We present analysis of multiple Chandra and XMM-Newton spectra, separated by 9-19 years, of four of the youngest central compact objects (CCOs) with ages < 2500 yr: CXOU J232327.9+584842 (Cassiopeia A), CXOU J160103.1-513353 (G330.2+1.0), 1WGA J1713.4-3949 (G347.3-0.5), and XMMU J172054.5-372652 (G350.1-0.3). By fitting these spectra with thermal models, we attempt to constrain each CCOs long-term cooling rate, composition, and magnetic field. For the CCO in Cassiopeia A, 14 measurements over 19 years indicate a decreasing temperature at a ten-year rate of 2.2+/-0.2 or 2.8+/-0.3 percent (1sigma error) for a constant or changing X-ray absorption, respectively. We obtain cooling rate upper limits of 17 percent for CXOU J160103.1-513353 and 6 percent for XMMU J172054.5-372652. For the oldest CCO, 1WGA J1713.4-3949, its temperature seems to have increased by 4+/-2 percent over a ten year period. Assuming each CCOs preferred distance and an emission area that is a large fraction of the total stellar surface, a non-magnetic carbon atmosphere spectrum is a good fit to spectra of all four CCOs. If distances are larger and emission areas are somewhat smaller, then equally good spectral fits are obtained using a hydrogen atmosphere with B <= 7x10^10 G or B >= 10^12 G for CXOU J160103.1-513353, B <= 10^10 G or B >= 10^12 G for XMMU J172054.5-372652, and non-magnetic hydrogen atmosphere for 1WGA J1713.4-3949. In a unified picture of CCO evolution, our results suggest most CCOs, and hence a sizable fraction of young neutron stars, have a surface magnetic field that is low early in their life but builds up over several thousand years.
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