# Determining Hubble Constant and Scale Factor of Universe

weldon
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.

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.

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?

weldon
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)

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.

weldon
is it you cant 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.

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?

weldon
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 ?

Bingo, aging the star can't tell you any upper limit for the age of the Universe, only a lower one.

weldon
Awesome, so that would mean that the only limit it puts in the Hubble constant would be 11.2Gya?

Yes, well 1/11.2 Gya but I think that is what you meant ;)

weldon
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.

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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.

weldon
is it 11Rthen=Rnow? Those numbers seem to make more sense...