HR Diagram

Star classification

• In the early part of the 20th century, a classification scheme was devised for stars based on their spectra. The scheme was originally based only on the relative strengths of Hydrogen lines in the stars' atmosphere. Type A stars had the strongest hydrogen lines, type O the weakest. The different classes were then rearranged in order of decreasing surface temperature. Some letters were rejected (e.g., C, D, E) due to redundancy.
  • The original system based on the strength of hydrogen lines was flawed because two stars with the same line strength could actually be two very different stars, with very different temperatures, as can be seen in this diagram.
  • This video discusses the spectral classification of stars and offers some historical context.
• Today, stars are classified according to their surface temperature. Each temperature range is known as a spectral type or class. From hottest to coolest the order is: (hotter) O B A F G K M (cooler)
  • Our Sun has a surface temperature of about 6,000 degrees C and is therefore designated as a G star.
• Note there can be some confusion regarding the various letters. For example, the bluish star Sirius, the brightest star in the night sky, is actually a binary system, consisting of a bright Sirius A (the one we see) paired with a dim Sirius B (not visible without a powerful telescope). These letters (A and B) are not related to the spectral type and are simply used to distinguish the two stars. By coincidence, Sirius A happens to belong to spectral type A and Sirius B belongs to the spectral type B. Proxima Centauri is a three-star system (Proxima Centauri A, Proxima Centauri B, Proxima Centauri C) but these letters once again have nothing to do with their respective spectral types.
• Different star classes are characterized by the prominence of certain spectral lines
• There are several mnemonics to remember this sequence
  • Oh Be A Fine Girl/Guy Kiss Me (This is the most famous one)
  • Only Boys Accepting Feminism Get Kissed Meaningfully
  • Old Baboons Angrily Fling Green Kiwis and Mangos
  • Only Bumbling Astronomers Forget Generally Known Mnemonics
  • Only Bad Astronomers Feel Good Knowing Mnemonics

Class	Temperature	Apparent color	Mass (solar masses)	Radius (solar radii)	Luminosity (solar luminosity)	Approximate main-sequence life span (years)	Hydrogen lines	% of all Main Sequence Stars
O	30,000–60,000 K	blue	64	16	1,400,000	~10 million	Weak	~0.00003%
B	10,000–30,000 K	blue white	18	7	20,000	~100 million	Medium	0.13%
A	7,500–10,000 K	white	3.1	2	40	~1 billion	Strong	0.6%
F	6,000–7,500 K	white	1.7	1.4	6	~5 billion	Medium	3%
G	5,000–6,000 K	yellowish white	1.1	1.1	1.2	~10 billion	Weak	7.6%
K	3,500–5,000 K	yellow orange	0.8	0.9	0.4	~50 billion	Very weak	12.1%
M	2,000–3,500 K	orange red	0.4	0.5	0.04	~100 billion	Very weak	76.45%

Luminosity classes

• Each spectral type (OBAFGKM) is divided into 10 subclasses, designated with a number, 0-9. The spectral types and sub-classes represent a temperature sequence, from hotter (O stars) to cooler (M stars), and from hotter (subclass 0) to cooler (subclass 9). So, for example, G0 is hotter than G1.
• Because two stars with the same surface temperature can be very different (e.g., red supergiant vs red dwarf), an additional label, known as luminosity class, is added to unambiguously describe a star.
• Luminosity class is designated with a Roman numeral and describes a stars state of evolution. For example, a giant (class III) is more evolved than a main-sequence star (class V).
• Examples:
  • The full classification for our Sun is G2 V. The G2 spectral type means it is yellow-white in color and the luminosity class V means it a hydrogen-burning, main-sequence star.
  • Betelgeuse is an M2 or a red supergiant.
  • Proxima Centauri is an M5 V, similar in color and surface temperature to Betelgeuse, but less evolved and far dimmer because of its far smaller size.

Symbol	Class of Star	Example
I	Supergiants	Betelgeuse, Antares
II	Bright giants	Canopus
III	Giants	Aldebaran
IV	Subgiants	Procyon
V	Main sequence	Sun, Sirius A
wd or D	White dwarfs	Sirius B

Hertzsprung-Russel (HR) diagram

• When stars are plotted on a luminosity vs surface temperature diagram (HR diagram), several interesting patterns emerge:
  • Most stars fall on the Main Sequence.
  • On the Main Sequence, the more massive stars are bigger, hotter, more luminous, and die faster.
  • The life span of stars ranges from about 10 million years for the blue giants to about 100 billion years for the red dwarfs.
  • The most common type of star is the red dwarf (lower right); the least common type is the blue giant (upper left).
• This classification was originally proposed in 1912 by astronomers Ejnar Hurtzprung and Henry Norris Russell, hence the designation HR diagram.
• Luminosity of stars if often expressed in units of the Sun's luminosity (L = 3.9 x 1026 Joules/s).
• The HR diagram spans a rather large range in luminosity, from 10-4L on the low end to as much as 106L on the high end.
• This video might be helpful in reading an HR diagram and also goes over some variations.
• This interactive applet might help you visualize some of the properties of the HR diagram.

Star size

• Of the 12 brightest stars in our sky, most are giants and supergiants.
• Our Sun is a main-sequence star dwarfed by a supergiant like Betelgeuse.
• Star mass ranges from 0.08xMsun to 100xMsun:
  • Stars more massive than about 100xMsun release too much energy through nuclear fusion and are unstable.
  • Stars less massive than 0.08Msun are too small to sustain nuclear fusion. Very large objects below this limit are sometimes called brown dwarfs.

Stellar Lifetimes

• The lifetime of a star is directly proportional to the amount of fuel it has (i.e., mass) and inversely proportional by the rate at which it burns the fuel (i.e., luminosity). Putting these together, we can estimate the lifetime t to be proportional to M/L.
• Empirically, for stars on the main sequence, luminosity is roughly propotional to the cube of the mass (L ~ M^3). Consequently, plugging this in for L, we find that the lifetime is inversely proportional to a power of the mass (t~1/M^2.5).
• Since the most massive stars are about 100 times the mass of the Sun, their lifetimes must be about 1,000 times shorter, or about 10^6 (10^10/10^4)years. This is indeed what we see; the most masive stars burn out in about 4 million years.
• Similarly, the least massive stars are about one tenth of a solar mass. They survive about 100 times longer than our Sun, or about 10^12 years. Because this is well over ten times the present age of the universe, none of these smaller stars have died yet.

Clusters

• Many stars are found in one of two types of clusters: open and globular.
  • A famous star cluster visible to the naked eye is the Pleiades, also known as the Seven Sisters.
  • Our Solar System is not part of a star cluster.
• The HR diagram is generated through a careful study of star clusters. Clusters are important because:
  • All the stars in a cluster lie at about the same distance from Earth.
  • All the stars in a cluster formed at about the same time.
• The age of a cluster corresponds to the main sequence turnoff point.
  • Stars with life spans equal to this age are exiting the main sequence.
  • Smaller stars with life spans longer than this age are still on the main sequence.
  • Larger stars with life spans shorter than this age are off the main sequence (dead).
• Open clusters are or are characterized by:
  • Few stars (10-1000)
  • Relatively small (about 30 ly)
  • Always found in the galactic disk
  • Relatively young (less than 7 BY)
  • Enriched in the heavy elements
• Globular clusters are or are characterized by:
  • Lots of stars (104-106)
  • Relatively large (~50-150 ly)
  • Found mostly in halo
  • Relatively old (12-16 BY)
  • Virtually no heavy elements

Summary of stellar properties

Property	How it is determined
Brightness	directly measured
Color	-Compare brightness in two different E&M spectrum bands. -Examine spectra of star
Temperature	Use color or spectra
Distance	-Directly measured via parallax -Indirectly measured via method of standard candles
Luminosity	-use brightness and distance -Eclipsing Binary: Use Temperature and Size
Radial Velocity	Doppler shift of spectral lines
Transverse Velocity	proper motion and distance
Rate of Spin	Doppler broadening of Spectral Lines
Size	-Luminosity and Temperature -directly measure in an Eclipsing Binary
Mass	-Use Kepler's 3rd Law in Binary System. -Infer from Luminosity and Temperature. -Infer from spectral lines.
Chemical Composition	Spectral Lines
Strength of Magnetic Field	Spectral Lines
Age	Main-Sequence Turn-off Point in a cluster

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