**RVFC: Radial Velocity Follow-up Calculator**

The RVFC is a web-based tool used to calculate the number of radial velocity measurements required to detect the semi-amplitude of a transiting exoplanet at a desired detection significance. These calculations can be performed in the general case of correlated RV noise and in the white noise limit which is less computationally expensive but is often not an accurate approximation to real empirical RV time-series. Calculations of the number of RV measurements―and total observing time―are useful for planning RV follow-up observations and how to distribute observing time among a set of targeted transiting planetary systems. The inherent assumptions in the RVFC and instructions on its use are provided below. Additionally, the model and calculator are described in detail in this paper.

The **python-based backend of the RVFC** is also available here for those who prefer to run their calculations locally.

**v1.0***2018-07-01:*initial version of the RVFC.

- the planet's orbital solution is well-approximated as circular.
- the value of the transiting planet's orbital period
*P*and time of mid-transit*T*_{0}are known to ultra-high precision compared to the RV semi-amplitude*K*such that correlations between the measured values of*P*,*T*_{0}, and*K*are unimportant.

● When calculating the number of RV measurements with the RVFC―when the RV noise model is white―we further assume that:

- the window function of the RV time-series is (approximately) sampled uniformly over the planet's full orbital phase.
- there is a characteristic scalar RV uncertainty equal to the rms of the RV residuals following the removal of planetary signals.

- 1) after selecting
*option 1*the user will be redirected to a page from which they must select one of two possible suboptions (i.e. 1.1 or 1.2). The difference between these options are related to the user's a-priori knowledge of other additive RV noise sources such as from stellar activity and from additional planets in the system. - 2) after selecting a suboption, the submission page with a set of empty fields will be displyed for the user to fill. Most fields are required to successfully run the RVFC and are highlighted with an "*". The exception being the planetary mass which if left blank, the planet's mass will be estimated from its radius using an empirically-derived mass-radius relation.
- 3) the specification of the spectrograph parameters can be done individually by hand or alternatively, any of a set of spectrographs with default parameter values can be resolved from the corresponding drop-down menu. The default values are not fixed and may be modified before proceeding if desired.
- 4) Note on the stellar magnitude: the passband corresponding to the input stellar magnitude is determined by the
wavelength domain of the spectrograph specified by the user. This wavelength range
*must*span either the*V*or*J*central wavelengths (i.e. 555 and 1250 nm respectively). - 5) once all of the required fields are filled the RVFC can be run via the submission button at the bottom of the form. If any required fields are missing or invalid then the submission page will be reloaded with warning messages indicating which fields need to be modified before resubmitting the RVFC calculation.

- 1) after selecting
*option 2*the user will be redirected to a page from which they must select one of three possible suboptions (i.e. 1.1, 1.2 or 1.3). The difference between these options are related to the user's a-priori knowledge of additive RV noise sources—such as from stellar activity or from additional planets in the system—or the effective RV rms. - 2) after selecting a suboption, the submission page with a set of empty fields will be displyed for the user to fill. Most fields are required to successfully run the RVFC and are highlighted with an "*". The exception being the planetary mass which if left blank, the planet's mass will be estimated from its radius using an empirically-derived mass-radius relation.
- 3) once all of the required fields are filled the RVFC can be run via the submission button at the bottom of the form. If any required fields are missing or invalid then the submission page will be reloaded with warning messages indicating which fields need to be modified before resubmitting the RVFC calculation.

● The various sources of additive RV noise included in the RVFC calculations include the photon-noise limited RV precision, stellar activity, RV rms from additional planets in the system, and a systematic uncertainty from the RV noise floor. These parameters can be set explicitly by the user or sampled from empirical distributions depending on which RVFC suboption is selected.

● If the RVFC is run in the presence of correlated RV noise, it is recommended that the number of Gaussian process (GP) trials be set to ≳ 10 as these results are sensitive to the window function of the observations which are not fixed and should be sampled. Note however that more GP trials will result in a longer wall time for the calculation. When more than one GP trial is submitted the median and median absolute deviation of the results over the multiple GP trials are returned. Alternatively, the number of GP trials can be set to zero to only consider the white noise calculation.

● The window functions adopted when using the RVFC in the presence of correlated noise (i.e. number of GP trials > 0) are uniformly sampled in time. The ability to upload custom window functions is intended for future versions of the RVFC.

● Questions and comments about the RVFC (including any bug encounters) should be sent to cloutier@astro.utoronto.ca.