Discovery of the Optical Afterglow and Host Galaxy of Short GRB 181123B at z = 1.754: Implications for Delay Time Distributions

Short-duration (T₉₀ < 2 s) gamma-ray bursts (SGRBs) have long been linked to binary neutron star (BNS) and possibly neutron star–black hole (NS–BH) mergers through indirect observational evidence: the lack of associated supernovae (SNe; Fox et al. 2005; Hjorth et al. 2005a, 2005b; Kocevski et al. 2010; Berger 2014), host galaxy demographics demonstrating a mix of young and old stellar populations (Berger 2009; Leibler & Berger 2010; Fong et al. 2013), low inferred environmental densities (Soderberg et al. 2006; Fong et al. 2015), moderate to large offsets with respect to their host galaxies (Berger 2010; Fong et al. 2010; Church et al. 2011; Fong & Berger 2013; Tunnicliffe et al. 2014), and emission consistent with expectations for r-process kilonovae (Berger et al. 2013; Tanvir et al. 2013; Tanaka 2016; Metzger 2017; Gompertz et al. 2018; Hotokezaka et al. 2018; Lamb et al. 2019; Troja et al. 2019). The discovery of the BNS merger GW170817 (Abbott et al. 2017a) and the associated SGRB 170817A (Abbott et al. 2017b; Goldstein et al. 2017; Savchenko et al. 2017) provided direct evidence that at least some SGRBs originate from BNS mergers.

As gravitational wave (GW) facilities continue to make ground-breaking discoveries of the first BNS mergers to z ≈ 0.05 (Abbott et al. 2017a, 2020), SGRBs provide cosmological analogs that can probe the binary merger progenitor population and their rates and evolution to z ≈ 2. Since 2004, the Neil Gehrels Swift Observatory (Gehrels et al. 2004) has discovered >130 SGRBs (Lien et al. 2016). Dedicated campaigns to characterize their host galaxies have led to secure redshift determinations for ≈1/3 of the population, with a peak in the distribution at z ≈ 0.5 (Fong et al. 2013, 2017; Berger 2014). However, to date, only ≈5% of bursts have confirmed redshifts of z > 1. This drops to ≈1.5% (two events) when considering the confirmed secure SGRBs at z > 1.5: GRB 111117A at z = 2.211 (Selsing et al. 2018) and GRB 160410A at z = 1.717 (Selsing et al. 2016).¹⁹ In general, high-redshift SGRBs are particularly challenging to characterize for a number of reasons. First, a redshift typically requires detection of an optical afterglow for subarcsecond-precision localization and association with a host galaxy, and typical afterglow luminosities scaled to z > 1 have faint apparent magnitudes of r > 24 mag within hours of burst detection. Second, the sensitivity of Swift is known to fall off at higher redshifts for SGRBs compared to long GRBs due to the different thresholds in the respective detection channels (Guetta & Piran 2005). Third, there are a number of SGRBs with host galaxies that have inferred redshifts of z > 1.2 due to their featureless optical spectra (e.g., GRB 051210; Berger et al. 2007) but are too faint to characterize further with current near-infrared (NIR) capabilities. Finally, a broad distribution of delay times (the timescale including the stellar evolutionary and merger timescales) spanning 1 to several Gyr results in an event rate that will peak at low redshifts.

Given the observational challenges, the discovery of additional confirmed SGRBs at z > 1.5 may provide significant constraining power on the delay time distribution (DTD). In turn, the DTD inferred from SGRBs can be directly linked to the formation channel of BNS mergers, as primordial binaries versus dynamical assembly within globular clusters will result in different DTDs (Hopman et al. 2006; Belczynski et al. 2018). In the absence of other mechanisms, the merger timescale is determined by the loss of energy and angular momentum due to GWs (Peters 1964), which can be tied to the parameters of the binary (e.g., initial separation, ellipticity; Postnov & Yungelson 2014; Selsing et al. 2018). Many studies have constrained the SGRB DTD by fitting the SGRB redshift distribution, predominantly focused on the z < 1 population (Nakar et al. 2006; Berger et al. 2007; Jeong & Lee 2010; Hao & Yuan 2013; Wanderman & Piran 2015; Anand et al. 2018). Other constraints on the DTD have come from studies of the Galactic population of NS binaries (Champion et al. 2004; Beniamini et al. 2016a; Vigna-Gómez et al. 2018; Beniamini & Piran 2019) and SGRB host galaxy demography, as longer delay times will result in an increase in host galaxies with old stellar populations (Zheng & Ramirez-Ruiz 2007; Fong et al. 2013; Behroozi et al. 2014).

Here we present the discovery of the optical afterglow and host galaxy of GRB 181123B at z = 1.754, making this event the third confirmed event at z > 1.5 and the most distant, secure SGRB with an optical afterglow to date. In Section 2 we describe the discovery and community observations of GRB 181123B. We describe our photometric and spectroscopic observations of GRB 181123B in Section 3. In Sections 4 and 5, we discuss the burst explosion and host galaxy properties, respectively. Our results, including a discussion of GRB 181123B in context with the population of SGRBs and the implications for the DTD, are given in Section 6. Finally, we summarize our conclusions in Section 7.

Unless otherwise stated, all observations are reported in AB mag and have been corrected for Galactic extinction in the direction of the burst (Schlafly & Finkbeiner 2011). We employ a standard cosmology of H₀ = 69.6, Ω_M = 0.286, Ω_vac = 0.714 (Bennett et al. 2014).

On 2018 November 23 at 05:33:03 UT, the Burst Alert Telescope (BAT; Barthelmy et al. 2005) on board the Neil Gehrels Swift Observatory (Gehrels et al. 2004) discovered and located GRB 181123B at a refined position of R.A., decl. = 12^h17^m2799, 14°35'560 (38 positional uncertainty; 90% confidence) with a duration of T₉₀ = 0.26 ± 0.04 s in the 50–300 keV band (90% confidence; Lien et al. 2018). In addition, GRB 181123B showed minimal spectral lag (Norris et al. 2018) and a hardness ratio (between the 50–100 and 25–50 keV bands) of 2.4 (Lien et al. 2016). These properties classify GRB 181123B as a hard-spectrum SGRB. A power-law fit to the data results in a fluence, f_γ = (1.2 ± 0.2) × 10⁻⁷ erg cm⁻², in the 15–150 keV band (Evans et al. 2009). Swift's X-ray Telescope (XRT) began observing the field at δt = 80.25 s, where δt is the time after the BAT trigger in the observer frame, localizing an uncataloged X-ray source within the BAT region with an enhanced position of R.A., decl. = 12^h17^m2805, 14°35'524 with a positional uncertainty of 16 (90% confidence; Goad et al. 2007; Evans et al. 2009; Osborne et al. 2018). Follow-up observations performed by Swift's Ultraviolet/Optical Telescope (UVOT) resulted in no afterglow detection to a 3σ upper limit of V > 19.7 mag at a mid-time of δt = 5148 s (Oates & Lien 2018).

From the community, the Mobile Astronomical System of Telescope-Robots (MASTER; Lipunov et al. 2010) obtained optical follow-up observations at δt = 2.7 and 20.2 hr and did not detect any source in or around the XRT position to upper limits of ≳17 and ≳18.1 mag, respectively (Lipunov et al. 2018). In addition, radio observations with the Australia Telescope Compact Array (ATCA; Frater et al. 1992) were conducted at δt = 12.5 hr; no radio emission was detected to 3σ upper limits of 66 and 69 μJy at 5 and 9 GHz, respectively (Anderson et al. 2018).

3.1. Afterglow Observations

3.1.1. Gemini Optical Discovery

We initiated i-band target-of-opportunity (ToO) observations of the field of GRB 181123B with the Gemini Multi-Object Spectrograph (GMOS; Crampton et al. 2000), mounted on the 8 m Gemini-North telescope (PI: Fong; Program GN-2018B-Q-117), at a mid-time of 2018 November 23.618 UT or δt = 9.2 hr (Fong et al. 2018). We obtained 18 × 90 s of exposures, resulting in a total of 1620 s on source, at an airmass of 1.7 and average seeing of 10. We used a custom pipeline,²⁰ using routines from ccdproc (Craig et al. 2017) and astropy (Astropy Collaboration et al. 2013; Price-Whelan et al. 2018) to perform bias-subtraction, flat-fielding, and gain-correction calibrations. We aligned and coadded the data and performed astrometry relative to Gaia DR2 (Gaia Collaboration et al. 2016, 2018; Lindegren et al. 2018).

We obtained a second, deeper set of i-band Gemini-N/GMOS observations at a mid-time of 2018 November 25.637 UT (δt = 2.41 days) with significantly improved image quality compared to the first set (airmass of 1.3, seeing of 07). We detect an extended source in the epoch 2 observations near the XRT position, presumed to be the host galaxy (see Section 3.2). To assess any fading between epochs 1 and 2, we align the epoch 2 observations with respect to epoch 1 and perform image subtraction using HOTPANTS (Becker 2015; Figure 1) between the two epochs. A source is found within the enhanced XRT position in the difference image, which we consider to be the optical afterglow. Performing aperture photometry with standard IRAF (Tody 1986) packages directly on the residual image and photometrically calibrating to the Sloan Digital Sky Survey (Fukugita et al. 1996; Gunn et al. 2006; Eisenstein et al. 2011; Ahn et al. 2012), we measure an afterglow brightness of i = 25.10 ± 0.39 mag at δt = 9.2 hr. Calibrated to Gaia DR2, we determine a position at R.A., decl. = 12^h17^m2794, 14°35'5266 with a positional uncertainty of 010 accounting for the afterglow centroid and astrometric uncertainties. A summary of our observations and aperture photometry is given in Table 1.

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Table 1.  Afterglow and Host Galaxy Observations of GRB 181123B

Datea	δta	Filter	Telescope	Instrument	Total Exp. Time	Afterglow	Host	Aλb
(UT)	(days)				(s)	(AB mag)	(AB mag)	(AB mag)
				Imaging
2018 Nov 23.618	0.38	i	Gemini-N	GMOS	1620	25.10 ± 0.39	⋯	0.06
2018 Nov 23.669	0.43	J	Keck I	MOSFIRE	2880.5	>23.2	23.05 ± 0.32	0.03
2018 Nov 25.637	2.40	i	Gemini-N	GMOS	2400	⋯	23.79 ± 0.19	0.06
2018 Nov 25.496	2.27	J	MMT	MMIRS	3717.7	>23.3	22.65 ± 0.26	0.03
2018 Nov 26.655	3.42	J	Keck I	MOSFIRE	2138.5	⋯	22.85 ± 0.23	0.03
2019 Jan 17.545	55.31	K	MMT	MMIRS	1704	⋯	22.33 ± 0.23	0.01
2019 Jan 20.464	58.23	K	MMT	MMIRS	1394.2	⋯	22.39 ± 0.41	0.01
2019 Feb 3.312	72.08	r	Gemini-S	GMOS	1800	⋯	23.84 ± 0.19	0.08
2019 Feb 3.340	72.11	g	Gemini-S	GMOS	1800	⋯	24.08 ± 0.23	0.12
2019 Feb 3.370	72.14	z	Gemini-S	GMOS	1800	⋯	23.84 ± 0.22	0.04
2019 May 24.275	182.04	H	MMT	MMIRS	2987.4	⋯	22.61 ± 0.19	0.02
2020 Mar 5.329	468.10	Y	MMT	MMIRS	3584.9	⋯	22.78 ± 0.24	0.03
				Spectroscopy
2019 Feb 26.495	95.26	GG455	Keck II	DEIMOS	5400
2019 Apr 10.678	137.95	JH	Gemini-S	FLAMINGOS-2	3600

Notes. All magnitudes are in the AB system, and uncertainties correspond to 1σ.

^aBased on mid-time of observation. ^bGalactic extinction in the direction of the burst (Schlafly & Finkbeiner 2011).

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3.1.2. NIR Photometric Observations

We obtained J-band observations of GRB 181123B with the Multi-Object Spectrometer For Infra-Red Exploration (MOSFIRE; McLean et al. 2012), mounted on the 10 m Keck I telescope (PI: Miller; Program 2018B_NW254), at a mid-time of 2018 November 23.669 UT or δt = 10.4 hr (first reported in Paterson & Fong 2018). We obtained a total of 2880.5 s on source from 36 × 58 and 27 × 29 s exposures in cloudy conditions with 1'' seeing. We developed and used a custom MOSFIRE pipeline²¹ (using routines from ccdproc and astropy) to reduce the data in a similar manner to Gemini but with an additional sky-subtraction routine to take into account the varying IR sky. We aligned and coadded the data, dividing first by the exposure time to ensure equal weights, and performed astrometry relative to Gaia DR2.

We detect an extended source near the XRT position and initiated a second set of observations with Keck (Paterson et al. 2018) through a ToO program (PI: Fong; Program 2018B_NW249) at a mid-time of 2018 November 26.655 UT or δt = 3.42 days. We obtained 40 × 58 s exposures, for a total of 2138.5 s on source, in clear conditions with seeing of 09. The clear conditions and improved seeing of these observations provided a deeper image, allowing us to use it as a template for image subtraction. We align this image with the epoch 1 observations and perform image subtraction using HOTPANTS. We do not detect any residuals at the position of the afterglow to a 3σ limit of J ≳ 23.2 mag, calibrated to the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) and converted to the AB system. The images are shown in Figure 1.

We also obtained J-band observations with the Magellan Infrared Spectrograph (MMIRS; McLeod et al. 2012), mounted on the 6.5 m MMT telescope (PI: Fong; Program 2018C-UAO-G4), at δt = 2.27 days. We developed and used a custom MMIRS pipeline²² to reduce data in a similar manner to MOSFIRE. We perform image subtraction relative to the second epoch of Keck and do not detect any residuals at the position of the afterglow to a 3σ limit of J ≳ 23.3 mag, calibrated to 2MASS and converted to the AB system. We note that the lack of afterglow detection in the J-band is consistent with the steady brightness of the host galaxy over all three epochs (Table 1).

3.2. Host Observations

3.2.1. Host Galaxy Assignment

We quantify the probability that the coincident extended source is the host galaxy of GRB 181123B. Based on the XRT position alone, we calculate the probability of the chance coincidence (P_cc; Bloom et al. 2002) of the GRB with the galaxy to be P_cc = 0.012. From Gemini i-band imaging, we measure an afterglow brightness of i = 23.85 ± 0.19 mag and determine a position of R.A., decl. = 12^h17^m2791, 14°35'5227 with a positional uncertainty of 007. Relative to the optical afterglow position, we calculate an offset of 059 ± 016, taking into account the afterglow and host centroids and relative astrometric uncertainty. Using the optical afterglow, we calculate P_cc = 4.4 × 10⁻³. Calculating a P_cc for nearby extended sources in the field, the next most probable host has P_cc = 0.07, while all other sources have values close to unity. Thus, we conclude that the extended source is the host galaxy of GRB 181123B.

3.2.2. Multiband Imaging

We obtained late-time g-, r-, and z-band observations with Gemini-South/GMOS at δt ≈ 72 days (PI: Fong; Program GS-2018B-Q-112). We also obtained YHK observations, where the Y-band observations are calibrated to UKIRT (Hewett et al. 2006; Lawrence et al. 2007; Hodgkin et al. 2009) and converted to the AB system, with MMT/MMIRS (PI: Fong; Programs 2019A-UAO-G7 and 2020A-UAO-G212-20A) with δt > 50 days.

The details of these observations are summarized in Table 1. A color composite image of the field made from the g, r, i, z, J, and K filters, along with the photometry of the host galaxy from all bands, is shown in Figure 2.

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3.2.3. Keck Optical Spectroscopy

We obtained an optical spectrum of the host of GRB 181123B with the DEep Imaging Multi-Object Spectrograph (DEIMOS; Faber et al. 2003), mounted on Keck I (PI: Paterson; Program 2019A_O329). We obtained 3 × 1800 s exposures in clear conditions with 09 seeing. Using the 600ZD grating, a GG455 order-block filter, and a central wavelength of 7498 Å, the spectrum roughly covers the wavelength range 4400–9600 Å with a central resolving power, R = 2142. We used standard IRAF routines in the ctioslit package to reduce and coadd the data. We performed wavelength calibrations using an NeArKrXe arc taken just before the observations and used the standard star Feige 34 for spectrophotometric calibration. We extracted the error spectrum and normalized by $1/\sqrt{N}$, where N is the number of images used in the coadd. The resulting spectrum, scaled to the multiband photometry, is shown in Figure 3.

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The spectrum is featureless, with no lines above a signal-to-noise ratio (S/N) > 5. There is a faint continuum but no clear features. In particular, the lack of identifiable lines or features suggests that the host galaxy is at z > 1.4.

3.2.4. Gemini NIR Spectroscopy

We obtained NIR spectroscopy with the Facility Near-Infrared Wide-field Imager and Multi-Object Spectrograph for Gemini (FLAMINGOS-2; Eikenberry et al. 2004), mounted on the 8 m Gemini-South telescope, using a fast-turnaround program (PI: Paterson; Program GS-2019A-FT-107). Using a JH/JH grism/filter setup with a central wavelength of 13900 Å, we obtained 30 × 120 s exposures for a total of 3600 s on source, roughly covering the wavelength range 9800–18000 Å and with a central R = 1177. We used standard procedures from the gemini package within IRAF to reduce and coadd the data. We performed wavelength calibration using Ar arc lamp spectra and flux calibration and telluric line corrections with the standard star HIP 56736 using the generalized IDL routine xtellcor_general (Vacca et al. 2003) from the Spextool package (Cushing et al. 2004). We extracted the error spectrum in the same manner as the Keck spectrum; the FLAMINGOS-2 spectrum, scaled to the YJH photometry, is shown in Figure 3.

3.2.5. Redshift Determination

We identify a single emission line in the FLAMINGOS-2 spectrum with an S/N = 13.5 at 13390.0 Å. No other line features are present with S/N ≳ 5. Given that this is the only clear line in the spectrum, we explore whether the line can be matched to one of four possibilities based on the predominant features in star-forming (SF) galaxy spectra ([O ii] λ3727, Hβ λ4861, [O iii] λ4959/λ5007, or Hα λ6563) given the photometric redshift of photo-$z={1.77}_{-0.17}^{+0.30}$ based on the eight-filter host photometry (discussed in Section 3.2.2) and the absence of any other features over 4400–18000 Å.

If this line is Hα, the Hβ and [O ii] lines would fall in regions of low error and should have been detected. Similarly, if this line is either of the [O iii] λ4959/λ5007 doublet, the Hβ and [O ii] lines should have been detected. In this case, the resulting redshifts would be z = 1.70 and 1.67, respectively. If the line is [O ii], the resulting redshift of z = 2.59 is not consistent with the photo-z (see Section 5), and the Hβ line should have been detected. Finally, if the line is Hβ, the resulting redshift is fully consistent with the photo-z. The location of the [O iii] doublet is in a region of strong telluric absorption, the location of [O ii] is in a region of high noise, and the location of Hα is not covered. Considering that the [O ii] line is not detected due to the high noise, we calculate an [O ii]/Hβ ratio based on an S/N of 5 for the [O ii] line and assuming a similar line width, on the order of ≲5. We thus determine that the most likely candidate for this line is Hβ, which would place GRB 181123B at z = 1.754 ± 0.001. We thus use this redshift for our subsequent analysis.

Adopting the standard synchrotron model for a relativistic blast wave expanding into a constant density medium (Sari et al. 1998; Granot & Sari 2002), we use the broadband afterglow observations to infer physical parameters, such as the electron power-law index (p), isotropic-equivalent kinetic energy (E_K,iso), circumburst density (n), and fraction of electrons in the electric (_e) and magnetic field (_B) using the standard relations from Granot & Sari (2002). The relation of the observed flux to the physical parameters requires knowledge of the location of the spectral break frequencies with respect to the observing bands, and hence the part of the spectrum each band falls on.

For the X-rays, we download the Swift/XRT data available from the Swift website (Evans et al. 2009). We make use of the late-time observations for our fits due to excess flux at early times. We use the temporal and spectral power-law indices from the X-rays (α_X and β_X, respectively), to determine if the X-ray band falls below or above the cooling frequency, ν_c, through the calculation of p. Fitting a power law to the XRT light curve at δt > 700 s using χ²-minimization, we obtain ${\alpha }_{X}=-{0.96}_{-0.11}^{+0.13}$. We use XSPEC (Arnaud 1996) to fit a two-absorption power law to the XRT spectrum over δt = 561–16,171 s. Fixing the Galactic hydrogen column density, N_H,Gal = 3.08 × 10²⁰ cm⁻² (Willingale et al. 2013), and z = 1.754, we find an intrinsic hydrogen column density of ${N}_{{\rm{H}},\mathrm{int}}={8.40}_{-8.40}^{+61.10}\times {10}^{20}$ cm⁻² and photon index ${{\rm{\Gamma }}}_{X}={2.392}_{-0.422}^{+0.133}$. We determine ${\beta }_{X}=-{1.39}_{-0.42}^{+0.13}$ from the definition β_X ≡ 1 − Γ_X. Using the median values for the spectral parameters, we calculate an unabsorbed X-ray flux at 2.3 hr of F_X = 2.07 ± 0.43 erg s⁻¹ cm⁻² (0.3–10 keV) or F_ν,X = 0.13 μJy at 1.7 keV.

We calculate the value of p from both indices for two scenarios: ν_m < ν_X < ν_c, where ν_m is the peak frequency of the synchrotron spectrum, and ν_X > ν_c, requiring the value of p to be in agreement for each scenario. We find that ν_X > ν_c, with a weighted mean and 1σ uncertainty of $\langle p\rangle$ = 2.01 ± 0.15. Since typical values of p range between 2 and 3 due to implications that arise from the distribution of the Lorentz factors (e.g., de Jager & Harding 1992), we employ p = 2.1 in subsequent analysis.

Since the X-rays lie above ν_c, the isotropic-equivalent kinetic energy does not depend on the circumburst density and thus can be used to constrain E_K,iso directly, assuming fixed values for _e and _B. Fixing z = 1.754, D_L = 13,457 Mpc, ν_X = 1.7 keV (the logarithmic center of the 0.3–10 keV XRT band), and _e = _B = 0.1 (see Zhang et al. 2015), we use F_ν,X = 0.13 μJy at 0.10 days to calculate

$$\begin{eqnarray}&&{E}_{{\rm{K}},\mathrm{iso},52}=0.14\pm 0.03,\end{eqnarray} \tag{ 1 }$$

where E_K,iso,52 is E_K,iso in units of 10⁵² erg. An additional constraint can be set in the limiting case that ν_c is at the lower edge of the X-ray band, ν_c,max = 0.3 keV, which places a lower limit on the combination of E_K,iso and n of

$$\begin{eqnarray}&&{n}^{2}{E}_{{\rm{K}},\mathrm{iso},52}\gt 5.99\times {10}^{-5},\end{eqnarray} \tag{ 2 }$$

where n is in units of cm⁻³. For the optical and NIR bands, we assume that ν_m < ν_opt/NIR < ν_c. From i = 25.10 ± 0.39 at 0.38 days, we calculate F_ν,opt = 0.33 ± 0.14 μJy, and obtain

$$\begin{eqnarray}&&{n}^{0.4}{E}_{{\rm{K}},\mathrm{iso},52}=0.03\pm 0.01,\end{eqnarray} \tag{ 3 }$$

and the NIR constraint of F_ν,NIR < 1.87 μJy at 0.43 days, gives us

$$\begin{eqnarray}&&{n}^{0.4}{E}_{{\rm{K}},\mathrm{iso},52}\lt 0.32.\end{eqnarray} \tag{ 4 }$$

Finally, we use the available 9 GHz ATCA upper limit at 0.52 days (Anderson et al. 2018) and make the assumption ν_sa < ν_radio < ν_m, where ν_sa is the self-absorption frequency, to calculate

$$\begin{eqnarray}&&{n}^{0.6}{E}_{{\rm{K}},\mathrm{iso},52}\lt 0.2.\end{eqnarray} \tag{ 5 }$$

For the case where ν_radio < ν_sa, we find no difference in the cumulative allowed parameter space, which is primarily determined by the optical and X-ray detections and the cooling frequency constraint.

The allowed E_K,iso–n parameter space for GRB 181123B, calculated from combining the probability distributions from the above relations, is shown in Figure 4. We calculate the medians for the parameters, ${E}_{{\rm{K}},\mathrm{iso},52}={0.13}_{-0.02}^{+0.02}$ erg and $n={0.04}_{-0.01}^{+0.02}$ cm⁻³, from the 1D probability distributions.²³ We also calculate the above constraints for _B = 0.01, finding ${E}_{{\rm{K}},\mathrm{iso},52}={0.14}_{-0.02}^{+0.02}$ erg and $n={1.10}_{-0.32}^{+0.87}$ cm⁻³ (Figure 4). Motivated by the low value of _B ≈ 10⁻⁴–10⁻² derived for GW170817's afterglow (e.g., Wu & MacFadyen 2018; Hajela et al. 2019), as well as those derived for Swift SGRBs (Santana et al. 2014; Zhang et al. 2015), we explore the possibility of a low value of _B and find that the allowed parameter space is completely ruled out for _B ≲ 10⁻³ (for _e = 0.1). In summary, we derive E_K,iso ≈ 0.13–0.14 × 10⁵² erg and n ≈ 0.04–1.10 cm⁻³ for GRB 181123B. Using the value of E_K,iso and E_γ,iso = 5.0 × 10⁵¹ erg,²⁴ we also calculate a gamma-ray efficiency of 0.78, just above the median of 0.57 found by Fong et al. (2015) and in line with the higher values found by Beniamini et al. (2016b) when no synchrotron self-Compton component is included.

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To characterize the host galaxy of GRB 181123B, we use Prospector (Johnson & Leja 2017; Leja et al. 2017), a stellar population modeling code that employs a library of flexible stellar population synthesis (FSPS) models (Conroy et al. 2009; Conroy & Gunn 2010) and determines the best-fit solution and posterior parameter distributions with Dynesty (Speagle 2020) through a nested sampling algorithm (Skilling 2004, 2006). We fit our photometric data to independently determine the redshift, z_photo, as well as the following stellar population properties: rest-frame attenuation in mags (A_V), stellar metallicity (Z), mass (M_⋆ in units of solar mass), star formation history (SFH), and age of the galaxy at the time of observation (t_age). During fits, these parameters can either be set free to determine the posterior distribution or fixed to a specific value and adopt priors that are uniform across the allowed parameter space within FSPS. For the SFH, we employ a parametric delayed-τ model, such that SFR(t) ∝ te^−t/τ, with τ as an additional free parameter. We then use t_age and τ to convert to a mass-weighted age of the galaxy, t_gal, by ${t}_{\mathrm{gal}}={t}_{\mathrm{age}}-\tfrac{{\int }_{0}^{{t}_{\mathrm{age}}}\mathrm{SFR}(t){tdt}}{{\int }_{0}^{{t}_{\mathrm{age}}}\mathrm{SFR}(t){dt}}$. We use a Chabrier initial mass function (Chabrier 2003) and a Milky Way extinction law (R = 3.1/E(B − V); Cardelli et al. 1989), turn nebular emission on to model an SF galaxy, and add additional attenuation toward the nebular regions to account for the fact that stars in SF regions will generally experience twice the attenuation of normal stars (Calzetti et al. 2000; Price et al. 2014).

First, we perform a fit to determine the photometric redshift, z_photo, using the grizYJHK photometry and 1σ uncertainties of GRB 181123B's host galaxy, along with the relevant transmission curves for each filter (obtained from the corresponding website of each instrument;^{25 ,26 ,27} Crampton et al. 2000; McLean et al. 2012; McLeod et al. 2012). We allow a range of z = 0.2–4 and Z, A_V, τ, t_age, and M_⋆ to be additional free parameters. We find a single-peaked posterior distribution for the redshift using the final 1085 iterations of the sampling once the solution has converged (Figure 5), with z_photo = ${1.77}_{-0.17}^{+0.30}$. This is consistent with the redshift determined from the single emission line identified in the NIR spectrum if the line is Hβ. There is a low-probability tail (<0.1) extending to high redshifts, but solutions beyond z ≈ 2.5 are inconsistent with the spectrum and photometric colors.

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Next, we fix the redshift to the spectroscopically determined value of z = 1.754, set the maximum value of t_age to be the age of the universe at that redshift (3.755 Gyr), and fit for the remaining stellar population properties. To self-consistently account for attenuation while calculating the SFR, we also include an additional synthetic photometric data point calculated from the spectrum by defining a box filter of 300 Å width centered on the Hβ emission line. We find final values of log(Z/Z_⊙) = $-{0.57}_{-0.49}^{+0.36}$, A_V = ${0.23}_{-0.10}^{+0.4}$ mag, log(τ) = ${0.34}_{-0.39}^{+0.41}$ Gyr, and log(M_⋆) = ${9.96}_{-0.16}^{+0.13}$ M_⊙. Calculating the mass-weighted age from the SFH gives ${t}_{\mathrm{gal}}={0.91}_{-0.45}^{+0.42}$ Gyr. The corner plot produced by Prospector, showing the parameter posterior distributions, is shown in Figure 6, while the observed photometry (including the synthetic photometric point around Hβ), overplotted with the model spectrum and photometry, as well as the observed spectrum, is shown in Figure 7. We note that there are well-known degeneracies between A_V, Z, and t_age (Conroy 2013). We explore these degeneracies by fixing metallicity and rest-frame attenuation to a range of values to see how they affect the parameter solutions. Except when A_V is set to the extreme cases of 0 or 1 mag, which produce an unconstrained t_age and a poor fit to the data, respectively, the remaining parameter solutions remain within a narrow range of values.

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Scaling by the total mass formed, we find SFR = ${10.31}_{-2.83}^{+5.42}$ M_⊙ yr⁻¹ and log(sSFR) = $-{8.95}_{-0.28}^{+0.26}$ yr⁻¹ from the spectral energy distribution (SED). In principle, we can also use the NIR emission line to determine an SFR by calculating an Hα flux using relations from Kennicutt (1998). This method, however, is subject to stellar absorption and dust attenuation and relies on typical Hβ/Hα line ratios, which can lead to deviation from the true SFR by several factors (Moustakas et al. 2006). Indeed, without correction, we determine SFR_Hβ = 4.91 ± 0.43 M_⊙ yr⁻¹, ∼2 times lower than the SED SFR. We therefore consider the SFR calculated from the SED to be a true representation of the SFR.

6.1. Comparing GRB 181123B to the SGRB Population

At z = 1.754, GRB 181123B is among the most distant SGRBs with a confirmed redshift to date. Comparing the γ-ray T₉₀, hardness ratio, and fluence to those of Swift SGRBs across z = 0.1–2.2 (Lien et al. 2016), GRB 181123B lies near the median value compared to the rest of the population, solidifying its membership in this class. The SGRB GRB 111117A originates from a host galaxy at a higher redshift of z = 2.211 and also has similar γ-ray properties to those of other SGRBs (Selsing et al. 2018). In contrast, the high-redshift GRB 090426A at z = 2.609 has a measured T₉₀ ∼ 1.3 s, which would ostensibly place it in the SGRB class, but it has spectral and energy properties that are otherwise more similar to those of long GRBs (Antonelli et al. 2009; Levesque et al. 2010), so the classification and progenitor of this burst are unclear and we do not include it in our discussion of secure SGRBs. Due to its featureless optical host galaxy spectrum (Berger et al. 2007), GRB 051210 is likely at z > 1.4 but does not have a secure redshift. Finally, GRB 160410A has an afterglow redshift of z = 1.717 (Selsing et al. 2019) and is most likely an SGRB with extended emission (Sakamoto et al. 2016). This makes GRB 181123B one of a few SGRBs with a confirmed redshift at z > 1.5 and the highest-redshift secure SGRB to date with an optical afterglow detection.

We next examine the inferred afterglow and host galaxy properties of GRB 181123B in the context of the SGRB population. In Table 2, we present several properties for GRB 181123B, as well as where the event falls in the SGRB population as a percentile; in this scheme, a value of 50% is the median value of that parameter. At the most basic level, the faint apparent magnitude of the optical afterglow (i ≈ 25.1 at ∼9.1 hr) puts GRB 181123B in the lower 30%. However, when corrected for the redshift of the burst, GRB 181123B's afterglow luminosity is slightly above the median of other SGRBs at similar rest-frame times.

Table 2.  Comparison of Properties of GRB 181123B

Properties	GRB 181123B	SGRBsa	GRB 111117A
z	1.754 ± 0.001	98%	2.211
T90 (s)	0.26 ± 0.04	33%	0.46 ± 0.05
Hardness	2.4 ± 0.6	78%	2.8 ± 0.5
Eγ,iso,52 (erg)	0.50	79%	0.86
EK,iso,52b (erg)	0.13–0.14	39%	0.14–0.23
nb (cm−3)	0.04–1.10	72%–95%	0.005–0.13
L (L*)	0.9	65%	1.2
log(M⋆) (M⊙)	${9.96}_{-0.16}^{+0.13}$	51%	9.9
Age (Gyr)	${0.91}_{-0.45}^{+0.42}$	44%	0.5c
Proj. offset (kpc)	5.08 ± 1.38	44%	10.52 ± 1.68

Notes. Values for GRB 111117A are taken from Lien et al. (2016) and Selsing et al. (2018), except for E_K,iso and n, which are derived in this work. The SGRB comparison samples are from Fong et al. (2015, 2017) and Nugent et al. (2020).

^aPercentile for GRB 181123B compared to SGRB population. ^bValues assuming _B = 0.01–0.1. ^cThis is the derived SSP age, so it can be taken as a lower limit on the true age of the stellar population (see Conroy 2013).

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The detection of both the X-ray and optical afterglows of GRB 181123B allows us to constrain the isotropic-equivalent kinetic energy scale and circumburst density to E_K,iso ≈ 1.3 × 10⁵¹ erg and n ≈ 0.04–1.1 cm⁻³. For a direct comparison to GRB 111117A, we determine the allowed E_K,iso−n parameter space in the same manner as described in Section 4 using the X-ray afterglow detection and optical upper limit (Margutti et al. 2012; Sakamoto et al. 2013) at z = 2.211, finding E_K,iso = (1.4–2.3) × 10⁵¹ erg and n = 0.0045–0.13 cm⁻³, where the range is set by _B = 0.01–0.1. While the kinetic energy scales for both bursts are similar to those of SGRBs, with a median value of ≈2 × 10⁵¹ erg (Fong et al. 2015), the inferred circumburst density of GRB 181123B is at the higher end of the population (Table 2). Recently, Wiggins et al. (2018) used cosmological simulations and population synthesis models for BNS mergers to predict the circum-merger densities as a function of redshift. Overall, they found that the fraction of mergers occurring in high-density environments increases with redshift, with the median density changing from ≈10⁻³ cm⁻³ at z < 0.5 to ≈0.1 cm⁻³ at z > 1. While the larger circumburst density of GRB 181123B seems to align with this predicted trend, we note that the other bursts with inferred densities of >0.1 cm⁻³ predominantly originate at low redshifts of z < 0.5. Moreover, the expectation is for high circumburst densities to correspond to smaller offsets (modulo projection effects), but the projected physical offset of GRB 181123B is 5.08 ± 1.38 kpc, just below the population median of ≈6 kpc (W. Fong et al. 2020, in preparation). While the number of high-redshift bursts is admittedly too small at present for robust comparisons, based on the current sample at z > 1.5, we do not find any appreciable trends between SGRB afterglow properties and redshift.

To understand how GRB 181123B fits in the context of SGRB hosts, we collect data for 34 SGRBs with known redshifts and measured apparent r-band magnitudes of their host galaxies (m_r) from the literature (Leibler & Berger 2010; Levesque et al. 2010; Fong et al. 2013, 2017; Troja et al. 2016; Selsing et al. 2018, 2019; Lamb et al. 2019) and our own observations. We compare the values of m_r to the characteristic luminosity, L*, across redshift using available galaxy luminosity functions (Brown et al. 2001; Wolf et al. 2003; Willmer et al. 2006; Reddy & Steidel 2009; Finkelstein et al. 2015). For each redshift, we take the value of L* in the band that corresponds to the observed r-band blueshifted to its rest frame at that redshift. We then interpolate across redshift to create smooth contours corresponding to L*, 0.1L*, and 0.01L*. A comparison of the SGRB host population to the evolving galaxy luminosity function is shown in Figure 8. At z ≲ 1, SGRB hosts span the luminosity range of ≈0.05–1L*, while at z ≳ 1.5, they are on the upper end of the luminosity function. This trend can be easily explained by observational bias, as only the more luminous galaxies will be detectable at higher redshifts. At L ≈ 0.9L*, the host galaxy of GRB 181123B is similar to that of GRB 111117A (1.2L*; Figure 8 and Selsing et al. 2018). In terms of stellar mass (10^9.96 M_⊙) and (mass-weighted) stellar population age (0.9 Gyr), the host properties of GRB 181123B are also typical of the SGRB population, which has median values of ≈10^9.96 M_⊙ and 1.07 Gyr (Nugent et al. 2020; Table 2). The redshift and stellar population age of GRB 181123B imply that 50% of its stellar mass was formed when the universe was ≈2.8 Gyr old, corresponding to z ∼ 2.3, around the peak of the cosmic SFR density (Madau & Dickinson 2014).

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Next, we compare the host galaxy of GRB 181123B to the expected properties for galaxies at z ≈ 1.5–2. The rest-frame U − V and V − J colors have long been used to distinguish quiescent from SF galaxies to z ∼ 2 (Williams et al. 2009). At z = 1.754, the rest-frame U − V is roughly equivalent to z − H or Y − H, which we calculate to be ≈1.2 and ≈1.1 mag, respectively, for GRB 181123B's host galaxy. This places the host galaxy in the region occupied by unobscured SF galaxies in the UVJ diagram for all possible V − J at 1.5 < z < 2.0 (Fumagalli et al. 2014). Using the values of SFR ≈ 10 M_⊙ yr⁻¹ and log(sSFR) ≈ −8.9 yr⁻¹ derived from the SED, we find that the host of GRB 181123B lies just below the SF main sequence (SFMS) for galaxies of similar mass at the same redshift (Whitaker et al. 2014; Fang et al. 2018), and we find a similar result for the host of GRB 111117A based on the Hα-derived SFR (Selsing et al. 2018).

6.2. SGRB Redshift Distribution and Implications for Delay Times

With the detection of GRB 181123B, there are only three Swift SGRBs with confirmed redshifts at z > 1.5 (and only seven SGRBs at z > 1). The apparent lack of SGRBs at high redshifts can be attributed to a combination of (i) Swift detector insensitivity at high redshifts (e.g., Guetta & Piran 2005; Behroozi et al. 2014), (ii) the difficulty of obtaining secure redshifts in the so-called "redshift desert" (1.4 < z < 2.5) in which all strong nebular emission lines are redshifted to >1 μm and Lyα is not yet accessible, and (iii) the intrinsic DTD, imprinted from an NS merger progenitor (Belczynski et al. 2006). In this section, we explore the constraints we can place from the observed SGRB redshift distribution on DTD models, with a focus on high-z (z > 1.5) events.

In the context of their binary merger progenitors, the true fraction of SGRBs that originate at z > 1.5 has implications for the merger timescale distribution, binary progenitor properties (e.g., initial separations, eccentricities; Selsing et al. 2019), and r-process element enrichment, which, in turn, can have effects on galaxy properties across redshift (O'Shaughnessy et al. 2010, 2017; Safarzadeh et al. 2019d; Simonetti et al. 2019). Of particular importance are the delay times, the time interval encompassing the stellar evolutionary and merger timescales, which impact our understanding of compact binary formation channels (isolated binary evolution versus dynamical assembly in globular clusters). The two main functional forms that have been widely considered in the literature are a power-law DTD (characterized by t^−η) and a lognormal DTD (characterized by mean delay time τ and width σ). The observed SGRB distribution peaks at z ≈ 0.5 with a steep drop-off toward higher redshifts (Berger 2014; Fong et al. 2017), ostensibly favoring a lognormal DTD with long delay times of several Gyr (Hao & Yuan 2013). This functional form could be explained by dynamical formation in globular clusters, in which the delay time strongly depends on the relaxation timescale of the cluster for NS binaries to assemble, which can be several Gyr (Spitzer 1987; Hopman et al. 2006; Kremer et al. 2019; Ye et al. 2019). On the other hand, a power-law DTD naturally arises for primordial binaries (i.e., systems that were born as a pair and have coevolved) given a power-law distribution of initial orbital separations and coalescence due to GW losses (Peters 1964; O'Shaughnessy et al. 2007; Dominik et al. 2012). Indeed, SN Ia studies have found that the observations are consistent with a DTD described by a power law with η = 1 (Totani et al. 2008; Maoz et al. 2012; Graur et al. 2014).

Thus far, studies of the Galactic BNS population (Vigna-Gómez et al. 2018), as well as SGRB host galaxy demographics, are in rough agreement with power-law DTDs with η ≳ 1 (Zheng & Ramirez-Ruiz 2007; Fong & Berger 2013). We note that some studies have found an excess of more rapid mergers, finding steeper DTDs than η = 1 (Beniamini & Piran 2019), but each provides fairly weak constraints. If we are indeed missing a population of high-z SGRBs, this would indicate overall shorter delay times and provide an additional constraint on the DTD. Some studies have also suggested a possible bimodal DTD distribution (Salvaterra et al. 2008), but this is in tension with more recent theoretical studies showing that dynamical assembly of NS–NS and NS–BH mergers can only contribute a small fraction to the overall merger rates (Belczynski et al. 2018; Ye et al. 2020).

The current observed SGRB redshift distribution comprises 43 events (updated from Fong et al. 2017) out of a total of 134 Swift SGRBs detected to date (Lien et al. 2016). This sample comprises all SGRBs with a secure host association (P_cc < 0.1), and a spectroscopic afterglow or host redshift, or a well-sampled photometric host redshift. This serves as an initial basis for comparison to predicted redshift distributions with varying underlying DTDs, star formation histories, and luminosity functions. Much work has been done in the literature to perform the convolution between these functions and predict the observed redshift distributions (Guetta & Piran 2005; Nakar et al. 2006; Hao & Yuan 2013; Wanderman & Piran 2015; Anand et al. 2018). From these works, we collect eight representative predicted distributions that cover the entire observed SGRB redshift range (z ∼ 0.1–2.5) and are not already ruled out by current observations. Four models describe lognormal DTDs with τ = 4 and 6 Gyr and widths of σ = 0.3 and 1 Gyr (Nakar et al. 2006; Hao & Yuan 2013). The remaining four models are power-law DTDs with η = 0.5–2 (Nakar et al. 2006; Jeong & Lee 2010; Hao & Yuan 2013). We note that models with the same DTD parameters (τ, σ, η) may give rise to slightly different distributions due to the underlying assumptions on the star formation histories, luminosity functions, and detector sensitivity, which can result in significant changes (Figure 9).

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First, we use two-sample Kolmogorov–Smirnov (K-S) statistics to test the null hypothesis that each model is consistent with being drawn from the same underlying distribution as the observed redshift distribution of 43 SGRBs. With the exception of the lognormal distribution with τ = 4 Gyr (σ = 0.3 Gyr) from Hao & Yuan (2013), which predicts a peak in the distribution at z ≈ 0.75, all of the lognormal distributions are consistent with being drawn from the same underying distribution as the observed data, and we cannot reject the null hypothesis (p = 0.45–0.62). On the other hand, all of the power-law distributions with η ≥ 1 result in p < 0.05 and thus are not consistent with being drawn from the same underlying distribution, while the power-law DTD characterized by η = 0.5 is consistent (p = 0.3). It is clear that without taking into account observational biases, distributions dominated by long delay times are preferred (Hao & Yuan 2013).

This analysis, however, neglects the inherent biases in the observed SGRB redshift distribution. Thus, we explore the fraction of Swift SGRBs that could be originating at high-z among the current population. Previous studies have found that ≈33%–70% of SGRBs could be missing at redshifts of z > 0.7–1 (Berger et al. 2007; Selsing et al. 2018). Over 2004–2020, Swift detected 134 SGRBs (including 13 with extended emission; Lien et al. 2016), and 43 have secure redshift determinations (P_cc < 0.1; 31%). In the large majority of cases, the determination of a redshift depends on an association with a host galaxy, which requires precise positional information from the detection of an X-ray or optical afterglow (≲few arcsec precision). In the case of an afterglow detection, the lack of redshift can be attributed to the lack of a coincident host galaxy due to significant kicks and merger timescales, leaving large displacements between the burst and host galaxy (Berger 2010; Fong & Berger 2013; Tunnicliffe et al. 2014); offsets of ≳10 kpc are predicted to comprise as much as 40%–50% of the total population (Wiggins et al. 2018).²⁸ A faint host galaxy may also escape detection due to a low-luminosity or high-z origin (O'Connor et al. 2020). In this case, an apparently faint galaxy is more likely to originate at lower redshifts due to the increase in the faint-end slope of the galaxy luminosity function (Blanton et al. 2005; Parsa et al. 2016), although Figure 8 shows that SGRB hosts overall are drawn from the brighter end of the galaxy luminosity function. In total, the number of SGRBs that lack redshift information is 91. If we assume that 50% of these events arise at z > 1, this translates to ≈34% (46 events) of the current Swift SGRB population. If we take into account the 34 bursts that were subject to constraints that prevent the detection of an afterglow and subsequent redshift determination, such as satellite observing constraints, poor sight lines, or high Galactic extinction, and follow the same arguments as above, this results in ≈28% (28 bursts) of the current population that was not subject to significant observing constraints. These numbers can be directly compared to expectations from DTDs.

We perform an exercise to explore how many SGRBs need to be recovered at high redshifts before a given model can be ruled out ("recovered redshifts"). We concentrate here on high redshifts given that these have comparatively greater discriminating power between DTD models than low-redshift events. To convert each of the eight continuous model distributions into a representative redshift distribution, we draw 1000 events from each model and then scale to 134 events (Figure 9). For each model, we determine the fraction of SGRBs that could originate at z > 1.5 as predicted by the model. To account for counting statistics, we draw 134 bursts from each model distribution 1000 times and determine the 95% confidence region on the high-z fraction. We then compute the missing fraction demanded by each model as a function of the number of additional recovered redshifts at 1.5 < z < 3 (k), taking into account that there are already three known SGRBs at z > 1.5, so the observed population would be 3 + k. In Figure 9, when the missing fraction goes to zero, the model can be ruled out to 95% confidence.

We find that lognormal models with small widths of σ = 0.3 Gyr can be ruled out for as few as k ≲ 1–5 recovered redshifts, while the wider width, the σ = 1 Gyr model, could still accommodate k = 13 additional events recovered at z > 1.5. However, the shape of the low-redshift distribution is not supported by this model (Figure 9). For the power-law distributions, we find that a significantly larger number of high-z bursts are allowed before the models are ruled out to 95% confidence (k ≈ 19–42 recovered redshifts), although models with η = 0.5 and 2 significantly under- or overpredict the z < 1 population. We find similar results if we perform the same analysis with a population of 100 events (representing the Swift SGRB population with no observing constraints). Performing a K-S test on each of the new distributions assuming 100 events shows agreement with the 134 event results. With the addition of high-z bursts to the observations, the data quickly favor the power-law distribution with η = 1, and all lognormal distributions are ruled out by the null hypothesis. Our analysis shows that the SGRB population is more consistent with power-law DTD models with η = 1, and the recovery of only a few high-z bursts, together with the shape of the low-z population, will help to solidify the model parameters. From the η = 1 power-law model, we find that the expected number of SGRBs that originate at z > 1 is ≈45 events (33% of the current population). Compared to our estimate that ≈34% of Swift SGRBs originate at z > 1, this is another line of support for the η = 1 power-law model and thus a primordial NS binary formation channel.

In SNe Ia studies, similar work has been done to constrain the "prompt" fraction. Indeed, Rodney et al. (2014) found that observations suggest a prompt fraction of up to 50% (defined as events with delay times of <500 Myr), with the results fully consistent with a power-law DTD with η = 1. For BNS mergers, most recent simulations require a prompt channel to explain r-process enrichment in Milky Way stars and ultrafaint dwarf galaxies (Matteucci et al. 2014; Beniamini et al. 2016a; Safarzadeh et al. 2019c; Simonetti et al. 2019). A reliable estimate of the prompt SGRB fraction would require a careful assessment of observational biases, the true SGRB redshift distribution, and stellar population ages as a proxy for the progenitor age distribution. Nevertheless, additional future detections of SGRBs at z ≈ 2 and beyond might help to quantify the true prompt fraction of SGRBs.

We have presented the discovery of the optical afterglow and host galaxy of GRB 181123B at z = 1.754, contributing to a small but growing population of SGRBs at high redshifts. These results are based on a rapid-response and late-time follow-up campaign with Gemini, Keck, and the MMT. Our main conclusions are as follows.

• 1.  
  After GRB 111117A (z = 2.211), GRB 181123B is the second most distant bona fide SGRB with a confirmed redshift measurement. It is the most distant SGRB to date with an optical afterglow detection.
• 2.  
  The host galaxy of GRB 181123B is characterized by a stellar mass of ≈9.1 × 10⁹ M_⊙, luminosity of ≈0.9L*, and mass-weighted age of ≈0.9 Gyr. These are comparable to the median values of the SGRB host population across redshift.
• 3.  
  Compared to the SFMS of galaxies at 1.5 < z < 2.0, GRB 181123B lies just or significantly below this sequence and is thus forming stars at a lower rate than most SF galaxies of similar mass, indicating that it is moving toward quiescence.
• 4.  
  The current redshift distribution comprises 43 events and is consistent with most lognormal distributions with moderate delay times (≈4–6 Gyr). An analysis of the full Swift sample of 134 events, taking into account the difficulty of confirming high-z SGRBs, demonstrates that lognormal DTD models are overall disfavored. In particular, models with moderate delay times of ≈4–6 Gyr and small widths of σ = 0.3 Gyr can be ruled out to 95% confidence with an additional ≲1–5 Swift SGRBs recovered at z > 1.5. Lognormal models with wider widths of σ = 1 Gyr are less favored, given the lack of low-z SGRBs.
• 5.  
  Power-law DTDs with an index around unity are more consistent with the data and can accommodate ≈30 recovered SGRBs at z > 1.5 (22% of the current population). For this model, ≈45 of the remaining SGRBs are expected to have z > 1 (33% of the current population). This is consistent with our estimates of the observed fraction of SGRBs originating at z > 1 of ≈34% and with SGRBs originating from primordial NS binaries.

In order to properly constrain the DTD and probe the underlying formation channels of SGRBs and BNS mergers, it is important to uncover high-z bursts (z > 1.5). However, high-z bursts provide additional challenges for follow-up due to the additional observations needed and the resources available. The determination of the redshift of GRB 181123B required 6–10 m class telescopes and highlights the sheer difficulty of obtaining redshifts for host galaxies at z > 1.5, where the main spectral features are redshifted to NIR wavelengths with no major features at optical wavelengths. Moreover, even if SGRBs are drawn from the brighter end of the galaxy luminosity function, the host magnitudes are still J ≈ 22–23 mag. Dedicated efforts to characterize high-z candidates among the current population with state-of-the-art NIR instruments, as well as the planned James Webb Space Telescope and ELTs, will help to solidify the true high-z fraction among the current population. In the era of GW multimessenger astronomy, BNS mergers detected via GWs may also help constrain the DTD through studies of their host galaxies and connecting the redshift distributions of BNS mergers to those of SGRBs (e.g., Safarzadeh & Berger 2019; Safarzadeh et al. 2019b, 2019a).

We acknowledge Sarah Wellons, Allison Strom, and David Sand for helpful discussions that aided this work and Mansi Kasliwal for facilitating Keck observations. The Fong Group at Northwestern acknowledges support by the National Science Foundation under grant Nos. AST-1814782 and AST-1909358. This work was also supported in part by the National Aeronautics and Space Administration through grant HST-GO-15606.001-A from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555, and Chandra Award No. DD7-18095X, issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. M.N. is supported by a Royal Astronomical Society Research Fellowship. A.J.L has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No. 725246, TEDE; PI: Levan). A.A.M. is funded by the Large Synoptic Survey Telescope Corporation, the Brinson Foundation, and the Moore Foundation in support of the LSSTC Data Science Fellowship Program; he also receives support as a CIERA Fellow from the CIERA Postdoctoral Fellowship Program (Center for Interdisciplinary Exploration and Research in Astrophysics, Northwestern University). J.L. is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1701487. K.D.A. acknowledges support provided by NASA through the NASA Hubble Fellowship grant HST-HF2-51403.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555.

Based on observations obtained at the international Gemini Observatory (PIs: Paterson, Fong; Program IDs GS-2018B-Q-112, GN-2018B-Q-117, GS-2019A-FT-107), a program of NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation on behalf of the Gemini Observatory partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea).

W. M. Keck Observatory and MMT Observatory access was supported by Northwestern University and the Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA). Some of the data presented herein were obtained at the W. M. Keck Observatory (PIs: Miller, Fong, Paterson; Programs 2018B_NW254, 2018B_NW249, 2019A_O329), which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. Observations reported here were obtained at the MMT Observatory, a joint facility of the University of Arizona and the Smithsonian Institution (PI: Fong; Programs 2018C-UAO-G4, 2019A-UAO-G7, 2020A-UAO-G212-20A).

This research was supported in part through the computational resources and staff contributions provided for the Quest high-performance computing facility at Northwestern University, which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology.

This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester.

Facilities: Swift (XRT and UVOT) - Swift Gamma-Ray Burst Mission, Gemini-North (GMOS) - , Gemini-South (GMOS - , FLAMINGOS-2) - , Keck:I (MOSFIRE) - , Keck:II (DEIMOS) - , MMT (MMIRS). -