[Paper Review] Phases of Swift X-ray Afterglows

A. Panaitescu|arXiv (Cornell University)|Jul 17, 2006

Gamma-ray bursts and supernovae3 citations

TL;DR

This paper identifies four distinct decay phases in Swift X-ray afterglows, attributing the early fast decay to internal shocks and the subsequent slower phases to forward shock emission in a circumburst medium. It finds that energy injection into the forward shock and a wind-like ambient medium ($n \propto r^{-2}$) with evolving microphysical parameters best explain the observed light curves, particularly the persistent optical decay after energy injection ends.

ABSTRACT

The X-ray afterglows observed by Swift exhibit rich light-curves, with four phases of different decay rate. The temporal and spectral properties for a set of 47 bursts are used to identify the mechanisms which can explain these four phases. The early, fast-decaying phase can be attributed to the same mechanism which generated the burst emission (internal shocks in a relativistic outflow), while the following phases of slower decay can be identified with synchrotron emission from the forward shock sweeping the circumburst medium. Most likely, the phase of slowest decay is due to a continuous energy injection in the forward shock. That the optical power-law decay continues unabated after the end of energy injection requires an ambient medium with a wind-like density structure (n propto r^{-2}) and forward shock microphysical parameters that change with the shock's Lorentz factor. A later break of the X-ray light-curve can be attributed to a collimated outflow whose boundary becomes visible to the observer (a jet) but the optical and X-ray decays are not always consistent with the standard jet model expectations.

Motivation & Objective

• To identify and characterize the four distinct temporal decay phases observed in Swift X-ray afterglows.
• To determine the physical mechanisms responsible for each phase, particularly the origin of the slowest decay phase.
• To assess whether the standard forward-shock model with constant microphysical parameters can explain the data, or if modifications like energy injection or structured outflows are required.
• To investigate the consistency of optical and X-ray light-curve breaks with the standard jet model, especially in cases where breaks are chromatic or achromatic.
• To explore the implications of observed light-curve behavior for the circumburst medium density profile and the evolution of shock microphysical parameters.

Proposed method

• Analyzes X-ray light-curves and spectral slopes from a sample of 47 Swift afterglows observed up to October 2005.
• Uses power-law fits to identify four distinct decay phases: fast-decay, slow-decay, pre-jet-break, and post-jet-break.
• Compares observed decay indices ($\alpha_x$) and spectral slopes ($\beta_x$) with predictions from the standard forward-shock model and modified models including energy injection and structured outflows.
• Applies the jet model with lateral spreading to interpret post-jet-break behavior, testing for achromatic breaks.
• Evaluates the consistency of optical and X-ray decays with the standard jet model, particularly in cases where optical decay is slower than predicted.
• Derives constraints on microphysical parameter evolution using the requirement that the optical power-law decay continues unabated after energy injection ends, leading to a condition on the electron energy fraction evolution (equation 9).

Experimental results

Research questions

• RQ1 What physical mechanisms explain the four distinct decay phases observed in Swift X-ray afterglows?
• RQ2 Why does the optical light curve continue to decay as a power law after the end of energy injection, and what does this imply about the circumburst medium?
• RQ3 How can the absence of an optical break at the time of a chromatic X-ray light-curve break be explained within the forward-shock model?
• RQ4 To what extent do the observed X-ray and optical light-curve breaks in GRB afterglows conform to the predictions of the standard jet model?
• RQ5 What constraints do the observed light-curve properties place on the evolution of microphysical parameters in the forward shock?

Key findings

• The early fast-decay phase ($\overline{\alpha_{x1}} = 1.0 \pm 0.5$) is attributed to internal shocks in the relativistic outflow, consistent with burst emission mechanisms.
• The slow-decay phase ($\overline{\alpha_{x2}} = 0.6 \pm 0.3$) is best explained by continuous energy injection into the forward shock, requiring a cumulative energy input scaling as $\Gamma^{-1}$ to $\Gamma^{-3}$ down to $\Gamma_{\text{break}} = 50 \pm 25$.
• The pre-jet-break phase ($\overline{\alpha_{x3}} = 1.25 \pm 0.25$) is consistent with the standard forward-shock model only if microphysical parameters evolve with shock Lorentz factor, particularly in a wind-like medium ($n \propto r^{-2}$).
• The absence of an optical break at the time of a chromatic X-ray break implies evolving microphysical parameters; a sudden change in these parameters lacks physical motivation, favoring a dynamic change in shock energy input.
• The post-jet-break phase is consistent with the standard jet model, but the slow post-break optical decay in GRBs 050525A and 010222 cannot be explained by constant microphysical parameters, requiring evolving parameters that satisfy equation (9).
• The fraction of shock energy imparted to electrons is a factor of 2–6 higher during the burst than at the end of the slow-decay phase, which may explain the high GRB efficiency (10%–90%).