Sub-Burst Drift

Repeating FRBs drift downward in frequency: later emission arrives at lower frequencies. FLITS reports that drift as \( \mathrm{d}\nu/\mathrm{d}t \) in MHz per millisecond, negative for the usual downward "sad trombone" and positive for the rarer upward drift.

Everything on this page runs on the current selection — crop, event window, off-pulse windows, channel mask, spectral window, component regions and applied DM. Changing any of them invalidates the measurement, and FLITS discards the cached result rather than showing a stale one.

Two estimators, two questions

Estimator	What it measures	What it needs
`acf_2d`	The sub-burst slope: how the emission centroid moves in frequency as one component proceeds.	A single event window with enough time bins and channels.
`component_centroid`	The inter-component drift: the step in centre frequency from one sub-burst to the next.	At least two component regions (or two manual peaks).

Editing the component regions or the manual peaks discards a cached drift result, because the second estimator is built from them.

They are not the same number, and neither is wrong when they disagree. A burst whose components each drift by the same amount as the gaps between them will give one answer; a burst of separately drifting sub-bursts stacked at a different overall slope will give two. Report which one you mean.

The autocorrelation estimator is the primary result and populates drift_rate_mhz_per_ms. The component estimator is reported separately through component_drift_rate_mhz_per_ms and never blocks it.

How the autocorrelation estimator works

Each channel's off-pulse mean is subtracted, and the event window is cut out of the selected band.
The two-dimensional autocorrelation is computed by FFT and corrected for the channel mask: each lag is divided by the fraction of valid channel pairs it actually had, relative to what an unmasked window would have given. With nothing masked this is exactly the conventional autocorrelation; with channels zapped it removes the notch pattern the gaps would otherwise imprint on the surface. The finite-window taper is deliberately left alone, because a burst localised inside its window is not a stationary process.
A rotated two-dimensional Gaussian is fitted to the central peak, over the lags inside max_lag_fraction of the full range that survive min_overlap_fraction of their possible channel pairs. The zero-lag pixel is excluded, because it carries the noise variance as a delta function. FLITS refuses a fit whose width consumes 80% or more of either fitted lag span, because that width is being set by the boundary rather than measured from the peak; increase the lag fraction or improve the selections in that case.
The drift rate is the conditional-mean slope of the fitted ellipse, \( \Sigma_{\nu t} / \Sigma_{tt} \) — the rate at which the centre frequency moves with time.

Fitting for a covariance rather than an angle is what makes the reported number well defined. The slope of the ellipse's major axis is a different quantity that depends on how you scale the two axes against each other; FLITS reports it too, as acf_major_axis_slope_mhz_per_ms, because that is the convention frbgui uses and comparisons need it — but it is a diagnostic, not the drift rate. The two converge only for a very elongated ellipse.

The fitted widths also give the burst extent, after dividing out the factor \( \sqrt{2} \) between a Gaussian and its autocorrelation: acf_sigma_time_ms and acf_sigma_freq_mhz.

Where the uncertainty comes from

The statistical term is a seeded Monte Carlo, not the fit covariance. Each trial adds an independent noise realisation at the measured per-channel off-pulse sigma, recomputes the autocorrelation and refits; the scaled median absolute deviation of the refitted drift rates is the 1σ statistical error.

This is deliberate. Neighbouring autocorrelation pixels are strongly correlated, so the covariance of a least-squares fit that treats them as independent understates the error, sometimes by a large factor. The covariance value is still recorded, as drift_rate_fit_covariance_mhz_per_ms, so the two can be compared — but it is a diagnostic.

The Monte Carlo assumes the estimator responds to an added noise realisation the way it responds to the noise already present, which holds while the burst dominates the autocorrelation peak. When it does not, the low_acf_contrast flag is raised.

The seed is stored in the session snapshot, so flits replay reproduces the error bar exactly rather than approximately.

Drift and DM are degenerate

This is the part that matters for anything you publish.

A dispersion-measure error tilts a burst in the time-frequency plane in exactly the way intrinsic drift does. Over a band narrow enough for the sweep to look linear, nothing in the dynamic spectrum distinguishes the two. A drifting burst therefore has no single "correct" DM: maximising structure and maximising S/N give different answers, and both are defensible.

FLITS does not resolve this. It states it, in four numbers:

Field	Meaning
`dm_pc_cm3`	The DM the measurement was made at. A drift rate without this is not interpretable.
`acf_slope_ms_per_mhz`	The time-on-frequency slope of the fitted ellipse. This is the quantity a DM error moves linearly.
`dm_equivalent_pc_cm3`	The DM offset that would, on its own, produce the whole measured slope. Adding it to the applied DM flattens the burst.
`dm_sensitivity_mhz_per_ms_per_pc_cm3`	How much the drift rate moves per pc cm⁻³ of DM error.

The one to read first is dm_equivalent_pc_cm3. If it is smaller than your DM uncertainty, the drift is not resolved — the burst is equally well described as undrifting at a slightly different DM. FLITS raises drift_consistent_with_dm_error and says so in the result message when that is the case. The component estimator reports its own component_dm_equivalent_pc_cm3 on the same footing.

Why the slope and not the drift rate

A dedispersion error of \( \delta \) adds \( g\,(\nu - \nu_\mathrm{ref}) \) to every arrival time, with

\[ g = \frac{\partial}{\partial \mathrm{DM}} \left(\frac{\mathrm{d}t}{\mathrm{d}\nu}\right)\delta = -\frac{2k}{\nu^{3}}\,\delta , \]

which is a shear of the burst covariance in the time-frequency plane. Under that shear \( \Sigma_{\nu\nu} \) is untouched and \( \Sigma_{t\nu} \) picks up \( g\,\Sigma_{\nu\nu} \), so the time-on-frequency regression slope

\[ \frac{\mathrm{d}t}{\mathrm{d}\nu} = \frac{\Sigma_{t\nu}}{\Sigma_{\nu\nu}} = \rho\,\frac{\sigma_t}{\sigma_\nu} \]

simply shifts by \( g \). The drift rate is the other regression, \( \Sigma_{t\nu} / \Sigma_{tt} = \rho\,\sigma_\nu/\sigma_t \), and the two are reciprocals only when \( \rho = 1 \): in general their product is \( \rho^{2} \). Treating \( 1/(\mathrm{d}\nu/\mathrm{d}t) \) as the DM-linear quantity is a mistake that gets both the size and, near \( \rho^2 = 1/2 \), the sign of the DM sensitivity wrong. FLITS therefore converts through the slope:

\[ \delta_\mathrm{equiv} = -\frac{\nu^{3}}{2k}\, \frac{\mathrm{d}t}{\mathrm{d}\nu}, \qquad \frac{\partial}{\partial \mathrm{DM}} \left(\frac{\mathrm{d}\nu}{\mathrm{d}t}\right) = -\frac{2k}{\nu^{3}} \left(\frac{\sigma_\nu}{\sigma_t}\right)^{2} \left(1 - 2\rho^{2}\right), \]

evaluated at the mean frequency of the unmasked selected channels.

When the drift rate is publishable

FLITS classifies this measurement the way it classifies every other one.

Without a DM uncertainty the drift rate is statistical_only and not publishable, and carries the missing_dm_uncertainty flag. The number is real; what is missing is the systematic that usually dominates it.
With a DM uncertainty the DM systematic is propagated through the sensitivity above and combined in quadrature with the statistical term. The result is formal_1sigma and publishable, unless one of the blocking flags is raised.

drift_rate_status reports significance against the bar FLITS would actually quote, not against the statistical term alone: ok when the drift rate exceeds its combined uncertainty, unconstrained when it does not, and unquantified when there is no uncertainty at all — which is what running with the Monte Carlo disabled and no DM uncertainty gives you.

The blocking flags are heavily_masked (a quarter or more of the selected channels are gone), low_acf_contrast, monte_carlo_unavailable, and implicit_offpulse (no explicit off-pulse window, so the noise reference is a guess).

Monte Carlo requests are bounded to 512 trials in the browser, API, and replay path so an imported snapshot cannot accidentally turn one measurement into an unbounded computation. Non-finite controls fall back to their recorded defaults, and random seeds are normalized to the non-negative range accepted by NumPy.

The DM uncertainty comes from the DM sweep when the sweep still describes the applied DM; retune the DM by hand and FLITS drops it rather than reusing a number that now describes something else. Supply one explicitly to override.

An operator-supplied value is stored in the drift settings and travels in the session snapshot, so flits replay reproduces the same classification and not just the same number. Clear the field to go back to the sweep's own value.

The component estimator

Each component window contributes an intensity-weighted spectral centroid and an intensity-weighted arrival time, with uncertainties propagated from the per-channel off-pulse noise. Centroid frequency is then regressed on arrival time with weights \( 1/(\sigma_\nu^2 + d^2\sigma_t^2) \), iterated so the effective variance uses the fitted slope.

With exactly two components the fit is exact: the status is exactly_two_components and no \( R^2 \) is reported, because there is no residual to explain. Overlapping components bias their centroids toward each other, which flattens the regression; the sign survives but the magnitude is a lower bound.

Practical sequence

Dedisperse and record how. The drift rate is meaningless without the DM it was measured at, and a structure-maximised DM and an S/N-maximised DM will give different drift rates for the same burst.
Mask interference and set the spectral window. The autocorrelation is mask-corrected, but a band that is mostly gone still gives a weak fit.
Set the event window to the burst and the off-pulse windows to genuinely burst-free data — the per-channel sigma from those windows is what sets the error bar.
Mark component regions if the burst has more than one, to get the second estimator.
Run the measurement, then read dm_equivalent_pc_cm3 before the drift rate.
Supply a DM uncertainty before quoting the number anywhere.

DM Optimization — where the DM and its uncertainty come from, and why the structure-maximising metric partly addresses the degeneracy.
Measurements — how FLITS classifies uncertainties in general.
Model Fitting — fitburst fits the scattering timescale, which is a different asymmetry from drift and is easy to confuse with it in a single component.