Satellite galaxy

Classification of satellite galaxies

As mentioned above, satellite galaxies are generally categorized as dwarf galaxies and therefore follow a similar Hubble classification scheme as their host with the minor addition of a lowercase "d" in front of the various standard types to designate the dwarf galaxy status. These types include dwarf irregular (dI), dwarf spheroidal (dSph), dwarf elliptical (dE) and dwarf spiral (dS). However, out of all of these types it is believed that dwarf spirals are not satellites, but rather dwarf galaxies that are only found in the field.

Dwarf irregular satellite galaxies

Dwarf irregular satellite galaxies are characterized by their chaotic and asymmetric appearance, low gas fractions, high star formation rate and low metallicity. Three of the closest dwarf irregular satellites of the Milky Way include the Small Magellanic Cloud, Canis Major Dwarf, and the newly discovered Antlia 2.

Dwarf elliptical satellite galaxies

Dwarf elliptical satellite galaxies are characterized by their oval appearance on the sky, disordered motion of constituent stars, moderate to low metallicity, low gas fractions and old stellar population. Dwarf elliptical satellite galaxies in the Local Group include NGC 147, NGC 185, and NGC 205, which are satellites of our neighboring Andromeda galaxy.

Dwarf spheroidal satellite galaxies

Dwarf spheroidal satellite galaxies are characterized by their diffuse appearance, low surface brightness, high mass-to-light ratio (i.e. dark matter dominated), low metallicity, low gas fractions and old stellar population. Moreover, dwarf spheroidals make up the largest population of known satellite galaxies of the Milky Way. A few of these satellites include Hercules, Pisces II and Leo IV, which are named after the constellation in which they are found.

Transitional types

As a result of minor mergers and environmental effects, some dwarf galaxies are classified as intermediate or transitional type satellite galaxies. For example, Phoenix and LGS3 are classified as intermediate types that appear to be transitioning from dwarf irregulars to dwarf spheroidals. Furthermore, the Large Magellanic Cloud is considered to be in the process of transitioning from a dwarf spiral to a dwarf irregular.

Formation of satellite galaxies

According to the standard model of cosmology (known as the ΛCDM model), the formation of satellite galaxies is intricately connected to the observed large-scale structure of the Universe. Specifically, the ΛCDM model is based on the premise that the observed large-scale structure is the result of a bottom-up hierarchical process that began after the recombination epoch in which electrically neutral hydrogen atoms were formed as a result of free electrons and protons binding together. As the ratio of neutral hydrogen to free protons and electrons grew, so did fluctuations in the baryonic matter density. These fluctuations rapidly grew to the point that they became comparable to dark matter density fluctuations. Moreover, the smaller mass fluctuations grew to nonlinearity, became virialized (i.e. reached gravitational equilibrium), and were then hierarchically clustered within successively larger bound systems.

The gas within these bound systems condensed and rapidly cooled into cold dark matter halos that steadily increased in size by coalescing together and accumulating additional gas via a process known as accretion. The largest bound objects formed from this process are known as superclusters, such as the Virgo Supercluster, that contain smaller clusters of galaxies that are themselves surrounded by even smaller dwarf galaxies. Furthermore, in this model dwarfs galaxies are considered to be the fundamental building blocks that give rise to more massive galaxies, and the satellites that are observed around these galaxies are the dwarfs that have yet to be consumed by their host.

Accumulation of mass in dark matter halos

A crude yet useful method to determine how dark matter halos progressively gain mass through mergers of less massive halos can be explained using the excursion set formalism, also known as the extended Press-Schechter formalism (EPS). Among other things, the EPS formalism can be used to infer the fraction of mass ${\displaystyle M_2}$ that originated from collapsed objects of a specific mass at an earlier time $t_1<t_2$ by applying the statistics of Markovian random walks to the trajectories of mass elements in ${\displaystyle (S,\delta )}$-space, where $S={\sigma }^2(M)$ and ${\displaystyle \delta =\frac{\rho (x)-\overline{\rho }}{\overline{\rho }}}$ represent the mass variance and overdensity, respectively.

In particular the EPS formalism is founded on the ansatz that states "the fraction of trajectories with a first upcrossing of the barrier ${\delta }_S={\delta }_{critical}(t)$ at $S>S_1={\sigma }^2(M_1)$ is equal to the mass fraction at time ${\displaystyle t}$ that is incorporated in halos with masses $M<M_1$". Consequently, this ansatz ensures that each trajectory will upcross the barrier ${\displaystyle {\delta }_S={\delta }_{critical}(t)}$ given some arbitrarily large ${\displaystyle S}$, and as a result it guarantees that each mass element will ultimately become part of a halo.

Furthermore, the fraction of mass ${\displaystyle M_2}$ that originated from collapsed objects of a specific mass at an earlier time $t_1<t_2$ can be used to determine average number of progenitors at time ${\displaystyle t_1}$ within the mass interval $(M_1,M_1+d{M}_1)$ that have merged to produce a halo of ${\displaystyle M_2}$ at time ${\displaystyle t_2}$. This is accomplished by considering a spherical region of mass ${\displaystyle M_2}$ with a corresponding mass variance $S_2={\sigma }^2(M_2)$ and linear overdensity ${\delta }_2={\delta }_c(t_2)=\frac{{\delta }_c}{D(t_2)}$, where $D(t_2)$ is the linear growth rate that is normalized to unity at time $t_2$ and ${\delta }_c$ is the critical overdensity at which the initial spherical region has collapsed to form a virialized object. Mathematically, the progenitor mass function is expressed as:$${\displaystyle N(M_1,t_1|M_2,t_2)\mathrm{d}{\mathrm{M}}_1=\frac{M_2}{M_1}{f}_{PS}({\nu }_{12})|\frac{\mathrm{d}\ln ({\nu }_{12})}{\mathrm{d}\ln (M_1)}|\mathrm{d}{\mathrm{M}}_1}$$where ${\nu }_{12}=\frac{{\delta }_1-{\delta }_2}{\sqrt{S_1-S_2}}$ and $f_{PS}({\nu }_{12})=\sqrt{\frac{2}{\pi }}{\nu }_{12}\exp (\frac{-{\nu }_{12}^2}{2})$ is the Press-Schechter multiplicity function that describes the fraction of mass associated with halos in a range $\ln ({\nu }_{12})$.

Various comparisons of the progenitor mass function with numerical simulations have concluded that good agreement between theory and simulation is obtained only when ${\displaystyle \mathrm{\Delta }t=t_2-t_1}$ is small, otherwise the mass fraction in high mass progenitors is significantly underestimated, which can be attributed to the crude assumptions such as assuming a perfectly spherical collapse model and using a linear density field as opposed to a non-linear density field to characterize collapsed structures. Nevertheless, the utility of the EPS formalism is that it provides a computationally friendly approach for determining properties of dark matter halos.

Halo merger rate

Another utility of the EPS formalism is that it can be used to determine the rate at which a halo of initial mass M merges with a halo with mass between M and M+ΔM. This rate is given by

$${\displaystyle \mathcal{P}(\mathrm{\Delta }M|M,t)\mathrm{d}\ln \mathrm{\Delta }M\mathrm{d}\ln t=\frac{1}{\sqrt{2\pi }}[\frac{S_1}{(S_1-S_2)}{]}^{3/2}\exp [-\frac{{\delta }_c^2(S_1-S_2)}{2S_1{S}_2}]|\frac{\mathrm{d}\ln {\delta }_c}{\mathrm{d}\ln t}||\frac{\mathrm{d}\ln S_2}{\mathrm{d}\ln \mathrm{\Delta }M}|\frac{{\delta }_c}{\sqrt{S_2}}\mathrm{d}\ln t\mathrm{d}\ln \mathrm{\Delta }M}$$

where $S_1={\sigma }^2(M)$, $S_2={\sigma }^2(M+\mathrm{\Delta }M)$. In general the change in mass, ${\displaystyle \mathrm{\Delta }M}$, is the sum of a multitude of minor mergers. Nevertheless, given an infinitesimally small time interval ${\displaystyle \mathrm{dt}}$ it is reasonable to consider the change in mass to be due to a single merger events in which ${\displaystyle M_1}$ transitions to ${\displaystyle M_2}$.

Galactic cannibalism (minor mergers)

Throughout their lifespan, satellite galaxies orbiting in the dark matter halo experience dynamical friction and consequently descend deeper into the gravitational potential of their host as a result of orbital decay. Throughout the course of this descent, stars in the outer region of the satellite are steadily stripped away due to tidal forces from the host galaxy. This process, which is an example of a minor merger, continues until the satellite is completely disrupted and consumed by the host galaxies. Evidence of this destructive process can be observed in stellar debris streams around distant galaxies.

Orbital decay rate

As satellites orbit their host and interact with each other they progressively lose small amounts of kinetic energy and angular momentum due to dynamical friction. Consequently, the distance between the host and the satellite progressively decreases in order to conserve angular momentum. This process continues until the satellite ultimately mergers with the host galaxy. Furthermore, If we assume that the host is a singular isothermal sphere (SIS) and the satellite is a SIS that is sharply truncated at the radius at which it begins to accelerate towards the host (known as the Jacobi radius), then the time ${\displaystyle t_{\mathrm{f}ric}}$ that it takes for dynamical friction to result in a minor merger can be approximated as follows:$${\displaystyle t_{\mathrm{f}\mathrm{r}\mathrm{i}\mathrm{c}}=\frac{2.34}{\ln \mathrm{\Lambda }}\frac{{\sigma }_{\mathcal{M}}^2}{{\sigma }_{\mathrm{s}}^3}{r}_{\mathrm{i}}=\frac{2.7\mathrm{G}\mathrm{y}\mathrm{r}}{\ln \mathrm{\Lambda }}\frac{r_{\mathrm{i}}}{30\mathrm{k}\mathrm{p}\mathrm{c}}(\frac{{\sigma }_{\mathcal{M}}}{200\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}}{)}^2(\frac{100\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}}{{\sigma }_{\mathrm{s}}}{)}^3}$$where $r_i$ is the initial radius at $t=0$, ${\sigma }_{\mathcal{M}}$ is the velocity dispersion of the host galaxy, ${\displaystyle {\sigma }_{\mathrm{s}}}$ is the velocity dispersion of the satellite and ${\displaystyle \ln \mathrm{\Lambda }}$ is the Coulomb logarithm defined as $\ln \mathrm{\Lambda }=\ln (\frac{b_{\mathrm{m}\mathrm{a}\mathrm{x}}}{\mathrm{m}\mathrm{a}\mathrm{x}(r_{\mathrm{h}},GM/v_{\mathrm{t}\mathrm{y}\mathrm{p}}^2)})$ with $b_{max}$, $r_{\mathrm{h}}$ and $v_{\mathrm{t}\mathrm{y}\mathrm{p}}^2$ respectively representing the maximum impact parameter, the half-mass radius and the typical relative velocity. Moreover, both the half-mass radius and the typical relative velocity can be rewritten in terms of the radius and velocity dispersion such that $r_{\mathrm{h}}=\frac{{\sigma }_{\mathrm{s}}}{2^{3/2}{\sigma }_{\mathcal{M}}}r$ and ${\displaystyle \frac{GM}{v_{\mathrm{t}\mathrm{y}\mathrm{p}}^2}=\frac{\sqrt{2}{\sigma }_{\mathrm{s}}^2}{{\sigma }_{\mathcal{M}}^3}r}$. Using the Faber-Jackson relation, the velocity dispersion of satellites and their host can be estimated individually from their observed luminosity. Therefore, using the equation above it is possible to estimate the time that it takes for a satellite galaxy to be consumed by the host galaxy.

Minor merger driven star formation

In 1978, pioneering work involving the measurement of the colors of merger remnants by the astronomers Beatrice Tinsley and Richard Larson gave rise to the notion that mergers enhance star formation. Their observations showed that an anomalous blue color was associated with the merger remnants. Prior to this discovery, astronomers had already classified stars (see stellar classifications) and it was known that young, massive stars were bluer due to their light radiating at shorter wavelengths. Furthermore, it was also known that these stars live short lives due to their rapid consumption of fuel to remain in hydrostatic equilibrium. Therefore, the observation that merger remnants were associated with large populations of young, massive stars suggested that mergers induced rapid star formation (see starburst galaxy). Since this discovery was made, various observations have verified that mergers do indeed induce vigorous star formation. Despite major mergers being far more effective at driving star formation than minor mergers, it is known that minor mergers are significantly more common than major mergers so the cumulative effect of minor mergers over cosmic time is postulated to also contribute heavily to burst of star formation.

Minor mergers and the origins of thick disk components

Observations of edge-on galaxies suggest the universal presence of a thin disk, thick disk and halo component of galaxies. Despite the apparent ubiquity of these components, there is still ongoing research to determine if the thick disk and thin disk are truly distinct components. Nevertheless, many theories have been proposed to explain the origin of the thick disk component, and among these theories is one that involves minor mergers. In particular, it is speculated that the preexisting thin disk component of a host galaxy is heated during a minor merger and consequently the thin disk expands to form a thicker disk component.