Determining Hubble Constant and Scale Factor of Universe

In summary, the conversation discusses two questions related to astronomy. The first question involves calculating the limit on the possible values of the Hubble constant using the age of certain white dwarfs. The second question involves finding the ratio of the scale factor of the universe at the time the light was emitted to its current scale factor, using the redshift of a galaxy. Through discussion and clarification, it is determined that the limit on the Hubble constant is 1/11.2 Gya, and the ratio of scale factors is 11Rthen=Rnow. The conversation also includes a step-by-step explanation and confirmation of the equations used to solve these questions.
  • #1
weldon
8
0
Hi, I am in my second astronomy course and just received a twenty question take home final exam, and I am having trouble with two of the questions.

In 2004 astronomers reported finding evidence that certain white dwarfs are 12.1 +- 0.9 billion years old. Assuming an inflationary model in which the age of the universe is approximately equal to Hubble time, what limit does this measurement set on the possible values of Hubble constant H-0?

My work: if the age of the universe is equal to Hubble time, and Hubble time is equal to 1 over the Hubble constant, than wouldn't the limit of the age of the universe be 13 bya, thus 13bya = 1/H-0, and 11.2bya = 1/H-0, making the answer and the limit on the Hubble constant to be a value in between 1/13bya and 1/11.2bya? How would I make this information into a answer for that question?





In March 2004, astronomers reported measuring a record redshift for a galaxy. z=10. Assuming that this redshift is due to the expansion of the universe, what is the ratio of the scale factor of the universe when the light was emitted to its scale factor now? (In other words, find R-then / R-now where R is the scale factor of the universe)


I have no idea how to start this one.


Any steps in the right direction or links with these types of problems and their solutions would be much appreciated. Thank you.
 
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  • #2
weldon said:
In 2004 astronomers reported finding evidence that certain white dwarfs are 12.1 +- 0.9 billion years old. Assuming an inflationary model in which the age of the universe is approximately equal to Hubble time, what limit does this measurement set on the possible values of Hubble constant H-0?

My work: if the age of the universe is equal to Hubble time, and Hubble time is equal to 1 over the Hubble constant, than wouldn't the limit of the age of the universe be 13 bya, thus 13bya = 1/H-0, and 11.2bya = 1/H-0, making the answer and the limit on the Hubble constant to be a value in between 1/13bya and 1/11.2bya? How would I make this information into a answer for that question?

You are very close, but you need to think more closely about what limits the white dwarf ages place on the age of the Universe. You are assuming it tells you more than it really does.

weldon said:
In March 2004, astronomers reported measuring a record redshift for a galaxy. z=10. Assuming that this redshift is due to the expansion of the universe, what is the ratio of the scale factor of the universe when the light was emitted to its scale factor now? (In other words, find R-then / R-now where R is the scale factor of the universe)

What is the relationship between redshift and scale factor?
 
  • #3
Thanks for the quick response. I am not really sure what I am missing in the first question though. What is the limit that I am missing? Can i use the formula given here with the numbers it says? (13.6, 72)
 
  • #4
The formula and your application of it are correct. However one of the limits you state cannot be determined from aging white dwarfs, but the other can. Try and think of why.
 
  • #5
is it you can't tell the age of the universe because you do not know the luminoisity of the white dwarf? If so, I don't really have any idea what that would mean as far as finding the limits.
 
  • #6
It's much simpler than that, we can assume that there are no potential problems with aging white dwarves and just go with the measurement and limits given. Don't worry about luminosity etc etc.

Take a step back, can you tell me why the age of a white dwarf puts limits on the age of the universe?
 
  • #7
Is it because a white dwarf cannot be older than the universe, thus astronomers try to find the oldest white dwarf to measure the age of the universe? so that would mean that it does not limit the age of the universe at 13Gya ?
 
  • #8
Bingo, aging the star can't tell you any upper limit for the age of the Universe, only a lower one.
 
  • #9
Awesome, so that would mean that the only limit it puts in the Hubble constant would be 11.2Gya?
 
  • #10
Yes, well 1/11.2 Gya but I think that is what you meant ;)
 
  • #11
Thanks for your help on the first one Wallace. On the second one, would you use the equation
1 + z = R-then/R-now, meaning 11= R then/r now?
would you even know the scale in the equation, or is that as far as you can simplify it?

this is what I typed up/found. is it true or am I on the wrong track?

Using the formula for cosmic redshift 1 + z =Rthen/Rnow, the record breaking redshift z=10 that astronomers observed in march 2004 can be plugged into the equation to find the ratio of the scale factor of the universe when the light was emitted to its scale factor now. 1 + 10 = Rthen/Rnow 11 = Rthen/Rnow Thus the ratio of the scale factor of the universe when the light was emitted to its scale factor now is 11Rnow=Rthen.
 
Last edited:
  • #12
You almost have the equation and working correct, just re-check your 'then' and 'now'

As for the second question, there is no absolute value to the scale factor. It only has meaning in a ratio, so yes that is as far as you can go.
 
  • #13
is it 11Rthen=Rnow? Those numbers seem to make more sense...
 
  • #14
Yep, the universe was smaller then than today, so indeed those number make more sense!
 
  • #15
Thanks a lot for all your help tonight Wallace. Take care :)
 

1. What is the Hubble constant and why is it important in determining the scale factor of the universe?

The Hubble constant, denoted by the symbol H0, is a measurement of the rate at which the universe is expanding. It is an important parameter in determining the scale factor, which is a measure of the change in the size of the universe over time. The Hubble constant allows us to calculate the age of the universe, as well as understand the overall structure and evolution of the universe.

2. How is the Hubble constant determined?

The Hubble constant is determined through various methods, including observations of the cosmic microwave background radiation, measurements of the distances and velocities of galaxies, and the use of standard candles, such as Type Ia supernovae. These methods allow scientists to calculate the expansion rate of the universe and determine the value of the Hubble constant.

3. How has our understanding of the Hubble constant changed over time?

Our understanding of the Hubble constant has evolved over time as new observations and techniques have been developed. In the early 20th century, Edwin Hubble first discovered that the universe was expanding and estimated the value of the Hubble constant to be around 500 km/s/Mpc. Since then, with advancements in technology and more precise measurements, the accepted value of the Hubble constant has decreased to around 70 km/s/Mpc.

4. How does the Hubble constant relate to the Big Bang theory?

The Hubble constant is a crucial component of the Big Bang theory, which explains the origin and evolution of the universe. It is used to calculate the age of the universe and determine the rate of expansion since the Big Bang. The value of the Hubble constant also provides evidence for the theory, as it aligns with the predictions of the Big Bang model.

5. Why is there still debate and uncertainty surrounding the value of the Hubble constant?

Despite decades of research and advancements in technology, the value of the Hubble constant is still a topic of debate and uncertainty among scientists. This is due to various factors, such as the difficulty in accurately measuring the distances and velocities of galaxies, as well as the impact of dark matter and dark energy on the expansion of the universe. As new data and methods are continuously being developed, our understanding of the Hubble constant will continue to evolve.

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