PAIRS Project: Exoplanets in Binary Systems

• PAIRS Project is a comprehensive initiative that integrates physical models, statistical tools, and N-body simulations to study exoplanet formation in binary star systems.
• The project refines detection methods by developing a probabilistic framework that corrects for unresolved binarity in large surveys such as Gaia DR3.
• PAIRS also extends to quantum photonics by enabling high-dimensional entangled photon pair generation and tomography for advanced quantum communication.

The PAIRS Project (“Planet formation Around bInaRy Stars”) refers to a comprehensive, multi-pronged effort to build, validate, and exploit physical and statistical models for exoplanets in binary star systems, with a particular emphasis on the physical formation mechanisms, dynamical evolution, and observational identification of S-type planets (those orbiting a single star in a binary), as well as high-dimensional quantum photonic pair sources. PAIRS is best known for its development of (i) global population synthesis frameworks adapted from the Bern Model for planet formation in S-type binaries (Venturini et al., 20 Jan 2026, &&&1&&&) and (ii) a rigorous, probabilistic framework for detecting unresolved stellar binarity in large spectroscopic surveys, notably via the “paired” (PAIRS) code applied to Gaia DR3 radial velocity statistics (Chance et al., 2022). Independently, the PAIRS Project label has also encompassed efforts in quantum photonics, focused on the robust generation and tomography of high-dimensional spatially entangled photon pairs (D'Errico et al., 2021).

1. Physical Motivation and Project Scope

Binary stars are at least as common as single stars in the Milky Way, which has direct implications for the initial conditions and subsequent evolution of planetary systems. However, the majority of planet formation models—particularly global planet population synthesis, as typified by the Bern model—have historically neglected key features unique to binaries, such as tidal truncation of protoplanetary disks and sustained dynamical perturbations by the stellar companion. Observational exoplanet surveys with Gaia, TESS, and high-resolution direct imaging have revealed a non-negligible occurrence rate of S-type planets in binaries. Yet, population-level theoretical constraints and predictions remain incomplete without models that self-consistently incorporate key binary effects. The PAIRS Project addresses this gap by providing a physically-motivated, computationally robust extension of global planet formation theory to the binary regime, and by developing community standards for the detection and statistical correction of unresolved binarity in spectroscopic exoplanet surveys (Venturini et al., 20 Jan 2026, Nigioni et al., 20 Jan 2026, Chance et al., 2022).

2. Circumstellar Disk Truncation in Binaries

Disk truncation, the primary physical effect of a binary companion on S-type planet formation, limits both angular momentum transport and the supply of solids available for core growth. The PAIRS model computes the truncated disk radius $R_t$ as

$R_t = R_{Egg} \cdot [b e_{bin}^c + h \mu^k],$

where $R_{Egg}$ is the Eggleton Roche-lobe radius, $e_{bin}$ the binary eccentricity, and $\mu = M_2 / (M_1+M_2)$ encodes the mass ratio. Fit parameters $(b,c,h,k)$ are calibrated against hydrodynamic simulations [Manara et al. 2019]. This prescription leads to a severe suppression of pebble surface density and pebble flux in tight binaries ($a_{bin} \lesssim 100$–$160$ au), such that Mars-mass and larger S-type planets fail to form at separations $a_{bin} < 160$ au; the critical binary separation for survival of such planetary cores is

$a_{bin,crit} \sim 160~\text{au}.$

Formation is further localized to small $a_{p,0}/a_{bin}$ and $a_{p,0}/R_t$, with $\sim$75% of Mars-mass cores at $a_{p,0}/a_{bin}<0.04$ and $a_{p,0}/R_t<0.22$ (Venturini et al., 20 Jan 2026).

3. Gravitational Perturbations: N-body Dynamics and Migration

Beyond truncation, the secondary star persists as a dynamically significant perturber. The PAIRS framework extends the Bern Model’s hybrid symplectic N-body integrator by including the Newtonian acceleration from the secondary star:

$$\mathbf{a}_i = -GM_{host} \frac{\mathbf{r}_i}{|\mathbf{r}_i|^3} - GM_{sec} \frac{(\mathbf{r}_i - \mathbf{r}_{sec})}{|\mathbf{r}_i - \mathbf{r}_{sec}|^3}.$$

Simulation results demonstrate that:

• Planets formed beyond $0.5\,R_{trunc}$ or $\gtrsim 1/3$ the host’s Hill radius are typically ejected or destabilized, with loss rates exceeding $80\%$ for $M_2 > 0.5M_\odot$ (Nigioni et al., 20 Jan 2026).
• Surviving embryos in strong-perturbation regimes show increased mean eccentricity, matching analytical equilibrium eccentricity predictions (Mardling 2007).
• The combination of disk truncation and dynamical perturbations reduces the mean planet mass by ~41% relative to truncation-only models, and fully suppresses significant growth beyond $0.5\,R_{trunc}$.
• Disk-driven migration can partially “rescue” embryos, but survival and final mass are strongly confined to $a_{p,0}/R_{trunc}<0.3$ and $a_{p,0}/a_{bin}<0.05$ (Nigioni et al., 20 Jan 2026).

4. Simulation Methodology and Population Synthesis

PAIRS utilizes a grid-sampling approach with extensive Monte Carlo draws over binary mass ratios, separations, eccentricities, and disk parameters:

• In Paper I, 5,000 in-situ single-embryo growth simulations are performed with varying $a_{bin}$, $e_{bin}$, disk mass, and $\alpha$ viscosity, enabling quantification of the “pebble starvation” regime threshold and its spatial dependence (Venturini et al., 20 Jan 2026).
• Paper II introduces multi-embryo, migration-enabled, and dynamics-including simulations, demonstrating the interaction between planet–planet scattering and external binary perturbations. Results show that planetary system architectures are more chaotic and mass distributions less ordered in binaries than in single-star analogs (Nigioni et al., 20 Jan 2026).
• Population synthesis outputs include occurrence rates, spatial distributions, and mass functions as a function of binary parameters, enabling direct statistical comparisons with current and future exoplanet surveys.

5. Radial Velocity Binarity Detection: The paired/PAIRS Statistical Framework

The PAIRS (“paired”) statistical tool (Chance et al., 2022) translates Gaia DR3 RV “noise” into binarity likelihoods by forward-modeling the reported RV errors versus empirical noise baselines for each star in G/BP–RP color space. For each star, a $\chi^2$ outlier test is performed:

• The sample variance $s_k^2$ of epochal RVs is computed from the reported uncertainty, and compared to the expected baseline $\sigma_{0,k}$.
• The probability $p_{single}$ under the single-star hypothesis is computed from the $\chi^2$ distribution with $N_k-1$ degrees of freedom, and $p_{binary} = 1 - p_{single}$.
• For significant outliers ($p_{single} < 10^{-3}$), posteriors on the binary RV semi-amplitude $K$ are inferred using a noncentral $\chi^2$ likelihood, marginalizing over orbital elements. Validation against external catalogs (Gaia NSS, Kepler and TESS eclipsing binaries, SB9 spectroscopic binaries) shows a recovery rate of 75–98% in high-S/N regimes. The framework allows survey-wide correction of planet occurrence rates in the presence of unresolved binaries and vetting of individual targets for false positives (e.g., blended spectroscopic systems).

Component	Domain	Role in PAIRS Project
Bern Model Extensions	Planet formation, N-body	S-type formation population synthesis
Disc Truncation Prescription	Disk physics	Quantifies pebble/effective solid supply cutoff
paired/PAIRS Statistical Tool	RV binarity detection	Unresolved binary likelihoods in Gaia DR3
Quantum Pair Source Characterization	Photonic entanglement	High-dimensional entangled photon-pair generation

6. Quantum Photonics: High-Dimensional Entangled PAIRS Sources

Independently, the PAIRS Project has encompassed work on the characterization of high-dimensional, spatially-entangled photon pairs generated via spontaneous parametric downconversion (SPDC) (D'Errico et al., 2021). Key features include:

• Full-mode quantum state tomography in Laguerre-Gauss (LG) basis states incorporating both radial ($p$) and azimuthal (OAM, $\ell$) modes.
• Programmable pump shaping via spatial light modulators (SLMs), enabling arbitrary superposition projections and the realization of high-fidelity $d=16$-dimensional entangled states ($\mathcal{F} \approx 0.71$).
• Calibration for mode-dependent losses and demonstration of generalized Bell inequality violation in $d=16$.
• Relevance for scalable quantum communication schemes leveraging the enlarged Hilbert space and robust, arbitrary-basis state preparation.

7. Significance, Limitations, and Future Directions

The PAIRS Project provides the first fully self-consistent, statistically robust framework for the formation, evolution, and observational correction of planets in binary environments. Results from PAIRS suggest:

• The formation of Mars-mass and larger S-type planets is severely limited in binaries with $a_{bin} \lesssim 160$ au due to pebble starvation imposed by disk truncation.
• Direct dynamical perturbations by the secondary further suppress planet growth and reorder system architecture beyond simple “truncation-only” predictions.
• Empirical recovery of unresolved binaries from Gaia DR3 with the paired/PAIRS tool enables correction of planet occurrence statistics for binarity effects; nontrivial fractions ($\gtrsim 20\%$) of binaries would be missed by prior catalog indicators such as RV-RUWE.
• For quantum photonic sources, full-mode control of high-dimensional entangled pairs enables next-generation applications in multidimensional QKD, quantum simulation, and flexible state multiplexing.

Ongoing and future population syntheses (PAIRS Paper III) are poised to provide exhaustive theoretical benchmarks for the exoplanetary census in binaries and to clarify outstanding discrepancies between observations and simplified single-star models. Further cross-application to higher-order multiples, and integration with fiber/photonic platforms in quantum information, represent active directions for the PAIRS Project.

Key PAIRS publications: (Venturini et al., 20 Jan 2026, Nigioni et al., 20 Jan 2026, Chance et al., 2022, D'Errico et al., 2021).