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The Doppler Method for the Detection of Exoplanets. Professor Artie Hatzes
Читать онлайн.Название The Doppler Method for the Detection of Exoplanets
Год выпуска 0
isbn 9780750316897
Автор произведения Professor Artie Hatzes
Жанр Физика
Издательство Ingram
Figure 3.5 shows the actual RV error determined from solar spectra (day sky observations) using an iodine absorption cell at resolving powers of R = 2300, 15,000, and 200,000. These were taken with the same detector and spectrograph, but different gratings to provide different resolutions. The solid red curve is the function σ∝R−1, while the dotted curve is σ∝R−1/2. At first glance this seems to support σ∝R−1. Therefore, (1/2−α)=−1, which implies that α = 3/2 as opposed to unity. Keep in mind the caveat that these data were taken with the iodine absorption cell.
Figure 3.5. (Points) The radial velocity error taken with a spectrograph at different resolving powers. This is the actual data taken of the day sky all with the same S/N values. The solid red line shows a σ∝R−1 fit. The dashed black line shows a σ∝R−1/2 fit. The detector size is fixed for all data, thus the wavelength coverage is increasing with decreasing resolving power.
3.2 Stellar Characteristics
The properties of the star also have a large influence on your RV precision. The RV uncertainty depends on three major fundamental features of the star (stellar spectrum):
The projected rotational velocity of the star, or sin i.
The strength of stellar spectral lines.
The number density of stellar lines.
3.2.1 Stellar Rotational Velocity
In the absence of stellar variability, stellar rotation has the largest influence on the RV measurement error. Rotation broadens the width of the stellar lines and makes them shallower, thus making it more difficult to determine the centroid. Figure 3.6 shows the spectral region of two stars, the top of a B9 star and the lower panel of a K5 star. The hot star only has one spectral line in this region, and it is quite broad and shallow, due to the high projected rotation rate of the star,
Figure 3.6. (Top) A spectrum of a B9 star rotating at 230 km s−1. (Bottom) The spectrum of a K5 star.
Table 3.2 lists the median
Table 3.2. Median Rotational Velocities of Stars
Spectral Type |
|
---|---|
O4 | 110 |
O9 | 105 |
B5 | 108 |
A0 | 82 |
A5 | 80 |
F0 | 44 |
F5 | 11 |
G0 | 4 |
G5 | 3 |
K0 | 3 |
K5 | 2 |
M0 | 10 |
M4 | 16 |
M9 | 10 |
In terms of good RV precision, early-type stars are poor targets for RV measurements for two reasons. First, these stars are hot, and as such, they have much fewer spectral lines for RV measurements than for stars at the lower end of the main sequence. This is seen in the lower panel of Figure 3.6, where the K5 star has a higher density of spectral lines. Second, rapid rotation greatly degrades the RV precision.
Figure 3.7 shows the behavior of the RV uncertainty as a function of
Figure 3.7. The scale factor for the increase in the RV uncertainty as a function of the stellar
Equation (3.3) and the curves in Figure 3.7 should only be used to estimate the RV uncertainty for a star with a certain