Gymnasiearbete
08.04.2026
Mapping the Chemical and Spatial
Structure of the Sagittarius Stream with
Gaia and LAMOST
Bayesian Parameter Estimation and Cross-Validation of
Metallicity Distributions in Tidal Debris
Yelizar Balabanov
Staffan Sejsing
With the guidance of Eric Stempels, Head of the Division of Astronomy and Space Physics,
Uppsala University
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Abstract
This study performs a Bayesian isochrone analysis of 1,241 candidate members of the
Sagittarius Stream using MIST stellar evolution models, PyMultiNest nested sampling, Gaia
DR3 photometry, and LAMOST spectroscopic metallicities. The central methodological
finding is that Bayesian isochrone fitting is not reliable for deriving stellar ages or masses
from a distant, giant-dominated population: the horizontal branch stars yield a physically
impossible median age of 0.42 Gyr, and 11.8% of all stars return ages below 1 Gyr, a direct
consequence of the age–mass degeneracy inherent to evolved giant sequences. A strong
positive correlation is found between isochrone-fitted [Fe/H] and independent XGBoost
[M/H] estimates (r = 0.749), with a systematic offset of +0.133 dex attributed to
alpha-element enhancement and solar-scaled model biases. The three spatial components of
the stream — core, trailing arm, and leading arm — differ systematically in metallicity
(−0.540, −0.685, and −0.988 dex respectively), heliocentric distance (27, 29, and 37 kpc
respectively), and line-of-sight velocity (+143.8, −152.4, and −24.0 km/s respectively),
consistent with inside-out tidal stripping of a chemically complex progenitor.
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Table of contents
Abstract................................................................................................................................... 1
Table of contents.................................................................................................................... 2
1. Introduktion......................................................................................................................... 3
1.1.1 Hierarchical galaxy formation and stellar streams.....................................................3
1.1.2 The Sagittarius stream.................................................................................................. 4
1.1.3 Stellar populations and isochrones............................................................................. 5
1.1.4 The Gaia mission and astrometric data, external catalogues and data sources.....7
1.1.5 Uncertainty and error propagation...............................................................................8
1.1.6 Metallicity as a tracer of stellar populations............................................................. 10
1.1.7 Limitations of isochrone fitting for red giant branch stars......................................11
1.1.8 The leading and trailing arms of the Sagittarius Stream......................................... 12
1.2 Aim of the study..............................................................................................................13
1.3 Research questions........................................................................................................14
1.4 Delimitations................................................................................................................... 15
2. Method och materials....................................................................................................... 17
2.1 Computational Environment and Software Specifications.........................................17
2.2 Data Acquisition and Multi-stage Processing Pipeline............................................... 18
2.3 Bayesian Inference and Stellar Parameter Estimation................................................21
3. Results............................................................................................................................... 22
4. Analisys and Diskussion of result.................................................................................. 33
4.1 Research Question 1: Parameter Reliability................................................................ 33
4.2 Research Question 2...................................................................................................... 42
4.3 Research Question 3...................................................................................................... 49
4.4 Research Question 4...................................................................................................... 60
4.5 Research Question 5...................................................................................................... 67
5. Conclusions...................................................................................................................... 74
6. Evaluation of the Working Process.................................................................................76
Acknowledgements.............................................................................................................. 79
List of references.................................................................................................................. 80
Appendices............................................................................................................................85
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1. Introduktion
1.1.1 Hierarchical galaxy formation and stellar streams
Modern cosmology describes the formation of the large-scale structure of the Universe
through the ΛCDM (Lambda Cold Dark Matter) model, in which the energy density of the
Universe is dominated by dark energy and dark matter[1]. Consequently, large galaxies form
through the accretion of smaller galaxies and, less frequently, through mergers with galaxies
of similar mass. In this framework, large galaxies such as the Milky Way were not formed as
a single monolithic system, but were created through a series of accretion events and mergers
with other galaxies[2].
When a low-mass satellite galaxy enters the gravitational potential of a much more massive
host galaxy, tidal forces begin to dominate its evolution. These forces preferentially remove
stars from the outer regions of the satellite, creating elongated structures that trace the
satellite’s orbit around the host galaxy. While the removal of stars is significant and readily
observable, gas accretion occurs on shorter timescales and, depending on physical conditions,
can either trigger or suppress star formation in the host galaxy[5]. Over time, this process
leads to the complete disruption of the satellite galaxy, while its stars remain distributed along
coherent streams in phase space[3].
These stellar streams are dynamically cold structures[4], meaning that their member stars
share similar orbital properties and originate from a common progenitor. As a result, stellar
streams preserve information about both the disrupted system and the Milky Way's
gravitational potential. The spatial morphology and kinematics of streams can therefore be
used to test models of galaxy formation and to constrain the distribution of dark matter in the
Galactic halo. Furthermore, because stellar streams are relatively easy to detect and their
members can be reliably identified, they provide valuable tools for studying their progenitor
galaxies. Since gas is accreted on much shorter timescales than stellar stripping, the stellar
populations of streams reflect the properties of the progenitor system before its disruption. As
no new stars are formed within stellar streams after disruption, the analysis of such stars to
reconstruct the past properties of disrupted galaxies is known as stellar archaeology[6,7].
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1.1.2 The Sagittarius stream
The Sagittarius Stream is one of the most prominent and well-studied stellar streams in the
Milky Way halo. It originates from the Sagittarius dwarf spheroidal galaxy (Sgr dSph), a
satellite galaxy discovered in 1994 that is currently undergoing tidal disruption as it orbits the
Milky Way [8]. Subsequent observations demonstrated that the dwarf galaxy is being
progressively stripped of its stars by the Galactic tidal field, leading to the formation of an
extended stellar stream [9].
The stream consists of both a leading and a trailing arm, which trace the orbital path of the
progenitor system around the Milky Way [9, 10]. Observations show that the Sagittarius
Stream spans a large fraction of the sky and extends over tens of kiloparsecs [10]. Large
photometric surveys such as 2MASS and SDSS enabled the first detailed mapping of its
structure [11], while Gaia has provided high-precision astrometric data that allow reliable
identification of stream members through proper motions and parallaxes [11].
The dynamical evolution of the Sagittarius Stream is governed by repeated pericentric
passages of the dwarf galaxy around the Milky Way. During each close passage, tidal forces
remove stars from the outer regions of the satellite, gradually reducing its mass [9]. Numerical
models reproduce the observed morphology of the stream and show that its spatial structure is
sensitive to the mass distribution and shape of the Milky Way’s dark matter halo [12]. For this
reason, the Sagittarius Stream has become one of the primary tools for constraining the
Galactic potential [12].
The stellar populations within the Sagittarius Stream exhibit a broad range of metallicities and
ages, reflecting the complex star formation history of the progenitor galaxy. Spectroscopic
studies have revealed both relatively metal-rich and metal-poor components, suggesting
prolonged star formation before disruption [13]. Since no new stars are formed after tidal
stripping, the stellar populations of the stream preserve a fossil record of the progenitor
system, making it an important target for studies of Galactic archaeology [14].
Due to its spatial extent, brightness, and well-characterised stellar populations, the Sagittarius
Stream represents a key laboratory for investigating both hierarchical galaxy formation and
the structure of the Milky Way halo. In this work, it serves as the primary target for analysing
stellar populations using MIST isochrones in combination with Gaia astrometric data.
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1.1.3 Stellar populations and isochrones
Stellar populations provide crucial information about the formation and evolutionary history
of galaxies [14]. A stellar population is generally defined as a group of stars that share similar
ages, chemical compositions, and formation environments [14]. In dwarf galaxies and stellar
streams, such as the Sagittarius Stream, the analysis of stellar populations allows
reconstruction of the star formation history of the disrupted progenitor system [14].
Stars evolve according to well-established physical principles governed primarily by their
initial mass and chemical composition [16]. As a result, stars of different masses follow
predictable evolutionary paths in the Hertzsprung–Russell (H–R) diagram or, observationally,
in colour–magnitude diagrams (CMDs) [16]. Features such as the main sequence turn-off
(MSTO), red giant branch (RGB), and horizontal branch (HB) provide diagnostic information
about the age and metallicity of a stellar population [16].
An isochrone is a theoretical curve in a colour–magnitude diagram representing stars of
different masses that share the same age and chemical composition [16]. Isochrones are
constructed from stellar-evolution models and enable comparison between theoretical
predictions and observational data [16]. By fitting isochrones to observed CMDs, it is
possible to estimate key parameters of a stellar population, including age, metallicity, and
distance [16].
Modern stellar evolution models incorporate updated opacities, nuclear reaction rates,
convection prescriptions, and chemical abundances. One widely used model set is the MIST
(MESA Isochrones and Stellar Tracks) database, which is based on the MESA stellar
evolution code [17]. MIST isochrones cover a broad range of ages and metallicities, making
them particularly suitable for analysing complex stellar systems such as dwarf galaxies and
stellar streams [17].
In the context of the Sagittarius Stream, isochrone fitting is an effective method for
determining the age distribution and metallicity spread of its member stars. Because no new
star formation occurs after tidal stripping, the stellar populations observed in the stream
reflect the progenitor galaxy's evolutionary history prior to disruption, an approach commonly
referred to as Galactic archaeology [14,18]. Therefore, comparing observed Gaia photometric
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data with theoretical MIST isochrones enables quantitative reconstruction of the star
formation history and chemical evolution of the system [17,18].
The combination of precise Gaia astrometry and modern stellar evolution models provides a
powerful framework for studying stellar populations in disrupted systems [18]. Isochrone
analysis not only constrains the physical properties of the stream but also contributes to a
broader understanding of hierarchical galaxy formation and Galactic archaeology [14].
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1.1.4 The Gaia mission and astrometric data, external catalogues
and data sources
The present analysis is based on the Sagittarius Stream catalogue compiled by Cunningham et
al. [19], which contains 34,240 candidate Sagittarius stream stars. In this work, several
associated datasets were combined into a unified working catalogue in order to perform robust
stellar population modelling. The dataset incorporates effective temperatures and surface
gravities (log_g) estimated by Andrae et al. [27] using XGBoost machine learning algorithms,
metallicities ([Fe/H]) derived from the LAMOST spectroscopic survey [21], and distances
adopted from the original Cunningham et al. catalogue [19]. Furthermore, the dataset utilises
other essential stellar parameters provided by the Gaia mission, including line-of-sight
extinction (A_V) and broad-band photometry in the G, BP, and RP bands [22].
For the foundational astrometric and photometric data, this analysis relies on Gaia Data
Release 3 (DR3) [22]. The Gaia DR3 catalogue provides high-precision astrometry for more
than 1.8 billion sources, with typical parallax uncertainties ranging from 0.02 to 0.04 mas for
bright stars (G < 15), increasing to approximately 0.1 to 0.5 mas for fainter sources at G
approx. 20 [22]. To ensure the reliability of the astrometric solutions, the renormalised unit
weight error (RUWE) was employed as a quality indicator. Only stars with RUWE < 1.4 were
retained, thereby excluding sources with potentially unreliable single-star solutions, such as
unresolved binaries [23]. Finally, the Gaia uncertainty tool, combined with a conservative
baseline error floor of 0.005 mag, was used to estimate the uncertainties in the broad-band
photometry [24].
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1.1.5 Uncertainty and error propagation
Proper handling of observational uncertainties is strictly required for robust Bayesian stellar
parameter estimation. In this work, the observational errors are not merely treated as limits of
precision but as standard deviations defining the Gaussian likelihood functions used by the
nested sampling algorithm (MultiNest) to explore the parameter space of stellar models. The
quality of the final posterior distributions is therefore directly dependent on the accuracy and
realism of the input uncertainties — underestimated errors produce artificially narrow
posteriors, while overestimated errors reduce the constraining power of the data.
For the photometric data from Gaia DR3 (G, BP, and RP bands), the formal catalogue
uncertainties are often exceptionally small for bright sources, frequently falling below 0.001
mag [24]. Although these values accurately reflect the internal precision of the Gaia
photometric pipeline, they do not account for systematic effects such as calibration residuals,
colour-dependent biases, or spatial non-uniformities in the photometric solution [24]. To
prevent the statistical model from being artificially dominated by photometry at the expense
of astrometric or spectroscopic constraints, a systematic error floor of 0.005 mag was added in
quadrature to the instrumental uncertainties, following established validation procedures for
Gaia photometry [24]. This ensures a more balanced and realistic likelihood weighting during
the isochrone fitting process.
The uncertainties for the effective temperature (T_eff), surface gravity (log g), and metallicity
([Fe/H]) were directly adopted from the Andrae et al. [27] and LAMOST [21] catalogues.
These errors represent the 1σ confidence intervals of the respective spectroscopic and
machine-learning derivation pipelines. For stars where uncertainties in T_eff or log g were not
explicitly provided, conservative error estimates of 500 K and 0.08 dex, respectively, were
adopted, following the calibration of typical systematic uncertainties for Gaia DR3
astrophysical parameters established by Andrae et al. (2023) [27].
The line-of-sight extinction A_V and its associated uncertainty were taken from Gaia DR3.
Where the reported extinction uncertainties were asymmetric, they were symmetrised by
adopting the mean of the upper and lower bounds as the Gaussian standard deviation. While
this introduces a minor approximation, it is a necessary step to satisfy the Gaussian likelihood
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assumption of the MultiNest sampler, and the effect on the posterior distributions is negligible
for the moderate extinction values characteristic of the Sagittarius Stream field [22].
A critical step in the error propagation involved the astrometric data. Because the Sagittarius
Stream is located at a significant heliocentric distance of approximately 20 to 55 kpc [26], the
raw Gaia DR3 parallaxes for these stars frequently possess low or negative signal-to-noise
ratios and cannot be used directly as distance constraints [22]. At such distances, the typical
Gaia DR3 parallax uncertainty of 0.1–0.5 mas corresponds to a fractional distance uncertainty
exceeding 100%, rendering the raw parallaxes uninformative [22]. Instead, robust heliocentric
distances and their associated uncertainties provided by Vasiliev et al. [26] were utilised.
However, because the standard input for stellar modelling tools such as the isochrones Python
package requires parallax, these distances were converted into synthetic parallaxes (ϖ) in
milliarcseconds using the standard inversion:
ω = 1 / 𝑟.
The corresponding parallax uncertainties (σ_ϖ) were calculated using the first-order Taylor
expansion for error propagation:
2
σ_ω = σ_𝑟 / 𝑟 .
This mathematical transformation enables the model to interpret distance constraints and their
physical limitations correctly. Ultimately, stars with larger heliocentric distances or larger
photometric uncertainties naturally yield broader posterior probability distributions for their
derived parameters, accurately reflecting the true epistemological limits of the underlying
data.
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1.1.6 Metallicity as a tracer of stellar populations
The chemical composition of stars, most commonly expressed as iron abundance [Fe/H], is
one of the most powerful tracers of the formation and evolutionary history of a stellar system
[14]. Since iron and other heavy elements are produced through successive generations of
stellar nucleosynthesis and supernovae, the metallicity of a star reflects the chemical state of
the interstellar medium at the time of its formation [14]. Consequently, a stellar population
that formed early in the history of a galaxy, when the interstellar medium had not yet been
significantly enriched, will exhibit systematically lower [Fe/H] values than a population that
formed later [31].
The metallicity distribution function (MDF) — the statistical distribution of [Fe/H] values
across a stellar population — therefore encodes the integrated star formation and chemical
enrichment history of the host system [31]. In dwarf spheroidal galaxies such as the
Sagittarius progenitor, the MDF typically spans a broad range of metallicities, reflecting a
prolonged and complex star formation history [13]. The presence of multiple distinct peaks
within an MDF may indicate the existence of chemically discrete stellar sub-populations,
formed during separate episodes of star formation or enrichment [13].
Spectroscopic studies of the Sagittarius dwarf galaxy and its stream have revealed a broad
MDF extending from approximately [Fe/H] ≈ −2.0 to [Fe/H] ≈ 0.0, with evidence for both
metal-rich and metal-poor components [13]. This chemical complexity distinguishes
Sagittarius from simpler systems and suggests a prolonged star formation history prior to tidal
disruption [31]. Because no new star formation occurs within a stellar stream after tidal
stripping [7], the metallicity distribution of stream members constitutes a preserved chemical
record of the progenitor galaxy, making it a central tool in Galactic archaeology [14].
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1.1.7 Limitations of isochrone fitting for red giant branch stars
Isochrone fitting is a widely used method for estimating stellar ages and other physical
parameters from photometric and spectroscopic data. However, its reliability is strongly
dependent on the evolutionary stage of the stars being analysed [32]. For stars on the main
sequence, particularly near the main sequence turn-off (MSTO), isochrones of different ages
are well separated in the colour–magnitude diagram, enabling relatively precise age
determinations [33]. In contrast, for stars on the red giant branch (RGB), isochrones of widely
different ages converge to nearly identical loci in the CMD, producing a fundamental
degeneracy that severely limits the precision of age estimates [32].
This degeneracy arises because the morphology of the RGB is governed primarily by
metallicity and stellar mass rather than age [32]. As a result, Bayesian isochrone fitting
applied to RGB stars typically yields age posterior distributions that are broad and strongly
influenced by prior assumptions, rather than by the observational data [32]. Soderblom (2010)
identifies this as one of the principal limitations of isochrone-based age dating, noting that for
evolved giant stars the formal uncertainties returned by fitting algorithms often underestimate
the true epistemic uncertainty [33].
In contrast, metallicity ([Fe/H]) is well constrained by isochrone fitting even for RGB stars,
because the position of the RGB in the CMD is sensitive to chemical composition [32].
Parameters such as surface gravity (log g) and luminosity (log L) are similarly well
determined for giants, as they are directly related to the observable position of the star in the
CMD [33]. The reliability of each derived parameter therefore varies significantly depending
on the evolutionary stage of the stellar sample, and a critical evaluation of
parameter-by-parameter reliability is essential for any isochrone analysis of a predominantly
giant population [32, 33].
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1.1.8 The leading and trailing arms of the Sagittarius Stream
As the Sagittarius dwarf spheroidal galaxy orbits the Milky Way, tidal forces continuously
strip stars from its outer regions, depositing them along the orbital path of the progenitor [9].
This process creates two structurally and kinematically distinct components: the leading arm,
which precedes the main body of the dwarf galaxy along its orbit, and the trailing arm, which
extends behind it [10]. The leading and trailing arms, therefore, sample stars that were
stripped at different epochs in the interaction history, with the leading arm generally
containing material removed during earlier pericentric passages [10].
Because tidal stripping preferentially removes stars from the outer — and typically more
metal-poor — regions of the dwarf galaxy first [31], the two arms are expected to exhibit
systematic differences in their stellar population properties. Observational studies have
confirmed that the leading and trailing arms differ in their mean metallicities, spatial
distances, and line-of-sight velocities [10, 12]. Numerical models of the stream further
demonstrate that the spatial separation and velocity structure of the two arms are sensitive to
the mass and shape of the Milky Way's dark matter halo [12].
The orbital geometry of the stream is commonly described using the Sagittarius coordinate
system (Λ, B), in which Λ represents the angular position along the stream's great circle, with
positive values corresponding to the leading arm and negative values to the trailing arm [10].
In the present sample, the leading arm contains stars at a mean heliocentric distance of
approximately 45 kpc, while the trailing arm stars are located at a mean distance of
approximately 20 to 40 kpc, consistent with the expected geometry of the stream [10]. The
analysis of population differences between the two arms therefore provides a direct
observational test of models of tidal stripping and chemical evolution in the Sagittarius
system [7, 31].
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1.2 Aim of the study
The primary aim of this study is to perform a multi-parameter analysis of the stellar
populations in the Sagittarius Stream using Bayesian isochrone fitting on a combination of
high-precision Gaia DR3 astrometry, broadband photometry, and external spectroscopic data.
Rather than focusing exclusively on a single stellar parameter, this work systematically
evaluates which physical properties — including metallicity, luminosity, mass, and age — can
be reliably constrained for an evolved giant population through this methodology.
A central objective of the study is to critically assess the reliability of Bayesian isochrone
fitting as an analytical tool for this specific stellar sample, thereby contributing a
methodological perspective to the field. In parallel, the derived metallicity distributions are
used to investigate the stream's chemical structure, including a spatial analysis of [Fe/H] along
the stream's orbital coordinate and a comparative examination of the leading and trailing
arms. These results are further contextualised through cross-validation with independent
metallicity estimates from Gaia XP spectra provided by Andrae et al. (2023) [27].
Ultimately, this research aims to utilise the stellar populations of the Sagittarius Stream as a
preserved chemical record of the disrupted Sagittarius dwarf spheroidal galaxy, thereby
contributing to the broader field of Galactic archaeology and to the ongoing effort to
understand the hierarchical assembly of the Milky Way.
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1.3 Research questions
1. Which stellar parameters of the Sagittarius Stream can be reliably constrained through
Bayesian isochrone fitting applied to Gaia DR3 data?
2. How do the isochrone-fitted [Fe/H] values correlate with independent metallicity estimates
from Gaia XP spectra (Andrae et al. 2023)?
3. What is the spatial distribution of stellar metallicity along the Sagittarius Stream?
4. Is Bayesian isochrone fitting a reliable method for deriving stellar parameters for an
evolved giant population such as the Sagittarius Stream?
5. Do the leading and trailing arms of the Sagittarius Stream differ systematically in their
stellar population properties and line-of-sight velocities?
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1.4 Delimitations
To maintain a strict focus on the research questions and ensure the feasibility of the study,
several distinct delimitations have been established regarding the scope of the analysis:
Restricted Use of Kinematic Data: Although line-of-sight velocities (vlos) from the
Cunningham et al. catalogue are utilised for a descriptive comparison between the leading and
trailing arms, this work does not perform dynamical modelling, orbit integration, or analysis
of proper motions. The kinematic data are used solely to characterise population-level
differences between the two arms, not to constrain the gravitational potential of the Milky
Way.
Sample Selection: The analysis does not attempt to identify new member stars of the
Sagittarius Stream or perform independent membership probability cuts. It relies exclusively
on the pre-existing catalogue of 34,240 candidate stars compiled by Cunningham et al.
(2024), accepting their membership criteria as the baseline for the population sample. The
final high-purity subsample of 1,241 stars results from quality filtering applied to this
catalogue, not from independent stream identification.
Stellar Evolution Models: Isochrone fitting is limited to the MESA Isochrones and Stellar
Tracks (MIST) grids (Choi et al. 2016). A comparative analysis using alternative stellar
evolution models, such as PARSEC or Dartmouth isochrones, is not conducted within the
framework of this project, and systematic uncertainties arising from model choice are
acknowledged but not quantified.
Metallicity Sources: The metallicity cross-validation is restricted to the XGBoost-based
estimates from Andrae et al. (2023) available within the working catalogue. A broader
comparison involving other independent spectroscopic surveys, such as APOGEE or
GALAH, falls outside the scope of this study.
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2. Method och materials
2.1 Computational Environment and Software Specifications
To ensure the reproducibility of the results, the following computational environment was
utilised for all data processing and Bayesian inference tasks. The analysis was performed
within the Windows Subsystem for Linux 2 (WSL2) framework, running the Ubuntu 24.04.3
LTS (Noble) distribution. This environment provided the necessary POSIX-compliant
infrastructure for compiling and executing the Fortran-based MultiNest libraries within a
Python-driven pipeline.
The core of the analysis was implemented using Python 3.12.3. The following specialised
scientific libraries were employed:
●​ isochrones: Used as the primary framework for stellar model grid interpolation and
handling the MIST (MESA Isochrones and Stellar Tracks) database.
●​ PyMultiNest: Provided the Python interface for the MultiNest v3.12 algorithm,
enabling the multimodal nested sampling required to derive posterior probability
distributions for stellar ages.
●​ astropy: Used for astronomical coordinate transformations, unit handling, and the
calculation of synthetic parallaxes.
●​ pandas & numpy: Employed for high-performance data manipulation and vectorised
operations on the Sgr Stream dataset.
●​ matplotlib & seaborn: Utilised for generating diagnostic visualisations, including
Colour-Magnitude Diagrams (CMD) and age distribution plots.
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2.2 Data Acquisition and Multi-stage Processing Pipeline
The preparation of the stellar sample involved a rigorous multi-stage pipeline designed to
integrate heterogeneous data sources and produce two distinct working catalogues: a
comprehensive catalogue of all stream candidates for broad population-level analysis, and a
high-purity subsample for Bayesian isochrone fitting. The entire process was documented and
implemented across a series of Jupyter Notebooks (Appendices 1–4, 6, 10). The primary
catalogue is provided as Appendix 8.
1. Initial Sample and Cross-matching
The process began with the acquisition of the Sagittarius Stream candidate catalogue from the
Zenodo repository [25]. This primary sample contains 34,240 stars identified by Cunningham
et al. (2024) [19]. To supplement this data with comprehensive astrometry and photometry, a
cross-match with the Gaia Data Release 3 (DR3) archive [22] was performed using the unique
source_id as the primary identifier (see Appendix 1). The resulting datasets were merged into
a unified framework while ensuring that no column headers were duplicated (see Appendix
2). This merged dataset, containing all available Gaia and catalogue parameters for all 34,240
candidate stars, constitutes the foundational working catalogue for the broad metallicity
analysis conducted in this study.
2. Photometric Uncertainty Refinement
Standard Gaia flux uncertainties often require correction for systematic effects [24]. To
address this, the Gaia Photometric Error Tool was utilised to calculate more realistic and
calibrated uncertainties for the G, BP, and RP bands (see Appendix 5). These refined error
estimates were subsequently integrated into the master catalogue using a dedicated merging
script (see Appendix 3). To prevent the Bayesian model from becoming overly sensitive to
infinitesimal errors, a systematic error floor of 0.005 mag was added in quadrature to all
photometric uncertainties, following established validation procedures for Gaia photometry
[24]. This correction was applied both to the full 34,240-star catalogue (see Appendix 10),
producing a corrected comprehensive dataset provided as Appendix 11, and to the high-purity
isochrone fitting subsample as part of the filtering step described below.
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3. Quality Filtering and Membership Constraints
To construct the high-purity subsample required for Bayesian isochrone fitting, several strict
selection cuts were applied (see Appendix 4):
●​ Astrometric Quality: Only sources with RUWE < 1.4 were retained to minimise
contamination from binary systems or poor astrometric fits [23].
●​ Membership Probability: A threshold of 90% was set for membership probability to
ensure the sample represents the Sagittarius Stream population as defined in the
primary catalogue [25].
●​ Chemical Constraints: Stars lacking metallicity ([Fe/H]) measurements from
LAMOST [21] or Gaia were excluded, as this parameter is a critical prior for breaking
the age-metallicity degeneracy.
4. Parameter Standardisation and Uncertainty Calibration
Final adjustments were made to transform observational data into physical inputs for the
isochrones package (see Appendix 4):
●​ Distance to Parallax: Distances from Vasiliev et al. [26] were converted into
synthetic parallaxes using a first-order Taylor expansion for error propagation, as
described in Section 1.1.5. These same Vasiliev et al. distances are adopted
consistently for all spatial analyses across both the full catalogue and the
isochrone-fitted subsample, as the isochrone-derived distances were used as input
priors during fitting and therefore cannot serve as independent estimates.
●​ Extinction (A_V): Asymmetric extinction uncertainties from Gaia DR3 were
symmetrised by adopting the mean of the upper and lower bounds.
●​ Spectroscopic Priors: For stars where uncertainties were not explicitly provided,
conservative errors for effective temperature (50 K) and surface gravity (0.08 dex)
were adopted, following the calibrations of Andrae et al. (2023) [27].
Following this comprehensive filtering and quality control process, the initial sample of
34,240 candidates was narrowed down to a final high-purity dataset of 1,241 stars. This
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curated sample, possessing robust error estimates and complete physical parameters, served as
the basis for the subsequent Bayesian inference described in Section 2.3.
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2.3 Bayesian Inference and Stellar Parameter Estimation
The derivation of stellar ages and fundamental physical properties for the curated sample was
performed using the isochrones Python package [28]. This software employs a robust
Bayesian framework to fit observational data against theoretical stellar evolution models. For
this study, the MESA Isochrones and Stellar Tracks (MIST) grids [29] were utilised as the
theoretical foundation. By interpolating across these grids, the algorithm systematically
compares the observed parameters—specifically photometric magnitudes G, BP, RP,
atmospheric properties T, log_g, [Fe/H], and synthetic parallaxes—against simulated stars of
varying masses, ages, and metallicities.
The core of this methodology relies on Bayes' theorem to calculate the posterior probability
distribution for each star's physical properties. The likelihood function evaluates the
goodness-of-fit between the observed data (including their carefully calibrated uncertainties,
as established in Section 2.2) and the theoretical MIST models. This likelihood is then
weighted by prior probability distributions (priors), which introduce necessary physical
constraints to the system. For instance, a standard Initial Mass Function (IMF) is applied as a
prior for stellar mass, while specific boundary constraints are set for age, distance, and
extinction A_V. The inclusion of highly constrained priors, particularly the spectroscopic
metallicity and synthetic parallax, is crucial for breaking classical astronomical degeneracies,
such as the age-metallicity degeneracy.[34]
To efficiently explore this complex, multi-dimensional parameter space (mass, age,
metallicity, distance, and extinction), the estimation process utilised the MultiNest algorithm
(Nested Sampling) [30]. Unlike standard Markov Chain Monte Carlo (MCMC) methods,
nested sampling is specifically optimised to navigate complex, multi-modal posterior
distributions and provides a robust estimate of the Bayesian evidence.
The complete computational setup, including the initialisation of the StarModel object and the
specific configuration of the MultiNest sampler for the 1,241 stars, is documented in detail
within the accompanying codebase (see Appendix 6). The output of this procedure yields not
only the most probable value (median) for each derived parameter but also the full posterior
probability distribution, enabling a systematic multi-parameter analysis of the Sagittarius
Stream's stellar populations and a critical evaluation of which parameters are reliably
constrained by the available data.
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3. Results
As a result of the isochrone fitting process, a comprehensive .csv catalogue containing the
derived physical parameters (such as age, metallicity, temperature, and luminosity) for each
analysed star was generated. A .csv file including combined data from the original catalogue
and the Gaia catalogue is provided as Appendix 11. A sample of the isochrone fitting results
is provided in Appendix 7. The key findings are visualised in Figures 1 through 9 below. The
code used for these visualisations is included as Appendix 9.
Figure 1 illustrates the age distribution of the fitted subset of stars in the Sagittarius Stream.
The distribution displays a structured, non-uniform shape with several peaks across the age
range of 0 to 13 Gyr.
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Figure 2 displays the [Fe/H] distribution of the fitted subset of stars. The histogram reveals
two main concentrations, centred at approximately −0.5 dex and −1.25 dex.
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Figure 3 presents the age–metallicity distribution for the fitted subset of stars, plotting [Fe/H]
on the y-axis against age on the x-axis.
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Figure 4 shows the Hertzsprung–Russell (HR) diagram for the fitted subset of stars, plotting
absolute bolometric magnitude (M_bol) on the y-axis against effective temperature (T_eff) on
the x-axis. The colour gradient indicates the derived age of each star along the evolutionary
track.
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Figure 5 presents the Kiel diagram (log g vs log T_eff) for the fitted subset of stars,
illustrating the distribution of the sample in the surface-gravity–effective-temperature plane.
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Figure 6 shows the isochrone-fitted [Fe/H] plotted against the XGBoost-derived [M/H] from
Andrae et al. (2023) [27] for the fitted subset of stars. A 1:1 reference line is included for
comparison.
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Figures 7a and 7b show the distribution of metallicity along the stream coordinate Λ for the
fitted subset of stars and for the full catalogue, respectively.
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Figure 8a shows the distribution of stars across the Λ coordinate for the fitted subset of 1,241
stars. Three spatially distinct regions are indicated in the figure.
Figures 8b–8f present results exclusively for stars within the fitted subsample, divided
according to these three regions.
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Figure 8b shows the [Fe/H] distributions of the core, leading arm, and trailing arm
populations overlaid in a single histogram.
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Figures 8c, 8d, and 8e show the [Fe/H] distributions of the core, leading arm, and trailing
arm, respectively.
Figure 8f shows the distribution of line-of-sight velocities (v_los) for the core, leading arm,
and trailing arm populations overlaid in a single histogram.
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Figure 9 shows the [M/H] distribution of the full Sagittarius Stream catalogue by
Cunningham et al. (2024) [19], comprising 34,240 candidate stars.
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4. Analisys and Diskussion of result
4.1 Research Question 1: Parameter Reliability
Which stellar parameters of the Sagittarius Stream can be reliably constrained through Bayesian
isochrone fitting applied to Gaia DR3 data?
4.1.1 Analytical approach
To evaluate the reliability of each parameter derived from the Bayesian isochrone fitting
procedure, a four-step validation framework was applied. Rather than relying on external
references as a starting point, the analysis proceeds from the observational data itself,
concluding independently before comparing them with the existing literature. The full code
for this analysis is provided in Appendix A.
The four steps are structured as follows. First, the fitted photometric magnitudes are compared
directly against the Gaia DR3 observed values to establish a photometric anchor. Second, the
parameters most sensitive to photometry — effective temperature, surface gravity, and
metallicity — are cross-validated against independent XGBoost spectrophotometric estimates
from Cunningham et al. (2024) [19], derived using the method of Andrae et al. (2023) [27].
Third, an internal physical consistency check is applied using the Stefan–Boltzmann law to
assess the self-consistency of luminosity and radius with the validated temperature. Fourth,
age and mass are examined for signs of isochrone degeneracy through their mutual correlation
structure and the physical plausibility of the derived values.
It is noted that the column labelled age in the output catalogue is stored in units of
log₁₀(age/yr), following the MIST isochrone convention (Choi et al. 2016) [15]. All age values
reported in this section have been converted to physical units in Gyr using the relation:
𝑎𝑔𝑒_𝐺𝑦𝑟 = 10
𝑎𝑔𝑒
9
/ 10 ,
with uncertainties propagated accordingly as
𝑎𝑔𝑒
σ_𝑎𝑔𝑒_𝐺𝑦𝑟 = 10
9
· 𝑙𝑛(10) · σ_𝑎𝑔𝑒 / 10 .
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4.1.2 Step 1: Photometric anchor
The most fundamental test of the fitting procedure is whether the best-fit isochrone model
reproduces the observed Gaia DR3 photometry. The fitted G, BP, and RP magnitudes were
compared against the corresponding observed values for all 1,241 stars. The Pearson
correlation coefficients are r(G) = 0.998, r(BP) = 0.998, and r(RP) = 0.997, with mean offsets
of −0.007, +0.006, and +0.010 magnitudes, respectively. The fitted BP−RP colour yields r =
0.999 and a mean offset of −0.005 mag.
These results confirm that the fitting procedure correctly recovers the input Gaia photometry
to within a few thousandths of a magnitude across the entire sample. This photometric
consistency serves as the observational anchor for all subsequent validation steps: any
parameter that is physically tied to the spectral energy distribution is expected to be reliably
constrained.
4.1.3 Step 2: Cross-validation with independent XGBoost estimates
Three astrophysically fundamental parameters — effective temperature (T_eff), surface
gravity (log g), and metallicity ([Fe/H]) — were cross-validated against independent estimates
derived from Gaia XP spectrophotometry using the XGBoost machine learning method
(Andrae et al. 2023 [27]; Cunningham et al. 2024 [4]). The results are summarised in Table 1.
Parameter
r
Mean offset
σ_diff
Status
T_eff (K)
0.949 −37 K
128 K
log g (dex)
0.928 −0.025 dex
0.200 dex Reliable
[Fe/H] (dex)
0.749 +0.133 dex
0.260 dex Reliable
Distance (kpc) 0.866 +0.64 kpc
4.51 kpc
Reliable
Reliable
Table 4.1 Cross-validation of isochrone-fitted parameters against independent XGBoost
estimates.
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The effective temperature shows strong agreement between the two methods (r = 0.949), with
a mean offset of only −37 K, which corresponds to less than 1% of the median T_eff value of
4,150 K. This level of agreement is within the expected scatter between photometric
isochrone fitting and spectrophotometric methods for cool giant stars. Surface gravity shows
equally strong agreement (r = 0.928), with a near-negligible systematic offset of −0.025 dex.
Distance estimates from the isochrone fitting correlate well with the catalogue values (r =
0.866), with a mean offset of +0.64 kpc. This small systematic offset is consistent with known
parallax zero-point corrections in Gaia DR3 [23].
Metallicity shows a moderate-to-strong correlation (r = 0.749) but a systematic offset of
+0.133 dex, with isochrone-fitted [Fe/H] values being more metal-rich than the XGBoost
[M/H] estimates. This offset is physically expected: the isochrone fitting returns [Fe/H] (the
iron abundance). At the same time, the XGBoost method estimates the total metal abundance
[M/H], which for alpha-element-enhanced old stars differs from [Fe/H] by a factor of
approximately [35]
[𝐹𝑒/𝐻]
∆[𝑀/𝐻] ≈ [𝐹𝑒/𝐻] + 𝑙𝑜𝑔(0. 638 · 10
+ 0. 362).
The offset and its physical interpretation are discussed in detail in Section 4.2. Crucially, the
strong positive correlation confirms that the isochrone-fitted metallicity is tracking a real
physical signal in the data.
4.1.4 Step 3: Internal physical consistency
The Stefan–Boltzmann law requires that the luminosity, radius, and effective temperature of a
star satisfy
𝐿
𝑅
𝑇_𝑒𝑓𝑓
𝑙𝑜𝑔( 𝐿_☉ ) = 2 · 𝑙𝑜𝑔( 𝑅_☉ ) + 4 · 𝑙𝑜𝑔( 𝑇_☉ ),
where T_☉ = 5,778 K. This relation was used as an internal consistency check. The Pearson
correlation between the fitted log L and the quantity
𝑅
𝑇_𝑒𝑓𝑓
2 · 𝑙𝑜𝑔( 𝑅_☉ ) + 4 · ( 𝑇_☉ )
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computed from the independently fitted radius and temperature is r = 0.982, with a mean
offset of +0.003 dex and a scatter of σ = 0.077 dex. The residuals show no systematic trend
with luminosity.
This result confirms that the three parameters logL, radius, and T_eff form a self-consistent
set satisfying the fundamental law of stellar physics. Since T_eff was independently validated
in Step 2, the agreement with the Stefan–Boltzmann relation establishes that log L and radius
are reliable by physical transitivity.
Picture 10 shows the correlation between different stellar parameters within the stellar
stream.
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Picture 11 shows 6 strongest correlations between parameters.
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4.1.5 Step 4: Degenerate parameters — age and mass
Unlike temperature, luminosity, and surface gravity, stellar age has no direct photometric
observable that anchors it independently. The age of a star is inferred by matching its position
in the colour–magnitude diagram to an isochrone of a particular age and metallicity. For
evolved giant stars, however, isochrones of widely different ages can intersect in the same
region of the CMD, creating a fundamental degeneracy.
After converting from log₁₀(yr) to Gyr, the derived ages span 0.0004–12.7 Gyr with a median
of 2.66 Gyr and a median uncertainty of σ_age = 1.001 Gyr (38% relative). While the
uncertainty magnitude is consistent with literature expectations for giant stars (Soderblom
2010 [33]; Pont et al. 2004 [32]), the distribution of age values reveals a clear problem when
examined by evolutionary phase.
Phase
N
Phase 2 — RGB
Median age (Gyr) σ_age (Gyr)
110 3.61
Phase 3 — CHeB/HB 44
1.702
0.42
0.157
Phase 4 — EAGB
547 3.46
1.696
Phase 5 — TPAGB
537 2.38
0.677
Table 4.2. Median derived age by evolutionary phase.
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Picture 12 shows the age mass correlation and age distribution by evolutionary phase.
The CHeB/HB stars (phase 3) yield a median age of only 0.42 Gyr — a value that is
physically implausible for a member of the Sagittarius Stream, which is expected to consist
predominantly of an old stellar population (>5 Gyr based on the known star formation history
of the Sagittarius dwarf galaxy). Additionally, 146 stars (11.8% of the total sample) across all
phases yield fitted ages below 1 Gyr. The presence of such young ages in a sample selected as
probable Sagittarius Stream members indicates that the fitting procedure is producing
physically incorrect results for a significant fraction of the sample.
The pairwise Pearson correlation analysis (Appendix 12) further reveals a strong
anti-correlation between age and mass: r(age, mass) = −0.704 and r(age, initial mass) =
−0.706, both with p ≈ 0. This coupling arises because on a MIST isochrone, a star's age and
mass are linked — a star of a given luminosity and temperature can correspond to a young,
more massive star or an older, less massive one. The fitting procedure localises the posterior
along this age–mass ridge but cannot distinguish between these solutions from photometry
alone. Furthermore, the correlation r(mass, initial mass) = +0.996 confirms that these two
columns carry essentially identical information and do not represent independent physical
outputs.
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4.1.6 Summary and comparison with literature
The four-step validation framework yields the following data-driven reliability classification:
These findings are consistent with theoretical expectations established in the literature. Pont
and Eyer (2004) [32] demonstrated that for red giant branch stars, the age–metallicity
degeneracy in the CMD makes stellar ages fundamentally difficult to constrain from
photometry alone, and that the resulting posteriors tend to be dominated by the prior rather
than the likelihood. Soderblom (2010) [33] identified the same problem in the broader context
of stellar age determination, noting that isochrone ages for giant stars carry intrinsic
uncertainties of 1–3 Gyr at best, and often larger for stars in advanced evolutionary phases.
Dotter et al. (2010) [36] showed specifically that horizontal branch stars — corresponding to
MIST phase 3 used in this study — exhibit a luminosity degeneracy that can cause isochrone
fitting to converge on anomalously young ages, consistent with the median of 0.42 Gyr found
here for CHeB/HB stars.
The age-mass coupling observed in this dataset (r ≈ −0.70 overall) is a direct consequence of
the isochrone ridge geometry described above. While the individual age uncertainties of ~1
Gyr are not by themselves unusually narrow, the physical implausibility of the fitted values
for a significant fraction of the sample — particularly for HB stars — indicates that the
posteriors are anchored to the wrong region of isochrone space. The problem is therefore not
one of precision but of accuracy: the model is confident in a physically incorrect solution.
For the remaining analysis in this thesis, age, mass, and initial mass are excluded as primary
analysis parameters. All further results in Sections 4.2 through 4.5 rely on the reliably
constrained quantities: [Fe/H], log g, log L, T_eff, and distance.
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Parameter
Status
T_eff
Reliable
r = 0.949 vs X
log g
Reliable
r = 0.928 vs X
[Fe/H]
Reliable
r = 0.749 vs X
log L
Reliable
Stefan–Boltz
Radius
Reliable
Physically co
Distance
Reliable
r = 0.866 vs c
G, BP, RP
Reliable
r = 0.997–0.9
Age
Unreliable CHeB/HB m
Mass
Unreliable r(age, mass)
Table 4.3. Parameter reliability classification from the
independent validation.
Initial mass Unreliable r(mass, initia
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4.2 Research Question 2
How do the isochrone-fitted [Fe/H] values correlate with independent metallicity estimates from Gaia
XP spectra (Andrae et al. 2023)?
4.2.1 Overview and physical context
The Bayesian isochrone fitting returns [Fe/H] as a derived parameter for each of the 1,241
analysed stars. An independent estimate of the total metal abundance [M/H] for the same stars
is available from the XGBoost machine learning method applied to Gaia XP
spectrophotometry by Andrae et al. (2023) [27], as incorporated into the Cunningham et al.
(2024) catalogue [19]. Because these two estimates are derived from entirely different
methodologies — Bayesian isochrone fitting in a multi-dimensional parameter space versus a
data-driven spectrophotometric regression — their comparison provides a direct and
independent test of whether the isochrone-fitted metallicity is tracking a real astrophysical
signal. The code for this analysis is provided in Appendix 13.
A fundamental distinction must be established before interpreting the results. The isochrone
fitting returns [Fe/H], the iron abundance relative to solar, while the XGBoost method
estimates [M/H], the total metal abundance including all elements weighted by their solar
proportions [16]. For old stellar populations with significant alpha-element enhancement —
as expected for the Sagittarius Stream based on APOGEE spectroscopy (Hasselquist et al.
2021 [31]) — [M/H] is systematically larger than [Fe/H]. The conversion between the two
quantities follows the relation derived by Salaris et al. (1993) [35]:
(α/𝐹𝑒)
[𝑀/𝐻] = [𝐹𝑒/𝐻] + 𝑙𝑜𝑔(0. 638 · 10
+ 0. 362)
For [α/Fe] ≈ +0.2 dex, characteristic of metal-poor Sagittarius Stream stars at [Fe/H] < −1.0
[31], this predicts [M/H] > [Fe/H] by approximately +0.14 dex, meaning [M/H]_XGBoost >
[Fe/H]_iso if both methods are unbiased. A positive offset in the sense [Fe/H]_iso −
[M/H]_XGBoost could therefore reflect either a genuine alpha-enhancement effect, a
systematic bias in one or both methods, or a combination of both.
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4.2.2 Comparison A — Direct: [Fe/H]_iso vs [M/H]_XGBoost
The Pearson correlation between the isochrone-fitted [Fe/H] and the XGBoost [M/H] is r =
0.749 (p = 1.91 × 10⁻²²³) (this study, Appendix 13). The regression slope is 1.009 —
near-identical to the ideal value of 1.0 — confirming proportional scaling across the full
metallicity range. The mean offset is [Fe/H]_iso − [M/H]_XGBoost = +0.133 dex (median
+0.135 dex, σ = 0.260 dex) (this study, Appendix 13). Of the 1,241 stars, 677 (54.6%) fall
within ±0.2 dex of the 1:1 line, and 1,141 (91.9%) within ±0.5 dex.
Figure 13 Direct comparison of fitted [Fe/H] to [M/H]
The offset by evolutionary phase is summarised in Table 4.4. The EAGB and TPAGB stars
show consistent offsets of +0.12 to +0.15 dex with correlations of r = 0.739 and r = 0.833,
respectively. RGB stars (phase 2) show a near-zero offset of −0.024 dex. The CHeB/HB stars
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(phase 3) are strongly anomalous with an offset of +0.449 dex and a weak correlation of r =
0.407, directly corroborating the unreliability of this phase established in Section 4.1.
Phase
N
Phase 2 — RGB
r
Mean offset [dex] σ [dex]
110 0.725 −0.024
Phase 3 — CHeB/HB 44
0.306
0.407 +0.449
0.357
Phase 4 — EAGB
547 0.739 +0.151
0.266
Phase 5 — TPAGB
537 0.833 +0.115
0.185
Table 4.4. Correlation and offset by evolutionary phase (this study, Appendix 13).
4.2.3 Comparison B — Alpha-corrected: [M/H]_calc vs [M/H]_XGBoost
To test whether the systematic offset of +0.133 dex can be explained by alpha-element
enhancement, [M/H] was computed explicitly for each star using the Salaris et al. (1993) [35]
formula, with [α/Fe] modelled as a function of [Fe/H] following the APOGEE results of
Hasselquist et al. (2021) [31] for the Sagittarius Stream. The adopted piecewise model is:
[α/Fe] = +0.20 for [Fe/H] < −1.0 (plateau); a linear decline from +0.20 to +0.05 for −1.0 ≤
[Fe/H] < −0.5; and [α/Fe] = +0.05 for [Fe/H] ≥ −0.5 (near-solar). The median [α/Fe] applied
across the sample is 0.097 dex (this study, Appendix 13).
The corrected comparison yields r = 0.741 (p = 1.80 × 10⁻²¹⁶), slope = 0.897, and a mean
offset of +0.211 dex (σ = 0.238 dex) (this study, Appendix 13). The results of both
comparisons are summarised in Table 4.5.
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Comparison A —
Comparison B — Alpha-corrected
Direct
r
0.749
0.741
Slope
1.009
0.897
Mean offset [dex] +0.133
+0.211
σ [dex]
0.260
0.238
Within ±0.2 dex
54.6%
45.5%
Within ±0.5 dex
91.9%
90.2%
Table 4.5. Summary of Comparisons A and B (this study, Appendix 13).
4.2.4 Why does the alpha-correction worsen the agreement?
The counterintuitive result that applying the physically motivated alpha-correction increases
the offset from +0.133 to +0.211 dex requires explanation. Two effects contribute to this
outcome.
First, the MIST isochrones used in this study are solar-scaled (Choi et al. 2016 [17]), meaning
they do not incorporate alpha-element enhancement. For an alpha-enhanced star, the effective
opacity — and therefore the CMD position — is governed by [M/H], not [Fe/H]. A
solar-scaled isochrone fitter matching the observed CMD position will therefore return
[Fe/H]_iso ≈ [M/H]_true, systematically overestimating the iron abundance relative to the
true [Fe/H] [17, 35]. When the Salaris correction is then applied on top of an already inflated
[Fe/H]_iso, the result is doubly overcorrected — the offset increases rather than decreases.
Second, the XGBoost method has known systematic biases for cool, metal-poor giant stars.
Andrae et al. (2023) [27] acknowledge that their method is less well calibrated at the
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metal-poor end of the distribution, where the training sample is sparse. The median XGBoost
[M/H] for this sample is −0.838 dex (this study), placing the bulk of the sample in this less
well-calibrated regime. The XGBoost estimates may therefore systematically underestimate
[M/H] for the most metal-poor stars, further widening the apparent offset when the
alpha-correction is applied.
These two effects together explain why Comparison B does not improve upon Comparison A.
The direct comparison (A) with offset +0.133 dex is therefore the more interpretable result, as
it does not introduce the additional uncertainty of an assumed [α/Fe] model based on a
different, albeit related, stellar sample.
4.2.5 Comparison with telescope observations
To contextualise these results, the isochrone-fitted [Fe/H] distribution is compared with
spectroscopic metallicity measurements from independent telescope observations. Hasselquist
et al. (2021) [31] used high-resolution APOGEE spectroscopy to study Sagittarius Stream
stars, reporting a metallicity distribution spanning approximately [Fe/H] ≈ −1.5 to 0.0 dex
with a peak near [Fe/H] ≈ −0.5 dex for the core population and more metal-poor values in the
outer arms. Monaco et al. (2005) [13] derived a broad metallicity distribution for the
Sagittarius dwarf galaxy itself extending from approximately [Fe/H] ≈ −2.0 to 0.0 dex using
medium-resolution spectroscopy, with evidence for both metal-rich and metal-poor
sub-populations.
The present isochrone-fitted [Fe/H] distribution spans −1.99 to +0.55 dex with a median of
−0.658 dex (this study), and Figure 14 shows two concentrations near −0.5 dex and −1.25 dex.
This bimodal structure is broadly consistent with the metal-rich and metal-poor populations
identified spectroscopically by Hasselquist et al. (2021) [31] and Monaco et al. (2005) [13].
The XGBoost [M/H] distribution in the full 34,240-star catalogue (Figure 9) has a median of
−0.838 dex (this study), shifted toward more metal-poor values relative to the isochrone
subsample. This is expected since the isochrone subsample was selected to include only stars
with LAMOST spectroscopic [Fe/H] measurements [21], which preferentially selects brighter
and slightly more metal-rich stars compared to the full photometric catalogue.
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Picture 14 comparison between calculated[M/H] and gaia provided [M/H].
Picture 15 presentation of offset by evolutionary phase and metallicity.
4.2.6 Summary
Both comparisons confirm that the isochrone-fitted [Fe/H] is strongly correlated with the
independent XGBoost [M/H] (r = 0.749, slope ≈ 1.0), validating it as a reliable metallicity
tracer for the RGB, EAGB, and TPAGB populations. The direct offset of +0.133 dex is
physically expected from the combination of the [Fe/H]–[M/H] distinction [35], solar-scaled
model biases [17], and XGBoost calibration effects [27]. The alpha-corrected comparison
demonstrates that the offset cannot be fully explained by alpha-enhancement alone — the
XGBoost method systematically underestimates [M/H] for this metal-poor giant population
[27]. The isochrone-fitted metallicity distribution is consistent with published APOGEE and
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spectroscopic results [31, 13], confirming that the fitting procedure recovers the known
chemical structure of the Sagittarius Stream. The CHeB/HB stars (phase 3) are excluded from
all further metallicity analyses in Sections 4.3 through 4.5.
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4.3 Research Question 3
What is the spatial distribution of stellar metallicity along the Sagittarius Stream?
4.3.1 Sample and region definitions
All analyses in this section use the fitted subsample of N = 1,197 stars (CHeB/HB excluded)
with membership probability prob_sgr > 0.75, as well as the full Cunningham et al. (2024)
[19] catalogue filtered to the same membership threshold (N = 33,012). The code for this
analysis is provided in Appendix 14.
Region boundaries are derived from two complementary KDE analyses rather than arbitrary
values (Appendix 14, Figure 15). The core is defined by the full-width at half-maximum
(FWHM) of the Lambda KDE peak of the fitted subsample, which places the half-maximum
crossing points at Λ ≈ ±12°. The arms are defined as everything outside the core: the leading
arm spans Λ > +12°, and the trailing arm spans Λ < −12°. This definition encompasses the
transition zones as physically part of the arms. The KDE valleys at Λ ≈ −43° and +38° mark
the onset of the densely populated arm regions within the subsample but do not define
separate zones.
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Picture 15: visualisation of the boundaries of stream regions
Metallicity populations are defined by the minimum of the KDE of the [Fe/H] distribution
(bw = 0.18), which reveals two clear peaks at [Fe/H] = −1.16 and −0.53 dex separated by a
valley minimum at [Fe/H] = −0.97 dex (Appendix 14, Figure A14_feh_kde_populations).
Stars with [Fe/H] ≥ −0.97 dex are classified as the metal-rich population (N = 875), and
stars with [Fe/H] < −0.97 dex as the metal-poor population (N = 322). This bimodal
structure is independently visible in both the isochrone-fitted [Fe/H] and the XGBoost [M/H]
distributions.
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Picture 16: distribution of metallicities across the stellar population
Note on disk contamination: the full catalogue contains a metal-rich feature at Λ ≈ 15–20°,
visible in the hexbin map (Figure A14_2d_hexbin). Analysis shows that after applying the
prob_sgr > 0.75 filter, 229 stars remain in this zone with median [M/H] = −0.45 dex —
substantially more metal-rich than genuine stream stars — consistent with residual Galactic
disk contamination. This region is flagged on all relevant figures and excluded from
quantitative arm analyses.
Picture 17: binned map of Sagittarius stream
4.3.2 Spatial distribution of the stream
The galactocentric XY projection of the Sagittarius Stream is shown in Figure
A14_stream_map_sun, constructed using Galactic coordinates (l, b) and isochrone-fitted
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distances, with the Sun placed at the origin and the Galactic Centre at (−8.122, 0) kpc
(GRAVITY Collaboration 2018) [37]. The stream extends from approximately 15 to 89 kpc
from the Sun (this study, Appendix 14), tracing a large arc through the Galactic halo. The
leading arm lies at systematically larger heliocentric distances (median ~36 kpc) than the core
(~27 kpc) or trailing arm (~29 kpc), consistent with the known orbital geometry of the stream
[10, 12].
The dominant population map (Figure 18) shows that the metal-rich population (blue)
overwhelmingly dominates the core bins (>80% in most bins), while the leading arm bins
shift progressively toward metal-poor dominance (red) with increasing Λ. The square-bin grid
maps (Figure A14_2d_grid_map) confirm a consistent spatial metallicity structure across both
datasets, with mean [Fe/H] ranging from approximately −0.5 dex in the core to −1.0 to −1.3
dex in the leading arm.
Figure 18: dominant populations within different regions of the Sagittarius Stream.
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Figure 19: average metallicity in each bin.
4.3.3 Regional metallicity statistics
The median [Fe/H] values for the three regions are summarised in Table 4.6, together with
full-catalogue XGBoost [M/H] values as an independent cross-check.
Region
Core (±12°)
N
Median
N (full
Median
(sub)
[Fe/H]_iso
cat.)
[M/H]_XGBoost
519
−0.540
22,365
−0.787
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Trailing arm
310
−0.685
6,517
−0.945
368
−0.988
4,130
−0.939
(<−12°)
Leading arm
(>+12°)
Table 4.6. Median metallicity per region (this study, Appendix 14).
The ordering is consistent across both datasets: core is the most metal-rich, leading arm the
most metal-poor, trailing arm intermediate. All pairwise Mann-Whitney U tests are highly
significant (this study, Appendix 14): Core vs Leading p = 3.30 × 10⁻⁵³; Core vs Trailing p =
5.47 × 10⁻¹⁰; Leading vs Trailing p = 3.49 × 10⁻¹³. This ordering is further confirmed by the
KDE comparison (Figure 20), the cumulative distributions (Figure 21), and the box plots
(Figure 22). All three visualisation methods show the same consistent shift from metal-rich
core to metal-poor leading arm.
Figure 20: metallicity comparison
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Figure 21: metallicity distribution within stellar stream.
Figure 22: metallicity distribution in each region of the stellar stream.
4.3.4 Population analysis by region
The most striking result of the spatial analysis is the dramatic variation in the metal-poor
fraction across the three regions, summarised in Table 4.7.
Region
Metal-rich (≥−0.97) Metal-poor (<−0.97)
MP
fraction
Core
N=462, med=−0.510 N=57, med=−1.189
11.0%
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Trailing arm
N=217, med=−0.559 N=93, med=−1.241
30.0%
Leading arm N=181, med=−0.680 N=187, med=−1.309
50.8%
Table 4.7. Metal-rich and metal-poor population fractions per region (this study, Appendix
14).
The metal-rich population overwhelmingly dominates the core, with only 11.0% of stars being
metal-poor. The trailing arm shows an intermediate fraction of 30.0%. Most remarkably, the
leading arm has a near-equal split with 50.8% metal-poor stars — nearly five times the core
fraction (this study, Appendix 14). The metal-poor fraction as a function of Λ (Figure 23)
shows a monotonic increase from core to leading arm, with each 20° bin exhibiting
progressively higher metal-poor fractions.
Within each region, the two populations show similar absolute median [Fe/H] values
regardless of region (metal-rich: −0.51 to −0.68 dex; metal-poor: −1.19 to −1.31 dex), which
suggests that the same two underlying stellar populations are present throughout the stream
but in proportions that change systematically with distance from the core.
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Figure 23: metallicity distribution between different parts of the Sagittarius stream.
4.3.5 Metallicity gradient analysis
The Pearson correlation between [Fe/H] and Λ across the full fitted subsample is r = −0.253
(p = 7.13 × 10⁻¹⁹) (this study, Appendix 14), indicating a statistically significant but moderate
overall trend. However, when the gradient is tested within each arm separately, different
results emerge. Within the leading arm, the gradient slope is −0.0010 dex/degree with r =
−0.082 and p = 0.116 — statistically indistinguishable from zero (this study, Appendix 14).
Within the trailing arm, the slope is −0.0035 dex/degree with r = −0.151 and p = 0.008 —
marginally significant but physically very weak, corresponding to only ~0.5 dex over the
entire trailing arm extent.
This finding reveals that the metallicity structure of the Sagittarius Stream is better described
as a discrete compositional step between regions than a continuous spatial gradient. The
global r = −0.253 arises primarily from the core-to-arm contrast rather than from a smooth
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within-arm gradient. This is further visible in the binned gradient plots (Figure 24), where the
within-arm median [Fe/H] bins show no systematic trend in the leading arm and only a weak
trend in the trailing arm.
Figure 24: metallicity distribution regarding coordinates within the stellar stream.
4.3.6 Comparison with literature
The metallicity ordering and population fractions found here are fully consistent with the
inside-out tidal stripping model of the Sagittarius system. Hasselquist et al. (2021) [31]
showed using APOGEE spectroscopy that the Sagittarius Stream leading arm is
systematically more metal-poor than the core, with the trailing arm at intermediate
metallicities — precisely the ordering found here across both the isochrone-fitted subsample
and the full XGBoost catalogue. They interpret this as a consequence of tidal stripping
preferentially removing stars from the outer, more metal-poor regions of the progenitor galaxy
during earlier pericentric passages [31].
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Law and Majewski (2010) [12] demonstrated through N-body modelling that the leading and
trailing arms sample material stripped at different orbital epochs, with the leading arm
generally containing older, tidally processed material from larger galactocentric radii. The
near-equal metal-poor fraction in the leading arm (50.8%) compared to only 11.0% in the core
directly supports this interpretation: the leading arm has preferentially accreted the outer,
metal-poor population of the progenitor [31, 12].
The absence of a significant within-arm gradient in the leading arm (p = 0.116) is consistent
with the expectation that each orbital wrap samples a relatively homogeneous population at
the time of stripping, producing a step-like rather than gradient-like spatial metallicity
structure [12]. The weak trailing arm gradient (slope = −0.0035 dex/degree, p = 0.008) may
reflect a more complex stripping history with multiple pericentric passages contributing stars
of slightly different metallicities at different orbital phases.
The absolute metallicity values are in good agreement with published spectroscopic results.
Monaco et al. (2005) [13] reported a core metallicity peak near [Fe/H] ≈ −0.5 dex, consistent
with the core median of −0.540 found here. The leading arm median of −0.988 dex and the
presence of a near-equal metal-poor fraction are consistent with the outer, more metal-poor
populations identified in APOGEE [31] and medium-resolution spectroscopic studies [13].
4.3.7 Summary
The spatial metallicity analysis of the Sagittarius Stream reveals three key results. First, there
is a statistically robust metallicity ordering: core (median [Fe/H] = −0.540) > trailing arm
(−0.685) > leading arm (−0.988), confirmed by both isochrone fitting and independent
XGBoost estimates, with all pairwise differences highly significant (p < 10⁻⁹). Second, the
metallicity variation is best described as a discrete compositional step — the metal-poor
fraction increases monotonically from 11.0% in the core to 50.8% in the leading arm, while
within-arm gradients are either absent (leading arm: p = 0.116) or physically weak (trailing
arm: slope = −0.0035 dex/degree). Third, the same two metallicity populations (metal-rich
peak at [Fe/H] ≈ −0.53 dex; metal-poor peak at [Fe/H] ≈ −1.16 dex) are present in all three
regions, but in dramatically different proportions. These results provide strong observational
support for the inside-out tidal stripping model of the Sagittarius system [31, 12, 13].
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4.4 Research Question 4
Is Bayesian isochrone fitting a reliable method for deriving stellar parameters for an evolved giant
population such as the Sagittarius Stream?
4.4.1 Overview
This section synthesises the findings from Sections 4.1 and 4.2 into a direct methodological
evaluation of Bayesian isochrone fitting applied to the Sagittarius Stream giant population.
The analysis addresses reliability at two levels: which individual parameters are trustworthy,
and whether the method as a whole is appropriate for this type of stellar sample. The code for
this analysis is provided in Appendix 15.
The fitted sample of 1,241 stars spans four MIST evolutionary phases (this study, Appendix
15): RGB (phase 2, N = 110, 8.9%), CHeB/HB (phase 3, N = 44, 3.5%), EAGB (phase 4, N =
547, 44.1%), and TPAGB (phase 5, N = 537, 43.3%). The sample is therefore dominated by
stars in advanced evolutionary stages (EAGB and TPAGB comprising 87.4% of the sample),
for which the CMD position is governed primarily by metallicity, luminosity, and surface
gravity rather than age.
4.4.2 Parameter-by-parameter reliability assessment
The signal-to-noise ratios and relative uncertainties across all fitted parameters are
summarised in Table 4.8.
Parameter Rel. uncertainty SNR (median) Reliability
T_eff
0.9%
117
Reliable
log L
1.6%
63
Reliable
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log g
4.9%
22
Reliable
[Fe/H]
4.1%
20
Reliable
Radius
5.3%
19
Reliable
Mass
13.4%
7.5
Unreliable
Age
37.6%
2.6
Unreliable
Table 4.8. Parameter precision and reliability classification (this study, Appendix 15).
The five reliable parameters — T_eff, log L, log g, [Fe/H], and radius — are all directly
constrained by observational data. T_eff is determined by stellar colour through the
photometric bands [17]; log L follows from distance and apparent magnitude; log g and
[Fe/H] are constrained by the CMD position in combination with spectroscopic priors. Their
mutual self-consistency is confirmed by the Stefan–Boltzmann relation:
𝑟(𝑙𝑜𝑔_𝐿, 2 · 𝑙𝑜𝑔_𝑅 + 4 ·
𝑙𝑜𝑔_𝑇_𝑒𝑓𝑓
𝑇_☉
) = 0. 982
(this study, Appendix 15), demonstrating that the fitting procedure produces physically
coherent outputs for these quantities.
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Picture 25: signal-to-noise ratio across different evolutionary phases within the fitted subset.
Picture 26: visualisation of the Stefan-Boltzmann internal check
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4.4.3 Unreliability of age and mass: evidence and mechanism
Age. The age column is stored in the output catalogue as log₁₀(age/yr) following the MIST
convention [17], and is converted to physical units (Gyr) using age_Gyr = 10^age / 10⁹ before
interpretation. After this conversion, the fitted ages span 0.07–12.7 Gyr with a median of 2.66
Gyr and a median uncertainty of 1.001 Gyr (38% relative) (this study, Appendix 15). While
the uncertainty magnitude is broadly consistent with what Soderblom (2010) [33] identifies as
the realistic precision limit for isochrone ages of giant stars (~1–3 Gyr), the distribution of
fitted values by evolutionary phase reveals a fundamental problem.
The CHeB/HB stars (phase 3, EEP 629–700) yield a median age of only 0.42 Gyr (this study,
Appendix 15) — a value that is physically impossible for Sagittarius Stream members. The
stream's star formation history is well established to be predominantly old, with the bulk of
star formation occurring more than 5–8 Gyr ago [7]. A median age of 0.42 Gyr implies a
stellar population that formed after the Sagittarius progenitor had already been substantially
disrupted, which contradicts the known archaeology of the system. Moreover, 146 stars
(11.8%) across all phases yield fitted ages below 1 Gyr (this study, Appendix 15), and 423
stars (34.1%) yield ages below 2 Gyr — all implausible for a Sagittarius Stream population.
The mechanism for this failure is well established in the literature. Dotter et al. (2010) [36]
showed that horizontal branch stars — corresponding to MIST phase 3 — occupy a
luminosity range in the CMD that the isochrone model maps onto young, massive turn-off
stars from younger isochrones. Because the CMD position of an HB star resembles that of a
~0.3–1 Gyr main sequence turn-off point in a solar-scaled grid, the fitter converges on a
young age with artificially high confidence. This is a direct consequence of fitting
solar-scaled MIST isochrones [17] to a population that is known to be alpha-enhanced [31],
compounded by the HB luminosity degeneracy identified by Dotter et al. (2010) [36]. As
established in Section 1.1.7, Pont and Eyer (2004) [32] and Soderblom (2010) [33] both
identify this as a fundamental limitation of isochrone-based age dating for giant stars.
Mass. The strong anti-correlation between age and mass — r(age, mass) = −0.704 (p ≈ 0)
(this study, Appendix 15) — confirms that these two parameters are not derived independently.
On a MIST isochrone, a star's position in the CMD that is matched by the algorithm maps
onto a ridge in age–mass space: an older, lower-mass solution is nearly photometrically
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identical to a younger, higher-mass solution. The posterior localises somewhere along this
ridge, but neither age nor mass is independently anchored by the available photometric data.
The correlation r(mass, initial mass) = +0.996 (this study, Appendix 15) further demonstrates
that current and initial mass are effectively redundant outputs carrying no additional
independent physical information.
Picture 27: age mass relation, and mass vs initial mass distribution.
4.4.4 Phase-dependent reliability
An important nuance emerges when reliability is examined by evolutionary phase. The [Fe/H]
SNR varies substantially between phases: phase 3 (CHeB/HB) yields a median [Fe/H] SNR of
only 3.2, compared to 15.4 for RGB (phase 2) and 30.7 for TPAGB (phase 5) (this study,
Appendix 15). This confirms that metallicity — while generally reliable — is also poorly
constrained for horizontal branch stars, consistent with the findings of Section 4.2 where
phase 3 showed an anomalous offset of +0.449 dex relative to XGBoost estimates. This
phase-dependent failure reinforces the decision to exclude CHeB/HB stars from all metallicity
analyses in Sections 4.2 and 4.3.
By contrast, T_eff shows uniformly high SNR across all phases (112–142), as expected for a
parameter determined primarily by stellar colour, which is insensitive to the age–mass
degeneracy. Surface gravity similarly shows stable SNR across phases (17–37). Luminosity
shows a slight increase from phase 2 to phase 5, reflecting the increasing luminosity of more
evolved giants.
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4.4.5 Overall methodological assessment
Bayesian isochrone fitting with MIST models and PyMultiNest [30] is a powerful and
computationally robust method that reliably constrains the thermodynamic and structural
parameters of evolved giant stars — T_eff, log g, log L, [Fe/H], and radius — when applied to
a sample with good photometric and spectroscopic priors. The self-consistent
Stefan–Boltzmann check (r = 0.982) and the cross-validation with independent XGBoost
estimates (r = 0.749 for [Fe/H], r = 0.949 for T_eff) confirm that the fitting procedure is
physically coherent and produces meaningful outputs for these quantities.
However, the method is not appropriate for deriving stellar ages or masses for a
predominantly giant population without additional constraints beyond broadband photometry
and spectroscopic metallicity. The fitted age distribution contains 11.8% of stars with ages
below 1 Gyr — physically impossible for Sagittarius Stream members — and the CHeB/HB
phase yields systematically incorrect ages (median 0.42 Gyr) due to the well-documented
horizontal branch luminosity degeneracy [36]. Age and mass are therefore excluded from all
further analyses in this thesis.
This conclusion is consistent with the established understanding in the field. Soderblom
(2010) [33] identified the RGB and HB as the evolutionary stages most susceptible to
isochrone age degeneracy, noting that formal age uncertainties from fitting algorithms
underestimate the true epistemic uncertainty for evolved stars. Pont and Eyer (2004) [32]
showed that Bayesian isochrone posteriors for giant stars are typically prior-dominated rather
than data-driven for age, while being genuinely data-constrained for metallicity and surface
gravity. The present results confirm both conclusions through independent empirical analysis
of the Sagittarius Stream dataset.
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Picture 28: Kiel diagram showing the distribution of evolutionary stages and metallicity
within the stellar stream.
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4.5 Research Question 5
Do the leading and trailing arms of the Sagittarius Stream differ systematically in their stellar
population properties and line-of-sight velocities?
4.5.1 Overview
This section compares the three spatial components of the Sagittarius Stream — core, leading
arm, and trailing arm — across multiple independently constrained stellar parameters:
metallicity [Fe/H], line-of-sight velocity (v_los), surface gravity (log g), luminosity (log L),
effective temperature (T_eff), heliocentric distance, and evolutionary phase composition. All
analyses use the fitted subsample with prob_sgr > 0.75 and CHeB/HB stars excluded (core N
= 519, leading arm N = 368, trailing arm N = 310). The code for this analysis is provided in
Appendix 16.
As established in Section 4.3, the three regions differ significantly in metallicity. Section 4.5
extends this comparison to kinematic and structural parameters, providing a more complete
picture of the systematic differences between stream components.
4.5.2 Metallicity differences
The metallicity results from Section 4.3 are summarised here for completeness. The core
shows a median [Fe/H] = −0.540 dex (σ = 0.271), the trailing arm −0.685 dex (σ = 0.415), and
the leading arm −0.988 dex (σ = 0.384) (this study, Appendix 16). All pairwise differences are
highly significant: Core vs Leading p = 3.30 × 10⁻⁵³, Core vs Trailing p = 5.47 × 10⁻¹⁰,
Leading vs Trailing p = 3.49 × 10⁻¹³ (Mann-Whitney U) (this study, Appendix 16).
A notable additional finding is the difference in [Fe/H] dispersion between components. The
core shows a narrower interquartile range (IQR = 0.291 dex) compared to the leading arm
(IQR = 0.627 dex) and trailing arm (IQR = 0.586 dex) (this study, Appendix 16). The broader
metallicity spread in the arms is consistent with the expectation that tidal stripping samples
stars across a wider range of galactocentric radii — and therefore a wider range of original
metallicities — than the retained core population.
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Picture 29: [Fe/H] distribution among different parts of the stellar stream.
4.5.3 Kinematic differences
The line-of-sight velocity distributions of the three regions are dramatically and cleanly
separated (this study, Appendix 16). The core has a median v_los = +143.8 km/s (σ = 13.4
km/s), the leading arm −24.0 km/s (σ = 41.4 km/s), and the trailing arm −152.4 km/s (σ = 30.3
km/s). All three pairwise differences are extremely significant (all p < 10⁻¹⁰⁰, Mann-Whitney
U) (this study, Appendix 16).
The kinematic separation between the three components provides independent validation of
the spatial classification based on Lambda boundaries. The total velocity separation between
the leading and trailing arms of approximately 128 km/s, and between the core and trailing
arm of approximately 296 km/s, are consistent with the expected orbital velocities of stars at
different phases of the Sagittarius orbit [10, 12]. The trailing arm's strongly negative v_los
reflects material moving away from the observer along the Galactic line of sight as it recedes
along the trailing orbital path, while the leading arm's near-zero but slightly negative v_los
reflects material approaching in a different part of the orbit [10]. The core's strongly positive
velocity reflects the main body of the stream moving towards the observer at its current
orbital phase.
This kinematic clean separation across three independently derived spatial regions — based
on Lambda coordinates, not on v_los — confirms that the three regions genuinely sample
physically distinct components of the stream's orbit [12].
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Picture 30: line-of-sight velocities of different parts of the stellar streams.
4.5.4 Structural parameter differences
Beyond metallicity and kinematics, the three stream components show systematic differences
in fitted stellar parameters that reflect differences in their underlying stellar populations (this
study, Appendix 16).
Surface gravity. The core has a systematically lower median log g = 0.739 dex compared to
the leading arm (1.212 dex) and trailing arm (1.323 dex), all significantly different (MW p <
10⁻²⁰) (this study, Appendix 16). Stars with lower surface gravity are physically larger and
more evolved. This difference is primarily a consequence of the evolutionary phase
composition described below.
Luminosity. The core shows higher median log L = 3.188 compared to the leading arm
(2.870) and trailing arm (2.724) (this study, Appendix 16). More luminous stars at a given
T_eff are physically larger and more evolved, consistent with the lower log g in the core.
Effective temperature. The core is systematically cooler (median T_eff = 3,901 K) than the
leading arm (4,351 K) and trailing arm (4,324 K) (this study, Appendix 16). Cooler giants at
similar luminosities are again more physically extended, consistent with the log g trend.
These three correlated differences — lower log g, higher log L, lower T_eff in the core — all
point to the same underlying cause: the core contains a systematically more evolved stellar
population than the arms.
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Picture 31: distribution of different parameters among different parts of the stellar stream.
4.5.5 Evolutionary phase composition
The evolutionary phase composition reveals a striking and physically significant difference
between regions (this study, Appendix 16):
Phase
Core
Leading arm
Trailing arm
RGB (phase 2)
4.4% (N=23)
14.4% (N=53)
11.0% (N=34)
EAGB (phase 4)
27.4% (N=142)
55.4% (N=204)
64.8% (N=201)
TPAGB (phase 5) 68.2% (N=354)
29.9% (N=110)
23.5% (N=73)
Table 4.9. Evolutionary phase composition by region (this study, Appendix 16).
The core is dominated by TPAGB stars (68.2%), which are the most evolved and luminous
cool giants. The leading and trailing arms are instead dominated by EAGB stars (55% and
65% respectively), with TPAGB comprising only ~24–30%. This difference directly explains
the observed differences in log g, log L, and T_eff between the components: TPAGB stars are
systematically more luminous, cooler, and larger than EAGB stars at the same metallicity.
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The physical interpretation of this difference requires caution. It may partly reflect a genuine
population difference — the core retaining a different stellar mass function or more evolved
stars — but it may also reflect a photometric selection effect: TPAGB stars are intrinsically
brighter and more easily detected at the greater distances of the arms, yet they appear
proportionally fewer there. This could indicate that the arm samples are relatively less
complete for the most evolved, reddest giants. Disentangling these effects would require
comparison with luminosity functions and detailed completeness modelling, which falls
outside the scope of this study.
Picture 32: evolutionary phase distribution within the stellar stream.
4.5.6 Distance
The median heliocentric distances confirm the expected geometric structure of the stream:
core 26.9 kpc, trailing arm 28.7 kpc, and leading arm 36.6 kpc (this study, Appendix 16). The
leading arm spans a particularly wide distance range (15.3–89.2 kpc), reflecting the extended
orbital path sampled by the leading arm wrap [10]. The trailing arm shows a narrower
distribution (14.8–78.4 kpc) consistent with a more recently stripped population at
intermediate orbital phases.
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Picture 33: distance distribution among different parts of the stellar stream.
4.5.7 Comparison with literature
The kinematic differences found here are fully consistent with N-body models and
observations of the Sagittarius Stream. Majewski et al. (2003) [10] predicted and observed
that the leading and trailing arms of the stream have systematically different line-of-sight
velocities as a function of orbital phase, with the trailing arm at negative v_los and the leading
arm near zero or slightly negative in the present Galactic quadrant — precisely the pattern
observed here. Law and Majewski (2010) [12] further showed that the velocity separation
between components provides constraints on the Milky Way's dark matter halo shape,
confirming that the measured kinematics carry genuine physical information about the
stream's orbital history.
The metallicity ordering (core most metal-rich, leading arm most metal-poor) is consistent
with the inside-out stripping model confirmed observationally by Hasselquist et al. (2021)
[31] using APOGEE spectroscopy, as discussed in detail in Section 4.3.
The broader [Fe/H] dispersion in the arms (σ ≈ 0.38–0.42 dex) compared to the core (σ = 0.27
dex) is consistent with findings from Monaco et al. (2005) [13], who identified a complex,
multi-component MDF in the Sagittarius system and noted that the outer stream populations
show a broader metallicity range than the central dwarf galaxy.
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4.5.8 Summary
The leading arm, trailing arm, and core of the Sagittarius Stream differ systematically across
all analysed parameters. The most significant differences are: (1) metallicity — core is 0.45
dex more metal-rich than the leading arm (p = 3.30 × 10⁻⁵³); (2) kinematics — the three
components are cleanly separated in v_los with a total range of ~300 km/s, independently
confirming the spatial classification; (3) evolutionary phase composition — the core is
dominated by highly evolved TPAGB stars (68%) while the arms are dominated by EAGB
(55–65%); and (4) structural parameters — the core shows systematically lower log g, higher
log L, and lower T_eff, consistent with its more evolved stellar population. These systematic
differences are consistent with the expected properties of a stream produced by inside-out
tidal stripping of an alpha-enhanced, chemically complex progenitor [31, 12, 13, 10].
Picture 34: multiparameter comparison between different parts of the Sagittarius Stream.
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5. Conclusions
This study performed a multi-parameter Bayesian isochrone analysis of 1,241 high-purity
candidate members of the Sagittarius Stream using MIST stellar evolution models [17] and
the PyMultiNest nested sampling algorithm [30], drawing on Gaia DR3 photometry and
astrometry [22], LAMOST spectroscopic metallicities [21], and the stream catalogue of
Cunningham et al. (2024) [19].
Research Question 1. Six physical parameters — T_eff, log g, [Fe/H], log L, radius, and
distance — are reliably constrained by the fitting procedure, with cross-validation correlations
of r = 0.866–0.949 against independent estimates. Stellar age, mass, and initial mass are
unreliable: the CHeB/HB population yields a physically impossible median age of 0.42 Gyr,
11.8% of all stars return ages below 1 Gyr, and the age–mass anti-correlation (r = −0.704)
confirms that these quantities are not independently anchored by photometry. This is a direct
consequence of the horizontal branch luminosity degeneracy [36] and the fundamental
isochrone age degeneracy for giant stars [32, 33].
Research Question 2. The isochrone-fitted [Fe/H] correlates strongly with the independent
XGBoost [M/H] estimates of Andrae et al. (2023) [27] (r = 0.749, slope = 1.009), confirming
that the fitting recovers a genuine astrophysical metallicity signal. The systematic offset of
+0.133 dex is physically expected from the solar-scaled nature of the MIST models [17], the
[Fe/H]–[M/H] distinction for alpha-enhanced stars [35], and XGBoost calibration limitations
at the metal-poor end [27]. The recovered metallicity distribution — bimodal, centred near
−0.5 and −1.25 dex — is consistent with published APOGEE and spectroscopic results for the
Sagittarius system [31, 13].
Research Question 3. The stream exhibits a robust metallicity ordering: core (median [Fe/H]
= −0.540) > trailing arm (−0.685) > leading arm (−0.988), with all pairwise differences highly
significant (p < 10⁻⁹). This structure is best described as a discrete compositional step rather
than a continuous gradient: within-arm gradients are either absent (leading arm, p = 0.116) or
negligible (trailing arm, slope = −0.0035 dex/degree). The metal-poor fraction increases
monotonically from 11.0% in the core to 50.8% in the leading arm, providing strong
observational support for the inside-out tidal stripping model [31, 12].
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Research Question 4. Bayesian isochrone fitting with MIST models and PyMultiNest
reliably constrains the thermodynamic and structural parameters of evolved giant stars when
applied with high-quality photometric and spectroscopic priors, as confirmed by the
Stefan–Boltzmann internal consistency check (r = 0.982). However, it is not appropriate for
deriving stellar ages or masses for a predominantly giant population without additional
constraints beyond broadband photometry, because the resulting posteriors are
prior-dominated rather than data-driven for these quantities [32, 33].
Research Question 5. The three stream components differ systematically across all analysed
parameters. Beyond the metallicity ordering established under RQ3, they are cleanly
separated in line-of-sight velocity (core: +143.8 km/s; leading arm: −24.0 km/s; trailing arm:
−152.4 km/s), independently confirming the spatial classification [10, 12]. The core is
dominated by TPAGB stars (68.2%) and shows lower log g, higher log L, and lower T_eff
than the arms, which are dominated by EAGB stars (55–65%). The broader metallicity
dispersion in the arms relative to the core is consistent with tidal stripping sampling a wider
range of galactocentric radii [13]. These differences are collectively consistent with inside-out
tidal disruption of an alpha-enhanced, chemically complex dwarf spheroidal progenitor [31,
12, 10].
Future directions. Three extensions follow naturally from this work. First, the use of
alpha-enhanced isochrone grids — such as BaSTI or PARSEC — would eliminate the
solar-scaled model bias identified here. Second, incorporating asteroseismic log_g and mass
measurements as additional priors would help break the age–mass degeneracy for the RGB
subsample [33]. Third, extending the analysis to the second and third orbital wraps of the
Sagittarius Stream would allow a more complete chemical mapping of the full orbital path,
contributing to a deeper reconstruction of the star formation and enrichment history of the
Sagittarius progenitor.
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6. Evaluation of the Working Process
The project originated from a question about stellar migration within the Milky Way galaxy.
The initial idea was to investigate how stars migrate across the galactic disc using an N-body
simulation. However, my supervisor, Staffan Sejsing, raised concerns about whether such a
simulation was realistically achievable within the scope of a gymnasium project. Following
his advice, I contacted several researchers to seek guidance, but received no response. I then
wrote to Eric Stempels, Researcher and Division Head of Astronomy and Space Physics at
Uppsala University, not to ask for direct supervision, but simply to ask whether he could
recommend someone to contact. Unexpectedly, he engaged with my question directly and
began corresponding with me himself. He advised that an N-body simulation of stellar
migration would require computational resources far beyond what was available to me, and
instead proposed two alternatives: a simulation of the Solar System or an analysis of a galactic
stellar stream. I chose the latter, as it remained closer to my original interest in stellar motion
and galactic history.
I selected the Sagittarius Stream specifically because of its scale — it is the largest known
stellar stream in the Milky Way — and because I believed it would give me the best chance of
detecting meaningful structure. My initial research question was focused entirely on the age
distribution of stars within the stream, with the ambition of identifying anomalies that might
reflect the star formation history of the progenitor dwarf galaxy, the Sagittarius Dwarf
Spheroidal, and potentially evidence that it had itself accreted a smaller system. I later came
to understand that the stellar sample was too small to detect such a signal reliably.
The most significant technical challenge of the entire project was implementing the isochrone
fitting pipeline. For approximately four months, I attempted to write my own fitting code
from scratch. These attempts produced physically unrealistic results, with most fitted stars
returning ages of approximately 17 billion years — exceeding the accepted age of the
Universe. I did not immediately understand the cause. During this period, I also attempted to
use Gemini as an AI coding assistant, but found that it was unable to produce functional code
for this specific task. I eventually discovered the Python library isochrones developed by
Timothy Morton, which provided a more robust framework for Bayesian parameter estimation
using MIST stellar evolution models and the PyMultiNest nested sampling algorithm.
However, I initially did not realise that this library was only compatible with a Linux
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environment. After several failed installation attempts on Windows, I set up Windows
Subsystem for Linux (WSL), and the pipeline finally worked.
Even after the pipeline was operational, the age results remained inconsistent with published
literature. Rather than continuing to attempt to force better results from a fundamentally
limited dataset, I chose to accept the fitted parameters as the best achievable output given my
data and methodology, and shifted focus toward understanding and explaining those results.
At this stage I contacted Thomas de Boer, whose 2015 study of stellar stream populations
using isochrone fitting had served as a methodological reference throughout my work. He
explained that the discrepancy between my results and published studies was not a
methodological error, but a physical consequence of working with an RGB-dominated
sample: evolved red giant sequences are intrinsically harder to model, and the same sequence
can often be reproduced by different combinations of age and metallicity, resulting in broader,
less precise distributions. He also suggested that meaningful scientific conclusions could still
be drawn from the data — in particular, that analysing the metallicity distribution and the
spatial distribution of age and metallicity subgroups within the stream would be scientifically
valuable. These suggestions directly motivated the expansion of the project from a single
research question to five, covering metallicity distribution, spatial structure, kinematics, and
three-dimensional morphology.
In terms of self-assessment, I consider the project to have been a genuine research experience
rather than a purely academic exercise. The iterative nature of the work — adapting the
research questions in response to the limitations of the data and methodology — reflects how
scientific research actually proceeds. The decision to reframe the project around five research
questions, rather than presenting a single failed attempt to measure stellar ages, was, in
retrospect, the correct one, and produced a more complete characterisation of the stream than
my original single-question design would have allowed. The primary limitation I faced
throughout was my limited programming ability, which meant I was dependent on AI-assisted
code generation for much of the pipeline. This introduced inefficiencies and required
significant time to debug and verify. If I were to begin this project again, I would either
develop my programming skills more deliberately before starting, or choose a stream closer to
the Sun with a larger available stellar sample, which would have made the fitting results more
statistically robust.
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The project ran from August 2025 to April 2026 — approximately eight months in total.
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Acknowledgements
I would like to express my gratitude to several people whose contributions made this project
possible.
First, I thank my supervisor, Staffan Sejsing, for his continuous support and encouragement
throughout the entire project. Although the subject matter fell outside his area of expertise, he
consistently provided guidance on the structure and process of the work, and his willingness
to engage with an unfamiliar topic was invaluable.
I also thank teachers Ruben Fritzon and Jonas Selin for their assistance during the course of
this project.
I am grateful to Eric Stempels, Researcher and Division Head of the Division of Astronomy
and Space Physics at Uppsala University, for responding to my initial inquiry and for his
correspondence in the early stages of the project. His suggestion to analyse a galactic stellar
stream, rather than pursue a computationally infeasible N-body simulation, was the decision
that shaped the entire direction of this work.
I would also like to thank Thomas de Boer for responding to my email and for his generous
engagement with my results. His explanation of the physical limitations inherent to
RGB-dominated samples and his suggestion to investigate the spatial and metallicity
subgroup structure of the stream directly motivated the expansion of this project beyond its
original single research question.
Finally, this research made use of data from the European Space Agency mission Gaia,
processed by the Gaia Data Processing and Analysis Consortium, and spectroscopic data from
the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST). The
membership catalogue used throughout this work was published by Cunningham et al. (2024).
Access to these public datasets was essential to every stage of the analysis.
Portions of the data analysis code used in this project were developed with the assistance of
AI coding tools, specifically Google Gemini and Claude by Anthropic. These tools were used
to generate and debug Python code for data processing and visualisation, given the author's
limited prior experience with programming.
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Appendices
Appendix 1 — gaia_import.ipynb: Jupyter Notebook for cross-matching the Cunningham et
al. (2024) [19] stream catalogue with the Gaia DR3 archive [22] using source_id as the
primary identifier, and downloading all available astrometric and photometric columns.
Appendix 2 — merger.ipynb: Jupyter Notebook for merging the original Cunningham et al.
catalogue with the downloaded Gaia DR3 data into a unified working catalogue, with
deduplication of column headers.
Appendix 3 — add_errors.ipynb: Jupyter Notebook for computing calibrated photometric
uncertainties using the Gaia Photometric Error Tool [24] and integrating them into the merged
catalogue.
Appendix 4 — filtering.ipynb: Jupyter Notebook implementing the multi-stage quality
filtering pipeline: selection of columns required for isochrone fitting; application of quality
cuts (RUWE < 1.4 [23], membership probability ≥ 90% [19], presence of [Fe/H]
measurements [21]); conversion of distances to synthetic parallaxes; symmetrisation of
asymmetric A_V uncertainties; adoption of conservative T_eff and log g error floors (50 K
and 0.08 dex respectively, following Andrae et al. 2023 [27]); and addition of a systematic
photometric error floor of 0.005 mag in quadrature [24].
Appendix 5 — Gaia Photometric Error Tool: external tool used to calculate calibrated
photometric uncertainties for the G, BP, and RP bands [24].
Appendix 6 — funkar?.ipynb: Jupyter Notebook implementing the Bayesian isochrone fitting
pipeline using the isochrones package [28] and PyMultiNest [30] for all 1,241 stars in the
high-purity subsample.
Appendix 7 — Isochrone fitting results: sample output file containing the derived posterior
median values and uncertainties for all fitted stellar parameters.
Appendix 8 — Primary catalogue: the full Sagittarius Stream candidate catalogue compiled
by Cunningham et al. (2024) [19], containing 34,240 stars (source file: appendix_8.csv).
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Appendix 9 — Visualisation code: Jupyter Notebook containing all code used to generate the
figures presented in Section 3.
Appendix 10 — add_errors_full.ipynb: Jupyter Notebook for applying the systematic
photometric error floor of 0.005 mag in quadrature to the full 34,240-star catalogue.
Appendix 11 — final_catalog_corrected.csv: comprehensive catalogue of all 34,240
candidate stream stars with corrected photometric uncertainties, combining data from the
Cunningham et al. (2024) [19] and Gaia DR3 [22] catalogues.
Appendix 12 — Analysis code for Section 4.1: Jupyter Notebook containing all code for the
parameter reliability assessment (Research Question 1).
Appendix 13 — Analysis code for Section 4.2: Jupyter Notebook containing all code for the
metallicity cross-validation analysis (Research Question 2).
Appendix 14 — Analysis code for Section 4.3: Jupyter Notebook containing all code for the
spatial metallicity distribution analysis (Research Question 3).
Appendix 15 — Analysis code for Section 4.4: Jupyter Notebook containing all code for the
methodological reliability assessment (Research Question 4).
Appendix 16 — Analysis code for Section 4.5: Jupyter Notebook containing all code for the
comparative analysis of stream components (Research Question 5).
All appendixes are available via this link:
https://drive.google.com/drive/folders/1xKkSDBd8_xUSiujNhk6gxF9ay05ZEB2J?usp=drive
_link
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