  We perform a detailed investigation on the cosmological constraints on the
holographic dark energy (HDE) model by using the Planck data. HDE can provide a
good fit to Planck high-l (l>40) temperature power spectrum, while the
discrepancy at l=20-40 found in LCDM remains unsolved in HDE. The Planck data
alone can lead to strong and reliable constraint on the HDE parameter c. At 68%
CL, we get c=0.508+-0.207 with Planck+WP+lensing, favoring the present phantom
HDE at > 2sigma CL. Comparably, by using WMAP9 alone we cannot get interesting
constraint on c. By combining Planck+WP with the BAO measurements from
6dFGS+SDSS DR7(R)+BOSS DR9, the H0 measurement from HST, the SNLS3 and Union2.1
SNIa data sets, we get 68% CL constraints c=0.484+-0.070, 0.474+-0.049,
0.594+-0.051 and 0.642+-0.066. Constraints can be improved by 2%-15% if we
further add the Planck lensing data. Compared with the WMAP9 results, the
Planck results reduce the error by 30%-60%, and prefer a phantom-like HDE at
higher CL. We find no evident tension between Planck and BAO/HST. Especially,
the strong correlation between Omegam h^3 and dark energy parameters is helpful
in relieving the tension between Planck and HST. The residual
chi^2_{Planck+WP+HST}-chi^2_{Planck+WP} is 7.8 in LCDM, and is reduced to 1.0
or 0.3 if we switch dark energy to the w model or the holographic model. We
find SNLS3 is in tension with all other data sets; for Planck+WP, WMAP9 and
BAO+HST, the corresponding Delta chi^2 is 6.4, 3.5 and 4.1, respectively.
Comparably, Union2.1 is consistent with these data sets, but the combination
Union2.1+BAO+HST is in tension with Planck+WP+lensing, corresponding to a Delta
chi^2 8.6 (1.4% probability). Thus, it is not reasonable to perform an
all-combined (CMB+SNIa+BAO+HST) analysis for HDE when using the Planck data.
Our tightest self-consistent constraint is c=0.495+-0.039 obtained from
Planck+WP+BAO+HST+lensing.

Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory