In the last decade Dark Energy has joined Dark Matter as one of the most pressing issues in physics and astrophysics today. Key in the discovery of Dark Energy, the unknown source causing the acceleration of the Universe's expansion, has been Type Ia Supernovae (SNe Ia). In the next decade, efforts will be concentrated on learning the exact nature of the Dark Energy, whether it be a Cosmological Constant, quintessence, or modified gravity, using SNe Ia and other cosmological probes.
In this text version of a presentation given for Second Year Seminar, I will discuss what exactly SNe Ia are in Section 1 and how they can be used to study Dark Energy in Section 2. Section 3 will give an overview of NASA's Joint Dark Energy Mission and one of the competitors, the Advanced Dark Energy Physics Telescope (ADEPT). In Section 4, I will discuss the simulations required to evaluate the ability of ADEPT SNe observations to constrain the nature of Dark Energy.
Figure 1 illustrates the progenitor of a Type Ia Supernova. It begins as a binary star system in which one of the stars is more massive. More massive means the star evolves faster, and so it becomes a red giant earlier. The smaller companion pulls off the outer envelope of the giant and begins accreting matter onto itself. Eventually the giant collapses and becomes a White Dwarf.
A White Dwarf star is a dead star that has exhausted its ability to fuse elements in its core. No longer supported against self-gravity by this fusion, it is now supported by electron degeneracy pressure. There is a limit to how massive a star can be before the electron degeneracy pressure is not strong enough to support the star against self-gravity and it collapses into a neutron star. This mass limit is called the Chandrasekhar mass and has a value of about 1.4 Solar Masses.
Some time after the first star has become a White Dwarf, the second star continues its own evolution and becomes a red giant. This is the important step in the creation of a Type Ia Supernova. The White Dwarf now begins accreting matter onto itself from its red giant companion. If it attains the Chandrasekhar mass, it becomes unstable and explodes in a supernova event.
When we observe a supernova, what we see is basically a bright point that wasn't there before. In order to use SNe Ia there needs to be some method of distinguishing them from the core-collapse supernovae. There are a few ways to do this.
The spectrum of a Type Ia supernova is luckily quite different than its core-collapse counterparts. To begin with, it exhibits a Silicon II absorption feature at 6150 Angstroms that is unique to Type Ia's. The spectrum also shows a lack of Hydrogen lines, which is a feature of all Type I's and separates them from Type II's. Figure 2 shows exampes of the different types of supernovae spectra (Fillipenko 1997).
Another way to distinguish a Type Ia supernova from other types is to look at its near-infrared light curve. A light curve gives the SN magnitude as a function of time, showing the rise to maximum brightness and subsequent decline. A unique property of SNe Ia is that their I-band light curves exhibit a second peak 20-30 days after the initial peak (Kasen 2006). If a supernova is observed in the I-band (which is to say that the observed band is blue-shifted back roughly to the rest-frame I-band at the supernova's redshift), then a Type Ia may be identified by this second peak.
A third factor which helps to identify Type Ia Supernovae is that the host galaxies in which they reside are generally red, evolved, and elliptical. This is a general consequence of the longer time-scales which are required to produce SNe Ia, and that the more massive progenitors of core-collapse supernovae more often appear in spiral galaxies. Though the host galaxy morphology cannot be used alone to identify a supernova, it can be combined with other factors to increase or decrease the likelihood that a SN is a Type Ia or some other type.
Since Type Ia Supernovae involve an explosion that occurs at around the Chandrasekhar mass, they are a very homogeneous phenomenon and so have about the same luminosity. This means that they are an astronomical standard candle: if you know the intrinsic brightness and can measure the observed brightness, you can use the inverse square law to determine the distance to the object. The inverse square law tells us that the brightness of an object falls off as one over the distance squared. (This distance is called the luminosity distance, for obvious reasons.)
SNe Ia are also very bright compared to other standard candles, which means they can be seen at high redshifts and so are important to cosmology. This is due to the following: the expansion of the universe is inferred from the observation of a correlation between recession velocity and distance -- the farther away an object is, the faster it is moving away from us. Velocity relates to redshift, and so the ability to determine distances out to high redshifts allows us to measure the rate of expansion. This rate is given by Hubble's constant in the local universe where the expansion is a linear relationship: v=H_0*d. However, this relation can in general be much more complex, as it depends on the densities of the various components of the universe. For example, matter tends to slow down the expansion, and if the universe is curved that will also affect the expansion rate. We have observed that the expansion is accelerating, and since we don't know of anything that can cause this acceleration, we call it Dark Energy.
The inverse square law in astronomers' units is given by the distance modulus,
where m is the apparent magnitude, M is the absolute magnitude (intrinsic brightness), and d_L(z) is the luminosity distance in Megaparsecs. This can in turn be written in terms of the cosmological energy density parameters (energy density divided by the critical density for closure of the universe):
and w(z) is the equation of state parameter for dark energy (Dodelson 2003; Goliath et al. 2001). In the above, Ω_M is the matter energy density parameter and Ω_DE is the parameter for dark energy, and the curvature parameter has been set to zero (corresponding to a flat universe).
The exact way in which the dark energy density scales with redshift is unknown, because we do not know the dark energy equation of state. The equation of state relates density to pressure; photons, neutrinos, matter, etc. all have different equation of state parameters. What we would like to find out is the equation of state for dark energy. We know that it is negative, which is why it is acting as a sort of anti-gravity, and WMAP observations of the Cosmic Microwave Background have constrained it to be less than ~ -0.8 (Bennett et al. 2003), but we'd like to pin it down more. Supernovae are one way to do this.
Figure 3 shows the current state of supernova cosmology in the form of a Hubble Diagram giving both ground- and HST-discovered supernovae distances (given by the distance modulus μ) and velocities (given by the redshift). The inset shows the binned HST data in the form of residuals from an empty cosmology. Other configurations of the energy density and equation of state parameters are also shown for comparison. It is clear that a universe dominated by dark energy is favored, but there is little leverage on the equation of state parameter because of the small amount of high redshift supernovae so far observed. What is needed is a statistically significant sample of high redshift supernovae.
NASA has recognized the need for a space-based mission to investigate the nature of the dark energy and has dubbed this effort the Joint Dark Energy Mission (JDEM). Three proposals have been accepted for a two year study, and if NASA decides to fund JDEM in the near future, one of these may fly. The JHU-led Advanced Dark Energy Physics Telescope (ADEPT) will be primarily a survey of ~ 100 million high-z galaxies for the purposes of a Baryon Acoustic Oscillation (BAO) study. A galaxy BAO study measures the initial Acoustic Oscillation signal on the scale of galaxies and gives the expansion history of the universe in a different way than do supernovae. In addition, ADEPT will observe ~ 1000 high redshift SNe Ia. The two other missions are SNAP, the SuperNova Acceleration Probe, and DESTINY, the Dark Energy Space Telescope. SNAP is designed to observe SNe Ia and also complete a Weak Lensing study, and DESTINY is a supernovae I and II survey.
My advisor Adam Riess and I have been working on simulating what ADEPT supernova observations will be like and determining whether we will be able to achieve our science goals. The basic steps in the supernova simulator are as follows:
The above represents one simulated ADEPT mission, which is what we would expect to observe if the cosmology parameters we started with are exactly right. However, all of the above can be repeated for different parameters, and a full Monte Carlo simulation will be able to investigate the cosmology parameter space and run many ADEPT experiments quite cheaply. The goal is to characterize the expected errors in the parameter-estimation and to determine how well ADEPT will be able to constrain the nature of Dark Energy.
Type Ia Supernovae are not only an odd astrophysical phenomenon, they're also an important tool for studying cosmology. The JHU-led mission ADEPT hopes to study the nature of the Dark Energy using both a BAO study and high redshift SNe Ia observations. In order for this to happen, we need to determine whether ADEPT will be able to delineate between different cosmological models, and to do this realistically requires complex simulations, of which the list in Section 4 is only a basic outline. The true conclusion will not be until NASA decides ADEPT's fate at the end of 2008, so stay tuned.