3. ESTADO DEL ARTE
3.3. MARCO CONCEPTUAL
As previously stated, the temperature and, by extension, the phase of the gas are also important in the context of evolution. Gas may be both heated and cooled, within and outside of the galaxies, by several di↵erent processes. We begin by broadly discussing heating mechanisms, followed by cooling mechanisms, and then discuss the implications of the gas temperature and phase on galaxy evolution.
Heating
The primary means through which gas is heated outside of galaxies isvirialization. This mechanism is described by the virial theorem, which states that in a gravitationally bound system in equilibrium
2hKi=hUi, (1.1)
where the terms hKi and hUi refer to the time-averaged kinetic and potential energies, respectively. While this applies to any system of particles (e.g., galaxies in a group or
stars in a globular cluster), when we consider a system of gas particles, we note that the characteristic temperature of the system can be described using the relation
1
2hUi=hKi= 3
2kTvirial, (1.2)
where k is the Stefan-Boltzmann constant and Tvirial is the virial temperature. The potential energy indicated is dictated by the mass distribution of the system. Note that this applies to any system of bound particles, therefore galaxies may virialize the gas surrounding them with their own potential, in addition to heating by the group or cluster. Clearly, the larger hUi becomes, the hotter the gas will be under ideal conditions. The application of the virial theorem to observations is useful because it allows us to calculate the mass of the X-ray emitting gas in galaxy clusters and groups from the temperature and light distributions of the X-rays (if the assumptions of equilibrium and spherical symmetry are valid and the signal-to-noise ratio of the X-ray observations is sufficiently high).
In addition to virialization, gas both inside and outside of galaxies may be heated by shocks. Inside of galaxies, the shocks from supernovae may heat gas to temperatures of
⇠106 107 keV (cf. the Local Bubble; Cox & Reynolds 1987). These supernovae may eject gas along a path perpendicular to the plane of the galaxy in a phenomenon similar to a galactic fountain. If ejected with enough energy, the gas may escape the potential well of the galaxy. This e↵ect is illustrated using the example of M82, a starbursting galaxy in the M81 group. Seen in Figure 1.3, the intense star formation (⇠10 M yr 1; Barker et al. 2008) in a relatively low-mass galaxy has lead to an abundance of supernovae in the nuclear region of the galaxy with a rate of ⇠0.1 yr 1 (Bartel et al. 1987; McLeod et al. 1993). Referred to as a galactic superwind, the hot gas can be seen to large distances from the plane of M82 (Strickland et al. 1997 and references therein).
Figure 1.3: Multiwavelength image of M82, where blue represents X-rays, green and orange colors are optical light, and red is mid-infrared light imaged with the Chandra X-ray Observatory, Hubble Space Telescope, and Spitzer Space Telescope, respectively. Notice the large plumes of hot gas that lie perpendicular to the semi-major axis of the galaxy. This hot gas has been expelled by numerous supernovae due to enhanced star formation within the disk (see Suchkov et al. 1996 for a full discussion). Image credit: X- ray: NASA/CXC/JHU/D.Strickland; Optical: NASA/ESA/STScI/AURA/The Hubble Heritage Team; IR: NASA/JPL-Caltech/Univ. of AZ/C. Engelbracht.
In this scenario, gas in clusters and groups is heated by the motions of the galaxies them- selves. Unlike virialization, which is related to the kinematics of the galaxies as a result of the total system mass, shock heating of gas relies on galaxies moving supersonically through gas in the surrounding medium. The rapid compression of the gas heats it to much higher temperatures and likely ionizes it (though it may not dissociate molecular gas; see, e.g., Cluver et al. 2013).
Finally, an additional mechanism to heat gas inside galaxies and in their surrounding environment is photoionization. One method for this type of heating is the presence of an active galactic nucleus (AGN). High-energy photons from the accretion of gas onto a supermassive black hole stream out from the galaxy nucleus, typically in a biconical
geometry, and ionize the surrounding gas (in particular, this refers to the narrow line region, which may extend many kpc from the nucleus; Koski 1978; Ogle et al. 2000). Depending on the geometry of the AGN/host galaxy, the ionizing radiation may a↵ect the host galaxy itself, or the gas in the circumgalactic medium. As AGNs tend to be rare in groups, and those that are present are quite weak (e.g., Del Olmo et al. 2010; Mart´ınez et al. 2010; Tzanavaris et al. 2014), we do not include gas heated by AGNs in our observational discussion. In addition, the ultraviolet light from young, massive stars will ionize any surrounding neutral gas. We refer the reader to Section 1.3.3 for a full discussion of this e↵ect.
Cooling
As energy is radiated away, hot gas becomes cooler. If the gas temperature is in excess of
⇠106K, as is the focus of the thesis, and the gas is optically thin (i.e., radiation is allowed to escape the gas with minimal absorption), then the primary means through which energy is lost is bremsstrahlung radiation, also called free-free emission. Bremsstrahlung radiation occurs when a free, charged particle (usually an electron) accelerates due to the electromagnetic force exerted on it by another particle. The kinetic energy lost by the particle in the encounter is radiated away. In the case of a hot plasma, bremsstrahlung radiation is the result of encounters between free electrons and ions. As can be seen in Equation 1.2, the average kinetic energy of the particles in the plasma is directly proportional to the temperature of the gas. Therefore, repeated encounters between free electrons and ions reduce the average kinetic energy of the system through radiation and result in cooling. In general, the rate at which this cooling occurs per unit volume can be represented as
rcool =n2⇤(T), (1.3)
where n is the particle density and ⇤(T) is the cooling efficiency with units erg cm3 s 1. Thus, the cooling rate has units of erg cm 3 s 1. The n2 dependence signifies the inter-
action between free particles in the gas. In principle, we can determine the time required for a hot plasma to cool by equating the product of the cooling rate, volume of the gas, and cooling time with the total kinetic energy of the gas. Seward & Charles (2010) approximate this time, assuming only bremsstrahlung radiation, as
tcool ⇡(2.5⇥107)n 1(kT)1/2, (1.4) where tcool is in units of years.
In addition to bremsstrahlung radiation, cooling may also occur due to line, or bound- bound, emission. The relative importance of line emission in radiative cooling depends upon the temperature and chemical makeup of the gas. As can be seen in Figure 1.4, the relative importance of line emission in cooling is negligible compared to bremsstrahlung radiation untilT .106K. In hot gas, iron is the primary element responsible for line cool- ing. In particular, semi-forbidden transitions in highly ionized species such as Fe XVIII and Fe XIX emit at X-ray wavelengths (Raymond et al. 1976).
The Importance of Gas Temperature and Phase
The existence and properties of gas both inside and outside of galaxies are important when considering the evolution of galaxies. We remind the reader that molecular gas is the fuel for star formation. As the gas is converted into other phases (e.g., warm ionized) by various processes, the loss of molecular gas quenches star formation. It is for this reason that elliptical galaxies have very low star formation rates, as most of the gas exists in a hot, ionized halo surrounding the galaxy. If this gas could be cooled e↵ectively, then it would return to a neutral atomic state and potentially aid in the formation of new generations of stars.
Brems strah lung Total Cooling Forbidden Lines Semi-Forbidden Lines
Figure 1.4: The cooling efficiency ⇤ as a function of temperature. The short-dash, long- dash, short-long-dash, and solid lines represent the semi-forbidden line, forbidden line, bremsstrahlung, and total cooling efficiencies. Note that at temperatures above⇠106 K, bremsstrahlung radiation becomes the dominant cooling mechanism. Figure adapted from Raymond et al. (1976).