A Size Estimate for Galaxy GN-z11

GN-z11 is the highest redshift galaxy spectroscopically confirmed with the Hubble Space Telescope (HST). Previous measurements of the effective radius of GN-z11 utilized galfit, which is not optimized to measure structural parameters for such a faint, distant object. Using a new software program called forcepho on HST data for the first time, we derive a size from images in the F160W band obtained both from the complete CANDELS survey and additional midcycle observations in order to contribute to the knowledge base on the size evolution, size-luminosity, and size-mass relation of early galaxies. We find a half-light radius mean of 0''.036 \(\pm\) 0''.006 corresponding to a physical size of 0.15 \(\pm\) 0.025 kpc. This size, smaller than the point spread function, is dramatically smaller than previous estimates with shallower HST data using galfit but consistent with recent measurements using forcepho on new JWST data arXiv:2302.07234. Such a small size, combined with the JWST/NIRSpec spectroscopic observations arXiv:2305.12492, suggests that GN-z11's high luminosity is dominated by an AGN.


INTRODUCTION
High-redshift galaxies represent some of the first structures to form in our universe.By understanding the physical properties of these galaxies, we can refine our theoretical models and better interpret our observations (Stark 2016;Dayal 2019).These galaxies, particularly those at z ∼ 9 − 11, also existed at a time when the universe experienced a shift from a neutral to ionized state (e.g., Oesch et al. 2016).Constraints on their physical properties yield insights into their role in reionizing the universe (e.g., Bunker et al. 2010;Robertson et al. 2013).
First identified as GNS-JD2 in the HST/NICMOS data, GN-z11 was initially considered a possible dropout candidate due to its detection being limited to the 1.6 µm wavelength (Bouwens et al. 2010).Its proximity to another source made further conclusions difficult until 2014 when Oesch et al. (2014) classified it (under the designation GN-z10-1) as a z ∼ 9 − 10 galaxy, and later determined its redshift, through grism spectroscopy, to be z = 11.09+0.08  −0.12 (Oesch et al. 2016), a measurement more accurately constrained with more recent NIRSpec data to be z = 10.603(Bunker et al. 2023).One of the most distant galaxy observed with HST, GN-z11 is lo-cated in the CANDELS DEEP area in GOODS-North at (RA,DEC) = (12:36:25.46, +62:14:31.4).Holwerda et al. (2015) measured the structure of a sample of z ∼ 9 − 10 galaxies, including GN-z11 (designated GN-z10-1 in their paper), using the 2D fitting algorithm galfit (Peng et al. 2002(Peng et al. , 2010)).The two main drawbacks of galfit when determining the physical properties of galaxies at the distance and luminosity of GN-z11 are (a) the lack of posterior distributions complicate the interpretation of the uncertainty and (b) the software is not optimized for faint, distant objects.Holwerda et al. (2015) report a size for GN-z11 of 0.6 ± 0.3kpc.The uncertainty reported is statistical, however, and based on an estimate of models with similar estimated structural properties (see Ono et al. (2013) for a description of galfit uncertainties and biases).Further, their measurement was obtained by fixing the Sérsic index, n, and the axis-ratio, q, to limit the statistical uncertainty.These fixed parameter models have allowed for initial estimations of the size of GN-z11, but may suffer from systematic uncertainties from modeling choices.Here, we build on previous work with galfit using a new Bayesian size-fitting software, forcepho, which is optimized for faint, blended objects and provides robust uncertainties (Johnson et al., in prep).
In this research note, we present a size measurement of GN-z11 using forcepho.In Section 2, we present our observations and the methodology for carrying out the measurement, with a description of the software package forcepho.We present our size-measurement in Section 3 and the significance of this measurement, along with a discussion of more recent findings, is presented in Section 3. In Section 4 we provide a brief conclusion.
2. DATA ANALYSIS GN-z11 was imaged using the WFC3/IR camera aboard HST.Existing imaging of the GOODS-N field from the CANDELS survey consisted of ∼ 5 orbits covering the central ∼ 65 arcmin 2 of the GOODS-N field (Oesch et al. 2014).7 additional orbits in F160W were obtained as a result of a mid-cycle proposal for a total of 12 orbits, reaching 27.7 mag (5σ) (PI:Oesch, PID: 15977).See Oesch et al. (2014) and Illingworth et al. (2013) for a description of the data reduction.
We fit the structural parameters of GN-z11 using forcepho, which infers the fluxes and morphological parameters of galaxies via a Bayesian analysis (Johnson et al., in prep).Models are generated for our sources which are compared to the observations via a likelihood function as the posterior is sampled.Crucially, forcepho is differentiable, meaning that gradients of the likelihood function can be taken, allowing for significant optimization in the posterior sampling.Additionally, forcepho utilizes Gaussians to approximate the point spread functions (PSFs) -constructed empirically from a stack of point sources in the HLF imaging -and the Sérsic profiles.The sums of these Gaussian parameters are used for convolution, which greatly increases efficiency.We use forcepho to measure the size and other structural parameters of GN-z11 in the F160W band.In addition to the half-light radius, we also infer Sérsic index and the axis-ratio, not setting them to fixed values as in Holwerda et al. (2015).The major source of uncertainty in our measurements come from the similarity of the galaxy size to the size of the PSF.

RESULTS & DISCUSSION
We measure a half-light radius of 0".036±0".006which corresponds to a physical size of 0.15 ± 0.025 kpc, assuming a redshift of z = 10.603 as measured by Bunker et al. (2023).In Fig. 1 (top), we show the image, model, and residual (data -model) showing that the forcepho model is a good match to the data.We infer a flux in F160W of 139.16 ± 8.98 nJy, less than the initial Oesch et al. (2016) finding of 152 ± 10 nJy, but within the range of uncertainty.These measurements differ significantly from those obtained by Holwerda et al. (2015) (0.6 ± 0.3 kpc), finding of a much smaller half-light radius suggestive of a point source.The mean Sérsic index was measured to be 2.42 ± 1.12, and the axis-ratio was measured to have a mean of 0.91 ± 0.07.These measurements are higher than those found by more recent analysis which finds (n = 0.9 ± 0.1, q = 0.67 ± 0.05) using forcepho on 0.9-4.4µmJWST/NIRCam imaging (Tacchella et al. 2023).This could be due to the increased spatial resolution and signal-to-noise ratio of the JWST obervations or an intrinsically different shape in the longer wavelength bands.Fig. 1 (bottom) shows the posteriors from the MCMC sampling, including the mean values for each of these values.
Our measured half-light radius is significantly smaller than previous measurements based on HST imaging.This measurement is confirmed by recent analysis of data collected as part of the JWST Advanced Deep Extragalactic Survey (JADES).Utilizing NIRCam data in nine separate bands (F090W, F115W, F150W, F200W, F277W, F356W, F410M, F444W, and F335M), analysis shows a half-light radius of 0.016" ± 0".005 (Tacchella et al. 2023).
Given its high redshift, the remarkable luminosity of GN-z11 is hard to explain with stellar populations alone (Mason et al. 2015;Mashian et al. 2015;Trac et al. 2015;Tacchella et al. 2013).In their paper analyzing JADES NIRSpec spectroscopy of GN-z11, Bunker et al. (2023) examined the possible sources of photoionization and, based on emission line fluxes, suggested that an AGN is not a favored source of the luminosity, though can not be completely ruled out.Both Tacchella et al. (2023) and Bunker et al. (2023)  More recent analysis, however, points to the presence of an AGN within GN-z11, accounting for the unresolved nuclear component (the AGN) and the disk-like component (the galaxy) revealed in Tacchella et al. (Maiolino et al. 2023).This analysis, based on data taken as part of the JADES survey, relies on a deeper spectrum of GN-z11, and reveals features consistent with the presence of an AGN: the detection of [NeIV] and CII lines, extremely high gas density, and a deep, blueshifted absoprtion trough of CIV (Maiolino et al. 2023).In particular, the high densities are fully within the realm of Broad Line Regions (BLR) of AGN, with widths consistent with Narrow Line Seyfert 1 (NLS1) AGN (Maiolino et al. 2023).Previous studies suggest that GN-z11 hosts a population of Wolf-Rayet stars that may account for its luminosity (Cameron et al. 2023;Charbonnel et al. 2023;Senchyna et al. 2023).Maiolino et al. (2023) point out the absence of a strong NIVλ1718 line in conjunction with the observed NIVλλ1483,1486 doublet, as well as the presence of the previously mentioned [NeIV] and CII lines, neither of which is associated with WR stars (Maiolino et al. 2023).
Based on the spectral line widths and the continuum luminosity, the authors estimate a BH mass of about 1.6 × 10 6 M ⊙ (Maiolino et al. 2023).A bolometric luminosity of 10 45 erg/s is inferred, consistent with Super-Eddington accretion which the authors suggest is likely episodic (Maiolino et al. 2023).While it is possible this accretion rate extends to the past and the AGN was generated from a stellar black hole seed formed at z ∼12-15, more massive seed scenarios associated with direct black hole collapse (DBHC) and the merging of nuclear clusters would have provided easier routes to a BH of this mass (1.6 × 10 6 M ⊙ ) at this time (z = 10.6)(Maiolino et al. 2023).

CONCLUSIONS
In summary, we performed a new size-measurement for GN-z11, the highest redshift galaxy spectroscopically confirmed by HST, using the Bayesian fitting software forcepho.Our physical size of 0.15 ± 0.1 kpc is much smaller than previous measurements with galfit, but consistent with measurements based on newer JWST/NIRCam data (Tacchella et al. 2023).The size of GN-z11, along with its redshift and luminosity, present interesting possibilities for the physical processes at play in such an early galaxy (Bunker et al. 2023;Tacchella et al. 2023).Our measurement of a very compact size in GN-z11 is consistent with WST/NIRSpec observations (Maiolino et al. 2023) suggesting that at least some of the remarkable luminosity of this object may be driven by an AGN.

Figure 1 .
Figure 1.TOP: Results of the forcepho modeling after optimization and sampling.The far left shows the original HST data image, the middle image shows the model constructed from the PSF, and the final image is the residual constructed from subtracting the model from the data.BOTTOM: Posteriors generated by forcepho after optimization and sampling.The MCMC sampling was performed over 2000 iterations, with the dotted red line representing the mean value for each posterior.
work is based on observations taken by the 3D-HST Treasury Program (GO 12177 and 12328) with the NASA/ESA HST, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.Support from HST-GO-15977, HST-GO-13871, and the CANDELS survey is gratefully acknowledged.
find evidence for a younger stellar population, with Tacchella et al. observing a weak Balmer/4000 Å break and Bunker et al. observing no Balmer Break whatsoever.