ModelCategories.md

Back to Modeling run

Model categories

In the current version, RTModel fits 7 different model categories by default. Each of them has a speficic label with two characters. This table summarizes the main information

Label	Model	Number of parameters
PS	Single-lens-single-source	4
PX	Single-lens-single-source with parallax	6
BS	Single-lens-binary-source	7
BO	Single-lens-binary-source with xallarap	10
LS	Binary-lens-single-source	7
LX	Binary-lens-single-source with parallax	9
LO	Binary-lens-single-source with circular orbital motion	12

Including or excluding model categories

By default, RTModel fits all the model categories listed above to the data, providing models for all of them and comparing their chi square to make its final assessment. However, the user may specify which model categories to fit and even include additional models not proposed in the default modeling run by specifying the corresponding option, as described in Initial conditions.

Additional model categories

Some additional model categories are available but not included in the default modeling run. They can be included by adding their label to the list of model categories as detailed in Initial conditions. At the moment, we have four additional categories, but more are on their ways.

Label	Model	Number of parameters
LK	Binary-lens-single-source with eccentric orbital motion	14
TS	Triple-lens-single-source	10
TX	Triple-lens-single-source with parallax	12
TO	Triple-lens-single-source with circular orbital motions	15

The following sections provide details about parameters and conventions of all categories listed above.

Note that some parameters are fit in logarithmic scale by RTModel for better performance. The only consequence for users is that the covariance matrix contained in model files is written for the ln parameters.

Single-lens-single-source (PS)

This is the basic microlensing model with a single-lens and a single-source. Note that RTModel only considers finite-source models. In most cases, there will be no constraints on the source radius anyway.

The parameters of this model are the following. We also indicate if the parameter is internally fit in logarithmic (ln) scale (see above).

Number	Parameter	Meaning	ln
1	u0	Impact parameter normalized to Einstein angle	X
2	tE	Einstein time in days	X
3	t0	Closest approach time in HJD
4	rho	Source radius normalized to Einstein angle	X

We note that only positive values of u0 are considered in this model since a distinction only comes when parallax is included.

Single-lens-single-source with parallax (PX)

This is the same as before with parallax vector included.

Number	Parameter	Meaning	ln
1	u0	Impact parameter normalized to Einstein angle
2	tE	Einstein time in days	X
3	t0	Closest approach time in HJD
4	rho	Source radius normalized to Einstein angle	X
5	piN	Parallax component along North
6	piE	Parallax component along East

Note that the positive and negative impact parameters correspond to different models when we include parallax. The parallax components are calculated with respect to the reference time t0.

Single-lens-binary-source (BS)

Here we consider two sources and one lens. The two sources have different fluxes and different finite radii. Here are the parameters:

Number	Parameter	Meaning	ln
1	tE	Einstein time in days	X
2	FR	Flux ratio of the secondary to the primary source	X
3	u01	Impact parameter of the primary source
4	u02	Impact parameter of the secondary source
5	t01	Closest approach time of the primary source
6	t02	Closest approach time of the secondary source
7	rho1	Source radius for the primary	X

Note that both sources may have positive or negative impact parameters.

The source radius is only given for the primary star, while the secondary star has a source radius calculated by the relation rho2 = rho1 * FR^(0.225), coming from approximate stellar mass-luminosity-radius relations for solar-type stars. This exponent can be changed by operating on the mass-radius and mass-luminosity exponents, as explained in Fitting.

Single-lens-binary-source with xallarap (BO)

Here we also include circular orbital motion of the two sources around a common center of mass:

Number	Parameter	Meaning	ln
1	tE	Einstein time in days	X
2	FR	Flux ratio of the secondary to the primary source	X
3	u01	Impact parameter of the primary source
4	u02	Impact parameter of the secondary source
5	t01	Closest approach time of the primary source
6	t02	Closest approach time of the secondary source
7	rho1	Source radius for the primary	X
8	piN	Parallax component along North
9	piE	Parallax component along East
10	gamma1	Angular velocity parallel to the lens axis
11	gamma2	Angular velocity perpendicular to the lens axis
12	gammaz	Angular velocity along the line of sight

See VBMicrolensing Binary Sources for a detailed explanation.

The mass ratio between the two component is calculated as qs = FR^(0.25) and the radius of the secondary is rho2 = rho1*FR^(0.225). These exponents can be changed by operating on the mass-radius and mass-luminosity exponents, as explained in Fitting.

Finally, note that we may also turn off the light from the secondary component, if we want to model a source orbiting a dark object.

Binary-lens-single-source (LS)

This is the "static" binary-lens model:

Number	Parameter	Meaning	ln
1	s	Separation between the lenses in Einstein radii	X
2	q	Mass ratio of the secondary to the primary lens	X
3	u0	Impact parameter normalized to Einstein angle
4	alpha	Angle between the source velocity and the vector pointing from the secondary to the primary lens
5	rho	Source radius normalized to Einstein angle	X
6	tE	Einstein time in days	X
7	t0	Closest approach time in HJD to the barycenter

For details about the source trajectory parameterization, please check VBMicrolensing Light Curves.

Binary-lens-single-source with parallax (LX)

Here we also include parallax as we did before for the single-lens case:

Number	Parameter	Meaning	ln
1	s	Separation between the lenses in Einstein radii	X
2	q	Mass ratio of the secondary to the primary lens	X
3	u0	Impact parameter normalized to Einstein angle
4	alpha	Angle between the source velocity and the vector pointing from the secondary to the primary lens
5	rho	Source radius normalized to Einstein angle	X
6	tE	Einstein time in days	X
7	t0	Closest approach time in HJD to the barycenter
8	piN	Parallax component along North
9	piE	Parallax component along East

Binary-lens-single-source with circular orbital motion (LO)

Finally, we also explore circular orbital motion for our binary lens:

Number	Parameter	Meaning	ln
1	s	Separation between the lenses in Einstein radii	X
2	q	Mass ratio of the secondary to the primary lens	X
3	u0	Impact parameter normalized to Einstein angle
4	alpha	Angle between the source velocity and the vector pointing from the secondary to the primary lens
5	rho	Source radius normalized to Einstein angle	X
6	tE	Einstein time in days	X
7	t0	Closest approach time in HJD to the barycenter
8	piN	Parallax component along North
9	piE	Parallax component along East
10	gamma1	Angular velocity parallel to the lens axis
11	gamma2	Angular velocity perpendicular to the lens axis
12	gammaz	Angular velocity along the line of sight

The three components of the orbital motion are expressed at time t0 in units of days^-1.

The component gamma1 is equivalent to ds/dt/s. The component gamma2 is dalpha/dt. The third component gammaz is generally poorly constrained, but is required to move along a physical circular orbit.

More details are available at VBMicrolensing Orbital Motion.

The subpackage plotmodel contains a function for translating from the fitting parameters to conventional orbital elements.

Binary-lens-single-source with eccentric orbital motion (LK)

Eccentric orbital motion is not fit by default, but can be requested by setting the corresponding option in the Initial Conditions.

Number	Parameter	Meaning	ln
1	s	Separation between the lenses in Einstein radii	X
2	q	Mass ratio of the secondary to the primary lens	X
3	u0	Impact parameter normalized to Einstein angle
4	alpha	Angle between the source velocity and the vector pointing from the secondary to the primary lens
5	rho	Source radius normalized to Einstein angle	X
6	tE	Einstein time in days	X
7	t0	Closest approach time in HJD to the barycenter
8	piN	Parallax component along North
9	piE	Parallax component along East
10	gamma1	Angular velocity parallel to the lens axis
11	gamma2	Angular velocity perpendicular to the lens axis
12	gammaz	Angular velocity along the line of sight
13	sz_s	Separation along the line of sight over projected separation
14	a_s3d	Semimajor axis over total separation

The two additional parameters are sufficient to completely define an eccentric orbit. More details are available at VBMicrolensing Orbital Motion.

The subpackage plotmodel contains a function for translating from the fitting parameters to conventional orbital elements.

Triple-lens-single-source (TS)

Static triple-lens model:

Number	Parameter	Meaning	ln
1	s	Separation between the first two lenses in Einstein radii	X
2	q	Mass ratio of the secondary to the primary lens	X
3	u0	Impact parameter normalized to Einstein angle
4	alpha	Angle between the source velocity and the vector pointing from the secondary to the primary lens
5	rho	Source radius normalized to Einstein angle	X
6	tE	Einstein time in days	X
7	t0	Closest approach time in HJD to the barycenter of the first two lenses
8	s2	Separation between the third lens and the first lens	X
9	q2	Mass ratio of the tertiary to the primary lens	X
10	beta	Angle between the third lens and the second lens as seen from the primary

A figure showing the geometry of the triple-lens is in VBMicrolensing Light Curves. Note that the origin is in the barycenter of the first two lenses, so this parameterization is particularly suited to situations in which the third lens makes a small perturbation to the primaries.

Triple-lens-single-source with parallax (TX)

Triple-lens model including parallax:

Number	Parameter	Meaning	ln
1	s	Separation between the first two lenses in Einstein radii	X
2	q	Mass ratio of the secondary to the primary lens	X
3	u0	Impact parameter normalized to Einstein angle
4	alpha	Angle between the source velocity and the vector pointing from the secondary to the primary lens
5	rho	Source radius normalized to Einstein angle	X
6	tE	Einstein time in days	X
7	t0	Closest approach time in HJD to the barycenter of the first two lenses
8	s2	Separation between the third lens and the first lens	X
9	q2	Mass ratio of the tertiary to the primary lens	X
10	beta	Angle between the third lens and the second lens as seen from the primary
11	piN	Parallax component along North
12	piE	Parallax component along East

Triple-lens-single-source with parallax and circular orbital motion (TO)

Triple-lens model including parallax and circular orbital motion:

Number	Parameter	Meaning	ln
1	s	Separation between the first two lenses in Einstein radii	X
2	q	Mass ratio of the secondary to the primary lens	X
3	u0	Impact parameter normalized to Einstein angle
4	alpha	Angle between the source velocity and the vector pointing from the secondary to the primary lens
5	rho	Source radius normalized to Einstein angle	X
6	tE	Einstein time in days	X
7	t0	Closest approach time in HJD to the barycenter of the first two lenses
8	s2	Separation between the third lens and the first lens	X
9	q2	Mass ratio of the tertiary to the primary lens	X
10	beta	Angle between the third lens and the second lens as seen from the primary
11	piN	Parallax component along North
12	piE	Parallax component along East
13	gamma1	Angular velocity parallel to the lens axis
14	gamma2	Angular velocity perpendicular to the lens axis
15	gammaz	Angular velocity along the line of sight

The three components of the orbital velocity are specified for the secondary around the primary. Then the third object is assumed to be coplanar with the second and on a circular orbit. These constraints fully fix the orbital velocity of the third object given the components of the second object.

It is also possible to keep the third object fixed while the secondary orbits the primary, as specified in Fitting. This is particularly useful to explore particular configurations more easily.

Go to Plotting models