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A z=5.34 Galaxy Pair in the Hubble Deep Field

We present spectrograms of the faint V-drop (V(606) = 28.1, I(814) = 25.6) galaxy pair HDF3-951.1 and HDF3-951.2 obtained at the Keck II Telescope. Fernandez-Soto, Lanzetta,&Yahil (1998) derive a photometric redshift of z(ph) = 5.28 (+0.34,-0.41; 2 sigma) for these galaxies; our integrated spectrograms show a large and abrupt discontinuity near 7710 (+- 5) Angstroms. This break is almost certainly due to the Lyman alpha forest as its amplitude (1 - fnu(short) / fnu(long)>0.87; 95% confidence limit) exceeds any discontinuities observed in stellar or galaxian rest-frame optical spectra. The resulting absorption-break redshift is z=5.34 (+- 0.01). Optical/near-IR photometry from the HDF yields an exceptionally red (V(606)-I(814)) color, consistent with this large break. A more accurate measure of the continuum depression blueward of Lyman alpha utilizing the imaging photometry yields D(A) = 0.88. The system as a whole is slightly brighter than L*(1500) relative to the z~3 Lyman break population and the total star formation rate inferred from the UV continuum is ~22 h(50)^-2 M(sun) yr^-1 (q(0) = 0.5) assuming the absence of dust extinction. The two individual galaxies are quite small (size scales<1 h(50)^-1 kpc). Thus these galaxies superficially resemble the Pascarelle etal (1996) ``building blocks''; if they comprise a gravitationally bound system, the pair will likely merge in a time scale ~100 Myr.


Introduction
We are presently targeting photometrically-selected faint galaxies for spectroscopic study at the Keck Telescopes with the goal of measuring redshifts and star-formation rates at early cosmic epochs. Selecting high-redshift galaxies based upon their continuum properties (c.f., Weymann et al. 1998) is important and complements work on emission line-selected galaxies at z ∼ > 4.5 found serendipitously (Dey et al. 1998) and from narrow-band imaging Hu, Cowie, & McMahon 1998). Studying galaxies at these high redshifts has important implications for tracing the formation of galaxies and large scale structure, mapping the history of star formation, and understanding the chemical history of the Universe.
The Hubble Deep Field (hereinafter HDF; Williams et al. 1996) has galvanized a renewed effort at estimating photometric redshifts (e.g., Lanzetta, Yahil, & Fernández-Soto 1996;Sawicki, Lin, & Yee 1997; see also Hogg et al. 1998). The extremely deep multiband integrations through the crisp eye of the Hubble Space Telescope (HST) supplemented by several deep campaigns across the electromagnetic spectrum (e.g., at radio, sub-millimeter, far-infrared, and near-infrared wavelengths - Fomalont et al. 1997;Hughes et al. 1998;Rowan-Robinson et al. 1997;Hogg et al. 1997;Eisenhardt et al. 1996; Thompson et al. 1998) -are an ideal data set with which to estimate redshifts based upon broad-band colors. High-redshift targets are robustly selected based upon the redshifted Lyman break at (1 + z) × 912Å and the redshifted Lyα discontinuity at (1 + z) × 1216Å, causing the galaxies to effectively disappear, or "drop out", at short wavelengths. U-band dropouts, corresponding to z ∼ 3, have been systematically studied by several groups (c.f., Steidel et al. 1996a;Lowenthal et al. 1997;Spinrad et al. 1998;Bunker et al. 1998). B-band dropouts, corresponding to z ∼ 4, and V -band dropouts, corresponding to z ∼ 5, are beginning to be addressed (Dickinson 1998;Weymann et al. 1998;Dey et al. 1998b). Our present list of potential z > 4 candidates (B-and V -dropouts) includes six galaxies with I 814 < 26.5 in the HDF (Fernández-Soto, Lanzetta, & Yahil 1998; AB scale used throughout 3 ). Their spectroscopic study, even with the large aperture of the Keck Telescopes and dark sky of Mauna Kea, is clearly a technical challenge. Weymann et al. 's (1998) confirmation of a galaxy at z = 5.60 illustrates that the V -drop technique works. A systematic survey, however, is necessary to assess that this population is not contaminated by lower-redshift interlopers such as galaxies with extremely high equivalent width emission lines (e.g., [O II]λ3727) in the I 814 filter. We describe the observations of one V -drop system, HDF 3-951.0. Our data imply a redshift of z = 5.34 for this system, one of the highest redshifts yet measured and among the first systematically pre-selected galaxies at z > 5.

Observations
HDF 3-951.0 is a faint galaxy "pair", comprised of HDF 3-951.1 and HDF 3-951.2, near the edge of the WF3 CCD of the HDF. In Fig. 1 we present F606W (V 606 ) and F814W (I 814 ) images of the galaxy. Extant photometry of this system is assembled in Table 1. Clearly the most outstanding photometric features of the composite (HDF 3-951.0) energy distribution are the non-detection at U 300 and B 450 , the marginal detection in V 606 , and the very red color in V 606 −I 814 . The energy distribution appears to flatten at longer wavelengths with I 814 − K ∼ < 2.0. These colors qualitatively suggest a high-redshift, star-forming system with the Lyα forest attenuating the spectrum below I 814 and OB stars dominating the rest-frame UV past Lyα. A more detailed technique employing template spectra and maximum likelihood analysis yields a photometric redshift of z ph = 5.28 +0.34 −0.41 (2σ) for this system and z = 5.72 +0.33 −0.34 (2σ) for HDF 3-951.1 alone (the brighter component; object #3 in Fernández-Soto, Lanzetta, & Yahil 1998; see also Lanzetta, Yahil, & Fernández-Soto 1996). Comparisons between photometric and spectroscopic redshift determinations show that the former is typically robust to ∆z ≈ 0.34 for objects with I 814 ∼ 25.5 and z > 3 (Fernández-Soto, Lanzetta, & Yahil 1998).
However, an accurate determination of the redshift requires deep spectroscopy, and so we observed the HDF during three observing runs in 1998 using the spectroscopic mode of the Low Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) at the Cassegrain focus of the Keck II Telescope. Only the data collected on UT 1998 February 19 were of high quality; UT 1998 January 20 suffered from poor seeing and high cirrus, while integrations on UT 1998 March 28 & 29 were plagued by poor seeing. All observations employed milled slitmasks constructed to allow simultaneous observations of seven B-and V -dropout galaxies. The 1. ′′ 5 wide slitlets were typically 20 ′′ long, allowing sufficient slit length for sky subtraction at the expense of a diminished number of targets. Slitmask observations were made at a position angle of 102.6 • (east of north) with the 400 l/mm grating (λ blaze ≈ 8500 A; ∆λ FWHM ≈ 11Å) sampling the wavelength range λλ5940 − 9720Å. Small spatial shifts (≈ 4 ′′ ) were performed between each ≈ 1800s exposure to facilitate removal of fringing in the near-IR regions of the spectrograms.
All data reductions were performed using the IRAF package and followed standard slit spectroscopy procedures. Wavelength calibration was performed using a NeAr lamp, employing telluric lines to adjust the zero-point. Flux calibration was performed using observations of G191B2B, Feige 34, HZ 44, and Wolf 1346 (Massey et al. 1988;Massey & Gronwall 1990) and accurate spectrophotometry was verified against the HDF photometry by convolving the spectra of HDF 3-951.0 and a brighter galaxy which serendipitously lay along one of the slitlets (HDF 3-493.0 -I 814 = 21.74, z = 0.848) with the F814W filter response function. HDF 3-951.0 was detected during all three observing runs. However, the February data (seeing ∼ 0. ′′ 7, photometric), comprising four integrations totaling 6900s, is of much higher signal-to-noise ratio; our final spectrum (Fig. 2) is composed from the February data alone.

Redshift Determination
Our final spectrogram of the unresolved pair of faint galaxies (Fig. 2) yields a fairly noisy but robust result: above 7720Å there is a roughly flat continuum (in f ν ) with a mean flux near 0.4µJy. Almost no light is detected below 7700Å (f ν < 0.05µJy), and an accordingly large and abrupt discontinuity exists at 7710 ± 5Å. An accurate measurement of the discontinuity wavelength is made difficult by the faint magnitudes considered and the challenges of sky subtraction in the 7700Å OH sky emission band. We note that the faintness and 0. ′′ 61 separation of HDF 3-951.1 and HDF 3-951.2 makes separate spectroscopy with ground-based instrumentation exceedingly difficult. Their unusual, yet similar colors, however, support the hypothesis that they lie at the same redshift. Disparate redshifts would lead to a dilution of the 7710Å break amplitude. The spectrum is also obviously inconsistent with a single high-equivalent width emission line dominating the I 814 flux and causing the extremely red V 606 − I 814 color. Our spectrophotometry yields a 2σ limit to the equivent width of an unresolved emission line W obs λ < 40Å for λ > 7800Å. If the red V 606 − I 814 color were due to an extremely strong emission line in I 814 , the required equivalent width would be at least W obs λ > 200Å, for a constant slope continuum fit to the V 606 and K upper limit magnitudes.
Discontinuities of this amplitude ( ∼ > 8) are unprecedented in optical spectra of stars and galaxies. Averaging the spectrum in 10 pixel (≈ 18Å) bins and considering Poissonian counting statistics, we find the average flux density above the discontinuity is f long ν (λλ8000 − 9000Å) = 0.432 ± 0.052µJy, while the average flux density below the discontinuity is f short ν (λλ6500 − 7500Å) = −0.036 ± 0.038µJy, i.e., consistent with no observable flux. There is, at this ≈ 28 magnitude level, a small systematic problem. The 95% (99%) confidence limit to the amplitude of this continuum depression, calculated from Monte Carlo simulations of the flux densities with the constraint that f ν > 0, is then 1 − f short ν /f long ν > 0.87 (0.82). In order of decreasing wavelength, discontinuities are commonly observed in UV/optical spectra of galaxies at rest wavelengths of 4000Å (D(4000)), 2900Å (B(2900)), 2640Å (B(2640)), 1216Å (Lyα), and 912Å (the Lyman limit). The hydrogen discontinuities derive from associated and foreground absorption and thus have no theoretical maximum. The longer rest-wavelength discontinuities derive from metal absorption in the stars and galaxies, and are thus dependent upon the age and metallicity of the galaxy (c.f., Fanelli et al. 1992;Spinrad et al. 1997). The largest measured values of D(4000) in lower-redshift, early-type galaxies are ≈ 2.6 (Dressler & Gunn 1990;Hamilton 1985), corresponding to 1 − f short ν /f long ν ≈ 0.62, while IUE spectra of main-sequence stars exhibit B(2900) ∼ < 3 and B(2640) ∼ < 3 (Spinrad et al. 1997), corresponding to 1 − f short ν /f long ν ∼ < 0.67. Therefore, we can safely rule out the low-redshift interpretations of the spectrum of HDF 3-951.0. The 7710Å break is also unlikely to be associated with a Lyman limit at z = 7.45; at that redshift, the Lyα forest would likely obliterate the rest-frame 912 − 1216Å spectrum. Lyα itself would be at 1.03µm, which is a very challenging wavelength for current CCD detectors. Identifying the break with Lyα is the lowest redshift and most likely interpretation under these circumstances.
Large breaks are occasionally seen in exotic objects as well. For instance, the iron low-ionization broad absorption line quasar (Fe Lo-BAL) FIRST J155633.8+351758 (Becker et al. 1997) has a discontinuity with 1 − f short ν /f long ν ≈ 0.85 around 2800Å. However, this object belongs to an exceedingly rare type of quasar, a classification which we can rule out for HDF 3-951.0 due to its resolved morphology. Furthermore, radio-loud broad absorption line quasars tend to have very red optical/near-IR colors (Hall et al. 1997).
We therefore associate the break with the Lyα forest, implying a redshift z = 5.34±0.01. The systematics of Lyα absorption might provide a systematic redward bias of ∆z ≈ 0.01 -in high-redshift galaxies, associated and foreground absorption generally displaces Lyα emission lines redward of their host galaxy systematic velocity by up to several hundred km s −1 . In fact, this mechanism also imprints an asymmetry onto the Lyα emission line, when present, thus providing a powerful discriminant between high-redshift Lyα and low-redshift [O II]λ3727 (see Dey et al. 1998a). The sharpness of the discontinuity and the flatness of the longer-wavelength spectrogram (in f ν ) are further arguments for identifying the break with the Lyα forest onset. For the remainder of this paper we adopt z = 5.34 for the redshift of the faint galaxy pair HDF 3-951.0.

Discussion
Our deep spectroscopy confirming the high-redshift of HDF 3-951.0, as well as Weymann et al. 's (1998) confirmation of HDF 4-473.0 at z = 5.60, illustrates that the photometric redshift technique, and, in particular, V -drop selection, is a robust method for selecting and studying the distant Universe. We now derive some basic physical properties of HDF 3-951.0, consonant with its faint magnitude.
If the UV continuum is dominated by light from young, hot stars, the star-formation rate (Ṁ) may be derived from the UV flux at λ 0 ∼ > 1240Å. Assuming the continuum emission from HDF 3-951.0 is unreddened and has a spectral slope of f ν ∝ λ 0 , consistent with the observations, we derive L 1500 = 22.9 × 10 40 h −2 50 erg s −1Å−1 and M 1500 = −21.5 AB mag for HDF 3-951.0 based upon the flux density between 8000 and 9000Å (see Table 1). Madau, Pozzetti, & Dickinson (1998) calculateṀ ≈ 10 −40 L 1500 M ⊙ yr −1 for L 1500 measured in units of erg s −1Å−1 and a > 100 Myr old population with a Salpeter IMF (0.1 < M < 125 M ⊙ ). This is roughly consistent with the relation derived from the Leitherer & Heckman (1995) models for a different IMF and much younger ages of < 10 Myr. These conversions are meant to be illustrative rather than definitive; they depend upon the assumed star-formation history, IMF, metallicity, and age. The lower limit on the inferred star-formation rate for HDF 3-951.0 is thus ≈ 22 h −2 50 M ⊙ yr −1 , assuming the absence of dust absorption. Dickinson (1998) finds that the ultraviolet luminosity function of Lyman-break galaxies at z ≈ 3 is well-modeled by a Schechter luminosity function of characteristic absolute magnitude M * 1500 ≈ −21 AB mag. This implies that the HDF 3-951.0 galaxies are individually sub-luminous, but slightly brighter than L * 1500 when considered as a single system uncorrected for extinction.
The star-formation rates may also be determined for the galaxy pair individually utilizing the imaging photometry, without reference to the spectrophotometry. Assuming a Heaviside function spectrum with f ν = 0 below 7710Å, and f ν ∝ λ 0 redward of 7710Å, the I 814 magnitudes may be used to calculate an upper limit on the flux density redward of Lyα. This then yields F 1500 and, with the above prescription, the inferred star formation rate (see Table 1). We findṀ = 13h −2 50 M ⊙ yr −1 for HDF 3-951.1 andṀ = 6h −2 50 M ⊙ yr −1 for HDF 3-951.2.
The flat red end of the spectrum of HDF 3-951.0 is similar to spectra of z ∼ 3 Lyman break galaxies (c.f., Steidel et al. 1996a) -systems which are well-represented by an OB stellar population with little dust. Deep Keck/LRIS spectroscopy of some of the brighter z ∼ 3 Lyman break population suggests that galaxies with Lyα in emission are generally flatter in f ν at λλ1220 − 1700Å, while those galaxies with Lyα in absorption are generally redder at these wavelengths . From a study of vacuum-UV IUE spectra of local starburst galaxies, Heckman et al. (1998) find that metal-rich starbursts are redder and more heavily extinguished (have larger values of L IR /L UV ), have stronger rest-frame UV absorption lines, and occur in more massive and brighter host galaxies. Similarly, the brightest Lyman break galaxies tend not to have Lyα in emission (Steidel, private communication), possibly a result of the galaxies lying in deeper potential wells and thus being more able to retain gas and dust which scatter and absorb the Lyα photons and redden the λ > 1220Å continuum. In this scenario, the apparent flatness of our HDF 3-951.0 spectrum at λ 0 > 1300Å is inconsistent with the lack of a measurable Lyα emission line. However, relatively small column densities of neutral gas with even very small dust content can destroy Lyα emission if this gas is static with respect to the ionized region where Lyα photons originate (c.f., Kunth et al. 1998).
HDF 3-951.0 is potentially reddened by foreground and associated dust, consistent with the lack of Lyα emission; our ground-based limits on the near-IR magnitude of the system constrains E B−V ∼ < 0.3 (for a dust-free Heaviside spectrum subject to extinction by a foreground screen of dust following the extinction law of Cardelli, Clayton, & Mathis 1989). This level of extinction would imply intrinsic star formation rates ∼ 45% higher than the values quoted above. A real measurement of the dustiness of the galaxy pair must await deep near-IR images of the field, as have recently been obtained with NICMOS on the HST.
Due to the sub-structure of its core, HDF 3-951.1 is not fit well by either a de Vaucouleurs r 1/4 law nor an exponential surface brightness profile. The exponential disk appears to dominate in a two-component model, and the scale length is 0. ′′ 23, equivalent to r disk = 1.3 (2.3) h −1 50 kpc. The elongation is b/a = 1.2. The fainter HDF 3-951.2 is well-fit by an exponential disk profile, with a scale length of 0. ′′ 12, corresponding to 0.65 (1.2) h −1 50 kpc, and is almost circular (b/a = 1.1). As with the z ≈ 3 population, we note that HDF 3-951 is significantly more compact at rest-frame UV wavelengths compared to local disk galaxies, which have typical scale lengths of ∼ 5 kpc at optical wavelengths (Freeman 1970).
The angular separation of 0. ′′ 61 projects to 3.4 (6.2) h −1 50 kpc for q 0 = 0.5 (0.1), implying that HDF 3-951.0 is a pair of sub-luminous systems of modest projected separation. What can we say about the evolutionary fate of HDF 3-951.0? Given the small physical sizes and projected separation, in all likelihood HDF 3-951.1 and HDF 3-951.2 will merge into a single galaxy. Assuming a relative velocity of ∆v = 200 km s −1 and a physical separation equal to the projected ≈ 5 kpc, the crossing time is ≈ 25 Myr. Thus we estimate the merger time scale for HDF 3-951.1 and HDF 3-951.2 is a few crossing times (c.f., Barnes & Hernquist 1996), or ∼ 100 Myr. Indeed, we suggest that HDF 3-951.1 and HDF 3-951.2 are already in the process of merging; we are perhaps witnessing the galaxies in a post-collision state, with the luminosity enhanced by merger-induced star formation. Studies of low-redshift merging systems find enhanced rates of star formation (Sanders et al. 1988), consistent with the apparently OB star-dominated spectrum of HDF 3-951.0.
We note that our I 814 images sample the rest-frame UV. Even in present-day galaxies, UV-emitting regions in galaxies are typically small. Alternatively, two regions of active star-formation within ≈ 5 kpc of each other may well be star-forming knots within the same galaxy. Longer-wavelength imaging will help resolve this question. Indeed, preliminary reductions of NICMOS observations of the HDF suggest that these objects remain separate in F160W images (rest-frame ∼ 2500Å; Dickinson, private communication). We note, finally, that the size and luminosity of HDF 3-951.0 suggest it to be a more distant version of the z ≈ 2.4 galaxies discussed by Pascarelle et al. (1996) which have typical half-light radii of 0. ′′ 1 − 0. ′′ 2.
What are the implications of the large continuum discontinuities in the Lyα region? How reliable is the nomimal factor of 10 at 95% confidence level we suggest, and how does it propagate to the D A parameter (Oke & Korycansky 1982, Madau 1995)? The largest discontinuities previously measured in quasar spectra at z ∼ > 4.5 are approximately a factor of 4 (see Fig. 4). Our determination of the f ν break amplitude for HDF 3-951.0 is made difficult since the composite galaxy spectrum is very faint at λλ6500 − 7700Å. Oke & Korycansky (1982) From the February 1998 data, we measure average flux densities of f ν (λλ1050 − 1170) = −0.029 ± 0.045µJy and f ν (λλ1250 − 1370) = 0.405 ± 0.055µJy. The implied 95% (99%) confidence limit to D A is then D A > 0.82 (0.75). The 1998 January and March data qualitatively support our large amplitude break, but quantitatively do not aid our numerical evaluation of it. Larger values are possible and future, more sensitive observations will determine a more precise value of D A for this system.
Alternatively, we can produce a photometric estimate of D A utilizing the Williams et al. (1996) broad band colors, the HST/WFPC2 filter curves, and the plausible assumption (born out by our spectra to date) that the f ν flux distributions above and below Lyα are flat. We assume a two-step spectral energy distribution with zero flux below the Lyman limit, f − ν between the Lyman limit and Lyα, and f + ν redwards of Lyα. For f ± ν ∝ λ 0 , 54% of the F606W flux comes from λ > 5782Å (the Lyman limit at z = 5.34) and 48% of the F814W flux comes from λ > 7710Å (Lyα at z = 5.34). For the observed magnitudes of HDF 3-951.0, this implies f − ν = 0.04µJy and f + ν = 0.33µJy. The resultant "photometric Lyαdiscontinuity", with V − I = 2.50 is D phot A = 0.88. This agrees with the break amplitude derived from the Keck spectrogram and is much higher than previously reported values of D A (also see Dey et al. 1998). In Fig. 4 we present recent measurements of D A from spectra of quasars and high-redshift galaxies, where HDF 3-951.0 is indicated by the more robust photometric measurement. The Weymann et al. (1998) points utilize their photometry, corrected for the Lyα emission line flux of 1.0 × 10 −17 erg cm −2 s −1 , and a f ν ∝ λ β spectrum fit to the NICMOS near-IR brightnesses (top point). The lower Weymann et al. (1998) point utilizes an f ν ∝ λ −0.4 spectrum, corresponding to their best-fit semi-empirical model.
Our concern about the break amplitude arises from its strength: Madau's (1995) theoretical estimate of the contribution of the Lyα forest to D A is only ≈ 0.79 at z = 5.34 and ≈ 0.83 at z = 5.60. This extrapolation assumes a distribution of high and low optical depth foreground Lyα clouds causing Lyman series absorption in the spectrum of a distant quasar or galaxy. The scatter around the Madau curve is substantial, even at lower redshifts, so the high values of D A at z > 5 may simply reflect the usual scatter observed in that parameter. However, at large enough redshift our line of sight must penetrate the end stages of reionization (c.f., Loeb 1998;Miralda-Escudé & Rees 1997) where a smooth distribution of neutral hydrogen gas will cause an additional Gunn-Peterson H I opacity at λ < 1216Å. Whether this starts at z = 5 or z ∼ > 10 remains an intriguing question. Are we seeing the first hints of the Gunn-Peterson trough in these distant systems? If we see enhanced (Gunn-Peterson) absorption short-ward of Lyα (corresponding to z ∼ 5) relative to the expected thickening of the Lyα forest, one might begin to further exploit spectrophotometry of these distant galaxies in a novel and useful manner.  Williams et al. (1996), 2σ limit on the near-IR magnitude is derived from ground-based observations with IRIM (Eisenhardt et al. 1996) for a bidimensional Gaussian with FWHM ≈ 1. ′′ 20. HDF 3-951 is undetected in U 300 and B 450 , implying 2σ limiting magnitudes of U 300 > 28.2 and B 450 > 28.9. The small inconsistency in that I HDF 3−951.0 < I HDF 3−951.1 + I HDF 3−951.2 is present in Williams et al. (1996) and likely derives from the faint magnitudes and close separations considered. § Flux density at 1500Å, F 1500 , is in units of 10 −20 erg s −1 cm −2Å−1 and is derived from I 814 assuming a f ν ∝ λ 0 spectrum for λ > 7710Å with no flux below 7710Å. See text for details.
† † First value derives from photometry, second (parenthetical) value derives from spectrophotometry utilizing the continuum flux near 1350Å and assuming a f ν ∝ λ 0 spectrum. See text for details. † L 1500 is in units of 10 40 erg s −1Å−1 , calculated for q 0 = 0.5 using F 1500 values. ‡ Star-formation rates, in units of M ⊙ yr −1 , assume q 0 = 0.5 and a Salpeter IMF with 0.1 < M < 125 M ⊙ (see Madau, Pozzetti, & Dickinson 1998 for details). For q 0 = 0.1 these rates are ≈ 3.3 times larger.  Fig. 2.-Spectrum of the color-selected galaxy HDF 3-951.0 at z = 5.34. Top spectrum is smoothed with a 5 pixel boxcar filter, bottom spectrum is co-averaged in 10 pixel bins with 1σ error bars assigned according to sky counts. The total exposure time is 6900s, and the spectrum was extracted using an 1. ′′ 3 × 1. ′′ 5 aperture. Horizontal bars on the bottom panel indicates the wavelength region considered for determination of D A .   (Weymann et al. 1998). The apparent systematic displacement of the Zuo & Lu (1994) points likely derives from their revised approach for determining the continuum blueward of Lyα: employing high signal-to-noise, high resolution spectra, they model and replace the Lyα forest absorption features.