Optical Spectral Variations of a Large Sample of Fermi Blazars

We have investigated the optical spectral behavior of a large sample of Fermi blazars (40 FSRQs and 13 BL Lacs), and found two new universal optical spectral behaviors. In the low state the optical spectrum gradually becomes softer (steeper) or harder (flatter) but more and more slowly when the brightness increases, and then tends to stable in the high state, which are briefly named the redder-stable-when-brighter (RSWB) and bluer-stable-when-brighter (BSWB) behaviors, respectively. 34 FSRQs and 7 BL Lacs exhibit clear RSWB behavior, and 2 FSRQs and 5 BL Lacs show distinct BSWB behavior, which mean that FSRQs favor more RSWB than BSWB behavior, while BL Lacs have no clear preference among both behaviors. We have put forward a unified nonlinear formula to quantitatively characterize the optical spectral behaviors of FSRQs and BL Lacs, which can fit both kinds of behaviors very well. We argue that the RSWB and BSWB behaviors originate from the same mechanism, and they are the universal optical spectral behaviors for blazars. The frequently observed redder-when-brighter (RWB) and bluer-when-brighter (BWB) trends can be considered to be the approximations of the behaviors of RSWB and BSWB, respectively. The rarely observed stable-when-brighter (SWB) trend can also be viewed as an approximation or a special case of the RSWB or BSWB behavior. We have developed a model with two constant-spectral-index components which can not only explain well both two kinds of optical spectral behaviors, but also successfully interpret the differential behaviors between FSRQs and BL Lacs.