the star formation is active in a diffuse region at separations of 1.4–4 kpc rather than in the clumpy regions that we see in regions A, B, C, and in other star-forming galaxies at this redshift.

There have been a number of multi-wavelength surveys of radio quiet type 1 QSOs at z ∼ 2 that have presented a range of conclusions about host galaxy star formation properties. High redshift QSO studies have either implied high SFRs in concurrent high-z type-I QSOs or have argued for a lack of star formation activity. In this section we summarize and compare surveys that share similar QSO properties to our sample (i.e., SMBH mass, bolometric luminosity, unobscured type 1).

Herschel PACS observations of AGNs and QSOs in the COSMOS extragalactic survey indicate a correlation between their bolometric luminosity and rest-frame 60 μm host galaxy emission (Rosario et al. 2013). Using the mean 60 μm flux (3.4 × 10⁴⁵ erg s⁻¹) in the 10⁴⁶⁻⁴⁷ erg s⁻¹ z = 1.5–2.2 bin in Table 1 from Rosario et al. (2013) indicate that the mean SFR should be of order 200 M_⊙ yr⁻¹, using the 70 μm SFR law presented in Calzetti et al. (2010). This is nearly an order of magnitude greater than the mean SFR in our sample, as indicated by narrow Hα emission line detection (78 and 29 M_⊙ yr⁻¹) and limits (22 M_⊙ yr⁻¹ for NIFS and 37 M_⊙ yr⁻¹ for OSIRIS, integrated over a 1''² box. See Section 5.3 for the discussion). The disagreement between our sample and the Herschel results could be due to just the limited number of sources observed (14 in Rosario et al. (2013) at a similar bolometric luminosity (10^45.5–47 erg s⁻¹) as the 5 QSOs in our sample). It is worth noting that the QSOs may be responsible for a significant portion of the total 60 μm luminosity, so derived 60 μm SFRs should be considered as upper limits.

HST observations of radio quiet QSOs at z ∼ 2 in Floyd et al. (2013) indicate an average SFR of 100 M_⊙ yr⁻¹ derived from rest-frame UV emission originating from the host galaxy. In their study they use both stellar and artificial PSFs to remove the bright QSO. The number of QSOs in our sample is similar to Floyd et al. (2013), which are type-1 and radio quiet. The SFR differences between our sample and Floyd et al. (2013) could be due to strong QSO contamination from residual emission from their PSF subtraction, or because star formation in our hosts is quite diffuse.

In contrast, studies such as Villforth et al. (2008) and Kotilainen et al. (2009) find quiescent galaxies that host radio quiet high-z QSOs. These observations are from seeing-limited (0.4–05) near-infrared imaging and are limited to disentangling the host galaxy at close angular scales (≲4 kpc). SDSS J0925+0655 and SDSS J0850+5843 share similar rest frame UV photometry to their samples; however, the other half of the QSOs in our study are 1–1.5 mag brighter. Including our results with these two other papers only yields a total of 15 high-z QSO that are observed to reside in "quiescent" z ∼ 2 galaxies in current literature.

At even higher redshifts, recent ALMA observations of z ∼ 6 QSOs (Wang et al. 2013; Willott et al. 2013) using the 158 μm [C ii] emission line reveal a detection in nearly 90% of the sources observed. The targets in their samples have similar properties to ours (i.e., BH mass, bolometric luminosities and Eddington ratios). In Willott et al. (2013) they reach a star formation limit of 40 M_⊙ yr⁻¹, assuming the [C ii] emission emanates solely from star formation. Yet sources in Wang et al. (2013) reach SFRs as high as 1000 M_⊙ yr⁻¹, which implies that sources with detected [C ii] have extreme SFRs in comparison to our detections and sensitivity limits at z = 2. These z ∼ 6 sources are all near the peak of their starburst phase, assuming that most of the [C ii] emission originates from star formation and not the QSO. According to present day M_{stellar,bulge}–M_bh relation and theoretical work (e.g., Somerville et al. 2008; Kormendy & Ho 2013) there is an expectation of simultaneous SMBH and galaxy growth, presumably via mergers at these high (>1 × 10⁴⁶ erg s⁻¹ cm⁻²) bolometric luminosities (Treister et al. 2012). In contrast, our observations show SFRs that are well below this expected initial burst and below the typical star-forming galaxies at z ∼ 2 (Erb et al. 2006; Förster Schreiber et al. 2009; Steidel et al. 2014).

The essential difference and advantage of our study compared to previous studies is that our detection and limits of SFRs can be made at differing spatial and velocity locations away from the QSO. In contrast, the majority of all studies we have discussed have integrated SFR limits over a large range of PSF and beam sizes. Based on our detection limits, it is clear that we do not detect the clumpy (1 kpc²), strong star formation regions (up to ∼10 M_⊙ yr⁻¹ kpc⁻²) in current IFS observed z ∼ 2 star-forming galaxies (Förster Schreiber et al. 2009; Law et al. 2009, 2012; Genzel et al. 2011). If there is underlying star formation undetected in these host systems, then the surface brightness profiles of the star formation has to be diffuse and integrated across a large area of the galaxy. If our limits are to match previous inferred SFRs of z ∼ 2 QSO hosts, then it would need to be diffuse with significant extinction.

The sample selection in our pilot survey is albeit random, since we were selecting based on achieving the best AO performance for PSF subtraction, therefore it is interesting that we would happen to select 3/5 type-I QSOs that are quiescent. The majority of our sample is similar to only a small number of observations of high-z QSO hosts residing in quiescent galaxies, and is in disagreement with other works that indicate simultaneous high SFRs and AGN activity. QSO duty cycles are still poorly understood; however, it does seem to appear that in a number of cases the QSO can still be active while star formation in the host has been effectively turned off. These results agree well with AGN feedback models that require that the feedback mechanism only carry a small portion of the total bolometric luminosity of the QSO (5%–10%) to effectively turn off star formation (Hopkins & Elvis 2010). On the other hand this also agrees with non-causal evolution of SMBHs and their host galaxies (Peng 2007; Jahnke & Macciò 2011), where the growth of the SMBH and star formation are unrelated and AGN feedback is not the main constituent in formation of local scaling relations, possibly because AGNs and star formation activity happen on different timescales. Our study, Kotilainen et al. (2009), and Villforth et al. (2008) are consistent with star formation timescales being significantly shorter than that of the QSO. There are likely numerous high angular resolution observations from HST and ground-based observations that have had null detections of high-redshift QSO host galaxies, that would benefit from being released to the community to improve these global statistics. Interestingly, this means there is likely a social selection bias of high-z QSO host galaxies, where authors typically only publish detections (hence QSO hosts with higher star formation properties) rather than their null detections. In any case, it is obvious that there are a large number of selection effects that need to be taken account, but clearly a larger sample of high-redshift QSOs would greatly benefit from IFS+AO observations and aid in our understanding of the demographics of high-z QSO host galaxies.