Looking at stars in the sky Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Constellations • In ancient times, constellations only referred to the brightest stars that appeared to form groups representing mythological figures. • Today, constellations are well-defined regions on the sky, irrespective of the presence or absence of bright stars in those regions. • Recently NASA added a “13th“zodiac sign because a region of space along the Earth ecliptic was missing. Panic among astrologers! Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Constellations are the result of a projection effect… ... and are mostly arbitrary Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Star names • There are way too many stars (even galaxies) for them to have names. • Historically, a few stars have been given names (Betelgeuse, Rigel, Aldebaran, Sirius...). Mostly because of their brightness in the night sky. • Naming convention within stars belonging to the same constellation – ordered in brightness (a,b,g,...). There are exceptions... Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Example: the southern cross Southern Cross (Crux) • a-cruxis (“Acrux” – actually a member of a triple star!) • b-cruxis (“Mimosa”) • g-cruxis (“Gacrux” – double star) • d-cruxis • e-cruxis • + Many more… (remember that constellations in astronomy refer to entire regions of space) Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky And while we are around the southern cross… Jewel box (d~6400 ly) Coalsack Nebula (d~600 ly) Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Near the southern cross… • The “Jewel Box” star cluster – Kappa Crucis Cluster (NGC 4755) Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Near the southern cross… Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky The stellar magnitude scale • Historically introduced by Hipparchus (160-127 BC) • Brightest stars – 1st magnitude • Faintest stars (unaided eye) – 6th magnitude • Nowadays the magnitude scale has been expanded to include all observed objects. It is based on the logarithmic scale of the brightness of a star -2 • Apparent (visual) magnitude (m or mv): A measure of log10(I), where I (in [W.m ]) is the “intensity” (flux) or brightness of light in the visible range measured at Earth. The modern definition maintains Hipparchus convention, i.e. the fainter the star, the higher the magnitude. Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky “Color” / bolometric magnitudes • The apparent magnitude can be defined in terms of total brightness, or the brightness through particular color filters • U filter – 300 to 400 nm (UV light) • B filter – 400 to 500 nm (blue light) • V filter – 500 to 600 nm (“visible” – green to red wavelengths) • Apparent brightness through these filters mU, mB and mV respectively. • In practice, we will be talking about apparent and absolute magnitude integrated over all wavelengths – bolometric magnitudes. Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky The stellar magnitude scale • In the 1900’s, the magnitude scale was defined as follows: “a difference of 5 in magnitude corresponds to a change of a factor 100 in brightness”. • Dm = m2 – m1 = 5 à flux ratio: I1/I2 = 100 (remember the Hipparchus convention!) I 1 = α (m2 −m1 ) =100 I2 with m2-m1 = 5. from which we can deduce a≈2.51 • Using log10 (exact formula): ." !" − !$ = −2.5 *+,"- .$ Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky The (visual) magnitude scale • Apparent visual magnitudes of other objects in the sky – can be a negative number! • Sirius (the brightest star in the sky): mv = -1.47 • Full Moon: mv = -12.5 • Sun: mv = -26.5! Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Exercise • What is the relative brightness of Sirius (mv=-1.47) compared to Vega (mv=0.03), i.e. what is the ratio of (ISirius/IVega)? ." Recall: !" − !$ = −2.5 *+,"- .$ Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Intrinsic luminosity • Apparent magnitude tells us how bright stars appear to be at Earth. Of more interest is their intrinsic luminosity - to calculate this we need to know the star’s distance • Luminosity L = total radiation emitted by star in all directions (in [W]) • At a distance r (e.g. distance to Earth), that radiation flows through the surface of an imaginary sphere, radius r, surface area 4pr2 • Hence the intensity at Earth, or -2 brightness in [W.m ]): L I = 4πr2 Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Absolute magnitude • Absolute magnitude (M) is defined as the apparent magnitude a star would have if it were at a standard distance of 10 parsecs [pc] (1 pc = 3.26 ly). • With this standard (but arbitrary) definition, one can use the absolute magnitude as a measurement of the luminosity L. It is an intrinsic property of the star, unrelated to its position relative to Earth. • One can show that: m − M = −5+ 5log(d) where d is the distance to the star in unit of pc. • More on this later on in the course… Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky The (relative) motion of stars in the night sky • Long exposure photographs show the relative motion of the stars (aka “star trails”) in the night sky (in fact the apparent motion is due to Earth’s rotation of course!). Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky The celestial sphere The celestial sphere • Two different coordinate systems (2) • (1) The one relative to the (1) orientation of the Earth in the sky • North / South celestial poles • Celestial equator plane • (2) The one relative to your location on Earth (Lat / Lon) • Zenith / Nadir • North / South / East / West Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Apparent motion of the celestial sphere • From a northern latitude – looking north (toward the North celestial pole) • Earth’s rotation goes eastward à relative motion causes the Celestial sphere to move westward around Earth (Sun rises in the East and sets in the West) Westward relative motion West East Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Apparent motion of the celestial sphere • From a northern latitude: • Looking east • Looking south • Relative motion of stars looks different at different latitudes. Westward relative motion • Due to the motion of Earth around the Sun, a given constellation rises 4 minutes earlier each night (day). Westward relative motion East West Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Alignment of celestial equator plane relative to latitude Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky The equatorial coordinate system • There is a need for a coordinate system that results in nearly constant values for the positions of celestial objects, despite the complexities of diurnal and annual motions. • The equatorial coordinate system is based on the latitude – longitude system of Earth but does not participate in the planet’s rotation. • Declination d is the equivalent of latitude and is measured in degrees north or south of the celestial equator (remember the celestial sphere!). • Right ascension a is analogous to longitude and is measured eastward along the celestial equator from the vernal equinox. Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Right ascension • In astronomy, the right ascension is given in hours, minutes and seconds $%&° • Hour: 1" = = 15° () Example: a = 19h50m47.0s $%&° • Minute: 1+ = = 0.25° ()×%& $%&° • Second: 10 = = 0.00417° ()×%&×%& • Why? The right ascension is naturally coupled a full rotation of the Earth, hence the use of 24h in place of 360º. • For precise tracking of the stars in the sky, one needs to take into account the effect of precession (see later). Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Exercise Convert the right ascension a = 19h50m47.0s in degrees [0º,360º] Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Proper motion • Relative motion of stars difficult to measure because stars are far away. Only the transverse velocity of the star results in a change of equatorial coordinates • Proper motion is defined as the angular rate #$ ' of change: ! ≡ = (. #% ) • Angular distance travelled as a function of change of right ascension Da and declination Dd (equatorial coordinates): ∆+,= (∆. cos 3),+(∆3), Fred Sarazin ([email protected]) Physics Department, Colorado School of Mines PHGN324: looking at stars in the sky Precession (I) • Gravity is pulling on a slanted top à wobbling around the vertical. • The Sun’s gravity is doing the same to the Earth. • The resulting “wobbling” of the Earth’s axis of rotation around the vertical with respect to the Ecliptic takes about 26,000 years and is called precession.