1 2009 Fermi Symposium, Washington, D.C., Nov. 2-5 A Model of the Spectral Evolution of Pulsar Wind Nebulae S. J. Tanaka and F. Takahara Department of Earth and Space Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan Recent observations suggest that many old pulsar wind nebulae (PWNe) are bright TeV γ -ray sources without a strong X-ray counterpart. In this paper, we study the spectral evolution of PWNe taking into account the energy which was injected when they were young for old PWNe. We model the evolution of the magnetic field and solve for the particle distribution inside a uniformly expanding PWN. The model is calibrated by fitting the calculated spectrum to the observations of the Crab Nebula at an age of a thousand years. We find that only a small fraction of the injected energy from the Crab Pulsar goes to the magnetic field, consistent with previous studies. The spectral evolution model of the Crab Nebula shows that the flux ratio of TeV γ -rays to X-rays increases with time, which implies that old PWNe are faint at X-rays, but not at TeV γ -rays. The increase of this ratio is primarily because the magnetic field decreases with time and is not because the X-ray emitting particles are cooled more rapidly than the TeV γ -ray emitting particles. Our spectral evolution model matches the observed rate of the radio flux decrease of the Crab Nebula. to the spectral evolution of PWNe. For example, de Jager & Djannati-Ata¨ı (2008) [3] discussed the pos- sibility that the aged PWNe can be seen as the TeV γ -ray sources without a strong X-ray counterpart. A pulsar releases its rotational energy as a relativis- tic magnetized outflow called a pulsar wind. The pul- sar wind collides with surrounding supernova ejecta, forms the termination shock, and creates a PWN [9]. The acceleration of the pulsar wind particles occurs at the termination shock and the PWN consists of the magnetic field and the ultrarelativistic particles [10, 12]. Such a created PWN emits photons ranging from radio to TeV γ -rays via the synchrotron radi- ation and the inverse Compton scattering. Current status of theoretical models as well as observational confrontations is reviewed by Gaensler & Slane (2006) [8]. In this paper, we revisit a spectral evolution model of PWNe. Although several spectral evolution mod- els of PWNe have been studied [4, 7, 17], several is- sues still remain to be further clarified. In our model, the PWN is simply treated as an expanding uniform sphere. We do not take into account effects of the spatial structure of the PWN, since it is somewhat costly and too detailed to see the whole spectrum. The energy inside the PWN is injected from the pul- sar spin-down energy, which is distributed between the relativistic particles and the magnetic field with a constant ratio. Our simple model can describe the observed basic features. We study the spectral evolution of the Crab Neb- ula for the first application of our model. The Crab Nebula can be used as a calibrator of our model when it will be applied to other PWNe in future. In section II, we describe our model of the PWN evolution. In section III, we apply this model to the Crab Nebula. In section IV, discussions and conclusions are made. The Crab Nebula is one of the best studied PWN at almost all observable wavelengths including its cen- tral pulsar, called the Crab Pulsar. Kennel & Coroniti (1984) [9] studied the spatial structure of the Crab Nebula, assuming that it is a steady state object (KC model). They found that the magnetization parame- ter σ , the ratio of the electromagnetic energy flux to the particle energy flux just upstream the termination shock of the pulsar wind, must be as small as 0.003 to explain the observed dynamical properties of the Crab Nebula. Atoyan & Aharonian (1996) [1] succeeded to reconstruct the current observed broadband spectrum of the Crab Nebula by the use of the KC model. The KC model is not fit to consider the evolution because it is a steady state model. However, it is very important to consider the spectral evolution of the Crab Nebula. We need to consider the spectral evolu- tion to explain the flux decrease rate of the Crab Neb- ula at radio and optical wavelengths [2, 13, 15]. More- over, we need to understand the spectral evolution of PWNe. Recent observations found many PWNe which have a variety of the characteristics, such as the ages, the expansion velocities, the morphologies, and the spectra of PWNe. This variety must be related In this paper, we assume that the PWN is a uniform sphere expanding at a constant velocity v$_{PWN}$ . The assumption of a constant velocity v$_{PWN}$ is the easiest way to take into account the expansion of the PWN, although the real behavior of the expansion velocity could be more complex as the work made by Gelfand et al. (2009) [7]. We consider that the age of the PWN is younger than 10kyr in this paper and that the constant velocity v$_{PWN}$ would be a good assumption eConf C091122 A. Energy Injection II. THE MODEL I. INTRODUCTION arXiv:1001.2360v1 [astro-ph.HE] 14 Jan 2010