Astronomy Lab 17 Griggs University HR Diagram Assignment

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Griggs University Astronomy Lab 17 HR Diagram To be completed after reading Arny, Chapter 13 Name: __________________ Objectives: To observe the relationship between a star’s intrinsic brightness (absolute magnitude) and surface temperature. To organize the data into an HR diagram and interpret the diagram. To determine the distance to the Pleiades star cluster by constructing its HR diagram. Definitions: Magnitude: a measure of the brightness of a star. The larger the magnitude, the fainter the star. Intensity (I): the rate we receive light energy at the earth from a given star. Apparent magnitude (m or V): the visual brightness of the star as observed from earth. The apparent magnitude depends on both the luminosity of the star and the distance. Brightest stars are 1st magnitude or less, faintest stars visible to naked eye are 6th magnitude. Each difference in magnitude of 1 corresponds to a ratio of intensity of 2.5  . Each difference in magnitude of 5 corresponds to a ratio of intensity of 100  . This may be written mathematically as, I  m1 − m2 = 2.5 log  2   I1  . (1) Absolute magnitude (M): the apparent magnitude a star would have if placed 10 pc away. It depends only on the star’s luminosity. From Eq. (1), we see  I 10 pc   m − M = 2.5 log  (2)  I  Where I10 pc is the brightness the star would have at 10 pc. Luminosity (L): the total power output of the star in units of either watts or solar luminosity units. Distance (d): The distance in pc = 1/p, where p is the parallax angle in seconds of arc. It is roughly the distance between nearest neighbor stars (1 pc  3.26 light years). The distance is related to the difference between apparent and absolute magnitudes, m – M, as shown below: The intensity drops off as the inverse-square of the distance, thus, I 10 pc I so  d   =   10 pc  2 (3) 2  d   d   = 5 log   m − M = 2.5 log  10 pc 10 pc     (4) Solving for d,  d  m−M log   = 5  10  m−M d = 10 5 10 d = 10 pc  10 (5) (6) m− M 5 (7) B - V Color Index: The difference between the magnitude of a star as measured with a blue filter and measured with a visual filter. If B - V is large and positive, the blue magnitude is larger than the visual magnitude and the star is reddish (low surface temperature). If B - V is negative, the visual magnitude is larger than the blue magnitude and the star is bluish (high surface temperature). Two Questions: Examine the two pictures of the same star taken with first a Blue filter and then with a Visual filter in place. Blue Filter Visual Filter 1. Which magnitude has a larger value? B or V _______ (Hint: a brighter star has a lower value for its magnitude) 2. Is B – V positive or negative? _______ Spectral Type: classification of the star based on spectrum. Hottest to coolest classes are O, B, A, F, G, K, M.. Here is a table relating Spectral Type, B - V, and Temperature: Table 0: Stellar Characteristics by Spectral Type Type B-V Surface Temp (K) O5 -0.32 50,000 B0 -0.24 20,000 B5 -0.16 16,000 A0 0.00 10,400 A5 +0.15 8,200 F0 +0.30 7,200 F5 +0.45 6,700 G0 +0.57 6,000 G5 +0.65 5,500 K0 +0.81 5,100 K5 +1.18 4,300 M0 +1.39 3,700 M5 +1.69 3,000 Part I Constructing an HR Diagram Open the Starry Night program and use the View menu to Hide Daylight and Hide Horizon. Under the Labels menu choose Stars. Find each of the following stars and right-click the star to Show Info and clicking on the Tab Other Data to record the properties in the Table below. A quick check on distance is to take the distance in light years given directly by Starry Night and divide by 3.26 light years/pc. Table I: 14 of the 100 brightest Stars in the Sky Name Sirius Absolute Magnitude (M) Luminosity (Solar Units) apparent magnitude m (or V) (m-M)/5 1.42 27 -1.47 -0.578 Algol Bellatrix Betelgeuse Rigel Pollux Aldebaran Mizar Procyon Polaris Capella Arcturus Altair Vega Table II: 10 of the Nearest Stars d= 1010(m-M)/5 (pc) B-V Color Index Spectral Class Tsurface 2.64 0.01 A0 8858 K (Kelvins) Name M Luminosity m d (pc) B-V (AU) +0.62 Spect Temp Alpha Centauri Barnard’s Star epsilon eridani epsilon indi tau ceti Sun 4.71 5800 Open the HR Diagram Excel file and input your own data. Copy and Paste Your HR Diagram Graph below! Right-click on your graphic image and choose Text Wrapping/Through so you can draw on top of it. Label the main sequence on your graph. Label any red giants on your graph. Where on your graph are the intrinsically brightest stars? _____________________ Where on your graph are the intrinsically faintest stars? _____________________ Where on your graph are the reddest stars? _____________________ Where on your graph are the bluest stars? _____________________ Where on your graph are the hottest stars? ________________________ Where on your graph are the coolest stars? ________________________ Where on your graph are the largest stars? ________________________ Where on your graph are the smallest stars? _______________________ Why are Table I stars in the upper portion of your graph and Table II stars in the lower portion? __________________________________________________________________ Circle the point on your graph representing the sun. Draw a line on your graph representing all stars with the same surface temperature as the sun. Draw a line on your graph representing all stars with the same absolute magnitude as the sun. Part II: Distance to main-sequence star Spica The main-sequence star Spica is spectral type B0 (B-V = -0.24) and has apparent magnitude m = 1.0. From your graph find B – V = -0.24 on the x-axis. Move vertically upward to find the point on your main sequence corresponding to B – V = -0.24. Look at the vertical axis to obtain the absolute magnitude for this main-sequence star. MSpica = ____________ . From Eq. (7) get the distance, dspica = _____________ pc For comparison purposes, use Starry Night to Find Spica and move cursor over the star to get the distance in light years. dSpica ly = ____________ light years Then divide by 3.26 light years/pc to get the distance in pc. dSpica pc = ____________ pc Part III: Distance and size of the open cluster M45 (the Pleiades of Job 9:9, Job 38:31 and Amos 5:8) In Starry Night, Find the open star cluster M45 and magnify. Choose one of the brighter stars in the cluster (you cannot use the object identified as M45, it is not really a star, instead chose from Atlas, Electra, Taygeta, Maia, Pleione or Merope) and right-click to show the Info Window. Record the apparent magnitude, m = __________ Record the absolute magnitude, M = ___________ Use Eq. (7) to determine the distance to the star and thus the entire cluster, dPleiades = ___________ pc Change the cursor to angular separation and drag across the cluster to measure its angular size, in degrees and minutes of arc, Adm = _______o ________’ Convert the minutes into decimal fractions of a degree by dividing by 60, Ad = ____.____o Use the angular size – to – linear size formula to convert to a linear size, A L = 360 2d or L = 2d ( A / 360) = ___________ pc Convert this linear size to light years (1 pc = 3.26 ly). Lly = ____________ light years How long would it take a beam of light to traverse the width of the Pleiades? _______________ years -10 -8 -6 -4 -2 M 0 2 4 6 8 10 12 14 -.3 -.1 0 .1 .3 .5 .7 B-V .9 1.1 1.3 1.5 1.7 ...
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Tutor Answer

andythewxman
School: UT Austin

Here you go. Please let me know if there are any questions. All values were obtained using Stellarium and calculations were made using the provided equations.

Griggs University
Astronomy Lab 17
HR Diagram
To be completed after reading Arny, Chapter 13
Name: __________________
Objectives: To observe the relationship between a star’s intrinsic brightness (absolute
magnitude) and surface temperature. To organize the data into an HR diagram and interpret the
diagram. To determine the distance to the Pleiades star cluster by constructing its HR diagram.
Definitions:
Magnitude: a measure of the brightness of a star. The larger the magnitude, the fainter the star.
Intensity (I): the rate we receive light energy at the earth from a given star.
Apparent magnitude (m or V): the visual brightness of the star as observed from earth. The
apparent magnitude depends on both the luminosity of the star and the distance. Brightest stars
are 1st magnitude or less, faintest stars visible to naked eye are 6th magnitude. Each difference
in magnitude of 1 corresponds to a ratio of intensity of 2.5  . Each difference in magnitude of
5 corresponds to a ratio of intensity of 100  . This may be written mathematically as,

I 
m1 − m2 = 2.5 log  2 
 I1 

.

(1)

Absolute magnitude (M): the apparent magnitude a star would have if placed 10 pc away. It
depends only on the star’s luminosity. From Eq. (1), we see

 I 10 pc 

(2)
m − M = 2.5 log 
 I 
Where I10 pc is the brightness the star would have at 10 pc.
Luminosity (L): the total power output of the star in units of either watts or solar luminosity
units.
Distance (d): The distance in pc = 1/p, where p is the parallax angle in seconds of arc. It i...

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Tutor went the extra mile to help me with this essay. Citations were a bit shaky but I appreciated how well he handled APA styles and how ok he was to change them even though I didnt specify. Got a B+ which is believable and acceptable.

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