Transcript The Spatially-Resolved Scaling Law of Star Formation

The Life Cycles of Stars
and our Sun
Your Questions
1. Have you
ever heard of
the sun song
by the group
They Might
be Giants?
`Fun websites’:
http://www.asu.edu/clas/hst/www/ahah/
Appreciating Hubble at Hyper-speed
http://www.stsci.edu/outreach/
1. How are distances between galaxies and between
galaxy clusters calculated? The Hubble Flow
v = Ho d
(Ho = 71 km/s/Mpc)
1. Observer 1 sees
both galaxies at
distance d with
speed v
2. Observer 2 sees
the furthest
galaxy at distance
2d, with speed 2v
d
v
1
d
v
2
2. Elaborate on the difference between the Dark Matter
theory and the MOdified Newtonian Dynamics theory
(MOND).
Describing Motion
• Motion is when the position of an object
changes in time
• If position does not change, the object is at
rest
• The describe motions we need to monitor
position and time
• The rate at which an objects covers a given
amount of space in a given amount of time is
called speed
v = d/t
(when you add a direction to speed, it is called
velocity)
Acceleration
• An acceleration is a
change in velocity.
• Acceleration occurs when
either the magnitude or
direction of the velocity (or
both) are altered.
• Uniform Circular Motion is
Accelerated Motion
Acceleration and Force
• An object in constant velocity (or at rest) has
no force acting on it. Or: if an object is being
accelerated, there must be a net force acting
on it (Newton’s first law)
• Acceleration is caused by force but also related
to the mass of the object (Newton’s second law)
Force = Mass x Acceleration
F = m·a
Or
a = F/m
The gravitational force on an object near
the surface of Earth is:
Fgrav = m·g
(g = 9.8m/s2)
Gravity
• We can summarize the universal law of
gravitation with the following statements:
– Every mass attracts every other mass through the
force of gravity.
– If mass #1 exerts force on mass #2, and mass#2
exerts force on mass#1, the force must depend o both
masses, namely:
– The force of attraction is directly proportional to the
product of the two masses.
– The force of attraction is inversely proportional to the
square of the distance between the masses.
The Law of Gravity
Near Earth’s
surface
M 1M 2
Fg  G
2
d
G=
6.67x10-11
Fg  gM 2
m3/kg/s2
M1
g G 2
d
 9.8m/s2
d
M1
M2
… so why don’t planets just fall
into the sun?
M1
M2
… because they miss it!
v
Fg
M1
Fg
M2
This is the concept of an orbit: M2 is being attracted by M1,
which causes an acceleration, but has sufficient tangential
velocity that the `fall’ becomes an orbit
The same is true for galaxies:
Their stars rotate around their
center of mass.
R
If you know the distance of
your star from the center, R,
and its speed, v, you can
calculate the mass of the
galaxy contained within the
radius R:
M(<R) = v2 R / G
For the sun:
M(<8kpc) = 9x1010 Msun
a = 2.5x10-8 cm/s2
And the acceleration:
a= v2 / R
…and when you reach the edges of
galaxies…
The `flat rotation curve’ seen beyond the visible edges of
galaxies does not agree with the expectation that the galaxy
`ends’. In this case one would expect a trend: v ~ R(-1/2)
1. DM:
Fg = ma = GMm/r2 , a= GM/r2
Fc = m v2 / r
(gravitational force)
(centripetal force)
Flat rotation curves imply `unseen’ mass in galaxies
2. MOND: F = m (a/ao) a = GMm/r2
ao = 1.2 10-8 cm s-2
Flat rotation curves stem from very small accelerations
at the edges of galaxies, where the Newtonian dynamics
is modified to imply: a= (Gmao)(1/2) / R
and v ~ const.
Current difficulties for MOND:
1. Gravitational lensing:
(still in progress; recent
MOND covariant
formulation)
2. Density profiles of galaxy clusters