  We have measured and characterized the thermal crosstalk in two different
arrays of transition-edge sensor (TES) X-ray micro-calorimeters with
frequency-domain multiplexing (FDM) readout. The TES arrays are fabricated at
SRON and are a 8$\times$8 and a 32$\times$32 "kilo-pixel" uniform array. The
amount of crosstalk is evaluated as the ratio between the averaged crosstalk
signal and the X-ray pulse amplitudes. The crosstalk ratios (CR) for our
detectors are compliant with the requirements for future X-ray space missions,
such as Athena X-IFU (CR$< 10^{-3}$ for first-neighbour pixels): we measured a
nearest-neighbour thermal crosstalk ratio at a level of $10^{-4}$, with a
highest crosstalk ratio of $4\times 10^{-4}$ for the kilo-pixel array (worst
case, center of array) and $1\times 10^{-4}$ for the 8$\times$8 array, with a
margin of improvement achievable by optimizing the Cu metallization and the
width of the Si supporting structures (muntins) in the backside of the TES
array chip. Based on the measured crosstalk ratios, we have estimated the
impact on the spectral resolution by means of noise equivalent power (NEP)
considerations and a Monte Carlo simulation, finding an average degradation in
quadrature of less than 40~meV, compliant with the < 0.2~eV requirement for
Athena X-IFU.
