Keywords

1 Introduction

New precision observational surveys in astronomy provide high-resolution empirical data for population synthesis. After presenting the basic methods of population synthesis (following closely Conroy 2013 and Maraston 2005), this paper argues for several related conclusions. The increased precision of the new methods requires the development of improved theoretical resources and models to provide the richest interpretation of the new data (as argued by Maraston and Strömbäck 2011). Further, the measurement of physical variables and parameters in population synthesis is best understood using a model-based account along the lines of Tal (2012) and Parker (2017). The paper concludes that, in the case of population synthesis, improved empirical data does not dispense with the need for theoretical reasoning in post-data analysis. The high-resolution data used in next-generation population synthesis demands ever richer theories and models, a process that results in hybrid enrichment of theoretical and observational methods and results.

2 Stellar Population Synthesis in Astrophysics

Stellar population synthesis involves generating simulations of the evolution and properties of an ensemble of stars. The method yields an overall picture of the stars as they age and interact with the interstellar medium. Astronomers refer to the evolutionary process of stars as the Main Sequence.Footnote 1 Stellar population synthesis maps not only the stars’ properties at the present time, but also their position on the Main Sequence, their histories, and their predicted evolution, yielding a moving picture of how stars age and interact with the interstellar medium.Footnote 2 Astronomers determine a star’s metallicity through diverse methods of spectroscopic classification (Heiter et al. 2014, Sect. 1). Knowledge of the age-metallicity relationship allows for inferences, not only about the properties of stars, but about their evolution and position on the Main Sequence.Footnote 3

A spectral energy distribution (SED) is “light emitted over all or a portion of the [far ultraviolet to far infrared] spectral domain, including broadband data and/or moderate-resolution spectra” (Conroy 2013, 393). Measurements of the spectral energy distribution are a key source of empirical data. Charlie Conroy sums up the foundation of population synthesis:

The spectral energy distributions (SEDs) of galaxies are shaped by nearly every physical property of the system, including the star-formation history, metal content, abundance pattern, dust mass, grain size distribution, stardust geometry, and interstellar radiation field. The principal goal of stellar population synthesis (SPS) is to extract these variables from observed SEDs. (2013, 393).

To get from empirical data (spectral energy distributions) to physical variables, one must make backwards inferences. Spectral energy distributions are ‘shaped’ by physical properties of stellar systems, including their interactions with the interstellar medium. Stellar population synthesis uses computer models and simulations to retrace the processes involved.

For instance, a theoretical Hertzsprung-Russell diagram plots a star’s effective temperature (Teff) and its luminosity on perpendicular axes, including the evolution of that relationship over a star’s life course. The H-R diagram reflects the classification of stars, including variables that are neither temperature nor luminosity but that have an effect on those variables: “Variations in composition can […] affect the stellar evolution timescales as well as the appearance of the evolution on the [Hertzsprung-Russell diagram]” (Hurley et al. 2000, Sect. 2). A star’s metal content, abundance patterns, and other physical properties affect that star’s evolution. With an accurate model of stellar evolution and a spectral energy distribution, one can determine the physical properties of the star by reverse inference.

The theory of stellar evolution is the foundation stone of modern population synthesis. From the late 1960s to the 80 s, “synthesis models were being developed that relied on stellar evolution theory to constrain the range of possible stellar types at a given age and metallicity… The substantial progress made in stellar evolution theory in the 1980s and 1990s paved the way for [this] approach to become the de facto standard in modeling the SEDs of galaxies” (Conroy 2013, 394). Stellar or evolutionary population synthesis is the name given to methods for modelling “spectrophotometric properties of stellar populations”, using “knowledge of stellar evolution” (Maraston 2005, 799). As Claudia Maraston notes, “This approach was pioneered by [Beatrice] Tinsley in a series of fundamental papersFootnote 4 that provide the basic concepts still used in present-day computations. The models are used to determine ages, element abundances, stellar masses, stellar mass functions, etc., of those stellar populations that are not resolvable in single stars, like galaxies and extragalactic globular clusters (GCs)” (ibid., 799).

Two features of stellar population synthesis are key. First, modern methods generate simulations of simple or complex stellar populations, not individual stars.Footnote 5 Second, the theory of stellar evolution is used to determine which types of stars could be represented in a given spectral energy distribution. While the spectral energy distributions are the observable empirical data in play, that data does not add up to much without the theory of stellar evolution to determine the types of stars that make up the target population.

Once that has been determined, one can move on to find values for the physical variables of interest. The simplest method is generation of a Simple Stellar Population (SSP), which “describes the evolution in time of the SED of a single, coeval stellar population at a single metallicity and abundance patternFootnote 6” (Conroy 2013, 395). An SSP, Conroy notes, “requires three basic inputs: stellar evolution theory in the form of isochrones, stellar spectral libraries, and an IMF [Initial Mass Function], each of which may in principle be a function of metallicity and/or elemental abundance pattern” (Conroy 2013, 395). An isochrone is the location of a type of star in the Hertzsprung-Russell diagram, which specifies that it belongs to a group of stars with the same age and metallic composition.Footnote 7 Isochrones are found by stellar evolution theory, and they determine the basic properties of a stellar population.

To move from stellar evolution theory to predicted observable SEDs, astrophysicists use stellar spectral libraries (Conroy 2013, Sect. 2.1.3, Sordo et al. 2010). There are two types of libraries, theoretical and empirical. Theoretical stellar spectral libraries use atomic and molecular spectral line lists to generate predictions of observable SEDs for ensembles of stars. Then “observed stars are assigned physical parameters based on a comparison with models” (Conroy 2013, 401). Population synthesis using a theoretical library generates values for physical parameters like age, stellar mass, and elemental composition using atomic and molecular spectral emission lines that are reasonably assumed to be appropriate for that type of star. Simulations using theoretical libraries are only as good as the data that goes into them. Atomic and molecular emission lines used in theoretical libraries may be incomplete, uncertain, or derived by theoretical calculation instead of empirical observation (Conroy 2013, 400–1).

Empirical stellar spectral libraries have the advantage that they are based on observed data. They do not rely on hypothetical values for the emission lines, so they do not have the kind of uncertainty associated with theoretical libraries. On the other hand, empirical libraries have the usual limitations of empirical observations.Footnote 8 Moreover, as Conroy notes, “the empirical libraries are woefully incomplete in their coverage of parameter space” (2013, 402). Current instruments may allow only for investigation of stars in certain areas, or of certain kinds of stars, which introduces sampling and detection bias.Footnote 9

A standard approach to population synthesis is to combine theoretical and empirical libraries. The combination allows the weaknesses and strengths of theoretical and empirical stellar libraries to complement each other. Theoretical libraries cover more of the parameter space, but are more uncertain. Empirical libraries are patchier in their coverage and display observational uncertainty, but provide robust data in certain domains.

3 Next-Generation Population Synthesis

The new era of precision astrophysics since the early 2000s has increased the quality of available empirical data significantly: “Galaxy evolution studies are reaching a high level of sophistication due to the very high quality of observational data permitted by modern technology, and the level of spectral details that such observations carry in” (Maraston and Strömbäck 2011, 2785–6).Footnote 10 The atomic and molecular emission and absorption lines that can be detected now can be pinpointed much more precisely and at higher resolution. The result has been a marked increase in the coverage and resolution of empirical spectral emission libraries, and of the surveys and maps of stars and galaxies that are available.

From what Elisabeth Lloyd has called a direct empiricist perspective, the new high-resolution empirical data would provide an improved perspective on the galaxy, independently of the theoretical libraries or models. The basic position of direct empiricism is that “data are treated as windows on the world, as reflections of reality, without any art, theory, or construction interfering with that reflection” (Lloyd 2012, 392). From this perspective, to deal with the challenges of population synthesis requires only improvements to empirical, observational methods, in order to gather better and better data. Over time, according to direct empiricism, the theoretical emissions libraries would wither away, replaced by robust empirical data that provides an independently convincing picture.

The development of population synthesis over time runs counter to the direct empiricist perspective. Population synthesis methods employ theories and models in analyzing data and in simulations. Stellar evolution theory is the foundation of population synthesis, and models recruit theoretical and empirical stellar libraries to generate simulations. Thus, the analysis that follows will employ the tools of model-based philosophy of science (Suppes 1962; Giere 2006; van Fraassen 2008; Lloyd 2012; Parker 2017).Footnote 11 The approach is based on the perspective that understanding a complex system “require[s] a combination of tools, including models, theory, the taking of measurements, and manipulations of raw data” (Lloyd 2012, 392). The analysis that follows will not defend any particular account of model-based reasoning, but it will assume the use of theories and models in the measurement and analysis of physical variables, in keeping with contemporary methods in population synthesis.

The two sections that follow will argue that model-based methods in next-generation population synthesis reinforce the following conclusions:

  1. 1.

    New high-resolution empirical data does not necessarily provide an improved scientific outlook independently. In fact, higher spectral resolution demands concomitant improvements in theoretical models or methods to provide a better overall perspective (Sect. 5.3.1).

  2. 2.

    The physical variables that are the target of population synthesis cannot be measured without models that employ significant theoretical resources,Footnote 12 at least, they cannot be so measured using current methods (Sect. 5.3.2).Footnote 13

3.1 High-Resolution Surveys and Theoretical Reasoning

The past few decades have seen exciting developments in new precision instruments that allow for a significant increase in the spectral resolution achievable. Higher resolution allows for the determination of narrower wavelength bands. The instruments of precision astrophysics provoke a tradeoff between the virtues of theoretical and empirical approaches to modeling stellar populations.

Astronomers Claudia Maraston and Gustav Strömbäck describe a trade-off between theoretical and empirical population synthesis methods occasioned by next-generation precision astronomy. It is clear that higher resolution data and images are preferable. Higher spectral resolution “is required for a detailed modelling of emission and absorption lines” (Maraston and Strömbäck 2011, 2786). While they note that “a high spectral resolution SED can be obtained either with theoretical or empirical stellar spectra” (ibid., 2786), Maraston and Strömbäck concur with Conroy that theoretical and empirical spectra have comparative advantages and limitations.Footnote 14 “Hence,” they conclude, “the approach of combining empirical and theoretical spectra is the most convenient one” (ibid.).

The new era of precision, high-resolution empirical data calls on significant theoretical and modeling resources, not fewer. “In this era of precision astrophysics,” Maraston and Strömbäck argue, “interpretative models, such as stellar population and galaxy models, need to keep pace with the fast observational development” (2011, 2785–6). Theories and models are used to interpret and analyze the data, and are even needed to measure physical parameters, as discussed in Sect. 5.3.2 below. Theoretical improvements must keep pace with the improvements in observational methods.

3.2 Model-Based Measurement of Physical Parameters

Determining the physical variables of a stellar system using population synthesis is the endpoint of a process that involves, not only reading off the state of a measuring instrument, but also two further steps: first employing the theory of stellar evolution as a constraint, and then using simulation to determine the value of the variables. According to some philosophical understandings of measurement, the second two steps would be considered inferences from measurement, rather than measurements.

Model-based theories include models and simulations in the process of measurement. Eran Tal’s theory of measurement argues that “a necessary precondition for the possibility of measuring is the specification of an abstract and idealized model of the measurement process” (Tal 2012, 17). For instance, idealizing assumptions may be employed to link a background theory to the experimental setup necessary to make a given measurement. Parker argues that, given a robust theory of measurement like Tal’s, “it is possible for computer simulations to be embedded in measurement practices and, indeed, for them to be embedded in measurement practices in such a way that simulation results constitute raw instrument readings or even measurement outcomes” (2017, 285). It may seem implausible that this would be the case. How can a simulation yield a more accurate measurement than a direct observation? Building on an example from Bas van Fraassen (2008, p. 146), Parker explains:

Suppose we are interested in measuring the temperature of a very small cup of hot tea at time t0, and we insert a mercury thermometer at that time; we wait a short while for the mercury to stop rising in the tube and take a reading. But thermodynamic theory tells us that the thermometer itself will affect the temperature of the tea and hence the reading obtained. To arrive at a more accurate temperature estimate for t0, our measurement process will need to include a step that corrects the thermometer reading for this interference. This might involve calculating the earlier temperature of the tea using the thermometer reading, thermodynamic theory, and our knowledge of the initial temperature of the thermometer. In this example, the equation that needs to be solved to obtain the corrected value might be solved directly, but in other cases corrected values might be obtained with the help of computer simulation. In those cases, simulation results can be direct measurement outcomes. (2017, 285)

Analogous reasoning applies, with some interesting changes, for population synthesis methods. The direct measurement in the astronomical case is the set of observed spectral energy distributions or SEDs. But SEDs are not as informative in the absence of population synthesis. Using the methods developed in the later twentieth century and described in Sect. 5.2 above, direct measurements can be combined with a theoretical analysis that identifies the kind of stars that are emanating the energy, and determine the type of stellar evolution in play. That analysis is then the source of simulations (population synthesis) that provide values for the target physical variables. These variables are measured, but not directly. Both the theoretical determination of the kinds of stars involved, and the synthesis of stellar populations on that basis, are necessary to measuring the physical properties of the target systems.

Population synthesis is an excellent case in support of Tal’s and Parker’s account of simulation-based measurement. Improving theories and models might expand the class of measurable phenomena equally as well as improving empirical instruments and data. Moreover, theory and observation work together in many cases. Improvements to empirical instruments can require enrichment of the theoretical resources that can be employed (Sect. 5.3.1). But by the same token, development of theory and models can allow for better interpretation of the data, better post-data analysis, and even better methods of instrumentation and calibration.

4 Conclusion

Next-generation methods of astronomical observation increase the precision and resolution of sky surveys, which in turn enriches the resources available for population synthesis via empirical stellar libraries. The improved observational methods in turn demand enriched theoretical and modeling resources, which ideally develop in tandem with novel data. The process of hybrid enrichment between theoretical and observational methods reinforces theory- and model-based philosophy of science. Population synthesis displays hybrid enrichment in two ways: the combined theoretical and observational methods complement each other and develop in tandem, and the process of measuring physical variables requires theories and models for robust post-data analysis.