08 JUNE 2004
ACRIMSAT/ACRIM 3 RADIOMETRY (Total Solar Irradiance)

Glenn Schneider, Steward Observatory, University of Arizona,

in collaboration with Jay Pasachoff, Williams College

with data provided by Richard C. Willson, Columbia University
Principal Investigator, ACRIM Experiments)

Where astronomy and climatology meet.  
A symbiosis between NASA Science Mission Directorate's Sun/Earth Connection and Origins themes, and the Earth Observing System.

Presented at the 205th Meeting of the American Astronomical Society - 13 January, 2005, San Diego, California

As abstracted in the Bulletin of the American Astronomical Society, 36, 5 © 2004:

The Effect of the Transit of Venus on ACRIM's Total Solar Irradiance Measurements: Implications for Transit Studies of Extrasolar Planets

We used 131-s-cadence observations made with ACRIM3 on ACRIMsat on 8 June 2004 to follow the effect of the transit of Venus, which lasted about 6 hours, on the total solar irradiance (TSI). Venus's angular diameter, in transit, is approximately 1/30 the solar diameter, so it covered approximately 0.1% of the sun's surface. With our ACRIM3 data, we measure temporal changes in TSI with a one-sigma per sample (unbinned) certainty of approximately 100 milliwatts per square meter (0.007%). We found a diminution in TSI of approximately 1.4 watts per square meter (approximately 0.1%, closely corresponding to the geometrically occulted area of the photosphere) at mid-transit compared with a mean pre/post transit TSI of 1365.9 watts per square meter. The measured light curve is complex because of the parallactic motion of Venus induced by the satellite's polar orbit, but exhibits the characteristic signature of photospheric limb-darkening when orbit-driven variations are accounted for. Analysis of the limb darkening can reveal temperature structure with height in the photosphere and asymmetries can, in principle, be attributable to planetary atmospheres. Similar observations will increasingly be detected from exoplanet transits, so detailed analysis of the transit within our solar system will provide a useful analogue for interpreting the many more such transits expected to be discovered within the next decade.

JMP's and GS's transit of Venus observations were supported by a grant from the Committee for Research and Exploration of the National Geographic Society. NASA provides support for RCW at Columbia University under contract NNG04HZ42C.

DISPLAY PAPER 135.11 presented in "Finding and Measuring Exoplanets" session.


We are using solar irradiance (total irradiance power) measurements obtained with the Active Cavity Radiometer (ACRIM) 3 instrument on ACRIMSAT to evaluate the radiometric (broad band photometric) detectability of extrasolar terrestrial planetary transits of their host stars using the 8 June 2004 transit of Venus as a "nearby" analog.  We are pursuing this line of inquiry in concert with a space-based imaging experiment using TRACE, as well as ground-based spectrophotometry and imaging programs.


ACRIMSAT is in a Sun synchronous orbit, but, unlike TRACE, it cannot observe the Sun continuously. ACRIMSAT's line-of-site to the Sun is occulted by the Earth every orbit.  As a result of its orbital geometry ACRIM 3 is actively measuring the total solar irradiance for about an hour orbit in each of its approximately 100 minute orbits.  This is not of concern to the primary mission for ACRIM - to monitor with higher precision long term variations in the solar radiometric output.  This does mean, however, that the Transit of Venus data set, which otherwise nominally provides samples once every 131.072 seconds, "suffers" from gaps due to visibility interruptions.

The line-of-site visibilities, and transit circumstances for ACRIM were determined for time intervals of the Venus transit post-priori using the satellite orbital "two line  element" (TLE) set provided by NORAD.  This element set was current as of 30 June 2004 and is used here for illustrative purposes. Historical elements of higher precision specifically for 8 June 2004 (thus unaffected by differential upper atmospheric drag) were subsequently  obtained to generate an epochal ephemeris of higher instantaneous fidelity and is being used in our detailed analysis of the ACRIM 3 data set.

The ACRIMSAT transit visibilities (based upon the 30 June 2004 TLE set) are illustrated in two animations  (as QuickTime movies) below.


ACRIMSAT & TRACE: Earth View from Sun


LEFT. The "view of ACRIMSAT & TRACE" as they orbit the Earth seen from the Sun during the transit.
Two satellites (not to scale!) are shown in this animation: ACRIMSAT, which is periodically occulted by the Earth, and TRACE, which has an continuous (uninterrupted) view of the Sun.  Note that (by chance of the orbit phase) that near the Northern and Southern extrema of the spacecraft orbits, the two satellites appear very close together as seen from the Sun.

RIGHT. The "view of the Sun and Venus" (to scale), as seen from ACRIMSAT as it orbits the Earth.
Note in the "view of the Sun and Venus" that Venus exhibits periodic position excursions as it traverses the solar disk due to the reflective orbital parallax of ACRIMSAT.  Frames in the animations that are gray indicate the Earth is occulting ACRIMSAT's line-of-site to the Sun (occasionally you may see the Earth's limb or a grid reference on the Earth's frame-filling disk in a single frame).


ACRIM 3 provides the total (0.2 to 2.0 micron) solar irradiance (watts per square meter) received at  1 AU.  The ACRIM 3 instrument provides this information (a "shutter cycle" read out) once every 131.072 seconds.  ACRIM 3 was designed to provide accurate and highly precise and traceable radiometry over decadal timescales, to detect changes in the total energy received from the Sun by the Earth. The basic data are the average of 32 seconds of sampling (at a 1.024 sec. cadence) during each set of shutter open (observations) and closed (calibration) measurements. The standard data products are binned into daily means. ACRIM 3 also provides shutter cycle results with a measurement uncertainty of approximately 0.1% and a precision of 0.01% (approximately 100 micromagnitudes in the extremely broad radiometric ACRIM 3 "pass band").  


The disk of Venus, when fully on the solar disk as viewed by ACRIMSAT, occults approximately 0.1% of the total area of the photosphere, so a radiometric detection of the transit by ACRIM 3 was readily expected - and was obtained. The ACRIM 3 Venus transit data, provided and radiometrically calibrated by the ACRIM Experiments team (extending to +/- approximately 5 hours on either side of the transit ingress and egress) is shown below in the form of a "light curve". Gaps in the ACRIM 3 light curve are primarily due to Earth occultations, though a small amount of data was apparently lost elsewhere in the downlink path from the spacecraft. Unfortunately, the transit egress (the interval between Contacts III and IV) was not visible from ACRIMSAT. TSI observations were also obtained from TIM (Total Irradiance Monitor) on the Solar Radiation and Climate Experiment (SORCE) spacecraft. Coincidentally, the phasing of the SORCE orbit w.r.t. its periods of Earth occultation during the Venus transit was very similar to ACRIMSAT's and egress was also unobserved by TIM. Note also that VIRGO on the SOHO spacecraft, located at L1 rather than in low Earth orbit, was not in the zone from which the transit was visible.

  (Click on the above graph to view at twice the size)

The black points, and the associated red error bars, are the ACRIM 3 measures and their 1-sigma uncertainties.  The blue circles are expected values from a geometrical orbit and solar limb darkening model (discussed below), during the transit (at 5 minute intervals) while the Sun was visible to ACRIMSAT. The Sun, as seen from ACRIMSAT, was occulted by the Earth during the times indicated by the regions of the vertical gray bars in the above graph, thus no data were obtained during those intervals.


The path of (the center of) Venus, as seen from ACRIMSAT, is depicted in the figure below (North is up in the figure).  As previously noted, the planetary parallax (shifting of the line-of-sight to Venus) induced by the spacecraft orbit, projected onto the disk of the Sun causes periodic spatial and temporal modulations in the location of Venus as it traverses the solar disk.  The "vertical" amplitude variation (i.e., in the North/South direction) result from the near-polar ACRIMSAT orbit. As Venus is of similar size as the Earth, and as ACRIMSAT is in a low Earth orbit, the vertical excursions are also comparable (but a bit larger than) to the diameter of Venus.  The "horizontal" (East/West) component manifests itself in non-linear spacings in the planetary position along its projected path in equal time intervals.  This results from  the ACRIMSAT orbit plane not being in the line-of-sight direction to the Sun. Note: with TRACE the modulation is more closely sinusoidal, as its orbit is perpendicular to the Earth/Sun line, but deviates from a linear (in spacecraft orbital phase angle) sinusoid because of the planet's orbital motion about the Sun.


As a result of the reflective spacecraft parallactic motion of Venus, its path across the Sun "nods" in heliocentric radius (r).  A table (in five minute increments) of the positions of Venus against the solar disk, relative to the heliocenter as seen from ACRIMSAT is given HERE. This motion induces  asymmetries in the ACRIM radiometric "light curve" as Venus occults portions of the solar disk of differing surface brightnesses (flux densities) in a radially dependent manner due to solar limb darkening.  One can see that during ingress Venus crosses from r = 1.0 to r = 0.9 (where the limb darkening function has a very steep gradient) twice as slowly as it does from r=0.9 to r = 1.0 upon egress.  Hence, the downward slope of the ingress light curve will be more shallow than during egress.  Additionally, one would expect small amplitude, orbit periodic variations in the intensity variations measured by ACRIM Venus "oscillates" between the brighter (smaller r) portion of the photosphere and positions closer to the solar limb (larger r). This is, at least in part for some of the "wiggles" which are seen at the "bottom" of the light curve, though some variation may also be due to intrinsic variations in the global TSI over the same time interval, and also as Venus occults regions of the photosphere which may be intrinsically brighter or dimmer (as discussed later).


A statistically significant shallow diminution in the radiometric flux density is seen after second contact but before mid transit, i.e., approximately -0.04% at 05:50 UT and approximately -0.08% at 06:15 UT compared to approximately -0.10% at mid transit, and a corresponding gradual rise before the loss of data due to Earth occultation upon egress.  This is attributable to radially differentiated solar limb darkening, with a strong photospheric radial surface brightness gradient as the limb of the Sun is approached. At 05:50 UT the center of Venus was app 0.933 solar radii from the heliocenter, whereas at mid-transit (appx 08:35 UT) the center of Venus was 0.650 solar radii from the heliocenter. This non-linearity in impact distance with time arises, primarily, from the modulation in Venus’s heliocentric velocity vector w.r.t. the limb (e.g., affecting the “limb crossing angles”) induced by ACRIMSATs orbital parallax.


We constructed a “model” light curve by building a series of two-dimensional synthetic images of the Sun, geometrically occulted by Venus as determined by the ACRIMSAT orbital ephemeris. 

Synthetic transit image for 05:40UT as seen from ACRIMSAT.

The synthetic solar images were limb-darkened with a resulting photospheric surface brightness radial profile, F(u), parametrically represented as suggested by Hestroffer and Magan (Astron. & Astroph. 333, 338, 1998):

  F(u) = 1 - a(1-u^b)   where:  u = sqrt(1-r^2)
                                    with r being the fractional solar radius.

This limb darkening function (in central intensity normalized form) and as used to generate a limb-darkened model image (shown 7.5% intensity contour intervals) are illustrated below:

A few other limb darkening references:
Greve & Neckel 1996 (2000-3000 angstoms)
Pierce & Slaughter 1977 (3033-7297 angstroms)
Koutchmy, Koutchmy & Kotov 1977 (1-4 microns)
Petro,  Foukal, Rosen,  Kurucz & Pierce 1984 (optical variability)


With iterative convergence, minimizing the sum of the squares of the residuals in the observed minus computed model data, the model light curve which best fits the ACRIM 3 data has F(u) characterized with a = 0.85 and b = 0.80, and recovered times of contacts very closely agreeing with expectations based upon the spacecraft orbital ephemeris.


Contact I   (external tangency at ingress) = 05:10:19 UT
Contact II  (internal tangency at ingress) = 05:35:35 UT
Contact III (internal tangency at egress)  = 10:59:15 UT
Contact IV  (external tangency at egress)  = 11:29:30 UT

The total area-integrated flux density (i.e., the TSI) “predicted” by the limb-darkened model as Venus transits the solar disk is compared to the ACRIM 3 radiometric measures for times when the Sun was visible to ACRIMSAT (overlaid in blue on the light curve plot).


We use the as-measured TSI variations in the flanking out-of-transit radiometry to assess "how good" (or deficient) our relatively simple model light curve fits the data.  I.e., how much of the fit residuals are due to instrumental measurement errors and intrinsic solar variations compared to imperfections in the model itself.  "Variations", here, not only include temporal variations in (area integrated) TSI but also spatially as Venus covers different parts of the photosphere that are not isotropic in intensity on small spatial scales. 

The left and right panels in the figure below show the distribution functions of the light curve fit residuals from three contiguous orbits (approximately 5 hours) of pre and post transit data (green), immediately before  C I and after C IV.  The median TSI measured for each of those periods differ by only 0.0002%, i.e. "constant" within the measurement errors. Conceivably there could be larger intrinsic solar variations during the time interval of the transit itself. The measured variation in TSI during these 5-hour flanking periods is approximately 0.008% at the 1 sigma level.  The 1-sigma residuals from the model light curve fit to the data during the period of the transit (red) are approximately 0.01%.

The difference in the dispersion in in-transit compared to pre/post-transit model light curve fit residuals is +25% in "as measured" TSI variability (after subtracting out the model light curve).  This in-transit increase in the dispersion in TSI of 0.002% is an order of magnitude larger than the dispersions about the median as-measured TSI's before and after the transit. One may posit one or more instrumental (1), systematic (2), and or real physical effects (3 and 4) contributing to this increase as delineated below: 
  1. Uncertainties in the end-to-end wavelength-dependent system responsivity function for ACRIM under its very broad pass band  (i.e., its spectral sensitivity).  These uncertainties are likely insignificant based upon the ACRIM 3 cavity design and pre-launch testing.

  2. Insufficient fidelity in the limb darkening model.  A quadratic model may be better, and could be tested, but a higher order (multi-parametric) model is likely unjustified given the interrupted phase coverage and single-epoch-only nature of the light curve.

  3. The effect of the atmosphere of Venus itself.

  4. The effect of Venus occulting regions of the photosphere differing in brightness on small spatial scales.
Neglecting or better characterizing (1) a higher order limb-darkening model (2) may be employed and tested by by parametric variation bounded by the instrumental spectral sensitivity calibration. With that, rigorous detection limits for the planetary atmosphere (3) may be ascertained, within the uncertainties in the local variations in photospheric intensity at the spatial scales of Venus (4).


What measured TSI variation resulted from position-dependent photospheric occultation for the actual “path” that Venus took is (and must remain) conjectural, as ACRIM 3 “sees” the Sun as a spatially unresolved source. This will also be case in the analysis of extrasolar terrestrial planet transit light curves of very high photometric precision (e.g., such as those to be obtained by the Kepler mission).

At the time of the transit, between contacts II and III, the planetary disk of Venus occulted 0.0942% of the solar photosphere. But, with an optically opaque atmosphere to 60 km (beyond the mesospheric cloud layer) above the surface the areal coverage was 0.0961%, thus (geometrically) blocking an additional 0.002% of the received TSI (if not preferentially forward scattered, refracted, or re-radiated by the atmosphere).  We tested the ability to discriminate against a 1% equivalent increment in an Earth-like planetary radius (by the presence of Venus's opaque atmosphere) in light of both spatial and temporal solar photospheric "surface" brightness (PSB) variations.

The solar PSB decreases radially from the heliocenter because of limb darkening. The PSB is also instantaneously non-heterogenous on angular scales of ~ 1" due to solar granulation, and on larger scales due to features such as sunspots.  Thus, the TSI received at ACRIM (and corrected to 1AU) is expected to vary as Venus occults different portions of the photosphere during its transit due to spatial variations in PSB, separate from also expected temporal variations. We investigated the likely amplitudes of PSB variations after compensating limb darkening as they may affect ACRIM 3 measures of TSI with contemporaneous high-resolution imagery obtained with the TRACE spacecraft in its very spectrally broad WL channel (appx. 0.1 - 1.0 microns).  

We performed temporally and spatially resolved (and independent) limb-darkening corrected differential photometry of regions flanking the location of Venus as it transitedthe photosphere. With that we obtained statistical expectations of the levels of variability in TSI due to partial photospheric occultation at the angular scale of Venus.

Left: Representative TRACE WL image (one of 100 time-sliced images for this spacecraft pointing spanning 40 minutes of time) of Venus transiting the solar photosphere with photometric apertures used (each enclosing 10, 923 TRACE pixels) to evaluate the temporal and spatial variability of the PSB on the size scale of Venus seen in projection.  Right: Difference image (at same display dynamic range) illustrating the change in PSB at the cadence of ACRIM 3 sampling (also illustrating the movement of Venus over 132s at the indicated times).

Variation in total solar flux density decrement (0.1 to 1.0 microns) due to photospheric occultation by a Venus-size planet arising from temporal and spatial PSB variations (illustrated for 9 regions of the Sun as in the previous figure, during the 8 June 2004 Venus transit). Boxes indicate upper and lower quartiles about measured medians (black lines) of 100 samples.  Bars indicate +/- 2-sigma variations about sample means, with 1-sigma (in delta percent) indicted above.

 - Temporal changes in TSI due to Venus occultation of any fixed region of the Sun tested (e.g., denoted A-I in Fig 1) were found to be  +/- ~ 0.0018% one-sigma (compared to a 0.0019% expected change in signal) with inter-region variations in internal dispersions of  +/- 0.00022%. Hence, a sensitivity to the presence vs. absence of a Venus-like opaque planetary atmosphere was tested at only a 1.05-sigma level of confidence.

 - TSI variations due to spatial anisotropies in PSB on Venus-size angular scales were found dispersed by ~ +/-0.0015% one-sigma about an expected decrement in TSI of 0.0961% due to the presence of Venus imposed on the photosphere with compensation for limb-darkening (I.e., a 1.3 sigma "detection" of the atmosphere of Venus).

The virtual equivalence of the two measures and their uncertainties implicates no significant systematic effects in this data set from large spatial scale PSB variations (after proper limb-darkening compensation) in excess of limiting detection sensitivities from temporal effects.


The spatially unresolved Venus transit light curve obtained by ACRIMSAT (and a similar one obtained by SORCE/TIM) is the closest proxy to an extrasolar terrestrial planetary (ETP) transit which exists. Given our apriori knowledge of this star/planet system geometry and properties, this data set may be exploited uniquely to test the detectability of ETP transits using methods contemplated by future space-based planet-finding missions. With sufficient photometric precision, proper characterization of the effects of stellar limb-darkening can yield information on the vertical structures in stellar atmospheres, and have the potential of informing of the existence of a transiting planetary atmospheres as well.

The amplitudes and dispersions of both the temporal and spatial solar PSB variations limit the ability to radiometrically discriminate with sufficient statistical significance the presence vs. absence of a Venus-like opaque planetary atmosphere for an Earth-sized transiting planet. ACRIM 3 has a single measure (i.e., 2.2 minute "shutter cycle") radiometric precision of 10-4. By comparison, the goal for Kepler differential photometry is a factor of 5 better on timescales of 2 to 16 hours will yielding 4-sigma planet detections for a single transit. But, the effects of intrinsic solar-like PSB variations as assessed from ACRIM 3 and TRACE measures of the recent Venus transit would likely preclude the photometric inference of planetary atmospheres for Earth-size planets of solar-like stars.  Hence, alternate stratagies such as spectroscopic capabilities on subsequent missions (e.g., an integral field spectrograph on TPF-C) must be considered.


We are indebted to Richard C. Willson, Principal Investigator for ACRIM experiments, for providing us with such an excellent and unique data set, and to the ACRIM team for building and commissioning such a fine instrument.  

Link to 2004 Transit of Venus Web Site at Williams College