Astronomy and cosmology

Production and Use of X-rays

Production of X-rays

X-rays are produced when high‑energy electrons interact with matter. Two main mechanisms dominate:

• Bremsstrahlung (braking radiation): Electrons are decelerated in the Coulomb field of nuclei, emitting a continuous spectrum.
• Characteristic X-rays: Electrons are ejected from inner shells of atoms; an electron from a higher shell fills the vacancy, emitting a photon with energy equal to the difference between the two levels.

The energy of a characteristic line is given by the Bohr model:

$$E_{n} = -\frac{Z_{\text{eff}}^2 R_{\infty}}{n^2}$$

where $Z_{\text{eff}}$ is the effective nuclear charge and $R_{\infty}$ is the Rydberg constant. The emitted photon energy is:

$$E_{\gamma} = E_{i} - E_{f}$$

Bremsstrahlung intensity for a target of atomic number $Z$ and electron energy $E$ is approximately:

$$I(u) \propto \frac{Z^2}{u} \exp\!\left(-\frac{hu}{kT}\right)$$

where $T$ is the mean kinetic temperature of the electrons.

Use of X-rays in Astronomy and Cosmology

Why X-rays?

X-rays are produced in extremely hot and energetic environments. Their high photon energies ($>0.1$ keV) allow us to probe:

• Plasma temperatures up to $10^8$ K.
• Strong gravitational fields near compact objects.
• Non‑thermal processes such as synchrotron emission.

Key X-ray Astronomy Missions

1. Einstein Observatory (1978–1981)
2. ROSAT (1990–1999)
3. Chandra X-ray Observatory (1999–present)
4. XMM-Newton (1999–present)
5. NuSTAR (2012–present)

Major X-ray Sources in the Universe

Source Type	Typical X-ray Luminosity ($L_X$)	Characteristic Energy Range (keV)	Key Physical Processes
Active Galactic Nuclei (AGN)	$10^{42}–10^{46}$ erg s⁻¹	0.1–100	Accretion disc, corona, relativistic jets
Neutron Stars / Pulsars	$10^{32}–10^{38}$ erg s⁻¹	0.1–10	Magnetospheric emission, surface hot spots
Supernova Remnants (SNR)	$10^{34}–10^{36}$ erg s⁻¹	0.1–10	Shock heating, synchrotron, thermal plasma
Galaxy Clusters	$10^{44}–10^{45}$ erg s⁻¹	0.1–10	Intra‑cluster medium (ICM) thermal bremsstrahlung
Cosmic X-ray Background (CXB)	$\sim 10^{-12}$ erg cm⁻² s⁻¹ sr⁻¹	0.1–10	Integrated emission from distant AGN and hot gas

X-ray Detection Techniques

X-ray photons cannot be focused by conventional lenses or mirrors. Instead, detectors convert photon energy into measurable signals:

• Scintillation detectors: X-ray photon excites a scintillator, producing visible light detected by a photomultiplier.
• Proportional counters: X-ray ionises a gas, producing an electron avalanche proportional to the photon energy.
• Charge-Coupled Devices (CCDs): X-ray photon generates electron-hole pairs in silicon; the charge is collected and read out.
• Transition Edge Sensors (TES): Operated at millikelvin temperatures; small temperature rise from photon absorption changes resistance.

Energy resolution ($\Delta E/E$) improves from $\sim 10\%$ (scintillators) to $\sim 1\%$ (TES).

Applications in Cosmology

1. Cluster Mass Measurements: The temperature $T$ of the ICM is related to the gravitational potential via the virial theorem:

$$\frac{3}{2}kT \approx \frac{GM_{\text{cluster}}\mu m_p}{2R}$$

where $\mu$ is the mean molecular weight and $R$ is the characteristic radius.

2. Large-Scale Structure: X-ray surveys map the distribution of hot gas in filaments, revealing the cosmic web.

3. Dark Energy Constraints: The evolution of cluster number density with redshift depends on the cosmological parameters $\Omega_m$ and $\Omega_\Lambda$.

4. Cosmic X-ray Background: Spectral fitting of the CXB provides the integrated emissivity of AGN over cosmic time, informing models of supermassive black hole growth.

Future Directions

1. High-resolution spectroscopy with microcalorimeters (e.g., XRISM).
2. Wide-field surveys (e.g., eROSITA) to detect millions of AGN.
3. Time-domain X-ray astronomy to study transient phenomena such as tidal disruption events.
4. Multi-messenger campaigns combining X-ray, gravitational wave, and neutrino observations.