# Sky Models¶

## Point Sources¶

For the OVRO LWA the two most important point sources for calibration are Cas A and Cyg A, which are the two brightest sources on the sky. The optimal time to solve for a calibration is when both of these sources are above the horizon.

Currently TTCal expects the sky model to be specified as a list of point sources. This is accomplished by listing the sources in a JSON file. For example the following file defines a sky model consisting of Cas A and Cyg A using the published spectra for Baars et al. 1977.

[
{
"ref": "Baars et al. 1977",
"name": "Cas A",
"ra": "23h23m24s",
"dec": "58d48m54s",
"I": 555904.26,
"Q": 0.0,
"U": 0.0,
"V": 0.0,
"freq": 1.0e6,
"index": [-0.770]
},
{
"ref": "Baars et al. 1977",
"name": "Cyg A",
"ra": "19h59m28.35663s",
"dec": "+40d44m02.0970s",
"I": 49545.02,
"Q": 0.0,
"U": 0.0,
"V": 0.0,
"freq": 1.0e6,
"index": [+0.085,-0.178]
}
]

Fields:

• ref is not used by TTCal, but is intended to be a record of the origin of the information used to define the source
• name is the name of the source
• ra and dec define the J2000 location of the source
• I, Q, U, and V define the Stokes parameters (in Jy) at the frequency freq (in Hz) Q, U, and V are optional and will be assumed to be zero if they are not given
• index defines the spectral index of the source (and higher order terms)

Higher order terms are defined such that

where $I_0$ is the Stokes-I flux at the reference frequency and $\alpha_n$ represents the values contained in index.

Note

The Sun, the Moon, and Jupiter are special cases. These solar system objects do not need to have their position specified. TTCal will automatically determine their location based on the current time. This works based on the name of the source. If you name a source “Sun”, “Moon”, or “Jupiter” it will be placed at the correct location.

## Gaussian Sources¶

Gaussians sources can be added to the sky model by defining major-fwhm, minor-fwhm, and position-angle.

• major-fwhm is the full width at half maximum (FWHM) of the major axis in arcseconds
• minor-fwhm is the FWHM of the minor axis in arcseconds
• position-angle is the angle the major axis makes with J2000 north where a positive angle is east of north

Note that the Stokes parameters I, Q, U, and V now give the integrated flux over the entire source. An example Gaussian source is given below:

...
{
"ref": "Michael's imagination",
"name": "A Gaussian source",
"ra": "12h34m56.78s",
"dec": "+12d34m56.78s",
"I": 123.45,
"freq": 70e6,
"index": [-0.770],
"major-fwhm": 200,
"minor-fwhm": 100,
"position-angle": -70
}
...

## Multi-Component Sources¶

When peeling sources with TTCal each source receives its own peeling solution. This is not always the desired behavior. For example if you are trying to peel Cyg A you might want to use two sources to describe the two radio lobes, but both sources should be peeled with the same solution. Multi-component sources allow you to define sources that are composed of any number of the other source types. For example:

...
{
"name": "Cyg A",
"components": [
{
"name": "east lobe",
...
},
{
"name": "west lobe",
...
}
]
}
...

## RFI Sources¶

TTCal allows the possibility that some sources may not originate from the far-field of the interferometer. That is, some sources may be so close to the interferometer that the curvature of the incoming wavefront cannot be neglected. The exact transition between the near-field and far-field depends on the wavelength, the maximum baseline of the inteferometer, and the desired dynamic range. In order to correctly account for near-field effects TTCal needs the longitude, latitude, and elevation of the source.

Note

The ITRF coordinate system requires the distance to the center of the Earth in place of the elevation.

Sources that do live in the near-field are likely sources of radio frequency interference (RFI), and therefore do not have the smooth power-law spectra expected of astronomical sources. Specifying the flux of an RFI source therefore requires you to give a list of frequencies and the flux at that frequency. For example:

...
{
"name": "Noisy Power Lines"
"sys": "WGS84",
"long": -118.31478,
"lat": 37.14540,
"el": 1226.709,
"rfi-frequencies": [3.0e7, 3.75e7, 4.5e7, 5.25e7, 6.0e7],
"rfi-I": [1.0, 2.0, 3.0, 4.0, 5.0]
}
...

The longitude and latitude must be given in degrees and the elevation (or distance from the center of the Earth) must be given in meters. The only valid coordinate systems are currently WGS84 and ITRF. You may optionally also supply the fields rfi-Q, rfi-U, and rfi-V to specify the corresponding Stokes parameters for the RFI emission.