The HR Diagram

By the end of this reading, you will be able to:

• Define

  apparent and absolute magnitude and apply the distance modulus to find distances or magnitudes

• Convert

  between magnitude differences and flux ratios using the Pogson relation

• Construct

  the observer’s HR diagram ($M_V$ vs. spectral type) and identify its features

• Derive

  lines of constant radius on the theorist’s HR diagram from Stefan-Boltzmann

• Identify

  the main sequence, giant branch, and white dwarf sequence and what places stars in each

• Explain

  why the main sequence is a mass sequence and connect it to the mass-luminosity relation

• Articulate

  the questions the HR diagram raises — and why physics (Module 3) is needed to answer them

When Ejnar Hertzsprung and Henry Norris Russell independently plotted stellar luminosity against temperature in the early 1900s, they expected scatter — a random spray of points. Instead, they found structure. Stars cluster into distinct regions: a long diagonal band (the main sequence), a clump of cool luminous stars (giants), and a scattering of hot dim stars (white dwarfs). This pattern was the first evidence that stars are organized by physics. Understanding that physics is the work of Module 3. This reading is about the pattern itself.

Part 1: The Magnitude System — The Astronomer’s Brightness Scale

The Problem: Stars Span a Ridiculous Range

Try the naive thing first: a linear brightness plot with Proxima, Betelgeuse, and the Sun on the same axis. Set Proxima near the bottom and scale upward by equal flux steps. Betelgeuse jumps to tens of millions of Proximas, and the Sun jumps tens of billions beyond that. Proxima and Betelgeuse collapse against zero while the Sun runs off-scale. On a linear axis, the plot is scientifically unusable.

We need a logarithmic ruler: the magnitude system — the last measurement tool before we can build the HR diagram.

Why Not Just Use Luminosity?

You already know how to measure a star’s luminosity in physical units: $L$ in $\text{erg}\,\text{s}^{-1}$, or in $L_\odot$. So why do astronomers still use magnitudes — logarithmic, inverted (brighter = smaller number), and historically odd? Three reasons:

1. Dynamic range. Stellar brightnesses span ten orders of magnitude ($10^{10}$). Logarithmic scales compress this into manageable numbers (roughly $-10$ to $+20$).
2. What detectors measure. Eyes, photographic plates, and CCDs respond to flux — energy per unit area per unit time — not luminosity. Magnitudes are tied directly to flux ratios.
3. Historical inertia. Hipparchus ranked stars from “first magnitude” (brightest) to “sixth magnitude” (faintest visible). Modern astronomy formalized this into a precise logarithmic system but kept brighter = smaller magnitude.

Apparent Magnitude: How Bright It Looks

The apparent magnitude $m$ measures how bright a star appears from Earth. It depends on intrinsic brightness and distance. The formal definition connects magnitude differences to flux ratios (the Pogson relation):

Here $F_1$ and $F_2$ are the fluxes and $m_1$, $m_2$ the apparent magnitudes. Because the scale is logarithmic, multiplicative flux changes become additive magnitude shifts.

Apparent magnitude

A logarithmic measure of how bright a star appears from Earth ($m$), set by both luminosity and distance. Smaller (more negative) means brighter; 5 magnitudes correspond to a factor of 100 in flux.

Key numbers to remember:

The anchor: 5 magnitudes = a factor of 100 in flux (by definition — Pogson’s ratio).

Multiple choice

If Star A is 5 magnitudes smaller (i.e. a smaller number) than Star B, is Star A’s flux smaller or larger than Star B’s, and by what factor?

Larger, by a factor of 100Smaller, by a factor of 100Larger, by a factor of 5Smaller, by a factor of 5

Worked Example 1Comparing Two Stars

Problem

Star A has apparent magnitude $m_A = 1.0$ and Star B has $m_B = 6.0$. How many times brighter is Star A than Star B?

Step·Magnitude difference, then flux ratio

$\Delta m = m_B - m_A = 6.0 - 1.0 = 5.0~\text{mag}$ $\frac{F_A}{F_B} = 10^{0.4 \times 5.0} = 10^{2.0} = 100$

Dimensional check

$\Delta m$ is dimensionless (a magnitude difference); $10^{0.4\Delta m}$ is a pure flux ratio ✓.

Result

Star A is $100\times$ brighter than Star B in apparent flux. Sanity check: Star A has the smaller magnitude ($m_A = 1.0$, smaller than $m_B = 6.0$), so it is indeed brighter ✓.

Absolute Magnitude: How Bright It Actually Is

Apparent magnitude mixes intrinsic luminosity with distance — a nearby dim star can look brighter than a distant luminous one. To compare stars fairly, remove the distance factor. The absolute magnitude $M$ is the apparent magnitude a star would have at a standard distance of $10~\text{pc}$ — a measure of its intrinsic brightness.

Absolute magnitude

The apparent magnitude a star would have if placed at the standard distance of $10~\text{pc}$ ($M$). It expresses intrinsic luminosity in the magnitude system, removing the distance dependence.

The Sun looks blindingly bright only because it’s close; at $10~\text{pc}$ it would be a modest $M = +4.83$. Betelgeuse looks unremarkable despite being intrinsically $10^5$ times more luminous because it’s far away.

The Distance Modulus: Connecting $m$, $M$, and $d$

The relationship between apparent magnitude, absolute magnitude, and distance is the distance modulus:

$m$ is apparent magnitude, $M$ absolute magnitude, $d$ the distance in parsecs; the quantity $(m - M)$ is the distance modulus. Where does it come from? It is the inverse-square law from Lecture 1 ($F = L/4\pi d^2$) rewritten in logarithmic language — the $d^2$ flux dependence becomes a $5\log_{10}(d)$ term. Same physics, different packaging.

Distance modulus

The difference $m - M = 5\log_{10}(d/10\,\text{pc})$ between apparent and absolute magnitude — a logarithmic readout of distance. Zero at $10~\text{pc}$; the inverse-square law in magnitude form.

Sanity checks: at $d = 10~\text{pc}$, $m - M = 5\log_{10}(1) = 0$, so $m = M$ ✓. At $d = 100~\text{pc}$, $m - M = 5\log_{10}(10) = 5$ — the star appears $5~\text{mag}$ (i.e. $100\times$) fainter ✓. At $d = 1{,}000~\text{pc}$, $m - M = 5\log_{10}(100) = 10$ — the star is $10^4\times$ fainter ✓.

Worked Example 2Finding Distance from Magnitudes

Problem

A Cepheid has apparent magnitude $m = 14.0$ and absolute magnitude $M = -4.0$. How far away is it?

Step·Distance modulus

$m - M = 14.0 - (-4.0) = 18.0~\text{mag}$

Step·Solve for distance

$18.0 = 5\log_{10}\!\left(\frac{d}{10\,\text{pc}}\right) \Rightarrow \log_{10}\!\left(\frac{d}{10\,\text{pc}}\right) = 3.6$ $\frac{d}{10\,\text{pc}} = 10^{3.6} \approx 3{,}981 \Rightarrow d \approx 4.0 \times 10^4~\text{pc} = 40~\text{kpc}$

Dimensional check

The log argument is the dimensionless ratio $d/10\,\text{pc}$; solving returns $d$ in parsecs ✓.

Result

A modulus of $18~\text{mag}$ gives ${\sim}40~\text{kpc}$, a plausible distance for a luminous Cepheid ✓.

Problem

1. A star has $m = 5.0$ and $M = 5.0$. How far away is it?
2. A star at $d = 1{,}000~\text{pc}$ has $m = 10.0$. What is its absolute magnitude?
3. The Sun has $M = +4.83$. What would its apparent magnitude be at $10~\text{pc}$? At $100~\text{pc}$?
4. Tricky: Two stars have the same $M$. Star A is $10\times$ farther than Star B. What is the difference in their apparent magnitudes?

Part 2: The Observer’s HR Diagram — Patterns from Data

A Radical Idea: Plot Everything

By the early 1900s, astronomers had measured apparent magnitudes and spectral types for thousands of stars, and parallaxes were giving absolute magnitudes. The obvious question: what happens if you plot absolute magnitude against spectral type? Ejnar Hertzsprung (1911) and Henry Norris Russell (1913) independently did exactly this. Every star has a different mass, age, and composition — so the natural expectation was noise, a random spray of dots. There was no theoretical reason in 1911 to expect anything else.

What they found instead was one of the most stunning patterns in science. The rice didn’t scatter — it fell along a narrow highway (a single diagonal band) with a few outlying clusters. This plot is the Hertzsprung-Russell diagram. Stars were not infinitely varied; something was organizing them. The pattern demanded an explanation — and that explanation would require an entirely new physics of stellar interiors.

Hertzsprung-Russell diagram

A plot of stellar luminosity (or absolute magnitude) against effective temperature (or spectral type) that organizes stars into the main sequence, giant branch, and white dwarf sequence. The single most important diagram in astrophysics — a classification chart, a mass map, and an evolution diagram at once.

Quick check

If spectral type primarily tracked composition rather than temperature, what would you expect the HR diagram to look like?

If the observer’s HR diagram still feels abstract, orient yourself with a more old-school map first. The classic version below labels familiar stars directly, so you can see the geography before translating it into the stripped-down data view.

Building the Diagram

The observer’s HR diagram (also a color-magnitude diagram, CMD) plots absolute magnitude $M_V$ on the vertical axis (brighter/more negative at the top) and spectral type O B A F G K M — equivalently color index $B - V$ — on the horizontal axis (hot blue stars left, cool red stars right, temperature decreasing rightward).

Color-magnitude diagram

The observer’s form of the HR diagram: absolute magnitude versus color index (or spectral type), built from photometry and distance alone — no physical theory required.

Crucially: neither axis requires theory. Spectral type is a direct classification from line patterns; absolute magnitude comes from apparent magnitude and parallax distance. This diagram is pure measurement — Observable → Model → Inference: we measure $m$ and spectral type, use the distance modulus to model $M$, then infer structure from how stars populate the diagram.

What the Diagram Shows

1. The Main Sequence — a narrow diagonal band from upper-left (hot, bright) to lower-right (cool, faint). About 90% of all stars fall on it, the Sun roughly in the middle. As you learned in Lecture 4, mass determines luminosity ($L \propto M^{3.5}$) and temperature for main-sequence stars, so the main sequence is a mass sequence — high-mass at upper left, low-mass at lower right.

Main sequence

The diagonal band on the HR diagram where hydrogen-core-burning stars spend ~90% of their lives, ordered by mass: high-mass stars are hot and luminous (upper left), low-mass stars cool and faint (lower right). It is the mass-luminosity relation made visible.

2. The Giant and Supergiant Region — a cluster in the upper-right: cool ($T \sim 3{,}000\text{–}5{,}000~\text{K}$) but very luminous ($100\text{–}10^4\,L_\odot$). These are red giants and supergiants. A main-sequence star at $3{,}500~\text{K}$ would be a dim M dwarf — so to be both cool and luminous, recall Stefan-Boltzmann ($L = 4\pi R^2\sigma T^4$): they must have enormous radii. A red giant is typically $10\text{–}100\,R_\odot$; a supergiant can exceed $1{,}000\,R_\odot$.

Red giant

An evolved star that has exhausted core hydrogen and expanded enormously (typically $10\text{–}100\,R_\odot$), becoming cool but very luminous — the upper-right region of the HR diagram.

Supergiant

The most luminous evolved stars, with radii reaching $100\text{–}1{,}000\,R_\odot$ (luminosity class I) — e.g. Betelgeuse. They occupy the very top of the HR diagram across a wide temperature range.

3. The White Dwarf Sequence — a scattering in the lower-left: hot ($T \sim 10^4\text{–}3 \times 10^4~\text{K}$) but very faint (${\sim}0.01\,L_\odot$). By the same logic — hot but faint means small — these are white dwarfs, Earth-sized ($R \sim 0.01\,R_\odot$): the remnant cores of dead stars.

White dwarf

The Earth-sized ($R \sim 0.01\,R_\odot$) remnant core of a low- or intermediate-mass star — hot but faint, in the lower-left of the HR diagram, cooling slowly with no ongoing fusion.

Luminosity Classes: Vertical Structure

Even at the same spectral type, stars differ enormously in luminosity. A K2 star could be a dwarf ($L \sim 0.4\,L_\odot$) or a giant ($L \sim 200\,L_\odot$) — same temperature, 500 times more luminous. Observers tell them apart through spectral line widths: higher surface gravity (compact dwarfs) raises atmospheric pressure and broadens lines; lower gravity (extended giants) gives narrower lines. This is the luminosity classification:

Luminosity class

The Roman-numeral part of a stellar classification (I supergiant, III giant, V dwarf, …), read from spectral line widths (surface gravity). It distinguishes stars of equal temperature but very different size and luminosity.

A complete classification includes both: the Sun is G2 V (G2 temperature ${\sim}5{,}800~\text{K}$, class V dwarf); Betelgeuse is M1 I (${\sim}3{,}600~\text{K}$, class I supergiant).

Quick check

1. Which corner of the observer’s HR diagram holds the hottest, most luminous stars? The coolest, faintest?
2. A star is spectral type K5, luminosity class III. Dwarf, giant, or supergiant? Hotter or cooler than the Sun?
3. Two stars are both G2. Star A is class V; Star B is class III. Which is more luminous, and why?
4. Why does spectral line width distinguish giants from dwarfs?

Part 3: The Theorist’s HR Diagram — Overlaying Physics

Same Patterns, Physical Axes

The observer’s diagram uses $M_V$ and spectral type. Theorists prefer physical quantities: luminosity $L$ (in $L_\odot$) and effective temperature $T_{\text{eff}}$ (in K), related through calibrations — $M_V \to L$ via the magnitude-luminosity relation, spectral type $\to T_{\text{eff}}$ (e.g. G2 → $5{,}800~\text{K}$). The conversion is:

$M - M_\odot = -2.5\log_{10}\!\left(\frac{L}{L_\odot}\right)$

(treating the $V$-band as a proxy for bolometric here). The theorist’s HR diagram plots $\log(L/L_\odot)$ against $\log T_{\text{eff}}$, temperature decreasing rightward. The remarkable fact: the same patterns appear on both versions — so they are real features of stellar physics, not artifacts of the measurement system.

Lines of Constant Radius

The theorist’s diagram lets you overlay theoretical relationships, the most important from the Stefan-Boltzmann law:

This connects $L$, $R$, and $T$. On the HR diagram $L$ and $T$ are the axes, so fixing $R$ defines a line: $L = 4\pi R^2\sigma T^4 \Rightarrow \log L = \text{const} + 4\log T$ (at fixed $R$).

These lines of constant radius are diagonals on the theorist’s HR diagram — each represents all combinations of $L$ and $T$ for a star of a given radius.

Numeric answer

At fixed radius, if a star’s temperature $T$ doubles, by what factor does its luminosity change?

Your answer

Reading the diagram with radius lines: main-sequence stars span ${\sim}0.1\,R_\odot$ (M dwarfs) to ${\sim}10\,R_\odot$ (O stars); giants sit on $R \sim 10\text{–}100\,R_\odot$ lines (luminous despite being cool); supergiants reach $R \sim 100\text{–}1{,}000\,R_\odot$; white dwarfs sit on $R \sim 0.01\,R_\odot$ lines (faint despite being hot).

Worked Example 3Radius from the HR Diagram

Problem

A red giant has $L = 400\,L_\odot$ and $T_{\text{eff}} = 4{,}000~\text{K}$. What is its radius compared to the Sun ($T_\odot = 5{,}800~\text{K}$)?

Step·Use the ratio form (no CGS constants)

$\frac{L}{L_\odot} = \left(\frac{R}{R_\odot}\right)^2\left(\frac{T}{T_\odot}\right)^4 \Rightarrow \left(\frac{R}{R_\odot}\right)^2 = \frac{L/L_\odot}{(T/T_\odot)^4} = \frac{400}{(4{,}000/5{,}800)^4}$

Step·Evaluate

$\frac{4{,}000}{5{,}800} = 0.690,\quad 0.690^4 = 0.226 \Rightarrow \left(\frac{R}{R_\odot}\right)^2 = \frac{400}{0.226} = 1{,}770 \Rightarrow \frac{R}{R_\odot} = 42$

Dimensional check

All quantities are solar ratios — units cancel; the answer is in solar radii ✓.

Result

The red giant has $R \approx 42\,R_\odot$ — typical for the red giant branch. Placed at the Sun’s center it would reach about halfway to Mercury ✓.

Problem

1. On the theorist’s HR diagram, which way do lines of constant radius slope?
2. A white dwarf has $T_{\text{eff}} = 2 \times 10^4~\text{K}$ and $L = 0.01\,L_\odot$. Estimate its radius in $R_\odot$.
3. Where would a star with $R = R_\odot$ and $T = 2 \times 10^4~\text{K}$ appear? Is such a star observed?

Part 2 built a map from measurements alone; Part 3 added radius. But neither tells us what orders stars along the main sequence. To explain that, we need the hidden parameter that sets both luminosity and temperature: mass.

Part 4: Mass — The Hidden Organizer

The Main Sequence Is a Mass Sequence

Here is the payoff from Lecture 4. Label main-sequence stars by their mass (from binary measurements) and a beautiful pattern appears: mass increases monotonically from lower-right to upper-left.

Read this as a syllogism. Premise 1: along the main sequence, luminosity and temperature change monotonically from lower-right to upper-left. Premise 2: for hydrogen-burning stars, both luminosity and temperature scale systematically with mass (Lecture 4). Conclusion: ordering main-sequence stars by luminosity/temperature is ordering them by mass — the sequence is a one-parameter family whose hidden coordinate is mass.

The main sequence is the locus of hydrogen-burning stars ordered by mass. The mass-luminosity relation ($L \propto M^{3.5}$) explains the ordering: mass sets core temperature, which sets the burning rate, which sets luminosity and surface temperature. But note what’s remarkable: mass appears on neither axis — yet it organizes the entire structure. The HR diagram is a projection of a higher-dimensional stellar-structure space onto two observable axes; mass is the hidden coordinate that orders the projection.

Spectroscopic parallax

A distance method (despite the name, unrelated to parallax): a main-sequence star’s spectral type fixes its absolute magnitude, and the distance modulus then yields the distance from the apparent magnitude.

What About Giants and White Dwarfs?

Giants and supergiants have left the main sequence — they exhausted core hydrogen and expanded; their HR position depends on mass, age, and evolutionary state. White dwarfs are remnants — no longer burning, simply cooling; their position depends on mass and cooling age. In short: the main sequence is where stars live; giants are where they go when they age; white dwarfs are where they end up when they die.

Part 5: An Evolution Diagram — Why Patterns Need Physics

Stars Move on the HR Diagram

The most profound reading of the HR diagram is not as a static chart but as a map of stellar evolution. A star does not stay put — it moves, slowly on the main sequence, then dramatically as it evolves. That motion is the response of a self-gravitating thermodynamic system to changing fuel: when core hydrogen is exhausted, the same fusion source can no longer support hydrostatic equilibrium, so the core contracts, releasing gravitational energy that heats deeper layers; the envelope expands, lowering surface temperature even as total luminosity rises. HR-diagram tracks are the visible footprint of gravity, thermodynamics, and nuclear burning acting together.

Axis convention reminder: luminosity up; temperature decreases to the right (hot left, cool right). This schematic is a map-reading aid, not a precision plot — follow each arrow as a phase transition.

The life story of a Sun-like star, traced on the diagram:

1. Birth: forms from a collapsing cloud and contracts toward the main sequence — starts cool and luminous (upper right), moving down and to the left.
2. Main sequence (${\sim}10~\text{Gyr}$): settles into hydrogen-burning equilibrium as a G2 V star, staying put for ${\sim}10$ billion years. This is why most stars are on the main sequence — that’s where they spend most of their lives.
3. Red giant phase: core hydrogen exhausted, core contracts, envelope expands — cooler but much more luminous, moving to the upper right.
4. Death: sheds its outer layers (planetary nebula); the core is left as a white dwarf — hot but tiny, in the lower left, then slowly cooling and fading down-and-right over billions of years.

Core contraction heats the interior (gravitational energy → thermal energy); envelope expansion lowers surface temperature even as luminosity rises. Motion on the diagram is the surface trace of that interior redistribution. A massive star ($10\,M_\odot$) follows a similar but faster, more dramatic path — only ${\sim}20~\text{Myr}$ on the main sequence, then supergiant, then likely a core-collapse supernova. Increasing mass changes the entire route through the upper diagram, not just the final remnant.

The key insight: mass determines the path — and the timescale. A low-mass star evolves slowly along one track; a high-mass star races along a different, more dramatic one. The HR diagram is a map of where stars go as they age, with mass as the control parameter.

What the HR Diagram Does Not Encode

The HR diagram is a projection: two coordinates ($L$ and $T$) cannot uniquely encode the full stellar state. Hidden coordinates include metallicity, rotation, magnetic fields, and binarity; age is also not uniquely encoded once stars leave the main sequence. Different combinations can place stars in similar regions while implying different structures and futures. Read it as a structured projection of higher-dimensional stellar physics — excellent for pattern recognition, but not a complete state description.

What the HR Diagram Cannot Explain

The diagram reveals patterns but does not, by itself, explain them. The questions it raises:

1. Why does the main sequence exist at all? What creates a stable equilibrium where a star radiates at constant luminosity for billions of years?
2. Why does mass determine position on the main sequence? What connects core mass to surface temperature and luminosity?
3. Why do stars become giants? What changes internally when hydrogen is exhausted, and why expand rather than simply turn off?
4. Why is there a maximum mass for white dwarfs? (There is — ${\sim}1.4\,M_\odot$, the Chandrasekhar limit.) What happens to more massive cores?
5. Why is there a minimum mass for stars? (Below ${\sim}0.08\,M_\odot$, objects never ignite hydrogen — brown dwarfs.) What sets this threshold?

None of these can be answered by measurement alone. They require models — physical theories of stellar interiors, nuclear fusion, and the balance between gravity and pressure. That is the subject of Module 3: Stellar Structure and Evolution.

Reference Tables

The Magnitude Scale: Key Values

Main-Sequence Properties by Spectral Type

Order-of-magnitude only; values depend on metallicity, rotation, and mass loss.

Summary: Finding Patterns, Needing Models

1. The magnitude system is a logarithmic brightness scale where 5 magnitudes = a factor of 100 in flux. Absolute magnitude removes distance, placing all stars at a standard $10~\text{pc}$.
2. The distance modulus ($m - M = 5\log_{10}(d/10\,\text{pc})$) connects observed brightness, intrinsic brightness, and distance — the inverse-square law in logarithmic form.
3. The observer’s HR diagram ($M_V$ vs. spectral type) is pure measurement, revealing the main sequence, giant branch, and white dwarf sequence.
4. The theorist’s HR diagram ($\log L$ vs. $\log T_{\text{eff}}$) overlays lines of constant radius from Stefan-Boltzmann — giants are enormous, white dwarfs tiny.
5. The main sequence is a mass sequence — ${\sim}0.08\,M_\odot$ (lower right) to ${\sim}150\,M_\odot$ (upper left). The mass-luminosity relation made visible.
6. The HR diagram is an evolution diagram. Stars move as they age; mass determines the path. The main sequence is where stars live; the giant branch where they age; the white dwarf sequence where they end up.
7. Patterns demand physics. Why does the main sequence exist? Why do stars become giants? What sets the maximum white dwarf mass? Module 3 answers these.

Observable → Model → Inference: The HR Diagram Chain

Retrieval — equation: distance-modulus▸

Glossary

Absolute magnitude

The apparent magnitude a star would have if placed at the standard distance of $10~\text{pc}$ ($M$). It expresses intrinsic luminosity in the magnitude system, removing the distance dependence.

Apparent magnitude

A logarithmic measure of how bright a star appears from Earth ($m$), set by both luminosity and distance. Smaller (more negative) means brighter; 5 magnitudes correspond to a factor of 100 in flux.

Color-magnitude diagram

The observer’s form of the HR diagram: absolute magnitude versus color index (or spectral type), built from photometry and distance alone — no physical theory required.

Distance modulus

The difference $m - M = 5\log_{10}(d/10\,\text{pc})$ between apparent and absolute magnitude — a logarithmic readout of distance. Zero at $10~\text{pc}$; the inverse-square law in magnitude form.

Hertzsprung-Russell diagram

A plot of stellar luminosity (or absolute magnitude) against effective temperature (or spectral type) that organizes stars into the main sequence, giant branch, and white dwarf sequence. The single most important diagram in astrophysics — a classification chart, a mass map, and an evolution diagram at once.

Luminosity class

The Roman-numeral part of a stellar classification (I supergiant, III giant, V dwarf, …), read from spectral line widths (surface gravity). It distinguishes stars of equal temperature but very different size and luminosity.

Main sequence

The diagonal band on the HR diagram where hydrogen-core-burning stars spend ~90% of their lives, ordered by mass: high-mass stars are hot and luminous (upper left), low-mass stars cool and faint (lower right). It is the mass-luminosity relation made visible.

Red giant

An evolved star that has exhausted core hydrogen and expanded enormously (typically $10\text{–}100\,R_\odot$), becoming cool but very luminous — the upper-right region of the HR diagram.

Spectroscopic parallax

A distance method (despite the name, unrelated to parallax): a main-sequence star’s spectral type fixes its absolute magnitude, and the distance modulus then yields the distance from the apparent magnitude.

Supergiant

The most luminous evolved stars, with radii reaching $100\text{–}1{,}000\,R_\odot$ (luminosity class I) — e.g. Betelgeuse. They occupy the very top of the HR diagram across a wide temperature range.

White dwarf

The Earth-sized ($R \sim 0.01\,R_\odot$) remnant core of a low- or intermediate-mass star — hot but faint, in the lower-left of the HR diagram, cooling slowly with no ongoing fusion.