To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure no-reply@cambridge.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
We start with some of the historical work on measuring distances to galaxies, leading to the Hubble (or Hubble-Lemaitre) law, a linear proportionality between recession velocity and and a galaxy’s distance, with a proportionality constant known as the Hubble constant. For more distant galaxies, it becomes increasingly difficult to detect and resolve even giant stars like Cepheid variables as individual objects, limiting their utility in testing the Hubble law to larger distances and redshifts. For much larger distances, an important alternative method is the Tully–Fisher relation.
To test which of these models applies to our universe, one needs to extend redshift measurements to large distances, out to several Giga-light years. The most successful approach has been to use white dwarf supernovae (SN type Ia) as very luminous standard candles. One of the greatest surprises of modern astronomy is that the expansion of the universe must be accelerating! This implies there must be a positive, repulsive force that pushes galaxies apart, in opposition to gravity. We dub this force "dark energy."
Earth’s moon is quite distinct from other moons in the solar system, in being a comparable size to Earth. We explore the theory that a giant impact in the chaotic early solar system led to the Moon’s formation, and bombardment by ice-laden asteroids provided the abundant water we find on our planet. Further we find that Earth’s magnetic field shields us from solar wind protons, that protect our atmosphere from being stripped away. The icy moons of Jupiter and Saturn are the best targets for exploring if life exists elsewhere in the solar system.
The close proximity of the Sun, and its extreme apparent brightness, makes it by far the most important star for lives here on Earth. In modern times we have access to powerful telescopes, both on the ground and in space, that observe and monitor the Sun over a wide range of wavelength bands. These vividly demonstrate that the Sun is in fact highly structured and variable over a wide range of spatial and temporal scales.
As a basis for interpreting observations of binary systems in terms of the orbital velocity of the component stars, we review the astrometric and spectrometric techniques used to measure the motion of stars through space. Nearby stars generally exhibit some systematic motion relative to the Sun, generally with components both transverse (i.e., perpendicular) to and along (parallel to) the observed line of sight.
Our initial introduction of surface brightness characterized it as a flux confined within an observed solid angle. But actually the surface brightness is directly related to a more general and fundamental quantity known as the "specific intensity." The light we see from a star is the result of competition between thermal emission and absorption by material within the star.
We now consider why stars shine with such extreme brightness. Over the long-term (i.e., millions of years), the enormous energy emitted comes from the energy generated (by nuclear fusion) in the stellar core, as discussed further in Chapter 18. But the more immediate reason stars shine is more direct, namely because their surfaces are so very hot. We explore the key physical laws governing such thermal radiation and how it depends on temperature.
As a star ages, more and more of the hydrogen in its core becomes consumed by fusion into helium. Once this core hydrogen is used up, how does the star react and adjust? Stars at this post-main-sequence stage of life actually start to expand, eventually becoming much brighter giant or supergiant stars, shining with a luminosity that can be thousands or even tens of thousands that of their core-H-burning main sequence. We discuss how such stars reach their stellar end points as planetary nebulae or white dwarfs.
To understand ways we might infer stellar distances, we first consider how we intuitively estimate distance in our everyday world, through apparent angular size, and/or using our stereoscopic vision. We explain a practical, quite direct way to infer distances to relatively nearby stars, namely through the method of trigonometric parallax. This leads to the definition of the astronomical unit and parsec, and the concept of solid angles on the sky, measured in steradians or square degrees.
What are the key physical properties we can aspire to know about a star? In this chapter we consider the properties of stars, identifying first what we can directly observe about a given star: position on the sky, apparent brightness, color/spectrum. When these observations are combined with a clear understanding of some basic physical principles, we can infer many of the key physical properties of stars. We also make a brief aside to discuss ways to get our heads around the enormous distances and timescales we encounter in astrophysics.
It is thought that isolated neutron stars receive a natal kick velocity at birth nearly aligned with their spin axis. Direct observational confirmation of this alignment is currently limited to a single source in a supernova remnant (PSR J0538+2817), for which the three-dimensional velocity has been well constrained. Meanwhile, pulsar polarisation statistics suggest the existence of a spin-kick correlation, though both aligned and orthogonal cases remain possible. However, if the velocities of radiopulsars are predominantly aligned with their spin axes, a systematic difference in the observed transverse velocities of pulsars with small and large magnetic obliquities would be expected. In particular, due to projection effects, weakly oblique rotators should exhibit smaller, less scattered transverse velocities. Conversely, the transverse velocities of pulsars with large magnetic inclination should reflect their actual three-dimensional velocities. This study uses this idea to analyse samples of 13 weakly and 25 strongly oblique pulsars with known distances and proper motions. We find that their peculiar velocities are distributed differently, with statistical confidence levels of 0.007 and 0.016 according to the Anderson–Darling and Kolmogorov–Smirnov tests, respectively. We performed a detailed population synthesis of isolated pulsars, considering the evolution of their viewing geometry in isotropic and spin-aligned kick scenarios. The observed split in the transverse velocity distributions and its amplitude are consistent with the spin-aligned kick model, but not with the isotropic case. At the same time, an orthogonal kick would predict a similar effect, but with the opposite sign. This provides robust support for pulsar spin kick alignment based on statistics, independently of polarisation.
Measurements of the ionisation state of the intergalactic medium (IGM) can probe the sources of the extragalactic ionising background. We provide new measurements of the ionising emissivity of galaxies using measurements of the ionising background and ionising photon mean free path from high-redshift quasar spectra at $2.5 \lt z \lt 6$. Unlike most prior works, we account for radiative-transfer effects and possible neutral islands from the tail of reionisation at $z \gt 5$. We combine our results with measurements of the UV luminosity function to constrain the average escaping ionising efficiency of galaxies, $\langle f_{\textrm{esc}} \xi_{\textrm{ion}}\rangle_{L_{\textrm{UV}}}$. Assuming galaxies with $M_{\textrm{UV}} \lt -11$ emit ionising photons, we find $\log (\langle f_{\textrm{esc}} \xi_{\textrm{ion}}\rangle_{L_{\textrm{UV}}}/{\textrm {erg}^{-1}Hz}) = 24.47_{-0.17}^{+0.09}$ and $24.75_{-0.28}^{+0.15}$ at $z=5$ and 6, and $1\sigma$ upper limits of $24.48$ and $24.31$ at $z = 2.5$ and 4, respectively. We also estimate the population-averaged $f_{\textrm{esc}}$ using measurements of intrinsic ionising efficiency from JWST. We find $\langle f_{\textrm{esc}} \rangle = 0.126_{-0.041}^{+0.034}$ and $0.224_{-0.108}^{+0.098}$ at $z=5$ and 6, and $1\sigma$ upper limits of $f_{\textrm{esc}}\lt 0.138$ and $0.096$ at $z=2.5$ and 4, respectively, for $M_{\textrm{UV}} \lt -11$. Our findings are consistent with prior measurements of $f_{\textrm{esc}} \lesssim 10\%$ at $z \leq 4$, but indicate a factor of several increase between $z = 4$ and 6. The steepness of this evolution is sensitive to the highly uncertain mean free path and ionising background intensity at $z\gt5$. Lastly, we find $1.10^{+0.21}_{-0.39}$ photons per H atom are emitted into the IGM between $z=6$ and $=5.3$. This is $\approx 4\times$ more than needed to complete the last 20% of reionisation absent recombinations, suggesting that reionisation’s end was likely absorption-dominated.
Spectroscopic observations are essential for confirming associations, measuring kinematics, and determining stellar populations in dwarf galaxies. Here, we present Keck Cosmic Web Imager spectra for 12 MATLAS survey dwarfs. For 9, we confirm recession velocities consistent with their literature-assumed host galaxies. We propose revisions of the host galaxy associations for MATLAS-631, 1494, and 1938. For MATLAS-1494, our measured redshift reclassifies it from an ultra-diffuse galaxy candidate to a dwarf galaxy that is of smaller physical size and places it in the field. It also appears old and passive, providing a challenge to models that invoke quenching by tidal effects. Additionally, we measure stellar population estimates for 7 of the 12 galaxies, finding a ‘mixed bag’ of old quenched galaxies and those that are currently forming stars. Compared to the literature we find generally younger ages and higher metallicities. This result may help reconcile the observed offset of MATLAS survey dwarf galaxies from the universal stellar mass–metallicity relationship reported by Heesters et al. (2023).