Atacama Large Millimeter/submillimeter Array Expanded Very Large Array Robert C. Byrd Green Bank Telescope Very Long Baseline Array An Absolute Flux Density Scale from 1 to 50 GHz Bryan Butler, Rick Perley National Radio Astronomy Observatory

Calibrating Interferometer Observations We calibrate many things with radio interferometric observations, including: 1.Delay 2.Bandpass 3.Polarization 4.Flux density scale 5.Time variable amplitude and phase I’m only talking about item 4 in this talk. Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab1

Calibrating the Flux Density Scale We calibrate the flux density scale in either of two ways: 1. Ab initio – If we knew everything about the atmosphere, telescope, receiver, electronics, etc., we could calibrate absolutely. 2. A posteriori - The radio equivalent of “standard stars.” 1. is extremely difficult to do in practice because there are so many things to measure accurately, so 2. is what is done, currently, for almost all radio interferometers. Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab2

The Baars et al. (1977) Scale The commonly-employed flux density scale in radio astronomy is based on the 1977 paper by Baars, Genzel, Pauliny-Toth and Witzel. This paper summarized prior work by various single-dish antennas, and is based on absolute measurements of Cassiopeia A, Cygnus A, Taurus A, and Virgo A (using calibrated horns). Claimed valid from 20 MHz to 35 GHz for Cas A and Cyg A (but little high frequency data). These sources are all heavily resolved by interferometers, and Baars et al. proposed a list of 13 more compact objects (secondaries) whose flux densities were referenced to the four primary calibrators. Polynomial expressions were provided for these secondary calibrators, typically valid from 400 MHz to 15 GHz. The most compact of these, 3C 286, 3C 147, and 3C 48, are widely used as flux density standards by radio wavelength interferometers today. But are the expressions correct? And are the sources variable over time? What about frequencies above 15 GHz? Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab3

The Baars et al. Primary Sources Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab4 The spectrum of three of the primary sources from Baars et al. Note how little data there is above ~10 GHz.

Cygnus A ~2 arcmin Core Lobes Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab5

VLA Flux Density Monitoring Program Since 1983 we have been observing flux density ratios between a number of the Baars et al. secondary sources. Note that the VLA cannot measure absolute flux densities, but is very good at determining ratios between the sources. We also cannot relate these to the Baars et al. primary sources because of resolution and saturation of those sources at the VLA. Frequencies from 1 GHz to 50 GHz (more restricted early in the program). 17 epochs. Sources: – Seven compact, steep-spectrum objects: 3C 48, 3C 123, 3C 138, 3C 147, 3C 196, 3C 286, and 3C 295. – Two planetary nebulae: NGC 7027, NGC – One evolved star: MWC 349. – Four planets: Venus, Mars, Uranus, Neptune. Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab6

The VLA “Big 4” Comparison of the measured ratios amongst the sources over the 28 year span of this project shows that four sources: 3C 123, 3C 196, 3C 286, and 3C 295 have unchanging ratios at all frequencies. Of these, only 3C 286 is sufficiently unresolved by the VLA in its highest resolution configuration at all frequencies to serve as a primary standard. Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab7

The VLA “Big 4” – An Example 3C 286/3C 295 ratio at 6 frequencies The change in ratio over the 28 year period is shown. Slope is in % per Century! None of the four sources has changed by more than ~1% over the duration of this experiment. Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab 8

How To Establish An Absolute Scale Since we cannot tie our observations of the Baars et al. secondary calibrators to the primary calibrators with VLA observations, we need to identify an object that we can observe with the VLA that has an absolutely known flux density across the range 1-50 GHz. We would have liked to have used Jupiter for this, because it has been extensively measured very accurately in the past (including by WMAP; Page et al. 2003), but it is also too heavily resolved by the VLA. As an alternative, the planet Mars has a well-established physical emission model (Rudy et al. 1987), which enables accurate calculation of its emission as a function of date and time, and was also accurately measured by WMAP (Weiland et al. 2011). Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab9

Mars – Rudy Model Based on data taken at the VLA at 2cm and 6cm. Baars et al. scale used (3C 286 was observed), so not entirely independent. Resulting images were fit with a full thermophysical model, fitting for dielectric constant and radio absorption length as a function of latitude. At the time, the north polar seasonal CO 2 cap was large, and easily seen in the images, so they also fit for the effective thermal parameters of the CO 2 caps. These bulk properties were then fed into a much more sophisticated thermophysical model which used results from Viking (thermal inertia and albedo as a function of location), and derived a surface and subsurface temperature profile as a function of both longitude (7.5 deg bins) and latitude (5 deg bins). Since the original model creation, it has been updated to include surface roughness effects, proper sub-pixel gridding, and potential resolution of the disk by whatever antenna might be used to observe it. Was compared to the Lellouch et al. Mars model as part of Herschel HIFI calibration effort – maximum deviation over a 10 year period was ~3%. Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab10

Mars – Rudy Model Some caveats: No separate surface roughness was included in the original model - the roughness was lumped in with the effective bulk dielectric constant of the surface. Because of this, adding in a separate surface roughness after the fact may give slightly erroneous answers. There is no subsurface scattering included in the model. There is no lateral heat transport included in the model. The model for the extent and depth of the seasonal CO 2 ice caps is fairly crude. Outdated maps of thermal inertia and albedo were used when deriving the thermophysical parameters. There is no atmosphere included in the model, which can cause the wrong surface temperatures to be derived, for example if there is a large (global, in the end case) dust storm. Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab11

Mars – Rudy Model Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab12

Mars – Rudy Model Correction Remember that the Rudy model is tied to Baars et al. but only via a secondary calibrator (3C 286). We need to find a way to get this model to be independent from Baars et al., and on an absolute scale. As mentioned above, WMAP is the key. WMAP observed Mars, and provided absolute brightness temperatures (which is the primary output of the Mars model) at all of its observing frequencies, calibrated against the CMB dipole (accurate to ~2%). Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab13

Mars – Rudy Model Correction WMAP mapped the entire sky at 5 frequencies from ~23 to ~93 GHz. An example from 23 GHz: Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab14

Mars – Rudy Model Correction WMAP also observed Mars at 7 epochs over a period of 7 years (Weiland et al. 2011; we only use 6 of these as the first was during a global dust storm). If we compare the absolutely calibrated WMAP Mars observations to the output of the Rudy model, we can investigate what corrections might be needed to the model to accurately reproduce the WMAP observations. We find a simple correction of 1.9% (downward) in the Rudy model to provide the best fit to the WMAP observations. Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab15

Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab16 20% 15% Mars – Rudy Model Correction

The Mars-Baars Scale Unfortunately we cannot use Mars at low frequencies because it becomes quite weak below about 5 GHz. We therefore use a modified Baars et al. scale for 3C 286 and 3C 295 at those frequencies, modified so that it matches up with the Mars scale at 4.8 and 8.4 GHz (the correction factor is about 1.5% downward to Baars et al., which is consistent with the Mars-WMAP adjustment). We then use 3C 286 and 3C 295 to set the flux densities for all other sources. The uncertainty in the flux density scale from 1-50 GHz is 3-5% (3% at the low frequency end, 5% at the high frequency end). Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab17

Fits for the VLA “Big 4” Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab18

The rest With the polynomial expressions for 3C 286 and 3C 295, the flux densities for the remaining objects are derived from their measured ratios to these two. The time evolution of these objects is then derived: 3C 196 and 3C 123 are completely stable, as expected. NGC 7027 is increasing below 2 GHz, and decreasing above (see Zijlstra et al. 2008). NGC 6572 appears to be stable. MWC 349 varies erratically. 3C 48, 3C 138, and 3C 147 show time variability which is large (as much as 20%) and not easily parameterized. The planets are variable in flux density, as expected, due to varying distance (and changing viewing geometry for Uranus). These flux densities are being used to improve existing models of their emission (Butler et al. 2001; Hofstadter & Butler 2003; Orton et al. 2007; etc.). Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab19

Summary We have derived a new flux density scale valid from 1-50 GHz, believed accurate to 3-5%, based on the absolute brightness of Mars from the Rudy model scaled by observations of WMAP for frequencies greater than 5 GHz and the Baars scale also scaled to fit with Mars at intermediate frequencies for frequencies less than 5 GHz (the “Mars-Baars scale”). This flux density scale is extended to a set of secondary calibrators through accurate ratio measurements made with the VLA. The sources 3C 123, 3C 286, 3C 196, and 3C 295 are stable over time, varying by less than ~.05% per year at all frequencies, and are suitable for flux density calibration for all radio instruments (depending on resolution issues). New and improved models of the emission of Venus, Uranus, and Neptune based on our VLA observations over the past ~20 years, and in combination with shorter wavelength observations (c.f. Marston talk) should provide better standards for observations from cm to IR wavelengths. Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab20

A Final Cautionary Note The fact that we know the flux densities of our primary calibrators to 3-5% does not mean that every observation done by a radio telescope is accurate to that level. It depends strongly on the details of the instrumental setup, sequence of sources observed (especially their relative elevations), other calibrations, and care in post-processing of data. But what we have done is make it at least possible to reach this level of accuracy, if observing, calibration, and post- processing are done correctly! Butler & Perley; Calibration & Standardization of Large Surveys & Missions in Astronomy & Astrophysics; April 2012; Fermilab21