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arxiv: 2604.07938 · v1 · submitted 2026-04-09 · 🌌 astro-ph.SR

eROSITA's cool star population explained

J. H. M. M. Schmitt , P.C. Schneider , S. Czesla , S. Freund , J. Robrade This is my paper

Pith reviewed 2026-05-10 17:56 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords stellar rotationX-ray activityconvective turnover timeRossby numberlate-type starseROSITATESSstellar activity
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The pith

The eROSITA X-ray activity distribution for cool stars is reproduced by saturation at a universal Rossby number once color-dependent convective turnover times are used.

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

The paper tests whether the standard rotation-activity paradigm applies across all late-type stars by combining TESS rotation periods with eROSITA X-ray data for 14004 objects. It finds that the derived convective turnover times match theoretical expectations and that a simple model based on these times reproduces the observed spread in L_X/L_bol versus Gaia color. Hotter stars show lower activity levels simply because their short turnover times prevent even rapid rotators from reaching the saturated regime. This confirms that the paradigm requires no spectral-type-dependent adjustments beyond the color dependence of the turnover time.

Core claim

Using the largest combined rotation and X-ray dataset to date, the convective turnover times derived from the sample closely agree with theoretical computations. This supports Rossby-number activity relations holding for all late-type main-sequence stars. The lower activity in earlier spectral types is a physical consequence of their short convective turnover times, which prevent them from rotating rapidly enough to reach saturation. A simple model incorporating the derived turnover times versus color reproduces the observed eROSITA X-ray activity distribution as measured by L_X/L_bol and Gaia BP-RP color.

What carries the argument

The Rossby number (rotation period divided by convective turnover time), with activity saturating at a single universal value independent of spectral type.

Load-bearing premise

That convective turnover times are accurately derived from the data and that saturation occurs at the same Rossby number for every spectral type.

What would settle it

A large sample of rapidly rotating F-type or late A-type stars showing L_X/L_bol ratios near the saturated value, or a failure of the turnover-time model to match the observed activity-color distribution.

Figures

Figures reproduced from arXiv: 2604.07938 by J. H. M. M. Schmitt, J. Robrade, P.C. Schneider, S. Czesla, S. Freund.

Figure 1
Figure 1. Figure 1: Comparison of TESS SAP light curve (red data points) and TESS [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of TESS periods as derived in this paper and [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of periods derived in this paper with those derived [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of periods derived in this paper with those derived [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Color magnitude diagram (based on Gaia values) for eROSITA detected stars with successful TESS period measurements, with the in￾dicated red polygonal region defining our MS sample. The data points are color coded according to period quality: green (grade 3), blue (grade 4), and red for higher grades. See text for details. but little studied spectroscopic binary of spectral type G8e; the TESS light curve sh… view at source ↗
Figure 7
Figure 7. Figure 7: Period (in days) vs. BP-RP color for the MS sample with grade [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: log(LX/ Lbol) vs. logarithmic period for MS stars in our sample; the stars studied by Wright et al. (2011a) are indicated by black dots. See text for details. Top panel: Stars in the color range 0.2 < BP-RP < 0.59, dubbed early F-type stars. Second panel from top: Stars in the color range 0.59 < BP-RP < 0.78, dubbed late F-type stars. Third panel from top: Stars in the color range 0.78 < BP-RP < 0.97, dubb… view at source ↗
Figure 9
Figure 9. Figure 9: LX/ Lbol vs. BP-RP color for stars in various period ranges. The stars studied by Wright et al. (2011a) are indicated by black dots. See text for details. Article number, page 8 of 19 [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: X-ray luminosity LX vs. BP-RP color for sample stars with successful period measurements as well as the selected low activity stars (red data points). See text for details. 3.3.2. X-ray activity versus color For almost all spectral types of stars shown in [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: LX/Lbol ratio vs. Rossby number for our sample stars with the different colors indicating different membership probabilities (green largest, red lowest), the black line is the best fit with the functional form as given by Eqs. 4 (top panel) and 5 (bottom panel). See text for details. 3.6. Convective turnover time As a byproduct of our fitting exercise, we also obtained the pa￾rameters A, B, C, and T0, whi… view at source ↗
Figure 13
Figure 13. Figure 13: "Best-fit" convective turnover time vs. BP-RP colors (derived [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 12
Figure 12. Figure 12: LX/Lbol ratio vs. Rossby number for our sample stars with the different colors indicating the different spectral types: blue indicating A and early F-type stars, green late F-type stars, yellow G-type stars, magenta K-type stars, and red M-type stars. Population medians (thick line) and the 90% contours (thin lines) of the population are also shown. The gray-shaded area indicates the density of the data p… view at source ↗
Figure 15
Figure 15. Figure 15: Toy model simulation of the LX/Lbol ratio vs. BP-RP color for the eROSITA detected cool star population. See text for details 3.8. The cool star eROSITA population at large With the results obtained above, it is now possible to understand the color and X-ray activity distribution of the cool star popu￾lation in an X-ray survey such as eROSITA. While a detailed population simulation and study would go far … view at source ↗
read the original abstract

The rotation-activity connection is the standard paradigm for interpreting chromospheric and coronal activity in late-type stars, namely, stars with outer convection zones. This paradigm states that activity increases with decreasing rotation period until a saturation limit is reached. By scaling rotation periods with the convective turnover time via the Rossby number, $\text{Ro}$, saturation is expected to occur at a universal value across all spectral types. In our paper, we systematically investigate the relationship between rotation and activity as measured though X-ray emission for a large sample of late-type stars to test the universal applicability of this paradigm. To this end, we utilized TESS short-cadence space photometry to determine the rotation periods for late-type stars identified in the eROSITA all-sky survey. This combined dataset provides rotation and X-ray measurements for 14004 stars, representing a sample size increase of more than an order of magnitude compared to previous studies. We find that the convective turnover times derived from this sample closely agree with theoretical computations, supporting the idea that Rossby number-activity relations hold for all late-type main sequence stars. The lower level of activity in earlier spectral types (e.g., F-type and late A-type stars) is a physical consequence of their short convective turnover times, which prevent them from rotating rapidly enough to ever reach the saturation regime. We demonstrate that a simple model incorporating our derived turnover times versus color can successfully reproduce the observed characteristics of the eROSITA X-ray activity distribution, as measured by the L$_X$/L$_{\text{bol}}$ ratio and {\it Gaia} BP-RP color.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper analyzes rotation periods measured from TESS short-cadence photometry and X-ray luminosities from the eROSITA all-sky survey for a sample of 14004 late-type stars. It derives convective turnover times tau_conv as a function of Gaia BP-RP color from the observed saturation behavior, reports close agreement between these empirical tau_conv values and theoretical computations, and shows that a simple model incorporating the derived tau_conv(color) reproduces the observed L_X/L_bol versus color distribution. The work concludes that this supports the universal Rossby-number saturation paradigm and physically explains the lower activity levels of earlier spectral types via their short convective turnover times.

Significance. The order-of-magnitude increase in sample size relative to prior studies is a clear strength, enabling statistically robust tests across a wide color range. The reported agreement between data-derived turnover times and independent theoretical calculations, together with the model's reproduction of the activity-color distribution, would provide useful empirical support for the standard rotation-activity paradigm if the derivation is shown to be non-circular. These elements constitute the primary advance.

major comments (2)
  1. [§4] §4 (derivation of convective turnover times): The procedure for extracting tau_conv(color) from the 14004-star sample must be specified in detail, including the exact criterion used to locate the saturation knee in P_rot or Ro space for each color bin, the assumed universal Ro_sat value, and whether the identification relies on L_X/L_bol thresholds. If the knee position is defined using the same activity measurements later fed into the reproduction model, the agreement with theoretical tau_conv and the successful model fit test consistency with the assumed functional form rather than furnishing an independent confirmation of the paradigm.
  2. [§5] §5 (model and comparison): The claim that the simple model 'successfully reproduces the observed characteristics' of the L_X/L_bol vs. BP-RP distribution should include quantitative metrics (e.g., Kolmogorov-Smirnov statistic or binned residuals) and an explicit statement of which functional assumptions (saturation level, unsaturated slope, Ro_sat) are taken from the data versus imposed a priori. Without this, it is unclear whether the reproduction constitutes a non-trivial test.
minor comments (2)
  1. [Abstract] The abstract and main text use inconsistent LaTeX formatting for L_X/L_bol; adopt a single notation throughout.
  2. [Figures] Figure captions should state the number of stars per color bin and any cuts applied to the 14004-star sample to allow direct assessment of statistical power.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. These have prompted us to improve the methodological transparency and quantitative rigor of the presentation. We respond to each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [§4] §4 (derivation of convective turnover times): The procedure for extracting tau_conv(color) from the 14004-star sample must be specified in detail, including the exact criterion used to locate the saturation knee in P_rot or Ro space for each color bin, the assumed universal Ro_sat value, and whether the identification relies on L_X/L_bol thresholds. If the knee position is defined using the same activity measurements later fed into the reproduction model, the agreement with theoretical tau_conv and the successful model fit test consistency with the assumed functional form rather than furnishing an independent confirmation of the paradigm.

    Authors: We agree that §4 would benefit from a more explicit description of the derivation. In the revised manuscript we will specify the color binning, the precise criterion used to locate the saturation knee (the rotation period at which the median L_X/L_bol no longer increases with decreasing P_rot, identified via a piecewise fit in each bin), the adopted universal Ro_sat value, and confirm that the knee is located using the activity data within each bin. While the resulting tau_conv(color) is indeed derived from the same activity measurements that enter the reproduction model, the model itself applies this tau_conv to the individual P_rot values of all 14004 stars to predict their L_X/L_bol values and thereby tests whether the empirically determined color dependence accounts for the observed activity distribution. The direct comparison of the derived tau_conv to independent theoretical calculations remains non-circular. We will add a short discussion clarifying that the exercise constitutes a self-consistent test of the Rossby-number paradigm rather than a fully independent verification. revision: yes

  2. Referee: [§5] §5 (model and comparison): The claim that the simple model 'successfully reproduces the observed characteristics' of the L_X/L_bol vs. BP-RP distribution should include quantitative metrics (e.g., Kolmogorov-Smirnov statistic or binned residuals) and an explicit statement of which functional assumptions (saturation level, unsaturated slope, Ro_sat) are taken from the data versus imposed a priori. Without this, it is unclear whether the reproduction constitutes a non-trivial test.

    Authors: We accept that quantitative metrics are needed to substantiate the reproduction claim. In the revised manuscript we will report the Kolmogorov-Smirnov statistic between the observed and modeled L_X/L_bol distributions together with binned median residuals as a function of BP-RP color. We will also add an explicit statement of the functional assumptions: the saturation level and unsaturated slope are taken from the literature (or fitted to the full sample), while Ro_sat and the tau_conv(color) relation are those derived in §4. This will make clear that the model tests the explanatory power of the empirically determined convective turnover times for the color dependence of activity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent photometry and external theory

full rationale

The paper measures rotation periods independently from TESS short-cadence photometry on an eROSITA-selected sample of 14004 stars, then derives empirical convective turnover times by analyzing the rotation-activity relation across colors. These times are compared directly to theoretical computations from stellar models (external to the dataset), and a simple model incorporating the color-dependent turnover times is shown to reproduce the observed L_X/L_bol distribution versus Gaia BP-RP. This constitutes a consistency check and physical interpretation of the data rather than a reduction of the central claim to a fitted parameter or self-referential definition by construction. No load-bearing self-citation, ansatz smuggling, or uniqueness theorem from prior author work is invoked to force the result.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on the standard rotation-activity paradigm and derives turnover times empirically while assuming they align with theory; no new entities are introduced.

axioms (2)
  • domain assumption Activity saturates at a universal Rossby number value across spectral types
    Invoked as the core of the paradigm being tested in the abstract.
  • standard math Rossby number is defined as rotation period divided by convective turnover time
    Standard definition used throughout the rotation-activity literature and applied here.

pith-pipeline@v0.9.0 · 5602 in / 1238 out tokens · 42776 ms · 2026-05-10T17:56:11.862344+00:00 · methodology

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Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages

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    2021, An Introduction to Stellar Magnetic Activity Basri, G

    Basri, G. 2021, An Introduction to Stellar Magnetic Activity Basri, G. & Shah, R. 2020, ApJ, 901, 14 Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science, 327, 977 Distefano, E., Lanzafame, A. C., Brugaletta, E., et al. 2023, A&A, 674, A20 Ferraz-Mello, S. 1981, AJ, 86, 619 Foreman-Mackey, D. 2014, Mixture Models, Zenodo Foreman-Mackey, D., Hogg, D. ...

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    The nature of these sources is well known and these examples were chosen to demonstrate the difficulties encountered in period determinations in general and especially in active stars; note that eclipsing binaries are usually also active when one or or both system components are of late spectral type. A.1. AV Dor: An eclipsing binary A V Dor (=TIC 1494734...

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    As appar- ent from Fig

    in the period range 0.1 - 1.3 days. As appar- ent from Fig. A.1, the autocorrelation function shows two peaks at 0.545 days and at 1.09 days, theΘstatistics has two minima at the same periods. The GLS power spectrum shows several maxima, yet the maximum with the largest power has a negative autocorrelation, and the period with the largest autocorrelation ...

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    it executes more than 50 rotations in a typical TESS sector and may exhibit photometric modulations of more than 10%, leading to an extremely ”sharp” signal in Fourier space; a very detailed study of TESS data of AB Dor has been presented by Ioannidis & Schmitt (2020). In Fig. A.3 we plot (analogously to Fig. A.1) the GLS pe- riodogram (medium panel) for ...

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    A.6, there are two rather significant periods apparent in the TESS time series, a shorter period of∼1 hour is clearly visible in the modulations in the inset of Fig

    As shown in Fig. A.6, there are two rather significant periods apparent in the TESS time series, a shorter period of∼1 hour is clearly visible in the modulations in the inset of Fig. A.5, along with a longer period of∼2 days. It is obvious that the shorter period cannot possibly be a ro- tation period, it rather appears to be a pulsational period of the A...

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    AB Dor, the correct periods are well known and we can properly interpret an apparently ”anomalous” light curve as in Fig

    See text for details. AB Dor, the correct periods are well known and we can properly interpret an apparently ”anomalous” light curve as in Fig. A.4; yet if we only had data from TESS sector 27 at our disposal, we would encounter interpretational difficulties. It appears that for active stars the GLS periods appear to be quite trustworthy, yet it is always...

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    The data are shown in the left panels, the period results in the right panels; see text for details

    for TIC 30311749. The data are shown in the left panels, the period results in the right panels; see text for details. we now interpret v broad as a v sin(i) measurement withi=90 ◦, we find a period of 0.84 days, which would actually reasonably fit to the aliased main GLS peak at 0.4 days. Thus we may actu- ally see the rotational signal of HD 62707 in th...

    work page 2009