arXiv subjects

Michael Janssen

Publications and source records attributed to Michael Janssen.

At least 19 recordsLinked to original sources

arXiv2026

Dynamics and geometry of the inner sub-parsec-scale jet in 3C 279 observed with the Event Horizon Telescope

The 2021 Event Horizon Telescope observations resolve the innermost jet region of the blazar 3C279 with unprecedented detail. The reconstructed images consistently reveal a compact core elongated nearly orthogonal to the large-scale jet axis. This rarely observed morphology recurs across multiple epochs and from 22-230 GHz and is therefore intrinsic rather than an imaging artifact. Geometric model fitting identifies several components with apparent speeds up to 10c, requiring bulk Lorentz factors greater than 10.3 and constraining viewing angles to extremely small values (smaller than one degree). Rest-frame brightness temperatures are systematically low (between 10^9 and 10^10 K), consistent with optically thin emission at 230 GHz. These results suggest that the jet bends toward the observer on sub-parsec scales, producing strong relativistic beaming. Possible drivers of the observed jet bending and temporal evolution include the jet's interaction with the interstellar medium, kink or Kelvin--Helmholtz instabilities, magnetic reconnection near the horizon, or binary-induced precession. However, the current temporal coverage of VLBI data remains insufficient to distinguish between these mechanisms. Continued multifrequency VLBI monitoring will be essential to constraining the dynamics and geometry of the jet base in 3C279.

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arXiv2026

Constraining the jet base emission of M87* with past and future Event Horizon Telescope observations

We investigate the detectability of the jet base of M87* at Event Horizon Telescope (EHT) observing frequencies. Although M87 is known to host a prominent relativistic jet, detecting jet emission close to the black hole at horizon scales remains challenging. Our goal is to determine the minimum jet intensity that can be reliably detected with the recent EHT array configurations. We use synthetic EHT data generated for three array configurations corresponding to the 2021 and 2022 observing campaigns and to a near future EHT campaign. As input models, we employ semi analytic accretion jet models in which the jet emission can be tuned independently of the accretion flow. The synthetic data are reconstructed with regularized maximum likelihood and Bayesian imaging. Jet detectability is assessed through flux density recovery, image fidelity, and uncertainty maps. We find that jet detectability strongly depends on the jet intensity, the array configuration, and imaging methodology. Using our analysis, we determine a lower limit on the jet intensity that can be reliably recovered. The 2022 EHT array configuration represents a significant improvement over earlier arrays, enabling a more robust reconstruction of faint jet features. Our results indicate that the current EHT array is already sensitive to weak jet emission at horizon scales in M87*. The improved short-baseline coverage introduced in 2022 makes faint inner jet features more easily detectable. If the inner jet contributes a significant fraction of the unresolved compact flux, it should become visible in post-2021 observations. On the other hand, if no clear jet signature is found, this would suggest that the horizon-scale jet contributes only a small part of the compact emission. The continued expansion of the EHT will further improve the detection of such jet emission in M87*.

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arXiv2026

Probing anisotropic particle acceleration and limb-brightening in Centaurus A's jet

Relativistic jets are among the most fascinating objects in the Universe, and recent high-resolution Very Long Baseline Interferometric (VLBI) observations, including the Global mm-VLBI Array and the Event Horizon Telescope (EHT), are able to resolve their structure close to their launching site. These observations reveal strongly limb-brightened jet structures for Centaurus A (Cen A), M 87 and 3C 84. Thus, the question arises which physical mechanism can generate the limb-brightened structure, and if this structure is common for jets from low-luminosity active galactic nuclei (LLAGN) seen under large viewing angles. Therefore, as a pilot study, we aim to model the EHT observations of Cen A. We performed a 3D two-temperature general-relativistic magnetohydrodynamic (GRMHD) simulation of an accreting supermassive black hole (SMBH) and jet launching to study the plasma dynamics and computed the connected emission via general relativistic radiative transfer (GRRT) calculations considering possible anisotropies in the distribution of the radiating particles. In order to adjust our simulations to the EHT observations of Cen A, we carried out a Bayesian fitting in the Fourier plane. We find that GRMHD simulations of magnetically arrested disks (MADs) combined with anisotropically emitting particle distributions along the direction of the magnetic field, parametrized by a value $\eta=0.07$, are able to mimic the recent EHT observations of Cen A. In addition, we extracted a black hole mass of $M_\mathrm{BH} = 6\times10^7 M_\odot$ and a viewing angle of $\vartheta=72\deg$. Our obtained model can reproduce key features of the EHT and Atacama Large Millimeter/submillimeter Array (ALMA) observations in total and polarized emission. Finally, we predict that the black hole shadow in Cen A will be observable at a frequency of $\sim$ 3 THz.

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arXiv2026

Locating the missing large-scale emission in the jet of M87* with short EHT baselines

In Very-Long Baseline Interferometric arrays, nearly co-located stations probe the largest scales and typically cannot resolve the observed source. In the absence of large-scale structure, closure phases constructed with these stations are zero and, since they are independent of station-based errors, they can be used to probe data issues. Here, we show with an expansion about co-located stations, how these trivial closure phases become non-zero with brightness distribution on smaller scales than their short baseline would suggest. When applied to sources that are made up of a bright compact and large-scale diffuse component, the trivial closure phases directly measure the centroid relative to the compact source and higher-order image moments. We present a technique to measure these image moments with minimal model assumptions and validate it on synthetic Event Horizon Telescope (EHT) data. We then apply this technique to 2017 and 2018 EHT observations of M87* and find a weak preference for extended emission in the direction of the large-scale jet. We also apply it to 2021 EHT data and measure the source centroid about 1 mas northwest of the compact ring, consistent with the jet observed at lower frequencies.

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arXiv2026

Ring Asymmetry and Spin in M87*

Event Horizon Telescope (EHT) images of the supermassive black hole M87* depict an asymmetric ring of emission. General relativistic magnetohydrodynamic (GRMHD) models of M87* and its accretion disk predict that the amplitude and location of the ring's peak brightness asymmetry should fluctuate due to turbulence in the source plasma. We compare the observed distribution of brightness asymmetry amplitudes to the simulated distribution in GRMHD models, across varying black hole spin $a_{*}$. We show that, for strongly magnetized (MAD) models, three epochs of EHT data marginally disfavor $|a_{*}| \lesssim 0.2$. This is consistent with the Blandford-Znajek model for M87's jet, which predicts that M87* should have nonzero spin. We show quantitatively how future observations could improve spin constraints, and discuss how improved spin constraints could distinguish between differing jet-launching mechanisms and black hole growth scenarios.

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arXiv2025

Probing jet base emission of M87* with the 2021 Event Horizon Telescope observations

We investigate the presence and spatial characteristics of the jet base emission in M87* at 230 GHz, enabled by the enhanced uv coverage in the 2021 Event Horizon Telescope (EHT) observations. The addition of the 12-m Kitt Peak Telescope and NOEMA provides two key intermediate-length baselines to SMT and the IRAM 30-m, giving sensitivity to emission structures at scales of $\sim250~\mu$as and $\sim2500~\mu$as (0.02 pc and 0.2 pc). Without these baselines, earlier EHT observations lacked the capability to constrain emission on large scales, where a "missing flux" of order $\sim1$ Jy is expected. To probe these scales, we analyzed closure phases, robust against station-based gain errors, and modeled the jet base emission using a simple Gaussian offset from the compact ring emission at separations $>100~\mu$as. Our analysis reveals a Gaussian feature centered at ($\Delta$RA $\approx320~\mu$as, $\Delta$Dec $\approx60~\mu$as), a projected separation of $\approx5500$ AU, with a flux density of only $\sim60$ mJy, implying that most of the missing flux in previous studies must arise from larger scales. Brighter emission at these scales is ruled out, and the data do not favor more complex models. This component aligns with the inferred direction of the large-scale jet and is consistent with emission from the jet base. While our findings indicate detectable jet base emission at 230 GHz, coverage from only two intermediate baselines limits reconstruction of its morphology. We therefore treat the recovered Gaussian as an upper limit on the jet base flux density. Future EHT observations with expanded intermediate-baseline coverage will be essential to constrain the structure and nature of this component.

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arXiv2025

Bayesian polarization calibration and imaging in very long baseline interferometry

Extracting polarimetric information from very long baseline interferometry (VLBI) data is demanding but vital for understanding the synchrotron radiation process and the magnetic fields of celestial objects, such as active galactic nuclei (AGNs). However, conventional CLEAN-based calibration and imaging methods provide suboptimal resolution without uncertainty estimation of calibration solutions, while requiring manual steering from an experienced user. We present a Bayesian polarization calibration and imaging method using Bayesian imaging software resolve for VLBI data sets, that explores the posterior distribution of antenna-based gains, polarization leakages, and polarimetric images jointly from pre-calibrated data. We demonstrate our calibration and imaging method with observations of the quasar 3C273 with the VLBA at 15 GHz and the blazar OJ287 with the GMVA+ALMA at 86 GHz. Compared to the CLEAN method, our approach provides physically realistic images that satisfy positivity of flux and polarization constraints and can reconstruct complex source structures composed of various spatial scales. Our method systematically accounts for calibration uncertainties in the final images and provides uncertainties of Stokes images and calibration solutions. The automated Bayesian approach for calibration and imaging will be able to obtain high-fidelity polarimetric images using high-quality data from next-generation radio arrays. The pipeline developed for this work is publicly available.

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arXiv2025

VIPCALs: A fully automated calibration pipeline for very long baseline interferometry data

Very long baseline interferometry (VLBI) is a powerful technique that can achieve sub-milliarcsecond resolution. However, it requires complex and often manual post-correlation calibration to correct for instrumental, geometric, and propagation-related errors. Unlike connected-element interferometers, VLBI arrays typically provide raw visibilities rather than science-ready data, and existing pipelines are largely semi-automated and reliant on user supervision. We present VIPCALs, a fully automated, end-to-end calibration pipeline for continuum VLBI data that operates without human intervention or prior knowledge of the dataset. Designed for scalability to thousands of sources and heterogeneous archival observations, VIPCALs addresses the needs of initiatives such as the Search for Milli-Lenses (SMILE) project. Implemented in Python using ParselTongue, VIPCALs reproduces the standard AIPS calibration workflow in a fully unsupervised mode. Besides the usual calibration tasks, the pipeline also performs automatic reference antenna selection, calibrator identification, and generates diagnostic outputs for inspection. We validated it on a representative sample of Very Long Baseline Array (VLBA) data corresponding to 1000 sources from the SMILE project. VIPCALs successfully calibrated observations of 955 of the test sources across multiple frequency bands. Over 91% of the calibrated datasets achieved successful fringe fitting on target in at least half of the solutions attempted. The median ratio of calibrated visibilities to initial total visibilities was 0.87. The average processing time was below 10 minutes per dataset, demonstrating both efficiency and scalability. VIPCALs enables robust, reproducible, and fully automated calibration of VLBI continuum data, significantly lowering the entry barrier for VLBI science and making large-scale projects like SMILE feasible.

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arXiv2025

The putative center in NGC 1052

Many active galaxies harbor powerful relativistic jets, however, the detailed mechanisms of their formation and acceleration remain poorly understood. To investigate the area of jet acceleration and collimation with the highest available angular resolution, we study the innermost region of the bipolar jet in the nearby low-ionization nuclear emission-line region (LINER) galaxy NGC 1052. We combined observations of NGC 1052 taken with VLBA, GMVA, and EHT over one week in the spring of 2017. For the first time, NGC 1052 was detected with the EHT, providing a size of the central region in-between both jet bases of 250 RS (Schwarzschild radii) perpendicular to the jet axes. This size estimate supports previous studies of the jets expansion profile which suggest two breaks of the profile at around 300 RS and 10000 RS distances to the core. Furthermore, we estimated the magnetic field to be 1.25 Gauss at a distance of 22 {\mu}as from the central engine by fitting a synchrotron-self absorption spectrum to the innermost emission feature, which shows a spectral turn-over at about 130 GHz. Assuming a purely poloidal magnetic field, this implies an upper limit on the magnetic field strength at the event horizon of 26000 Gauss, which is consistent with previous measurements. The complex, low-brightness, double-sided jet structure in NGC 1052 makes it a challenge to detect the source at millimeter (mm) wavelengths. However, our first EHT observations have demonstrated that detection is possible up to at least 230 GHz. This study offers a glimpse through the dense surrounding torus and into the innermost central region, where the jets are formed. This has enabled us to finally resolve this region and provide improved constraints on its expansion and magnetic field strength.

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arXiv2025

A multi-frequency study of sub-parsec jets with the Event Horizon Telescope

The 2017 observing campaign of the Event Horizon Telescope (EHT) delivered the first very long baseline interferometry (VLBI) images at the observing frequency of 230 GHz, leading to a number of unique studies on black holes and relativistic jets from active galactic nuclei (AGN). In total, eighteen sources were observed: the main science targets, Sgr A* and M87 along with various calibrators. We investigated the morphology of the sixteen AGN in the EHT 2017 data set, focusing on the properties of the VLBI cores: size, flux density, and brightness temperature. We studied their dependence on the observing frequency in order to compare it with the Blandford-K\"onigl (BK) jet model. We modeled the source structure of seven AGN in the EHT 2017 data set using linearly polarized circular Gaussian components and collected results for the other nine AGN from dedicated EHT publications, complemented by lower frequency data in the 2-86 GHz range. Then, we studied the dependences of the VLBI core flux density, size, and brightness temperature on the frequency measured in the AGN host frame. We compared the observations with the BK jet model and estimated the magnetic field strength dependence on the distance from the central black hole. Our results indicate a deviation from the standard BK model, particularly in the decrease of the brightness temperature with the observing frequency. Either bulk acceleration of the jet material, energy transfer from the magnetic field to the particles, or both are required to explain the observations.

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arXiv2024

Demographics of black holes at $<$100 R$_{\rm g}$ scales: accretion flows, jets, and shadows

Using the Event Horizon Telescope (EHT), the gravitationally lensed rings around the supermassive black holes (SMBHs) in Messier 87 (M87) and Sagittarius A* (Sgr A*) have now been successfully imaged at a resolution under 10 gravitational radii (R$_{\rm g}$ $ = \rm{GM/c^2}$). To expand studies beyond M87 and Sgr A*, we have constructed the Event Horizon and Environs (ETHER) sample, a comprehensive database encompassing approximately 3.15 million SMBH mass estimates, $\sim$ 20,000 Very-Long Baseline Interferometry (VLBI) radio flux densities, and $\sim$ 36,000 hard X-ray flux densities. This database is designed to identify and optimize target selection for the EHT and its upgrades on the ground and in space. We have identified a Gold Sample (GS) of nearby low-luminosity Active Galactic Nuclei (AGNs) within it that are ideal for studying jet bases and potentially imaging black hole shadows. We observed 27 of these AGNs using the EHT from 2022 to 2024, providing an opportunity to resolve and image accretion flows and jets at resolutions of $\leq$ 100 R$_{\rm g}$. Only a few SMBHs have sufficiently high enough flux density to be imaged at scales of $\leq$ 50 R$_{\rm g}$ with the present EHT. Among these are M87, Sgr A*, NGC4594 (Sombrero/M104), NGC4261, and NGC4374 (Messier 84/M84). Of these, NGC4261, Sombrero, and M84 have been observed and/or are scheduled for deep imaging with EHT+ALMA from 2023 to 2025. Sombrero, NGC4261, M84, NGC4278, and NGC5232 are clearly detected in our EHT+ALMA observations in 2022, indicating that the 230 GHz flux density from the accretion flows is significantly high. Ongoing imaging of the ETHER GS will enable measurements of black hole mass and spin, help constrain General Relativity, and enrich our understanding of jet launching and accretion inflows across a broad multi-parameter space, including black hole mass, spin, accretion rate, and orientation.

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arXiv2024

First Very Long Baseline Interferometry Detections at 870{\mu}m

The first very long baseline interferometry (VLBI) detections at 870$\mu$m wavelength (345$\,$GHz frequency) are reported, achieving the highest diffraction-limited angular resolution yet obtained from the surface of the Earth, and the highest-frequency example of the VLBI technique to date. These include strong detections for multiple sources observed on inter-continental baselines between telescopes in Chile, Hawaii, and Spain, obtained during observations in October 2018. The longest-baseline detections approach 11$\,$G$\lambda$ corresponding to an angular resolution, or fringe spacing, of 19$\mu$as. The Allan deviation of the visibility phase at 870$\mu$m is comparable to that at 1.3$\,$mm on the relevant integration time scales between 2 and 100$\,$s. The detections confirm that the sensitivity and signal chain stability of stations in the Event Horizon Telescope (EHT) array are suitable for VLBI observations at 870$\mu$m. Operation at this short wavelength, combined with anticipated enhancements of the EHT, will lead to a unique high angular resolution instrument for black hole studies, capable of resolving the event horizons of supermassive black holes in both space and time.

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arXiv2024

Bayesian self-calibration and imaging in Very Long Baseline Interferometry

Self-calibration methods with the CLEAN algorithm have been widely employed in Very Long Baseline Interferometry (VLBI) data processing in order to correct antenna-based amplitude and phase corruptions present in the data. However, human interaction during the conventional CLEAN self-calibration process can impose a strong effective prior, which in turn may produce artifacts within the final image and hinder the reproducibility of final results. In this work, we aim to demonstrate a combined self-calibration and imaging method for VLBI data in a Bayesian inference framework. The method corrects for amplitude and phase gains for each antenna and polarization mode by inferring the temporal correlation of the gain solutions. We use Stokes I data of M87 taken with the Very Long Baseline Array (VLBA) at 43GHz, pre-calibrated using the rPICARD CASA-based pipeline. For antenna-based gain calibration and imaging, we use the Bayesian imaging software resolve. To estimate gain and image uncertainties, we use a Variational Inference method. We obtain a high-resolution M87 Stokes I image at 43GHz in conjunction with antenna-based gain solutions using our Bayesian self-calibration and imaging method. The core with counter-jet structure is better resolved, and extended jet emission is better described compared to the CLEAN reconstruction. Furthermore, uncertainty estimation of the image and antenna-based gains allows us to quantify the reliability of the result. Our Bayesian self-calibration and imaging method is able to reconstruct robust and reproducible Stokes I images and gain solutions with uncertainty estimation by taking into account the uncertainty information in the data.

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arXiv2023

First GMVA observations with the upgraded NOEMA facility: VLBI imaging of BL Lacertae in a flaring state

We analyze a single-epoch Global mm-VLBI Array (GMVA) observation of the blazar BL Lacertae (BL Lac) at 86 GHz from April 2021. The participation of the upgraded, phased Northern Extended Millimetre Array (NOEMA) adds additional sensitivity to the GMVA, which has facilitated the imaging of BL Lac during an unprecedentedly strong $\gamma$-ray flare. We aim to explore the nature of the inner subparsec jet of BL Lac and the impact of the NOEMA participation in the observation. For the data reduction, we employed two advanced automatic pipelines: rPICARD for the flux density calibration as well as the model-agnostic signal stabilization and GPCAL for the antenna leakage calibration. The conventional hybrid imaging (CLEAN + amplitude and phase self-calibration) was applied to the calibrated visibilities to generate final VLBI images. We performed a ridge-line analysis and Gaussian model-fits on the final jet image to derive the jet parameters. In our data, the presence of NOEMA improves the image sensitivity by a factor of 2.5. The jet shows a clear wiggling structure within 0.4 mas from the core. Our ridge-line analysis suggests the presence of a helical jet structure (i.e., a sinusoidal pattern). Six circular Gaussian components were fitted to the inner jet region. We estimated an apparent brightness temperature of $\sim$3 $\times$ 10$^{12}$ K in the two innermost components. They are likely to be highly boosted by relativistic beaming effect. We find four significant polarized knots in the jet. Interestingly, two of them are located in the core region. Finally, we suggest a number of physical scenarios to interpret our results.

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arXiv2023

Polarimetric Geometric Modeling for mm-VLBI Observations of Black Holes

The Event Horizon Telescope (EHT) is a millimeter very long baseline interferometry (VLBI) array that has imaged the apparent shadows of the supermassive black holes M87* and Sagittarius A*. Polarimetric data from these observations contain a wealth of information on the black hole and accretion flow properties. In this work, we develop polarimetric geometric modeling methods for mm-VLBI data, focusing on approaches that fit data products with differing degrees of invariance to broad classes of calibration errors. We establish a fitting procedure using a polarimetric "m-ring" model to approximate the image structure near a black hole. By fitting this model to synthetic EHT data from general relativistic magnetohydrodynamic models, we show that the linear and circular polarization structure can be successfully approximated with relatively few model parameters. We then fit this model to EHT observations of M87* taken in 2017. In total intensity and linear polarization, the m-ring fits are consistent with previous results from imaging methods. In circular polarization, the m-ring fits indicate the presence of event-horizon-scale circular polarization structure, with a persistent dipolar asymmetry and orientation across several days. The same structure was recovered independently of observing band, used data products, and model assumptions. Despite this broad agreement, imaging methods do not produce similarly consistent results. Our circular polarization results, which imposed additional assumptions on the source structure, should thus be interpreted with some caution. Polarimetric geometric modeling provides a useful and powerful method to constrain the properties of horizon-scale polarized emission, particularly for sparse arrays like the EHT.

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arXiv2023

A search for pulsars around Sgr A* in the first Event Horizon Telescope dataset

The Event Horizon Telescope (EHT) observed in 2017 the supermassive black hole at the center of the Milky Way, Sagittarius A* (Sgr A*), at a frequency of 228.1 GHz ($\lambda$=1.3 mm). The fundamental physics tests that even a single pulsar orbiting Sgr A* would enable motivate searching for pulsars in EHT datasets. The high observing frequency means that pulsars - which typically exhibit steep emission spectra - are expected to be very faint. However, it also negates pulse scattering, an effect that could hinder pulsar detections in the Galactic Center. Additionally, magnetars or a secondary inverse Compton emission could be stronger at millimeter wavelengths than at lower frequencies. We present a search for pulsars close to Sgr A* using the data from the three most-sensitive stations in the EHT 2017 campaign: the Atacama Large Millimeter/submillimeter Array, the Large Millimeter Telescope and the IRAM 30 m Telescope. We apply three detection methods based on Fourier-domain analysis, the Fast-Folding-Algorithm and single pulse search targeting both pulsars and burst-like transient emission; using the simultaneity of the observations to confirm potential candidates. No new pulsars or significant bursts were found. Being the first pulsar search ever carried out at such high radio frequencies, we detail our analysis methods and give a detailed estimation of the sensitivity of the search. We conclude that the EHT 2017 observations are only sensitive to a small fraction ($\lesssim$2.2%) of the pulsars that may exist close to Sgr A*, motivating further searches for fainter pulsars in the region.

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arXiv2023

The Event Horizon Telescope Image of the Quasar NRAO 530

We report on the observations of the quasar NRAO 530 with the Event Horizon Telescope (EHT) on 2017 April 5-7, when NRAO 530 was used as a calibrator for the EHT observations of Sagittarius A*. At z=0.902 this is the most distant object imaged by the EHT so far. We reconstruct the first images of the source at 230 GHz, at an unprecedented angular resolution of $\sim$ 20 $\mu$as, both in total intensity and in linear polarization. We do not detect source variability, allowing us to represent the whole data set with static images. The images reveal a bright feature located on the southern end of the jet, which we associate with the core. The feature is linearly polarized, with a fractional polarization of $\sim$5-8% and has a sub-structure consisting of two components. Their observed brightness temperature suggests that the energy density of the jet is dominated by the magnetic field. The jet extends over 60 $\mu$as along a position angle PA$\sim -$28$^\circ$. It includes two features with orthogonal directions of polarization (electric vector position angle, EVPA), parallel and perpendicular to the jet axis, consistent with a helical structure of the magnetic field in the jet. The outermost feature has a particularly high degree of linear polarization, suggestive of a nearly uniform magnetic field. Future EHT observations will probe the variability of the jet structure on ${\mu}$as scales, while simultaneous multi-wavelength monitoring will provide insight into the high energy emission origin.

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arXiv2022

CASA on the fringe -- Development of VLBI processing capabilities for CASA

New functionality to process Very Long Baseline Interferometry (VLBI) data has been implemented in the CASA package. This includes two new tasks to handle fringe fitting and VLBI-specific amplitude calibration steps. Existing tasks have been adjusted to handle VLBI visibility data and calibration meta-data properly. With these updates, it is now possible to process VLBI continuum and spectral line observations in CASA. This article describes the development and implementation, and presents an outline for the workflow when calibrating European VLBI Network or Very Long Baseline Array data in CASA. Though the CASA VLBI functionality has already been vetted extensively as part of the Event Horizon Telescope data processing, in this paper we compare results for the same dataset processed in CASA and AIPS. We find identical results for the two packages and conclude that CASA in some cases performs better, though it cannot match AIPS for single-core processing time. The new functionality in CASA allows for easy development of pipelines or Jupyter notebooks, and thus contributes to raising VLBI data processing to present day standards for accessibility, reproducibility, and reusability.

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