Lab 12: Cosmos

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.

Group Number/Name:

Name:

Partner Names:

Favorite Report: Y / N

Task Master:

Task 1: Slipher and Hubble.
Task 2: Redshift.
Task 3: Hubble's Law.
Task 4: Proper Distance and Luminosity Distance.
Task 5: Supernova Distances. This task may require a demonstration by the instructor.
Task 6: The Cosmic Scale Factor. This task may require a micro lecture by the instructor.
Task 7: Cosmological Redshift Is the Primary Cosmic Distance Measure.
Task 8: CMB.
Task 9: The Diffuse Extragalactic Background Radiation (DEBRA).
Task 10: The Accelerating Universe.
Task 11: The Standard Model of Cosmology. (Omit since underconstruction.)
Task 12: The Big Bang. (Omit since underconstruction.)
Task 13: The Large-Scale Structure. (Omit since underconstruction.)
Task 14: The Multiverse. (Omit since underconstruction.)
Task 15: Naked-Eye Observations (RMI only).

Task 1: Slipher and Hubble:
Sub Tasks:
1. Read the 2 figures below (local link / general link: vesto_slipher.html; (local link / general link: edwin_hubble.html) ). Have you read it? Y / N
2. Where did Slipher work? ______________________________
3. Slipher's important discovery is:
  1. that most galaxies have blueshifts. ____
  2. that most galaxies have redshifts. ____
  3. that galaxies were galaxies. ____
  4. Hubble's law. ____
4. Edwin Hubble (1889--1953) published his discovery of the extragalactic nature of the spiral nebulae (now called spiral galaxies) in:
  1. 1900. ____
  2. 1924. ____
  3. 1929. ____
  4. 1936. ____
  5. 1953. ____
End of Task
Task 2: Redshift:
Sub Tasks:
1. Read the figure below (local link / general link: cosmological_redshift.html). Have you read it? Y / N
2. What is the redshift for a redshift velocity ± 10**3 km/s to 1-digit precision (i.e., rounded off to 1 digit)? Which case (upper or lower) is a blueshift?
  Answer:
3. What is the redshift velocity for z = 2 in units of c (i.e., in SYMBOLS)? Is the redshift velocity VALUE obtained this physically possible for either or both of of ordinary physical velocity or recession velocity? Is the redshift velocity VALUE obtained an accurate value for either or both of ordinary physical velocity or recession velocity?
  Answer:
End of Task
Task 3: Hubble's Law:
Sub Tasks:
1. Read the figure below (local link / general link: hubble_diagram.html). Have you read it? Y / N
2. The empirical discovery of Hubble's law for the observable universe (with weak evidence and little noticed, in 1927 and with convincing evidence, and much noticed, in 1929) was the empirical discovery of the ______________________________. Note Hubble's law is NOT the same thing as ______________________________ since you can have ______________________________ without Hubble's law, but NOT vice versa.
3. Hubble's law is _____________.
4. A fiducial value for the Hubble constant is _____________.
5. The Hubble constant is actually an inverse time quantity as one can see since its conventional units are (km/s)/Mpc which work out to be units of inverse time. If the recession velocities for objects participating in the mean expansion of the universe were constant, what would be the time in SYMBOLS since the observable universe was a point? HINT: Remember Hubble's law v = H_0*r and say v is constant. How long has it been since r was zero? ________________
6. The time quantity found in the last question is a characteristic time for the expansion of the universe called the Hubble time t_H. It is NOT the age of the universe since the recession velocities have NOT been constant. However, for most expanding universe models, it is of order of the age of the universe. Complete the following conversion calculation to 4-digit accuracy/precision (i.e., rounded off to 4 digits accurately):
  Answer:
```
 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 .  
```
7. The Hubble time times the vacuum light speed gives the Hubble length (L_H = c*t_H = c/H_0), a characteristic size scale for the observable universe. The Hubble length for most expanding universe models is of order of the proper-distance radius of the observable universe.
  What is the Hubble length in Giga-light-years (Gly)? HINT: What is the vacuum light speed in units of Gly/Gyr?
  Answer:
End of Task
Task 4: Proper Distance and Luminosity Distance:
Sub Tasks:
1. Read the subsection Proper Distance and Luminosity Distance above. Have you read it? Y / N
2. Proper distance is a distance:
  1. that CAN BE measured at one instant 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. ___
  2. determined using the formula r_L = sqrt[ L/( 4π*F) ] in all cases if extinction is negligible. ___
  3. that is the length of an object undergoing FitzGerald contraction in the inertial frame of measurement. ___
  4. is NOT an improper distance. ___
  5. is NOT an improper fraction. ___
3. Luminosity distance is:
  1. a distance that CAN BE measured at one instant 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. ___
  2. a quantity with units of length determined using the formula r_L = sqrt[ L/( 4π*F) ] in all cases if extinction is negligible. ___
  3. a distance that is the length of an object undergoing FitzGerald contraction in reference frame of measurement. ___
  4. a distance that is NOT an improper distance. ___
  5. a distance that is NOT an improper fraction. ___
End of Task
Task 5: Supernova Distances:
Sub Tasks:
1. Read the applet figure below (local link / general link: naap_supernovae.html). Have you read it? Y / N
2. What kind of supernovae provided the luminosity distances that were the first convincing evidence for the accelerating universe?
  1. Type II supernovae (SNe II). ___
  2. core collapse supernovae. ___
  3. Type Ib supernova (SNe Ib). ___
  4. Type Ia supernovae (SNe Ia). ___
  5. Type IIn supernovae (SNe IIn). ___
3. Push all the buttons of the applet figure below (local link / general link: naap_supernovae.html) to see what they do. Also move the BAR with the ARROW and the light curves with the HAND. Also fill in all the boxes with values. Have you pushed, moved, and filled everything? Y / N
  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:
4. Now fit the light curves of the supernovae in the applet as best you can to the fiducial SN Ia light curve to obtain the luminosity distances.
  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.
5. Describe your the level agreement (e.g., good, middling, poor, none) between your fitted luminosity distances and the accepted values in separate paragraphs for each of normal SNe Ia, peculiar SNe Ia, and non-SNe Ia. Since peculiar SNe Ia and non-SNe Ia only have normal SNe Ia luminosity by accident, one gets good or middling agreement for them by accident.
  Answer:
```
  ____________________________________________________________________________________________
  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

  ____________________________________________________________________________________________ 
```
End of Task
Task 6: The Cosmic Scale Factor:
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:
1. Read the figure below (local link / general link: expanding_universe.html). Have you read it? Y / N
2. Many cosmic quantities that vary with cosmic time (but NOT on average with position in the observable universe) scale as a power (AKA exponent) of the cosmic scale factor a(t). Thus
  
  Q ∝ a**p ,
  
  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
  
  Q = Q_0*(a/a_0)**p ,
  
  where subscript 0 means PRESENT-TIME VALUE 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.
3. What are the PRESENT-TIME VALUES of a, Q, n, ε, and E in symbols? Answer: __________________________
4. Now if we say p = 2, then Q scales like a**2 which means we have proportionality Q ∝ a**2 and formula Q = Q_0*(a/a_0)**2.
  If p = -1, what is the scaling, the proportionality, and the formula for Q?
  Answer:
5. Say you have N particles in cubical box with side length L, what is the volume V of the cubical box in terms of L and what is the number density n = N/V in terms of N and L? HINT: See the figure below (local link / general link: cube_unit.html) and gas_animation.html. Answer: ___________________ and ___________________
6. Say the cubical box side length L scales with a(t) and the number of particles in the box stays constant on average. Some particles leave, but others enter, and so the average number stays constant.
  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 __________
7. Say the photons (the particles of electromagnetic radiation (EMR)) in the expanding universe have mean wavelength λ in general.
  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: _____________
8. The photons in the expanding universe can be approximated as conserved. Let n be their number density at a general time. What is their energy density E at a general time as function of n_0, ε_0, a, and a_0, and as a function of E_0, a, and a_0? How does the energy density scale with a?
  Answer:
9. The energy density of a blackbody radiation field is proportional to the 4th power of its (kelvin) temperature: i.e., E ∝ T**4.
  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?
  Answer:
End of Task
Task 7: Cosmological Redshift Is the Primary Cosmic Distance Measure:
Sub Tasks:
1. Read the subsection Cosmological Redshift Is the Primary Cosmological Distance Measure above Have you read it? Y / N
2. The cosmological redshift is the primary cosmic distance measure because it is:
  1. a direct observable and relatively easy to measure from spectroscopy ________________
  2. a direct observable and relatively easy to measure from photometry. ________________
  3. an indirect observable and relatively easy to measure from photometry. ________________
  4. an indirect observable and relatively easy to measure from spectroscopy ________________
  5. an indirect observable and relatively hard to measure from photometry. ________________
End of Task
Task 8: CMB:
Sub Tasks:
1. Read the figure below (local link / general link: cmb.html). Have you read it? Y / N
2. Given that recombination happened at cosmological redshift z ≅ 1100, what is the ratio a_0/a = z + 1 for that z to 2-digit precision? ________________
  What does this result mean?
  Answer:
3. Given that the cosmic background radiation (CBR) (which is a blackbody radiation field) obeys T = T_0*(a_0/a), what approximately was its temperature to 2-digit accuracy/precision at recombination? ________________
End of Task
Task 9: The Diffuse Extragalactic Background Radiation (DEBRA):
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:
1. Read the figure below (local link / general link: diffuse_extragalactic_background_radiation.html.html). Have you read it? Y / N
2. What is the dominant component of DEBRA? ___________
3. What is the weakest component of DEBRA shown? ___________
4. What is the photon energy of a photon with λ_μ = 1 to 5-digit accuracy/precision in electron-volts (eV)? ___________
End of Task
Task 10: The Accelerating Universe:
Sub Tasks:
1. Read the figure below (local link / general link: accelerating_universe.html). Have you done so? Y / N
2. The term accelerating universe is used to describe a cosmological model in which the rate of expansion of the universe (i.e., the rate of change of the rate of change of the cosmic scale factor a) is:
  1. increasing. ________________
  2. decreasing. ________________
  3. zero. ________________
  4. undetermined. ________________
  5. indeterminable. ________________
3. According to the current Λ-CDM model, the age of the observable universe is ________________ .
4. According to the current Λ-CDM model, the transition cosmic time between deceleration and acceleration of the observable universe is ________________ .
End of Task
Task 11: The Standard Model of Cosmology (Omit since underconstruction):
Sub Tasks:
1. Read the figure below (local link / general link: accelerating_universe.html). Have you done so? Y / N
End of Task
Task 12: The Big Bang (Omit since underconstruction):
Sub Tasks:
1. Read the figure below (local link / general link: accelerating_universe.html). Have you done so? Y / N
End of Task
Task 13: The Large-Scale Structure (Omit since underconstruction):
Sub Tasks:
1. Read the figure below (local link / general link: accelerating_universe.html). Have you done so? Y / N
End of Task
Task 14: The Multiverse (Omit since underconstruction):
Sub Tasks:
1. Read the figure below (local link / general link: inflation_eternal.html). Have you done so? Y / N
End of Task
Task 15: Naked-Eye Observations (RMI only):

EOF
End of Task

Lab 12: Cosmos

Group Number/Name:

Name:

Partner Names:

Favorite Report: Y / N

Q ∝ a**p ,

Q = Q_0*(a/a_0)**p ,