Tackling artefacts in the timing of relativistic pulsar binaries: towards the SKA

David J. Champion; Huanchen Hu; Michael J. Keith; Michael Kramer; Nataliya K. Porayko; Willem van Straten

REVIEW 3 major objections 6 minor 1 cited by

Tackling artefacts in the timing of relativistic pulsar binaries: towards the SKA

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The Double Pulsar's orbital dispersion-measure variation was an artefact of neglecting the Doppler-shifted spin frequency during de-dispersion; the same approximations will bias Shapiro-delay measurements for tight edge-on binaries.

desk verdict A clean, likely-correct Doppler explanation for the Double Pulsar's 20-year-old DM artefact; the SKA-era Shapiro-bias claim in Section 6 is the part that needs harder scrutiny. read the letter →

arxiv 2501.16421 v1 pith:C4CB2TSZ submitted 2025-01-27 astro-ph.HE astro-ph.IMgr-qc

Huanchen Hu , Nataliya K. Porayko , Willem van Straten , Michael Kramer , David J. Champion , Michael J. Keith This is my paper · ORCID

classification astro-ph.HEastro-ph.IMgr-qc

keywords pulsartimingrelativisticbinariesdispersionmeasureDopplershiftShapirodelaydata-processingartefactsPSRJ0737-3039Aphasepredictors

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

Tight relativistic binaries move fast enough that the pulsar's apparent spin frequency changes measurably within an orbit. When that Doppler shift is omitted from the correction that removes frequency-dependent propagation delays (de-dispersion), the measured dispersion measure—the electron column density along the line of sight—appears to swing with orbital phase; for the Double Pulsar the paper reproduces the $\sim 0.05\,\mathrm{pc\,cm^{-3}}$ wobble reported twenty years ago, in shape and amplitude. Two smaller second-order effects, temporal and spectral dispersive Doppler smearing, add orbital-phase-dependent profile smearing that can also masquerade as DM variation, with a functional form that depends on orbital eccentricity. The paper further shows that polynomial phase predictors used by current processing software cannot follow the sharp logarithmic Shapiro delay of edge-on orbits shorter than about four hours, biasing Shapiro-delay and other timing-parameter measurements for the most sensitive upcoming telescopes. These artefacts sit exactly at the precision level where tests of gravity and neutron-star mass measurements are made, so understanding them is a prerequisite for the next generation of pulsar timing.

What carries the argument

The load-bearing object is the one-dimensional polynomial phase predictor used in folding. Instead of evaluating the exact de-dispersed phase $\phi(t,f)=\phi^{(1)}(t-\Delta t_{\rm DM}[t,f,f_0];f_0)$, current software computes $\tilde{\phi}(t,f)\simeq\phi^{(1)}(t;f_0)-\nu^{(1)}(t_{\rm mid};f_0)\,\Delta t_{\rm DM}(t_{\rm mid},f,f_0)$, using a single reference frequency $f_0$ and a single mid-sub-integration epoch for the whole band. The key identity derived from this mismatch is $\delta\mathrm{DM}=\left(\sqrt{(1-\beta)/(1+\beta)}-1\right)\mathrm{DM}_0\simeq-\beta\,\mathrm{DM}_0$, which converts the neglected orbital Doppler factor into an apparent phase-dependent DM. For the second-order effects, the Taylor expansion of the phase predictor produces $\Delta\phi(t,f)=\Delta t_{\rm DM}[\ddot{\phi}_0\,\Delta t-\tfrac12\dddot{\phi}_0\,\Delta t^2+\cdots]-\tfrac12\Delta t_{\rm DM}^2[\ddot{\phi}_0+\dddot{\phi}_0\Delta t+\cdots]+\cdots$, whose leading term grows with sub-integration length (TDDS) and whose next term grows toward low frequency (SDDS). The Shapiro-delay failure is diagnosed by comparing the exact logarithmic delay $\Delta_S^{(\rm LO)}=-2r\ln\Lambda_u$ with the polynomial expansion used by standard predictors.

What would settle it

Re-process the original Green Bank Telescope observations behind the reported Double Pulsar DM curve with the full binary ephemeris, so the dispersive-phase correction uses the Doppler-shifted spin frequency at each orbital phase; the artefact interpretation predicts the apparent DM curve collapses to a constant $\mathrm{DM}_0$, whereas any surviving orbital modulation of order $0.05\,\mathrm{pc\,cm^{-3}}$ would indicate a real propagation component.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the apparent orbital DM modulation attributed to plasma propagation is, at dominant order, exactly what you get by equating the true dispersive phase shift—computed with the Doppler-shifted observed spin frequency $\nu(t)=\nu_0\sqrt{(1-\beta)/(1+\beta)}$—with a 'solitary-pulsar' correction that uses the fixed spin frequency $\nu_0$. The result is an apparent DM offset $\delta\mathrm{DM}\simeq -\beta\,\mathrm{DM}_0 = -(v_r/c)\,\mathrm{DM}_0$, which for PSR J0737−3039A peaks near $0.05\,\mathrm{pc\,cm^{-3}}$ and traces the line-of-sight orbital velocity, matching the reported curve. The paper then identifies two second-order artefacts from assuming the spin frequency is constant over the sub-integration time (temporal dispersive Doppler smearing, TDDS) and over the band (spectral dispersive Doppler smearing, SDDS): both cause orbital-phase-dependent dispersive smearing that mimics DM variation, with magnitudes set by radial acceleration and the dispersive delay, and with eccentricity controlling the waveform. Finally, the paper shows that the polynomial phase predictors used in standard folding cannot represent the sharp logarithmic Shapiro delay for edge-on binaries with periods below about four hours, leaving spiky timing residuals at superior conjunction that bias the measured Shapiro range and shape parameters.

Load-bearing premise

The load-bearing premise is that current pulsar pipelines actually fold with a one-dimensional polynomial phase predictor evaluated at a single reference frequency and a single mid-sub-integration time across the whole band, so that the orbital Doppler shift really is neglected during de-dispersion.

Editorial extensions

If this is right

De-dispersing before any time-averaging removes both TDDS and SDDS, so the orbital smearing artefacts disappear by changing only the order of data-processing steps.
At SKA-Low frequencies, SDDS dominates for sub-integrations shorter than about half the dispersive delay (38 s for the Double Pulsar parameters), giving smearing of order 10 ms for a 1-hour orbit and 100 ms for a 15-minute orbit; at SKA-Mid, TDDS instead dominates once the sub-integration exceeds about 0.6 s.
For edge-on binaries with orbital periods under roughly four hours, current polynomial predictors leave spiky residuals centred at superior conjunction; these residuals grow as the predictor's time span and the sub-integration length grow, and they bias the Shapiro range and shape parameters—estimated at about 2σ at the SKA's final configuration—even when statistical noise is tiny.
Enabling the barycentric correction for the dispersive delay removes the apparent annual DM modulation, whose maximum relative amplitude is about $10^{-4}$ for pulsars near the ecliptic plane.

Reading between the lines

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

If the DDV interpretation is correct, previously published orbital DM variations in other relativistic binaries should be re-checked: the missed Doppler shift predicts a specific phase curve tied to the line-of-sight velocity, so matching that curve is not by itself evidence of a real electron-column change.
A cheap, testable extension is to look for the same artefact in any strongly accelerated pulsar—for example in a globular cluster—processed with one-dimensional predictors; the predicted apparent DM curve follows the radial velocity and should be reproducible without new physics.
The Shapiro-delay folding failure points to a concrete software design target: add the analytic logarithmic Shapiro term directly to the phase model, or move to a two-dimensional phase predictor, rather than trying to fit the cusp with more polynomial coefficients.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know up front. The main result is right and simple: the apparent orbital DM variation in the Double Pulsar, first reported then withdrawn by Ransom et al. (2004), is what you get when the dispersive phase correction uses a constant spin frequency instead of the Doppler-shifted one. Equating the two phase expressions gives δDM ≈ −(v_r/c) DM0 (Eq. 9), which yields around 0.05 pc cm^-3 at the reported orbital phases, and their simulation reproduces both the shape and amplitude. That settles a 20-year-old artefact that had been loosely attributed to wind or propagation effects. Second, read Section 6 carefully — it is the soft underbelly.

What is genuinely new: the explicit DDV expression, the naming and first-order derivation of TDDS and SDDS from the Taylor expansion of the phase predictor, and the TopoDDV estimate for Earth's annual motion with the psrchive barycentric correction left disabled. The derivations are parameter-free algebra, checked against the withdrawn Ransom et al. measurement and against simulations built on a real ephemeris. The paper is clearly written, and Table 3 — artefact, cause, solution — is a genuinely useful reference for the software side of the field.

Soft spots, in proportion to how soft they are. Section 6 is more self-referential than the rest. The text admits PsrSigSim generates pulse times from the polyco polynomial itself, so the conjunction residuals in Figs. 15 and 17 show the predictor's phase error relative to the best-fit exact timing model. That is a legitimate way to expose the polynomial's failure to track the logarithmic Shapiro term, but it is not a clean exact-signal-in / approximate-folding-out simulation, and the Table 2 bias estimates inherit that ambiguity. The estimation method behind Table 2 is also under-described. The mathematical failure of a polynomial to fit a sharp log is not in doubt, but before trusting the SKA projections I would want a forward model that generates from the exact timing model and folds with the polynomial. Two smaller points: the claim that current pipelines still use the one-dimensional phase approximation of Eq. (3) is plausible but not verified against a real processing chain, and the simulation code is not pinned to a commit hash, which weakens reproducibility of the specific figures.

This is for pulsar timers and the FAST/SKA data-processing groups. The central artefact explanation is solid and the taxonomy clears up real confusion in the literature; the paper deserves a serious referee. I would send it out, with the Section 6 demand for an exact-ephemeris test attached.

Referee Report

3 major / 6 minor

Summary. This paper investigates signal-processing artefacts in pulsar timing of relativistic binaries, focusing on the Double Pulsar PSR J0737-3039A. The authors first show that the apparent orbital DM variation reported by Ransom et al. (2004) can be explained as a dispersive Doppler variation (DDV): neglecting the Doppler-shifted spin frequency when computing the dispersive phase shift produces an apparent DM offset δDM ≈ -(v_r/c) DM0 (Eq. 9), with amplitude about 0.05 pc cm^-3, matching the reported value. They then derive and simulate two second-order effects, temporal and spectral dispersive Doppler smearing (TDDS and SDDS), and show that these also cause orbital-phase-dependent apparent DM variations. The paper additionally considers topocentric analogues of these effects and argues that polynomial phase predictors (polyco) fail to accurately model the sharp logarithmic Shapiro delay for edge-on orbits with periods below about 4 hours, leading to potentially significant biases in Shapiro-delay parameter measurements with sensitive instruments such as FAST and the SKA.

Significance. The DDV explanation is a clean, parameter-free derivation with a concrete numerical prediction that matches an external observation, and the paper correctly distinguishes this first-order effect from the second-order smearing effects TDDS and SDDS, which have been repeatedly confused in the literature. The scaling relations in Eqs. (14) and (15) and the summary table are useful practical tools for observers, and the proposed mitigation (de-dispersion before frequency or time averaging) is actionable. The section on topocentric artefacts is a welcome extension. However, the SKA/Shapiro-delay bias claim is less convincing: the simulations in Section 6 appear to use the same polynomial approximation for both generation and folding, so the residuals shown in Figs. 15-17 and the bias estimates in Table 2 do not independently test the predictor against the exact timing model. This weakens a central claim for the future-SKA part of the paper, although the underlying mathematical concern about polynomial representation of the logarithmic Shapiro delay is well founded.

major comments (3)

[Section 6, Fig. 15 and Table 2] The simulations used to demonstrate the Shapiro-delay/polyco problem are not an independent test because PsrSigSim generates the pulsar data files 'based on the polynomial expansion of the timing solution (predictor)', as stated in Section 6. If generation and folding use the same polyco coefficients (or the same TZNSPAN/coefficient set), the residuals in Figs. 15-17 show only the inconsistency between two uses of the same approximation, not the error relative to the exact timing model. The paper does not specify whether the generator used an exact tempo/tempo2 ephemeris and a high-resolution predictor, or whether generation and folding share the same approximation. Thus the simulated bias estimates in Table 2, and the claim that polynomial predictors will bias Shapiro-delay measurements at SKA sensitivity, are not supported by the current simulations. The authors should regenerate these simulations with an exact-ephemeris forward model (generating pulse times from the full DD model with the Shapiro logarithmic term) and then fold with polyco, so that the difference directly quantifies the predictor error.
[Section 2, Eq. (3) and Section 4.1] The premise that current pipelines (dspsr, psrchive, presto) use the one-dimensional phase approximation of Eq. (3), applying a polynomial evaluated at one reference frequency and one mid-sub-integration time across the whole band, is load-bearing for all three artefacts (DDV, TDDS, SDDS). This is asserted on page 3 but not documented with code-level references or a concrete audit. Please provide a brief but explicit description of where each package makes this approximation (e.g., the relevant function or configuration), or state clearly which default settings are assumed. Without this, the reader cannot judge whether the predicted artefact amplitudes apply to the actual software used by the community, including the handling of the barycentric correction discussed in Section 5.
[Section 4.2.1, Fig. 9 and surrounding text] The claim that the apparent DM variation from TDDS for the Double Pulsar is 'consistent with what has been seen with MeerKAT when processing the data in a similar fashion' is not quantified. Because the TDDS amplitude is an order of magnitude smaller than the DDV and because the variation depends on profile shape and orbital eccentricity, a visual comparison alone is insufficient. Please provide a quantitative comparison, such as the best-fit amplitude and the residual chi-squared or RMS between the simulated and observed DM variations for the same orbital phase bins, or clearly label the statement as a qualitative similarity.

minor comments (6)

[Section 4.1, Eq. (6)] The symbol used for the radial velocity of the pulsar appears as '3psr r (t)' in the text; this is not defined and is confusing. Please write it as v_psr^r(t) or a similar standard notation and define it at first use.
[Section 4.2.1, Eq. (11) and surrounding text] The derivative notation using the symbols ':' and ';' (e.g., 'ϕ0' and ':ϕ0') is non-standard and not explained. Please replace with conventional dot notation (e.g., dϕ/dt, d²ϕ/dt²) or define the notation explicitly near Eq. (11).
[Section 5.1, Eq. (16)] The definition 'where D = D× DM' uses the same symbol D for the dispersion constant and the product D×DM. Please use a distinct symbol for the product to avoid ambiguity.
[Section 6, first paragraph after Table 1] The phrase 'the discrepancies of interest should be visible in the residuals after subtracting the best-fit timing model' relies on the underlying generator using the same predictor; this should be clarified earlier in the section, as noted in Major Comment 1, so that the reader is not misled about the independence of the test.
[References] The reference for Ransom et al. (2004) is given as an arXiv eprint (astro-ph/0406321). Since the paper is described as having been withdrawn, please provide the withdrawal status and any associated comment or erratum in the reference list or a footnote, so interested readers can locate the original and the retraction.
[Abstract and Section 7] The abstract states that the polynomial approximation fails for 'orbits less than 4 hours', but the simulations in Fig. 15 were run for 4.5 h, 3 h, 2.45 h, and 1 h, so the 4-hour threshold is an interpolation between the simulated points. Please state this explicitly or add a simulation at a period just above and below 4 hours to justify the threshold.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the analytic derivations are parameter-free and the simulations forward-model the stated approximations, benchmarked against external data.

full rationale

The paper's central DDV claim follows algebraically by equating the dispersive phase computed with the Doppler-shifted spin frequency (Eq. 6) and with the rest-frequency spin (Eq. 7), yielding Eq. (9); this is a closed-form consequence, not a fitted parameter. The comparison with Ransom et al. (2004) is external, using the known orbital velocity and DM0 of PSR J0737-3039A rather than values adjusted to match the reported DM curve. The TDDS/SDDS expressions (Eqs. 13-15 and 18-19) are Taylor expansions of the difference between Eqs. (3) and (4), and the associated simulations are consistency checks of those analytic formulae, not inversions in which the target result is used as input. Section 6's Shapiro-delay bias estimates do rely on PsrSigSim generating phase-connected data via a polyco polynomial, as the text explicitly notes; however, this is a controlled injection of the predictor error into synthetic TOAs followed by a fit to the exact timing model, so the reported biases in s and r are a nontrivial propagation of that error rather than a restatement of the input. The self-citation to Hu et al. (2022) supplies the Double Pulsar ephemeris and a prior qualitative mention of the folding issue, but the present paper's derivations and external benchmarks do not reduce to that citation.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claims rely on standard dispersion and Doppler relations plus a domain assumption about how current software folds data. The three free parameters listed are hand-chosen simulation and predictor settings that set the scope of the claimed '<4 h' threshold and eccentricity dependence; none is fitted to make the target result appear. No new physical entities are introduced; DDV, TDDS, SDDS, TopoDDV and TopoTDDS are names for processing artefacts, not new particles or forces.

free parameters (3)

Synthetic orbital periods used in folding tests = 1, 3, 4.5 hours
Hand-selected values in Settings 3a and 3b that define the 'under 4 hours' threshold claim in Section 6; the threshold is not derived analytically.
Synthetic orbital eccentricities in smearing tests = 0.0, 0.088, 0.6
Chosen in Setting 2a to probe how apparent DM variation depends on eccentricity in Fig. 9; these are exploratory settings, not fitted values.
Phase-predictor resolution (TZNSPAN, coefficient count) = 1-3 minutes, 20-30 coefficients
The magnitude and visibility of the Shapiro-delay folding artefact depend on these software parameters; the paper samples a small grid rather than providing a general limit.

assumptions (5)

domain assumption The cold-plasma dispersion relation with delay t_DM = D x DM / f^2 is the correct description of dispersion in the interstellar medium and in pulsar software.
Adopted at Eq. (1) and used in all artefact derivations; any additional non-cold-plasma propagation would alter the inferred artefacts.
domain assumption The current processing chain folds data with a one-dimensional phase predictor evaluated at a single reference frequency and mid-sub-integration time, as in Eq. (3).
This is the premise on which DDV, TDDS and SDDS are defined; stated in Section 2 for dspsr, psrchive and presto.
standard math Taylor expansions of the phase predictor in Eqs. (11)-(13) converge over the sub-integration and bandwidth used in the simulations.
The derivations retain leading terms in Δt and Δt_DM; convergence is assumed rather than demonstrated for the most compact orbits.
standard math The Shapiro delay formula from Blandford and Teukolsky (1976), Eqs. (20)-(21), is the correct timing-model description that the polynomial predictor approximates.
Used in Section 6 to explain why polynomial predictors fail at superior conjunction.
domain assumption The simulated PSR J0737-3039A ephemeris and template profile from Hu et al. (2022) are accurate enough to reproduce the real processing artefacts.
The comparison to the Ransom et al. (2004) result depends on the true orbital parameters and DM0 being adopted in the simulation.

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Cite this review

Pith. "Pith review of Tackling artefacts in the timing of relativistic pulsar binaries: towards the SKA." pith.science (2026). https://pith.science/paper/C4CB2TSZ

@misc{pith2026250116421,
  author       = {Pith},
  title        = {Pith review of: Tackling artefacts in the timing of relativistic pulsar binaries: towards the SKA},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C4CB2TSZ}},
  note         = {Machine review of arXiv:2501.16421}
}

read the original abstract

Common signal-processing approximations produce artefacts when timing pulsars in relativistic binary systems, especially edge-on systems with tight orbits, such as the Double Pulsar. In this paper, we use extensive simulations to explore various patterns that arise from the inaccuracies of approximations made when correcting dispersion and Shapiro delay. In a relativistic binary, the velocity of the pulsar projected onto the line-of-sight varies significantly on short time scales, causing rapid changes in the apparent pulsar spin frequency, which is used to convert dispersive delays to pulsar rotational phase shifts. A well-known example of the consequences of this effect is the artificial variation of dispersion measure (DM) with binary phase, first observed in the Double Pulsar 20 years ago. We show that ignoring the Doppler shift of the spin frequency when computing the dispersive phase shift exactly reproduces the shape and magnitude of the reported DM variations. We also simulate and study two additional effects of much smaller magnitude, which are caused by the assumption that the spin frequency used to correct dispersion is constant over the duration of the sub-integration and over the observed bandwidth. We show that failure to account for these two effects leads to orbital phase-dependent dispersive smearing that leads to apparent orbital DM variations. The functional form of the variation depends on the orbital eccentricity. In addition, we find that a polynomial approximation of the timing model is unable to accurately describe the Shapiro delay of edge-on systems with orbits less than 4 hours, which poses problems for the measurements of timing parameters, most notably the Shapiro delay. This will be a potential issue for sensitive facilities like the FAST and the forthcoming Square Kilometre Array (SKA); therefore, a more accurate phase predictor is indispensable.

Figures

Figures reproduced from arXiv: 2501.16421 by the authors.

**Figure 1.** Illustration of the pulsar signal from a binary pulsar to timing data products. The binary motion of the pulsar around the binary barycentre (BB) causes Doppler shift of pulsar spin frequency. The pulsar signal propagates through ionised interstellar medium and suffers dispersive delay, causing the low-frequency signal to be delayed more than the signal at higher frequency. The plot on the right demonstrates this ef… view at source ↗

**Figure 2.** Example of simulated pulsar data files as shown by pazi command of the psrchive software: the Double Pulsar profile (left panel) and broad Gaussian profile used in the paper (right panel). in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Timing variations of simulated by PsrSigSim software as a function of true anomaly for 4×12.5 MHz sub-bands covering a 50 MHz band centered at 427 MHz. The setup repeats the one used in the Ransom et al. (2004). The apparent variations in timing residuals have the same magnitude of ∼ 200 µs as reported by Ransom et al. (2004). the binary model (in other words we assumed that the spin frequency is constant over th… view at source ↗

Figures from the paper (11 more)

**Figure 5.** Figure 5: Dispersive time delay within a narrow 2 MHz-band as a comparison to [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 7.** Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

**Figure 9.** Figure 9: Apparent DM variation caused by orbital profile smearing for different eccentricities using the J0737−3039A profile. specification of the simulated dataset is described by Setting 2a in [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]

**Figure 8.** Figure 8: Pre-fit and post-fit residuals after fitting for DM are shown in relation to frequency. Both figures are for the same orbital phase (ψ ∼ 130◦ ) but with different pulse profiles. (a) Circular orbit with the J0737−3039A profile (see [PITH_FULL_IMAGE:figures/full_fig_p0…

**Figure 10.** Figure 10: Schematic of folding with wrong spin periods, the resulted averaged profile (red) becomes broader and flatter. Viewing from top down, folding with a long spin period shifts the centre of the averaged profile to the left; from bottom up, folding with a short spin peri…

**Figure 11.** Figure 11: Maximum smearing with respect to sub-integration length for SKA-Low (left y-axis) and SKA-Mid (right y-axis) calculated using Eqs. (14) and (15), assuming the spin period and DM of PSR J0737−3039A, mass of 1.4 M⊙, and circular orbits. The blue, orange, and green lines…

**Figure 13.** Figure 13: The TDDS effect in the simulated SKA-Low data for T = 100 s to make the effect more prominent. The corresponding residuals are demonstrated in [PITH_FULL_IMAGE:figures/full_fig_p009_13.png]

**Figure 14.** Figure 14: Timing residuals of the TDDS effect simulated for the SKAMid data (Setting 2b). The magnitude of the effect gradually increases with the sub-integration time T as predicted by Eq. (14). 5. Topocentric Doppler effects In the previous section we have discussed three di…

**Figure 15.** Figure 15: TOA residuals of the simulated data files vs. orbital phase for binary systems with orbital periods of 4.5 h, 3 h, 2.45 h and 1 h. The spiky features appearing at the superior conjunction (ψ = 90◦ ) demonstrate the limitations of the current software, in this case, t…

**Figure 16.** Figure 16: Same as [PITH_FULL_IMAGE:figures/full_fig_p010_16.png]

**Figure 17.** Figure 17: TOA residuals of the simulated data files as a function of the orbital phase: for a fictional binary with orbital period Pb = 2.45 h on the left and for the Double Pulsar on the right. For all cases the original time resolution of the generated data files is TZNSPAN=1…

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