TransFit-CSM: A Fast, Physically Consistent Framework for Interaction-Powered Transients

TL;DR

TransFit-CSM presents a fast, physically grounded framework that self-consistently couples thin-shell ejecta–CSM dynamics with time-dependent radiative diffusion from a moving, shock-tied heating boundary. By solving the coupled shell dynamics and diffusion equations, the model naturally produces diffusion-mediated light-curve peaks and avoids Arnett-like assumptions in optically thick CSM. Bayesian fits to SN 2006gy and SN 2010jl demonstrate how massive, extended CSM with eruptive pre-SN mass loss shapes the observables and permits interpretable posteriors for ejecta and CSM properties. This framework thus provides a practical bridge between analytic models and full radiation-hydrodynamic simulations, enabling population-level inferences for current and future time-domain surveys.

Abstract

We present TransFit-CSM, a fast and physically consistent framework for modeling interaction-powered transients. The method self-consistently couples the ejecta circumstellar medium (CSM) shock dynamics to radiative diffusion from a moving heating boundary tied to the shocks, so that both the photon escape path and the effective diffusion time evolve with radius and time. We solve the mass and momentum equations for the forward and reverse shocks together with the diffusion equation in the unshocked CSM. TransFit-CSM reproduces the canonical sequence of an early dark phase, a diffusion-mediated rise and peak, and a post-interaction cooling tail, and it clarifies why Arnett-like peak scalings break down in optically thick CSM. The framework is well suited for Bayesian inference and constrains physical parameters of the ejecta and CSM from bolometric or joint multi-band light curves. Applications to SN 2006gy and SN 2010jl yield accurate fits and physically interpretable posteriors, highlighting the dominant role of pre-supernova mass loss in shaping the observables. Because it is both computationally efficient and physically grounded, TransFit-CSM bridges simple analytic prescriptions and radiation-hydrodynamic simulations, enabling population-level inference for current and future time-domain surveys.

Figures (10)

• Figure 1: Schematic illustration of the SN--CSM interaction within the TransFit-CSM framework. Photons generated at the shock front ($R_{\rm sh}$) are initially trapped in the optically thick medium ($\tau \gg 1$) and diffuse outward through multiple scatterings (random-walk trajectories). Once they reach the photosphere ($R_{\rm ph}$, where $\tau \approx 2/3$), the medium becomes optically thin, and photons free-stream toward a distant observer. Key radii and the shock velocity ($v_{\rm sh}$) are indicated for clarity.
• Figure 2: Default density structure of the supernova ejecta and CSM adopted in TransFit-CSM. The ejecta profile is represented by a broken power law, with a flat inner core ($\rho_{\mathrm{ej}}\propto r^{-\delta}$) and a steep outer envelope ($\rho_{\mathrm{ej}}\propto r^{-n}$). The transition velocity $v_{\mathrm{tr}}$ marks the boundary between the inner and outer ejecta components. The CSM is modeled as a power-law density distribution ($\rho_{\mathrm{csm}}\propto r^{-s}$), extending from $R_{\mathrm{csm,in}}$ to $R_{\mathrm{csm,out}}$.
• Figure 3: The effective diffusion time $t_{\mathrm{diff}}$ between the shock and the photosphere, shown as a function of time. Each colored line represents a different value for the CSM density slope $s$. The gray dashed line marks the constant timescale $t_0$ assumed by Chatzopoulos2012, included for comparison.
• Figure 4: Bolometric light-curve morphologies of interaction-powered SNe for compact ($\xi \gg 1$, left) and extended ($\xi \ll 1$, right) CSM. The blue lines show the bolometric luminosity $L_{\rm bol}$, while the red dashed lines indicate the shock power $L_{\rm heat}$. Vertical dashed lines mark $t_{\rm dark}$, $t_{\rm peak}$, and $t_{\rm se}$. Fixed parameters are $M_{\rm ej}=5\,M_\odot$, $E_{\rm sn}=10^{51}\,\mathrm{erg}$, $M_{\rm csm}=1\,M_\odot$, $R_{\rm csm,in}=5\times10^{2}\,R_\odot$, $s=2$, $\kappa=0.2\,\mathrm{cm^{2}\,g^{-1}}$, and $\epsilon_{\rm int}=1$. The outer radii are $R_{\rm csm,out}=5.0\times10^{3}\,R_\odot$ (left) and $R_{\rm csm,out}=5.0\times10^{4}\,R_\odot$ (right).
• Figure 5: Effect of the CSM outer radius $R_{\rm csm,out}$ (left) and CSM mass $M_{\rm csm}$ (right) on supernova bolometric light curves. In the left panel, $R_{\rm csm,out}$ is varied with $M_{\rm csm}=1M_\odot$; in the right panel, $M_{\rm csm}$ is varied with $R_{\rm csm,out}=1.0\times10^{4}R_\odot$. All other parameters are fixed to $M_{\rm ej}=5M_\odot$, $E_{\rm sn}=10^{51}\mathrm{erg}$, $R_{\rm csm,in}=5.0\times10^{2},R_\odot$, $s=2$, $\kappa=0.2\mathrm{cm^{2}g^{-1}}$, and $\epsilon_{\rm int}=1$.