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Appendix C  Appendix: Models, Conventions, and Reference Frames

This appendix lists the available parameters, conventions, reference frames, and information on flux standards used in CASA.

C.1  Flux Density Models for setjy

setjy adds a source model given the source name, frequency, a standard (really, a set of models), and possibly a time. At cm wavelengths the flux density (FD) calibrators are typically one of several bright extragalactic sources. These objects are comparatively faint and less well characterized at shorter wavelengths, so for (sub)mm astronomy it is common to use Solar System objects.

Reliably setting the FD scale with astronomical calibrators requires that they be bright, not too resolved, and have simple dependencies on frequency and time. These criteria are somewhat mutually exclusive, so the number of calibrator sources supported by setjy is fairly small, although it could certainly be added to. This appendix is for describing the models that setjy uses. Choosing a FD calibrator of course has to be done before the observation and the observatory may provide additional information.

C.1.1  Long wavelength calibration

Synchrotron sources can vary over a light crossing time, so ones used as FD calibrators must have most of their emission coming from an extended region. The additional requirement that they be nearly unresolved therefore forces them to be distant, meaning that candidates which also have high apparent fluxes are quite rare. The following standards mostly share the same set of objects, and monitor their FDs every few years to account for variations. No interpolation is done between epochs, though - you are encouraged to choose the standard which observed your FD calibrator closest to the time you observed it at. The measurements are interpolated in frequency, however, using second to fourth degree polynomials of the frequency’s logarithm.


Table C.1: Recognized Flux Density Calibrators. Note that the VLA uses J2000 calibrator names. CASA accepts all strings that contain the names below. E.g. ’PKS 1934-638’ will be recognized
3C NameB1950 NameJ2000 NameAlt. J2000 NameStandards
3C480134+3290137+331J0137+33091,3,4,5,6, 7
3C1230433+2950437+296J0437+29402
3C1380518+1650521+166J0521+16381,3,4,5,6
3C1470538+4980542+498J0542+49511,3,4,5,6, 7
3C1960809+4830813+482J0813+48131,2,7
3C2861328+3071331+305J1331+30301,2,3,4,5,6, 7
3C2951409+5241411+522J1411+52121,2,3,4,5,6, 7
1934-638J1939-63421,3,4,5,6,8
3C3801828+4871829+487J1829+48457
Standards are: (1) Perley-Butler 2010, (2) Perley-Butler 2013, (3) Perley-Taylor 99, (4) Perley-Taylor 95, (5) Perley 90, (6) Baars, (7) Scaife-Heald 2012, (8) Stevens-Reynolds 2016

C.1.1.1  Baars

The only standard to not have the year in the name. It is 1977.

The models are second order polynomials in log(ν), valid between 408 MHz and 15 GHz.

The paper is Baars, J. W. M., Genzel, R., Pauliny-Toth, I. I. K., & Witzel, A. 1977, A&A, 61, 99 with a commentary by Kellermann, K. I. 1999, A&A 500, 143.

C.1.1.2  Perley 90

This standard also includes 1934-638 from Reynolds (7/94) and 3C138 from Baars, J. W. M., Genzel, R., Pauliny-Toth, I. I. K., & Witzel, A. 1977, A&A, 61, 99.

Details can be found at http://www.vla.nrao.edu/astro/calib/manual/baars.html.

C.1.1.3  Perley-Taylor 95

Perley and Taylor (1995.2); plus Reynolds (1934-638; 7/94) Details can be found at http://www.vla.nrao.edu/astro/calib/manual/baars.html.

C.1.1.4  Perley-Taylor 99

Perley and Taylor (1999.2); plus Reynolds (1934-638; 7/94) Details can be found at http://www.vla.nrao.edu/astro/calib/manual/baars.html.

C.1.1.5  Perley-Butler 2010

A preliminary version of Perley-Butler 2013 (§ C.1.1.6). This version has also coefficients for sources that showed some degree of variability, see Perley, R. A., & Butler, B. J. 2012, ApJS, submitted (http://arxiv.org/abs/1211.1300).

C.1.1.6  Perley-Butler 2013

Flux scale for the constant flux sources 3C123, 3C196, 3C286, and 3C295. The models are time-dependent.
Reference: Perley, R. A., & Butler, B. J. 2013, ApJS, 206, 16

C.1.1.7  Scaife-Heald 2012

Low frequency, 30-300MHz, calibrators 3C48, 3C147, 3C196, 3C286, 3C295, and 3C380.
Reference: Scaife, A. M., & Heald, G. H. 2012, MNRAS, 423, 30

C.1.1.8  Stevens-Reynolds 2016

Low frequency (<11GHz) polynomial for PKS1934-638 from Reynolds and updated high frequecy polynomial from Stevens.
Reference: Partridge et al. 2016, ApJ 821,1

C.1.2  Short wavelength calibration

The usual approach in this regime is to use models that are, to first order, thermal sources in the Solar System. Their apparent brightness of course varies in time with their distance from the Earth (and Sun), and orientation if they are not perfect spheres with zero obliquity. However, most of them have almost constant surface properties, so once those properties are measured their apparent brightness distributions can in principle be predicted for any time, given an ephemeris. Planets, in particular, however, have more complex spectra and effects such as atmospheric lines, magnetic fields, seasons, polar caps and surface features need to be taken into account when they are available and significant. In CASA the Solar System objects supported by setjy are available through the ‘Butler-JPL-Horizons 2010’, and ’Butler-JPL-Horizons 2012’ standards. The models are described in ALMA Memo 594 available on https://science.nrao.edu/facilities/alma/aboutALMA/Technology/ALMA_Memo_Series/alma594/abs594.

The following objects are supported in the Butler-JPL-Horizons 2012.

C.1.2.1  Venus

The model spans the frequencies from  300MHz to 1THz. No atmospheric lines such CO,H2O, HDO, and etc are included. Modeled based on Clancy et al. 2012.

C.1.2.2  Mars

Full implementation of the model of Rudy et al (1987) , tabulated as a function of time and frequency (30-1000GHz). No atmospheric lines are included.

C.1.2.3  Jupiter

Model for 30-1020GHz (from Glenn Orton, private communication), does not include synchrotron emission.

C.1.2.4  Uranus

Model for 60-1800GHz (from Glenn Orton and Raphael Moreno, private communication), contains no rings or synchrotron.

C.1.2.5  Neptune

Model for 2-2000 GHz (from Glenn Orton and Raphael Moreno, private communication), contains no rings or synchrotron.

C.1.2.6  Io

Spline interpolation of data points from 15 to 29980 GHz (references: please refer to the ALMA memo 594 Table 1). Strongly not recommended to use for the primary flux calibrator for ALMA observations.

C.1.2.7  Europa

Spline interpolation of data points from 15 to 29980 GHz (references: please refer to the ALMA memo 594 Table 1). Strongly not recommended to use for the primary flux calibrator for ALMA observations.

C.1.2.8  Ganymede

Spline interpolation of data points from 5 to 29980 GHz (references: please refer to the ALMA memo 594 Table 1).

C.1.2.9  Callisto

Spline interpolation of data points from 5 to 29980 GHz (references: please refer to the ALMA memo 594 Table 1).

C.1.2.10  Titan

Model from Mark Gurwell, from 53.3-1024.1 GHz. Contains surface and atmospheric emission. The atmosphere includes N2-N2 and N2-CH4 Collision-Induced Absorption (CIA), and lines from minor species CO, 13CO, C18O, HCN, H13CN and HC15N. See, e.g., Gurwell & Muhleman (2000); Gurwell (2004). Asteroids

C.1.2.11  Asteroids Ceres, Pallas, Vesta, Juno

Some asteroids, namely Ceres, Pallas, Vesta, and Juno are included in the Butler-JPL-Horizons 2012. The models consists of the constant brightness temperature in frequency. For Ceres, Pallas, and Vesta, updated models based on thermophysical models (TPM) (T. Mueller, private communication) which are tabulated in time and frequency, are available for the observations taken after January 1st 2015 0UT. SetJy task will automatically switch to the new models for the observations taken on and after that date. The TPM also available for Lutetia but it is not advised to use for the absolute flux calibration for ALMA. Each of the tabulated models contains the flux density at 30, 80, 115, 150, 200, 230, 260, 300, 330, 360, 425, 650, 800, 950, and 1000 GHz. The time resolution is 1 hour for Ceres and 15min for Lutetia, Pallas, and Vesta. The cubic interpolation is employed to obtain the flux densities at other frequencies.

C.1.2.11.1  Ceres

Model with a constant Tb = 185K over frequencies (Moullet et al. 2010, Muller & Lagerros 2002, Redman et al. 1998, Altenhoff et al. 1996) if time of the observations took place(tobs) is before 2015.01.01 0UT, TPM if tobs 2015.01.01 0UT.

C.1.2.11.2  Pallas

Model with a constant Tb = 189K (Chamberlain et al. 2009, Altenhoff et al. 1994) for tobs < 2015.01.01 0UT, and TPM for Tobs 2015.01.01 0UT

C.1.2.11.3  Vesta

Model with a constant Tb = 155K (Leyrat et al. 2012, Chamberlain et al. 2009, Redman et al. 1998, Altenhoff et al. 1994) for tobs < 2015.01.01 0UT, and TPM for Tobs 2015.01.01 0UT

C.1.2.11.4  Juno

Model with a constant Tb = 153K (Chamberlain et al. 2009, Altenhoff et al. 1994)

C.1.2.12  References

Altenhoff, W.J. et al. 1996. Precise flux density determination of 1 Ceres with the Heinrich-Hertz-Telescope at 250Hz, A&A, 309, 953
Altenhoff, W.J. et al. 1994. Millimeter-wavelength observations of minor planets, A&A, 287, 641
Chamberlain, M.A. et al. 2009. Submillimeter photometry and lightcurves of Ceres and other large asteroids, Icarus, 202, 487
Clancy, R.T. et al. 2012. Thermal structure and CO distribution for the Venus mesosphere/lower thermosphere: 2001-2009 inferior conjunction sub-millimeter CO absorption line observations, Icarus, 217, 779
Gurwell, M.A. & D.O. Muhleman 2000. Note: CO on Titan: More Evidence for a well-mixed vertical profile, Icarus, 145, 65w
Gurwell, M.A. 2004. Submillimeter Observations of Titan: Global Measures of Stratospheric Temperature, CO, HCN, HC3N, and the Isotopic Ratios 12C/13C and14N/15N, ApJ, 616, L7
Leyrat, C. et al. 2012. Thermal properties of (4) Vesta derived from Herschel measurements, A&A, 539, A154
Moullet, A. et al. 2010. Thermal rotational lightcurve of dwarf-planet (1) Ceres at 235 GHz with the Submillimeter Array, A&A, 516, L10
Muller, T.G. & J.S.V. Lagerros 2002. Asteroids as calibration standards in the thermal infrared for space observatories, A&A, 381, 324
Redman, R.O. et al. 1998. High-Quality Photometry of Asteroids at Millimeter and Submillimeter Wavelengths, AJ, 116, 1478
Rudy, D.J. et al. 1987. Mars - VLA observations of the northern hemisphere and the north polar region at wavelengths of 2 and 6 cm, Icarus, 71, 159

C.2  Velocity Reference Frames

CASA supported velocity frames are listed in Table C.2.


Table C.2: Velocity frames in CASA
NameDescription
RESTLaboratory
LSRKlocal standard of rest (kinematic)
LSRDlocal standard of rest (dynamic)
BARYbarycentric
GEOgeocentric
TOPOtopocentric
GALACTOgalactocentric
LGROUPLocal Group
CMBcosmic microwave background dipole
Undefinedundefined frame

C.2.1  Doppler Types

CASA supported Doppler types are listed in Table C.3.


Table C.3: Doppler types in CASA
NameDescription
RADIO  
Z  
RATIO  
BETA  
GAMMA  
OPTICAL 
TRUE  
RELATIVISTIC 

C.3  Time Reference Frames

CASA supported time reference frames are listed in Table C.4.


Table C.4: Time reference frames in CASA
NameDescription
LAST 
LMST 
GMST1 
GAST 
UT1 
UT2 
UTC 
TAI 
TDT 
TCG 
TDB 
TCB 
IAT 
GMST 
TT 
ET 
UT 

C.4  Coordinate Frames

CASA supported time coordinate frames are listed in Table C.5.


Table C.5: Coordinate frames in CASA
NameDescription
J2000mean equator and equinox at J2000.0 (FK5)
JNATgeocentric natural frame
JMEANmean equator and equinox at frame epoch
JTRUEtrue equator and equinox at frame epoch
APPapparent geocentric position
B1950mean epoch and ecliptic at B1950.0.
B1950_VLAmean epoch(1979.9)) and ecliptic at B1950.0
BMEANmean equator and equinox at frame epoch
BTRUEtrue equator and equinox at frame epoch
GALACTICGalactic coordinates
HADECtopocentric HA and declination
AZELtopocentric Azimuth and Elevation (N through E)
AZELSWtopocentric Azimuth and Elevation (S through W)
AZELNEtopocentric Azimuth and Elevation (N through E)
AZELGEOgeodetic Azimuth and Elevation (N through E)
AZELSWGEOgeodetic Azimuth and Elevation (S through W)
AZELNEGEOgeodetic Azimuth and Elevation (N through E)
ECLIPTCecliptic for J2000 equator and equinox
MECLIPTICecliptic for mean equator of date
TECLIPTICecliptic for true equator of date
SUPERGALsupergalactic coordinates
ITRFcoordinates wrt ITRF Earth frame
TOPOapparent topocentric position
ICRSInternational Celestial reference system

Note that TOPO refers to a time stamp at a given observation date. If more than one observation is concatenated this may lead to vastly erroneous values. Any conversion from TOPO to other frames such as BARY and LSRK should be performed for each individual observation, prior to concatenation or simultaneous imaging.

C.5  Physical Units

CASA also recognizes physical units. They are listed in Tables C.6, C.7, and C.8.


Table C.6: Prefixes
PrefixNameValue
Y(yotta)1024
Z(zetta)1021
E(exa)1018
P(peta)1015
T(tera)1012
G(giga)109
M(mega)106
k(kilo)103
h(hecto)102
da(deka)10
d(deci)10−1
c(centi)10−2
m(milli)10−3
u(micro)10−6
n(nano)10−9
p(pico)10−12
f(femto)10−15
a(atto)10−18
z(zepto)10−21
y(yocto)10−24


Table C.7: SI Units
UnitNameValue
$(currency)1 _
%(percent)0.01
%%(permille)0.001
A(ampere)1 A
AE(astronomical unit)149597870659 m
AU(astronomical unit)149597870659 m
Bq(becquerel)1 s−1
C(coulomb)1 s A
F(farad)1 m−2 kg−1 s4 A2
Gy(gray)1 m2 s−2
H(henry)1 m2 kg s−2 A−2
Hz(hertz)1 s−1
J(joule)1 m2 kg s−2
Jy(jansky)10−26 kg s−2
K(kelvin)1 K
L(litre)0.001 m3
M0(solar mass)1.98891944407× 1030 kg
N(newton)1 m kg s−2
Ohm(ohm)1 m2 kg s−3 A−2
Pa(pascal)1 m−1 kg s−2
S(siemens)1 m−2 kg−1 s3 A2
S0(solar mass)1.98891944407× 1030 kg
Sv(sievert)1 m2 s−2
T(tesla)1 kg s−2 A−1
UA(astronomical unit)149597870659 m
V(volt)1 m2 kg s−3 A−1
W(watt)1 m2 kg s−3
Wb(weber)1 m2 kg s−2 A−1
_(undimensioned)1 _


Table C.7: SI Units – continued
UnitNameValue
a(year)31557600 s
arcmin(arcmin)0.000290888208666 rad
arcsec(arcsec)4.8481368111×10−6 rad
as(arcsec)4.8481368111e×10−6 rad
cd(candela)1 cd
cy(century)3155760000 s
d(day)86400 s
deg(degree)0.0174532925199 rad
g(gram)0.001 kg
h(hour)3600 s
l(litre)0.001 m3
lm(lumen)1 cd sr
lx(lux)1 m−2 cd sr
m(metre)1 m
min(minute)60 s
mol(mole)1 mol
pc(parsec)3.08567758065×1016 m
rad(radian)1 rad
s(second)1 s
sr(steradian)1 sr
t(tonne)1000 kg


Table C.8: Custom Units
UnitNameValue
"(arcsec)4.8481368111×10−6 rad
"_2(square arcsec)2.35044305391× 10−11 sr
(arcmin)0.000290888208666 rad
(arcsec)4.8481368111×10−6 rad
”_2(square arcsec)2.35044305391×10−11 sr
’_2(square arcmin)8.46159499408×10−8 sr
:(hour)3600 s
::(minute)60 s
:::(second)1 s
Ah(ampere hour)3600 s A
Angstrom(angstrom)1e-10 m
Btu(British thermal unit (Int))1055.056 m2 kg s−2
CM(metric carat)0.0002 kg
Cal(large calorie (Int))4186.8 m2 kg s−2
FU(flux unit)10−26 kg s−2
G(gauss)0.0001 kg s−2 A−1
Gal(gal)0.01 m s−2
Gb(gilbert)0.795774715459 A
Mx(maxwell)10−8 m2 kg s−2 A−1
Oe(oersted)79.5774715459 m−1 A
R(mile)0.000258 kg−1 s A
St(stokes)0.0001 m2 s−1
Torr(torr)133.322368421 m−1 kg s−2
USfl_oz(fluid ounce (US))2.95735295625×10−5 m3
USgal(gallon (US))0.003785411784 m3


Table C.8: Custom Units – continued
UnitNameValue
WU(WSRT flux unit)5× 10−29 kg s−2
abA(abampere)10 A
abC(abcoulomb)10 s A
abF(abfarad)109 m−2 kg−1 s4 A2
abH(abhenry)10−9 m2 kg s−2 A−2
abOhm(abohm)10−9 m2 kg s−3 A−2
abV(abvolt)10−8 m2 kg s−3 A−1
ac(acre)4046.8564224 m2
arcmin_2(square arcmin)8.46-2159499408×10−8 sr
arcsec_2(square arcsec)2.35044305391×10−11 sr
ata(technical atmosphere)98066.5 m−1.kg.s−2
atm(standard atmosphere)101325 m−1.kg.s−2
bar(bar)100000 m−1.kg.s−2
beam(undefined beam area)1 _
cal(calorie (Int))4.1868 m2 kg s−2
count(count)1 _
cwt(hundredweight)50.80234544 kg
deg_2(square degree)0.000304617419787 sr
dyn(dyne)10−5 m kg s−2
eV(electron volt)1.60217733×10−19 m2 kg s−2
erg(erg)10−7 m2 kg s−2
fl_oz(fluid ounce (Imp))2.84130488996×10−5 m3
ft(foot)0.3048 m
fu(flux unit)10−26 kg s−2
fur(furlong)201.168 m
gal(gallon (Imp))0.00454608782394 m3


Table C.8: Custom Units – continued
UnitNameValue
ha(hectare)10000 m2
hp(horsepower)745.7 m2 kg s−3
in(inch)0.0254 m
kn(knot (Imp))0.514773333333 m s−1
lambda(lambda)1 _
lb(pound (avoirdupois))0.45359237 kg
ly(light year)9.46073047×1015 m
mHg(metre of mercury)133322.387415 m−1 kg s−2
mile(mile)1609.344 m
n_mile(nautical mile (Imp))1853.184 m
oz(ounce (avoirdupois))0.028349523125 kg
pixel(pixel)1 _
sb(stilb)10000 m−2 cd
sq_arcmin(square arcmin)8.46159499408×10−8 sr
sq_arcsec(square arcsec)2.35044305391×10−11 sr
sq_deg(square degree)0.000304617419787 sr
statA(statampere)3.33564095198×10−10 A
statC(statcoulomb)3.33564095198×10−10 s A
statF(statfarad)1.11188031733×10−12 m−2 kg−1 s4 A2
statH(stathenry)899377374000 m2 kg s−2 A−2
statOhm(statohm)899377374000 m2 kg s−3 A−2
statV(statvolt)299.792458 m2 kg s−3 A−1
u(atomic mass unit)1.661×10−27  kg
yd(yard)0.9144 m
yr(year)31557600 s

C.6  Physical Constants

The physical constants included in CASA can be found in Table C.9.


Table C.9: Physical Constants
 
ConstantNameValue
pi3.14..3.14159
ee2.71..2.71828
clight vel.2.99792×108 m s−1
Ggrav. const6.67259×1011 N m2 kg−2
hPlanck const6.62608×10−34 J s
HIHI line1420.41 MHz
Rgas const8.31451 J K−1 mol−1
NAAvogadro #6.02214×1023 mol−1
eelectron charge1.60218×10−19 C
mpproton mass1.67262×10−27  kg
mp_memp/me1836.15
mu0permeability vac.1.25664×10−6 H m−1
eps0permittivity vac.1.60218×10−19 C
kBoltzmann const1.38066×10−23 J K−1
FFaraday const96485.3 C mol−1
meelectron mass9.10939×10−31  kg
reelectron radius2.8179e×10−15  m
a0Bohrs radius5.2918×10−11  m
R0solar radius6.9599×108  m
k2IAU grav. const20.000295912 AU3 d−2 S0−1


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