The Doppler Method for the Detection of Exoplanets. Professor Artie Hatzes

and is an extraneous signal that is not removed by flushing (reading out) the CCD. It is caused by electrons generated in the previous exposure that are trapped at impurity sites on the detector. The electrons that are released in subsequent exposures appear as a residual image (Figure 2.23). The time it takes for the trapped electrons to be released depends on the device.

      Figure 2.23. Residual images in a CCD. (Left) An image of a star with a high count level. (Right) An image of the CCD after reading out the previous exposure. There is a low-level (a few counts) image of the star remaining on the CCD.

      For infrared (IR) arrays, the persistence effect can be larger than that for CCDs. Figure 2.24 shows the persistence measured for a Hawaii 4 IR array used by the European Southern Observatory. For an exposure level of 100,000 detected electrons, after 30 s, the residual image has approximately 250 electrons. This is not so much of a problem if the next exposure is also at a high intensity level (a 0.25% effect). However, a subsequent exposure with, say, 10,000 detected electrons (S/N = 100) means that it will be contaminated by the spectrum of the previous star at the 2.5% level. This contamination will influence your RV measurement.

      Figure 2.24. Residual images in a CCD. (Left) An image of a star with a high count level. Persistence as measured in a Hawaii 4 infrared detector. (Data courtesy of ESO.)

      Persistence in optical CCDs is generally small, and this author, for one, has never had to worry about it. This is particularly true if you are only achieving a modest RV precision of greater than, say, 10 m s⁻¹. However, it you really want to measure ultraprecise RVs below 1 m s⁻¹ or in the cm s⁻¹, then persistence in your device should be measured to assess if this is a problem.

      Persistence can be handled in three ways:

       Limiting the intensity levels of the observation.

       Flushing the CCD with dark bias frames a number of times to reduce the intensity of the residual image. However, this reduces the efficiency of your observations.

       Treating the contamination from the previous observations in your data reduction pipeline.

References

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Kaufer, A. & Pasquini, L. 1998, Proc. SPIE, 3355, 844

Schroeder, D. J. 1987, Astronomical Optics (New York: Academic)

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      ¹The focal ratio is defined as the focal length of the telescope, f, divided by its diameter, D.

      ²The interference pattern is merely the Fourier transform of the aperture, and as we will see in Chapter 7, there is an inverse relationship between the spatial domain and the Fourier frequency domain.

      ³In the 1980s, my fellow graduate student G. Donald Penrod once made the poetic remark, “There is a glorious match between CCD detectors and echelle spectrographs.” So true!

      

      The Doppler Method for the Detection of Exoplanets

      A P Hatzes

      Chapter 3

      Factors Influencing the Radial Velocity Measurement

      The radial velocity (RV) precision that one can achieve depends on many factors: the performance of the spectrograph, the properties of the star, sources of instrumental errors, and finally, stellar variability. Some of these you have control over. For instance, you can take efforts to minimize the systematic errors of your instruments, or you can get more observations of a star in order to “beat down” the noise due to stellar variability. Other factors you cannot control, and these depend on the basic properties of the spectrograph, which are fixed at the design level (e.g., wavelength coverage, resolution) while others depend on the type of star you observe.

      So, we can divide these “uncontrollable” factors into two broad categories:

      1 Factors due to the instrumental characteristics.These primarily include the spectral resolution, wavelength coverage, and signal-to-noise ratio (S/N) of your spectrum. There are of course other factors that can introduce errors such as instrumental shifts, variations in the spectrograph, improper barycentric corrections, etc. These topics will be covered in subsequent chapters. What we will address here are the basic properties of the spectrograph and the RV precision you would achieve if it worked as a perfect instrument.

      2 Factors due to the properties of the star. This is largely dominated by the spectral type of the star (spectral information) and its rotational velocity.

      In other words, the only control the researcher has is in the choice of an appropriate target star. Stars can also influence the RV measurement through its intrinsic variability in the form of pulsations or stellar activity. The “stellar noise” aspects will be addressed in Chapters 9