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Chemodynamics of Bo\"otesI with $S^{5}$: Revised Velocity Gradient, Dark Matter Density, and Galactic Chemical Evolution Constraints

T0 review · 4 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper claims that after removing the perspective-rotation signature of a moving rigid body, Boötes I retains a 4σ, orbit-aligned line-of-sight velocity gradient, along with a resolved metallicity gradient and a dark matter profile…

desk verdict A genuinely useful dataset and a likely real revision of Boötes I's velocity gradient, but the headline 4σ is not supported by the reported statistics and needs a proper null test before it can be quoted. read the letter →

arxiv 2509.02546 v1 pith:5YRC3Y36 submitted 2025-09-02 astro-ph.GA

Nathan R. Sandford , Ting S. Li , Sergey E. Koposov , Kohei Hayashi , Andrew B. Pace , Denis Erkal , Jo Bovy , Gary S. Da Costa
show 9 more authors
Lara R. Cullinane Alexander P. Ji Kyler Kuehn Daniel B. Zucker Guilherme Limberg Gustavo E. Medina Joshua D. Simon Yong Yang S5 Collaboration
This is my paper · ORCID
classification astro-ph.GA
keywords BoötesIultra-faintdwarfgalaxyvelocitygradientperspectiverotationdarkmatterdensityprofilegalacticchemicalevolutionstellarkinematicsmetallicity
topics Dark Matter
open problems Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Boötes I is one of the closest and best-studied ultra-faint dwarf galaxies, yet its dynamics and chemistry have been read from samples that barely reach one half-light radius. This paper merges about 15 years of archival spectra with new S5 observations to build the largest sample of member stars in any Milky Way ultra-faint dwarf: 148 members extending to roughly 7 half-light radii. Its central claim is that once the geometric 'perspective rotation' of a moving rigid body is subtracted — something never before done for an ultra-faint dwarf — Boötes I still shows a real line-of-sight velocity gradient of 1.2 km/s per half-light radius, aligned with its orbit. If true, the gradient is a fossil of the galaxy's dynamical history, and earlier claims of a much steeper gradient would be wrong. The same dataset tightens the dark matter inner slope ($\gamma=1.0^{+0.5}_{-0.6}$, weakly cusped) and constrains chemical evolution to rapid, inefficient star formation with outflows that eject roughly 200 solar masses of gas per solar mass of stars.

What carries the argument

The load-bearing object is a coordinate-and-velocity model: the galaxy is treated as an extended rigid body moving at the systemic proper motion, and the line-of-sight velocity field expected from that motion alone — perspective rotation — is computed from the adopted distance, proper motion, and on-sky position of each star. Subtracting that predicted field leaves the 'intrinsic' gradient. Around this sit three other mechanisms: a Gaussian mixture model that assigns membership from velocity, metallicity, and proper motion; an axisymmetric Jeans model with a generalized Hernquist dark halo (inner slope $\gamma$, outer slope $\beta$, flattening $Q$, velocity anisotropy $\beta_z$) fitted to the unbinned line-of-sight velocity dispersion; and the one-zone galactic chemical evolution model of Weinberg et al. (2017) fitted to the metallicity distribution function, with parameters for star-formation timescale, truncation time, star-formation efficiency, and mass-loading factor.

What would settle it

Re-fit the same 148-star catalog with an independent proper motion measurement for Boötes I and with membership probabilities left free; if the claimed 1.2 km s$^{-1} r_h^{-1}$ residual gradient does not survive in magnitude and direction, it was an artifact of the rigid-body perspective correction. A companion test is to search for extra-tidal members beyond roughly 8–13 half-light radii, the tidal radius estimated in the paper, whose presence or absence would distinguish tidal stripping from internal rotation.

Watch

Extended reading notes

Core claim

The paper's headline discovery is kinematical. Modeling Boötes I as a solid body moving with its measured Gaia proper motion and distance predicts a perspective-rotation velocity gradient of $0.105\pm0.004$ km s$^{-1}$ arcmin$^{-1}$ across the observed field; the paper subtracts this and finds a residual intrinsic gradient of $0.12^{+0.04}_{-0.03}$ km s$^{-1}$ arcmin$^{-1}$ ($1.2^{+0.4}_{-0.3}$ km s$^{-1} r_h^{-1}$), at about 4$\sigma$ significance, oriented along Boötes I's orbit. This is much shallower and differently oriented than the $0.40\pm0.10$ km s$^{-1}$ arcmin$^{-1}$ gradient reported previously, which the paper argues is not reproducible from the data. The paper also reports a resolved radial metallicity gradient of $-0.010\pm0.003$ dex arcmin$^{-1}$ ($-0.10\pm0.03$ dex $r_h^{-1}$), a dark matter inner slope $\gamma=1.0^{+0.5}_{-0.6}$ that weakly favors a cusp while not ruling out a core, and chemical evolution parameters — star-formation timescale $\tau_{\rm SFH}=0.2\pm0.1$ Gyr, star-formation efficiency $\mathrm{SFE}=0.07^{+0.04}_{-0.03}$ Gyr$^{-1}$, mass-loading factor $\eta=203^{+27}_{-36}$ — describing a short, inefficient burst of star formation with strong outflows.

Load-bearing premise

The entire 'intrinsic' gradient rests on treating Boötes I as a rigid solid body with the adopted Gaia proper motion and RR Lyrae distance, and on assuming that membership cuts, binary masking, and sample selection cannot produce a velocity pattern that mimics the residual gradient.

Editorial extensions

If this is right

  • The previously reported steep ($0.40\pm0.10$ km s$^{-1}$ arcmin$^{-1}$) gradient in Boötes I is not reproduced; the intrinsic gradient is about 1.2 km s$^{-1} r_h^{-1}$, so dynamical interpretations built on the steep value need revision.
  • Because the corrected gradient is aligned with the orbit but the estimated tidal radius ($\sim8$–$13r_h$) lies beyond the sampled stars, tides alone may not explain it; the origin is left open between tidal deformation, rotation, and a past merger.
  • With 115 clean velocities, the inferred velocity dispersion drops to $4.0^{+0.4}_{-0.3}$ km s$^{-1}$, and the dark matter inner slope $\gamma=1.0^{+0.5}_{-0.6}$ weakly favors the cuspy halos predicted by cold dark matter, though cores remain allowed.
  • The large, homogeneous 92-star metallicity sample and the resolved metallicity gradient place Boötes I on the Local Group mass–metallicity relation and support self-enrichment as the source of its metallicity spread, without requiring a merger.
  • The chemical evolution fits imply $\eta\sim200$: for every solar mass of stars formed, about 200 solar masses of gas are ejected, so strong feedback, not necessarily reionization truncation, shaped Boötes I's chemical evolution.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the same rigid-body perspective correction were applied to other spatially extended ultra-faint dwarfs, some previously reported 'tidal' velocity gradients might shrink or reorient; the paper's own bootstrap shows that without correction a spurious gradient is recovered 99% of the time, so this is a caution for the field.
  • A decisive test of the tidal versus rotation interpretation is to measure [$\alpha$/Fe] or neutron-capture abundances for stars beyond $3r_h$: chemically distinct populations would point to an accreted or major-merger origin, while smooth gradients would favor internal or tidal processes.
  • The inferred mass-loading factor of $\sim200$ suggests that gas removal in ultra-faint dwarfs is dominated by feedback-driven outflows; if this holds generally, chemical evolution models of other ultra-faint dwarfs with fixed low $\eta$ may systematically underestimate outflow strength.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The paper combines new S5 AAT spectroscopy with archival AAT, MMT, and VLT data to build a 148-member sample of the ultra-faint dwarf galaxy Boötes I, identifies 15 new binary candidates from a 16-year baseline, and fits systemic properties with a Gaussian mixture model. The headline results are an intrinsic line-of-sight velocity gradient of 1.2±0.3 km/s/rh after correcting for solid-body perspective rotation, a resolved metallicity gradient of −0.10±0.02 dex/rh, a dark matter inner slope γ=1.0+0.5/−0.6 from axisymmetric Jeans modeling, and one-zone chemical evolution parameters favoring rapid (τSFH≈0.2 Gyr), inefficient star formation with a large mass-loading factor (η≈200). The paper explicitly discusses tensions with the previous steep velocity gradient of Longeard et al. (2022), compares the observed gradient with an N-body simulation, and candidly lists several modeling limitations.

Significance. If correct, the paper would provide the first perspective-rotation-corrected velocity gradient in a Milky Way ultra-faint dwarf, based on the largest kinematic and metallicity sample in any such galaxy, and would add meaningful constraints on Boötes I's dark matter profile and chemical evolution. The strengths include the homogeneous S5 data reduction, careful binary identification, explicit cross-checks across four independent datasets, an N-body mock with a perspective-rotation baseline, and a publicly available combined catalog. These are substantial contributions. However, the headline 4σ detection is not supported by the reported component uncertainties, the significance test for the intrinsic gradient is not properly formulated, and some of the quoted chemical evolution constraints are explicitly prior-dominated rather than independently derived from the new MDF. These issues are fixable but require revision, so the paper should not be accepted in its current form.

major comments (4)
  1. [Abstract; §5.1 and Table 3] The claimed "4σ" detection of the intrinsic velocity gradient is not traceable to the reported component uncertainties. With Δv'_1=−0.09±0.03 and Δv'_2=−0.08±0.05 km/s/arcmin, the residual vector against the null of zero intrinsic gradient has χ²≈(0.09/0.03)²+(0.08/0.05)²≈11.6 for 2 degrees of freedom before accounting for any correlation, i.e. p≈0.003, roughly a 3σ signal rather than 4σ. Quoting the ratio of the positive-definite magnitude 0.12 km/s/arcmin to one error bar is not a valid significance for a two-component vector. The authors should report the full covariance matrix of the inferred gradient components and present a likelihood-ratio or Bayes-factor test comparing the zero-intrinsic-gradient model with the model including an intrinsic gradient.
  2. [§5.1, bottom panels of Figure 6] The bootstrap test quoted in §5.1 calibrates the distribution of the observed gradient under the null that only perspective rotation is present, finding that a non-zero observed gradient is recovered 99% of the time; this is expected under that null and does not test whether the residual after subtracting the rigid-body template is significant. The paper needs a null test defined on the residual: e.g. posterior predictive draws of the perspective-only model compared to the observed residual vector. In addition, the quoted correction uncertainty of 0.004 km/s/arcmin appears to propagate only random errors in the adopted proper motion and distance; the documented discrepancy with Li et al. (2021) noted in §4.4 should be propagated or tested, since the intrinsic gradient is defined relative to the adopted rigid-body template.
  3. [Table 4, Section 6] The prior listed for log10ρ0 in Table 4 is U(−5,−5), which is a delta function rather than the broad prior described in the text; if taken literally, this prior would make the reported Jeans constraints on ρ0 and γ impossible. This appears to be a typographical error, but it must be corrected and the intended bounds stated explicitly, because the dark matter inference in Section 6 depends directly on this prior.
  4. [§7 and Abstract] The paper explicitly states in §7 that the inference of τSFH=0.2±0.1 Gyr is "dominated by the tight priors set by CMD-based SFH" from Durbin et al. (2025). The abstract and summary nevertheless present the rapid star formation timescale as a new constraint from the chemical evolution analysis. This overstates the independent information in the MDF; the authors should either refit with a broader prior and report the sensitivity, or rephrase the abstract and summary to state that the MDF is consistent with, but does not independently determine, the short star formation timescale.
minor comments (3)
  1. [§6] There is a duplicated word in the sentence "consistent consistent with expectations from cold dark matter cosmology" that should be corrected.
  2. [§4.4 and Table 3] The text reports the proper-motion discrepancy with Li et al. (2021) but does not quantify how that alternate proper motion would shift the perspective-rotation template of 0.105 km/s/arcmin in §5.1; adding this one-number sensitivity estimate would greatly strengthen the paper.
  3. [§5.1.3] The discussion of tidal versus rotational origin is appropriately cautious, but the sentence "To confidently discrimination between rotational ... and tidal origins" contains a grammatical error that should be fixed.

Circularity Check

1 steps flagged · score 4.0 of 10

GCE 'rapid star formation' constraint is dominated by its CMD-based prior; the headline kinematics, metallicity gradient, and dark-matter fit are otherwise self-contained.

  1. fitted input called prediction [Section 7 (Chemical Evolution Modeling), Table 4, Appendix D (Equations D9 and D13)]
    "To infer the values of these parameters, we adopt the likelihood function given by Equation D13 and adopt weakly informative priors motivated by the CMD-based SFH from Durbin et al. (2025, see Table 4). ... While the data is sufficient to disfavor the shortest SFH timescales (< 150 Myr), the inference of τSFH is dominated by the tight priors set by CMD-based SFH (80–350 Myr)."

    The paper's summary claims a new GCE constraint on Boo I's rapid star formation, τSFH = 0.2 ± 0.1 Gyr, derived from the MDF. But the posterior for τSFH is explicitly dominated by the adopted uniform prior U(0.08, 0.35) Gyr, which was itself chosen from the external CMD-based SFH of Durbin et al. (2025). The MDF likelihood does not independently determine the rapidity of star formation; the reported 'constraint' is therefore the prior echoed back, not a prediction from the MDF. This is a partial reduction of the rapid-SFH claim to its input prior. The other GCE parameters (τSFE, η) are not prior-dominated, and the headline velocity and metallicity gradients are independent fits, so the circularity is confined to the τSFH claim.

full rationale

The paper's headline results are not circular. The velocity gradient, intrinsic gradient after perspective-rotation subtraction, and metallicity gradient are all fits to the newly assembled spectroscopic sample. The perspective-rotation correction is a forward model computed from the adopted proper motion and distance, not a fit of the claimed residual; no equation reduces the intrinsic gradient to the observed gradient by construction. The dark-matter analysis reuses the axisymmetric Jeans machinery of Hayashi et al. (2023), a coauthor's published standard method, but the posterior for γ is a new fit to the larger dataset; no uniqueness theorem or exclusive methodology is imported from the self-citation to force the result. The only substantive circular step is in the GCE analysis: the τSFH posterior is dominated by the prior chosen from the CMD-based SFH, so the paper's 'new constraint' on rapid star formation reduces to that prior. This is explicitly acknowledged in the text, but it still makes the GCE rapidity claim prior-dominated rather than independently derived from the MDF. The significance of the velocity gradient (whether it is truly 4σ) is a statistical calibration concern, not a circularity concern, and is therefore not scored here. Overall, the central claims retain independent empirical content, with partial circularity limited to the τSFH inference.

Assumptions & free parameters 10 free parameters · 6 assumptions · 0 invented entities

The paper rests on standard parametric likelihoods, rigid-body perspective rotation, steady-state axisymmetric Jeans equilibrium, and a one-zone chemical evolution model. No new particles or forces are introduced; the dark matter halo is parameterized with a standard generalized Hernquist profile. The principal non-observational inputs are model forms and priors, listed above.

free parameters (10)
  • Intrinsic line-of-sight velocity gradient Δv'_B = 0.12+0.04/-0.03 km/s/arcmin (1.2 km/s/rh)
    Central fitted quantity in Section 5.1; depends on the GMM fit and the perspective rotation correction.
  • Boo I systemic velocity v0,B = 103.0±0.4 km/s
    GMM fit to the combined sample; used as the baseline in the velocity gradient analysis.
  • Velocity dispersion σv,B = 4.0+0.4/-0.3 km/s
    GMM fit after masking binaries and RR Lyrae stars; enters the Jeans analysis.
  • Radial metallicity gradient Δ[Fe/H]B = -0.010±0.003 dex/arcmin (-0.10±0.03 dex/rh)
    Inferred linear metallicity gradient in the GMM; one of the paper's headline measurements.
  • DM inner slope γ = 1.00+0.52/-0.60
    Main dark matter result from the axisymmetric Jeans model; weakly favors a cusp but cannot exclude a core.
  • DM halo parameters Q, log10bhalo, log10ρ0, βz, α, β, i = Q=1.18, log10bhalo=3.07, log10ρ0=-1.88, -log10(1-βz)=0.25, α=1.76, β=6.39, i=70.47 deg
    Eight-parameter Jeans model; several parameters remain unconstrained and show standard degeneracies.
  • GCE star formation timescale τSFH = 0.2±0.1 Gyr
    Inferred from the MDF but explicitly dominated by the CMD-based prior; not independently constrained by the new data.
  • GCE star formation efficiency timescale τSFE = 13.9+7.6/-5.3 Gyr (SFE 0.07 Gyr^-1)
    Inferred from the one-zone WAF17 model fit to the MDF.
  • GCE mass-loading factor η = 203+27/-36
    Inferred outflow strength; depends on adopted yields and on assumptions about direct metal ejection.
  • Star formation truncation time ttrunc = >0.5 Gyr (95% lower limit)
    Only a lower limit is recovered from the MDF fit.
assumptions (6)
  • domain assumption Gaussian mixture model factorizes velocity, metallicity, and proper motion likelihoods and uses specified Gaussian and linear forms for Boo I and the Milky Way foreground.
    Equations 8-18; membership and systemic properties depend on these functional forms.
  • domain assumption The perspective-rotation signature can be modeled as a rigid solid-body field using the inferred systemic proper motion, with no other projection effects.
    Section 5.1 and the bottom left panel of Figure 6; the correction subtracts this field and labels the residual intrinsic.
  • domain assumption Boo I is in dynamical equilibrium and its stellar motions satisfy the axisymmetric Jeans equations with constant anisotropy and zero streaming motion.
    Appendix C Equations C1-C3; Section 6.1 admits this may be invalid if tides are present.
  • ad hoc to paper The stellar tracer follows an axisymmetric Plummer profile aligned with a generalized axisymmetric Hernquist dark matter halo.
    Appendix C Equations C4-C7; a flexible but unvalidated mass model.
  • domain assumption The WAF17 one-zone GCE model with instantaneous mixing, adopted IMF yields, and a power-law SN Ia delay describes Boo I's enrichment.
    Appendix D Equations D9-D14; inferred τSFE and η are conditional on this model and the yield choice.
  • domain assumption The N-body simulation initial conditions, including a Plummer stellar component, NFW halo, MWPotential2014, and an LMC Hernquist model, represent Boo I and its environment.
    Section 2.6; used to interpret whether the observed gradient has a tidal origin.

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Cite this review

Pith. "Pith review of Chemodynamics of Bo\"otesI with $S^{5}$: Revised Velocity Gradient, Dark Matter Density, and Galactic Chemical Evolution Constraints." pith.science (2026). https://pith.science/paper/5YRC3Y36

@misc{pith2026250902546,
  author       = {Pith},
  title        = {Pith review of: Chemodynamics of Bo\"otesI with $S^5$: Revised Velocity Gradient, Dark Matter Density, and Galactic Chemical Evolution Constraints},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5YRC3Y36}},
  note         = {Machine review of arXiv:2509.02546}
}
abstract

We combine new spectroscopic observations of the ultra faint dwarf galaxy (UFD) Bo\"otes I (Boo I) from the Southern Stellar Stream Spectroscopic Survey ($S^{5}$) with $\sim$15 years of archival spectroscopic data to create the largest sample of stellar kinematics and metallicities to date in any Milky Way UFD. Our combined sample includes 148 members extending out to $\sim$7 half-light radii ($r_h$), including 24 newly confirmed members, 18 binary candidates, 15 RR Lyrae stars, and 92 [Fe/H] measurements. Using this larger and more spatially extended sample, we provide updated constraints on Boo I's systemic properties, including its radial population gradients. Properly accounting for perspective rotation effects in a UFD for the first time, we detect a $4\sigma$ line-of-sight velocity gradient of $1.2\pm0.3$ km s$^{-1}$ $r_h^{-1}$ aligned along Boo I's orbit and discuss its potential tidal origins. We also infer a metallicity gradient of $-0.10\pm0.02$ dex $r_h^{-1}$ in agreement with previous studies. Using an axisymmetric Jeans model, we provide updated constraints on Boo I's dark matter density profile, which weakly favor a cusped ($\gamma=1.0^{+0.5}_{-0.6}$) dark matter profile. Lastly, we re-analyze Boo I's metallicity distribution function with a one-zone galactic chemical evolution model and place new constraints on its rapid, inefficient star formation and strong galactic outflows.

Figures

Figures reproduced from arXiv: 2509.02546 by the authors.

Figure 1
Figure 1. The log-number density of the Boo I N-body simulation. The simulated orbit and apparent proper mo￾tion (without Solar reflex correction) of the system are repre￾sented by the cyan line and magenta arrow respectively. Ten bootstrapped mock samples are included as colored points. Gray ellipses indicate the observed 1, 3, 5, and 10 half-light radii of Boo I from Mu˜noz et al. (2018) [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 2
Figure 2. Difference between individual epoch velocity measurements and the mean velocity as a function of time for each of the potential Boo I binary stars in our combined sample. The stars are ordered by decreasing p-value. Star 1230831597176581248 (Boo1 111) is included despite its low binary probability because there is weak evidence of binarity from individual epoch VLT (Koposov et al. 2011; Jenkins et al. 2021) and MIKE… view at source ↗
Figure 3
Figure 3. Distribution of median membership probabilities of our S 5 sample. The subset of stars in our sample with good radial velocity measurements (i.e., σv < 10 km s−1 , σ[Fe/H] < 0.5 dex, and neither a binary candidate or RRL star) and good [Fe/H] measurements (i.e., σv < 10 km s−1 , σ[Fe/H] < 0.5 dex, and neither a HB or RRL star) are represented by the red and blue histograms respectively. A membership threshold of pme… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Top Left. Extinction-corrected CMD of the S 5 sample. High-probability Boo I members with good radial velocity (and [Fe/H]) measurements are represented by (filled) circles. Open triangle and square markers represent RRL stars and binary candidates respectively, while …
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: Each panel shows the on-sky spatial distribution of Boo I members colored by their heliocentric l.o.s. velocity. The orbit and proper motion vector of Boo I are represented in each panel by the cyan line and magenta arrow respectively, while the observed and intrinsic …
Figure 7
Figure 7. Figure 7: Velocity field of the Boo I N-body simulation without (left) and with (right) accounting for the effect of perspective rotation. In the left-hand panel, the velocity gradient is dominated by the perspective rotation, while in the right-hand panel the velocity gradient …
Figure 8
Figure 8. Figure 8: Top. Dispersion of heliocentric l.o.s. velocities around the inferred systemic velocity gradient as a function of radius for high probability Boo I members in the S 5 (left; magenta circles) and combined (right; black circles) datasets. Bottom. Velocity dispersion of B…
Figure 9
Figure 9. Figure 9: Top. Distribution of stellar metallicity as a function of radius for high probability Boo I members in the S 5 (left; magenta circles) and combined (right; black circles) datasets. The inferred metallicity gradients and their 1σ uncertainty are represented by the solid…
Figure 10
Figure 10. Figure 10: Inferred dark matter density profile along the major axis for the default S 5 (left) and combined (right) datasets. In each panel, the solid lines show the median value of posterior samples, while the dark and light shaded regions show the 68% and 95% confidence inter…
Figure 11
Figure 11. Figure 11: Left. MDF (top) and cMDF (bottom) of the S 5 dataset (magenta lines). The dashed red lines show the MDF and cMDF corresponding to the maximum a posteriori values from the GCE modeling, while the solid blue lines and shaded regions show the median and 68/95% confidence…
Figure 12
Figure 12. Figure 12: The inferred mass-loading factor of Boo I from the S 5 and combined datasets (magenta and black stars respectively) compared to the mass-loading factors inferred by the chemical evolution studies of Johnson et al. (2023) for Wukong/LMS-1 and GSE (blue and red circles …
Figure 13
Figure 13. Figure 13: The inferred SFE of Boo I from the S 5 and combined datasets (magenta and black stars respectively) compared to the SFEs reported by previous chemical evolution studies of LG dwarf galaxies (Lanfranchi & Matteucci 2004; Lanfranchi et al. 2006; Lanfranchi & Matteucci 2…

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