Galaxies, Redshift and the Expanding Universe
Calibrated standard candles give distances, and small redshifts estimate recession speeds. The velocity-distance slope gives the present expansion rate H0. Its inverse is an age scale; cosmic age also depends on expansion history. Uniform expansion has no preferred centre.
What a learner can do afterwards
- Calculates a standard-candle distance from luminosity and flux, and estimates recession speed from a small redshift
- Calculates the Hubble time 1/H0 and explains why it need not equal the universe's age
- Explains why a homogeneous uniform-expansion model gives comoving observers the same large-scale relation without a preferred centre
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A standard candle has a calibrated luminosity L, its emitted power. Flux F is received power per unit area. For a nearby source emitting equally in all directions, with dust dimming corrected, F = L/(4 pi d^2), so d = sqrt(L/(4 pi F)). At fixed luminosity, doubling distance reduces flux to one quarter. Faintness alone cannot distinguish distance from low luminosity.
For Cepheids of the same calibrated class and observing band, a longer pulsation period means greater mean luminosity. Measure the period, apply the calibrated relation, then compare luminosity with flux. Independent nearby distances set the calibration. Type Ia supernovae extend the ladder after brightness corrections. These white-dwarf explosions differ from the core-collapse supernovae discussed previously.
Redshift is z = (observed wavelength - rest wavelength)/rest wavelength. Expansion stretches light during its journey. For small z, v is approximately cz, where c is light's speed. This estimates recession speed when local motion is negligible. Large cosmological redshifts require an expansion model for interpretation. Nearby galaxies have local motions and can approach us.
For low-redshift galaxies whose local motions are small, v = H0 d. Plot speed v vertically and distance d horizontally: the slope is H0, today's fractional expansion rate. Thus d/v = 1/H0, the Hubble time. A megaparsec (Mpc) is 3.09 x 10^19 km. For H0 in km/s/Mpc, divide that kilometre value by H0 to get seconds. Divide seconds by 3.15 x 10^16 to get billion years. Use many galaxies to reduce local-motion effects.
Extrapolating today's distance and recession speed back to zero separation at constant speed gives the Hubble time. Expansion has changed over time, so cosmic age requires a model of that history. A reliably dated star gives another constraint: the universe must be at least as old as the star. This lower bound does not determine H0 or the exact cosmic age.
In a homogeneous model with uniform expansion, large-scale separations grow by the same factor. Comoving observers follow this expansion; each finds the same distance-speed relation at a given cosmic time. The model selects no expansion centre. Our recession pattern alone does not prove the model. Rising dough illustrates separation, but its edge and centre are not features of this cosmological model. Gravity-bound galaxies need not expand.
Calibrated candles give distance. Small redshifts estimate speed. H0 gives a Hubble time; cosmic age needs expansion history. Uniform expansion has no preferred centre.
Lesson, questions and flashcards written for this dataset. Supplied OpenStax Astronomy records were consulted for scientific facts and teaching structure.
Readings and flashcards written for this dataset, with OpenStax Astronomy consulted for facts. Our Expanding Universe is credited to the American Museum of Natural History (AMNH). AMNH's rights notice states its ownership, permits personal educational use, and restricts commercial use, reproduction, distribution, derivative works and public display. Cepheid variables 1 is credited to Khan Academy; its reuse terms remain unverified.
More to read
What a redshift tells us
A spectral line has a rest wavelength measured in a laboratory. Redshift compares the observed wavelength with that reference: subtract the rest wavelength, then divide by it. The result z has no units because both wavelengths use the same unit.
When z is small, multiplying it by light's speed gives an approximate recession speed if local motion is negligible. This is a limited approximation. For a large cosmological redshift, an expansion model is needed to connect the observation with distance or recession speed.
In a homogeneous model with uniform expansion, observers following the expansion find the same large-scale distance-speed relation at the same cosmic time. The model selects no expansion centre. Individual galaxies can depart from the relation because of local motions, and nearby galaxies can approach us. A statement about large-scale expansion does not require every neighbouring galaxy to recede.
From a calibrated candle to a distance
Suppose a source looks faint. Its flux does not tell you whether it is distant, emits little light, or lies behind dust. A standard-candle method supplies a luminosity estimate from calibration, while observations supply flux. Dust dimming must also be accounted for.
For a nearby source that emits equally in all directions, the corrected flux obeys F = L/(4 pi d^2). Solving for d gives the positive square root of L/(4 pi F). A distance therefore depends on both measured flux and the luminosity calibration.
Cepheids connect pulsation periods with mean luminosities. Independent nearby distance measurements set that relation's scale. Cepheids in suitable host galaxies can then help calibrate type Ia supernovae. Type Ia distances use brightness corrections; their uncorrected peak luminosities are not identical.
Errors in a shared calibration can shift later distances together. Agreement should be tested with independent methods rather than assumed. At large cosmological redshift, the flux relation defines luminosity distance, which can differ from present physical separation.
Measuring a Cepheid cycle
A Cepheid's period is the time for its brightness pattern to repeat. The interval from a bright phase to a faint phase is only part of a cycle. Distance work uses mean brightness across the cycle rather than treating one bright observation as the star's usual output.
Henrietta Leavitt studied Cepheids at approximately the same distance. This allowed brightness differences to reveal a relation between period and luminosity. Finding the relation did not by itself establish an absolute luminosity scale. That required independent distance measurements for calibration.
Apply the relation for the appropriate Cepheid class and observing band. Within that calibrated relation, longer periods indicate greater mean luminosities. The inferred luminosity and measured flux then give a distance estimate after dust corrections. The method still has uncertainty from measurement, calibration and differences among stars.
Reading distant quasar light
A quasar is a luminous galactic nucleus powered by gas accreting onto a supermassive black hole. The radiation comes from matter outside the event horizon. It does not escape from inside the black hole. The nucleus can outshine much of its host galaxy.
Quasars are not limited to young galaxies. A remote quasar shows us its nucleus at the time its light was emitted. Interpreting its cosmological redshift with an expansion model connects the observation to distance and lookback time. The small-redshift speed approximation is not suitable for every quasar.
Absorption lines can reveal gas between a quasar and the observer. A spectrum does not necessarily detect every intervening cloud. Surveys also miss objects outside their detection limits. Quasar counts therefore need careful interpretation before they can be used to study how galactic activity changed over time.
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