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Source: Satellite galaxy

A satellite galaxy is a smaller companion galaxy that travels on bound orbits within the gravitational potential of a more massive and luminous host galaxy (also known as the primary galaxy). Satellite galaxies and their constituents are bound to their host galaxy, in the same way that planets within the Solar System are gravitationally bound to the Sun. While most satellite galaxies are dwarf galaxies, satellite galaxies of large galaxy clusters can be much more massive. The Milky Way is orbited by about fifty satellite galaxies, the largest of which is the Large Magellanic Cloud.
Moreover, satellite galaxies are not the only astronomical objects that are gravitationally bound to larger host galaxies (see globular clusters). For this reason, astronomers have defined galaxies as gravitationally bound collections of stars that exhibit properties that cannot be explained by a combination of baryonic matter (i.e. ordinary matter) and Newton's laws of gravity. For example, measurements of the orbital speed of stars and gas within spiral galaxies result in a velocity curve that deviates significantly from the theoretical prediction. This observation has motivated various explanations such as the theory of dark matter and modifications to Newtonian dynamics. Therefore, despite also being satellites of host galaxies, globular clusters should not be mistaken for satellite galaxies. Satellite galaxies are not only more extended and diffuse compared to globular clusters, but are also enshrouded in massive dark matter halos that are thought to have been endowed to them during the formation process.
Satellite galaxies generally lead tumultuous lives due to their chaotic interactions with both the larger host galaxy and other satellites. For example, the host galaxy is capable of disrupting the orbiting satellites via tidal and ram pressure stripping. These environmental effects can remove large amounts of cold gas from satellites (i.e. the fuel for star formation), and this can result in satellites becoming quiescent in the sense that they have ceased to form stars. Moreover, satellites can also collide with their host galaxy resulting in a minor merger (i.e. merger event between galaxies of significantly different masses). On the other hand, satellites can also merge with one another resulting in a major merger (i.e. merger event between galaxies of comparable masses). Galaxies are mostly composed of empty space, interstellar gas and dust, and therefore galaxy mergers do not necessarily involve collisions between objects from one galaxy and objects from the other, however, these events generally result in much more massive galaxies. Consequently, astronomers seek to constrain the rate at which both minor and major mergers occur to better understand the formation of gigantic structures of gravitationally bound conglomerations of galaxies such as galactic groups and clusters.

History

= Early 20th century

galaxy

= Modern times

= Motivations to study satellite galaxies

satellite

Classification of satellite galaxies

satellite

galaxy

= Dwarf irregular satellite galaxies

satellite

= Dwarf elliptical satellite galaxies

satellite

galaxy

= Dwarf spheroidal satellite galaxies

satellite

= Transitional types

satellite

Formation of satellite galaxies

satellite

= Accumulation of mass in dark matter halos

by applying the statistics of Markovian random walks to the trajectories of mass elements in

(
S
,
δ
)

{\displaystyle (S,\delta )}

-space, where

S
=

σ

2

(
M
)

{\textstyle S=\sigma ^{2}(M)}

and

δ
=

ρ
(
x
)
−

ρ
¯

ρ
¯

{\displaystyle \delta ={\rho (x)-{\bar {\rho }} \over {\bar {\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

δ

S

=

δ

c
r
i
t
i
c
a
l

(
t
)

{\textstyle \delta _{S}=\delta _{critical}(t)}

at

S
>

S

1

=

σ

2

(

M

1

)

{\textstyle S>S_{1}=\sigma ^{2}(M_{1})}

is equal to the mass fraction at time

t

{\displaystyle t}

that is incorporated in halos with masses

M
<

M

1

{\textstyle M
". Consequently, this ansatz ensures that each trajectory will upcross the barrier

δ

S

=

δ

c
r
i
t
i
c
a
l

(
t
)

{\displaystyle \delta _{S}=\delta _{critical}(t)}

given some arbitrarily large

S

{\displaystyle S}

, and as a result it guarantees that each mass element will ultimately become part of a halo.
Furthermore, the fraction of mass

M

2

{\displaystyle M_{2}}

that originated from collapsed objects of a specific mass at an earlier time

t

1

<

t

2

{\textstyle t_{1}
can be used to determine average number of progenitors at time

t

1

{\displaystyle t_{1}}

within the mass interval

(

M

1

,

M

1

+
d

M

1

)

{\textstyle (M_{1},M_{1}+dM_{1})}

that have merged to produce a halo of

M

2

{\displaystyle M_{2}}

at time

t

2

{\displaystyle t_{2}}

. This is accomplished by considering a spherical region of mass

M

2

{\displaystyle M_{2}}

with a corresponding mass variance

S

2

=

σ

2

(

M

2

)

{\textstyle S_{2}=\sigma ^{2}(M_{2})}

and linear overdensity

δ

2

=

δ

c

(

t

2

)
=

δ

c

D
(

t

2

)

{\textstyle \delta _{2}=\delta _{c}(t_{2})={\delta _{c} \over D(t_{2})}}

, where

D
(

t

2

)

{\textstyle D(t_{2})}

is the linear growth rate that is normalized to unity at time

t

2

{\textstyle t_{2}}

and

δ

c

{\textstyle \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:

N
(

M

1

,

t

1

|

M

2

,

t

2

)

d

M

1

=

M

2

M

1

f

P
S

(

ν

12

)

|

d
⁡
ln
⁡
(

ν

12

)

d
⁡
ln
⁡
(

M

1

)

|

d

M

1

{\displaystyle N(M_{1},t_{1}|M_{2},t_{2})\operatorname {dM_{1}} ={\frac {M_{2}}{M_{1}}}f_{PS}(\nu _{12}){\Bigg |}{\operatorname {d} \ln(\nu _{12}) \over \operatorname {d} \ln(M_{1})}{\Bigg |}\operatorname {dM_{1}} }

where

ν

12

=

δ

1

−

δ

2

S

1

−

S

2

{\textstyle \nu _{12}={\delta _{1}-\delta _{2} \over {\sqrt {S_{1}-S_{2}}}}}

and

f

P
S

(

ν

12

)
=

2
π

ν

12

exp
⁡
(

−

ν

12

2

2

)

{\textstyle f_{PS}(\nu _{12})={\sqrt {2 \over \pi }}\nu _{12}\exp({-\nu _{12}^{2} \over 2})}

is the Press-Schechter multiplicity function that describes the fraction of mass associated with halos in a range

ln
⁡
(

ν

12

)

{\textstyle \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

Δ
t
=

t

2

−

t

1

{\displaystyle \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

P

(
Δ
M

|

M
,
t
)
d
⁡
ln
⁡
Δ
M
d
⁡
ln
⁡
t
=

1

2
π

[

S

1

(

S

1

−

S

2

)

]

3

/

2

exp
⁡

[

−

δ

c

2

(

S

1

−

S

2

)

2

S

1

S

2

]

|

d
⁡
ln
⁡

δ

c

d
⁡
ln
⁡
t

|

|

d
⁡
ln
⁡

S

2

d
⁡
ln
⁡
Δ
M

|

δ

c

S

2

d

ln
⁡
t

d

ln
⁡
Δ
M

{\displaystyle {\mathcal {P}}(\Delta M|M,t)\operatorname {d} \ln \Delta M\operatorname {d} \ln t={\frac {1}{\sqrt {2\pi }}}{\Bigg [}{\frac {S_{1}}{(S_{1}-S_{2})}}{\Bigg ]}^{3/2}\exp {\Bigg [}-{\frac {\delta _{c}^{2}(S_{1}-S_{2})}{2S_{1}S_{2}}}{\Bigg ]}{\Bigg |}{\frac {\operatorname {d} \ln \delta _{c}}{\operatorname {d} \ln t}}{\Bigg |}{\Bigg |}{\frac {\operatorname {d} \ln S_{2}}{\operatorname {d} \ln \Delta M}}{\Bigg |}{\frac {\delta _{c}}{\sqrt {S_{2}}}}\mathrm {d} \ln t\,\mathrm {d} \ln \Delta M}

where

S

1

=

σ

2

(
M
)

{\textstyle S_{1}=\sigma ^{2}(M)}

,

S

2

=

σ

2

(
M
+
Δ
M
)

{\textstyle S_{2}=\sigma ^{2}(M+\Delta M)}

. In general the change in mass,

Δ
M

{\displaystyle \Delta M}

, is the sum of a multitude of minor mergers. Nevertheless, given an infinitesimally small time interval

dt

{\displaystyle \operatorname {dt} }

it is reasonable to consider the change in mass to be due to a single merger events in which

M

1

{\displaystyle M_{1}}

transitions to

M

2

{\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

t

f

r
i
c

{\displaystyle t_{\mathrm {f} ric}}

that it takes for dynamical friction to result in a minor merger can be approximated as follows:

t

f
r
i
c

=

2.34

ln
⁡
Λ

σ

M

2

σ

s

3

r

i

=

2.7

G
y
r

ln
⁡
Λ

r

i

30

k
p
c

(

σ

M

200

k
m

s

−
1

)

2

(

100

k
m

s

−
1

σ

s

)

3

{\displaystyle t_{\mathrm {fric} }={\frac {2.34}{\ln \Lambda }}{\frac {\sigma _{\mathcal {M}}^{2}}{\sigma _{\mathrm {s} }^{3}}}r_{\mathrm {i} }={\frac {2.7\ \mathrm {Gyr} }{\ln \Lambda }}{\frac {r_{\mathrm {i} }}{30\ \mathrm {kpc} }}{\bigg (}{\frac {\sigma _{\mathcal {M}}}{200\ \mathrm {km} \ \mathrm {s^{-1}} }}{\bigg )}^{2}{\bigg (}{\frac {100\mathrm {\ km\ s^{-1}} }{\sigma _{\mathrm {s} }}}{\bigg )}^{3}}

where

r

i

{\textstyle r_{i}}

is the initial radius at

t
=
0

{\textstyle t=0}

,

σ

M

{\textstyle \sigma _{\mathcal {M}}}

is the velocity dispersion of the host galaxy,

σ

s

{\displaystyle \sigma _{\mathrm {s} }}

is the velocity dispersion of the satellite and

ln
⁡
Λ

{\displaystyle \ln \Lambda }

is the Coulomb logarithm defined as

ln
⁡
Λ
=
ln
⁡

(

b

m
a
x

m
a
x

(

r

h

,
G
M

/

v

t
y
p

2

)

)

{\textstyle \ln \Lambda =\ln {\Big (}{\frac {b_{\mathrm {max} }}{\mathrm {max} (r_{\mathrm {h} },GM/v_{\mathrm {typ} }^{2})}}{\Big )}}

with

b

max

{\textstyle b_{\max }}

,

r

h

{\textstyle r_{\mathrm {h} }}

and

v

t
y
p

2

{\textstyle v_{\mathrm {typ} }^{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

h

=

σ

s

2

3

/

2

σ

M

r

{\textstyle r_{\mathrm {h} }={\frac {\sigma _{\mathrm {s} }}{2^{3/2}\sigma _{\mathcal {M}}}}r}

and

G
M

v

t
y
p

2

=

2

σ

s

2

σ

M

3

r

{\displaystyle {\frac {GM}{v_{\mathrm {typ} }^{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.