Exoplanet Stars Are Not Variable Stars

Occasionally I notice that a new observer is using procedures for observing and image analysis that are meant for use with variable star tasks and which therefore are not optimized for the task of exoplanet observing. Whereas experience with AAVSO tasks is helpful to someone starting to observe exoplanets, the two tasks are different enough that many of the procedures for AAVSO tasks should not be adhered to while learning to observe exoplanets. This web page is meant to highlight the differences, and provide ideas for adjusting strategies in observing, image measurement and spreadsheet analysis that will benefit the results for exoplanets.


Most AAVSO tasks have the goal of monitoring changes in a star's brightness from one night to another. This requires the use of nearby reference stars, that are still referred to by the term "comparison stars" (revealing that the term originated in the days when visual observing was employed). Each reference star must have a known brightness for each filter band, and these brightness values must be the same for time scales of years and decades. Since variations of the target star's brightness will be inferred by comparing measurements by different observers it is necessary that each observer's reported brightness be corrected for such instrumental effects as filter passband differences. This means that something called "CCD Transformation Equations" be employed (link). It also means that stars can only be used for "comparison" if they have been calibrated by an advanced observer (professional astronomer). This calibration procedure involves "all-sky photometry" (link) - a procedure that is so difficult that I'm unaware of any amateurs who can do it. Since all-sky photometry is time consuming it is common for a variable star to have only a few stars nearby that have been calibrated, and until these calibrations have been performed it is not possible for different observers to perform accurate brightness measurements of the variable star that are suitable for comparison. It is common for a variable star to be "compared" with just one other nearby star, a star that has been calibrated and is chosen to have a similar brightness and color to the variable. These are things that must be understood in order to contribute to most AAVSO tasks.

Wow! Anyone experienced with exoplanet observing would shudder while reading the previous paragraph! So many of the concerns for AAVSO observers are simply irrelevant for exoplanet observing. For an exoplanet observer it is unecessary for ANY of the nearby stars be calibrated. To use just one comparison star (called reference stars by CCD observers) would be foolhardy; as many reference stars as possible should be used, and since none of them need to be calibrated there will always be plenty available for use no matter how "unknown" the star field is (I try to use as many as 28 uncalibrated reference stars). And when the magnitude differences between the exoplanet star and the many reference stars are measured there is never a need for specifying the magnitude of any of the reference stars. 

Whereas an AAVSO observer strives to achieve an accuracy of ~0.03 magnitude for a specific filter band, for a night's observations of a given variable star, the exoplanet observer has absolutely no accuracy goals in mind. The exoplanet observer strives for PRECISION, not ACCURACY! His task is for a precision of 0.002 magnitude, and accuracy be damned! (If you don't understand the difference between accuracy and prescision, it is described at the end of this web page.)

So, how does exoplanet observing and analysis differ from AAVSO variable star observing? Let's count the ways.


For AAVSO variable stars it is necessary to use a reference star whose magnitude has been established by a professional astronomer (e.g., Arne Henden). On rare occasions two or more such reference stars are used, called "ensemble differential photometry." When this is done the variable star's magnitude is reported (by the image processing program) to be the average of what each of the reference stars calls for. In establishing a set of nearby stars to be calibrated for this purpose it is customary that their brightnesses span the range that the variable star undergoes during the many years required for it to experience the full range of its brightness variations. This isn't necessary for CCD observers, but it is for visual observers. The stars that are calibrated for this purpose are called a "sequence" for the variable in question. Since establishing accurate magnitudes for the "sequence" requires all-sky photometry, and since this is too difficult for amateurs, a variable star cannot be adequately observed by more than one observer until a professional astronomer has established a "sequence" of calibrated stars near the variable, and has also confirmed that none are variable themselves. 

For exoplanet observing it is not necessary to know the magnitude for any stars that are to be used for reference! The only requirement for using a nearby star for reference is that it not vary during the several hours of the observing session. (Well, sometimes there's an additional "requirement" - actually a "preference" - to not use any reference stars that have a color vastly different from the target star.) Any observer who is accustomed to using a commercial program for processing images for AAVSO tasks is likely to be puzzled about this, and will wonder what to do when it's time to select a "comp" star (an archaic term left over from the days when most monitoring of variables was done visually). My advice to such an observer is to choose any nearby star you want for use as a "comp" star, provided it's not saturated at any time during the observing session, and assign it any old magnitude that catches your fancy. For "thrills" give it a magnitude of 100; it just won't matter in the final analysis. If you want to use a second "comp" star for reference, you may also assign it any magnitude you want; try -100. Mathematically it just won't matter. Remember, for an exoplanet star we don't care what magnitude you report for it; we only care how the star varies in brightness during the observing session.


Scintillation is a variabtion on very short time scales (millisecond to seconds) of a star's brightness, and it is related to "twinkling." Scintillation and twinkling are caused by temperature inhomogeneities immediately below the tropopause (at 10 to 16 km altitude). Turbulence causes these inhomogeneities (the same "clear air turbulence," or CAT, that affects commercial jet aircraft). Temperature inhomogeneities bend the path of a photon's wave front by very small amounts, and from the standpoint of a silicon atom in your CCD chip, poised to absorb a photon's energy and release a photoelectron, parts of the photon's wavefront intercept an atmosphere that bends the wavefront one way and other parts bend it another way, so that when the photon arrives at the CCD the wavefronts with different atmopsheric paths will have phase differences at the silicon atom that can reinforce or diminish the energy available for absorption (compared to the situation of no atmospheric effects). The scintillation at one location will differ slightly from that at another location, such as a few inches away, and this means that large telescope apertures will average down the amplitude of scintillation. The eye, with an aperture of ~1/3 inch, sees a larger scintillation amplitude than is measured using a telescope (and the eye is subject to a component of scintillation produced by temperature and humidity inhomogeneities at low altitudes). For example, a 10-inch aperture telescope observing at 30 degrees elevation for a 10-second exposure will typically exhibit scintillation variations of ~0.008 magnitude. For an AAVSO task, where the goal may be an accuracy ~ 0.03 magnitude, scintillation is unimportant. But for an exoplanet observer, with a goal of ~2 mmag precision, an 8 mmag component of variation is important. If one nearby star is used as reference, the magnitude defference between the two stars will exhibit a root-2 greater scintillation than for either star alone (because scintillation variations are uncorrelated for separations greater than about 10 "arc). Using just one reference star in our example would produce a scintillation component of ~12 mmag per 10-second exposure. By using many reference stars the target star's scintillation can be brought back to the 8 mmag level. The penalty for not using many reference stars is equivalent to using exposure times that are half of what in fact were used, so this is equivalent to reducing the "information" from an observing session by a factor two!  The lesson from this paragraph, for the exoplanet observer, is to use many reference stars.

For anyone interested in calculating typical scintillation levels for a specific observing situation here's an equation published by Dravins et al (1998):


where sigma is fractional scintillation, D is telescope aperture diameter [centimeters], Z is air mass, h is observing site altitude [meters], ho is 8000 meters and g is exposure time [seconds] (g is refers to "gate time," a common term in electronics circles). Scintillation level can vary by a factor two in a matter of hours since it is determined by turbulence conditoins at the tropopause, which exhibit large spatial variations (think of a frozen field of temperature inhomogeneities drifting through the observing line-of-site).


SNR, or signal-to-noise ratio, is very important for exoplaent observers, and it is relatively unimportant for AAVSO variable star observers. Variations in an exoplanet's light curve due to SNR will be given by 1/SNR; so when SNR = 500 it contriubtes a 2 mmag component to stability. It is therefore important for exoplanet observing to choose an exposure time that produces counts (analog digital units) whose maximum value is just below saturation, but never greater than the saturation level for the entire observing session. For a typical CCD the saturation level may be ~40,000 counts. If a nearby star is to be used for reference it also must be kept below this level. During the observing session focus changes will change the size of star images on the CCD; the so-called point-spread-function will undergo changes in FWHM as focus changes. This, in turn, will change the maximum counts for a star (Cx) during an observing session. Cx will be proportional to 1/FWHM2, so as the star field approaches its highest elevation, where seeing is best (FWHM is smallest), Cx is likely to be at greatest risk of saturating. Some observers will intentionally de-focus when seeing improves so much that saturation might occur. This is OK for bright stars (<11th mag for a 14-inch), but for faint stars the loss of SNR due to a broader FWHM is undesirable. Careful attention has to be paid to choosing an exposure time at the beginning of an observing session that does not produce saturation when seeing is best.


High precision can be lost if the fraction of photons falling close to CCD pixel edges is high. This means that you don't want FWHM to be small in terms of pixels. The rule-of-thumb is that FWHM should exceed ~2.5 pixels in order to maintain high precision (~2 mmag). This has implications for image scale (also referred to as "plate scale" by old-timers), defined as "seconds of arc per pixel." If your seeing is typically FWHM ~ 3 "arc, for example, image scale should be no greater than ~1.2 "arc/px. If it's larger, don't count on high precision. If it's smaller, don't count on the best SNR. The reason smaller image scales have lower SNR is related to the noisiness of CCD pixels, treated next.


Each pixel reading will exhibit a "noisiness" that is the sum of three components: dark current (thermal agitation of molecules and movement of electrons in the electronics), sky background brightness (e.g., moonlight) and read-out noise. When a bright star contributes to the counts at a pixel location there's an additional component of noise that becomes important: Poisson noise, an uncertainty that is the square-root of the total counts (whether for one pixel or all pixels within a signal aperture). To minimize dark current it's important to cool the CCD. The professionals use liquid nitrogen (~80 K), but we amateurs must be content with the smaller amount of cooling produced by a thermoelectric cooler (TEC). To minimize sky background noise it is important to use as small a signal aperture size as possible while using a large sky background annulus. Choosing the best aperture sizes (signal radius, gap width and background annulus width) is a big subject, and I can't go into detail here. However, I will state that noisiness problems are reduced by maintaining good focus because this provides flexibility in choosing small photometry signal apertures for the purpose of maximizing SNR. The effect of read-out noise is reduced by using long exposures, with as few readouts per observing session as possible. Clearly, lot's of issues have to be considered in choosing an optimum observing strategy and an optimum image measuring strategy for exoplanet observing. Few of these issues concern the AAVSO variable star observer since their goal is ~0.03 magnitude accuracy as opposed to 0.002 magnitude precision.


For AAVSO type variable star observing it's not important to autoguide or have a perfect polar axis alignment, but for exoplaent observing this is important.

Let's first consider the demands of exoplanet observing. If the star field can be kept fixed to the pixel field during a long observing session there should be no temporal trends or variations in an exoplanet's light curve due to an imperfect flat field. Indeed, it would not be necessary to even apply a flat field calibration if the star field could be kept perfectly positioned. Autoguiding may keep the autoguider star at the same location on the autoguider chip, but unless the polar axis alignment is perfect image roatation will move the star field through pixel locations. This pixel motion will be greatest at declinations near a celestial pole, and will be greatest on that part of the main chip that is physically farthest from the autoguider chip. It is difficult to achieve flat fields that are more accurate than ~0.025 magnitude across most of the FOV, and for small pixel movements the imperfect flat field calibration may produce variations in flux, compared to other locations, that amount to a few mmag. By plotting magnitude/magnitude scatter diagrams of star pairs during an observing session it is possible to evaluate how large these variations are. For exoplanet observing image stabilization using SBIG's tip/tilt image stabilizer (AO-7, AO-L) can provide short timescale stability as well as long term stability (provided the polar axis is well aligned so that image rotation is reduced).

When variations of a few mmag are unimportant, as with AAVSO type observing of variable stars, it won't matter that the image rotates, and it won't matter where the stars are positioned on the CCD. This is because flat field calibration can be achieved at the 0.05 magnitude accuracy level with little effort. Furthermore, if several reference stars are used their flat field errors will "average out" somewhat.


Setting the photometry apertures properly for exoplanet images is an important part of achieving stability during an observing session. There are three aperture values to be chosen: signal aperture radius, gap annulus width and sky background annulus width. The most important of these is the first one, which I'll refer to as R. The value of R in relation to FWHM determines the fraction of flux captured by the signal aperture in relation to the toal flux from the star that's registered by the CCD. The "missing flux" can be expressed as a "flux correction" that should be applied if all photons are to be accounted for. The following graph is a plot of "Required Correction" versus the ratio R/FWHM for a typical image.

Typical relationship between aperture size and missing flux (flux that's not captured by the signal aperture).

If R is small the "flux capture fraction" is small, requiring a large "correction." For example, in the above graph if R = 3 × FWHM the measured flux should be increased by ~22 mmag. As seeing varies while R remains fixed this correction will vary. For a telescope with imperfect optics (that includes all telescopes), the size of the point-spread-function, PSF, will vary across the image. The details of this variation will change with focus setting. Therefore, a too small R will produce flux capture fractions that differ across the image, and that change during an observing session. If R is set too large SNR suffers. A large R also increases the likelihood that the signal aperture will contain defects, such as cosmic ray hits or hot and cold pixels due to an imperfect dark frame calibration. A large R also increases the chances that a nearby star will swell in size during bad seeing episodes and contribute some of its flux to the target star's signal aperture. I've seen this last effect cause trends of several mmag. The ideal solution is to employ a "dynamic aperture" such that the image measuring program takes a measure of FWHM for each image and then sets R to whatever multiple of FWHM the user specifies (such as R = 3 × FWHM). Unfortunately, MaxIm DL does not provide this feature yet, and I can't afford to pay them to develop it. (I sometimes perform a "poor man's dynamic aperture" by repeating the readings using a range of R values then later combining them to match FWHM versus time.)

AAVSO observations won't matter if they're affected by a few mmag of systematic errors. Therefore, if the variable star goal is an accuracy of 0.05 magnitude, for example, aperture choices are not very important. Simply adopting R = 3 × FWHM, assuming that all stars suffer the same "missing flux fraction" (corresponding to ~20 mmag), could allow the observer to believe that he's dealt with the matter sufficiently. This would be a safe procedure when systematic errors of ±0.02 magnitude are acceptable, which is the case for all AAVSO variable star observing tasks. For exoplanet observers this detail matters.


Precision is the consistency of measurements, regardless of any calibration error shared by all of them. When all calibration errors (systematic errors) remain constant, precision is given by the Poisson equation: SE = 1/SQRT(N), where N is the number of discrete events leading to the measured value, N.

Accuracy consists of two components: precision and calibration uncertainties. Since these two components are uncorrelated (the sign of one is unrelated to the sign of the other), the two components are added orthogonally. This means the accuracy uncertainty, SEa = SQRT( SEp2 + SEc2), where SEp is precision (also called stochastic uncertainty) and SEc is calibration uncertainty. SEc is almost always subjectively estimated.

In AAVSO related photometry a worthy goal for accuracy is ~0.03 magnitude (although 0.02 and slightly lower are possible from ground-based observations if careful procedures are followed). For exoplanet observing, on the other hand, it is acceptable that a set of observations have an accuracy SE of 0.1 magnitude, or 1 magnitude or even 10 magnitudes! It's totally irrelevant how accurate an exoplaent light curve is. For AAVSO variable star observing accuracy is everything, and accuracy SE > 0.1 magnitude is almost never acceptable. In order to achieve an accuracy of 0.05 magnitude, for example, it is adequate for precision to be < ~0.02 magnitude (SNR > 50). This level of imprecision is useless for ALL exoplanet work. No wonder the two tasks require different strategies for observing and image analysis.

(Uncertainty is stated in terms of SE, standard error, which assumes that the probability function for a measurement is Gaussian. This, in turn, permits the use of "least squares" and "chi-square" statistical tools  to be used for fitting measurements instead of Bayesian Estimation Theory, the "gold standard" for matching measurements with models.)

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WebMaster: Bruce GaryNothing on this web page is copyrighted. This site opened: June 28, 2008 Last Update: 2009.04.21