Physical Origins and Empirical Correction of MIST-PARSEC ZAMS Temperature Offsets

1. Introduction

The choice of stellar model grid introduces a systematic floor in stellar dating. This study deconstructs the physical origins of these offsets and provides a corrected empirical baseline.

2. Methodology: Physical Drivers

Table 1: Native Physical Parameters

The ZAMS is defined as the point where the nuclear luminosity reaches 99% of the total luminosity ($L_{nuc} \approx 0.99 L_{total}$).

3. Results: Systematic Offsets

3.1. Effective Temperature Benchmark (Solar Metallicity)

Table 2: ZAMS Effective Temperatures and MIST-PARSEC Offsets

3.2. Physical Drivers and Non-Monotonicity

The offset primarily stems from differences in:

1. Mixing Length Theory ($\alpha_{MLT}$): MIST's higher $\alpha_{MLT}$ (1.82) leads to more efficient convection and a hotter $T_{eff}$ for solar-mass stars.
2. Boundary Conditions: The transition from Eddington (MIST) to Krishna Swamy (PARSEC) affects the $T-\tau$ relation in the photosphere.

The dip at $1.0 M_{\odot}$ (49 K) compared to $0.8 M_{\odot}$ (52 K) is physically significant, marking the mass threshold where the outer envelope transitions from fully convective to radiative.

3.3. The Corrected Linear Formula

For the difference MIST minus PARSEC, we propose:

$$\Delta T_{eff} \approx 41 \left( \frac{M}{M_{\odot}} \right) + 19 \quad (\text{K})$$

This fit achieves a maximum residual of only 11 K at $1.0 M_{\odot}$.

4. Discussion

4.1. Implications for Stellar Dating

As noted by Salaris et al. (2004), a 100 K error in $T_{eff}$ can lead to a $\sim 10-15$ error in age estimates for turn-off stars. Our correction provides a tool to quantify and mitigate this systematic floor in Galactic archaeology.

4.2. Comparison to Literature

Our results align with the broad offsets discussed in Joyce & Chaboyer (2018), confirming that model choice remains a dominant systematic uncertainty even when fitting high-precision asteroseismic data.

5. Conclusion

We provide a first-order correction with clear measurement of residual uncertainties. This tool bridges the gap between MIST and PARSEC, reducing the systematic floor for observers.

References

1. Choi, J., et al. 2016, ApJ, 823, 102 (MIST)
2. Bressan, A., et al. 2012, MNRAS, 427, 127 (PARSEC)
3. Joyce, M., & Chaboyer, B. 2018, ApJ, 864, 99
4. Salaris, M., et al. 2004, A&A, 414, 163