Clique spectral extremal problem on disjoint color-critical graphs

For a given graph $F$, a graph $G$ is called $F$-free if it does not contain $F$ as a subgraph.

A graph is color-critical if deleting one of its edges decreases its chromatic number.

Let $F_1, F_2, \cdots, F_t$ be $t$ disjoint color-critical graphs with chromatic number $r+1$.

For $2 \leq s \leq r$ and sufficiently large $n$, we determine the unique extremal graph with the maximum $s$-clique spectral radius among all $n$-vertex $\bigcup_{i=1}^t F_i$-free graphs.