Hello! I am writing to you to ask for some clarification in your documentation on how you derive your expression for maximum orbital frequency. I am using this code to search for giant planets around red clump stars, and the minimum period I calculate is very different than what TLS algorithm is using to search for transits.
In your paper, you say that the most short- period (high-frequency) circumstellar orbit is given by
$$f_{max} = \frac{\sqrt{GM_{s}/(3R_{s}})^{3}}{2\pi}$$
where the $3R_{s}$ term is calculated from the Roche limit, assuming a pessimistic density of $\rho_{p} = 1 g/cm^{3}$. I do not see a derivation for this formula in your paper, but I assume you're using Kepler's 3rd law
$$f_{max} = 1/P = \frac{\sqrt{GM_{s}/(a})^{3}}{2\pi}$$
And you are using the roche limit to calculate the semi major axis. For a rigid transiting body, the roche limit is given by,
$$a = R_{s} (2 \frac{\rho_{s}}{\rho_{p}})^{1/3}.$$
Or, for a fluid transiting body, the roche limit is given by,
$$a \approx 2.44R_{s} (\frac{\rho_{s}}{\rho_{p}})^{1/3}.$$
It says that you are assuming $\rho_{p} = 1 g/cm^{3}$, but I do not see any assumption about $\rho_{s}$. Now, if use this assumption of planet density and I plug in my value for a typical density of a RC star (0.002 $g/cm^{3}$), I get
$$a^{3} = 0.004 R_{s}^{3}$$
for a rigid body and
$$a^{3} = 0.03 R_{s}^{3}$$
These are both extremely different from the value than the $a^{3} = (3R_{s})^3$ from your paper. Are you inputing a typical density for a solar mass star (~1.4 $g/cm^{3}$ for the sun)? Because that would produce an $a^{3}$ term that is roughly $(3R_{s})^3$.
I don't see anything in the paper that makes this assumption, so I could be misinterpreting something, but this formula is restricting the period range that TLS searches and I believe shorter periods are physically possible.
Please let me know if this makes sense. Thank you so much!
Hello! I am writing to you to ask for some clarification in your documentation on how you derive your expression for maximum orbital frequency. I am using this code to search for giant planets around red clump stars, and the minimum period I calculate is very different than what TLS algorithm is using to search for transits.
In your paper, you say that the most short- period (high-frequency) circumstellar orbit is given by
where the$3R_{s}$ term is calculated from the Roche limit, assuming a pessimistic density of $\rho_{p} = 1 g/cm^{3}$ . I do not see a derivation for this formula in your paper, but I assume you're using Kepler's 3rd law
And you are using the roche limit to calculate the semi major axis. For a rigid transiting body, the roche limit is given by,
Or, for a fluid transiting body, the roche limit is given by,
It says that you are assuming$\rho_{p} = 1 g/cm^{3}$ , but I do not see any assumption about $\rho_{s}$ . Now, if use this assumption of planet density and I plug in my value for a typical density of a RC star (0.002 $g/cm^{3}$ ), I get
for a rigid body and
These are both extremely different from the value than the$a^{3} = (3R_{s})^3$ from your paper. Are you inputing a typical density for a solar mass star (~1.4 $g/cm^{3}$ for the sun)? Because that would produce an $a^{3}$ term that is roughly $(3R_{s})^3$ .
I don't see anything in the paper that makes this assumption, so I could be misinterpreting something, but this formula is restricting the period range that TLS searches and I believe shorter periods are physically possible.
Please let me know if this makes sense. Thank you so much!