A Catastrophic Failure to Build a Massive Galaxy around a Supermassive Black Hole at z = 3.84

We selected J1639+2824 for observations using the IRCS camera (Kobayashi et al. 2000) together with the AO188 system (Hayano et al. 2010) on Subaru telescope based on several factors that enable AO-assisted imaging, mainly (1) the availability of a bright guide star (GS; R < 15) for tip-tilt correction within 18'' and (2) a sufficiently bright star for point-spread function (PSF) reconstruction located at similar distance from the GS. The latter criterion is important to minimize uncertainties in the PSF reconstruction due to PSF degradation with increasing distance from the GS. This quasar has a favorable configuration between the QSO, GS, and PSF star as shown in the left panel of Figure 1. The IRCS camera uses a 1024 × 1024 pixel InSb Aladdin III detector, which affords a 52'' × 52'' field of view (FoV) with a 52 mas pixel scale. We adopted a five-point dither pattern with a step size of 5'' in order to remove bad pixels.

Zoom In Zoom Out Reset image size

We observed J1639+2824 in the K band during 2012 May, 2013 April, and 2014 February with a total exposure time of ≈10 ks for the final stacked image leading to a limiting magnitude of 24.0 mag (AB, 10σ for a point source). The observing conditions vary considerably during the three runs, resulting in AO-assisted seeing between 015 and 04. Data reduction was performed using the IRAF package IRCS-IMGRED for flat-field correction, sky subtraction, alignment, and stacking. The stacked image has a resolution of 03 at the position of the quasar.

Table 1.  Properties of SDSS J1639+2824

Quasar	SDSS J1639+2824
R.A.	16:39:09.10
Decl.	+28:24:47.15
zoptical	3.82
zCO	3.840
Lbol	1048.3 ± 0.1 erg s−1
FWHM(CO)	495 ± 30 km s−1
${L}_{\mathrm{CO}}^{{\prime} }$	5.59 ± 1 × 1010 K km s−1 pc2
MBH	${2.5}_{-1}^{+2}\times {10}^{10}$ M⊙
${M}_{\mathrm{dyn},\mathrm{CO}}$	${4}_{-4}^{+10}\times {10}^{10}$ M⊙
${M}_{\mathrm{dyn},\mathrm{stellar}}$	<1.5 × 1010 M⊙

Download table as:  ASCIITypeset image

To detect any faint extended host galaxy under the bright nuclear point source, it is crucial to accurately estimate the shape of the PSF at the position of the QSO. Having a PSF star close to the quasar and at the same distance from the GS are critical to this task, since we minimize PSF shape variability given that the FoV contains only very few stars for detailed PSF shape modeling. We fit the PSF star with a set of Gaussian (for the core) plus Moffat (for the extended wing component) profiles to create a high signal-to-noise ratio (S/N) PSF model that is then scaled and subtracted from the quasar using GALFIT (Peng et al. 2010) as shown in Figure 1. For our analysis we consider the effect of a color-dependent PSF shape typically affecting diffraction limited observations to be not significant (see, e.g., Decarli et al. 2012; Mechtley et al. 2012, 2016) since our observations are dominated by seeing and a position dependence rather than reaching the diffraction limit due the weather. Nevertheless, we are aware of this potential uncertainty that would have given us a more conservative host detection given the difference in color between the PSF star (H − K = 0.1 mag) and quasar (H − K = 0.6 mag) since bluer objects tend to be narrower (Bahcall et al. 1997), which, on the other hand, would have made a potential detection easier.

A robust estimate of the SMBH mass is crucial to investigate the coevolution of the SMBH with its host. The SDSS DR7 quasar catalog provides an SMBH mass based on the broad C iv line of M_BH = 2.9 × 10¹⁰ M_⊙ (Shen et al. 2011; see Figure 2). The SDSS spectrum of J1639+2824 shows broad absorption line features possibly affecting the UV-line based BH mass and since C iv is known to be problematic as an SMBH mass estimator for luminous active galactic nucleus (AGN; Shen & Liu 2012; Trakhtenbrot & Netzer 2012). Therefore, we obtained a spectrum covering the Hβ emission line using the Subaru/IRCS at the K band in 2012 May and 2016 February to independently verify the mass estimate. The Hβ line is well detected in both epochs, which are corrected for galactic extinction (although the effect is <0.01 mag) and combined into the spectrum shown in Figure 2. We fit the Hβ line profile with a model consisting of a power law for the local continuum, a single Gaussian for the broad Hβ line, and a double Gaussian for [O iii] λλ4959, 5007. While the [O iii] detection is tentative, this does not affect the fit of the Hβ line. We perform our spectral measurement based on this best-fit model, shown in Figure 2.

Zoom In Zoom Out Reset image size

We observe the CO(4 − 3) line of J1639+2824 using ALMA by observing at 95.25 GHz (program ID: ALMA #2015.1.01602.S) on 2015 October 31 for 52.9 minutes (21.7 minutes on-source) using 36 antennas at baselines ranging from 84 to 16,196 m. The flux and bandpass calibrations were done by observing J1751+0939; J1647+2705 was used as the phase calibrator. The raw visibilities were calibrated with the ALMA data reduction pipeline on CASA 4.5.0, and imaging was carried out with the CASA CLEAN task. We then spectrally binned the data to achieve a spectral resolution of 180 km s⁻¹ and applied Gaussian tapering in the uv-plane beyond 900 kλ, corresponding to a baseline length ≳2800 m, to aid the line detection. The resulting native (i.e., untapered) synthesized beam is 0106 × 0065, and the tapered beam is 0187 × 0130. In Figure 3, we show the CO(4 − 3) map and the spectrum of the line. The CO redshift is z_CO = 3.840, slightly offset from the optical redshift of z = 3.82, based on the broad Hβ emission line. The CO(4 − 3) line is detected at 9.0σ in the tapered map, with the detection being 5.9σ in the native resolution map, indicating that emission is spatially resolved at these scales. The dust continuum is not detected. We estimate the CO(4 − 3) line luminosity to be L' = 5.59 ± 0.6 × 10¹⁰ K km s⁻¹ pc². We do not see any sign of rotation in the position–velocity-diagram, but given the few velocity bins of the CO spectrum, we cannot make any definite statement if rotation is present or not.

Zoom In Zoom Out Reset image size

We observe that the CO(4 − 3) extent is marginally spatially resolved at the native resolution because the aforementioned application of Gaussian tapering results in a slightly higher S/N (≃7 versus 9). As such, we measure the intrinsic source size in the uv-plane, which can utilize the information from longer baselines, unlike an image-based measurement that is inherently limited by the native resolution corresponding to the median baseline length. We carry out the uv-based size measurement using GILDAS (version jul18a). The CASA-calibrated visibilities at the channels containing the CO(4 − 3) line (Figure 3, right panel) were spectrally and temporally averaged and then exported to GILDAS. We fitted source models to the visibilities using the task uv_fit and subtracted the models from the data. We find that a uniform residual noise is achieved when an elliptical Gaussian model is adopted. In the fit, all parameters of elliptical Gaussian models, including the centroid, flux, major/minor axes, and position angle, are free (i.e., not fixed). The dirty image of the CO(4 − 3) emission, the best-fit model, and the residual are shown in Figure 4. The best-fit source model is described by an elliptical Gaussian with a major FWHM of 120 ± 31 mas, minor FWHM of 54 ± 18 mas, and PA of 7 ± 12 deg. This source extent is adopted for the dynamical modeling in Section 3.2.

Zoom In Zoom Out Reset image size

The Subaru/IRCS K-band image shows that the surface brightness profile of the rest-frame optical emission is well characterized by an unresolved point source as shown in Figure 1 based on a model of the PSF and the subtraction of it from the total K-band emission. That is, we do not detect any extended emission originating from the stellar component of the host galaxy. The surface brightness profiles of the PSF and QSO are apparently identical, further assuring that our analysis is robust against spatial variations of the PSF.

With the nondetection of the host galaxy emission, we place an upper limit on the stellar mass based on the addition of a simulated host galaxy to our K-band image that includes the quasar. A set of synthetic images of the host galaxy is generated, assuming an effective radius of ∼2 kpc that corresponds to 03 at the target redshift and matches our resolution in the final stacked image. Such sizes are typical for massive (M_stellar > 10¹⁰ M_⊙) galaxies at z = 3 (Trujillo et al. 2004; Akiyama et al. 2008; Ichikawa et al. 2012; van der Wel et al. 2014). For the model galaxies, we assume either a disk (Sérsic index n = 1) or an elliptical profile (Sérsic index n = 4) having a range of rest-frame U − V colors ($-1\lt U-V\lt 0.6$) to determine the impact of the M/L variation on the detection of the host galaxy. We run our detection routine in the same manner as the original data while recovering the host galaxy at the 3σ level to represent a minimal detection threshold. Two examples of the recovered host galaxies are shown in the top panel of Figure 5 for the two cases n = 1 (simulated Host A) and n = 4 (simulated Host B). For n = 1, we determine an upper limit on the stellar mass to be between $\mathrm{log}\,({M}_{\mathrm{stellar}}/{M}_{\odot })=10.8\mbox{--}11.3$ depending on the color of the host. For n = 4, this limit is typically higher $\mathrm{log}\,{M}_{\mathrm{stellar}/{M}_{\odot }}=11.1\mbox{--}11.5$. In the bottom panel of Figure 5 we compare our K-band detection limit for the more extreme case of n = 4 with the broadband spectral energy distribution (SED) of the quasar. Due to the brightness of the quasar the galaxy would have to be at least a factor 10–20 more luminous to have any significant impact on the SED, which is well described by the TQSO1 AGN template from Polletta et al. (2007).

Zoom In Zoom Out Reset image size

In Figure 6 (left panel), we indicate how far SDSS J1639+2824 is displaced from the local relation (McConnell & Ma 2013) between the mass of SMBHs and their total stellar mass. Considering the local relation (dashed line), we expect a stellar mass over an order of magnitude greater than our mass limit for SDSS J1639+2824. Taking into account biases in the selection of luminous quasars (e.g., Lauer et al. 2007; Schulze & Wisotzki 2011; Portinari et al. 2012), we still would expect a higher stellar mass (${M}_{\mathrm{stellar}}\sim 4.5\times {10}^{11}$ M_⊙), based on the black curve in Figure 6, compared to our upper limit. At the very least, SDSS J1639+2824 is offset by 0.3 dex in stellar mass for a compact red host galaxy. The offset may even be larger when considering the bulge mass since our estimates are based on a disk-dominated host galaxy rather than a bulge-dominated system.

Zoom In Zoom Out Reset image size

To further assess the lack of stellar material surrounding SDSS J1639+2824, we use ALMA to measure the dynamical mass within a half-light radius using the CO(4 − 3) line. CO emission is detected with ALMA at 9σ and is spatially resolved (Figure 3). We estimate the dynamical mass following two approaches, including that given in Tan et al. (2014) for the spherically symmetric case (Equation (1)),

$$\begin{eqnarray}&&{M}_{\mathrm{dyn}}(r\lt {r}_{1/2})=\displaystyle \frac{5{\sigma }^{2}\,{r}_{1/2}}{G},\end{eqnarray} \tag{ 1 }$$

where σ is the FWHM of the CO line divided by 2.35, G is the gravitational constant, and r_1/2 is the half-light radius. For the dynamical mass measurement we note that two assumptions are made: (I) the CO emission is gravitationally bound; (II) for the inclination angle measurement we assume that the intrinsic shape of the galaxy is perfectly symmetric. Second, we consider the case of a rotating thin disk model by the following equation:

$$\begin{eqnarray}&&{M}_{\mathrm{dyn}}(r\lt {r}_{1/2})=\displaystyle \frac{6\times {10}^{4}\,{\rm{\Delta }}{v}_{\mathrm{FWHM}}^{2}\,{r}_{1/2}}{{\sin }^{2}i},\end{eqnarray} \tag{ 2 }$$

where Δv_FWHM is the FWHM of the CO emission line, r_1/2 is the half-light radius, and i is the disk inclination angle. We perform a fit to the CO spatial distribution of the emission with an elliptical Gaussian model to determine r_1/2 and i. The disk inclination (i = 64° ± 13°) is derived from the ratio of the deconvolved sizes of the minor and major axes, 005 ± 002 and 012 ± 003, respectively. We find that the CO gas traces a very compact region of 0.9 ± 0.2 kpc in diameter, which is smaller than the typical sizes of [C ii] regions observed in z = 6 quasars (≃3 kpc; e.g., Wang et al. 2016). From the CO profile, we estimate the FWHM of the line to be 495 km s⁻¹. We find a dynamical mass of $\mathrm{log}({M}_{\mathrm{dyn}}/{M}_{\odot })=10.5\pm 0.2$ for case I. For case II, we estimate a dynamical mass of $\mathrm{log}({M}_{\mathrm{dyn}}/{M}_{\odot })=9.7\pm 0.4$, which is well below the BH mass, although the value strongly depends on the inclination angle. We further adopt a value of 20 deg, which is within the range for a similarly massive quasar (Wang et al. 2016) that results in a dynamical mass of $\mathrm{log}({M}_{\mathrm{dyn}}/{M}_{\odot })=10.6\pm 0.4$. This dynamical mass is comparable to those that have been observed for QSO host galaxies at z ∼ 6 using [C ii] (Figure 6, right panel; see Wang et al. 2016 for a recent compilation). Strikingly, the ratio M_BH/M_dyn is 0.6 for SDSS J1639+2824 assuming the spherical symmetric case or for a rotating disk, which is a factor of 50 higher than the 21 systems at z = 6 (M_BH/M_dyn ∼ 0.1) of Wang et al. (2016) as shown in Figure 6. The rotating disk case has significantly larger error bars given the uncertainties in velocity, radius, and inclination angle, but considering an inclination angle as low as i = 10° the mass would be $\mathrm{log}({M}_{\mathrm{dyn}}/{M}_{\odot })=11.2$, still more than 1σ offset from the black curve shown in Figure 6.

On the contribution from the gas mass to the dynamical mass, we estimate the total gas mass from the CO luminosity. Here, we assume a ratio r(4 − 3)/r(1 − 0) of 10 (Carilli & Walter 2013) to estimate the CO(1 − 0) luminosity. With an assumption of X_CO = 0.8 (Carilli & Walter 2013), the molecular gas mass is ${M}_{{{\rm{H}}}_{2}}=4.5\times {10}^{9}\,{M}_{\odot }$. Using the Milky Way value of X_CO = 4, the gas mass is ${M}_{{{\rm{H}}}_{2}}=2.2\times {10}^{10}\,{M}_{\odot }$, which would further reduce the potential stellar mass estimate in the case of a rotating disk.

We then place a constraint on the stellar mass contribution to the dynamical mass since the SMBH and molecular gas account for a significant fraction (∼60%) of the total mass. It is not surprising that the velocity field of the CO gas is affected by the SMBH since the sphere of influence of the SMBH is larger than the beam size of ALMA based on an estimate assuming a velocity dispersion σ = 200 km s⁻¹. Accounting for these components, we find the limit on the stellar mass to be M_stellar < 1.5 × 10¹⁰ M_⊙ by applying conservative assumptions on the dynamical mass and gas mass. In Figure 6 (right panel), we indicate the stellar mass limit for SDSS J1639+2824 based on dynamical arguments given above. We further confirm with ALMA the extreme offset of SDSS J1639+2824 due to its upper limit on the stellar mass content in relation to that expected based on the local mass relation. This rules out a massive and compact stellar host that we might have missed with the Subaru observations, although our resolution is a factor three lower than the size limit estimate from ALMA. Based on our simulations any significant stellar component on larger scales would have also been detected in the K-band image as long as the stars are not tidally stripped or have low surface brightness levels well below our detection limit. In addition, we cannot entirely rule out a strongly extincted host galaxy, although we do not see any evidence for significant extended dust affecting the quasar spectrum. On the other hand, we cannot fully rule out a major merging system, although it should also be visible in the gas component that does not show any such asymmetries or close companions. This may support a scenario where the growth of the SMBH precedes that of its host galaxy.

With such a disparity between the SMBH mass and that of its host, this may bring into question the accuracy of the SMBH mass estimate based on C iv that can be susceptible to non-Keplerian effects such as outflows. To address this issue, we use our Subaru/IRCS NIR spectrum to measure the velocity width of the Hβ emission line. We find a broad FWHM of 7800 ± 900 km s⁻¹ and a continuum luminosity $\lambda {L}_{5100}={10}^{47.4}$ erg s⁻¹ (Figure 1, right panel). We use these measurements to estimate a SMBH mass ${M}_{\mathrm{BH}}={2.5}_{1}^{2}\times {10}^{10}$ M_⊙ based on the recipe given in Vestergaard & Peterson (2006), which is remarkably consistent with the C iv SMBH mass estimate given the typical large systematic errors of 0.3 dex for Hβ and 0.4 dex for C iv. We derive a bolometric luminosity of L_bol = 10^{48.3 ± 0.1} erg s⁻¹ using a bolometric correction factor to L₅₁₀₀ of 9.2 (Shen et al. 2008) and thereby an Eddington ratio L_bol/L_Edd = 0.69, showing that the quasar is still accreting at a significant level.