Master Degree in Astronomy and Astrophysics – University of Rome

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To be admitted to the master’s degree programme in Astronomy and Astrophysics, students must hold a bachelor’s degree, a three-year academic diploma or any other suitable title of study got abroad and deemed as equivalent by the University.

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Faculty of Mathematical, Physical and Natural Sciences


The Master’s Degree Programme in Astronomy and Astrophysics has a two-year duration and awards 120 ECTS. Admission to this programme is not restricted and takes place by means of the assessment of the student’s curricular requisites and personal skills.

The learning outcomes of the Master’s Degree Programme in Astronomy and Astrophysics depend on the relating class (LM-58, Science of the Universe).

Masters graduates in Astronomy and Astrophysics have achieved the following learning outcomes:

• a mastery of the scientific research method, based on a sound background in classical and modern physics and the necessary expertise in the use of mathematical methodologies and IT tools;

• an excellent knowledge of modern astronomy and astrophysics, with wide scientific, operational, observation and theoretical skills in the issues relating to the class;

• advanced skills in modern instrumentation and observation techniques, in the data collection and analysis procedures as well as in model building.

Thanks to this degree programme, masters graduates can be admitted to PhD schools, 2nd level professional masters and can hold technical and managerial duties in Civil Service and in the private sector.

In particular, masters graduates may become laboratory technicians, scientific programmers, data analysts, software developers for scientific and industrial applications, commercial technicians for customer support (for example, in case of instrumentation manufacturers). By taking advantage of their cross-curricular mathematical and technical skills, masters graduates may successfully cooperate with other professionals such as engineers, managers and IT specialists.

Admission requirements

To be admitted to the master’s degree programme in Astronomy and Astrophysics, students must hold a bachelor’s degree, a three-year academic diploma or any other suitable title of study got abroad and deemed as equivalent by the University.

Students must have a good knowledge of classical and modern physics, elements of chemistry and of the required mathematics and computer science tools. They are required to have a good command of Italian, both oral and written. They must also be able to effectively use English, both oral and written, in their specific framework and for the exchange of general information (B-1 level according to the QCER, Quadro comune europeo diriferimento per la conoscenza delle lingue, Common European Framework of Reference for Languages).
To be admitted to the master’s degree programme, bachelor’s graduates must have
acquired at least:
overall 20 ECTS in mathematics and/or computer science disciplines (MAT/01-MAT/08,
INF/01 and ING-INF/05);
5 ECTS in chemistry disciplines (CHIM/01-03 and CHIM/06);
65 ECTS in physics disciplines (FIS/01-FIS/08), out of which at least 40 ECTS in
experimental physics (FIS/01), 12 ECTS in theoretical physics, mathematical models and
methods (FIS/02), 5 ECTS in physics of matter and/or in nuclear and subnuclear physics
(FIS/03 and FIS/04).
The procedures for the assessment of the students’ curricular requisites and personal skills are established in the Educational regulations of the study programme.


First year (Year of enrolment 2019/2020)

GENERAL RELATIVITY 1012186 First semester 6 FIS/02
SUPERIOR PHYSICS 1012178 First semester 6 FIS/02
Astrophysics Laboratory  1051847 First semester 6
PHYSICAL COSMOLOGY 1044601 Second semester 6 FIS/05
STELLAR ASTROPHYSICS 1012131 Second semester 6 FIS/05
THEORETICAL ASTROPHYSICS 1044553 Second semester 6 FIS/05
OBSERVATIONAL COSMOLOGY 1044551 Second semester 6 FIS/05
ASTRONOMICAL OPTICS 1012184 Second semester 6 FIS/05
DYNAMICS OF STAR SYSTEMS 1012137 Second semester 6 FIS/05
HIGH ENERGIES ASTROPHYSICS 1012129 Second semester 6 FIS/05
EXTRAGALACTIC ASTROPHYSICS 1012130 Second semester 6 FIS/05
PLANETS AND EXOPLANETS 10589158 Second semester 6 FIS/05
Astrophysics Laboratory  1051847 Second semester 6
English Language AAF1901 Second semester 4

Second year (Year of enrolment 2018/2019)

TEORICAL COSMOLOGY 1012136 First semester 6 FIS/05
SELF-GRAVITATING SYSTEMS 1012165 First semester 6 FIS/05
Chemical Evolution of the Universe 1056018 First semester 6 FIS/05
EXPERIMENTAL GRAVITATION 1055363 First semester 6 FIS/01
METHODS OF SPACE ASTROPHYSICS 1044550 First semester 6 FIS/01
FINAL EXAM AAF1036 Second semester 38


Students are recommended to visit the following degree programme webpage:
and the website of the Department of Physics:
The admission procedures provided after requisite assessment are indicated in art. 8 of the University Programme Manifesto published at

Programme details


Introduction to plasma Physics
Charged Particle motion in magnetic and electric fields
Sound waves
Shock waves
Thermal and electrical conductivity of Plasma
Plasma waves
MHD waves
Introduction to Plasma Kinetic theory
Electromagnetic emission
Special relativity recall
Relativistic Doppler
Relativistic electromagnetic emission
Radiative transport
Thermal radiation
Bremsstrahlung emission and free-free emission
Synchrotron emission
Scattering Thomson, Compton, inverse Compton

Recommended text

[FC] Francis F. Chen, Introduction to Plasma Physics and controlled Fusion. Vol. 1, Springer
[BT] Baumjohann, Treumann, Basic Space Plasma Physics, Imperial College Press, 1997
[CC] Clarcke C.J. Carswell R.F., Atrophysical Fluid Dynamics. CUP, 2007
[PS] C. Pucella, S.E Segre, Fisica dei plasmi, Zanichelli
[LL] L.D. Landau, E.M. Lifshitz, Fluid Mechanics, vol 6 of cource of theoretical physics, Pergamon Press
[ABP] E. Amaldi, R. Bizzarri, G. Pizzella, Fisica Generale (elettromagnetismo, relatività, ottica), Zanichelli Editore
[RL] G. B. Rybicki, A.P. Lightman, Radiative Processes in Astrophysics, Wiley
[HB] Hale Bradt, Astrophysics Processes: The Physics of Astronomical Phenomena, Cambridge University Press


Recommended text

[G] D. Griffith, Introduction to Elementary Particles

[P] D. H. Perskin, Particle Astrophysics

[R] Ryder, Quantum Field Theory

[RL] G. B. Rybicki, A.P. Lightman, Radiative Processes in Astrophysics

[B] G. Bertone (ed.), Particle Dark Matter


[G] D. Griffith, Introduction to Elementary Particles [P] D. H. Perskin, Particle Astrophysics [R] Ryder, Quantum Field Theory [RL] G. B. Rybicki, A.P. Lightman, Radiative Processes in Astrophysics [B] G. Bertone (ed.), Particle Dark Matter


Quantum mechanics Hamiltonian and Lagrangian mechanics

Astrophysics Laboratory 

1) IR, FIR, mm-wave spectroscopy

The spectroscopic method. Importance of Spectroscopy in Astrophysics.
Spectroscopy and interference. The prism as an interferometer.
Spectral resolution of pris spectrometers. Use of the prism spectrometer.
Diffraction grating as a N-beams interferometer. Resoution, Instrument Function.
The Fabry-Perot spectrometer. Resoution, Finesse, Pre-dispersors.
Fourier-transform Spectroscopy. Generality. The Michelson spectrometer.
Spectral resolution versus optical path difference.
Throughput and spectral resolution. Applications.
Sampling the interferoegram, Aliasing. Dielectric beamsplitter theory.
Front-division FTS. Martin-Puplett FTS. Wirte Grids. FIRAS. The multiplex advantage.
Interferogram scanning methods.

2) Advanced detectors for IR, FIR, mm-waves

Cryogenic Bolometers. Semiconductor sensors. JFET readout. AC bias and differential readout.
Calibration and qualification measurements. Superconducting bolometers (TES).
Constant-voltage bias and electrothermal feedback.
TES readout. Superconductivity and applications. Cooper pairs, long-range coherence,
Josephson tunnelling, SQUID. Multiplexing. Kinetic Inductance Detectors.
Properties, theory and applications.

3) Polarization-sensitive detectors for IR, FIR, mm-waves

Polarization and Stokes parameters. Stokes vectors, Muller matrices.
Matrices for Diattenuators, Retarders, Rotators. Linear Polarimeter.
Modulation and demodulation methods for polarimetry.
Half-wave or quarter-wave polarimeters. Polarization-sensitive bolometers.

4) Measurements of the Cosmic Microwave Background (CMB)

CMB observables: brightness, anisotropy, polarization and spectral dependance.
Intrinsic detection limits. Telescopes, photometers, polarimeters, spectrometers
for CMB measurements. Ground-based and spece-based observations. Calibration
methods. Importance of sidelobes, diffraction, stray-light.
Importance of differential measurements. CMB observables and their power spectra.
Detection limits. Quantum noise of the CMB. Noise and integration time.
Grey-body noise. Detector sensitivity for different CMB observables.
Systematic effects in CMB measurements. Sample systematic tests.
Examples of calibration for CMB anisotropy measurements: CMB Dipole, planets,
compact sources, degree-scale anisotropy as sky calibrators for system gain.
Beam calibration. Effect of point-sources in CMB measurements.
past, current and future CMB and foregrounds measurement programs.

5) Statistical analysis of experimental data

Data analysis: estimation of parameters, prediction of data values, model comparison.
Probability. Frequentist approach. Axioms of probability. Probability rules. Association probability-events.
Conditional probability. Independence. Bayes theorem and its power. Probability distributions.
Bayesan inference. Statistics. Unbiased, biased, de-biased statistics. Statstics debiasing and robustness.
Random numbers generators. Characteristc function. The variance of the mean. Error propagation equation.
Multivariate distribution. Data modelling. Likelihood function. Maximum likelihood estimator. Bayesian likelihood analysis.
Confidence levels. Line fit example. Case of more than 2 parameters.
Monte-Carlo methods. Metropolis Hastings algorithm. Monte-Carlo Makov chains. Bootstrap.



Friedmann’s cosmological model. Friedmann equations. Energy components. Baryonic matter and dark matter. Cosmological constant. Deceleration parameter. Age of the universe. Angular distance and luminosity distance in cosmology. Hubble law. Measurement of the Hubble constant.

Standard candles and standard sirens. Evidence for dark energy through measurements of SN-Ia luminosity distances. Current accelerating universe: theoretical models and problems. Primordial universe and relativistic components. Cosmic background radiation (CMB) and its black body spectrum. Estimation of the energy component in neutrinos through CMB measurements. Primordial nucleosynthesis and abundance of light elements. Estimation of the number of neutrino families by primordial nucleosynthesis. Energy component in massive neutrinos. Limits on neutrino mass from cosmological observations. Structure formation on cosmological scales.Jeans lenght. Temporal evolution of perturbations in linear regime for baryonic and obscure components. The problems of the standard model and the inflationary paradigm. Inflationary models. Primordial spectrum of inflationary fluctuations. Power spectrum of the fluctuations and comparison with current data. Anisotropy of cosmic background radiation and its formation mechanisms. Angular spectrum of anisotropic fluctuations and dependence on cosmological parameters. Polarization of CMB, scalar and tensor modes. Stochastic gravitational wave background and its possible determination. Future prospects.

Recommended text

– Introduction to Cosmology (second edition). Barbara Ryden. Cambridge University press.
– Modern Cosmology. Scott Dodelson. Academic Press.
– Structure Formation in the Universe. T. Padmanabhan, University of Cambridge.
– Cosmology. Nicola Vittorio. CRC press.


Classical mechanics. Electromagnetism. Special relativity. Non-relativistic quantum mechanics.



Part I: preliminaries
Introduction to stellar astrophysics
Fundamental properties of stars
The Milky Way

Part II: the physics of stars
Equations of stellar structure
Properties of stellar matter
Nuclear energy production
Polytropic stellar models and homology relations
The main sequence
The Hayashi line

Parte III: stellar evolution
Main sequence
Helium burning
Evolution of low-mass stars
Evolution of intermediate-mass stars
Evolution of massive stars
Stellar tracks in the HR diagram
End phases of stellar evolution and stellar remnants
Population III stars

Part IV: star formation
Fundamental properties of the interstellar medium
Properties of molecular clouds
Formation and stability of molecular clouds
Jeans criterion and fragmentation
Collapse and evolution of protostars

Part V: galaxy-scale star formation and evolution
The star formation law
The initial mass function
Stellar population synthesis
Chemical evolution of galaxies
Stellar feedback

Additional topics for interested students: cosmic-scale star formation and evolution
Galaxies at high redshift
The cosmic star formation history
Statistical properties of galaxies

Recommended text
Kippenhahn, Weigert & Weiss, Stellar Structure and Evolution – Second Edition, Springer (2012)

Castellani, Astrofisica Stellare, free access to updated electronic edition

Mo, Van den Bosch and White, Galaxy Formation and Evolution, Cambridge University Press (2010)

Stahler & Palla, The Formation of Stars, Wiley VCH (2004)


A fundamental pre-requisite is that students must have the knowledge requested by the first level University degree in Physics or in Astronomy and Astrophysics. Specific competences are requested in classical physics, quantum mechanics, atomic and molecular processes, nuclear physics. It is important that students have basic knowledge of astronomy (measurements of distance, mass, and luminosity, photometric and spectroscopic observational techniques), astrophysics (fundamental evolutionary phases of the Universe, general properties of stars and galaxies, the most important radiative processes in astrophysics), and in the theory of weak interactions.

Theoretical Astrophysics


Fundaments of vector analysis

– The formal operatro nabla.
– The gradient in cartesian, polar and cylindrical coordinates.
– The divertgence and the curl of vectors.
– Vector fields and their conservativity.
– Divergence and Stokes theorems.

Fundaments of fluid-dynamics

– Fluids: lagrangian and eulerian treatment of their dynamics.
– Constitutive equations.
– Conservation laws.
– Equilibria of ideal fluids in presence of external or self-consistent fields.
– Lane- Emden equation.
– Gravitational instability: Jeans theory.

Funaments of theory of gravitation

– Single particle potential. Mechanical and potential energy.
– Newtonian, one body, problem. Application to point like satellite motion, with dissipation.
– Laplace and Poisson field equations.
– Gauss and Newton theorems. Gravitational energy.
– Central force fields and their qualitative treatment.
– Oscillations. Inverse prblem in mechanics.
– Classical, Newtonian 2-body, 3-body and N-body problem. Constants of motion. Adimensionalization of equations of motion.
– Self gravitating systems. Time scales. Gravitational deflections. Collisional and violent relaxation. Stellar ejection and evaporation.

Recommended text
Notes of the course (in italian) are available at the link
The official text book of the course is “Classical Newtonian Gravity”, by Roberto Capuzzo Dolcetta, Unitext for Physics, Springer Verlag.

Landau, L.D., Lifshits, E.M., Mechanics, Course of Theoretical Physics, vol. 1, Elsevier-Butterworth-Heinemann (1976) Landau, L.D., Lifshits, E.M., The Classical Theory of Fields, Course of Theoretical Physics, vol. 2, Pergamon Press, Oxford (1980) Binney, J., Tremaine, S.: Galactic Dynamics, 2nd ed., Princeton Univ. Press, Princeton (2011 Mc Robert, T.M., Spherical Harmonics, Pergamon Press, Oxford (1967) Misner, C.W., Thorne, K.S., Wheeler, J.A., Gravitation, W.H. Freeman \& Co., New York (1972)

Advanced calculus, including theory of many variable functions, vector analysis, classical and analytical (lagrangian and hamiltonian) mechanics.

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