A 2.4% DETERMINATION OF THE LOCAL VALUE OF THE HUBBLE CONSTANT
*
Adam G. Riess
1,2
, Lucas M. Macri
3
, Samantha L. Hoffmann
3
, Dan Scolnic
1,4
, Stefano Casertano
2
,
Alexei V. Filippenko
5
, Brad E. Tucker
5,6
, Mark J. Reid
7
, David O. Jones
1
, Jeffrey M. Silverman
8
, Ryan Chornock
9
,
Peter Challis
7
, Wenlong Yuan
3
, Peter J. Brown
3
, and Ryan J. Foley
10,11
1
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA; ariess@stsci.edu
2
Space Telescope Science Institute, Baltimore, MD, USA
3
George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Department of Physics & Astronomy, Texas A&M University,
College Station, TX, USA
4
Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL, USA
5
Department of Astronomy, University of California, Berkeley, CA, USA
6
The Research School of Astronomy and Astrophysics, Australian National University, Mount Stromlo Observatory, Weston Creek, ACT, Australia
7
Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA
8
Department of Astronomy, University of Texas, Austin, TX, USA
9
Astrophysical Institute, Department of Physics and Astronomy, Ohio University, Athens, OH, USA
10
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA
11
Department of Astronomy, University of Illinois at Urbana-Champaign, Urbana, IL, USA
Received 2016 March 21; revised 2016 May 13; accepted 2016 May 16; published 2016 July 21
ABSTRACT
We use the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST) to reduce the uncertainty in the local
value of the Hubble constant from 3.3% to 2.4%. The bulk of this improvement comes from new near-infrared (NIR)
observations of Cepheid variables in 11 host galaxies of recent type Ia supernov ae (SNeIa), more than doubling the
sample of reliable SNeIa having a Cepheid-calibrated distance to a total of 19; these in turn leverage the magnitude-
redshift relation based on ∼300 SNeIa at z<0.15. All 19 hosts as well as the megamaser system NGC 4258 have been
observed with WFC3 in the optical and NIR, thus nullifying cross-instrument zeropoint errors in the relative distance
estimates from Cepheids. Other noteworthy improvements include a 33% reduction in the systematic uncertainty in the
maser distance to NGC 4258, a larger sample of Cepheids in the Large Magellanic Cloud (LMC),amorerobust
distance to the LMC based on late-type detached eclipsing binaries (DEBs), HST observations of Cepheids in M31, and
new HST-based trigonometric parallaxes for Milky Way (MW) Cepheids. We consider four geometric distance
calibrations of Cepheids: (i) megamasers in NGC 4258, (ii) 8DEBsintheLMC,(iii) 15 MW Cepheids with parallaxes
measured with HST/FGS, HST/WFC3 spatial scanning and/or Hipparcos,and(iv ) 2 DEBs in M31. The Hubble
constant from each is 72.25±2 .51, 72.04±2.67, 76.18±
2.37, and 74.50±3.27 k m s
−1
Mpc
−1
, respectively. Our
best estimate of H
0
=73.24±1.74 km s
−1
Mpc
−1
combines the anchors NGC 4258, MW, and LMC, yielding a
2.4% determination (all quoted uncertainties include fully propagated statistical and systematic components).Thisvalue
is 3.4σ higher than 66.93±0.62 km s
−1
Mpc
−1
predicted by ΛCDM with 3 neutrino flavors having a mass of 0.06eV
and the new Planck data, but the discrepancy reduces to 2.1σ relative to the prediction of 69.3±0.7 km s
−1
Mpc
−1
based on the comparably precise combination of WMAP+ACT+SPT+BAO observations, suggesting that systematic
uncertainties in CMB radiation measurements may play a role in the tension. If we take the conflict between Planck
high-redshift measurements and our local determination of H
0
at face value, one plausible explanation could involve an
additional source of dark radiation in the early universe in the range of ΔN
eff
≈0.4–1. We anticipate further significant
improvements in H
0
from upcoming parallax measurements of long-period MW Cepheids.
Key words: cosmological parameters – cosmology: observations – distance scale – galaxies: distances and redshifts
Supporting material: machine-readable tables
1. INTRODUCTION
TheHubbleconstant(H
0
) measured locally and the sound
horizon observed from the cosmic microwave background
radiation (CMB) provide two absolute scales at opposite ends
of the visible expansion history of the universe. Comparing the
two gives a stringent test of the standa rd cosmological model. A
significant disagreement would provide evidence for fundamental
physics beyond the standard model, such as time-dependent or
early dark energy, gravitational physics beyond General Relativ-
ity, additional relativistic particles, or nonzero curvature. Indeed,
none of these features has been excluded by anything more
compelling than a theoretical preference for simplicity over
complexity. In the case of dark energy, there is no simple
explanation at present, leaving direct measurements as the only
guide among numerous complex or highly tuned explanations.
Recent progress in measuring the CMB from WMAP
(Bennett et al. 2013; Hinshaw et al. 2013) and Planck (Planck
Collaboration et al. 2016) have reduced the uncertainty in the
distance to the surface of last scattering (z∼1000) to below
0.5% in the context of ΛCDM, motivating complementary
efforts to improve the local determination of H
0
to percent-level
precision (Suyu et al. 2012;Hu2005). Hints of mild tension at
the ∼2–2.5σ level with the 3%–5% measurements of H
0
stated
by Riess et al. (2011), Sorce et al. (2012), Freedman et al.
(2012), and Suyu et al. (2013) have been widely considered
and in some cases revisited in great detail (Bennett et al. 2014;
The Astrophysical Journal, 826:56 (31pp), 2016 July 20 doi:10.3847/0004-637X/826/1/56
© 2016. The American Astronomical Society. All rights reserved.
*
Based on observations with the NASA/ESA Hubble Space Telescope,
obtained at the Space Telescope Science Institute, which is operated by AURA,
Inc., under NASA contract NAS 5-26555.
1
Dvorkin et al. 2014; Efstathiou 2014; Spergel et al. 2015;
Becker et al. 2015), with no definitive conclusion except for
highlighting the value of improvements in the local observa-
tional determination of H
0
.
1.1. Past Endeavors
Considerable progress in the local determination of H
0
has
been made in the last 25 years, assisted by observations of
water masers, strong-lensing systems, supernovae (SNe), the
Cepheid period–luminosity (P–L) relation (also known as the
Leavitt law; Leavitt & Pickering 1912), and other sources used
independently or in concert to construct distance ladders (see
Freedman & Madore 2010; Livio & Riess 2013, for recent
reviews).
A leading approach utilizes Hubble Space Telescope (HST)
observations of Cepheids in the hosts of recent, nearby SNeIa to
link geometric distance measurements to other SNeIa in the
expanding universe. The SNIa HST Calibration Program
(Sandage et al. 2006) and the HST Key Project (Freedman
et al. 2001) both made use of HST observations with WFPC2 to
resolve Cephe ids in SNIa hosts. However, the useful range of
that camera for measuring Cepheids, 2 5 Mpc, placed severe
limits on the number and choice of SNeIa that could be used to
calibrate their luminosity (e.g., SNe 1937C, 1960F, 1974G).A
dominant systematic uncertainty resulted from the unreliability of
those nearby SNeIa which were photographically observed,
highly reddened, spectroscopically abnormal, or discovered after
peak brightness. Only two objects (SNe 1990N and 1981B) used
by Freedman et al. (2001, 2012) and four by Sandage et al. (2006)
(the above plus SN 1994ae and SN 1998aq)
were free from these
shortcomings, leaving a very small set of reliable calibrators
relative to the many hundreds of similarly reliable SNeIa
observed in the Hubble flow. The resulting ladders were further
limited by the need to calibrate WFPC2 at low flux levels to the
ground-based systems used to measure Cepheids in a single
anchor, the Large Magellanic Cloud (LMC).TheuseofLMC
Cepheids introduces additional systematic uncertainties because
of their shorter mean period (
D
áñPlog
≈0.7 dex) and lower
metallicity (
()
D
log O H
=−0.25 dex, Romaniello et al. 2008)
than those found with HST in the large spiral galaxies that host
nearby SNeIa. Despite careful work, the estimates of H
0
by the
two teams (each with 10% uncertainty) differedby20%,owingin
part to the aforementioned systematic errors.
More recently, the SH0ES (SNe, H
0
, for the Equation of State
of dark e nergy) team used a number of advancements to refine
this approach to determining H
0
. Upgrades to the instrumentation
of HST doubled its useful range for resolving Cepheids (leading to
an eight-fold improvement in volume and in the expected number
of useful SNIa hosts ), first with the Advanced Camera for
Surveys (ACS; Riess et al. 2005, 2009b) and later with the Wide
Field Camera 3 (WFC3; Riess et al. 2011, hereafter R11) owing to
the greater area, higher sensitivity, and smaller pixels of these
cameras. WFC3 has other superior features for Cepheid
reconnaissance, including a white-light filter ( F350LP) that more
than doubles the speed for discovering Cepheids and measuring
their periods relative to the traditional F555W filter, and a
5arcmin
2
near-infrared (NIR) detector that can be used to reduce
the impact of differential extinction and metallicity differences
across the Cepheid sample. A precise geometric distance to
NGC 4258 measured to 3% using water masers (Humphreys
et al. 2013, hereafter H13) has provided a new anchor galaxy
whose Cepheids can be observed with the same instrument and
filters as those in SNIa hosts to effectively cancel the effect of
photometric zeropoint uncertainties in this step along the distance
ladder. Tied to the Hubble diagram of 240 SNe Ia (now >300
SNeIa; Scolnic et al. 2015; Scolnic & Kessler 2016),thenew
ladder was used to initially determine H
0
with a total uncertainty
of 4.7% (Riess et al. 2009a, hereafter R09). R11 subsequently
improved this measurement to 3.3% by increasing to 8 the
number of Cepheid distances to reliable SNIa hosts, and formally
including HST/FGS trigonometric parallaxes of 10 Milky Way
(MW) Cepheids with distance D<0.5 kpc and individual
precision of 8% (Benedict et al. 2007). The evolution of the
error budget in these measurements is shown in Figure 1.
Here we present a broad set of improvements to the SH0ES
team distance ladder including new NIR HST observations of
Cepheidsin11SNIa hosts (bringing the total to 19),arefined
computation of the distance to NGC 4258 from maser data,
additional Cepheid parallax measurements, larger Cepheid
samples in the anchor galaxies, and additional SNeIa to constrain
the Hubble flow. We present the new Cepheid data in Section 2
andinS.L.Hoffmannetal.(2016, in preparation; hereafter H16).
Other improvements are described throughout Section 3,anda
consideration of analysis variants and systematic uncertainties is
given in Section 4. We end with a discussion in Section 5.
2. HST OBSERVATIONS OF CEPHEIDS IN
THE SH0ES PROGRAM
Discovering and measuring Cepheid variables in SNIa host
galaxies requires a significant investment of observing time on
Figure 1. Uncertainties in the determination of H
0
. Uncertainties are squared to
show their individual contribution to the quadrature sum. These terms are given
in Table 7.
2
The Astrophysical Journal, 826:56 (31pp), 2016 July 20 Riess et al.
HST. It is thus important to select SN Ia hosts likely to produce
a set of calibrators that is a good facsimile of the much larger
sample defining the modern SNIa magnitude-redshift relation
at 0.01<z<0.15 (e.g., Scolnic et al. 2015; Scolnic & Kessler
2016). Poor-quality light curves, large reddening, atypical SN
explosions, or hosts unlikely to yield a significant number of
Cepheids would all limit contributions to this effort. Therefore,
the SH0ES program has been selecting SNeIa with the
following qualities to ensure a reliable calibration of their
fiducial luminosity: (1) modern photometric data (i.e., photo-
electric or CCD), (2) observed before maximum brightness and
well thereafter, (3) low reddening (implying A
V
<0.5 mag),
(4) spectroscopically typical, and (5) a strong likelihood of
being able to detect Cepheids in its host galaxy with HST. This
last quality translates into any late-type host (with features
consistent with the morphological classification of Sa to Sd)
having an expectation of D40 Mpc, inclination <75°, and
apparent size >1′. To avoid a possible selection bias in SNIa
luminosities, the probable distance of the host is estimated via
the Tully–Fisher relation or flow-corrected redshifts as reported
in NED.
12
We will consider the impact of these selections in
Section 4.
The occurrence of SNeIa with these characteristics is
unfortunately quite rare, leading to a nearly complete sample of
19 objects observed between 1993 and 2015 (see Table 1).
Excluding SNe from the 1980s, a period when modern
detectors were rare and when suitable SNeIa may have
appeared and gone unnoticed, the average rate of production is
∼1yr
−1
. Regrettably, it will be difficult to increase this sample
substantially (by a factor of ∼2) over the remaining lifetime of
HST. We estimate that a modest augmentation of the sample (at
best) would occur by removing one or more of the above
selection criteria, but the consequent increase in systematic
uncertainty would more than offset the statistical gain.
Reliable SNeIa from early-type hosts could augment the
sample, with distance estimates based on RR Lyrae stars or the tip
of the red-giant branch (TRGB) for their calibration. Unfortu-
nately, the reduced distance range of these distance indicators for
HST compared with Cepheids (2.5 mag or D<13 Mpc for
TRGB, 5 mag or D<4 Mpc for RR Lyrae stars) and the factor of
∼5smallersampleofSNeIa in early-type hosts limits the sample
increase to just a few additional objects (SN 1994D, SN 1980N,
1981D, and SN 2006dd with the latter three all in the same host;
Beaton et al. 2016), a modest fraction of the current sample of 19
SNeIa calibrated by Cepheids.
Figure 2 shows the sources of the HST data obtained on
every host we use, gathered from different cameras, filters, time
periods, HST programs and observers. All of these publicly
available data can be readily obtained from the Mikulski
Archive for Space Telescopes (MAST; see Table 1). The utility
of the imaging data can be divided into two basic functions:
Cepheid discovery and flux measurement. For the former, a
campaign using a filter with central wavelength in the visual
band and ∼12 epochs with nonredundant spacings spanning
∼60–90 days will suffice to identify Cepheid variables by their
unique light curves and accurately measure their periods
(Madore & Freedman 1991; Saha et al. 1996; Stetson 1996)
.
Revisits on a year timescale, although not required, will yield
increased phasing accuracy for the longest-period Cepheids.
Image subtraction can be very effective for finding larger
samples of variables (Bonanos & Stanek 2003), but the
additional objects will be subject to greater photometric biases
owing to blends which suppress their amplitudes and chances
of discovery in time-series data (Ferrarese et al. 2000).
Flux measurements are required in order to use Cepheids as
standard candles for distance measurement and are commonly
done with HST filters at known phases in optical ( F555W,
F814W) and NIR ( F160W) bands to correct for the effects of
interstellar dust and the nonzero width in temperature of the
Cepheid instability strip. We rely primarily on NIR “Wesen-
heit” magnitudes (Madore 1982),defined as
() ()=- -mmRVI,1
H
W
H
where H=F160W, V=F555W, I=F814W in the HST
system, and R≡A
H
/(A
V
− A
I
). We note that the value of R due
to the correlation between Cepheid intrinsic color and
luminosity is very similar to that due to extinction ( Macri
et al. 2015), so the value of R derived for the latter effectively
also reduces the intrinsic scatter caused by the breadth of the
instability strip. However, to avoid a distance bias, we include
only Cepheids with periods above the completeness limit of
detection (given in H16) in our primary fit. (In future work we
will use simulations to account for the bias of Cepheids below
this limit to provide an extension of the Cepheid sample.)
In HST observations, Cepheid distances based on NIR
measurements have somewhat higher statistical uncertainties than
those solely based on optical photometry owing to the smaller
field of view (FOV), lower spatial resolution, and greater blending
Table 1
Cepheid Hosts Observed with HST/WFC3
Galaxy SNIa
Exp.Time (s)
Prop IDs UT Date
c
NIR
a
Opt.
b
M101
d
2011fe 4847 3776 12880 2013 Mar 03
N1015 2009ig 14364 39336 12880 2013 Jun 30
N1309
d
2002fk 6991 3002 11570, 12880 2010 Jul 24
N1365
d
2012fr 3618 3180 12880 2013 Aug 06
N1448 2001el 6035 17562 12880 2013 Sep 15
N2442 2015F 6035 20976 13646 2016 Jan 21
N3021
d
1995al 4426 2962 11570, 12880 2010 Jun 03
N3370
d
1994ae 4376 2982 11570, 12880 2010 Apr 04
N3447 2012ht 4529 19114 12880 2013 Dec 15
N3972 2011by 6635 19932 13647 2015 Apr 19
N3982
d
1998aq 4018 1400 11570 2009 Aug 04
N4038
d
2007sr 6795 2064 11577 2010 Jan 22
N4258
d
Anchor 34199 6120 11570 2009 Dec 03
N4424 2012cg 3623 17782 12880 2014 Jan 08
N4536
d
1981B 2565 2600 11570 2010 Jul 19
N4639
d
1990N 5379 1600 11570 2009 Aug 07
N5584 2007af 4929 59940 11570 2010 Apr 04
N5917 2005cf 7235 23469 12880 2013 May 20
N7250 2013dy 5435 18158 12880 2013 Oct 12
U9391 2003du 13711 39336 12880 2012 Dec 14
Notes.
a
Data obtained with WFC3/IR and F160W.
b
Data obtained with WFC3/UVIS and F555W, F814W,orF350LP used to
find and measure the flux of Cepheids.
c
Date of first WFC3/IR observation.
d
Includes time-series data from an earlier program and a different camera—see
Figure 2.
12
The NASA/IPAC Extragalactic Database (NED) is operated by the Jet
Propulsion Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration (NASA).
3
The Astrophysical Journal, 826:56 (31pp), 2016 July 20 Riess et al.
from red giants. However, as characterized in Section 4.2,thisis
more than offset by increased robustness to systematic uncertain-
ties (such as metallicity effects and possible breaks in the slope of
the P–L relation) as well as the reduced impact of extinction and a
lower sensitivity to uncertainties in the reddening law. The latter is
quantified by the value of R in Equation (1), ranging from 0.3 to
0.5 at H depending on the reddening law, a factor of ∼4lower
than the value at I. At the high end, the Cardelli et al. (1989)
formulation with R
V
=3.3 yields R=0.47. The Fitzpatrick
(1999) formulation with R
V
=3.3 and 2.5 yields R=0.39 an d
R=0.35, respectively. At the low end, a formulation appropriate
for the inner MW (Nataf et al. 2015) yields R=0.31. We analyze
the sensitivity of H
0
to variations in R in Section 4.
2.1. Cepheid Photometry
The procedure for identifying Cepheids from time-series
optical data (see Table 1 and Figure 2) has been described
extensively (Saha et al. 1996;Stetson1996; Riess et al. 2005;
Macri et al. 2006); details of the procedures followed for this
sample are presented by H16, utilize the DAO suite of software
tools for crowded-field PSF photometry, and are similar to those
used previously by the SH0ES team. The complete sample of
Cepheids discovered or reanalyzed by H16 in these galaxies
(NGC4258andthe19SNIa hosts) at optical wavelengths
contains 2062 variables above the periods for completeness
across the instability strip (with limits estimated using the HST
exposure-time calculators and empirical tests as described in that
publication). There are 1566 such Cepheids in the 19 SNIa
hosts within the smaller WFC3-IR fields alone. The positions of
the Cepheids within each target galaxy are shown in Figure 3.
For hosts in which we used F350LP to identify Cepheid light
curves, additional photometry was obtained over a few epochs in
F555W and F814W. These data were phase-corrected to mean-
light values using empirical relations based on light curves in
both F555W and F350LP from Cepheids in NGC 5584. Figure 4
shows composite Cepheid light curves in F350LP/F555W for
each galaxy. Despite limited sampling of the individual light
curves, the composites clearly display the characteristic “saw-
toothed” light curves of PopulationI fundamental-mode Cep-
heids, with a rise twice as fast as the decline and similar mean
amplitudes across all hosts.
For every host, optical data in F555W and F814W from
WFC3 were uniformly calibrated using the latest reference files
from STScI and aperture corrections derived from isolated stars
in deep images to provide uniform flux measurements for all
Cepheids. In a few cases, F555W and F814W data from ACS
Figure 2. HST observations of the host galaxies of ideal SNeIa. The data used to observe Cepheids in 19 SNIa hosts and NGC 4258 were collected over 20 years
with four cameras and over 600 orbits of HST time. 60–90 day campaigns in F555W and F814W or in F350LP were used to identify Cepheids from their light curves
with occasional reobservations years later to identify Cepheids with P>60 days. Near-IR follow-up observations in F160W are used to reduce the effects of host-
galaxy extinction, sensitivity to metallicity, and breaks in the P–L relation. Data sources: (1) HST SNIa Calibration Project, Sandage et al. (2006); (2) HST Key
Project, Freedman et al. (2001); (3) Riess et al. (2005); (4) Macri et al. (2006); and (5) Mager et al. (2013).
4
The Astrophysical Journal, 826:56 (31pp), 2016 July 20 Riess et al.
Figure 3. Images of Cepheid hosts. Each image is of the Cepheid host indicated. The magenta outline shows the field of view of WFC3/IR, 2 7 on a side. Red dots
indicate the positions of the Cepheids. Compass indicates north (long axis ) and east (short axis).
5
The Astrophysical Journal, 826:56 (31pp), 2016 July 20 Riess et al.
