Hertzprung-Russel and colormagnitude. ASTR320 Wednesday January 31, 2018

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1 Hertzprung-Russel and colormagnitude diagrams ASTR320 Wednesday January 31, 2018

2 H-R diagram vs. Color- Magnitude Diagram (CMD) H-R diagram: Plot of Luminosity vs. Temperature CMD: Plot of magnitude vs. color index Remember definition of Absolute magnitude: M = m 5 log 10 d + 5

3 Hertzsprung-Russell Diagram Plot of Luminosity versus Temperature: estimate T from Spectral Type estimate L from apparent brightness & distance Done independently by: Eljnar Hertzsprung (1911) for star clusters Henry Norris Russell (1913) for nearby stars Eljnar Hertzsprung Henry Norris Russell

4 Luminosity (L sun ) H-R Diagram Main Sequence: Strong correlation between Luminosity and Temperature Holds for 85% of nearby stars including the sun All other stars differ in size: Giants & Supergiants: Very large radius, but same masses as M-S stars White Dwarfs: Very compact stars: ~R earth but with Supergiants White Dwarfs Giants ~M sun! 40,000 20,000 10,000 5,000 2,500 Temperature (K)

5 Axes of the H-R Diagram The vertical axis displays the luminosity of the stars. This is either as a ratio compared with that of the Sun or as absolute magnitude, M. One point to be careful of when using absolute magnitude is to remember that the lower or more negative the absolute magnitude, the more luminous the star. The brightest stars therefore appear at the top of the H-R diagram with the vertical axis having the most negative value of M at the top.

6 H-R Diagram Can be a very useful tool for studying relative properties of stars If you know the distance!

7 H-R Diagram Compare Barnard s Star to Mira Δm=15 Compare Mira to Betelgeuse Δm=5 Different luminosities tell you about the different physical properties of the stars

8 H-R Diagram Supergiants Rigel and Deneb have the same effective temperature as Sirius but have extremely high luminosities. They have large radii than Sirius hence greater surface areas and higher luminosities. Sirius is a main sequence star but because it is hotter than the red main sequence Barnard's Star it is much more luminous than it.

9 H-R Diagram Procyon B and Barnard's Star share the same low luminosity with an absolute magnitude of about +13. Procyon B however is much hotter than Barnard's Star thus emits much more energy per second per unit surface area. Given that they have the same total power output Procyon B must therefore have less surface area than Barnard's Star, that is its radius is smaller.

10 Relative photometry But what if we don t know the distance? Measuring the brightness of one star compared to another is called relative photometry Because observations in astronomy are difficult to do absolutely (they are typically made under "field conditions", where Earth s atmospheric transmission varies with time and with equipment having a wide range of wavelength sensitivities), it is more natural to make measurements by comparison of one source to another with the same equipment and close in time Relative brightnesses are much more accurately determinable than "absolute fluxes"

11 Relative photometry For example: the absolute flux of the Sun at visual wavelengths is still not established to better than a few percent! Comparison of magnitudes and fluxes derived for the Sun. From Bessell et al. (1998, A&A, 333, 231).

12 Relative photometry Remember the definition of magnitude: m 2 m 1 = 2.5 log 10 ( F 2 F 1 ) We are always comparing stars and on a relative scale When there is no consideration of the 0 point of magnitude system, only brightness ratios (magnitude differences) can be measured-- we call this relative photometry

13 Absolute photometry When we care about the magnitudes (and fluxes) of stars on a set, universal scale, this is absolute photometry Don't confuse this with "absolute magnitudes", which is different Setting up a universal magnitude system means defining for the equation m 2 m 1 = 2.5 log 10 ( f 2 ) f 1 a set flux value f 2 corresponding to m 2 Then we can evolve to a definition of magnitudes that looks like: m = 2.5 log 10 f + const This requires establishing a set of standard stars with agreed upon fluxes.

14 Standard stars One method is to pick one star in the sky as the universal reference. The traditional convention has been to choose the star Vega (α Lyrae) because: It is easily observable (in the northern hemisphere -- where most astronomy was being done when the system was set up). As a hot star, Vega has a relatively smooth SED fairly resembling a blackbody. Historically Vega was decided to define 0 mag in every bandpass. Then: 2.5 log 10 f f vega = 0 m m = 2.5 log 10 f f vega

15 Magnitudes and distances We can use relative magnitudes to estimate relative distances, if they have the same absolute magnitude: f 1 m 1 m 2 = 2.5 log 10 = 2.5 log f 10 ( d d ) 1 For example: m 1 m 2 = 5 log 10 d 2 d 1 = 5 log 10 ( d 1 d 2 ) d 2 d 1 = 10 m 1 m 2 = 5 log 10 = 5 m 1 m 2 = 5 So a star with 10x greater distance is 5 mags fainter (100x fainter in flux)

16 Photometric parallax You can use the color of a star to gauge its distance Identify "spectral type" of the star by its color, gauged by photometry in different filters, (which is like very coarse spectroscopy) Once we have the spectral type, and an assumed luminosity class of the star, in principle you know the absolute magnitude, and then can get the distance through the distance modulus This method of deriving a distance is called measuring a photometric parallax

17 Photometric parallax Obviously this is not as good as trigonometric parallaxes, due to the color ambiguities we ve discussed For example, red stars can be either very luminous red giants or very dim red dwarfs. Making a mistake in confusing the two can lead to distance errors off by factors of 100 or more There are many kinds of blue stars, from blue supergiants to white dwarfs. Errors in proper identification can lead to distance errors off by factors of 10,000 or more The hope is that such large errors in distance can be readily identified through other means (or by "sanity checking" that these erroneous results make sense)

18 Color-magnitude diagram Even if we don t know the distance, we can use the relative magnitudes of stars to study their properties CMD: plot of color versus magnitude Measure color using the color index Measure apparent magnitude This is most easily done in a group or cluster of stars, since they should all lie at the same distance We ll talk about open and globular clusters here

19 Axes of the color-magnitude diagram CMD: plot of color index versus apparent magnitude Or absolute magnitude if you know the distance, as shown here

20 Open clusters Young clusters of stars loosely bound by gravity Recent star formation (notice the many blue stars) High metallicity, not much stellar evolution Pleiades, a young, nearby open cluster The Jewel Box cluster

21 Relative ages Compare CMDs of multiple clusters to estimate their ages

22 Globular clusters Old, dense clusters No blue stars No recent star formation CMD for globular cluster M55

23 Relative ages Compare CMDs of multiple clusters to estimate their ages Open cluster Globular cluster

24 Open vs. Globular Clusters Open cluster: 1000 s of stars of a wide range of temperatures (young stellar population) Globular cluster: 100,000s of stars, only cool red stars present (old stellar population)

25 Stellar evolution CMD of the triple main sequence of the globular cluster NGC 2808, taken from Piotto et al. (2007). The stars are all proper-motion members of the cluster and a correction has been made for differential reddening along the line of sight. Inset: theoretical isochrones for an age of 12.5 Gyr, with different helium content ((m M) 0 =15, E(B V)=0.18). From Kalirai & Richer 2010

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