N r C Triangle Delta -Z
N = CZ
N = H o
*NOTE: TEST # -OCTOBER 14, 2010, STUDENT I.D., CALCULATOR, PENCIL,
~1963: Moarten Schmidt realized that we were looking at EXTEMELY red-shifted
Hydrogen lines = large Triangle Delta.
Because V Triangle Delta, the radial velocity of Quasars is large.
Because V d,rthe distance to the Quasars is great.
Hydrogen Spectrum in Lab compared to 3C273.
^TWO BLUES ^434 ^ONE GREEN ^ONE RED.
What is the radial velocity of 3C273?
V =rC Triangle Delta
Let Triangle Delta = Z such that
V =rCZ = Z is called the “(red-shifted)”
V =rC (503-434) nm/434 nm
V =rC (0.16) = 0.16 C
= 16% of the speed of light!
V = 0.16 (3 x 10 ) m/s
r 7 4
4.8 x 10 m/s = 4.8 x 10 km/s.
*NOTE: Divide by 1000 to convert form from m/s to km/s.
Similarly, 3C48 was moving at 0.33C = 33% of the speed of light!
Hundreds of quasars are now known and ALL are EXTREMELY red-shifted.
What is the distance to 3C273?
*NOTE: Question on TEST # 1!
d = V r
H o 4
d = 4.8 x 10 km/s
d = 640 Mpc
d = (640 x 10 pc) (3.26 ly) = 2.09 x 10 ly
d ~ 2 billion light-years distant.
Relativistic Velocity Equation:
The fattest, most distant Quasar known has Z = 10.
Consider a Quasar with Z = 4.11.
Since V =rCZ, is this Quasar moving at 4.11 times the speed of light?
NO! No material object can exceed the speed of light.
For Z > ~ 0.5, we must turn to Relativity.
V =r[(Z + 1) – 1] C
[(Z + 1) + 1]
Relativistic Velocity Calculation:
V =r[(4.11 + 1) – 1] C
V =r25.11 C
V =r0.93C = 93% of the speed of light!
Distance to the Quasar:
If Hubble Law is valid, this Quasar must be VERY far away.
d = V
d = 0.93 (3 x 10 km/s)
d = 3720 Mpc = 12 x 10 ly9
d = 12 billion light-years distant!
To see Quasars over such vast (“Cosmological”) distances, they must intrinsically be
Quasars often emit as much energy as 100 to 1000 normal galaxies combined.
How big are they? What are they?
The size may be determined by a technique known as
*NOTE: SUN = SOL; MOON = LUNAR.
Moon “Beside” Quasar: Moon Occults Quasar:
Oo-Quasar Oo-Quasar Apparent size of Quasar =