arXiv subjects

Joeri van Leeuwen

Publications and source records attributed to Joeri van Leeuwen.

At least 19 recordsLinked to original sources

arXiv2026

HI rotation curves and mass-size relation for 568 galaxies from the Apertif Wide-area Extragalactic Survey

The extended HI rotation curves of galaxies are one of the most powerful tools for studying galaxy evolution and for testing different dark matter and modified gravity models. However, their sample sizes have historically been limited to a few hundred galaxies, mostly due to the survey speed of radio interferometers. Here, we present a first data release of HI kinematic models from the Apertif Wide-area Extragalactic Survey (AWES). Starting from 1924 galaxies detected in HI, we constructed 568 reliable kinematic models, which provide rotation curves, velocity dispersion profiles, surface density profiles, and HI disk geometries. This dataset constitutes the largest homogeneous HI rotation curve sample to date. The HI disks of the modeled galaxies span three orders of magnitude in HI mass, have outer rotation velocities between ~20 and ~300 km/s, and extend from 2 to more than 60 kpc. The number of data points of the rotation curves ranges from 3 to 23, with a peak value at 4 and a broad tail to larger values. The rotation curves display a variety of inner shapes, but in general, they tend to become flat at large radii. Based on the HI surface density profiles derived during the kinematic modeling, we studied the HI mass-size relation with a large homogeneous sample of 213 galaxies. The relation is very tight, with an observed scatter along the mass direction of ~0.101 dex and an inferred intrinsic scatter along the same direction of only 0.067 +/- 0.007 dex. The best fitting slope is 1.96 +/- 0.03 when fitting for mass as a function of size, indicating that HI disks have a constant average surface density.

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arXiv2026

Connecting radio pulsars, magnetars, and XDINSs in a unified evolutionary framework using simulation-based inference

Understanding the Galactic population of isolated neutron stars within a unified framework provides key insights into their birth properties, evolutionary pathways, and the connections between different neutron star classes. In this work, we aim to reproduce both the observed radio and quiescent X-ray emission from isolated neutron stars, including radio pulsars, magnetars and X-ray dim isolated neutron stars (XDINSs). We develop a comprehensive population synthesis framework that models neutron star birth properties, their dynamical, rotational, and magneto-thermal evolution, as well as radio and X-ray emission, and the selection effects of corresponding surveys. To simulate realistic X-ray spectra, we account for magnetospheric resonant cyclotron scattering and interstellar absorption. Additionally, we model the observational bias introduced by magnetar outbursts, by linking the outburst rate to magnetic stresses in the stellar crust. We then employ a simulation-based inference method, namely truncated sequential neural posterior estimation, to reconstruct the birth properties, such as the initial magnetic field distribution. We find that the Galactic neutron star population can be described by a two-component log-normal distribution of birth magnetic fields with peaks at $5 \times 10^{12}$ G and $10^{14}$ G, respectively. We further find that the Galactic neutron star birth rate is around 3-4 per century. Our results help establish the contribution of neutron stars as central engines of powerful astrophysical transient phenomena, such as fast radio bursts, super-luminous supernovae and gamma ray bursts.

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arXiv2026

Indication for Decreasing Dispersion Measure in the Population of Repeating Fast Radio Bursts and Connection to Young Supernova Remnant Expansion

Fast Radio Bursts (FRBs) are millisecond-duration, highly energetic radio transients of uncertain origin. Repeating FRBs provide an excellent population for investigating their nature, particularly through studies of parameter evolution. Out of the 63 repeaters monitored by CHIME, we select the 19 sources with more than 10 detected bursts, and examine their long-term dispersion measure (DM) evolution. Seven sources show statistically significant DM evolution and are classified as the golden sample. Of these, five exhibit a decreasing DM trend and two show an increasing trend. We then perform a binomial test under the null hypothesis that decreasing and increasing DM variation trends have equal probabilities. The current combined sample, including our golden sample and additional repeaters with reported DM change rate from the literature, gives a p-value of 0.033, supporting that decreasing DM trends are more common in the repeating FRB population. This statistical result is consistent with scenarios in that the local electron density around repeaters generally decreases with time, for example, due to expansion of a young supernova remnant (SNR). Finally, within the SNR expansion model, we provide an illustrative estimate of the SNR contributions to the DM for different ejecta masses.

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arXiv2026

Identification of a Radio Counterpart to SN 2025ulz in the S250818k Localization Area

On 2025 August 18, the LIGO-Virgo-KAGRA collaboration reported S250818k, a sub-threshold gravitational-wave (GW) candidate consistent with a binary neutron star (NS) merger potentially involving a sub-solar-mass NS. Optical follow-up by the Zwicky Transient Facility identified AT2025ulz, a transient temporally coincident with the GW trigger that initially resembled a kilonova but was later classified as a young stripped-envelope Type IIb supernova (SN), dubbed SN 2025ulz. A key question is whether SN 2025ulz harbors fast, possibly collimated, non-thermal ejecta indicative of a central engine, as invoked in "superkilonova" scenarios linking sub-solar-mass NSs to accretion-disk fragmentation or core fission. We present early-to-late-time multi-band radio observations of SN 2025ulz obtained with the Karl G. Jansky Very Large Array as part of the JAGWAR program, complemented by observations with the upgraded Giant Metrewave Radio Telescope and MeerKAT. We detect a faint but significant radio counterpart to SN 2025ulz at 6-10 GHz. The data are consistent with non-thermal emission from SN ejecta interacting with circumstellar material, favoring a compact progenitor and relatively fast ejecta akin to those of Type cIIb SNe. Our data are also consistent with emission from an off-axis jet peaking at about 50-100 days after the GW trigger. Overall, our radio detection is compatible with a superkilonova scenario and would motivate future systematic multi-wavelength follow-up of core-collapse events coincident with sub-solar NS GW candidates, should the association between S250818k and SN 2025ulz be supported by offline GW analyses.

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arXiv2025

A deep search for radio pulsations from the 1.3 M$_{\odot}$ compact-object binary companion of young pulsar PSR J1906+0746

Double pulsar systems offer unrivaled advantages for the study of both astrophysics and fundamental physics. But only one has been visible: PSR J0737$-$3039; and its component pulsar B has now rotated out of sight due to the general-relativistic effect of geodetic precession. We know, though, that these precession cycles can also pivot pulsars into sight, and that this precession occurs at similar strength in PSR J1906+0746. That source is a young, unrecycled radio pulsar, orbiting a compact object with mass $\sim $1.32 M$_{\odot}$. This work presents a renewed campaign to detect radio pulsations from this companion, two decades after the previous search. Two key reasons driving this reattempt are the possibility that the companion radio beam has since precessed into our line of sight, and the improved sensitivity now offered by the FAST radio telescope. In 28 deep observations, we did not detect a credible companion pulsar signal. After comparing the possible scenarios, we conclude the companion is still most likely a pulsar that is not pointing at us. We next present estimates for the sky covered by such systems throughout their precession cycle. We find that for most system geometries, the all-time beaming fraction is unity, i.e., observers in any direction can see the system at some point. We conclude it is still likely that PSR J1906+0746 will be visible as a double pulsar in the future.

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arXiv2024

Comprehensive analysis of the Apertif Fast Radio Burst sample: similarities with young, energetic neutron stars

Understanding the origin of fast radio bursts (FRBs) has become the main science driver of recent dedicated FRB surveys. Between July 2019 and February 2022, we carried out ALERT, an FRB survey at 1370 MHz using the Apertif instrument installed at the Westerbork Synthesis Radio Telescope (WSRT). Here we report the detection of 18 new FRBs, and we study the properties of the entire 24 burst sample detected during the survey. For five bursts, we identify host galaxy candidates with >50% probability association. We observe an average linear polarisation fraction of $\sim$43% and an average circular polarisation fraction consistent with 0%. A third of the FRBs display multiple components. The sample next reveals a population of highly scattered bursts, which is most likely to have been produced in the immediate circumburst environment. Furthermore, two FRBs show evidence for high rotation measures, reaching |RM|>$10^3$ rad m$^{-2}$ in the source reference frames. Together, the scattering and rotation measures ALERT finds prove that a large fraction of FRBs are embedded in complex media such as star forming regions or supernova remnants. Through the discovery of the third most dispersed FRB so far, we show that one-off FRBs can emit at frequencies in excess of 6 GHz. Finally, we determine an FRB all-sky rate of $459^{+208}_{-155}$ sky$^{-1}$ day$^{-1}$ above a fluence limit of 4.1 Jy ms, and a fluence cumulative distribution with a power law index $γ=-1.23\pm0.06\pm0.2$, which is roughly consistent with the Euclidean Universe predictions. Through the high resolution in time, frequency, polarisation and localisation that ALERT featured, we were able to determine the morphological complexity, polarisation, local scattering and magnetic environment, and high-frequency luminosity of FRBs. We find all these strongly resemble those seen in young, energetic, highly magnetised neutron stars.

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arXiv2024

Birth and Evolution of Fast Radio Bursts: Strong Population-Based Evidence for a Neutron-Star Origin

While the appeal of their extraordinary radio luminosity to our curiosity is undiminished, the nature of fast radio bursts (FRBs) has remained unclear. The challenge has been due in part to small sample sizes and limited understanding of telescope selection effects. We here present the first inclusion of the entire set of one-off FRBs from CHIME/FRB Catalog 1 in frbpoppy. Where previous work had to curate this data set, and fit for few model parameters, we have developed full multi-dimensional Markov chain Monte Carlo (MCMC) capabilities for frbpoppy -- the comprehensive, open-science FRB population synthesis code -- that allow us to include all one-off CHIME bursts. Through the combination of these two advances we now find the best description of the real, underlying FRB population, with higher confidence than before. We show that $4\pm3\times10^{3}$ one-off FRBs go off every second between Earth and $z$=1; and we provide a mock catalog based on our best model, for straight-forward inclusion in other studies. We investigate CHIME side-lobe detection fractions, and FRB luminosity characteristics, to show that some bright, local FRBs are still being missed. We find strong evidence that FRB birth rates evolve with the star formation rate of the Universe, even with a hint of a short (0.1$-$1 Gyr) delay time. The preferred contribution of the hosts to the FRB dispersion agrees with a progenitor birth location in the host disk. This population-based evidence solidly aligns with magnetar-like burst sources, and we conclude FRBs are emitted by neutron stars.

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arXiv2024

Polar cap region and plasma drift in pulsars

Pulsars often display systematic variations in the position and/or intensity of the subpulses, the components that comprise each single pulse. Although the drift of these subpulses was observed in the early years of pulsar research, and their potential for understanding the elusive emission mechanism was quickly recognised, there is still no consensus on the cause of the drift. We explore the electrodynamics of two recently proposed or refined drift models: one where plasma lags behind corotation, connecting the drift with the rotational pole; and another where plasma drifts around the electric potential extremum of the polar cap. Generally, these are different locations, resulting in different drift behaviours, that can be tested with observations. In this study, however, we specifically examine these models in the axisymmetric case, where the physics is well understood. This approach seems counter-intuitive as both models then predict similar large-scale plasma drift. However, it allows us to show, by studying conditions \emph{within} the sparks for both models, that the lagging behind corotation (LBC) model is inconsistent with Faraday's law. The modified carousel (MC) model, where plasma drifts around the electric potential extremum, not only aligns with Faraday's law, but also provides a future direction for developing a comprehensive model of plasma generation in the polar cap region. Unlike previous models, which considered the drift only inside the discharging regions, the MC model reveals that the electric field \emph{between} the discharges is not completely screened, and plasma drifts there -- a paradigm shift for the drifting subpulse phenomenon.

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arXiv2024

Transformer models for astrophysical time series and the GRB prompt-afterglow relation

Transformer models have recently become very successful in the natural language domain. Their value as sequence-to-sequence translators there, also makes them a highly interesting technique for learning relationships between astrophysical time series. Our aim is investigate how well such a transformer neural network can establish causal temporal relations between different channels of a single-source signal. We thus apply a transformer model to the two phases of Gamma-Ray Bursts (GRBs), reconstructing one phase from the other. GRBs are unique instances where a single process and event produces two distinct time variable phenomena: the prompt emission and the afterglow. We here investigate if a transformer model can predict the afterglow flux from the prompt emission. If successful, such a predictive scheme might then be distilled to the most important underlying physics drivers in the future. We combine the transformer model with a novel dense neural network setup to directly estimate the starting value of the prediction. We find that the transformer model can, in some instances, successfully predict different phases of canonical afterglows, including the plateau phase. Hence it is a useful and promising new astrophysical analysis technique. For the GRB test case, the method marginally exceeds the baseline model overall, but still achieves accurate recovery of the prompt-afterglow fluence-fluence correlation in reconstructed light curves. Despite this progress, we conclude that consistent improvement over the baseline model is not yet achieved for the GRB case. We discuss the future improvements in data and modeling that are required to identify new physical-relation parameters or new insights into the single process driving both GRB phases.

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arXiv2024

A Needle in a Cosmic Haystack: A Review of FRB Search Techniques

Ephemeral Fast Radio Bursts (FRBs) must be powered by some of the most energetic processes in the Universe. That makes them highly interesting in their own right and as precise probes for estimating cosmological parameters. This field thus poses a unique challenge: FRBs must be detected promptly and immediately localised and studied based only on that single millisecond-duration flash. The problem is that the burst occurrence is highly unpredictable and that their distance strongly suppresses their brightness. Since the discovery of FRBs in single-dish archival data in 2007, detection software has evolved tremendously. Pipelines now detect bursts in real-time within a matter of seconds, operate on interferometers, buffer high-time and frequency resolution data, and issue real-time alerts to other observatories for rapid multi-wavelength follow-up. In this paper, we review the components that comprise a FRB search software pipeline, we discuss the proven techniques that were adopted from pulsar searches, we highlight newer, more efficient techniques for detecting FRBs, and we conclude by discussing the proposed novel future methodologies that may power the search for FRBs in the era of big data astronomy.

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arXiv2023

DeepGlow: an efficient neural-network emulator of physical afterglow models for gamma-ray bursts and gravitational-wave events

Gamma-ray bursts (GRBs) and double neutron-star merger gravitational wave events are followed by afterglows that shine from X-rays to radio, and these broadband transients are generally interpreted using analytical models. Such models are relatively fast to execute, and thus easily allow estimates of the energy and geometry parameters of the blast wave, through many trial-and-error model calculations. One problem, however, is that such analytical models do not capture the underlying physical processes as well as more realistic relativistic numerical hydrodynamic (RHD) simulations do. Ideally, those simulations are used for parameter estimation instead, but their computational cost makes this intractable. To this end, we present DeepGlow, a highly efficient neural network architecture trained to emulate a computationally costly RHD-based model of GRB afterglows, to within a few percent accuracy. As a first scientific application, we compare both the emulator and a different analytical model calibrated to RHD simulations, to estimate the parameters of a broadband GRB afterglow. We find consistent results between these two models, and also give further evidence for a stellar wind progenitor environment around this GRB source. DeepGlow fuses simulations that are otherwise too complex to execute over all parameters, to real broadband data of current and future GRB afterglows.

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arXiv2023

The Green Bank North Celestial Cap Survey. VIII. 21 New Pulsar Timing Solutions

We present timing solutions for 21 pulsars discovered in 350 MHz surveys using the Green Bank Telescope (GBT). All were discovered in the Green Bank North Celestial Cap pulsar survey, with the exception of PSR J0957-0619, which was found in the GBT 350 MHz Drift-scan pulsar survey. The majority of our timing observations were made with the GBT at 820 MHz. With a spin period of 37 ms and a 528-day orbit, PSR J0032+6946 joins a small group of five other mildly recycled wide binary pulsars, for which the duration of recycling through accretion is limited by the length of the companion's giant phase. PSRs J0141+6303 and J1327+3423 are new disrupted recycled pulsars. We incorporate Arecibo observations from the NANOGrav pulsar timing array into our analysis of the latter. We also observed PSR J1327+3423 with the Long Wavelength Array, and our data suggest a frequency-dependent dispersion measure. PSR J0957-0619 was discovered as a rotating radio transient, but is a nulling pulsar at 820 MHz. PSR J1239+3239 is a new millisecond pulsar (MSP) in a 4-day orbit with a low-mass companion. Four of our pulsars already have published timing solutions, which we update in this work: the recycled wide binary PSR J0214+5222, the non-eclipsing black widow PSR J0636+5128, the disrupted recycled pulsar J1434+7257, and the eclipsing binary MSP J1816+4510, which is in an 8.7 hr orbit with a redback-mass companion.

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arXiv2023

The Apertif Radio Transient System (ARTS): Design, Commissioning, Data Release, and Detection of the first 5 Fast Radio Bursts

Fast Radio Bursts must be powered by uniquely energetic emission mechanisms. This requirement has eliminated a number of possible source types, but several remain. Identifying the physical nature of Fast Radio Burst (FRB) emitters arguably requires good localisation of more detections, and broadband studies enabled by real-time alerting. We here present the Apertif Radio Transient System (ARTS), a supercomputing radio-telescope instrument that performs real-time FRB detection and localisation on the Westerbork Synthesis Radio Telescope (WSRT) interferometer. It reaches coherent-addition sensitivity over the entire field of the view of the primary dish beam. After commissioning results verified the system performed as planned, we initiated the Apertif FRB survey (ALERT). Over the first 5 weeks we observed at design sensitivity in 2019, we detected 5 new FRBs, and interferometrically localised each of these to 0.4--10 sq. arcmin. All detections are broad band and very narrow, of order 1 ms duration, and unscattered. Dispersion measures are generally high. Only through the very high time and frequency resolution of ARTS are these hard-to-find FRBs detected, producing an unbiased view of the intrinsic population properties. Most localisation regions are small enough to rule out the presence of associated persistent radio sources. Three FRBs cut through the halos of M31 and M33. We demonstrate that Apertif can localise one-off FRBs with an accuracy that maps magneto-ionic material along well-defined lines of sight. The rate of 1 every ~7 days next ensures a considerable number of new sources are detected for such study. The combination of detection rate and localisation accuracy exemplified by the 5 first ARTS FRBs thus marks a new phase in which a growing number of bursts can be used to probe our Universe.

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arXiv2023

New upper limits on low-frequency radio emission from isolated neutron stars with LOFAR

Neutron stars that show X-ray and $γ$-ray pulsed emission must, somewhere in the magnetosphere, generate electron-positron pairs. Such pairs are also required for radio emission, but then why do a number of these sources appear radio quiet? Here, we carried out a deep radio search towards four such neutron stars that are isolated X-ray/$γ$-ray pulsars but for which no radio pulsations have been detected yet. These sources are 1RXS J141256.0+792204 (Calvera), PSR J1958+2846, PSR J1932+1916 and SGR J1907+0919. Searching at lower radio frequencies, where the radio beam is thought to be wider, increases the chances of detecting these sources, compared to the earlier higher-frequency searches. We thus carried a search for periodic and single-pulse radio emission with the LOFAR radio telescope at 150 MHz. We used the known periods, and searched a wide range of dispersion measures, as the distances are not well constrained. We did not detect pulsed emission from any of the four sources. However, we put very constraining upper limits on the radio flux density at 150 MHz, of $\lesssim$1.4 mJy.

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arXiv2022

The Green Bank North Celestial Cap Survey. VII. 12 New Pulsar Timing Solutions

We present timing solutions for 12 pulsars discovered in the Green Bank North Celestial Cap (GBNCC) 350 MHz pulsar survey, including six millisecond pulsars (MSPs), a double neutron star (DNS) system, and a pulsar orbiting a massive white dwarf companion. Timing solutions presented here include 350 and 820 MHz Green Bank Telescope data from initial confirmation and follow-up as well as a dedicated timing campaign spanning one year. PSR J1122$-$3546 is an isolated MSP, PSRs J1221$-$0633 and J1317$-$0157 are MSPs in black widow systems and regularly exhibit eclipses, and PSRs J2022+2534 and J2039$-$3616 are MSPs that can be timed with high precision and have been included in pulsar timing array experiments seeking to detect low-frequency gravitational waves. PSRs J1221$-$0633 and J2039$-$3616 have Fermi Large Area Telescope $γ$-ray counterparts and also exhibit significant $γ$-ray pulsations. We measure proper motion for three of the MSPs in this sample and estimate their space velocities, which are typical compared to those of other MSPs. We have detected the advance of periastron for PSR J1018$-$1523 and therefore measure the total mass of the double neutron star system, $m_{\rm tot}=2.3\pm0.3$ M$_{\odot}$. Long-term pulsar timing with data spanning more than one year is critical for classifying recycled pulsars, carrying out detailed astrometry studies, and shedding light on the wealth of information in these systems post-discovery.

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arXiv2022

Investigating the detection rates and inference of gravitational-wave and radio emission from black hole neutron star mergers

Black hole neutron star (BHNS) mergers have recently been detected through their gravitational-wave (GW) emission. BHNS mergers could also produce electromagnetic (EM) emission as a short gamma-ray burst (sGRB), and/or an sGRB afterglow upon interaction with the circummerger medium. Here, we make predictions for the expected detection rates with the Square Kilometre Array Phase 1 (SKA1) of sGRB radio afterglows associated with BHNS mergers. We also investigate the benefits of a multimessenger analysis in inferring the properties of the merging binary. We simulate a population of BHNS mergers and estimate their sGRB afterglow flux to obtain the detection rates with SKA1. We investigate how this rate depends on the GW detector sensitivity, the primary black hole (BH) spin, and the neutron star equation of state. We then perform a multimessenger Bayesian inference study on a fiducial BHNS merger. We simulate its sGRB afterglow and GW emission and take systematic errors into account. The expected rates of a combined GW and radio detection with the current generation GW detectors are likely low. Due to the much increased sensitivity of future GW detectors like the Einstein Telescope, the chances of an sGRB localisation and radio detection increase substantially. The unknown distribution of the BH spin has a big influence on the detection rates, however, and it is a large source of uncertainty. Furthermore, for our fiducial BHNS merger we are able to infer both the binary source parameters as well as the parameters of the sGRB afterglow simultaneously when combining the GW and radio data. The radio data provides useful extra information on the binary parameters such as the mass ratio but this is limited by the systematic errors involved. A better understanding of the systematics will further increase the amount of information on the binary parameters that can be extracted from this radio data.

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arXiv2022

Seeing the forest and the trees: a radio investigation of the ULIRG Mrk 273

Galaxy mergers have been observed to trigger nuclear activity by feeding gas to the central supermassive black hole. One such class of objects are Ultra Luminous InfraRed Galaxies (ULIRGs), which are mostly late stage major mergers of gas-rich galaxies. Recently, large-scale ($\sim$100 kpc) radio continuum emission has been detected in a select number of ULIRGs, all of which also harbour powerful Active Galactic Nuclei (AGN). This hints at the presence of large-scale radio emission being evidence for nuclear activity. Exploring the origin of this radio emission and its link to nuclear activity requires high sensitivity multi-frequency data. We present such an analysis of the ULIRG Mrk 273. Using the International LOFAR telescope (ILT), we detected spectacular large-scale arcs in this system. This detection includes, for the first time, a giant $\sim$190 kpc arc in the north. We propose these arcs are fuelled by a low power radio AGN triggered by the merger. We also identified a bright $\sim$45 kpc radio ridge, which is likely related to the ionised gas nebula in that region. We combined this with high sensitivity data from APERture Tile In Focus (Apertif) and archival data from the Very Large Array (VLA) to explore the spectral properties. The ILT simultaneously allowed us to probe the nucleus at a resolution of $\sim$0.3 arcsec, where we detected three components, and, for the first time, diffuse emission around these components. Combining this with archival high frequency VLA images of the nucleus allowed us to detect absorption in one component, and a steep spectrum radio AGN in another. We then extrapolate from this case study to the importance of investigating the presence of radio emission in more ULIRGs and what it can tell us about the link between mergers and the presence of radio activity.

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arXiv2022

MeerKAT observations of the reversing drifting subpulses in PSR J1750-3503

We present an analysis of the subpulse drift in PSR J1750-3503, which is characterized by abrupt transitions of drift direction. As the pulsar does not exhibit other mode changes or clear nulling, it is an ideal candidate system for studying the phenomenon of drift direction change. For $\sim 80\%$ of the time the subpulses are characterized by positive drift - from early to later longitudes - while the drift direction is negative in the other $\sim 20\%$. The subpulse separation for single pulses with positive drift, $P_2=(18.8\pm 0.1)^{\circ}$, is higher then for single pulses with negative drift, $P_2=(17.5\pm 0.2)^{\circ}$. When the drift is stable, the measured repetition time of the drift pattern is $P_3^{\rm obs}=(43.5 \pm 0.4) P$, where $P$ is pulsar period. We show that the observed data can be reproduced by a carousel models with subpulse rotation around the magnetic axis using purely dipolar configuration of surface magnetic field. The observed drift characteristics can be modeled assuming that the actual repetition time $P_3<2P$, such that we observe its aliased value. A small variation in $P_3$, of the order of $6\%$ (or less assuming higher alias orders), is enough to reproduce the characteristic drift direction changes we observe.

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