Radiation damage to the Hubble Space Telescope has been several years out of phase with the Solar cycle

Abstract: As well as obtaining beautiful images of the Universe, the Hubble Space Telescope's CCD detectors are sensitive radiation dosimeters that have been monitored in Low Earth Orbit for more than 24 years. The rate of radiation damage they received has varied over each Solar cycle, but several years out of phase with the appearance of sunspots or coronal mass ejections. We investigate functional forms that successfully fit the time series of damage to telescopes elsewhere in the Solar system. We obtain remarkably accurate fits to Hubble data but with physically absurd parameter values. During image post-processing, such fits can be used empirically, to correct more than 99.5% of the radiation damage's effect on image quality. However, fits to the time series with physically reasonable parameters produce worse performance. Our results highlight the diversity of radiation environments in different parts of our Solar system, and the complexity of Low Earth Orbit in particular. Our results also motivate continued monitoring of radiation damage to currently operational spacecraft, to more reliably predict the rate of degradation in (and useful lifespan of) future missions.

• The paper shows that radiation-induced charge-transfer inefficiency in HST’s ACS/WFC varies with the approximately 11-year Solar cycle, reaching its maximum growth rate about 4.3 years before Solar maximum.
• Using more than 24 years of detector monitoring, the authors find an 18.5% modulation and show that sunspot and CME models require phenomenological or physically implausible parameters, including an 8.4-year CME delay.
• The revised electron-cloud volume model improves numerical stability for noisy, low-signal exposures, while empirical calibration and CTI correction recover more than 99.5% of radiation-related image-quality degradation.

The paper examines the temporal evolution of radiation-induced Charge Transfer Inefficiency (CTI) in the Advanced Camera for Surveys/Wide Field Channel (ACS/WFC) aboard the Hubble Space Telescope (HST), using more than 24 years of in-orbit detector monitoring. Its central result is that the rate of radiation damage varies over the approximately 11-year Solar cycle but is substantially phase-shifted relative to conventional Solar-activity proxies. The maximum CTI growth rate occurs approximately 4.3 years before the sunspot maximum, while the modulation amplitude is approximately 18.5%. The authors test whether this behavior can be explained by Galactic Cosmic Rays (GCRs), sunspots, or Coronal Mass Ejections (CMEs), and find that models capable of fitting the HST time series with high accuracy require physically implausible parameters. The paper also presents a modification to the electron-cloud volume model used in CTI correction, improving numerical stability for low-signal exposures (2608.18214).

Radiation damage and its observational signature

Displacement damage from energetic charged particles produces lattice defects in the silicon substrate of a CCD. During readout, these defects temporarily capture photoelectrons and release them after characteristic delays. The resulting deferred charge forms trails in the transfer direction, reducing photometric fidelity and perturbing source morphology, astrometry, and weak-lensing observables. Because the charge-transfer process is repeated over hundreds or thousands of pixel transfers, even a modest per-transfer inefficiency produces a measurable image-level effect.

Figure 1: CCD readout geometry and radiation-induced charge trailing in HST detectors.

The HST ACS/WFC detectors provide an unusually long baseline for studying this process. Warm pixels and other localized image features act as calibration sources: the amplitude of their trails measures the accumulated density of active charge traps. This observable is not a direct particle counter, but it is a sensitive in-orbit dosimetric proxy whose temporal behavior broadly agrees with independent indicators such as the growth of sink pixels. The paper therefore treats the detector itself as a continuously sampled radiation monitor.

The practical relevance is substantial. Existing pixel-based CTI models, calibrated using in-orbit data and progressively refined over the HST mission, can recover more than 99.5% of the image-quality degradation attributed to radiation damage. The implication is that accumulated CTI is not necessarily an irrecoverable loss for calibrated imaging: the dominant residual uncertainty lies in accurately characterizing the detector state at the epoch of each exposure.

Figure 2: HST imaging before and after CTI correction, showing removal of the radiation-induced trails.

Solar-cycle phase offset in HST degradation

The paper begins from the empirical observation that the HST CTI time series is not in phase with the sunspot cycle. The accumulated trap density is modeled as the sum of a secular GCR-like term and a Solar-modulated contribution based on the integrated sunspot number. The best-fitting sunspot model has a lag of $430^{+11}_{-5}$ days and a negative Solar coefficient. In this parameterization, increased sunspot activity reduces the inferred damage rate, consistent with the established anticorrelation between Solar modulation and GCR flux.

However, the approximately one-year lag does not explain the principal phase relationship of the degradation rate. The damage rate reaches its maximum approximately 4.3 years before Solar maximum. The negative sunspot coefficient can reproduce the broad phase because elevated Solar activity suppresses GCRs, but it does not establish that sunspots or their associated particle populations are the causal driver of the detector damage. The fitted relationship is phenomenological and conflates Solar modulation, geomagnetic transport, and the local radiation environment in Low Earth Orbit (LEO).

The relevant time series and competing fits are shown below.

Figure 3: HST trap-density evolution, Solar activity, CME events, and alternative temporal models.

The authors next test a CME-based model. CME events are represented as impulses weighted by the measured fluence of protons above 10 MeV from NOAA Geostationary Operational Environmental Satellite data. In its physically direct form, the model assumes that CME-associated particle fluence produces an immediate increase in trap density. This construction fits CCD degradation measured for Euclid and Gaia, both operating near the Sun–Earth L2 point, but provides a poor fit to HST data for all physically reasonable parameter values.

A highly accurate HST fit becomes possible only after introducing a smoothed response with a delay between CME detection and detector damage. The positive-CME model produces a lag of $3074 \pm 1$ days, approximately 8.4 years, together with a smoothing scale of $89.2 \pm 1.2$ days. The fit reproduces detailed features of the HST time series, including the reduction in the damage rate around 2025. Yet the inferred delay is physically untenable: particle fluence measured at geosynchronous orbit cannot plausibly produce displacement damage in an HST detector more than eight years later through the mechanism represented by the model.

This is the paper’s most important methodological distinction: a model can be statistically highly successful while its fitted parameters invalidate its physical interpretation. The excellent CME fit should therefore be regarded as an empirical interpolant, not as evidence that CME protons cause delayed HST damage on an eight-year timescale.

Forcing the CME coefficient to be negative yields a lag of $424.7 \pm 2.1$ days, essentially identical to the sunspot-model lag. This sign corresponds to Solar activity suppressing GCR-induced damage rather than directly increasing trap production. Nevertheless, the model fails to reproduce the observed dynamic range. In particular, it cannot simultaneously account for the steep excess damage rate around 2010 and the shallower reduction during approximately 2014–2020, even when the CME-fluence exponent is driven toward zero so that CMEs are effectively counted rather than fluence-weighted.

The comparison demonstrates that the radiation environment sampled by HST is not reducible to a single Solar proxy. LEO introduces geomagnetic shielding, trapped-particle populations, orbital inclination and altitude effects, South Atlantic Anomaly exposure, and time-dependent coupling between Solar activity and the Van Allen belts. These factors can produce temporal behavior qualitatively different from that observed at L2. The paper accordingly rejects a universal Solar-cycle transfer function for predicting detector degradation across spacecraft locations.

Empirical correction versus physical prediction

Although the physically motivated models do not explain the HST time series, the authors show that accurate image correction does not require a correct causal radiation model. A piecewise-linear empirical representation of the trap-density history provides an adequate estimate of the detector state at observed epochs and enables correction of approximately 99% of the imaging trailing; the broader CTI-correction framework achieves better than 99.5% recovery of image quality.

This separation between retrospective correction and prospective prediction is central. For archival processing, the relevant requirement is an accurate estimate of trap density, trap species, release times, cloud geometry, and detector operating conditions at the exposure date. A piecewise-linear fit can satisfy this requirement without encoding a physical radiation mechanism. For mission planning, however, the same fit has no predictive validity beyond the calibrated time interval. Extrapolating it would merely assume that the unresolved environmental drivers continue their previous piecewise behavior.

Consequently, the paper does not claim that the Solar cycle is irrelevant. Rather, it establishes that the observed HST modulation cannot be predicted reliably from sunspot counts or CME fluences alone. The implication for future missions is operational: detector degradation must be monitored in situ, rather than inferred exclusively from generic environment models or Solar indices.

Stabilizing the electron-transport model

The second contribution concerns the forward model used to simulate charge transport through a damaged CCD and invert that process during CTI correction. Such models require, at minimum, a description of the effective volume occupied by an electron cloud and prescriptions for trap capture and release.

The previous cloud-volume parameterization was a thresholded power law. It assigned zero volume below a nonnegative notch depth and became non-differentiable at the threshold. This discontinuity creates pathological behavior near the threshold, particularly in bias and dark exposures whose pixel values fluctuate around zero. Positive noise excursions can interact with traps while negative excursions are assigned no effective volume, generating asymmetrical artificial trailing.

The revised function permits a formally negative notch depth and extends the volume model to negative signal values. An exponential continuation is chosen so that the derivative remains finite and continuous at zero. This modification is not intended to imply a literal negative electron population or a directly measurable negative physical well depth. It is a regularized surrogate model designed to remain well behaved under measurement noise and during iterative inversion.

The fitted shape parameters are approximately $\beta=0.486$ for parallel transfer and $\beta=0.524$ for serial transfer. The inferred negative notch depths are approximately $-218$ and $-1407$ in the corresponding parameterization. At full well, the modeled effective volumes are approximately $45.4$ and $54.6~\mu\mathrm{m}^{3}$ for parallel and serial transport, respectively.

Figure 4: Comparison of the revised cloud-volume model with detailed TCAD simulations for parallel and serial transport.

The revised form fits detailed Silvaco TCAD simulations about as well as the earlier alternative model, while providing two practical advantages: it is defined for negative noisy pixel values, and it has a finite gradient at zero signal. The latter property stabilizes CTI correction for bias and dark exposures, where the signal distribution is concentrated near the transition point. The authors also identify a parameter degeneracy between the power-law index and notch depth when fitting warm-pixel trails. Reparameterizing the model using $3074 \pm 1$0 and $3074 \pm 1$1 produces approximately orthogonal constraints and improves numerical fitting behavior.

The model’s physical interpretation should be stated carefully. Its negative notch depth is an effective parameter introduced for regularization, not a direct measurement of detector architecture. Moreover, the TCAD comparison uses a different CCD device, so agreement validates the flexibility of the functional form rather than establishing detector-specific microscopic equivalence.

Trap-release distributions

The paper also considers whether newly generated traps should be modeled with a distribution of release times rather than discrete trap species with single characteristic time constants. At cryogenic operating temperatures, incomplete annealing can leave defects in a range of metastable configurations. If trap energy levels have an approximately Gaussian distribution, the exponential relation between release time and activation energy implies an approximately lognormal distribution of release times.

This provides a physically motivated extension of conventional CTI models. Nevertheless, the authors report no statistically significant evidence for a nonzero width of the release-time distribution in the available HST or Euclid trail-shape measurements. The result does not rule out a broadened population; it indicates that the current trail data do not constrain such broadening sufficiently to justify adding it as a required model component. The absence of detected evidence may reflect limited signal-to-noise, degeneracy with other transport parameters, or insufficiently discriminating readout configurations.

Limitations and open questions

The main limitation is causal identifiability. The HST record spans only slightly more than two Solar cycles, and the radiation environment in LEO is controlled by several coupled processes. Sunspot numbers and CME proton fluences are incomplete proxies for the particle populations responsible for displacement damage at HST’s orbital location. CME measurements from geosynchronous orbit also do not directly represent the particle spectrum incident on a detector in LEO after geomagnetic filtering and transport.

The CME model is additionally sensitive to the adopted event definition, proton-energy threshold, fluence weighting, smoothing prescription, and delay parameterization. The eight-year best-fit lag demonstrates model misspecification more directly than it demonstrates an unknown physical delay. Likewise, the empirical piecewise-linear model corrects historical observations but cannot predict future degradation.

The revised cloud-volume function contains an arbitrary transition location at zero signal, chosen for numerical stability rather than independently inferred from detector physics. Its calibration against TCAD data from a different CCD limits the strength of device-specific conclusions. Finally, the lack of statistically significant evidence for a nonzero width in the release-time distribution leaves unresolved whether the apparent discreteness of trap species is physical or simply a consequence of limited observational sensitivity.

The most specific open question is therefore how to construct a radiation-environment model that jointly incorporates Solar energetic particles, GCR modulation, trapped-belt populations, geomagnetic transport, orbital history, and detector-specific displacement-damage response while remaining predictive at HST’s LEO location. The paper also leaves open whether coordinated in-orbit measurements from multiple spacecraft can distinguish these contributions.

Conclusion

The paper establishes that HST CCD degradation is Solar-cycle dependent but markedly out of phase with sunspots and CMEs. Sunspot and CME models can produce accurate fits only by adopting either phenomenological signs or physically implausible delays, with the best positive-CME fit requiring an approximately eight-year lag. Thus, the temporal evolution of CTI in LEO cannot presently be predicted from simple Solar proxies.

At the same time, the paper demonstrates that high-fidelity retrospective correction remains possible. Empirical detector-state models, combined with physically informed CTI inversion, recover more than 99.5% of the radiation damage’s effect on image quality. The new smooth cloud-volume parameterization improves stability in low-signal regimes without claiming a unique microscopic interpretation. The resulting methodological lesson is precise: continued in-orbit calibration is sufficient for effective data restoration, but reliable forecasting of detector lifetime requires direct, sustained monitoring of radiation damage across distinct spacecraft environments (2608.18214).