SARAS 2 constraints on global 21-cm signals from the Epoch of
  Reionization
  Spectral distortions in the cosmic microwave background over the 40--200~MHz
band are imprinted by neutral hydrogen in the intergalactic medium prior to the
end of reionization. This signal, produced in the redshift range $z = 6-34$ at
the rest frame wavelength of 21 cm, has not been detected yet; and poor
understanding of high redshift astrophysics results in a large uncertainty in
the expected spectrum. The SARAS~2 radiometer was purposely designed to detect
the sky-averaged 21-cm signal. The instrument, deployed at the Timbaktu
Collective (Southern India) in April--June 2017, collected 63~hr of science
data, which were examined for the presence of the cosmological 21-cm signal. In
our previous work the first-light data from SARAS~2 radiometer were analyzed
with Bayesian likelihood-ratio tests using $264$ plausible astrophysical
scenarios. In this paper we re-examine the data using an improved analysis
based on the frequentist approach and forward modeling. We show that SARAS~2
data rejects 27 models, out of which 25 are rejected at a significance
$>5\sigma$. All the rejected models share the scenario of inefficient heating
of the primordial gas by the first population of X-ray sources along with rapid
reionization.
