Using the absolute ages of passively evolving galaxies observed at different redshifts , one can obtain the differential ages , the derivative of redshift z with respect to the cosmic time t ( i.e . { d } z / { d } t ) .
Thus , the Hubble parameter H ( z ) can be measured through the relation H ( z ) = - ( { d } z / { d } t ) / ( 1 + z ) .
By comparing the measured Hubble parameter at different redshifts with the theoretical one containing free cosmological parameters , one can constrain current cosmological models .
In this paper , we use this method to present the constraint on a spatially flat Friedmann-Robert-Walker Universe with a matter component and a holographic dark energy component , in which the parameter c plays a significant role in this dark energy model .
Firstly we consider three fixed values of c =0.6 , 1.0 and 1.4 in the fitting of data .
If we set c free , the best fitting values are c = 0.26 , \Omega _ { m 0 } = 0.16 , h = 0.9998 .
It is shown that the holographic dark energy behaves like a quintom-type at the 1 \sigma level .
This result is consistent with some other independent cosmological constrains , which imply that c < 1.0 is favored .
We also test the results derived from the differential ages using another independent method based on the lookback time to galaxy clusters and the age of the universe .
It shows that our results are reliable .