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We seek to determine the mechanism of like-charge attraction by measuring thetemperature dependence of critical divalent counterion concentration($\rm{C_{c}}$) for the aggregation of fd viruses. We find that an increase intemperature causes $\rm{C_c}$ to decrease, primarily due to a decrease in thedielectric constant ($\epsilon$) of the solvent. At a constant $\epsilon$,$\rm{C_c}$ is found to increase as the temperature increases. The effects of$T$ and $\epsilon$ on $\rm {C_{c}}$ can be combined to that of one parameter:Bjerrum length ($l_{B}$). $\rm{C_{c}}$ decreases exponentially as $l_{B}$increases, suggesting that entropic effect of counterions plays an importantrole at the onset of bundle formation.Comment: 12 pages, 3 figure

Temperature Effects on Threshold Counterion Concentration to Induce Aggregation of fd Virus