pith. sign in

arxiv: 2606.30624 · v1 · pith:D46AW3YUnew · submitted 2026-06-29 · 🌌 astro-ph.GA

Prescriptions for the stochasticity effect on the integrated X-ray luminosity of star-forming galaxies:Implications for selecting star-forming galaxies and AGN in X-ray surveys

Elias Kyritsis , Andreas Zezas , Konstantinos Kovlakas This is my paper

Pith reviewed 2026-06-30 04:43 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords X-ray luminosityhigh-mass X-ray binariesstochastic samplingstar-forming galaxiesX-ray surveysAGN selectionluminosity functionmetallicity
0
0 comments X

The pith

Stochastic sampling of high-mass X-ray binaries creates up to 1 dex scatter in galaxy X-ray luminosity that must be corrected before interpreting observations.

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

The paper demonstrates that the discrete nature of high-mass X-ray binary populations produces large stochastic variations in the total X-ray output of star-forming galaxies. Monte Carlo realizations of the X-ray luminosity function across a grid of star-formation rates and metallicities are used to map the resulting distributions and extract their statistical bounds. Surfaces fitted to these bounds supply ready prescriptions that return the expected luminosity range for any given SFR and metallicity without repeating the simulations. When applied to local and high-redshift samples the prescriptions show that stochastic scatter can shift luminosities into the low-luminosity AGN regime and must be removed before differences are ascribed to galaxy evolution or survey selection. A further simulation set reveals mild redshift dependence in the size of the scatter, reaching a minimum near z approximately 2.5.

Core claim

Monte Carlo sampling of the HMXB XLF over a broad SFR-metallicity grid yields Lx probability distributions whose upper and lower envelopes are parametrized by fitted surfaces; these surfaces supply practical formulas that return the stochastic bounds on integrated X-ray luminosity for any input SFR and metallicity.

What carries the argument

Fitted surfaces to the upper and lower bounds of Monte Carlo-derived Lx distributions from the HMXB XLF.

If this is right

  • Stochastic scatter can increase observed Lx by up to 1 dex at low redshift, causing overlap with the low-luminosity AGN regime and biasing source classification.
  • Mild redshift evolution of the scatter appears between z=0.5 and z=5, with the smallest scatter near z~2.5.
  • Flux-limited surveys introduce quantifiable biases in Lx-SFR scaling relations that the prescriptions can correct.
  • Outliers in observed Lx can be tested against the stochastic bounds rather than interpreted solely as unusual intrinsic galaxy properties.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The prescriptions could be folded into Bayesian source classification pipelines for wide-field X-ray surveys to reduce AGN contamination.
  • If the XLF normalization itself varies with redshift or environment, the reported minimum scatter at z~2.5 would shift.
  • Analogous stochastic corrections might be derived for other discrete tracers such as supernova rates or gamma-ray burst counts.
  • Direct application to individual galaxies would require an estimate of their recent star-formation history rather than a single SFR value.

Load-bearing premise

The underlying shape and normalization of the high-mass X-ray binary luminosity function are treated as fixed and known at all star-formation rates and metallicities.

What would settle it

Comparison of the predicted Lx scatter envelopes against the observed luminosity distribution in a large, SFR- and metallicity-matched sample of star-forming galaxies would show whether the simulated bounds reproduce the data.

Figures

Figures reproduced from arXiv: 2606.30624 by Andreas Zezas, Elias Kyritsis, Konstantinos Kovlakas.

Figure 1
Figure 1. Figure 1: Indicative X-ray luminosity distributions for low, moderate, and high SFR-[12 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Distributions of the upper and lower LX bounds of the 99% HDI as a function of the SFR and [12 + log(O/H)] (black stars). The surfaces show the best-fit results of the upper and lower LX bounds of the 99% HDI together with their residuals (orange stars) as a function of the SFR and the metallicity. The corresponding fit surfaces for the 68%, 90%, and 99.9% HDIs are presented in Appendix A. formed a pre-fit… view at source ↗
Figure 3
Figure 3. Figure 3: The LX/SFR ratio as a function of metallicity. The upper and lower 90%, 99%, and 99.9% HDI bounds of the expected LX from stochastic sampling are shown as shaded bands of different colours for each data set. Violet stars with grey-shaded regions correspond to the sample of Adamcová et al. (2024), brown stars with orange-shaded regions to Kyritsis et al. (2025), and blue squares with cyan-shaded regions to … view at source ↗
Figure 4
Figure 4. Figure 4: The LX/SFR ratio as a function of redshift. The upper and lower 68%, 90%, 99%, and 99.9% HDI bounds of the expected LX from stochastic sampling are shown as shaded bands of dif￾ferent colours. The majority of the objects are consistent with the scaling relations which accounts for the effect of metallicity. Blue squares correspond to the sample of Brorby et al. (2016), while black stars to the sample of Mi… view at source ↗
Figure 5
Figure 5. Figure 5: The LX excess, defined as log10L HDI X, upb or lowb - log10L L16 X as a function of SFR for all the redshift bins considered in this simulation study. The various HDIs indicated by shaded areas of different colours. The black dashed line indicates the line of equality between the LX from stochastic sampling and the LX from the redshift-dependent scaling relation of Lehmer et al. (2016) (L16). The shift of … view at source ↗
Figure 6
Figure 6. Figure 6: The LX excess at the 99% LX bounds from the L16 as a function of redshift for two indicative SFR values: 0.5 M⊙/yr (yellow shaded area) and 2.5 M⊙/yr (orange shaded area) populations. Furthermore, a galaxy simulation study across z = 0.5–5 showed mild intrinsic redshift evolution of the stochastic scatter. Its behaviour mirrors the evolution of SFR and metal￾licity, with minimum scatter at z ≃ 2.5 where th… view at source ↗
read the original abstract

(abridged) The integrated X-ray luminosity (Lx) of star-forming galaxies is dominated by high-mass X-ray binary (HMXB) populations. The discrete nature of these populations introduces stochastic sampling effects that distort the X-ray Luminosity Function (XLF) and bias observed scaling relations. We investigate how stochastic sampling of the HMXB XLF affects the predicted integrated Lx across a wide range of star-formation and metallicity conditions, quantifying the scatter to provide a statistical framework for interpreting X-ray observations. Using Monte Carlo simulations, we derive Lx distributions over a broad grid of star-formation rate (SFR) and metallicity values. By measuring statistical quantities describing these distributions, we parametrize the luminosity scatter by fitting surfaces to the upper and lower Lx bounds as functions of SFR and metallicity. We provide practical prescriptions to compute the expected Lx for given SFR and metallicity, fully accounting for stochastic effects without rerunning costly XLF sampling. Applying these to local and high-redshift samples shows stochasticity must be considered before attributing Lx differences to intrinsic properties. A simulation study across z=0.5-5 reveals mild redshift evolution of stochastic scatter, with minimum scatter at z~2.5. Our prescriptions quantify biases in scaling relations introduced by flux-limited surveys. At low redshifts, stochastic effects can raise Lx by up to 1 dex, overlapping with the low-luminosity AGN regime and biasing source classification in deep surveys. These prescriptions offer a framework for constraining scatter, quantifying extreme outliers, and refining X-ray source classification in current and future surveys.

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 / 1 minor

Summary. The paper uses Monte Carlo sampling of a fixed HMXB XLF across a grid of SFR and metallicity values to generate distributions of integrated Lx. It then fits parametric surfaces to the upper and lower bounds of these distributions, yielding prescriptions for the expected Lx (including stochastic scatter) as functions of SFR and metallicity. These are applied to local/high-z samples and a z=0.5-5 simulation to argue that stochasticity must be accounted for before attributing Lx variations to intrinsic galaxy properties or AGN, with implications for source classification in flux-limited surveys.

Significance. If validated, the prescriptions would supply a practical, reusable tool for incorporating stochastic sampling effects into Lx-SFR-metallicity scaling relations without repeated XLF sampling. The approach of generating independent MC realizations and fitting bounding surfaces is a clear strength, as is the redshift-evolution analysis showing minimum scatter near z~2.5. However, the overall significance is limited by the absence of any propagation of input XLF uncertainties or direct comparison against observed Lx scatter.

major comments (2)
  1. [Abstract / Methods] Abstract and method description: The HMXB XLF shape and normalization are taken as fixed and known across the entire SFR-metallicity grid, with no propagation of their parameter uncertainties or covariance into the Monte Carlo Lx distributions or the fitted bounding surfaces. Because the prescriptions are derived directly from this single input XLF, any systematic error in it shifts the entire set of surfaces and quoted scatter bounds by a comparable amount.
  2. [Results / Surface fitting] Surface-fitting procedure (post-MC analysis): No validation metrics, cross-validation, or comparison to observed Lx scatter in real galaxies are reported. The post-hoc fitting of upper/lower bounds to the MC output therefore risks over-fitting the particular simulation realizations without demonstrating that the surfaces recover the true stochastic scatter when tested against independent data.
minor comments (1)
  1. [Results] The notation for the fitted bounding surfaces (e.g., functional form, coefficients) should be presented with explicit equations and tabulated best-fit parameters for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and the recommendation for major revision. Below we respond point-by-point to the two major comments. We agree that both points identify genuine limitations and will revise the manuscript accordingly by adding explicit discussion of the fixed XLF assumption and by including a direct comparison of the predicted scatter to observed local samples.

read point-by-point responses

  1. Referee: [Abstract / Methods] Abstract and method description: The HMXB XLF shape and normalization are taken as fixed and known across the entire SFR-metallicity grid, with no propagation of their parameter uncertainties or covariance into the Monte Carlo Lx distributions or the fitted bounding surfaces. Because the prescriptions are derived directly from this single input XLF, any systematic error in it shifts the entire set of surfaces and quoted scatter bounds by a comparable amount.

    Authors: We agree that the adopted HMXB XLF (taken from the literature) is held fixed, so that the derived surfaces and scatter bounds are conditional on that specific choice. Our focus is the additional stochastic variance arising from discrete sampling of a known XLF rather than a full marginalization over XLF parameter uncertainties. A complete propagation would require a hierarchical Bayesian treatment that lies outside the present scope. In the revised manuscript we will insert a dedicated paragraph in the Methods section that states this assumption explicitly, quantifies the sensitivity to plausible XLF variations where possible, and cautions users that the quoted bounds do not include XLF systematic errors. revision: partial

  2. Referee: [Results / Surface fitting] Surface-fitting procedure (post-MC analysis): No validation metrics, cross-validation, or comparison to observed Lx scatter in real galaxies are reported. The post-hoc fitting of upper/lower bounds to the MC output therefore risks over-fitting the particular simulation realizations without demonstrating that the surfaces recover the true stochastic scatter when tested against independent data.

    Authors: The surfaces are analytic fits to the statistical quantiles of the Monte Carlo distributions; because the input model is fully known, the fits reproduce the simulated scatter by construction and we have verified internal goodness-of-fit. We nevertheless accept that external validation against real data is desirable. In the revised manuscript we will add a new subsection that compares the predicted Lx scatter (at fixed SFR and metallicity) with the observed dispersion in local star-forming galaxy samples for which independent SFR and metallicity measurements exist. Any residual differences will be discussed in terms of additional physical or observational scatter sources. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is simulation-driven and independent

full rationale

The paper runs Monte Carlo realizations of HMXB XLF sampling over an SFR-metallicity grid, measures the resulting Lx distribution statistics, and fits bounding surfaces to produce the prescriptions. This is an independent computational mapping, not a self-definition, fitted-input-as-prediction, or self-citation reduction. No load-bearing step reduces by construction to the input XLF parameters; the output parametrizes stochastic scatter that is not algebraically forced. The approach is self-contained against external simulation benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are identifiable beyond the standard assumption that the HMXB XLF is an accurate input.

pith-pipeline@v0.9.1-grok · 5841 in / 1121 out tokens · 43314 ms · 2026-06-30T04:43:20.152708+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

49 extracted references

  1. [1]

    2024, A&A, 691, A27

    Adamcová, B., Svoboda, J., Kyritsis, E., et al. 2024, A&A, 691, A27

    2024

  2. [2]

    2019, MNRAS, 483, 711

    Anastasopoulou, K., Zezas, A., Gkiokas, V ., & Kovlakas, K. 2019, MNRAS, 483, 711

    2019

  3. [3]

    R., Lehmer, B., Fragos, T., et al

    Basu-Zych, A. R., Lehmer, B., Fragos, T., et al. 2016, ApJ, 818, 140

    2016

  4. [4]

    R., Lehmer, B

    Basu-Zych, A. R., Lehmer, B. D., Hornschemeier, A. E., et al. 2013, ApJ, 774, 152

    2013

  5. [5]

    Brorby, M., Kaaret, P., Prestwich, A., & Mirabel, I. F. 2016, MNRAS, 457, 4081

    2016

  6. [6]

    2024, A&A, 684, A75

    Curti, M., Maiolino, R., Curtis-Lake, E., et al. 2024, A&A, 684, A75

    2024

  7. [7]

    2020, MNRAS, 491, 944

    Curti, M., Mannucci, F., Cresci, G., & Maiolino, R. 2020, MNRAS, 491, 944

    2020

  8. [8]

    Das, A., Mesinger, A., Pallottini, A., Ferrara, A., & Wise, J. H. 2017, MNRAS, 469, 1166

    2017

  9. [9]

    2017, A&A, 605, A70

    Davidzon, I., Ilbert, O., Laigle, C., et al. 2017, A&A, 605, A70

    2017

  10. [10]

    B., Graziani, L., Ciardi, B., et al

    Eide, M. B., Graziani, L., Ciardi, B., et al. 2018, MNRAS, 476, 1174

    2018

  11. [11]

    W., Lang, D., & Goodman, J

    Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306

    2013

  12. [12]

    M., Civano, F., Fabbiano, G., et al

    Fornasini, F. M., Civano, F., Fabbiano, G., et al. 2018, ApJ, 865, 43

    2018

  13. [13]

    M., Civano, F., & Suh, H

    Fornasini, F. M., Civano, F., & Suh, H. 2020, MNRAS, 495, 771

    2020

  14. [14]

    D., Lehmer, B

    Geda, R., Goulding, A. D., Lehmer, B. D., Greene, J. E., & Kulkarni, A. 2024, ApJ, 965, 67

    2024

  15. [15]

    D., Doore, K., et al

    Gilbertson, W., Lehmer, B. D., Doore, K., et al. 2022, ApJ, 926, 28

    2022

  16. [16]

    2022, in Handbook of X- ray and Gamma-ray Astrophysics, ed

    Gilfanov, M., Fabbiano, G., Lehmer, B., & Zezas, A. 2022, in Handbook of X- ray and Gamma-ray Astrophysics, ed. C. Bambi & A. Sangangelo, 105

    2022

  17. [17]

    J., & Sunyaev, R

    Gilfanov, M., Grimm, H. J., & Sunyaev, R. 2004, MNRAS, 351, 1365

    2004

  18. [18]

    J., Gilfanov, M., & Sunyaev, R

    Grimm, H. J., Gilfanov, M., & Sunyaev, R. 2002, A&A, 391, 923

    2002

  19. [19]

    J., Gilfanov, M., & Sunyaev, R

    Grimm, H. J., Gilfanov, M., & Sunyaev, R. 2003, MNRAS, 339, 793

    2003

  20. [20]

    Kaaret, P., Feng, H., & Roberts, T. P. 2017, ARA&A, 55, 303

    2017

  21. [21]

    2024, A&A, 688, A159

    Kouroumpatzakis, K., Svoboda, J., Zezas, A., et al. 2024, A&A, 688, A159

    2024

  22. [22]

    2020, MNRAS, 494, 5967

    Kouroumpatzakis, K., Zezas, A., Sell, P., et al. 2020, MNRAS, 494, 5967

    2020

  23. [23]

    2021, MNRAS, 500, 962

    Kouroumpatzakis, K., Zezas, A., Wolter, A., et al. 2021, MNRAS, 500, 962

    2021

  24. [24]

    2022, A&A, 665, A28

    Kovlakas, K., Fragos, T., Schaerer, D., & Mesinger, A. 2022, A&A, 665, A28

    2022

  25. [25]

    J., et al

    Kovlakas, K., Zezas, A., Andrews, J. J., et al. 2020, MNRAS, 498, 4790

    2020

  26. [26]

    2019, Journal of Open Source Software, 4, 1143

    Kumar, R., Carroll, C., Hartikainen, A., & Martin, O. 2019, Journal of Open Source Software, 4, 1143

    2019

  27. [27]

    2025, A&A, 694, A128

    Kyritsis, E., Zezas, A., Haberl, F., et al. 2025, A&A, 694, A128

    2025

  28. [28]

    J., Ilbert, O., et al

    Laigle, C., McCracken, H. J., Ilbert, O., et al. 2016, ApJS, 224, 24

    2016

  29. [29]

    J., Reines, A

    Latimer, L. J., Reines, A. E., Bogdan, A., & Kraft, R. 2021, ApJ, 922, L40

    2021

  30. [30]

    D., Basu-Zych, A

    Lehmer, B. D., Basu-Zych, A. R., Mineo, S., et al. 2016, ApJ, 825, 7

    2016

  31. [31]

    D., Eufrasio, R

    Lehmer, B. D., Eufrasio, R. T., Basu-Zych, A., et al. 2021, ApJ, 907, 17

    2021

  32. [32]

    D., Eufrasio, R

    Lehmer, B. D., Eufrasio, R. T., Tzanavaris, P., et al. 2019, ApJS, 243, 3

    2019

  33. [33]

    D., Ferrell, A

    Lehmer, B. D., Ferrell, A. P., Doore, K., et al. 2020, ApJS, 248, 31

    2020

  34. [34]

    D., Tyler, J

    Lehmer, B. D., Tyler, J. B., Hornschemeier, A. E., et al. 2015, ApJ, 806, 126

    2015

  35. [35]

    F., et al

    Linden, T., Kalogera, V ., Sepinsky, J. F., et al. 2010, ApJ, 725, 1984

    2010

  36. [36]

    & Dickinson, M

    Madau, P. & Dickinson, M. 2014, ARA&A, 52, 415

    2014

  37. [37]

    & Fragos, T

    Madau, P. & Fragos, T. 2017, ApJ, 840, 39

    2017

  38. [38]

    M., & Moriya, T

    Marchant, P., Langer, N., Podsiadlowski, P., Tauris, T. M., & Moriya, T. J. 2016, A&A, 588, A50

    2016

  39. [39]

    2018, MNRAS, 478, 2576

    Mezcua, M., Civano, F., Marchesi, S., et al. 2018, MNRAS, 478, 2576

    2018

  40. [40]

    D., Morrison, G

    Mineo, S., Gilfanov, M., Lehmer, B. D., Morrison, G. E., & Sunyaev, R. 2014, MNRAS, 437, 1698

    2014

  41. [41]

    2012, MNRAS, 419, 2095

    Mineo, S., Gilfanov, M., & Sunyaev, R. 2012, MNRAS, 419, 2095

    2012

  42. [42]

    2023, A&A, 672, A99 Nikoli´c, I., Mesinger, A., Davies, J

    Misra, D., Kovlakas, K., Fragos, T., et al. 2023, A&A, 672, A99 Nikoli´c, I., Mesinger, A., Davies, J. E., & Prelogovi´c, D. 2024, A&A, 692, A142

    2023

  43. [43]

    2021, A&A, 647, A1

    Predehl, P., Andritschke, R., Arefiev, V ., et al. 2021, A&A, 647, A1

    2021

  44. [44]

    2023, A&A, 678, A164

    Riccio, G., Yang, G., Małek, K., et al. 2023, A&A, 678, A164

    2023

  45. [45]

    2024, ApJ, 974, 14

    Sacchi, A., Bogdán, Á., Chadayammuri, U., & Ricarte, A. 2024, ApJ, 974, 14

    2024

  46. [46]

    S., Steinhardt, C

    Speagle, J. S., Steinhardt, C. L., Capak, P. L., & Silverman, J. D. 2014, ApJS, 214, 15

    2014

  47. [47]

    E., et al

    Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261

    2020

  48. [48]

    2026, in Encyclopedia of Astrophysics, V ol

    Zezas, A. 2026, in Encyclopedia of Astrophysics, V ol. 3, 299–324

    2026

  49. [49]

    2012, A&A, 546, A36 Article number, page 11 of 14 A&A proofs:manuscript no

    Zhang, Z., Gilfanov, M., & Bogdán, Á. 2012, A&A, 546, A36 Article number, page 11 of 14 A&A proofs:manuscript no. aa59947-26 Appendix A: Best-fit surfaces for the 68%, 90%, and 99.9% HDIs In this Appendix we present the best-fit surfaces of the upper and lower LX bounds of the 68%, 90%, and 99.9% HDIs together with their residuals as a function of the SFR...

    2012