Lab #4 The Hubble Law

“-” means that the spectra are easy to identify

Links to the Galaxy Images

Links to the Galaxy Spectra

Example: NGC 1357

NGC 1357 image

Back to galaxy selection page

Resets this page

Example: NGC 13571. Visually find the long axis of the galaxy:

Example: NGC 13572. Click on one end of the galaxy:

The page will report the x,y pixel positions

Example: NGC 1357

The page will report the 2nd set of x,y pixel positions

3. Click on the other side of the galaxy:

Example: NGC 13574. Record the angular size you just measured

Example: NGC 13575. If you missclicked use the “Try Again” link to reset the page:

“Oops!”

Example: NGC 13576. Use the “Back” icon to return to the galaxy selection page.

Example: NGC 1357

NGC 1357 spectraBack to the galaxy section page

Close-up of the Calcium H and K line region

Close-up of the Hydrogen line region

NGC 1357 spectra

Calcium H and KThe absorption lines due to calcium will be among the strongest ("deepest") of all the lines.

The black lines at the bottom of the figure (Ca K and Ca H) show the location of the rest wavelengths. These rest wavelengths are also spelled out at the top of the figure.

As you can be seen, the measured wavelengths will show a sizeable shift toward redder wavelengths.

On the spectra, you will be clicking at the bottom of each of

these strong absorption features.

Calcium H and KThe absorption lines due to calcium will be among the strongest ("deepest") of all the lines.

The black lines at the bottom of the figure (Ca K and Ca H) show the location of the rest wavelengths. These rest wavelengths are also spelled out at the top of the figure.

As you can be seen, the measured wavelengths will show a sizeable shift toward redder wavelengths.

On the spectra, you will be clicking at the bottom of each of

these strong absorption features.

Calcium H and KThe absorption lines due to calcium will be among the strongest ("deepest") of all the lines.

The black lines at the bottom of the figure (Ca K and Ca H) show the location of the rest wavelengths. These rest wavelengths are also spelled out at the top of the figure.

As you can be seen, the measured wavelengths will show a sizeable shift toward redder wavelengths.

On the spectra, you will be clicking at the bottom of each of

these strong absorption features.

Calcium H and KThe absorption lines due to calcium will be among the strongest ("deepest") of all the lines.

The black lines at the bottom of the figure (Ca K and Ca H) show the location of the rest wavelengths. These rest wavelengths are also spelled out at the top of the figure.

As you can be seen, the measured wavelengths will show a sizeable shift toward redder wavelengths.

On the spectra, you will be clicking at the bottom of each of

these strong absorption features.

Click bottom of Calcium K line

The page reports the wavelength that you clicked.

Record this number to 5 significant digits

Note: an Angstrom is 10-10 meters (or 1/10 of a nanometer)

Click bottom of Calcium H line

The page reports the wavelength that you clicked.

Record this number to 5 significant digits

Hydrogen As seen in this figure, there are two strong emission lines that are slightly redder than the rest wavelength of hydrogen , shown by the black vertical line at the bottom.

Pick the strong emission line that is to the left (blueward) of the other strong emission line, even if the other one has more intensity. (The strong emission line on the right is usually due to oxygen.)

We expect the wavelength shift for this hydrogen line to be slightly greater than that of the calcium lines.

Hydrogen As seen in this figure, there are two strong emission lines that are slightly redder than the rest wavelength of hydrogen , shown by the black vertical line at the bottom.

Pick the strong emission line that is to the left (blueward) of the other strong emission line, even if the other one has more intensity. (The strong emission line on the right is usually due to oxygen.)

We expect the wavelength shift for this hydrogen line to be slightly greater than that of the calcium lines.

Hydrogen As seen in this figure, there are two strong emission lines that are slightly redder than the rest wavelength of hydrogen , shown by the black vertical line at the bottom.

Pick the strong emission line that is to the left (blueward) of the other strong emission line, even if the other one has more intensity. (The strong emission line on the right is usually due to oxygen.)

We expect the wavelength shift for this hydrogen line to be slightly greater than that of the calcium lines.

Hydrogen

The hydrogen can sometimes be tricky to find, there is a line just to the left of it that sometimes can be fairly large, or produce a “hump” on the H emission feature. Here are some examples.

Hydrogen

The hydrogen can sometimes be tricky to find, there is a line just to the left of it that sometimes can be fairly large, or produce a “hump” on the H emission feature. Here are some examples.

Click top of the Hydrogen line

The page reports the wavelength that you clicked.

Record this number to 5 significant digits

Making the data useful1. You measured the angular size of

the galaxy in milliradians (mrad). In this example 1.011 mrad.

Making the data useful1. You measured the angular size of

the galaxy in milliradians (mrad). In this example 1.011 mrad.

2. We are using the assumption that the visible part of these large spiral galaxies are all 22 kiloparsecs (kpc) across

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Making the data useful1. You measured the angular size of the

galaxy in milliradians (mrad). In this example 1.011 mrad.

2. We are using the assumption that the visible part of these large spiral galaxies are all 22 kiloparsecs (kpc) across

3. Since they have a small angular size, we can use the rule of small angles to find the distance (like in the parallax lab)

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Making the data useful

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

€

d =s

a s: size of galaxy (kpc)

a: Angular size of the galaxy (mrad)

d: Distance to the galaxy (Mpc)

Given the units on “s” and “a” this formula as written will return the distance to the galaxy in megaparsecs (Mpc)

Making the data useful

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

€

d =s

aIn this example:

a = 1.011 mrad

s = 22 kpc

so:

d = s/a = 22/1.011 = 21.8 Mpc

The distance to each galaxy is one of the measurements you need!

Making the data useful1. You have the wavelength of 3 lines

from the galaxy (Calcium H, Calcium K, and Hydrogen ).

Making the data useful1. You have the wavelength of 3 lines

from the galaxy (Calcium H, Calcium K, and Hydrogen ).

2. You have the rest wavelength of all three of these lines.

Making the data useful1. You have the wavelength of 3 lines

from the galaxy (Calcium H, Calcium K, and Hydrogen ).

2. You have the rest wavelength of all three of these lines.

3. You can now calculate the radial velocity of the galaxy. This should be expressed in terms of the fraction of the speed of light v/c = “z”

€

λobs − λ restλ rest

=v

c= z

Making the data useful

€

λobs − λ restλ rest

=v

c= z

In this example:

Calcium K

Calcium H

Hydrogen

€

z =3962.0 − 3933.7

3933.7= .0072

€

z =3998.0 − 3968.5

3968.5= .0074

€

z =6608.4 −6562.8

6562.8= .0069

€

zaverage = .0072

The average redshift of each galaxy is the other measurement you need!

Now: Do the rest of the galaxies!

Tips:

• Practice with NGC 1357 (the one used in this example).

• Your numbers should be similar (but not exactly the same) as the ones in this example

Now: Do the rest of the galaxies!

Tips:

• Some galaxies do not have a “-” next to them on the list.

• These galaxies have spectra that are not easy to interpret.

• Check with your instructor on how to deal with them!