Type Ia SN: Standardizable Candles?

The common lore is that Type Ia Supernovas take place in close binary systems composed of a carbon-oxygen white dwarf and a normal companion star. The particular type of binary systems are referred to as Cataclysmic Variables (CVs).

CVs are short orbital period (hours to days) binary star systems composed of a white dwarf and a low mass main seqeunce star (in general, sometimes the companion star is a red evolved star). As their name implies, cataclysmic variables (CV's) are sites for cataclysmic events. However, the events are not so cataclysmic as to destroy the binary star systems (in general). The events lead to rapid increases in the luminosities of the systems. There are three main types of cataclysmic variables (CV's), Dwarf Novae, Recurrent Novae, and Classical Novae. Also, many CVs are strong sources of x-ray emission, and CVs may be the progenitors of Type I Supernovas.

In this section, we go over the properties of white dwarf stars and why CVs are natural candidates for Type Ia SNs.

Properties of White Dwarfs

White dwarfs are the endpoints of the evolution of low mass stars. They are interesting objects in that they are supported by degenerate electron pressure and thus do not need internal nuclear energy sources. White dwarfs radiate because they are born hot and because they slowly contract releasing gravitational energy as they cool.

White dwarfs cannot be more massive than 1.4 M(sun) (Chandrasekhar Limit, see below) and they have radii on the order of the radius of the Earth, R(wd) ~ 10,000 kilometers. Comment -- this means that white dwarfs are extremely dense; densities on the order of 200,000 grams per cc to 100,000,000 grams per cc. Recall that the density of lead is ~ 11 grams per cc. A sugar cube of white dwarf material would weigh anywhere from 400 pounds to 200 tons at the surface of the Earth!

Mass-Radius Relationship

There is a well-defined relationship between the mass of a white dwarf and its radius. The relationship is not intuitive in that the larger the mass of the white dwarf, the smaller is its radius!!

This can be understood by noting the size of the degenerate pressure depends on the density of the gas in such a way that the pressure is greater when the density is greater. That is, the higher the density, the higher the pressure and the harder it is to compress the white dwarf.

If one thinks a little about the mass-radius relationship, a plausible scenario arises. Because the more massive the white dwarf, the stronger is the tendency for gravity to force the white dwarf to contract. To counteract this tendency, higher pressure is needed (and so higher density is needed) and the radius of a massive white dwarf must be small to balance gravity. For a very massive white dwarf, the radius must be tiny. Question: Is there a limit on how small one can make the radius of a white dwarf to compensate for an increase in the mass of the white dwarf? Answer: Yes, there is a limit. Performing a detailed analysis, one can show that for a white dwarf of mass ~ 1.4 M(sun), the radius of the white dwarf must be 0 kilometers in order for the density to be large enough for the degenerate electron pressure to counter-act the force of gravity. Huh. Say what?? What does this mean?

This means that there is an upper limit to the mass of a white dwarf. The limit is ~ 1.4 M(sun) and is referred to as the Chandrasekar Limit

An interesting possibility for white dwarf evolution concerns white dwarfs which are in short orbital period (P ~ hours) binary star systems. Such systems are so small that the white dwarf is actually able to steal material from its companion star. Such binary systems are known as cataclysmic variables.

Cataclysmic Variables

Cataclysmic variables are short orbital period (hours to days) binary star systems composed of a white dwarf and a low mass main seqeunce star, in general (sometimes the companion star is a red evolved star). As their name implies, cataclysmic variables (CV's) are sites for cataclysmic events. However, the events are not so cataclysmic as to destroy the binary star systems, usually. The events lead to rapid increases in the luminosities of the systems. There are four main types of cataclcysmic variables (CV's), Dwarf Novae, Recurrent Novae, Classical Novae, and Type Ia Supernovas. Many CV's are strong sources of x-ray emission.

Mass Transfer in Cataclysmic Variables

The systems must have short orbital periods (hours to a few days) or else the stars will be too far apart to exchange significant amounts of mass. Let's define some things.

What happens in close binary systems, depends upon the secondary (the less massive star). There may be detached, semi-detached, and contact systems depending upon whether the secondary star fills its Roche lobe. CV's are semi-detached systems. The companion fills its Roche lobe and transfers material to the white dwarf.

What Happens in Accreting White Dwarf Binaries?

X_RAY BINARIES

Gravitational Energy

  • The material accelerates as it falls onto the white dwarf. If I dropped some mass onto a white dwarf it would hit the surface of the white dwarf at a speed of around 10,000 kilometers per second. This is a lot of kinetic energy (gained at the expense of the potential energy of the white dwarf).

  • In dwarf nova systems, the energy which powers the outbursts is gravitational in nature -- it comes from the energy the material gained by falling onto the white dwarf.

  • Dwarf nova outbursts are smaller and occur much more often (every several weeks to months) than nova outbursts.

      Comments:

    • efficiency = 1/2 mv2/mc2 = 1/2 (v/c)2 ~ 0.0005

    • efficiency ~ 0.007

      ===> nuclear burning efficiency is higher

  • The release of the gravitational energy can also lead to the production of x-ray emission near the surface of the white dwarf. The Classical Nova and Dwarf Nova, GK Per is also a strong source of x-rays.

Classical Novae and Type Ia SN, Standardizable Candles?

The common lore is that Classical Novae and Type Ia SN occur in close mass-transfer binary systems composed of a carbon-oxygen white dwarf and a normal companion star, that is, in Cataclysmic Variables (CVs). CVs are short orbital period (hours to days) binary star systems composed of a white dwarf and a low mass main seqeunce star (in general, sometimes the companion star is a red evolved star). As their name implies, cataclysmic variables (CV's) are sites for cataclysmic events. However, the events are not so cataclysmic as to destroy the binary star systems (in general). The events lead to rapid increases in the luminosities of the systems. Here, we consider the not so cataclysmic Classical Novae and the very cataclysmic Type Ia Supernovas.

Energy Sources for Classical Novae and Type Ia Supernovas

CVs generate energy either through nuclear burning or through gravity (accretion). Classical Novae and Type Ia Supernovas power themselves through nuclear energy.

The material which flows onto the white dwarf simply piles up on the surface of the white dwarf. The material is rich in hydrogen since it comes from the envelope of the companion star. This is a key point, because white dwarfs being the ashes of nuclear burning have no nuclear fuel left. The companion replenishes its fuel supply.

Depending upon whether the mass flow (accretion) is high or low, different outcomes may result.

For slow accretion rates, the material as it piles up can lose its energy gained as it fell onto the white dwarf. The material remains cold and reaches high densities. The scenario is then:

For the fast accretion rate, the material does not have time to lose its energy it gained as it fell onto the white dwarf. The material thus increases in temperature and pressure strongly as it accretes onto the white dwarf.