Discrepancy between the uncertainties in Pantheon+SH0ES.dat and the diagonal of the covariance in Pantheon+SH0ES_STAT+SYS.cov

[wxxwwxxw-sketch]

Dear all,

From what I learned from the README in "Pantheon+_Data/4_DISTANCES_AND_COVAR/", the column MU_SH0ES_ERR_DIAG in the file "Pantheon+SH0ES.dat" should correspond to the square root of the diagonal of the covariance in the .cov file. However, as one can easily check, this is not the case. For example, from the first row of data in the .dat, at zHD=0.00122, MU_SH0ES_ERR_DIAG is 1.51645, whereas the first diagonal element in the .cov file is 0.03177108, which is obviously not the square of 1.51645. This .cov file includes the full systematic and statistical uncertainties, so there can be no other sources to explain this discrepancy. Could anyone please let me know if I misunderstand something?

Moreover, since the uncertainties of the apparent magnitude $m_B$ is related to the distance modulus $\mu$ by a simple relation $m_B-\mu=-19.253$, $m_B$ and $\mu$ should have the same covariance. But the README file says that the file "Pantheon+SH0ES_STAT+SYS.cov" contains Cepheid host covariance in addition to the SNe-only covariance. (Indeed, one can see from the .dat file that the columns m_b_corr_err_DIAG and MU_SH0ES_ERR_DIAG do differ by a tiny amount .) Does this imply that one should not use this .cov file when applying the SNe-only data m_B to constrain cosmological parameters?

Thanks in advance!

Best regards,
wx

[wxxwwxxw-sketch]

Oh, I just found that the same question has been raised here before,
#6
That issue has been closed, but the question there was essentially not fully answered. So, I am sorry to ask an old question again, but I am still looking forward to a full answer.