The line shapes of multiplet components of the complex x-ray photoemission spectra of the Ta 4f core levels in 1T-and 4Hb-TaS2 are shown to have different asymmetries associated with the charge density wave induced differences in the densities of states at distinct Ta sites which produce site specific local screening of the photohole. This underlines an important general effect in the interpretation of line shapes in x-ray photoemission. PACS numbers: 79.60.Jv, 79.60.Bm The screening of the photohole produced in x-ray core level photoemission (XPS) from a metal produces an inelastic tail to the low kinetic energy (KE) side of the XPS line. The resulting asymmetry depends on the excitations available to the screening carriers, i.e. , on the joint density of states (JDOS) near the Fermi energy (EF) [1]. A charge density wave (CDW) splits XPS lines because of the distinct chemical shifts for atomic sites with different local electron densities [2]: We show that the line shapes of the resulting multiplet components also differ because the local densities of states (LDOSs) are also modified by the CDW, and that detailed line shape fitting for several polytypes of TaS2 extracts parameters related to the electronic structure near specific atomic sites in the CDW supercell.TaS2 has hexagonal sheets of Ta atoms sandwiched between similar S sheets to form layers; the Ta coordination by the S atoms is either trigonal prismatic or octahedral.The 2H and 1T polytypes have unit cells with two trigonal prismatic and one octahedral layer, respectively, while 4Hb-TaS 2 has four, alternating between "1T"-and "2H"-like. Their electronic structures are similar; above the S 3p valence bands lies the Ta d band holding one electron per formula suit, and resulting in metallic properties. But in detail these d bands, and therefore their CDW behavior, differ; a quasicommensurate inplane~13 X~13 CDW exists for 1T-TaS~even at room temperature [3], at which 2H-TaS2 has no CDW. Below 180 K, 1T-TaSz adopts the 1T3 phase studied here, with a commensurate~13 &&~13 CDW with three distinct Ta sites -a, with one atom, and b and c with six atoms each -with different local charge densities. 4Hq-TaS2 shows behavior characteristic of both layer types; below 315 K it exhibits a~13 X~13 CDW associated with its 1T layers and below 22 K a 3 X 3 CDW characteristic of the 2H polytype [3,4]. Empirical arguments [2], and scanning tunneling microscopy (STM) [5], suggested a CDW amplitude in 1T3-TaS2 of a considerable fraction of an electron, though another [6] based on chemical shifts and a self-consistent calculation suggested 0.05 electron. A simple linear combination of atomic orbitals (LCAO) calculation for 1T3-TaS2, explicitly including the effects of A A2 P",(E) =, B(E -e") + 1 -,B(E),where A is the appropriate matrix element; convolving these for multiple excitations, and assuming A is small, gives the overall probability of energy loss E, P(E)~A~( e" ' -1) e ' 'exp g dt.-jL V P, V the CDW on the Ta d bands, shows that the LDOS is different for each...