Long-term Variability of H$_2$CO Masers in Star-forming Regions

We present results of a multi-epoch monitoring program on variability of 6$\,$cm formaldehyde (H$_2$CO) masers in the massive star forming region NGC$\,$7538$\,$IRS$\,$1 from 2008 to 2015 conducted with the GBT, WSRT, and VLA. We found that the similar variability behaviors of the two formaldehyde maser velocity components in NGC$\,$7538$\,$IRS$\,$1 (which was pointed out by Araya and collaborators in 2007) have continued. The possibility that the variability is caused by changes in the maser amplification path in regions with similar morphology and kinematics is discussed. We also observed 12.2$\,$GHz methanol and 22.2$\,$GHz water masers toward NGC$\,$7538$\,$IRS$\,$1. The brightest maser components of CH$_3$OH and H$_2$O species show a decrease in flux density as a function of time. The brightest H$_2$CO maser component also shows a decrease in flux density and has a similar LSR velocity to the brightest H$_2$O and 12.2$\,$GHz CH$_3$OH masers. The line parameters of radio recombination lines and the 20.17 and 20.97$\,$GHz CH$_3$OH transitions in NGC$\,$7538$\,$IRS$\,$1 are also reported. In addition, we observed five other 6$\,$cm formaldehyde maser regions. We found no evidence of significant variability of the 6$\,$cm masers in these regions with respect to previous observations, the only possible exception being the maser in G29.96$-$0.02. All six sources were also observed in the H$_2^{13}$CO isotopologue transition of the 6$\,$cm H$_2$CO line; H$_2^{13}$CO absorption was detected in five of the sources. Estimated column density ratios [H$_2^{12}$CO]/[H$_2^{13}$CO] are reported.