1. Lab #4 The Hubble Law

3. - means that the spectra are easy to identify Links to the Galaxy Images Links to the Galaxy Spectra

4. Example: NGC 1357

5. NGC 1357 image Back to galaxy selection page Resets this page

6. Example: NGC 1357 1. Visually find the long axis of the galaxy:

7. Example: NGC 1357 2. Click on one end of the galaxy: The page will report the x,y pixel positions

8. Example: NGC 1357 The page will report the 2nd set of x,y pixel positions 3. Click on the other side of the galaxy:

9. Example: NGC 1357 4. Record the angular size you just measured

10. Example: NGC 1357 5. If you missclicked use the Try Again link to reset the page: Oops!

11. Example: NGC 1357 6. Use the Back icon to return to the galaxy selection page.

12. Example: NGC 1357

13. NGC 1357 spectra Back to the galaxy section page Close-up of the Calcium H and K line region Close-up of the Hydrogen line region

14. NGC 1357 spectra

15. Calcium H and K The 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.

16. Calcium H and K The 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.

17. Calcium H and K The 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.

18. Calcium H and K The 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.

19. 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)

20. Click bottom of Calcium H line The page reports the wavelength that you clicked. Record this number to 5 significant digits

22. 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.

23. 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.

24. 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.

25. 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.

26. 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.

27. Click top of the Hydrogen line The page reports the wavelength that you clicked. Record this number to 5 significant digits

28. Making the data useful 1.You measured the angular size of the galaxy in milliradians (mrad). In this example 1.011 mrad.

29. Making the data useful 1.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

30. Making the data useful 1.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)

31. Making the data useful 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)

32. Making the data useful In 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!

33. Making the data useful 1.You have the wavelength of 3 lines from the galaxy (Calcium H, Calcium K, and Hydrogen ).

34. Making the data useful 1.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.

35. Making the data useful 1.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

36. Making the data useful In this example: Calcium K Calcium H Hydrogen The average redshift of each galaxy is the other measurement you need!

37. 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

38. 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!