Non-Photospheric Radius Expansion (Non-PRE)

Updated 26 October 2025

Non-PRE is defined as X-ray burst events where the photosphere remains largely static, with only modest changes despite intense radiation.
The spectral formation in Non-PRE events is driven by atmospheric structure and variable mass-loss rates, leading to deviations from the canonical F ∝ T⁴ relation.
Understanding Non-PRE dynamics is crucial for refining neutron star parameter measurements and interpreting burning regimes across hydrogen and helium-rich environments.

Non-Photospheric Radius Expansion (Non-PRE) refers to transient astrophysical phenomena, notably in X-ray bursts from accreting neutron stars, novae, and magnetars, where high-energy emission and atmospheric dynamics occur without the characteristic rapid, large-scale outward movement of the photosphere seen in Photospheric Radius Expansion (PRE) events. In Non-PRE, the emitting layer remains relatively static or undergoes only modest, continuous changes rather than a dramatic expansion/contraction cycle. Such behavior is governed by radiative, compositional, and dynamical properties of the compact object’s atmosphere, especially in regimes near or below the Eddington luminosity. Non-PRE events are distinguished by unique spectral and temporal characteristics, significantly impacting inferences about fuel composition, atmospheric structure, and the underlying physical processes.

1. Physical Interpretation and Phenomenology

Non-PRE episodes arise when the radiative flux remains below the local Eddington limit, precluding the large-scale photospheric expansion typical of PRE bursts. Instead, atmospheric dynamics may consist of steady-state or modestly expanding envelopes, possibly accompanied by radiation-driven winds at higher luminosities but still lacking the hallmark double-peaked temporal structure found in PRE. In static models, the atmosphere is characterized by hydrostatic equilibrium, while in dynamic, expanding atmosphere models, a spherically symmetric wind overlays the static base. These models may employ a “beta-law” velocity profile:

$v(r \geq r_0) = v_\infty (1 - r_0/r)^\beta$

with density given by

$\rho(r) = \frac{\dot{M}}{4\pi r^2 v(r)}$

where $v_\infty$ is the terminal velocity, $r_0$ the outer radius of the static base, $\beta$ the wind acceleration exponent, and $\dot{M}$ the mass-loss rate (Rossum et al., 2010). In Non-PRE states, the photosphere is embedded within the dynamical atmosphere, emitting from a region that is not undergoing rapid expansion or contraction.

2. Spectral Formation and Diagnostic Signatures

The spectral properties of Non-PRE events are directly shaped by atmospheric structure and mass loss. In expanding atmosphere models, elevated mass-loss rates lead to increased density in the wind, which weakens ionization edges (e.g., C, N, O edges at 25.3 Å, 18.6 Å, 16.8 Å), producing harder X-ray spectra and necessitating lower effective temperatures ( $T_\text{eff}$ ) in spectral fits than those required by static models (Rossum et al., 2010). These models imply a modified relation between bolometric flux ( $F_b$ ) and blackbody temperature ( $T_\text{bb}$ )

$F_b = \alpha T_\text{bb}^\gamma$

where the power-law index $\gamma$ departs from the canonical value of 4, indicating either a variable emitting area or a changing color-correction factor $f_c$ . Observed deviations in the cooling-phase flux–temperature relation from the canonical $F \propto T^4$ relationship confirm this behavior for both hard and soft non-PRE bursts (Zhang et al., 2010).

Typical Non-PRE bursts appear as single-peaked events without the flux dips or spectral softening signatures associated with photospheric expansion and contraction. Blue-shifted absorption lines in SSS-phase novae spectra reveal ongoing mass loss, providing dynamic evidence of a moving photosphere embedded in the wind (Rossum et al., 2010).

3. Atmospheric Composition and Burning Regimes

Analysis of Non-PRE bursts, particularly in the low-mass X-ray binary 4U 1636–53, reveals that atmospheric composition and ignition conditions differ systematically from those in PRE events (Zhang et al., 2010). Hard non-PRE bursts tend to ignite in hydrogen-rich atmospheres, while soft non-PRE and PRE bursts are associated with helium-rich environments. The distribution of blackbody temperatures at varying flux levels during burst decay is diagnostic: higher temperatures at low fluxes in hard non-PRE bursts support hydrogen burning, while softer non-PRE and PRE bursts maintain lower temperatures, consistent with helium burning.

Heavy element abundances evolve during burst cooling, with metals produced during the thermonuclear flash sinking faster than hydrogen or helium, resulting in a declining metal abundance that modulates the color-correction factor. This settling must be accounted for in spectral modeling, as it affects inferred neutron star radii and masses.

4. Photospheric Radius, Luminosity, and Wind Transition

Steady-state envelope and wind models demonstrate that, in Non-PRE events, the photospheric radius ( $r_\text{ph}$ ) evolves monotonically as luminosity increases (Guichandut et al., 2021). Static expanded envelopes maintain $r_\text{ph} \lesssim 50$ –70 km at near-Eddington luminosities, but transition smoothly to wind solutions with $r_\text{ph} \approx 100$ –1000 km for slightly higher luminosity. The critical luminosity dictating this transition is locally determined by

$L_{\text{cr}} = \frac{4\pi G M c}{\kappa(\rho,T)} (1-2GM/(rc^2))^{-1/2}$

where $\kappa(\rho,T)$ incorporates Klein–Nishina corrections. Most observed PRE bursts with modest radius expansion can be modeled with static envelopes; Non-PRE events are naturally described as remaining entirely within this envelope or entering wind solutions without dramatic, rapid expansion.

5. Application to Magnetar and Nova Burst Physics

In magnetar burst contexts, Non-PRE events contrast with bursts that achieve the magnetic Eddington limit (Watts et al., 2010). If the energy release occurs in an optically thin region or if the flux does not reach this modified critical level,

$L_{\text{crit}} \approx \left(\frac{\omega_c}{\omega}\right)^2 L_{\text{Edd}}$

then a well-defined photosphere cannot expand, resulting in Non-PRE emission. Absence of characteristic dips or double-peaked light curves in observed magnetar bursts signals conditions below the expansion threshold or dominated by optically thin, magnetospheric processes. In SSS-phase novae, expanding PHOENIX atmospheric models have shown that the non-PRE regime leads to unique interpretations of chemical abundances and line strengths; wind-driven dynamics make strong depletion of key elements unnecessary and reverse interpretation compared to static models (Rossum et al., 2010).

6. Implications for Neutron Star Parameter Measurement and Modeling

Non-PRE characteristics—especially variable emitting areas and non-canonical cooling behavior—present challenges for measuring neutron star radii and masses based on burst spectra. The assumption of constant area implicit in standard blackbody fits may introduce substantial systematic uncertainties if $f_c$ or the actual emitting region evolves during the burst (Zhang et al., 2010). During burst contraction phases, even when $T_\text{eff}$ is within 3% of its maximum, the photosphere can be elevated by $\sim$ 1 km, affecting radius inference from touchdown flux and gravitational redshift measurements (Guichandut et al., 2021). Consequently, detailed radiative transfer and time-dependent modeling—especially including metallicity evolution and dynamic wind structure—is required for accurate neutron star equation-of-state constraints.

7. Methodological Considerations and Observational Diagnostics

Time-resolved spectral analysis, such as performed on RXTE PCA data for hundreds of bursts, enables detailed classification and comparison of PRE and Non-PRE events (Zhang et al., 2010). Model atmospheres may be constructed as spherically symmetric, steady-state, or hybrid (hydrostatic base plus dynamic envelope/wind), with key observables including flux–temperature relations, absorption edge strengths, line blue shifts, and photospheric radius evolution. Spectral shifts at the photosphere, primarily due to gravitational redshift ( $[1 - 2GM/(rc^2)]^{-\frac{1}{2}}$ ), remain below a few percent, with special-relativistic Doppler correction moderating the net effect (Guichandut et al., 2021). A plausible implication is that systematic observational errors from incorrectly identifying true touchdown or static regions could be of order $\sim$ 10%.

Steady-state models are appropriate for slowly evolving, plateau phases, but rapid transitions during burst rise necessitate fully dynamic treatment—this is particularly relevant for interpreting onset and decay of Non-PRE phenomena, including wind launching and envelope relaxation (Guichandut et al., 2021).

Non-PRE events represent a diverse set of astrophysical phenomena where the absence of dramatic photospheric expansion informs unique dynamics, composition, and diagnostic signatures in neutron star burst environments, SSS-phase novae, and magnetar flare physics. These observational and modeling features have significant implications for the inference of fundamental stellar parameters, interpretation of spectral evolution, and the development of robust atmosphere and wind models.