Common Units and Numerical Values

These tables collect the units and orders of magnitude most often needed when writing, making estimates and refereeing. For specific formulas, return to where they are first defined in the main text; when estimating, check the units, order of magnitude and conditions of validity together.

Fundamental Constants and Astronomical Conversions

Quantity	Common value	Reminder when using
Speed of light	\(c=2.998\times10^{10}\,{\rm cm\,s^{-1}}\)	Baseline light travel time \(B/c\): \(1\,{\rm km}\) is about \(3.3\,\mu{\rm s}\), \(1000\,{\rm km}\) about \(3.3\,{\rm ms}\).
Planck constant	\(h=6.626\times10^{-27}\,{\rm erg\,s}\)	Single-photon energy \(E=h\nu=hc/\lambda\).
Boltzmann constant	\(k_{\rm B}=1.381\times10^{-16}\,{\rm erg\,K^{-1}}\)	Brightness temperature, Planck occupation number and thermal noise all need it.
Jansky	\(1\,{\rm Jy}=10^{-23}\,{\rm erg\,s^{-1}\,cm^{-2}\,Hz^{-1}}\)	AB magnitude and photon-rate estimates often start from Jy.
Parsec	\(1\,{\rm pc}=3.086\times10^{18}\,{\rm cm}\)	\(1\,{\rm AU}\) subtends \(1''\) at \(1\,{\rm pc}\).
Solar radius	\(R_\odot=6.96\times10^{10}\,{\rm cm}\)	Very often used when estimating stellar angular diameters and binary-star scales.
Solar luminosity	\(L_\odot=3.83\times10^{33}\,{\rm erg\,s^{-1}}\)	Used together with \(F_{\rm bol}\), \(T_{\rm eff}\) and \(\theta\).

Angles, Wavelengths and Baselines

Quantity	Common value	Related location in the text
Angular conversions	\(1\,{\rm rad}=206265''\); \(1\,{\rm mas}=4.848\times10^{-9}\,{\rm rad}\); \(1\,\mu{\rm as}=4.848\times10^{-12}\,{\rm rad}\)	Chapter A Guided Tour: What Does a Telescope Actually Record, and Where Is This Book Taking You?, Chapter Spatial Coherence, van Cittert–Zernike, and Intensity Interferometry.
Optical wavelengths	Blue-light intensity interferometry is often at \(400\)–\(450\,{\rm nm}\); broadband imaging often uses \(500\)–\(800\,{\rm nm}\)	Chapter Spatial Coherence, van Cittert–Zernike, and Intensity Interferometry, Chapter Observation Design, Error Budget, and Feasibility.
Diffraction scale	\(\lambda/B\) is about \(1\,{\rm mas}\) at \(500\,{\rm nm}\) and \(100\,{\rm m}\)	Hundred-meter-scale arrays are suited to the angular diameters of bright stars.
First-null scale	The first null of a \(1\,{\rm mas}\) uniform disk near \(416\,{\rm nm}\) is at about \(100\,{\rm m}\)	Chapter Spatial Coherence, van Cittert–Zernike, and Intensity Interferometry.
\(\mu{\rm as}\) structure	\(10\,\mu{\rm as}\) at \(500\,{\rm nm}\) corresponds to \(\lambda/\theta\sim10\,{\rm km}\)	Nearby supernovae, small-scale AGN structure and far-future long-baseline cases.
Projected baseline	\(B_\perp\) varies with target altitude, hour angle and array geometry	A fixed physical baseline cannot substitute for a full night of \(u,v\) coverage.

Time, Frequency and Coherence

Quantity	Common value	Related location in the text
Frequency conversion	\(500\,{\rm nm}\) corresponds to \(6.0\times10^{14}\,{\rm Hz}\)	Optical bandwidth often needs conversion between \(\Delta\lambda\) and \(\Delta\nu\).
Optical coherence time	A filter of order \(10\,{\rm nm}\) in the visible typically gives \(10^{-14}\)–\(10^{-13}\,{\rm s}\)	Chapter The Coherence Functions g^{(1)}, g^{(2)} and the Siegert Relation.
Correlation bin	Tabletop experiments can reach ps–ns; astronomical intensity interferometry is often limited by electronic response and data rate	Chapter Correlators and Event-Table Data Analysis, Chapter Teaching Experiments and Computational Experiments.
Detector jitter	Excellent SPAD, PMT and TDC systems can reach tens of ps–ns; system synchronization must be calibrated separately	Chapter Detectors, Clocks, and Event Tables.
Dead time	SPADs are often at ns–\(\mu{\rm s}\); PMTs and electronic chains also have recovery times	Dead time creates negative correlation at short delays.
Afterpulsing	Probability can reach the \(10^{-4}\)–\(10^{-2}\) level	Creates positive correlation at the detector’s characteristic delay.
Integration-time scaling	Purely statistical errors usually fall as \(T^{-1/2}\)	Once the systematic-error floor is reached, continued integration does not improve things automatically.

Photon Rates, Magnitudes and Background

Quantity	Common value	Related location in the text
AB-magnitude flux	AB zero point in Chapter Observation Design, Error Budget, and Feasibility; photon-rate estimate in Chapter A Guided Tour: What Does a Telescope Actually Record, and Where Is This Book Taking You?	When writing a proposal, give the bandwidth, efficiency, area and background at the same time.
Change in magnitude	For a target \(1\,{\rm mag}\) fainter, the photon rate drops to about \(10^{-0.4}\simeq0.40\) of the original	Chapter Observation Design, Error Budget, and Feasibility, Chapter From White Paper to Research Plan.
Telescope area	A \(D=12\,{\rm m}\) ideal geometric area is about \(113\,{\rm m^2}\); the actual effective area must be multiplied by efficiency and obscuration	Cherenkov-telescope optical efficiency, filters and detector QE all enter.
Background dilution	When the target flux fraction is \(f\), the second-order correlation excess is suppressed roughly as \(f^2\)	Chapter Detectors, Clocks, and Event Tables.
Narrow-line observation	The narrower the line, the longer the coherence time, but the total photon number and filter leakage may worsen	Be-star disks, maser/laser and BLR cases all need to report line/continuum separation.
Night-sky brightness	Varies with lunar phase, zenith distance, filter and field-lens size	Do not treat a dark-field background as applicable at every target position.

Instrumentation and Data Volume

Quantity	Common value	Related location in the text
Single-channel sampling data rate	At \(\Delta t=4\,{\rm ns}\), \(16\) bit and a single channel, about \(4\,{\rm Gb\,s^{-1}}\)	Chapter Detectors, Clocks, and Event Tables.
Multichannel inflation	64 spectral channels push the same example to about \(256\,{\rm Gb\,s^{-1}}\) per telescope	Requires real-time correlation, compression or on-chip accumulation.
Number of baselines	4 telescopes give 6 baselines; 60 give 1770 baselines	Chapter Spatial Coherence, van Cittert–Zernike, and Intensity Interferometry.
Calibrator star	Should be as close as possible to the target in sky position, color and brightness, and have a known angular diameter	Chapter Observation Design, Error Budget, and Feasibility.
Quality slicing	Slice by sky transparency, target altitude, background rate, dead time and channel status	Reporting only wall-clock time is not enough to reproduce the experiment.
Systematic floor	A correlation-amplitude floor at the \(10^{-5}\)–\(10^{-4}\) level is already enough to dominate many SII targets	Chapter Common Misconceptions.

Astrophysical Orders of Magnitude

Quantity	Common value	Related location in the text
Bright-star angular diameter	Nearby bright stars are often of order \(0.2\)–\(5\,{\rm mas}\)	Chapter Stars as Quantum Light Sources, Chapter First-Generation Quantum-Astronomy Science Cases.
Early Type Ia velocity	Photospheric velocities are often \(8000\)–\(15000\,{\rm km\,s^{-1}}\)	Chapter Bursts, Transients, and Multi-Messenger Quantum Astronomy, Chapter Teaching Experiments and Computational Experiments.
Nearby-supernova angular radius	At \(20\,{\rm Mpc}\), \(v=10^4\,{\rm km\,s^{-1}}\), day 15 is about a few \(\mu{\rm as}\)	Only km- to ten-km-scale baselines carry appreciable information.
Crab period	About \(33\,{\rm ms}\)	Phase-resolved photon statistics require preserving absolute time.
AGN broad-line region	Light-curve lags are often days to months, and the angular scale is usually extremely small	Requires combining reverberation, angular displacement and model priors.
CMB temperature	\(2.725\,{\rm K}\)	Chapter Quantum Problems in Cosmology; optical photon statistics cannot be applied directly.