SMILE: Milli-Lens Search via VLBI

• Search for Milli-Lenses (SMILE) is a VLBI survey that detects gravitational lens systems with milli-arcsecond separations in compact radio-loud AGN to probe dark matter models.
• The project employs multi-frequency observations, automated calibration pipelines, and rigorous candidate selection to differentiate genuine lensing signals from intrinsic radio structure.
• It integrates extensive redshift campaigns and theoretical modeling to compare observed milli-lens incidence against predictions from CDM, WDM, and SIDM scenarios.

Search for Milli-Lenses (SMILE) is a Very Long Baseline Interferometry (VLBI) survey program designed to identify or constrain gravitational lens systems with milli-arcsecond image separations in compact radio-loud active galactic nuclei. Its central scientific target is the lens-mass regime $10^6$–$10^9\,M_\odot$, where dense dark sub-galactic haloes, free-floating supermassive compact objects, and related populations can produce image splittings on angular scales accessible to VLBI. The program developed from an archival pilot on 13,828 Astrogeo VLBI sources into a clearly defined CLASS-derived sample of 4,968 flat-spectrum radio sources, and it couples imaging, redshift acquisition, and large-scale calibration infrastructure in order to compare the observed incidence of milli-lensing with theoretical predictions for different dark-matter models (Casadio et al., 2021, Pötzl et al., 2024, Blinov et al., 6 Jul 2026, Loudas et al., 2022).

1. Scientific rationale and lensing regime

SMILE is motivated by the fact that sub-galactic scales remain one of the least secure domains of dark-matter phenomenology. Cold dark matter, warm dark matter, and self-interacting dark matter differ strongly in their predictions for the abundance and internal density structure of haloes below the scale of normal galaxies, while lenses in the $10^6$–$10^9\,M_\odot$ range probe precisely that regime (Pötzl et al., 2024, Loudas et al., 2022). The 2026 spectroscopy paper explicitly places this within the long-standing discrepancy between the large number of low-mass haloes predicted by $\Lambda$CDM and the smaller number currently observed (Blinov et al., 6 Jul 2026).

In the SMILE framework, a milli-lens is a system in which a compact background radio source is multiply imaged with separations on milliarcsecond scales. The pilot paper gives the characteristic scaling

$$\Delta \theta \sim 2\times 10^{-6}\left(\frac{M_{\mathrm{SMCO}}}{M_\odot}\right)^{0.5}\,\mathrm{arcseconds},$$

which places $10^6$–$10^9\,M_\odot$ lenses in the approximate range $\sim 1$–$100$ mas (Pötzl et al., 2024). The earlier survey-definition paper described the target regime as strong gravitational lenses on milli-arcsecond scales $10^9\,M_\odot$0 mas, with the scientifically emphasized compact-object separation range at $10^9\,M_\odot$1–$10^9\,M_\odot$2 mas (Casadio et al., 2021).

VLBI is indispensable because only VLBI resolves radio structure on milliarcsecond scales. In SMILE, this is not merely a matter of higher image quality: the entire program depends on distinguishing genuine multiple compact images from intrinsic parsec-scale radio structures. The principal contaminant class is compact symmetric objects (CSOs), whose projected sizes are typically $10^9\,M_\odot$3 kpc, and redshift knowledge is required to convert angular separations into physical scales when assessing that ambiguity (Blinov et al., 6 Jul 2026). The pilot discrimination framework therefore relies on lensing invariants that should survive improved angular resolution: conservation of surface brightness, conservation of spectral shape, stability of flux ratios over time, and stability of image separation (Pötzl et al., 2024).

The time-delay scale is one reason those tests are powerful. The pilot paper quotes

$10^9\,M_\odot$4

so intrinsic source variability should appear nearly simultaneously in both images for observations separated by days, months, or years (Pötzl et al., 2024). A plausible implication is that long-term flux-ratio drift is generally inconsistent with simple milli-lensing unless additional propagation effects intervene.

2. Survey definition and source samples

SMILE evolved from a heterogeneous archival pathfinder into a defined survey sample. The first phase used the Astrogeo VLBI image database, described as the largest publicly available VLBI image archive, and visually inspected 13,828 unique sources with data at 2.3, 5, and 8 GHz (Casadio et al., 2021, Pötzl et al., 2024). The long-term statistical survey, however, is built from the Cosmic Lens All-Sky Survey (CLASS), a well-defined radio sample designed to support population-level inference (Pötzl et al., 2024, Blinov et al., 6 Jul 2026).

The CLASS parent survey contains 11,685 radio-loud sources selected with declination in $10^9\,M_\odot$5, Galactic latitude $10^9\,M_\odot$6, $10^9\,M_\odot$7 mJy, and spectral index $10^9\,M_\odot$8 between 1.4 and 5 GHz, with $10^9\,M_\odot$9 (Pötzl et al., 2024). From CLASS, SMILE defined a flux-limited, complete subsample of 4,968 sources with $10^6$0 mJy (Blinov et al., 6 Jul 2026). These are predominantly flat-spectrum, radio-loud active galaxies suited to VLBI-based lens searches.

Survey element	Definition	Role
Astrogeo pilot	13,828 unique VLBI sources at 2.3, 5, and 8 GHz	Pathfinder candidate search
CLASS parent survey	11,685 radio sources with $10^6$1, $10^6$2 mJy, $10^6$3	Parent catalog
SMILE survey sample	4,968 CLASS sources with $10^6$4 mJy	Statistical milli-lens search

The distinction between the archival pilot and the CLASS-based survey is fundamental. The Astrogeo sample is heterogeneous in array, sensitivity, resolution, and $10^6$5-coverage, so it is useful for refining rejection logic but not for robust dark-matter population inference (Pötzl et al., 2024). By contrast, the CLASS-derived SMILE sample is explicitly intended to become a redshift-informed “sufficient sample” for comparing observed milli-lens incidence with theory (Pötzl et al., 2024).

3. Candidate identification and contaminant rejection

The original SMILE pilot used a staged visual-selection pipeline on the 13,828-source Astrogeo set. All UV-FITS files and clean components were re-imaged with circular restoring beams of diameter

$10^6$6

and final images were standardized to 1024$10^6$71024 pixels at 0.3 mas per pixel, corresponding to a field of view of about $10^6$8 mas (Casadio et al., 2021). A custom web interface displayed all available frequencies simultaneously, and classifiers marked sources simply as “Lens” or “No Lens.”

The first pass involved 5 PhD scientists and 9 undergraduate Physics students, with each source inspected once. To monitor attentiveness, 200 mock lens images were injected; after reinspection of unreliable classifications, the final estimated loss rate at the screening stage was about $10^6$9 (Casadio et al., 2021). The candidate count then evolved from 950 real sources after the first pass to 954 after expert recovery, then to 128 after expert visual screening, then to 59 after lens-expert review, and finally to 40 after a surface-brightness preservation cut with apparent surface-brightness ratio $10^9\,M_\odot$0 (Casadio et al., 2021). That relaxed threshold was chosen because Astrogeo data are heterogeneous and may have poor $10^9\,M_\odot$1-coverage and short integrations.

The 2024 pilot project converted this initial list into a much stricter discrimination framework. From the 40 pilot candidates, 38 had available X-band data, 35 were within the EVN declination range and were observed with the European VLBI Network at 4.9 and 22.2 GHz, and 31 of the initial 40 were ruled out (Pötzl et al., 2024). The formal rejection scheme discards a source as a milli-lens if it fails any of five tests: morphology, surface-brightness ratio, flux-ratio stability over time, conservation of spectral shape, and separation stability. The adopted thresholds were $10^9\,M_\odot$2, $10^9\,M_\odot$3, flux-ratio stability within combined $10^9\,M_\odot$4 between epochs, and no significant radial proper motion at the $10^9\,M_\odot$5 level (Pötzl et al., 2024).

In practice, the most discriminating tests were spectral-shape conservation and the surface-brightness ratio, each rejecting 23 sources; morphology rejected 9, flux-ratio stability 3, and separation stability 1 (Pötzl et al., 2024). This shows that the dominant challenge is not detecting doubles, but rejecting intrinsic radio morphologies that mimic lensing. The pilot identified compact symmetric objects as the main contaminant population and found 34 viable CSO candidates as a by-product (Pötzl et al., 2024).

After this filtering, 9 viable milli-lens candidates remained: J0024-4202, J0210-2213, J0923-3435, J1143+1834, J1218-2159, J1632+3547, J1653+3503, J1805-0438, and J2347-1856 (Pötzl et al., 2024). The authors also state that most or all of the remaining candidates will likely be rejected with sufficiently sensitive and higher-cadence follow-up, which underscores that the pilot’s principal contribution is methodological rather than confirmatory (Pötzl et al., 2024).

4. Redshift completeness and supporting spectroscopy

Redshifts are an enabling requirement for SMILE rather than an auxiliary convenience. The spectroscopy paper states that reliable redshifts convert angular measurements into physical linear scales, enable intrinsic luminosity and jet-kinematic estimates, and support cosmological and population studies (Blinov et al., 6 Jul 2026). They are also necessary for interpreting compact VLBI morphologies, especially when deciding whether multiple milliarcsecond components correspond to a physically small intrinsic source such as a CSO or to distinct lensed images.

A broad literature and catalog compilation was therefore performed across the full 4,968-source SMILE list. The cross-match used OCARS, SDSS DR18, Milliquas v8, PS1-STRM, DESI Legacy Imaging Surveys DR8 and DR10, DESI DR1, the LAMOST Quasar Survey DR1–DR12, the QZO catalog, and CatGlobe, with additional checks in SIMBAD and NED (Blinov et al., 6 Jul 2026). Even after this effort, 491 sources had no redshift estimate at all and 948 had only photometric redshifts, many with substantial discrepancies among catalogs (Blinov et al., 6 Jul 2026). This implies that 3,529 sources already had spectroscopic redshifts prior to the new campaign.

The spectroscopy paper is the first installment in a redshift-support series. It targeted the brightest accessible sources without spectroscopic redshifts, selected pragmatically rather than statistically: sources without $10^9\,M_\odot$6 and with either $10^9\,M_\odot$7 mag in Pan-STARRS DR1 or $10^9\,M_\odot$8 mag in Gaia DR2 were observed, and at each run the brightest available source was chosen (Blinov et al., 6 Jul 2026). This pilot strategy reflects the fact that sources lacking spectroscopy are generally optically fainter: the median Gaia DR3 $10^9\,M_\odot$9-band magnitude is 19.3 for sources with known spectroscopic redshifts and 20.5 for those lacking them, although the paper also notes that some bright sources were never observed spectroscopically or may have been observed during high synchrotron continuum states that diluted emission lines (Blinov et al., 6 Jul 2026).

Observations were obtained with the 1.3 m Skinakas telescope in Crete during 2022–2023 using an ANDOR iKon-L 936 BEX2-DD CCD and a 600 lines mm$\Lambda$0 grating, with nominal dispersion about 2 Å pixel$\Lambda$1, a 160 $\Lambda$2m slit, and typical resolving power $\Lambda$3 (Blinov et al., 6 Jul 2026). Reduction employed a custom Python pipeline using astropy, ccdproc, astroscrappy, scipy, and numpy, with bias subtraction, flat-fielding, L.A.Cosmic cosmic-ray removal, extraction of one-dimensional spectra, continuum normalization by iterative fourth-degree-polynomial fitting, and Gaussian fitting of individual features or blends (Blinov et al., 6 Jul 2026). The redshift procedure consisted of computing line-by-line redshifts, taking a weighted mean, and estimating the final uncertainty as the standard error of the mean (Blinov et al., 6 Jul 2026).

Fifteen targets were observed. Six yielded genuinely new spectroscopic redshifts, four more produced redshifts that were later found to have been published elsewhere, and five yielded no secure redshift (Blinov et al., 6 Jul 2026). The genuinely new success rate was therefore $\Lambda$4, while $\Lambda$5 spectra produced usable line-based redshifts if later external publication is ignored (Blinov et al., 6 Jul 2026). The six new secure redshifts were obtained for GB6 J010341+423925 $\Lambda$6, GB6 J184835+213156 $\Lambda$7, GB6 J195141+480145 $\Lambda$8, GB6 J201414+063439 $\Lambda$9, GB6 J203142+162147 $$\Delta \theta \sim 2\times 10^{-6}\left(\frac{M_{\mathrm{SMCO}}}{M_\odot}\right)^{0.5}\,\mathrm{arcseconds},$$0, and GB6 J222252+144119 $$\Delta \theta \sim 2\times 10^{-6}\left(\frac{M_{\mathrm{SMCO}}}{M_\odot}\right)^{0.5}\,\mathrm{arcseconds},$$1 (Blinov et al., 6 Jul 2026). The paper explicitly does not report new milli-lenses; it addresses redshift completeness as survey infrastructure.

5. Calibration, automation, and data infrastructure

SMILE’s observational scale makes blind VLBI calibration a scientific issue in its own right. The program requires the calibration of nearly 5,000 radio-loud targets observed over decades with heterogeneous setups, while VLBI data are generally delivered as correlated visibilities rather than science-ready images (Álvarez-Ortega et al., 18 Aug 2025, Kumar et al., 19 Apr 2026). Residual instrumental, geometric, and propagation-induced errors affect both phase and amplitude, and a dataset-by-dataset manual workflow would be prohibitive at SMILE scale.

Two automation frameworks have been developed in direct support of this requirement. VIPCALs is a fully automated, end-to-end continuum VLBI calibration pipeline implemented in Python with ParselTongue on top of AIPS (Álvarez-Ortega et al., 18 Aug 2025). It reproduces the standard AIPS calibration workflow in fully unsupervised form, including automatic reference-antenna selection, calibrator identification, and diagnostic generation. On a representative SMILE validation set of 1,000 sources, corresponding to 1,417 observations from 360 VLBA projects and 2,589 files totaling 19 TB, it successfully calibrated 955 of the 1,000 test sources across multiple frequency bands (Álvarez-Ortega et al., 18 Aug 2025). More than 91% of the calibrated datasets achieved successful fringe fitting on target in at least half of the attempted solutions, the median ratio of calibrated to initial visibilities was 0.87, and the average processing time was below 10 minutes per dataset on a single core (Álvarez-Ortega et al., 18 Aug 2025).

VASCO is the CASA-based counterpart. It extends the rPICARD framework with preprocessing of FITS-IDI and Measurement Set data, blind calibrator and reference-antenna selection via FFT-based fringe detection, and orchestration through ALFRD, a workflow manager that tracks progress and records results in real time (Kumar et al., 19 Apr 2026). VASCO was validated on 1,000 NRAO archival sources spanning 1995–2023, covering 1,372 band-separated observations across S, C, X, U, and K bands, and produced calibrated output for 978 sources, or 97.8%, with 22 failures due to corrupted or incomplete data (Kumar et al., 19 Apr 2026). Mean per-source execution time was about 30 minutes using MPI parallelization with up to 20 cores, and a 100-dataset benchmark showed that selective source extraction reduced average runtime from about 50 to about 30 minutes per source, a 39% improvement (Kumar et al., 19 Apr 2026).

For SMILE, these pipelines are not ancillary software projects but operational backbones. They standardize calibration choices across a survey-scale archive, preserve auditable table-level outputs, and make it plausible to move from raw heterogeneous VLBA data to calibrated visibilities suitable for systematic imaging and candidate vetting (Álvarez-Ortega et al., 18 Aug 2025, Kumar et al., 19 Apr 2026).

6. Theoretical interpretation for dark-matter models

The principal theory paper explicitly asks whether a sample of $$\Delta \theta \sim 2\times 10^{-6}\left(\frac{M_{\mathrm{SMCO}}}{M_\odot}\right)^{0.5}\,\mathrm{arcseconds},$$2 compact radio sources is sufficient to detect at least one milli-lens under different dark-matter scenarios (Loudas et al., 2022). Its core observable is the strong milli-lensing optical depth $$\Delta \theta \sim 2\times 10^{-6}\left(\frac{M_{\mathrm{SMCO}}}{M_\odot}\right)^{0.5}\,\mathrm{arcseconds},$$3, modeled semi-analytically as

$$\Delta \theta \sim 2\times 10^{-6}\left(\frac{M_{\mathrm{SMCO}}}{M_\odot}\right)^{0.5}\,\mathrm{arcseconds},$$4

with the expected number of lensed sources

$$\Delta \theta \sim 2\times 10^{-6}\left(\frac{M_{\mathrm{SMCO}}}{M_\odot}\right)^{0.5}\,\mathrm{arcseconds},$$5

The formalism treats the lensing system as a point-mass lens for the cross-section, while determining the effective lens mass from the central portion of an extended halo whose projected surface density exceeds the critical threshold (Loudas et al., 2022).

Within that framework, warm dark matter haloes are optically thin for strong gravitational milli-lensing, yielding zero expected lensing events in a SMILE-sized sample (Loudas et al., 2022). Cold dark matter predictions depend strongly on the low-mass concentration–mass relation. With a simulation-based concentration relation, the expected count is only $$\Delta \theta \sim 2\times 10^{-6}\left(\frac{M_{\mathrm{SMCO}}}{M_\odot}\right)^{0.5}\,\mathrm{arcseconds},$$6, whereas a steeper extrapolated concentration relation yields $$\Delta \theta \sim 2\times 10^{-6}\left(\frac{M_{\mathrm{SMCO}}}{M_\odot}\right)^{0.5}\,\mathrm{arcseconds},$$7 (Loudas et al., 2022). Self-interacting dark matter haloes with ordinary cored profiles do not lens efficiently on these scales, but SIDM haloes can act as strong milli-lenses if gravothermal collapse produces highly dense central cores; in the paper’s deliberately extreme collapsed-core scenario, the expected number rises to about 13 (Loudas et al., 2022).

These results make detections more discriminating than nondetections. A null result in $$\Delta \theta \sim 2\times 10^{-6}\left(\frac{M_{\mathrm{SMCO}}}{M_\odot}\right)^{0.5}\,\mathrm{arcseconds},$$8 sources is consistent with warm dark matter, standard SIDM cores, and low-concentration CDM, whereas a convincing detection would strongly disfavor the warm dark matter scenario modeled in the paper and would instead point toward unusually concentrated CDM haloes or compact collapsed SIDM cores (Loudas et al., 2022). The calculation, however, is idealized: it assumes spherical field haloes, neglects baryons, finite-source effects, explicit subhalo populations, and detailed observational selection functions (Loudas et al., 2022). This suggests that SMILE’s ultimate constraining power depends both on theoretical optical-depth calculations and on the survey’s empirical control of completeness and contamination.

7. Limitations, current status, and future trajectory

SMILE remains a staged program rather than a completed discovery survey. The Astrogeo pilot is explicitly heterogeneous and therefore unsuitable for robust population inference; its main function is to refine candidate rejection criteria and characterize contaminant classes (Pötzl et al., 2024). The spectroscopy campaign is a small pilot restricted to the brightest optically accessible targets and explicitly not a statistically representative subsample of all SMILE sources (Blinov et al., 6 Jul 2026). The 2026 spectroscopy paper is therefore best understood as survey infrastructure, not as a lens-discovery paper.

Several limitations recur across the project. In the imaging pilot, only 13 of the 35 EVN targets observed at 22.2 GHz were detected, and only 7 had both candidate lensed components detected at that frequency, which weakens the highest-resolution morphology and spectral tests (Pötzl et al., 2024). In spectroscopy, the first Skinakas campaign obtained only 6 new secure redshifts from 15 observed targets, illustrating how difficult flat-spectrum radio AGN can be as spectroscopic targets, especially when some are likely BL Lac objects with intrinsically weak or absent lines (Blinov et al., 6 Jul 2026). Redshift incompleteness also remains structurally important: after extensive catalog compilation, 491 SMILE sources still lacked any redshift estimate and 948 had only photometric redshifts, many of which disagree across catalogs (Blinov et al., 6 Jul 2026).

The project’s current status is therefore that of a progressively formalized survey stack. Candidate discrimination has advanced from permissive archival inspection to structured multi-frequency and multi-epoch rejection, redshift support is being expanded through dedicated spectroscopy, and automated calibration has reached the point where thousands of heterogeneous archival VLBA datasets can be processed reproducibly (Pötzl et al., 2024, Blinov et al., 6 Jul 2026, Álvarez-Ortega et al., 18 Aug 2025, Kumar et al., 19 Apr 2026). No confirmed milli-lens is reported in the materials summarized here.

The stated next steps are correspondingly practical. Future papers will present additional AGN redshifts from larger telescopes (Blinov et al., 6 Jul 2026). The candidate follow-up program includes further high-frequency observations with KVN, dedicated multi-epoch multi-frequency VLBA monitoring for the remaining pilot candidates, and eventual exploitation of ngVLA-LONG and SKA-VLBI (Pötzl et al., 2024). The long-term transition is from the heterogeneous Astrogeo pathfinder to the defined CLASS-based sample of about 5,000 sources with improved redshift coverage. In the original survey-definition paper, it was argued that if such a complete sample yields no milli-lenses, the upper limit on $$\Delta \theta \sim 2\times 10^{-6}\left(\frac{M_{\mathrm{SMCO}}}{M_\odot}\right)^{0.5}\,\mathrm{arcseconds},$$9 could improve by more than an order of magnitude relative to the earlier 300-source VLBI search of Wilkinson et al. (Casadio et al., 2021). That prospect captures the central logic of SMILE: even a null result becomes scientifically decisive once sample definition, redshift completeness, calibration uniformity, and contaminant rejection are all brought under control.