Calibrating the Star Formation Rate Indicator at an Observed Frequency of 15 GHz in Star-forming Galaxies

We present a new global SFR indicator at a rest-frame frequency of 40 GHz derived using the sample of 35 star-forming galaxies with a median $z \simeq 1.65$: $\log SFR_{40GHz} \ [M\textsubscript{\(\odot\)} \; yr^{-1}] = (1.16 \pm 0.13)\log L_{40GHz} \ [W/Hz] \ - \ (24.92 \pm 2.92)$. At this frequency, the indicator probes thermal free-free emission from ionized particles in HII regions around massive short-lived stars, indicating recent SFs. We adopt the primary VLA observations at Ku-band (12-18 or 15 GHz) covering 258 arcmin$^2$ on the sky, along with photometric redshift and photometry at FUV to radio waves from the COSMOS2015. AGNs are excluded from the samples based on X-ray counterparts in the \textit{Chandra} COSMOS-Legacy survey and an IRAC AGN color-color diagram. In addition, only sources with MIR-FIR (24-500 $\mu m$) counterparts above 3 SNR are selected to guarantee the SED-fitting efficiency at the wavebands. The samples' physical characteristics (i.e., stellar mass and total IR luminosity) are retrieved from their \texttt{MAGPHYS} best-fitting SEDs. Then, we infer the samples' SFR based on $SFR_{UV}$ and $SFR_{IR}$, which are derived from rest-frame 150nm and total IR luminosity, respectively. We expect to use the combination of both dust-obscured and -unobscured SFR tracers to recover total SFR values. However, we found that the $SFR_{IR}$ of most samples dominate over $SFR_{UV}$ with the factor $\gtrsim$ 100, indicating our samples are dusty star-forming. Thus, only $SFR_{IR}$ are used in further analyses in this work. After that, we exploit the Orthogonal Distance Regression (ODR) method to derive the linear trend between logarithmic $SFR_{IR}$ and Ku-band luminosity, in other words, the ultimate SFR indicator, as given in the beginning. However, the trend experiences a large scatter with a reduced $\chi^2$ value of 26.35. The causes of the scatter might be from small-sized and pre-selected samples used to calibrate it. Thus, it requires revision by using larger and unbiased radio catalogs. Finally, we examine the morphological characteristics of the samples using their i-band (rest-frame UV) cutouts from \textit{HST} and CFHT, as well as available \textit{JWST}/F444W (rest-frame optical to NIR) ones. We found that most of the SBs are mergers, while all the nearby MSs are regular spiral galaxies.