  Super-luminous supernovae (SLSNe) are tremendously luminous explosions whose
power sources and progenitors are highly debated. Broad-lined SNe Ic (SNe
Ic-bl) are the only type of SNe that are connected with long-duration gamma ray
bursts (GRBs). Studying the spectral similarity and difference between the
populations of hydrogen-poor SLSNe (SLSNe Ic) and of hydrogen-poor
stripped-envelope core-collapse SNe, in particular SNe Ic and SNe Ic-bl, can
provide crucial observations to test predictions of theories based on various
power source models and progenitor models. In this paper, we collected all of
the published optical spectra of 32 SLSNe Ic, 21 SNe Ic-bl, as well as 17 SNe
Ic, quantified their spectral features, constructed average spectra, and
compared them in a systematic way using new tools we have developed. We find
that SLSNe Ic and SNe Ic-bl, including those connected with GRBs, have
comparable widths for their spectral features and average absorption velocities
at all phases. Thus, our findings strengthen the connection between SLSNe Ic
and GRBs. In particular, SLSNe Ic have average \FeII absorption velocities of
$-15,000 +/- 2,600$ \kms~at 10 days after peak, which are higher than those of
SNe Ic by $\sim7,000$ \kms~on average. SLSNe Ic also have significantly broader
\FeII lines than SNe Ic. Moreover, we find that such high absorption and width
velocities of SLSNe Ic may be hard to explain by the interaction model, and
none of 13 SLSNe Ic with measured absorption velocities spanning over 10 days
has a convincing flat velocity-evolution, which is inconsistent with the
magnetar model in one dimension. Lastly, we compare SN 2011kl, the first SN
connected with an ultra-long GRB, with the mean spectrum of SLSNe Ic and of SNe
Ic-bl.
