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Add 03/03/22 The r_lim estimation below (using the 3\sigma_b) makes little sense unless the \sigma_b is very small.
A method to estimate the r_lim using the 2-p King equation:
Fit the 2-parameter King profile (r_t=inf) using the RDP. This estimates te rc but also the f_0
Integrate the result, subtracting the integral of the field density
Select the radius associated to ~95% of the area
The f_0 value can be used in the estimation of the r_t later on.
There's also an equation to estimate a r_lim value that I found in Bisht et al. (2020).
(f_bg is f_b but the f_b to the right is f(r))
This article says that this definition is taken from Bukowiecki et al. (2011), but it is not explained where it comes from. This last article mentions Peterson and King (1975) where the definition if the limiting radius is given as:
The limiting radius can be plausibly regarded as a real physical limit, beyond which the cluster cannot hold stars against the tidal force of the Milky Way. Again we define limiting radius operationally by means of the curves given in Paper III
The r_lim parameter can be obtained equating f(r) = f_b + 3*\sigma_b and solving for r.
Paper III (King 1966) and equates this "limiting radius" with the usual tidal radius.
In Maurya & Gour (2020) the r_lim is also used. It is obtained simply by assigning a density value at the position where the radius should be, and solving the equation. Thus the r_lim is an approximation to the tidal radius. The position where the radius "should be" is taken to be f_b+\sigma_b:
The text was updated successfully, but these errors were encountered:
Add 03/03/22 The
r_lim
estimation below (using the3\sigma_b
) makes little sense unless the\sigma_b
is very small.A method to estimate the
r_lim
using the 2-p King equation:r_t=inf
) using the RDP. This estimates terc
but also thef_0
The
f_0
value can be used in the estimation of ther_t
later on.There's also an equation to estimate a
r_lim
value that I found in Bisht et al. (2020).(
f_bg
isf_b
but thef_b
to the right isf(r)
)This article says that this definition is taken from Bukowiecki et al. (2011), but it is not explained where it comes from. This last article mentions Peterson and King (1975) where the definition if the limiting radius is given as:
The
r_lim
parameter can be obtained equatingf(r) = f_b + 3*\sigma_b
and solving forr
.Paper III (King 1966) and equates this "limiting radius" with the usual tidal radius.
In Maurya & Gour (2020) the
r_lim
is also used. It is obtained simply by assigning a density value at the position where the radius should be, and solving the equation. Thus ther_lim
is an approximation to the tidal radius. The position where the radius "should be" is taken to bef_b+\sigma_b
:The text was updated successfully, but these errors were encountered: