One Percent Determination of the Primordial Deuterium Abundance
*
Ryan J. Cooke
1,5
, Max Pettini
2,3
, and Charles C. Steidel
4
1
Centre for Extragalactic Astronomy, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK; ryan.j.cooke@durham.ac.uk
2
Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK
3
Kavli Institute for Cosmology, Madingley Road, Cambridge CB3 0HA, UK
4
California Institute of Technology, MS 249-17, Pasadena, CA 91125, USA
Received 2017 July 26; revised 2018 January 26; accepted 2018 January 27; published 2018 March 12
Abstract
We report a reanalysis of a near-pristine absorption system, located at a redshift
z
2.5256
4
abs
=
toward the quasar
Q1243+307, based on the combination of archival and new data obtained with the HIRES echelle spectrograph on
the Keck telescope. This absorption system, which has an oxygen abundance [O/H]=−2.769± 0.028 (;1/600
of the solar abundance), is among the lowest metallicity systems currently known where a precise measurement of
the deuterium abundance is afforded. Our detailed analysis of this system concludes, on the basis of eight D
I
absorption lines, that the deuterium abundance of this gas cloud is
log D H 4.622 0.015
10
=- ()
, which is in
very good agreement with the results previously reported by Kirkman et al., but with an improvement on the
precision of this single measurement by a factor of ∼3.5. Combining this new estimate with our previous sample of
six high precision and homogeneously analyzed D/H measurements, we deduce that the primordial deuterium
abundance is
log D H 4.5974 0.0052
10
P
=- ()
or, expressed as a linear quantity,
10 D H 2.527 0.030;
5
P
=()
this value corresponds to a one percent determination of the primordial deuterium abundance. Combining our
result with a big bang nucleosynthesis (BBN) calculation that uses the latest nuclear physics input, we find that the
baryon density derived from BBN agrees to within 2σ of the latest results from the Planck cosmic microwave
background data.
Key words: cosmology: observations – cosmology: theory – primordial nucleosynthesis – quasars: absorption lines –
quasars: individual (Q1243+307)
1. Introduction
Modern cosmology is described by just six model parameters,
all of which are known to within a few percent. This model
provides a reliable description of the universe from seconds after
the big bang until the present epoch. However, we know that the
Standard Model of cosmology and particle physics is incomplete.
Forexample,wehavenodefinitive description of dark matter and
dark energy, nor do we fully understand the properties of
neutrinos. New physics beyond the Standard Model may be
exposed by measuring the cosmological model parameters at high
precision, and there are many teams that are searching for this new
physics by studying the cosmic microwave background (CMB),
weak and strong lensing, and by observing standard candles,
rulers, and sirens, to name a few examples.
In recent years, there have also been several efforts to measure
the chemical abundances of the elements that were made during
the first minutes after the big bang, a process that is commonly
referred to as “big bang nucleosynthesis” (BBN ; for a general
review of the subject, see Steigman 2007; Cyburt et al. 2016;
Mathews et al. 2017). The abundances of the primordial elements
—which include the isotopes of hydrogen, helium, and lithium—
are sensitive to the physics of the early universe, and are therefore
a tool that allows us to test the Standard Model. Moreover,
measuring the abundances of these primordial elements currently
provides our earliest test of the Standard Model.
In order to reliably measure the primordial element abundances,
we must first identify environments that are as close as possible to
being pristine, and therefore still retain a primordial composition of
the light elements. The best available measurements of the
primordial element abundances come from different environments;
conventionally, the mass fraction of
4
He (Y
P
) is derived from the
emission lines of nearby H
II regions in metal-poor star-forming
galaxies (Izotov et al. 2014;Averetal.2015),
6
while the
primordial
7
Li abundance is determined from the atmospheres of
very metal-poor stars (Asplund et al. 2006;Aokietal.2009;
Meléndez et al. 2010; Sbordone et al. 2010; Spite et al. 2015).At
present, there are no reliable measurements of the primordial
3
He
abundance; however, with future facilities this measurement may
become possible (several different techniques are described by
Bania et al. 2002; McQuinn & Switzer 2009; Cooke 2015).
The only other primordial element that is accessible with
current facilities is deuterium, which can be measured using gas
clouds that are seen in absorption against the light of an
unrelated background light source (typically, a quasar)
(Adams 1976). Although this technique was proposed more
than four decades ago, the first measurements were only
achieved some 20 years later; even now, only a handful
detections of the neutral deuterium (D
I) absorption lines have
been made (Burles & Tytler 1998a, 1998b; Pettini & Bowen
2001;O’Meara et al. 2001, 2006; Kirkman et al. 2003;
Crighton et al. 2004; Pettini et al. 2008; Fumagalli et al. 2011;
Noterdaeme et al. 2012; Pettini & Cooke 2012; Cooke et al.
2014, 2016; Riemer-Sørensen et al. 2015, 2017; Balashev
et al. 2016; Zavarygin et al. 2017). However, as discussed
recently by Cooke et al. (2014), absorption line systems that
The Astrophysical Journal, 855:102 (16pp), 2018 March 10 https://doi.org/10.3847/1538-4357/aaab53
© 2018. The American Astronomical Society. All rights reserved.
*
Based on observations collected at the W.M. Keck Observatory 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.
5
Royal Society University Research Fellow.
6
Y
P
can also be measured from the small-scale CMB temperature
fluctuations (Planck Collaboration et al. 2016), albeit with lower precision.
1
have H I column densities near the threshold of a damped Lyα
system (DLA; N(H
I);10
20.3
cm
−2
)
7
are the most suitable
environments to precisely measure the primordial deuterium
abundance, (D/H)
P
(see also Riemer-Sørensen et al. 2017).In
this H
I column density regime, the H I Lyα transition exhibits
Lorentzian damped wings that uniquely determine the total
H
Icolumn density, while up to ∼10 high order unsaturated D I
lines are available to determine the total D I column density.
Even among DLAs, only those that are kinematically quiescent
are able to deliver a precise determination of (D/H)
P
, since the
D
I lines need to be optically thin and unblended with nearby
absorption lines. Empirically, it has been noted by several
authors that DLAs with simple kinematics tend to be more
common at the lowest metallicity (Ledoux et al. 2006; Murphy
et al. 2007; Prochaska et al. 2008; Jorgenson et al. 2013;
Neeleman et al. 2013; Cooke et al. 2015). Currently, there are
just six systems which satisfy the above conditions, all of
which have been homogeneously analyzed, as reported in
previous papers of this series (Cooke et al. 2014, 2016).
The primordial deuterium abundance is inferred under the
assumption that the ratio of deuterium to hydrogen atoms,
D/H≡N(D
I)/N(H I). There are several physical processes
that potentially weaken the validity of this assumption,
including: (1) The astration of deuterium as gas is cycled
through generations of stars (Dvorkin et al. 2016; van de Voort
et al. 2017, and the comprehensive list of references provided
by Cyburt et al. 2016); (2) the relative ionization of deuterium
and hydrogen in neutral gas (Savin 2002; Cooke & Pettini
2016); and (3) the preferential depletion of deuterium onto dust
grains (Jura 1982; Draine 2004, 2006). The first two physical
processes are expected to alter the measured D/H ratio by
0.1% when the metallicity is 1/100 solar and the neutral
hydrogen column density exceeds
10 cm
19
2
-
; this correction is
an order of magnitude below the current measurement
precision. The preferential depletion of deuterium onto dust
grains, however, has not been modeled in detail in metal-
poor DLAs.
Several studies have reported on the depletion of deuterium
in the local interstellar medium (ISM) of the Milky Way (Wood
et al. 2004; Prochaska et al. 2005; Linsky et al. 2006; Ellison
et al. 2007; Lallement et al. 2008; Prodanović et al. 2010).
However, the ISM of the Milky Way is relatively dust-rich
compared with the metal-poor DLAs that are typically used to
infer the primordial deuterium abundance. Observationally,
metal-poor DLAs are not expected to contain a significant
amount of dust (Murphy & Bernet 2016); even the most
refractory elements in the lowest-metallicity DLAs are hardly
incorporated into dust grains (Pettini et al. 1997; Vladilo 2004;
Akerman et al. 2005). However, Cooke et al. (2016) noted a
subtle (but statistically insignificant) decline of the deuterium
abundance with increasing metallicity, a trend that would be
expected if deuterium were preferentially incorporated into dust
grains.
Herein, we report a seventh high precision measurement of the
deuterium abundance in one of the most pristine environments
currently known, to assess whether or not the deuterium
abundance depends on metallicity. T he paper is organized as
follows: in Section 2, we describe the observational procedure and
the details of the data reduction process. The analysis technique
and the properties of the absorption system are then described in
Section 3. In Section 4, we report our new D/H abundance
measurement of this system, and investigate the properties of our
full sample. In Section 5, we deduce the primordial deuterium
abundance, based on seven D/H values, and provide new
measurements of the cosmological baryon density, and effective
number of neutrino species. Our conclusions are summarized in
Section 6. All reported uncertainties represent 68% confidence
intervals, unless otherwise stated.
2. Observations and Data Reduction
2.1. Observational Data
This paper presents an estimate of the primordial D/H
abundance using new, high quality data of a previously known
sub-DLA at an absorber redshift z
abs
;2.5257 toward the quasar
Q1243+307 (
z
2.558
em
, R.A.=12
h
46
m
10 9, decl.=+30°
31′31
2; J2000). A measure of the deuterium abundance of this
system was first reported by Kirkman et al. (2003), using data
taken with the High Resolution Echelle Spectrometer (HIRES;
Vogt et al. 1994) on the Keck I telescope during the years
1999–2000 (program IDs: U32H, U02H). These data consist
of a total exposure time of 55,800 s, divided into seven
exposures, acquired with the previous generation HIRES
detector; this detector had relatively low UV quantum efficiency
and significantly higher read noise at the bluest wavelengths
where the redshifted D
I absorption lines are observed. For these
reasons,
8
we have re-observed Q1243+307 using the modern
HIRES detector, which is considerably more sensitive at blue
wavelengths.
Our observations (program ID: N162Hb) consisted of 3×
3600 s and 1×3000 s exposures, and were carried out on 2016
March 30, in excellent seeing conditions (0
6 full width at
half maximum; FWHM), well matched to the chosen slit size
(C1 decker, 0
861×7 0). This decker provides a nominal
spectral resolution of R;48,000 (
v 6.25
FWHM
kms
−1
) for
a uniformly illuminated slit. Using an exposure of a thorium –
argon (ThAr) lamp, we directly measured the instrument
FWHM to be v
FWHM
=6.28±0.02 kms
−1
based on 2192
emission lines; throughout our analysis, we adopt this FWHM
value.
9
All science and calibration frames were binned 2× 2
during read-out. The final combined signal-to-noise ratio
(S/N) per 2.5kms
−1
pixel of our data near the observed
wavelength λ
obs
=3215 Å (i.e., the Lyman limit of the sub-
DLA) is S/N;25. The S/N is much higher at longer
wavelengths, and reaches a maximum value of S/N;80 per
2.5kms
−1
pixel near the sub-DLA’sLyα absorption line.
Finally, a single exposure of length 3600 s was acquired with
Keck+HIRES on 2006 June 2 (program ID: U152Hb, Lehner
et al. 2014;O’Meara et al. 2015), using a nearly identical setup
to our own observations ( hereafter referred to as the KODIAQ
data). We retrieved all of the aforementioned HIRES data of
7
In this paper, we use the term “DLA” to represent any absorption line
system with N(H
I)>10
20.3
cm
−2
and “sub-DLA” for systems with 10
19.0
<
N(H
I)/cm
−2
< 10
20.3
.
8
This system was not analyzed in our previous work (Cooke et al. 2014),
since the data were not publicly available at the time.
9
Ideally, the instrument FWHM should be determined using narrow telluric
absorption lines, since the quasar was not uniformly illuminating the slit during
the observations. Unfortunately, there are no telluric absorption bands covered
by our spectrum, and we have therefore adopted the FWHM value of a
uniformly illuminated slit. We note that this assumption should not affect our
determination of D
I/H I, because the equivalent width of an absorption line is
invariant under convolution with the instrumental FWHM. As discussed in
Section 3, the equivalent widths of the weak D
I absorption lines and the
damped profile of the strong Lyα absorption line uniquely determine the D
I
and H I column densities, respectively.
2
The Astrophysical Journal, 855:102 (16pp), 2018 March 10 Cooke, Pettini, & Steidel
Q1243+307 from the public Keck Observatory data archive.
10
A summary of the data that are used in our analysis is provided
in Table 1.
2.2. Data Reduction Methods
The modern HIRES data (program IDs: U152Hb, N162Hb)
were reduced using the HIRES Redux package (Bernstein
et al. 2015).
11
We adopted the standard processing steps,
including a bias level subtraction, correcting for the pixel-to-pixel
variations and dividing by the blaze function of each echelle order.
The echelle orders were traced using an exposure of a quartz lamp
taken through the C1 decker (i.e., the same slit that was used to
acquire the science frames). We employed an optimal sky
subtraction and object extraction technique (Kelson 2003),and
each pixel was assigned a wavelength using an exposure of a
ThAr lamp that bracketed each science exposure.
At the time of our analysis, the HIRES Redux package was not
able to reduce data acquired with the old HIRES detector (see,
however, O’Meara et al. 2017). We therefore reduced the
Kirkman et al. (2003) data (program IDs: U32H, U02H) using
version 5.2.4 of the
MAKEE data reduction pipeline,
12
adopting a
similar approach as that described by Suzuki et al. (2003).To
summarize, we performed a bias subtraction, a flatfield and blaze
correction, and traced the orders using an exposure of a quartz
lamp taken through a pinhole decker. The data were wavelength
calibrated using a ThAr lamp; we measured the widths of 1040
ThAr lines to be v
FWHM
=7.99±0.02 kms
−1
, which is in good
agreement with the nominal value of the instrument resolution
(v
FWHM
=8.0 kms
−1
). For the analysis of the Kirkman et al.
(2003) data set described below, we adopt our measured value of
the FWHM.
All reduced data were corrected to the heliocentric frame of
reference, and were converted to a vacuum wavelength scale.
Using UVES_
POPLER,
13
we combined the exposures of each
given data set to produce three separate spectra of Q1243+307:
one spectrum of the Kirkman et al. (2003) data, one of the
KODIAQ data, and the combined spectrum of our new data. As
described in Section 3, all three of these spectra are kept
separate from one another, but are analyzed simultaneously.
For illustration purposes, in Figure 1 we show the complete
combined spectrum of our new data (i.e., only the data acquired
in 2016), flux calibrated with reference to the Kirkman et al.
(2003) data.
3. Analysis Method
We now summarize the main aspects of our analysis method,
which is identical to that described in our previous work (Cooke
et al. 2014, 2016). We use the Absorption LIne Software (
ALIS),
which employs a χ-squared minimization procedure to minimize
the residuals between the data and a user-specified model,
weighted by the inverse variance of the data.
14
A key aspect of our analysis is that we simultaneously fit the
emission spectrum of the quasar and the absorption due to the
intervening absorption line system. This approach ensures that
the final error on D/H includes the uncertainty associated with
the quasar continuum placement. We include all available
information of the absorption system in our analysis, including
the H
I and D I Lyman series absorption lines and the
unblended metal absorption lines. The continuum near each
absorption line is fit during the minimization process assuming
that it is described by a low order Legendre polynomial.
Typically, the degree of the Legendre polynomial is 4, except
near the Lyα absorption line, where a Legendre polynomial of
degree 8 is used. We also include a global model parameter that
defines the zero-level of each data set, to account for small
residuals in the background subtraction and/or partial covering
of the background quasar by the foreground sub-DLA. All
three data sets are analyzed at the same time to obtain a global
best-fit model; we simultaneously fit the same absorption
model to all three data sets, while allowing the model of the
quasar continuum around every absorption line in each data set
to be different.
15
We also include two fitting parameters to
determine the global relative velocity shift between the three
data sets, to account for instrumental artifacts in the wavelength
calibration (e.g., Whitmore & Murphy 2015).
As discussed in Section 1, accurate estimates of the primordial
deuterium abundance are afforded by systems where the wings of
the Lyα absorption line are damped by the Lorentzian term of the
Voigt profile. In this regime, the damped wings uniquely
determine the H
I column density. For this reason, the data are
most sensitive to N(H
I) when the optical depth of the absorption
profile is τ0.7 (i.e., where the residual intensity is 50% of the
quasar continuum); for the sub-DLA toward Q1243+307, this
corresponds to all pixels within ±470 km s
−1
of the H I Lyα line
relative to the redshift defined by the narrow metal absorption
lines. In our analysis, we opted to include all pixels that are within
a velocity interval of
v470 km s 580
1
-
+
-
(see also
Section 3.1). Any blends that are identified within this velocity
Table 1
Journal of Keck HIRES Observational Data Used in This Analysis
Date Principal Program HIRES v
FWHM
Wavelength Exposure
Investigator ID Decker (km s
−1
) Range (Å) Time (s)
1999 Apr 17, 18 Tytler U32H C5 7.99±0.02 3190–4665 23,400
2000 Mar 13, 14 Tytler U02H C5 7.99±0.02 3190–4665 32,400
2006 Jun 2 Prochaska U152Hb C1 6.28±0.02 3225–6085 3,600
2016 Mar 31 Cooke N162Hb C1 6.28±0.02 3225–6085 14,400
10
Available from: https://koa.ipac.caltech.edu/cgi-bin/KOA/nph-KOAlogin.
11
HIRES Redux is available from: http://www.ucolick.org/~xavier/HIRedux/.
12
MAKEE is available from: http://www.astro.caltech.edu/~tb/makee/.
13
UVES_POPLER is maintained by Michael T. Murphy, and is available from
GitHub, via the following link: https://github.com/MTMurphy77/UVES_
popler.
14
ALIS is available for download from GitHub: https://github.com/rcooke-
ast/ALIS.
15
There are two reasons why the emission profile near each absorption line
may be different for the three data sets. First, the three data sets that are
analyzed in this paper were taken at different epochs; the quasar continuum and
emission lines may vary over the 16 year period spanned by the observations.
Second, these data sets were acquired with different instrument configurations;
the relative differences in the spectrograph efficiency as a function of
wavelength can change the apparent level of the quasar continuum.
3
The Astrophysical Journal, 855:102 (16pp), 2018 March 10 Cooke, Pettini, & Steidel
Figure 1. Final combined and flux-calibrated spectrum of Q1243+307 (black histogram) shown with the corresponding error spectrum (blue histogram) and zero level
(green dashed line). The red tick marks above the spectrum indicate the locations of the Lyman series absorption lines of the sub-DLA at redshift
z
2.5256
4
abs
=
. Note
the exquisite signal-to-noise ratio (S/N) of the combined spectrum, which varies from S/N;80 near the Lyα absorption line of the sub-DLA (∼4300 Å) to
S/N;25 at the Lyman limit of the sub-DLA, near 3215 Å in the observed frame.
4
The Astrophysical Journal, 855:102 (16pp), 2018 March 10 Cooke, Pettini, & Steidel
interval are modeled with a Voigt profile; outside this velocity
interval we only include pixels in the χ-squared minimization that
are deemed by visual inspection to be free of unrelated absorption.
We present the data and best-fitting model profile of the Lyα
absorption feature in Figure 2. The best-fitting model profile has
an H
I column density of
Nlog
10
(H I)/cm
−2
=19.761±0.026,
Figure 2. Lyα profile of the absorption system at
z
2.5256
4
abs
=
toward the quasar Q1243+307 (black histogram) overlaid with the best-fitting model profile (red
line), continuum (long dashed blue line), and zero-level (short dashed green line) . The top panels show the raw, extracted counts scaled to the maximum value of the
best-fitting continuum model. The bottom panels show the continuum normalized flux spectrum. The label provided in the top left corner of every panel indicates the
source of the data. The blue points below each spectrum show the normalized fit residuals, (data–model)/error, of all pixels used in the analysis, and the gray band
represents a confidence interval of ±2σ. The S/N is comparable between the two data sets at this wavelength range, but it is markedly different near the high order
Lyman series lines ( see Figures 4 and 5). The red tick marks above the spectra in the bottom panels show the absorption components associated with the main gas
cloud (Components 2, 3, 4, 5, 6, 8, and 10 in Table 2), while the blue tick marks indicate the fitted blends. Note that some blends are also detected in Lyβ–Lyò.
5
The Astrophysical Journal, 855:102 (16pp), 2018 March 10 Cooke, Pettini, & Steidel
