4.1. The “cosmic laboratory”

According to Anderl (Reference Anderl and Humphreys2016), when studying general regularities, astronomers make use of the “cosmic laboratory,” that is “the multitude of different phenomena and environments naturally provided by the universe” (652).

Embracing this idea, Anderl champions the use of observational counterparts to controlled experiments: natural experiments and quasiexperiments (661–62). As the “direct equivalent of randomized controlled experiments,” natural experiments refer to the situations where groups with and without a factor happen to be “as-if” randomly assigned such that all other factors are evenly distributed between two groups of situations; in quasiexperiments, the observed situations do not happen to be exactly randomized in all other confounding factors, and one needs to evaluate them separately.

Nevertheless, the applicability of these strategies is often limited. “Randomization” of situations can rarely be achieved due to the correlation between the factor under study and others. Quasiexperiments also require the acquaintance with contextual information to analyze all the confounding factors. In many circumstances, the distribution of the target and confounding factors among the two groups cannot be independently determined. For example, to study the change in physical properties of stars throughout their evolutionary tracks, one needs to statistically compare stars at one stage with those at another. However, due to the reduced dimension of time in our snapshot observation, this leads to a circularity: to determine how old and at which stage those stars are, an evolutionary model that matches observable properties with age should have already been assumed.

Under these circumstances, the statistical methods based on the “cosmic laboratory” metaphor do not accurately describe how astronomers make inferences. I suggest that the historical reconstruction of tokens plays a crucial methodological role here. A token could help to decipher regularities of a type, offer contextual information for other tokens, and serve as a center of coherent tests.

4.2. “Rosetta Stone” situations

Astrophysicists utilize certain special token situations that I call the “Rosetta Stone” situations. Analogous to the Rosetta Stone that enabled deciphering the Egyptian scripts with contingently attached Ancient Greek decree, Rosetta Stone situations involve token objects or processes with special properties that come from the historical contingencies of the target object or its surroundings. They provide external information to decipher the internal properties of those tokens. The internal properties can subsequently be generalized to the whole type of objects sharing the same mechanism and close physical parameters.

One example of “Rosetta Stones” is star clusters. While stars scattering in the Galaxy might have any age or metallicity, stars in clusters are assumed to be born around the same region and at a very close time, sharing similar ages and metallicity and varying only in mass. These assumptions make those clusters an additional source of temporal information. They constitute an isochrone of stars with different masses, from which age could be tightly constrained using established stellar evolutionary models. Another piece of external information comes from the spatial position of those clusters in the Milky Way. Given the growth history of galaxies, globular clusters in the halo area are supposed to be much older than the open clusters on the disk, enabling age comparison across stars. This external historical information supported several important discoveries, one among which is the general sequence of stellar evolution (Dick Reference Dick2013).

Rosetta Stone situations also circumvent another limitation of statistical methods: Certain properties being investigated are not accessible in a large number of stars. For example, for most stars far away, access to their internal physical processes and chemical elements is limited to the observation of the stellar atmosphere. With divergent sources of evidence that can be found in its vicinity, the Sun thus constitutes a privileged object of study. For example, the internal structure and dynamics of the Sun can be studied with helioseismology, which requires accurate close observation of its oscillation. Chemical components of the Sun are also more comprehensively collected with the study of meteorites formed out of the same gas cloud (Frebel Reference Frebel2015). The evolutionary history of the Sun thus reconstructed is crucial for building an evolutionary model for a whole type of star with similar mass, luminosity, and chemical components.

Wylie (Reference Wylie, Dawid, Twining and Vasilaki2011) has pointed out that detailed knowledge about the history of tokens plays crucial epistemic and methodological roles in providing independent evidence for coherence tests or complements. These roles can also be found in Rosetta Stone situations in astronomy. Astronomers often speak of a problem of degeneracy: observable kind-membership conditions of a “type” of objects or phenomena may underdetermine the real type in which the generalization of theories and methods is legitimate. For example, many classes of stars delimited with synchronic properties like color and luminosity do not guarantee that they share the same evolutionary model. Coherence tests with multiple lines of evidence help to identify subdivisions within an apparent “type” and clarify conditions for generalization. These multiple lines of evidence often come from the peculiar celestial objects whose histories interlock with each other and offer constraints to each other. In a recent episode studying the cooling model of white dwarfs, Cheng, Cummings, and Ménard (Reference Cheng, Cummings and Ménard2019) adopt two independent ways of determining the age of high-mass white dwarfs, one derived from the velocity dispersion of disk stars predicted by the dynamic model specific to the Milky Way history, the other from the stars’ photometric properties. Within the entire population of white dwarfs that share similar photometric properties, the dynamic method spots a novel subpopulation that is in fact much older than the rest, a distinction that cannot be made without knowing the peculiarity of the Milky Way dynamics.

Finally, Rosetta Stone situations also offer contextual information for other tokens with interlocking histories. For example, transient dynamical effects caused by some Milky Way structures in the past provide contextual knowledge about the radial migration of certain stars, which enables the inference of their source and explains their anomalies (Minchev and Famaey Reference Minchev and Famaey2010).

The use of “Rosetta Stones” highlights an important aspect of astronomy: the codevelopment of multiple research subdomains. First, the studies of general regularities and token historical events iteratively support and fuel each other. Rosetta Stone situations with better-known histories offer contextual information for building general models, understanding other particular systems, and unveiling new “Rosetta Stones.” Second, relatively autonomous subdomains that focus on different celestial objects, such as the studies of stellar physics, Milky Way dynamics, and larger-scale cosmology, are often cross-referenced to inform, support, or correct each other. Therefore, a complex web of evidence from both tokens and regularities, as well as from different subdomains, is crucial for the progress of astronomy.

5.1. Traces and historical inference

Cleland (Reference Cleland2002, Reference Cleland2011) proposes a pattern of evidential reasoning in historical sciences. First, scientists generate a number of rival hypotheses about a past event to explain available traces, and second, they search for a new trace (aka “smoking gun”) that could be best explained by one of the hypotheses, thus offering justification for it. Characteristic of many historical studies nonetheless, many have pointed out that an important element is missing.

The missing element is concerned with what can be counted as a “smoking gun” or a trace in general. Forber and Griffith (Reference Forber and Griffith2011), for example, point out that what data counts as a “smoking gun” should not be taken for granted, but historical scientists use caution when evaluating the quality of potentially decisive evidence. Proponents of midrange theories argue that the plausibility of a common-cause explanation cannot be secured simply because it explains certain contemporary phenomena, but this connection should also be backed by regularities that guarantee its univocality and reliability (Jeffares Reference Jeffares2008). Turner (Reference Turner and Victor2013) further points out that in historical sciences that have already acquired a large amount of data, scientists do not design hypotheses and then stumble upon a “smoking gun,” but they build theories and models by finding general patterns in the portion of data that is potentially relevant to some past events.

What these philosophers stress is that the standards by which a contemporary phenomenon is identified as a trace of a past event cannot be settled directly by the immediate epistemic gain brought by taking it as a trace. There is a more complex process of recognizing something as a trace, drawing relevance to a past event, and evaluating the reliability of such connections.

5.2. Identification of traces

Similar to the notion of evidence, a trace is not only a causal concept but also epistemological. Ontologically, a trace should at least be causally affected by some aspects of an event (Turner Reference Turner2007); epistemologically, a trace is what scientists could identify and use to make inferences about a past event given their background knowledge (Currie Reference Currie2018). These widely agreed characterizations nonetheless, it is still complicated how something can be reliably identified as a trace of something in the past.

Identification and classification of traces have been a central topic in astronomy. In the age of massive sky survey projects, massive data is coupled with the difficulty of identifying the relevant portion. Not all past events of interest leave lasting and univocal signatures that help to differentiate a trace from the rest of the data and connect it to the past. First, our limited ways of observation do not have access to many properties of a star. Second, certain historically informative properties are not captured by the way stars are typically classified for synchronic purposes. Third, it is often not the properties of an individual star that reveal the plausible connection to the past, but the statistical properties of a group of stars sharing a similar history. Thus, making inferences from a historically informative group usually goes hand in hand with identifying the exact members of the group. Finally, the applicability of midrange theories is often limited. The long lifetime of celestial bodies may introduce multiple local confounders, transformations, and decay. As a result, the contemporary properties that bear a salient relation to the past often alter from one target event to another. With this, instead of choosing a fixed set of properties supported by some general midrange theories for trace identification, it is more plausible to develop a method that could find the most prominent properties given a specific event under study.

Astronomers have developed strategies to identify historically informative groups of stars. They first build catalogs of stars with all their observable properties, and then apply a method called “phase space clustering” (PSC). “Phase space” denotes the space in which all possible states of a system can be represented. Each dimension of the space stands for a physical quantity of the system. Celestial bodies are often characterized by quantities such as age, metallicity, position, speed, angular momentum, energy, and orbital shape properties. PSC finds clusters and patterns in any space defined with several of these properties.

PSC proceeds iteratively from two directions. From the theory-driven direction, scientists construct candidate models and simulations to study how different settings of a past event may leave their influences. This forward simulation forecasts what observable quantities may be more characteristic of a hypothetical model and what the relevant distribution of observables might be. The data-driven direction analyzes available data in a number of promising phase spaces to find apparent correlations or clusters that may either match the model forecasts or hint at unrealized historical causes. Algorithms of data clustering introduce a measurement of similarities and differences in data, which presents evidential power for hypotheses that explain those similarities and differences (Cat Reference Cat, Wuppuluri and Anthony2022). This mitigates the lack of stable and systematic midrange theories and possible uncertainties in the forward approach.

One application of this method is the recent reconstruction of the Milky Way formation history. This episode started at a point when scientists were aware that galaxies are formed by smaller mergers but did not know the details of how the Milky Way was assembled. As scientists did not have a preliminary grasp of what patterns to look for, PSC started by clustering kinematic and metallicity data of all the galactic halo stars. Belokurov et al. (Reference Belokurov, Erkal, Evans, Koposov and Deason2018) identified two apparent clusters of stars sharply separated in the eccentricity-metallicity space. This turns out to be evidence of the presence of one massive merger event. With the scenario being secured backwardly, scientists forwardly construct simulations of how dwarf galaxies may merge into the Milky Way with varying parameters and project the possible patterns of remnants. The match between the projection and contemporary data indicates the most likely epoch, mass, and angular momentum of the progenitor. This led to the reconstruction of the Gaia-Enceladus progenitor galaxy.

Once reconstructed, the physical properties of the progenitor are used to forecast more patterns of its remnants and to reduce confounders when scientists search for other progenitors in different datasets and phase spaces. For example, Massari, Koppelman, and Helmi (Reference Massari, Koppelman and Helmi2019) analyze a new dataset differing in both objects and properties. The new dataset records globular clusters (GC) with more properties including age, metallicity, energy, angular momentum, and orbit shape. They extend models of several entering progenitors to GCs and generate potential patterns of them in the integrals of motion space. The GC assignment is then tested by their good fit to functions in another space, the age-metallicity relation space. By clustering data from both directions and in different spaces, scientists assigned most of the observable halo GCs to their origins without much conflict. With this method, observable ex-situ GCs have been mostly assigned to six major progenitors and a few small accretion events without inconsistency both in the reconstructed merging history and in the attribution of contemporary data.

5.3. Confirmation in PSC and its condition of success

The episode defies the simplified schema of historical inference. The identification of traces goes hand in hand with the gradual establishment of hypothetical models that identify and explain the traces. The correct recognition of traces is only gradually secured over the iterative course of assigning traces, specifying models, and fitting them together consistently.

I identify three sources of confirmatory power in the final evidential web consisting of models and data. First, the models explain data patterns not only in the dataset where they are first established but also in other datasets. The confirmatory power of this explanation comes from the increasing consilience of evidence that supports each model. Second, all the apparent clusters found in these datasets can finally be reasonably assigned to an event or explained away without much conflict. Third, the constructed models for the events are consistent with each other. An argument from miracle could be applied to the last two conditions: If several models or clusters drastically deviated from the real situation, it would have been impossible that the data finally turned out completely explained and the models were consistent. This web presents a threefold fitting-together between model and data, models, and clusters in different datasets.

This complex web undermines the possibility of finding an alternative web that accounts for the data to a similar degree, mitigating the underdetermination problem. It has been stressed by Wylie (Reference Wylie, Dawid, Twining and Vasilaki2011) and Currie (Reference Currie2018) that fitting together details in a local context has the epistemic virtue of countering underdetermination. PSC further extends this insight to a broader context, that is, to a series of studies that endeavor to explain different portions of available data and reconstruct a story of historical events.

Another epistemic virtue of PSC is that the combination of the two directions of identifying traces alleviates the concern about theory ladenness. Patterns and clusters are not only recognized solely according to properties projected by models but also by clustering algorithms. Therefore, even if models are occasionally involved in the process of data processing, it does not necessarily lead to the confirmation of itself.

A possible failure in this process is misrecognizing certain confounder star clusters as relevant. The Hercules stream, for example, was misrecognized as remnants of a merger event for their shared dynamic properties. The misrecognition is noticed and corrected when additional datasets about age and metallicity are collected and taken into consideration (Bensby et al. Reference Bensby, Oey, Feltzing, Gustafsson, Israelian and Meynet2008). Thus, one important condition of success in PSC is the collection of various datasets and the cross-validation between them. By various datasets, I mean datasets about different objects or physical properties. When reconstructing the Milky Way merger history, astrophysicists have been shifting between datasets of individual stars and globular clusters, as well as across phase spaces with different combinations of physical properties. With the cross-validation between different datasets, not only more background knowledge about different types of objects and physical processes is involved to inspect the validity of those clusters and models but also the invariance of clusters in data also enhances their reality.