RR Lyrae Variables in Messier 53: Near-infrared Period–Luminosity Relations and the Calibration Using Gaia Early Data Release 3
Bibliographic record
Abstract
Abstract We present new near-infrared, JHK s , period–luminosity relations (PLRs) for RR Lyrae variables in the Messier 53 (M53 or NGC 5024) globular cluster. Multi-epoch JHK s observations, obtained with the WIRCam instrument on the 3.6 m Canada–France–Hawaii Telescope, are used for the first time to estimate precise mean magnitudes for 63 RR Lyrae stars in M53 including 29 fundamental-mode (RRab) and 34 first-overtone mode (RRc) variables. The JHK s -band PLRs for RR Lyrae stars are best constrained for RRab types with a minimal scatter of 22, 23, and 19 mmag, respectively. The combined sample of RR Lyrae is used to derive the K s -band PLR, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>2.303</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0.063</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mi>log</mml:mi> <mml:mi>P</mml:mi> <mml:mo>+</mml:mo> <mml:mn>15.212</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0.016</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> , exhibiting a 1 σ dispersion of only 0.027 mag. Theoretical period–luminosity–metallicity (PLZ) relations are used to predict parallaxes for 400 Galactic RR Lyrae, resulting in a median parallax zero-point offset of −7 ± 3 μ as in Gaia Early Data Release 3 (EDR3), which increases to 22 ± 2 μ as if the parallax corrections are applied. We also estimate a robust distance modulus, μ M53 = 16.403 ± 0.024 (statistical) ± 0.033 (systematic) mag, to M53 based on theoretical calibrations. Homogeneous and precise mean magnitudes for RR Lyrae in M53 together with similar literature data for M3, M4, M5, and ω Cen are used to empirically calibrate a new RR Lyrae <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>PLZ</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> relation, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>0.848</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0.007</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mspace width="0.25em"/> <mml:mo>−</mml:mo> <mml:mn>2.320</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0.006</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mi>log</mml:mi> <mml:mi>P</mml:mi> <mml:mo>+</mml:mo> <mml:mn>0.166</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0.011</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mi>Fe</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> <mml:mo stretchy="false">]</mml:mo> </mml:math> , anchored with Gaia EDR3 distances and theoretically predicted relations, and to simultaneously estimate precise RR Lyrae-based distances to these globular clusters.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".