Credit/Permission: For text, © David Jeffery. For figures etc., as specified with the figure etc. / Only for reading and use by the instructors and students of the UNLV astronomy laboratory course.
This is a lab without observations.
Sections
We touch on the following topics:
Some of the
Tasks can be completed ahead of the lab period.
Doing some of them ahead of lab period would be helpful.
However, you can print a copy ahead of time if you like especially if
want to do some parts ahead of time.
You might have to compensate for updates in this case.
The Lab Exercise itself is NOT printed in the lab ever.
That would be killing forests
and the Lab Exercise is designed to be an active web document.
General remarks about quiz prep are given at
Quiz Preparation: General Instructions.
For DavidJ's lab sections, the quiz prep is doing all the items listed here and self-testing with the
Prep Quizzes and Prep Quiz Keys
if they exist.
However to complement and/or supplement the reading, you should at least
read the intro of a sample of the articles
linked
to the following keywords etc.
so that you can define and/or understand some keywords etc. at the level of our class.
A longer and list of keywords which you are NOT required to look at---but it would be useful to do so---is:
Sub Tasks:
Sub Tasks:
Sub Tasks:
What is the Hubble length
in Giga-light-years (Gly)?
HINT: What is the vacuum light speed
in units of Gly/Gyr?
Proper distance
is a distance
that CAN BE measured at one instant in time with a ruler for an object
(for which the distance is a length) at rest
in the inertial frame of
that one instant in time.
Note that we can measure at once instant in time the length of objects
going passed at relativistic velocities
(i.e., velocities v for which
v/c is NOT negilible in
the formulae
of special relativity),
but those lengths are affected by
FitzGerald contraction
and are shorter than
proper lengths (i.e., distances).
Note also, there are actuall various ways we can measure
proper distances
without using a ruler and which are NOT necessarily at one instant in time.
The sad fact is that we CANNOT directly measure
proper distances
to cosmologically remote astronomical objects.
Those proper distances
are NOT direct observables.
A direct observable in principle for cosmologically remote
astronomical objects is
luminosity distance.
Say we have an
astronomical object
(e.g., a supernova) with
known luminosity L.
We measure the flux F on
Earth.
If the observable universe
were static (which it's NOT) and
extinction
by interstellar dust
is negligible
(which NOT always the case), then by
conservation of energy
where r_L is the distance to the
astronomical object
and 4πr**2 is the surface area of
a sphere of radius r.
Solving for r_L gives
Given our conditions r_L is a proper distance
even though we have NOT measured it a one instant in
cosmic time with a ruler---we've done an equivalent
measurement.
Now the observable universe
is NOT static.
We live in an expanding universe.
The astronomical object
is NOT at present where it was when
light started out from it
and the growth of space
redshifted
the light as it propagated.
So r_L is NOT a
proper distance
for cosmologically remote
astronomical objects though
it becomes that asymptotically
as cosmological redshift z
goes to zero.
The agreement as cosmological redshift z
goes to zero is called
1st order agreement
in small cosmological redshift z.
We call distances calculated from the last formula (i.e., r_L's)
luminosity distances.
For systems that can be treated as static (and have negligible
extinction),
proper distance
and luminosity distance are
the same thing and one just says distance.
For cosmologically remote objects,
proper distance
and luminosity distance
are NOT the same thing.
But luminosity distance
still a direct observable and it can be predicted from
expanding universe models.
So luminosity distances
can be measured to cosmologically remote objects and used
to fix the parameters of
expanding universe models.
This is, in fact, a key way in which some of the parameters of
the currently favored
Λ-CDM model are determined.
Fortunately,
to 1st-order
in small cosmological redshift z,
proper distances
and luminosity distances agree
as aforesaid.
This fact is what allows us to test
Hubble's law
and determine the Hubble constant using
cosmologically non-remote
astronomical objects.
Sub Tasks:
Sub Tasks:
Have you really, really pushed, moved, and filled everything or are you just saying that you have to get
on the next sub task?
Answer:
If a light curve is for a
normal SN Ia a good fit can be done,
otherwise just do the best you can.
Complete the
Table: Supernova Luminosity Distances below
as you do the fits.
The observable universe
according to the
expanding universe theory
scales up with
cosmic scale factor a = a(t),
where t is cosmic time since the
Big Bang.
This scaling up is illustrated in the figure below
(local link /
general link: expanding_universe.html).
Sub Tasks:
where Q is a general cosmic quantity, p is a general power that can be fractional and/or negative, and
∝
means "proportional to".
Conventionally, one writes cosmic quantities as function of its present-value value and the present-time scale factor
a_0 thusly
where subscript 0
means and is vocalized
"sub 0" or "nought".
So Q_0 is vocalized "Q sub 0" or "Q nought".
At t_0, when a(t) equals a_0, Q = Q_0.
See the figure below
(local link /
general link: power_law.html)
for examples of set of power laws.
If p = -1, what is the scaling, the proportionality,
and the formula for Q?
What is the proportionality
between n and a(t) and what is the
formula for n in terms of n_0, a_0, and a(t)?
Answer: __________ and __________
The energy of a photon ε is proportional to
one over wavelength: i.e., ε ∝ 1/λ.
Now a photon
wavelength grows
with the expansion of the universe
as the photon propagates and scales with a(t).
Say λ_0 and ε_0 are, respectively, the present
mean wavelength and mean energy of the
photons.
What is λ as a function of λ_0, a, and a_0?
Answer: _____________
What is ε as a function of ε_0, a, and a_0?
Answer: _____________
Now the main component of
electromagnetic radiation (EMR)
in the observable universe
is essentially a non-interactive
blackbody radiation field
called the
cosmic background radiation (CBR)
which is a relic of the early hot phase of
the observable universe
near the time of the
Big Bang singularity.
At cosmic time present,
the cosmic background radiation (CBR)
is called the
cosmic microwave background (CMB).
The temperature T of the
cosmic background radiation (CBR)
is the cosmic temperature.
Given the preamble and the last sub task, what is T as a function of T_0, a, and a_0
and how does T vary with
cosmic time?
The
proper distance,
(cosmological) comoving distance,
luminosity distance,
and lookback time
(the cosmic time from
when a light started out to the present)
are all cosmological distance measures.
But the primary
cosmological distance measure
is cosmological redshift z since
it is a direct observable to all z and is often very easy to measure to high accuracy.
Proper distance,
comoving distance,
and lookback time
which are only direct observables to 1st order
in small z.
Luminosity distance is
direct obserable for general z, but only if we know the
luminosity of the source
and often we don't.
So in professional work, astronomers
usually use cosmological redshift z
as a proxy for all the others.
We say this galaxy, etc.
is at z such and such meaning at some distance from us in time and space.
For a given expanding universe model,
z can be used to calculate all the other
cosmological distance measure.
A the present time, the
Λ-CDM model (AKA concordance model or
standard model of cosmology (SMC)) (which fits all
observations very well) is the favored
expanding universe model.
The non-z cosmological distance measure
can be calculated from it as a function of z, but only numerically.
The figure below
(local link /
general link: cosmos_distance_z_10000_2.html)
shows the common
cosmological distance measure
as a function of z for the
Λ-CDM model.
Note "Luminosity" is luminosity distance
"LOS comoving" is proper distance
and
for the present time which equals comoving distance
by the definition of comoving distance.
So getting a/a_0 from z is easy.
But we do NOT get a(t) directly: i.e., "a" as a
function
of cosmic time.
If we did, we would know a lot more about the
observable universe.
It's a pity galaxies do NOT
have big clock faces on them
from which we could read cosmic time.
At it is, to get a(t) we need to adopt a particular model.
For the Λ-CDM model,
one has the approximate formulae????
where t_0 is the
age of the observable universe = 13.797(23) Gyr (Planck 2018),
t is cosmic time,
and t_L = t_0 - t is lookback time.
Sub Tasks:
Sub Tasks:
The diffuse
extragalactic background radiation (DEBRA)
is the whole spectrum of background
electromagnetic radiation (EMR)
observed at the present cosmic time.
It consists of
the cosmic background radiation (CBR)
plus all the
radiation emitted by
stars,
nebulae,
active galaxy nuclei (AGNs),
and other source
emitted since recombination
and NOT absorbed
and NOT identifiable as coming from specific sources.
DEBRA
is what you see when you point your instrument at empty
space
A semi-accurate spectrum of the
DEBRA
CBR
is shown in the figure below
(local link /
general link: diffuse_extragalactic_background_radiation.html.html).
Sub Tasks:
Sub Tasks:
There might be something more here,
sine die---but maybe on
Greek Kalends
(Augustus (63 BCE -- 14 CE)
quote).
Sub Tasks:
Sub Tasks:
Sub Tasks:
Sub Tasks:
Do the preparation required by your lab
instructor.
Keywords:
accelerating universe,
Alan Guth (1947--),
Alexander Alexandrovich Friedmann (1888--1925),
Alexei Starobinsky (1948--),
Andrei Linde (1948--),
Big Bang,
Λ-CDM model
(Wikipedia: Λ-CDM model: Parameters),
cosmic history,
cosmic microwave background (CMB),
cosmic time,
cosmological constant,
cosmological principle,
cosmological redshift,
dark energy,
dark matter,
Doppler effect,
Doppler shift,
Edwin Hubble (1889--1953),
expanding universe,
Future of the expanding universe: Graphical timeline,
galaxies,
galaxy clusters,
galaxy groups,
galaxy superclusters,
general relativity,
George Gamow (1904-1968),
Georges Lemaitre (1894--1966),
history of cosmology,
Hubble constant,
Hubble's law,
Inflation,
Knut Lundmark (1889--1958),
large-scale structure of the universe,
multiverse,
observable universe,
particle horizon,
pocket universe,
quantum cosmology,
recession velocity,
recombination epoch,
redshift,
Timeline of the Big Bang,
Vesto Slipher (1875--1969).
Hm.
Task Master:
EOF
In this section, we discover the expanding universe.
t_H = 1/H_0 = [1/(70 ((km/s)/Mpc) * h_70)] ,
where h_70 = H_0/[70 (km/s)/Mpc]
= [1/(70 (km/s)/Mpc) * h_70)]*[1 Gyr /(3.15576*10**16 s)]
*(3.0857*10**19 km/Mpc) ,
where 1 Gyr = 10**9 years
= ( _______ Gyr )/h_70 .
F = L/( 4π*rL**2) ,
rL = sqrt[ L/( 4π*F) ] ,
____________________________________________________________________________________________
Table: Supernova Luminosity Distances
____________________________________________________________________________________________
No. Supernova Type Accepted Distance Distance from Agreement
Light Curve Fitting (g = good, ∼ 10 %
(Mpc) (Mpc) m = middling, factor of ∼ 2
p = poor, otherwise)
____________________________________________________________________________________________
1 SN 1987A II pec 0.050
2 SN 1990N Ia 22.5
3 SN 1993J IIb 3.62
4 SN 1994I Ic 7.9
5 SN 1994Y IIn 29.5
6 SN 1994ae Ia 27.0
7 SN 1995D Ia 33.7
8 SN 1998aq Ia 20.89
9 SN 1998bu Ia 9.6
10 SN 1999aa Ia pec 73
11 SN 1999by Ia pec 17.6
12 SN 1999dq Ia pec 50.9
13 SN 1999ee Ia 43.0
____________________________________________________________________________________________
Q ∝ a**p ,
Q = Q_0*(a/a_0)**p ,
There is simple relationships between z and a(t) that are true for all
expanding universe models:
a0/a = z + 1 ,
z = a0/a - 1 ,
a/a0 = 1/(1+z)
a/a0 ≅ 1/[1 + H0t0ln(t0/t)] in general,
a/a0 ≅ 1 - H0tL for tL/t0 << 1,
a/a0 ≅ 1/[H0t0ln(t0/t)] for t0/t >> 1,
In this section, we consider the
cosmic microwave background (CMB).
What does this result mean?
There might be more here,
sine die---but maybe on
Greek Kalends
(Augustus (63 BCE -- 14 CE)
quote).
The standard model of cosmology (SMC)
is currently the Λ-CDM model.
There might be something here,
sine die---but maybe on
Greek Kalends
(Augustus (63 BCE -- 14 CE)
quote).
There might more here,
sine die---but maybe on
Greek Kalends
(Augustus (63 BCE -- 14 CE)
quote).
There might more here,
sine die---but maybe on
Greek Kalends
(Augustus (63 BCE -- 14 CE)
quote).
Goodnight all.
Post mortem comments that may often apply specifically to
Lab 12: Cosmos: