3. Materiales y Métodos
3.4 Determinación del efecto de los extractos hidroalcohólicos de C.
The results of the above analysis are shown in Table 5.1. Judge et al. suggest that the secondary companion is either a main sequence star later than G type or a white dwarf. Gontcharov and
0.003 0.0025 0.002 0.0015 0.001 0.0005 0 -0.0005 -0.001 -0.0015 1’’ N E
Figure 5.2: The reduced, background-removed coronagraphic image of δAndromedae. The first
Airy ring is visible around the companion. The stretch in the image is linear. The colorbar shows the relative intensity (as a fraction) compared to the primary
Kiyaeva measure a mass fractionmB/(mA+mB) = 0.5±0.1 for the binary system and then favor
the white dwarf assumption and suggest an even split of mass between primary and secondary, placing the white dwarf very near the Chandrasekhar mass limit.
0
500
1000
1500
2000
2500
Wavelength [nm]
5
0
5
10
15
20
25
30
5/2
Lo
g
10[Fl
ux
]+
co
ns
t
K giant (T = 4250K, logg = 2, R=13.6) K0 dwarf (T = 5250K, logg = 4.5, R=0.85¯) K5 dwarf (T = 4500K, logg = 4.5, R=0.72¯) K7 dwarf (T = 4000K, logg = 4.5, R=0.63¯)White dwarf (50000 K blackbody, R=.01¯)
Figure 5.3: Comparison of the approximate fluxes ofδAnd A, three K dwarfs, and a 50000K white
dwarf. The spectral models are from Castelli & Kurucz (2004). The grey bar shows the span of the Bracket-γfilter.
However, assuming that the companion is a white dwarf, its radius is constrained to be about 0.01 R, as white dwarfs of 0.5-1.4 Mspan the radius range of 0.014 to 0.005 R. Comparing the expected flux levels of a hot white dwarf to that of the primary (see Figure 5.3), the magnitude difference through the Bracket-γfilter would be about 12 magnitudes, not the measured 6, a discrep-
ancy of greater than 100 times our photometric uncertainty. Furthermore, such a hot white dwarf would have a UV continuum that was not detected in Judge et al., who constrain the white dwarf’s temperature to less than 10000K if it exists. This low temperature would make the magnitude difference even more extreme. The white dwarf possibility is thus definitively excluded.
On the other hand, the measured flux is quite consistent with a main-sequence K-type dwarf. Shown in Figure 5.3 are spectral models of K0, K5, and K7 stars, with our measured flux shown as a black dot. For theδAnd primary, the effective temperature and radius is taken from published results
(Table 5.1; note that the radius is known accurately from interferometry (Piau et al., 2011)). For the secondary, the effective temperatures and surface gravities are taken from Castelli & Kurucz (2004) and the radii are taken from Cox (2000). While the formal photometric error is smaller than the size of the datapoint, lack of knowledge about the companion’s radius and temperature make it impossible to give a completely specific spectral classification; the best we can say is that the companion is most likely a K-type dwarf. Making a more accurate measurement of the secondary spectral type is possible in principle. The simplest way would likely be a similarly precise coronagraphic measurement in J band, as the J-K colors of K dwarfs change by about 200 millimags over the spectral type. Alternatively, an AO-fed integral field spectrograph might be able to measure the spectral type from the CO band at approximately 2.3µm.
The conclusion that the companion is K-type is mostly consistent with previous work. As men- tioned before, Judge et al. concluded that a main sequence companion would have to be a star later than G-type. A K-dwarf has a mass of between 0.6-0.8 M; taking values of 1.1 - 1.2M forδAnd
A gives 0.3-0.4 as the mass fraction, reasonably consistent with the value of Gontcharov & Kiyaeva (2002) of 0.5 ±0.1. The results presented here demonstrate the potential of high contrast imag- ing applied to medium to long-period spectroscopic binaries. In particular, the contrast differences between main sequence stars in binaries are readily accessible to a coronagraphic system, and the information gained can improve orbit characterization, or as in our case, distinguish quickly between different companion possibilities.
Chapter 6
Part II–Speckle nulling wavefront
control for Palomar and Keck
Abstract
We present a speckle nulling code currently being used for high contrast imaging at the Palomar and Keck telescopes. The code can operate in open and closed loop and is self-calibrating, requiring no system model and minimal hand-coded parameters. Written in a modular fashion, it is straightfor- ward to port to different instruments. It has been used with systems operating in the optical through thermal infrared, and can deliver nearly an order of magnitude improvement in raw contrast. We will be releasing this code to the public in the near future.
6.1
Introduction
The largest current barrier to imaging extrasolar planets is the presence of “speckle” aberrations, which arise from errors in figure or transmissiveness of optical elements after the wavefront sensor of the adaptive optics system. These speckles show up in the focal plane as bright points of light that look similar to the point-spread function, typically tens to thousands of times brighter than any planetary companions that might be present in the image. To a large degree, observing approaches on ground-based telescopes are oriented towards removing speckles in post-processing. This includes techniques such as angular differential imaging (Marois et al., 2006a), spectral differential imaging (Marois et al., 2006b), and reference star differential imaging.
Rather than only remove speckles in post processing, it is possible to remove them “optically.” This has the advantage that the fundamental photon shot noise level is reduced, so all post-processing algorithms will have better performance, as they are all eventually limited by shot noise. There are a number of different techniques to reduce speckles optically. The most powerful general approach is called “electric field conjugation” (EFC) (Give’on, 2009), where the deformable mirror response function is linearized, small perturbations are put on it to determine the phase over the focal plane; then the linearized response function is used to compute the corrections in a specified control region. EFC has been used in a number of stable high contrast imaging testbeds, with contrasts of better than 10−8 being achieved in some cases (Thomas et al., 2010).
Electric field conjugation has not found wide implementation on high contrast imaging instru- ments on telescopes, perhaps because it requires an accurate model of the imaging system to achieve good performance. In many instruments, system states can change quite rapidly due to changing gravity vectors, temperature, or other states. This motivates us to consider a different algorithm for robust performance on non-ideal systems. An alternative to EFC is speckle nulling, an algorithm which identifies bright points of light in the image, uses the deformable mirror to create an artificial “speckle” at the same location, and calculates the phase of the original speckle by changing the phase of the artificial speckle (Savransky et al., 2012; Martinache et al., 2014). Finally, it uses the deformable mirror to put a speckle of the opposite phase on the original offending speckle, which makes it disappear. Doing this to many speckles at a specified location in the image plane will create a region of lowered intensity and higher contrast.
In this work, we will first present the background principles of speckles: how they arise, how they propagate, and how it is possible to (partially) correct them. Then we will describe the main points behind speckle nulling, and discuss our specific algorithmic implementation. Finally, we will present results of our speckle nulling code on different instruments at the Palomar and Keck observatories.