Introduction

This chapter attempts to provide a summary of the course I gave during the XXII Canary Island Winter School of Astrophysics. In no way should this chapter be perceived as the final answer to a problem. I hope that this chapter can serve as a basis for students and fellow scientists to go beyond what is written here. As in many approaches that I have pursued, this work is a snapshot of where I am and hopefully a possible starting point from which one can expand to other paths not yet ventured.

This chapter starts with a short historical introduction on signal processing and statistics or how our forefathers started doing data analysis more than 200 years ago. The second part is related to the sampling and acquisition of continuous physical signals for subsequent analysis in a digital world.

Introduction

The four lectures that I presented at the XXII Winter School of Astrophysics were an eclectic mix of topics loosely bound under the title of this chapter: an observer's views and tools. The presentations given by all of the lecturers at the Winter School are available at the time of this writing on the IAC Web site (see “about the school” and “lecturers and topics” on that web site). This chapter can be read in conjunction with the lecture presentations on that web site, but that is not required. This chapter does not completely follow the order of the presentations.

Chemically peculiar and pulsating stars of the upper main sequence

On and near the main sequence for Teff > 6, 600 K, there is a plethora of spectrally peculiar stars and photometric variable stars with a bewildering confusion of names. There are Ap, Bp, CP, and Am stars; there are classical Am stars, marginal Am stars, and hot Am stars; there are roAp stars and noAp stars; there are magnetic peculiar stars and nonmagnetic peculiar stars; He-strong stars, He-weak stars; Si stars, SrTi stars, SrEuCr stars, HgMn stars, PGa stars; λ Boo stars; stars with strong metals, stars with weak metals; pulsating peculiar stars, nonpulsating peculiar stars; pulsating normal stars; nonpulsating normal stars; δ Sct stars, δ Del stars, and ρ Pup stars; γ Dor stars, SPB stars, β Cep stars; γ Cas stars, λ Eri stars, α Cyg stars; sharp-lined and broad-lined stars, some of which are peculiar and some of which are not.

Introduction

Asteroseismology, and hence the study of stellar properties, is being revolutionized by the extremely accurate and extensive data from the CoRoT (Baglin et al., 2009) and Kepler (Borucki et al., 2009) space missions. Analysis of time series of unprecedented extent, continuity, and sensitivity has allowed the study of a broad range of stellar variability, including oscillations of a variety of pulsating stars (see, e.g., Gilliland et al., 2010; Christensen-Dalsgaard and Thompson, 2011, for reviews), and leading to comparative asteroseismology (or synasteroseismology) for main-sequence stars showing solar-like oscillation (Chaplin et al., 2011). Also, early analyses of Kepler data have demonstrated the power of asteroseismology in characterizing the central stars in planetary systems (Christensen-Dalsgaard et al., 2010; Batalha et al., 2011), and such investigations will undoubtedly play a major role in the continuing Kepler exploration of extrasolar planetary systems.

However, perhaps the most striking results of space asteroseismology have come from the investigation of red giants. Given the extensive outer convection zones of red giants, solar-like oscillations were predicted quite early (Christensen-Dalsgaard and Frandsen, 1983). Ground-based observations have been carried out in a few cases (e.g., Frandsen et al., 2002; De Ridder et al., 2006) but, owing to the very long periods of these huge stars, such observations are extremely demanding in terms of observing and observer's time. Space observations, on the other hand, allow nearly continuous observations over very extended periods, as demonstrated by early observations by the WIRE (Retter et al., 2003) and MOST (Barban et al., 2007) satellites.

Introduction

Helioseismology, the study of the Sun using solar oscillations, has provided us with the means to probe the solar interior. Since the discovery of the oscillations in 1962 (Leighton et al., 1962) and their interpretation as global oscillation modes by Ulrich (1970) and Leibacher and Stein (1971), helioseismology has been used extensively to study the interior of the Sun, mainly through inversions of solar frequencies. With space missions such as CoRoT (Baglin et al., 2006) and Kepler (Borucki et al., 2010) now observing oscillations of other stars, inversions of stellar frequencies may soon be feasible. There are two ways by which we could use seismic data to make inferences about the stars. The first way involves trying to find models whose frequencies match the observed frequencies, usually referred to as “forward modeling.” This is essentially what is done in most fields of astronomy. The end result of the process is a model that is the best match to the observations. The second way is to invert the data. Inversions use the data directly to make inferences about the star. In the case of inversions, we can make a distinction between the structure of the star and the structure of the best-fit model. These days inversions are used to study the solar interior, while forward modeling is used to study other stars.

It is not possible to do an inverse analysis unless we can do the forward analysis.

Introduction

My brief for the IAC Winter School was to cover observational results on helioseismology, flagging where possible implications of those results for the asteroseismic study of solar-type stars. My desire to make such links meant that I concentrated largely on results for low angular-degree (low-l) solar p modes, in particular results derived from “Sun-as-a-star” observations (which are, of course, most instructive for the transfer of experience from helioseismology to asteroseismology). The lectures covered many aspects of helioseismology – modern helioseismology is a diverse field. In these notes, rather than discuss each aspect to a moderate level of detail, I have instead made the decision to concentrate on one theme, that of “sounding” the solar activity cycle with helioseismology. I cover the topics from the lectures and I also include some new material, relating both to the lecture topics and to other aspects I did not have time to cover. Implications for asteroseismology are developed and discussed throughout.

The availability of long time series data on solar-type stars, courtesy of the NASA Kepler Mission (Chaplin et al., 2010; Gilliland et al., 2010) and the French-led CoRoT satellite (Appourchaux et al., 2008), is now making it possible to “sound” stellar cycles with asteroseismology. The prospects for such studies have been considered in some depth (Chaplin et al., 2007a, 2008a; Metcalfe et al., 2007; Karoff et al., 2009, e.g.), and in the last year the first convincing results on stellar-cycle variations of the p-mode frequencies of a solar-type star (the F-type star HD49933) were reported by García et al. (2010).

Background

The XXII Canary Islands Winter School of Astrophysics, organized by the Instituto de Astrofísica de Canarias (IAC), focuses on the new advances and challenges that asteroseismology provides in the domains of stellar structure, dynamics, and evolution. Every year the Winter School welcomes around 60 Ph.D. students and young postdocs and provides a unique opportunity for them to broaden their knowledge in a key field of astronomy.

Scientific rationale

When oscillations of the Sun were first discovered, a new era of science began. The observed frequencies could be used to probe deep into the stellar interior, the only measurements that could possibly pierce the stellar surface. Today, “helioseismology” has been responsible for some of our deepest understanding of the Sun: we know the radial and longitudinal rotation profile of the interior, we have measured the depth of the outer convection zone, and it has helped solve the so-called neutrino problem when the observations and theory predicted a much hotter central temperature than the observed neutrinos predicted. Today, these seismic observations are not only available in much higher quality, but they are also available for hundreds of other stars. In the last few years, many space missions (CoRoT and Kepler) have produced these data of exquisite quality, and for the first time we are in a position to study the Sun in the context of other stars, measure the fundamental parameters of single field stars to within 2 percent, learn about diffusion processes and the effects of rotation on the stellar structure, and test opacities and equations of state in extreme conditions.

What are solar-like oscillations?

Oscillations in the Sun are excited stochastically by convection. We use the term “solarlike” to refer to oscillations in other stars that are excited by the same mechanism, even though some of these stars may be very different from the Sun. The stochastic nature of the excitation produces oscillations over a broad range of frequencies, which in the Sun is about 1 to 4mHz (the well-known 5-minute oscillations). Stellar oscillations can also be excited via opacity variations (the heat-engine mechanism, also called the k mechanism), as seen in various types of classical pulsating stars (Cepheids, RR Lyraes, Miras, white dwarfs, δ Scuti stars, etc.).

For a star to show solar-like oscillations, it must be cool enough to have a surface convective zone. In practice, this means being cooler than the red edge of the classical instability strip, which includes the lower main sequence, as well as cool subgiants and even red giants. Indeed, solar-like oscillations with periods of hours (and longer) have now been observed in thousands of G and K giants (see Section 3.9). There is also good evidence that the pulsations in semiregular variables (M giants) are solar-like (Christensen-Dalsgaard et al., 2001; Bedding, 2003; Tabur et al., 2010), as perhaps are those in M supergiants such as Betelgeuse (Kiss et al., 2006).

What about hotter stars? By definition, solar-like oscillations are excited stochastically in the outer convection zone.