that lie between
60 and 80 km/s/Mpc, a range far narrower than the 50 to 100 range of 10--15
years ago.
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PS reprint
G. H. Jacoby
National Optical Astronomy Observatories, P.O. Box 26732, Tucson,
AZ 85726
) began in the 1920's,
and continue today, 70 years later. Obviously, progress was made in
those first 3--4 decades without the benefit of computers. It has
become evident during the past 10 years, though, that efforts to
measure H
accurately require highly evolved instruments/telescopes,
observing procedures, and reduction and analysis tools. Stressful
demands are being placed on computer software in each of these areas.
We now realize that an accurate (~10%) ``answer'' is unknowable
without computers because the methods rely heavily on statistical
analyses of large data sets and models of the underlying physical
systems. This paper reviews the status of the H
quest in terms of
the software needed to further many of the primary distance
determination techniques.
Allan Sandage (1993) nicely summarized the debate over the cosmological
distance scale: ``the problem of the Hubble Constant has not been
solved in favor of either scale. The absence of an experiment so clean
and compelling that it negates all others keeps the problem open.''
During the last few years, though, the technological advances and
improvements in various distance determination methods
offer near-term hope for agreement on the value of the Hubble Constant.
Most methods today predict values for H that lie between
60 and 80 km/s/Mpc, a range far narrower than the 50 to 100 range of 10--15
years ago.
Most of the recent progress originates with advances in our ability to collect and analyze data (e.g., new or improved telescopes such as CFHT, NTT, WIYN, and HST, sensitive and large format CCD detectors, fast computers, better analysis software such as DAOPhot and DoPhot). Additionally, notable revisions in our thinking and understanding have occurred (e.g., not all Type Ia supernovae are identical) and new techniques have been devised (e.g., using Type II supernovae, planetary nebulae, and surface brightness fluctuations).
Still, total convergence of all distance measurements has not happened.
A variety of software products are suggested at the end of this paper
to help in the quest for H
. These ideas are not mine, but rather
were provided by primary workers in the field today. It came as a
surprise to me that most of the software requests were not for data
reduction software, but rather, for better models of the astrophysical
processes and also for artificial intelligence assistants in the
reduction process to reduce the tedium of handling large volumes of
data.
The definition of H
is deceptively simple:
Velocities have been measured accurately for many decades,
but distances have always been in question. Ironically, as we improve
our understanding of the distance problem, the interpretation of
velocities for individual galaxies has assumed a new importance.
The ability to determine Cepheid-based distances for galaxies at
15--20 Mpc is no longer the panacea it once was thought to be because
the velocities of those galaxies do not represent the Hubble flow accurately.
Nevertheless, in this paper, I will concentrate solely on the distance
aspect of H
.
The high public visibility of H
studies is a consequence of the
apparent conflict between the large ages of the oldest stars in the
universe and the small ``Hubble Time'', T
, suggested by the
majority of H
determinations. The definition of H
follows that
of a classic time-rate-distance equation. If we know the velocity of
an object (a galaxy) and we measure its distance, we can compute how
long ago it began its journey (the time since the Big Bang). For values
of H
between 55 and 85 km/s/Mpc, T
is 12 to 20 Gyrs if there
has been no acceleration due to gravity or other forces during this
time. Of course, there is mass in the universe, and the mass density,
, is estimated to be between 0.2 and 1.0 of the critical value
needed to someday stop the expansion of the universe. If 
, then gravitational deceleration reduces T
by one-third,
yielding an age for the universe of 8 to 13 Gyrs.
This age for the universe generally is smaller than the
ages of stars, T
, derived from globular cluster studies. Inevitably,
clusters are found to be older than 15 Gyrs (Bolte & Hogan 1995). Since the
components of a universe cannot be older than the universe from which
they formed, we have an apparent contradiction. Some astronomers conclude
that one of the 2 primary parameters (H
, T
) is
incorrect. Usually, the finger pointing aims at H
, which in turn,
implies that the distances to galaxies are wrong. Instead, one can
utilize the apparent contradiction to help define other parameters
of the Big Bang such as 
or 
, the cosmological constant,
which acts as an accelerator and has the effect of increasing T
for
a given H
.
Before turning to the values of 
and 
, we must be
confident that the distances to galaxies are measured correctly.
Despite 70 years of hard work on the problem, distances remain a
controversial subject. Several factors account for the controversy:
Software has been called upon to assist with these inadequacies. That is, computers are used to:
To achieve these goals, software developments have aided in relaxing hardware limitations (detector non-linearities, removal of cosmic rays, corrections for point-spread-function variations). Software has become essential for extracting the key scientific variables, usually magnitudes, transforming their systematic errors into random ones, and deriving their uncertainties in an objective fashion.
Astronomers frequently overlook a critical revolution that has occurred in the last decade. Several software systems are available today at either no cost or low cost within which the average astronomer can reduce and analyze data easily. Ten years ago, each researcher was required to invest heavily in software development to be competitive with one's colleagues. Since the basic precept of the scientific method is that one researcher can reproduce the results of another, and software is a key component in that process, distributable software systems have had a profound impact on the reliability of scientific results. Furthermore, the profusion of software systems now allows for rigorous and independent checking of results using different algorithms, thereby guarding against insidious micro--bugs that may introduce small systematic errors.
On the other hand, astronomers rarely develop software anymore, and so there is a danger of treating software systems as ``black boxes'' with little understanding of the algorithms. The algorithms, however, are tested far more thoroughly under a wide variety of conditions by astronomers around the world than in the past when only a handful of astronomers used a local, home-grown package.
Many distance indicators have been proposed during the 20
century.
Today's most important ones were summarized by Jacoby (1995)
and are listed Table 1, along with the range over which these methods
can be applied with a modern 8--10-m class telescope, along with the typical
values of H
found using these methods. Other methods, such as brightest
cluster galaxies (BCGs---Postman & Lauer 1995), are very promising over
large distances, but have lower precision than most methods listed below.
Most values for H
lie between 60 and 80 km/s/Mpc. The ratio of
upper to lower typical values is only 1.33, a tremendous improvement
over the situation 10 years ago when the ratio was nearly 2.
No distance indicator is perfect, though; each is weak in some way when one considers that a good distance indicator...
The ultimate test for a distance indicator is whether it gives the right answer (criterion 6). In fact, we never know the right answer and so we must turn to intercomparisons between different methods since it is unlikely that 2 independent methods will repeatedly yield the same wrong answer. With the exception of direct geometrical methods such as trigonometric parallaxes, techniques yielding distances that cannot be compared are as useful as theories that cannot be tested. Jacoby et al. (1992) presented intercomparisons using the SBF method as the reference technique.
Figure 1 illustrates the distance comparison between the planetary nebula method and Cepheid variables. The superb agreement suggests that the distance scale business is converging. Additional intercomparisons can be found in Jacoby (1995).
Figure 1: A direct comparison between distances found using Cepheids and
planetary nebulae. The open circles represent comparisons by group membership
(NGC 1023 group and the Virgo Cluster) rather than on a same-galaxy
basis as the filled points do. The M31 triangle is the sole calibrator galaxy.
The dashed line represents perfect agreement. The lower panel plots
the comparison as the difference between
Cepheid and planetary nebula distances to enhance the deviations.
The typical difference between these methods is ~5%.
This figure is based on one from Soffner et al. (1996) with additional
new results for M96 and M101 from Feldmeier et al. (1996).
Figure 1: PS 62Kb
During the past 10 years, several new distance methods have been devised, and old ones have been rejuvenated with the development of new software. These methods also benefited greatly from improvements in detectors and telescopes that require sophisticated software for their operations.
Type Ia supernovae (SNIa---Hamuy et al. 1995; Riess et al. 1995) distances once assumed that all SNIa were identical. If true, they would have been the only known perfect standard candle. Phillips (1993), though, showed that the assumption is a simplification as SNIa have luminosities that vary by ~2 mag. Like Cepheids, there is a time-like parameter that correlates with the true luminosity, and a measure of the luminosity decline rate, or equivalently, the shape of the light curve, is required. Sophisticated multi-color light curve fitting techniques were developed to reduce the errors of this technique from ~20% to ~7%.
Type II supernovae (SNII---Schmidt et al. 1994) distances rely on a sophisticated computer model of the atmospheres of the supernova. The underlying idea has been around for many years: the temperature of the supernova photosphere is measured from its photometric colors (yielding an angular radius) and the expansion velocity is measured spectroscopically (yielding a rate of linear radius expansion). From 2 measures of these parameters at different times, the linear radius, distance, time since explosion, and luminosity follow. The software required to make this method reliable lies in the detailed modeling needed to derive the temperature of the expanding, relativistic, non-LTE atmosphere of the supernova.
Cepheid variables, the ``king'' of distance indicators can now be
observed at large distances with HST. Extracting their periods,
magnitudes, and colors requires extraordinary attention to detail at
every step in the data analysis path. A few percent off here or there,
and the distance is wrong by >10%. To minimize the effects that
different photometry algorithms may have on the distances, Ferrarese
et al. (1996) rely on 2 separate teams using 2 distinct software packages:
DAOPhot from Stetson (1987) and DoPhot from Schechter et al. (1993).
Results are intercompared when the reductions are complete, usually
revealing a few discrepancies in each of the analysis pathways. Without
these (or similar) highly evolved photometric analysis systems, it would
be impossible to determine H
accurately using Cepheids.
Two methods would not able to achieve their highest accuracy without software development. The planetary nebula luminosity function (PNLF---Ciardullo et al. 1989) method yields a distance that maximizes the likelihood that the observed brightness distribution of an ensemble of planetary nebulae agrees with the distribution of brightnesses for a reference ensemble, such as from the planetary nebulae found in M31. The specialized statistics software accounts for the effects of observational errors as a function of brightness, whether they are Gaussian or not, and avoids the deleterious effects of binning the magnitudes (as is done for generating histograms).
The globular cluster luminosity function (GCLF---Secker & Harris 1993) method also follows a set of maximum likelihood statistical procedures similar to the PNLF method. Here, though, the luminosity distribution includes an additional shape parameter to define the width of the nearly Gaussian distribution.
The surface brightness fluctuation (SBF---Tonry & Schneider 1988; Tonry et al. 1990) method relies on making very accurate models of the light distribution of galaxies, mostly ellipticals, with regions spoiled by stars, other galaxies, and globular clusters being masked out. These interlopers are tediously identified by eye, marking them with an image display cursor. Pixel-to-pixel variations in the galaxy luminosity beyond those expected from photon statistics and detector noise indicate the distance to the galaxy: the smoother the galaxy appearance (fewer variations from pixel to pixel), the further away the galaxy.
As I began this paper, my expectations were that future needs would be biased toward improving data reduction and analysis methods. That mind set was dead wrong! The basic tools are in place already; what the researchers in this field want are much better models of the underlying physical processes that enter into the distance indicator process. Knowing the physics is crucial to estimating the second order effects that may introduce systematic biases. The key needs are given in Table 2.
In addition, several scientists noted the need for more generally available and easier to use statistical packages to assess the true errors in the distance measurements. Extremely optimistic error estimates have plagued the distance scale field for most of its 70 year existence.
The software needs of researchers in studies of the extragalactic distance scale focus on modeling the astrophysical processes that allow various techniques to work. A physical basis is crucial to estimate and correct for the intrinsic uncertainties and systematic errors inherent in all distance measuring methods.
However, astronomers exhibit a disconcerting tendency to overlook software in more basic areas. There is an assumption that the following software will appear when needed, with little appreciation for the true costs.
Given the vastly improved tools that astronomers have now and will have
in the near future (large telescopes, big optical/IR arrays, fast
computers, telescopes in space), further reductions in the uncertainty
in H
are certain. The power of the new tools can be applied,
however, only if astronomers have the software needed to utilize
the technology and model the astrophysics.
I wish to thank the following experts in the cosmology, globular cluster age, and distance scale businesses for their assistance and contributions to this report: Ed Ajhar, Mark Birkenshaw, Mike Bolte, Stephane Courteau, Ron Eastman, Rob Kennicutt, Jim Peebles, Mike Pierce, Phil Pinto, Mark Phillips, Peter Stetson, and Doug Welch. In addition, Ian Gatley and Mike Merrill provided valuable insight into the future capabilities of IR instrumentation on large telescopes.
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