* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Penentuan Jarak dalam Astronomi II
Non-standard cosmology wikipedia , lookup
Physical cosmology wikipedia , lookup
Canis Minor wikipedia , lookup
Space Interferometry Mission wikipedia , lookup
Dark energy wikipedia , lookup
Auriga (constellation) wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Astronomical unit wikipedia , lookup
Cygnus (constellation) wikipedia , lookup
Cassiopeia (constellation) wikipedia , lookup
Aries (constellation) wikipedia , lookup
Open cluster wikipedia , lookup
International Ultraviolet Explorer wikipedia , lookup
Corona Australis wikipedia , lookup
Timeline of astronomy wikipedia , lookup
Gamma-ray burst wikipedia , lookup
Lambda-CDM model wikipedia , lookup
Perseus (constellation) wikipedia , lookup
History of supernova observation wikipedia , lookup
Observable universe wikipedia , lookup
Observational astronomy wikipedia , lookup
Stellar evolution wikipedia , lookup
Aquarius (constellation) wikipedia , lookup
H II region wikipedia , lookup
Stellar kinematics wikipedia , lookup
Hubble Deep Field wikipedia , lookup
Corvus (constellation) wikipedia , lookup
Future of an expanding universe wikipedia , lookup
Metoda Baade-Wesselink Hubungan Periode dan Luminositas bintang Cepheids Hubungan Periode –Luminositas –Metalisitas bintang RR Lyrae 4. Supernova tipe Ia 1. 2. 3. In Cepheid's and RR Lyraes, an extra energy flowing out is held up in the outer layers for a short while during the contraction phase and is released when the star is expanding This amplifies the contraction or departure from hydrostatic equilibrium in the outer layers Nuclear reactions go at a faster rate creating more radiative energy and hence more pressure halting the contraction. Perturbation are periodic in most cases, but some observations show also long non- pulsating phases. Pulsation is not due to variations in the rate of energy generation in the core but with the variation of the rate of escaping radiation Radial pulsations proposed by Arthur Ritter in 1879 assuming that pulsations are due to sound waves resonating in the stellar interior. Use hydrostatic equilibrium, dP/dr = - Gm(r)ρ/r2 = -4Gπrρ2/3 Period~√3π/2Gγρ This is the period mean density theorem, where we take ρ to be the mean density of the star. More complicated in Reality!! Cepheid’s are much more tenuous and have a smaller mean density and hence a longer period. RR Lyraes are compact with a high mean density. The Baade-Wesselink Method Walter Baade Adriaan Jan Wesselink (1893-1960) (1909-1995) • Method to get the distances to variable Pulsating stars proposed fisrt by Baade in 1926 and reviewed by Wesselink in 1946 • The Radius: The Variation of the Radius during one phase of pulsation: R R0 R (t ) P R(t ) q (Vr (t ) Vr (t ) )dt 0 P 1 Vr (t ) Vt (t )dt P0 (a) For a pair of phases with the same temperature and color (say, B-V), the Cepheid’s apparent magnitudes V differ due only to the ratio of stellar radii: R m 2.5 lg R R1 R2 B-V 2 1 2 2 (b) Radii difference Pulsation Phase (R1-R2) can be calculated by integrating the radial velocity curve, due to VR ~ dR/dt A number of pairs (R1 – R2) ~∫VR·dt and R1/R2 ≈ 10-0.2m give rise to the calculation of mean radius, <R> = (Rmax + Rmin)/2 The Baade-Wesselink Method,ct’d • The Effective temperature: Using stellar models one gets the effective temperature as a function of observable color properties and metallicity: Fe Log Teff f (V K ), , log g H • The Absolute magnitude: The Luminosity and absolute magnitude of a black body of a radius R and a temperature T is given by: R L 4 R 2 Te4 M v 2.5 log L M Bol Fe BC (log Teff , H , log g ) And combining with the apparent magnitude, one get the distance modulus and thus the distance The Distance to the Galactic Center was measured via the BW method d= 7.9 +/- 0.6 Kpc Distance to the M31: 740+/-40 Kpc Distance to the LMC: 50+/-2 Kpc Distance to the NGC6822: 475+/-30 kpc BW method Galactic Centrer (kpc) M31 (kpc) LMC (kpc) NGC 6822 (kpc) RR Lyrae 7.8 +/- 0.4 750+/-80 44+/-2 469+/-22 Cepheids 8.0+/- 0.5 760+/-50 50+/-2 477+/-35 other 8.0+/- 0.8 700+/-60 52+/-3 480+/-60 Among brightest stellar indicators, relatively young stars, found in abundance in spiral galaxies Many independent objects can be observed in a single galaxy Large amplitude & distinct sawtooth light curve facilitate discovery Long lifetimes: can be observed at other times and wavelengths P-L relationship has better precision Have been studied and theoretically modeled extensively and their physics is understood Atmospheric Models (logT, log g) Dust scattering, Absorption and Reddening. Corrections must be made for extinction with assumptions Metallicity: dependence of PL relationship on chemical composition very difficult to quantify (PL relationship has slight dependence on metallicity) Accurate calibration of PL relation at any given metallicity not yet established Limited reach ~30 Mpc Improvement to the BW technique using Interferometry P. Karvella et al 2004 N.Nordetto et al 2005 Lane et al 2002 Lane et al 2000, Nature 407,485 Distance Modulus using the BW method µNGC1705=28.54±0.26 mag µM31 = 24.63 ± 0.17 mag µNGC6822 = 23.36±0.17 mag µLeoI = 22.04 ± 0.14 mag µLeoII = 21.83 ± 0.13 mag µFornax = 20.66 ± 0.10 mag µDraco = 19.84 ± 0.14 mag µUMi= 19.41 ± 0.12 mag µLMC = 18.515 ± 0.085 mag Clementini et al 2003 (1) Cepheid Variables: * Period 1 - 100 days * Named After the first found, eg. Delta Ceph * F-type Massive stars M~5Mʘ, Age ~0.1Gyr * High Luminosity -6<Mv<-2 (2) RR Lyrae: * Period 0.5 – 1 day * O, A type stars, M~ 1Mʘ * Found in low metallicity systems * Luminosity L~100Lʘ , Mv~0 (3) W Virginis: * Old Variable Stars with 1-30 days * Low mass, low metallicity * -4.5<Mv<-0.5, called type II Cepheids (4) Mira Stars: * Period 80 - 100 days * Red Variables, most show emission lines More Classes: Cepheids and RR Lyrae variable stars populate Instability Strip on the HRD (see blue strip) where most stars become unstable with respect to radial pulsations Instability Strip crosses all branches, from supergiants to white dwarfs G.Tammann et al. (A&A V.404, P.423, 2003) Instability strip for galactic Cepheids (members of open clusters and with BBWB radii) in more details: MV-(B-V) and MI-(V-I) CMDs Young (< 100 Myr) and massive (3-8 MSun) bright (MV up to -7m) radially pulsating variable stars with strongly regular brightness change (light curves) Typical Periods of the pulsations: from ~1-3 to ~100 days (follow from P ~ (Gρ)-1/2 expression for free oscillations of the gaseous sphere: mean mass density of huge supergiants, ρ, is very small as compared to the Sun) Luminosities: from ~100 to 30 000 that of the Sun Evolution status: yellow and red supergiants, fast evolution to/from red (super)giants while crossing the instability strip (solid lines) Evolution tracks for 1-25MSun stars on the HRD 1907, Henrietta Leavitt (18681921), Harvard Observatory Astronomer, discovers CV’s luminosity and period follow very tight correlation M = - 2.59 log (P/days) -0.67 Longer period = brighter CV The duration of the Cepheids stage is typically less than 0.5 Myr and, taking also in consideration the rarity of massive stars at all, we guess that Cepheids form very poor galactic population Statistics of Cepheids discovered: ~3000 proven and suspected in the Galaxy, ~2500 in the LMC, ~1500 in the SMC, ~Thousands are found and, ~50 000 are expected to populate the Andromeda Galaxy (M31) Easily recognized by its high brightness and periodic magnitude change among other stars, even in distant galaxies (up to 50 Mpc) Typical population of young clusters, spiral and irregular galaxies Luminosity increases with the Period (P-L relation) Cepheids are still among most important “standard candles” Cepheid’s in M31 From Bonanos et al. 2003 Large Magellanic Cloud 43.2 ±1.8 kpc 47.0 ±2.2 kpc 50.2 ±1.2 kpc 47.5 ±1.8 kpc Fitzpatrick et al. (2003) Apparent mean I magnitude corrected for differential absorption inside LMC vs log P(days) for fundamental tone (FU) and first overtone (FO) cepheids: <I> ≈ a + b·lg P PFO / PFU ≈ 0.71 (Δ lg P ≈ 0.15) W(I) Brightest Cepheids Distances are the same: absolute magnitudes <MI> are also linear on log P ! Linearity of log P-log L relation retains also for Cepheids absolute magnitudes Simple estimate: Brightest LMC Cepheids reach <MV> ≈ -7m These “standard candles” can be seen from the distance ~50 Mpc (with ~27m limiting magnitude accessible to HST) Brightest Cepheids can be widely used as secondary sources of distance calibrations to spiral galaxies hosted by SN Ia etc. We can see Cepheids even in distant galaxies Overtone Cepheids are clearly seen on the “apparent magnitude – period” diagrams of nearby galaxies as having smaller periods for the same brightness Problem with Milky Way Cepheids: due to distance differences, how to identify overtone pulsators among Cepheids with different distances ? Milky Way Cepheids sample is supposed to be contaminated by unidentified first-overtone pulsators This problem greatly complicates the extraction of the P-L relation directly from observations of Milky Way cepheids (a) Trigonometric parallaxes (HIPPARCOS and HST FGS) (b) Membership of Cepheids in open clusters and associations (c) BBWB mean radii (d) Luminosity refinement by the statistical parallax technique Udalski et al. (1999) P-L relation: <M> = a + b·lg P (a) zero-point (b) slope Why not to estimate the slope of the P-L relation directly from LMC Cepheids ? – The slopes of the P-L relations in other galaxies may differ due to systematic differences in the metal abundances and Cepheids ages (A.Sandage & G.Tammann, 2006) Before ~2003, most astronomers used the slope of LMC Cepheids to refine zero-point of Milky Way Cepheids If metallicity effects are really important, application of single P-L relation to other galaxies populated by Cepheids can introduce additional systematic errors (see detailed discussion in A.Sandage et al., 2006) Cepheids color excess are uncertain because of: Finite width of the instability strip (~0.2m) due to evolution effects Uncertainty of cepheids “normal colors” Wesenheit index (Wesenheit function) is often used to reduce the effects of the interstellar extinction (B.Madore in “Reddening-independent formulation of the P-L relation: Wesenheit function”; ROB No.182, P.153, 1976) From true distance modulus we have: MV V 10 5 lg p (mas) AV Wesenheit index definition: Constant! AV W ( VI ) V 10 5 lg p (mas) (V I ) E( V I ) Wesenheit index do not depend on the extincton but only onSubstituting the normalapparent color color ( V I ) ( V I )0 E( V I ) Normal color as well as <MV> we derive: is linear on lg P AV (see instability strip picture!), W ( VI ) V 10 5 lg p (mas) AV ( V I )0 E( VP I ) so W(VI) is also linear on lg AV MV ( V I )0 W ( VI ) MV ( V I )0 E( V I ) where const β = AV/E(V-I) ≈ 2.45± follows from the extinction law Wesenheit Index can be introduced for any color: W(BV), W(VK) etc. W incorporates intrinsic color (and Period – Color relation) The advantage of using the Wesenheit index W instead of the absolute magnitude M is that (a) Wesenheit index is almost free of any assumptions on cepheids individual color excess, particularly in our Milky Way, and (b) it reduces the scatter of the P-L relations F.van Leeuwen et al. “Cepheid parallaxes and the Hubble constant” (MNRAS V.379, P.723, 2007) Wesenheit index W(VI) for 14 Cepheids with most reliable parallaxes from HIPPARCOS and HST FGS: Route to P-L relation W(VI) W(VI) W(VI) = α·lg P + γ days days Metallicity differences have been taken into account empirically, by adding the term proportional to Very poor statistics! the difference of the galactocentric distances (due to “mean” [Fe/H] Zero-points Slope gradient across the galactic disk, Δ[Fe/H] / ΔRG) ~ -0.05… -0.10 ± days days Multicolor (BVRCRICIJHK) P-L relations for galactic Cepheids D.An et al. “The distances to open clusters from mainsequence fitting. IV. Galactic Cepheids, the LMC, and the local distance scale” (ApJ V.671, P.1640, 2007) New distances New P-L for the galactic Cepheids: (c) Distance scale from BBWB radii Comparing Cepheids P-L derived from 23 cluster Cepheids (red) with that from Wesselink radii (blue) (D.Turner & J.Burke, 2002) Insignificant slop difference ~0.19 Mean: <MV>≈-1.20m-2.84m·lg P * Measurement of H0 with the goal of 10% accuracy was designated as one of the “Key Projects” of the HST * Using Cepheid variable stars to measure distances M.Marcony & G.Clementini (ApJ V.129, P.2257, 2005) Periods < 1d Examples of LMC RR Lyrae light curves in BV bands Observations vs theory Large amplitude, Δm ~ 1m Examples of the LMC RR Lyrae light curves in I band (OGLE program, I.Soszynski et al., Acta Astr. V.53, P.93, 2003) RR are simply discernible among field stars in stellar systems <MV> ≈ +1m NIR light curve of RR Lyr star: look at small amplitude. RR Lyr: nearest star of this type. Not so bright as Cepheids but very important for distance scale subject in the galactic halos, bulges and thick disk populations RR Lyrae variable stars in the Instability Strip on the HRD In contrast to Cepheids, RR Lyrae variables are among oldest stars of our Milky Way Evolution status: horizontal branch (HB) stars RR Lyrae variables populate galactic halos (H) and thick disks (TD) (as single stars), and globular clusters of different [Fe/H] Evolution stage: Helium core burning Age: ≥ 10 Gyr LifeTime: ~100 Myr RR Lyrae M2 V const ? BHB (EHB) TP H TD Close luminosities for the same [Fe/H] (rms ~ 0.15m) The duration of RR Lyrae stage (and HB stage at all) is negligible as compared to the age of stars, ≤100 Myr vs ~10-13 Gyr (<1%), but comparable with lifetime of Red Giants Therefore, HB population is comparable with RG population in size, but RR Lyrae form only a small fraction of all stars above Turn-Off point on the CMD Thousands of RR Lyrae are found and catalogued in the Milky Way halo and in its globular clusters Dots are separated by 10 Myr time interval HB position is almost the same for clusters of different age HF IS Gyr age Universality of RR Lyrae population luminosity D.VandenBerg et al. (ApJ V.532, P.430, 2000) theoretical ZAHB levels for different [Fe/H] and [α/Fe] values [Fe/H] seems to be the key parameter responsible for RR Lyrae optical luminosity The slopes of P - L and [Fe/H] - L relations seems to be definitely found from the theory as well as from observations in globular clusters and nearby galaxies differ by [Fe/H] Zero-point refinement is Main problem in RR Lyrae distance scale studies From late 1980th, it became customary to assume a linear relation between RR Lyrae optical absolute magnitude and metallicity of the form <Mopt> = a + b·[Fe/H] The calibration problem reduced to finding a and b by whatever calibration method was used. The three most popular have been: (a) theory (b) the BBWB moving atmosphere method (c) distances of globular clusters; HST & HIPPARCOS parallaxes (d) statistical parallaxe technique Is there universal slop of the <MV> - [Fe/H] relation? Theoretical slopes μ RR Lyrae models in NIR do obey to a well-defined PLZK relation: <MK> ≈ -0.775 − 2.07·lg P + 0.167·[Fe/H] with an intrinsic scatter of ~0.04m (with small contribution from [Fe/H] term) <MI> ≈ <MJ> ≈ <MH> ≈ <MK> ≈ +0.109 – 1.132·lg P + 0.205·[Fe/H] -0.476 – 1.773·lg P + 0.190·[Fe/H] -0.865 – 2.313·lg P + 0.178·[Fe/H] -0.906 – 2.353·lg P + 0.175·[Fe/H] <MV> ≈ +1.258 + 0.578·[Fe/H] + 0.108·[Fe/H]2 (this nonlinear function of [Fe/H] do not depend on lg P: <MV> ≈ +0.63m at [Fe/H]=-1.5 ) Usually, RR Lyrae distance scales are characterized by the mean absolute magnitude referred to [Fe/H] = -1.5, the maximum of [Fe/H] distribution function of RR Lyrae field stars and GGC (galactic globular clusters) Cepheids as very bright and uniquely identified stars are among most “popular” standard candles in the distant galaxies, but their distance scale is still uncertain by ~10% (systematic + random error) RR Lyrae are good standard candles used to refine the distances to the “beacon” galaxies (such as LMC/SMC, M31/33 etc.) in the Local Volume (up to ~10 Mpc), and to calibrate other secondary standard candles (SN Ia, Tulli-Fisher & FaberJackson relations etc.) Much work has to be done with Cepheids and RR Lyrae variables in recent years and in the future, in the context of GAIA and SIM observatories SNe advantage: extremely bright (as bright as whole the galaxy !) and easily discriminated (if you are lucky enough to detect it early) Seen in high-z galaxies, SNe can reveal early Universe’s kinematics and provide the check of the cosmological models Give rise to completely new physics of late stages of stellar evolution Supernovae explosion events are very rare and spectacular phenomena on the heavens Last two SNe in our Milky Way Galaxy: SN 1572 (Tycho Brage’s supernova Ia (?) in the Cassiopeia constellation) achieved -4m at the maximun brightness SN 1604 (Kepler’s supernova Ia in the Ophiuchus constellation) achieved -2.5m As expected, we could have miss a number of Supernovae events that have been exploded deep inside the galactic disc full of dense and opaque interstellar dust Bright SN1994D (Ia) SN1994D Milky Way-like galaxy A supernova can outshine an entire galaxy, and so be seen from very far away Why not to use for distance measurement ? Core collapse of a massive star: Type II Supernova If an accreting White Dwarf exceeds the Chandrasekhar mass limit, it collapses, triggering a Type Ia Supernova. Type I: No hydrogen lines in the spectrum Type II: Hydrogen lines in the spectrum Type I Subgroups are Ia (no H, no He), Ib/c (no H), outer stellar layers are already missing prior to the explosion – due to binary system evolution ?) Found in elliptical, spiral and irregular galaxies as well (Ia) or only in star-forming galaxies (I b/c – young population ?) Type II Hydrogen is observed in spectra Probably originated from high-mass stars Found only in star-forming galaxies SN1987A How to classify Supernovae? Type Ia – thermonuclear supernovae exploded in close binaries with companion white dwarf, which exceeds ~1.4 MSun Chandrasekhar limit as a result of the mass exchange Type Ib/c and II – core-collapse supernovae, final stages of the evolution of (very) massive stars that ends up as NS or BH (a) Single stars that are typically below ~8 MSun becomes red giant just after their life on the Main Sequence Red giants lose mass and evolve (often through a Planetary Nebulae stage) into White Dwarfs (b) More massive stars become supergiants Supergiants undergo Type II (and extremely massive – Type Ib/c) Supernova explosions, often leaving behind a stellar core which is a neutron star (NS), or a black hole (BH) Sun-like stars build up a Carbon-Oxygen (C-O) core, which does not ignite Carbon fusion With He-burning shell, stellar C-O core collapses and becomes degenerate White Dwarf The more massive a White Dwarf, the denser and smaller it is Pressure becomes larger, until – at the mass limit - electron degeneracy pressure can no longer hold up against gravity. WDs with more than ~ 1.4 solar masses can not exist! SN Ia event is due to mass transfer in close binary system with White Dwarf as a satellite of normal star, filling its Roche surface, through inner Lagrangian L1 point When the White Dwarf reaches the “Chandresekhar limit” of ~1.4 MSun, it implodes with a bright flash of energy released due to Carbon and Oxygen thermonuclear fusion inside the star In a binary system, each star controls a finite region of space, bounded by the Roche Lobes (or Roche surfaces) Lagrange points: points of stability, matter can rest (with zero velocity) without being pulled towards one of the stars Gas can flow over from one star to another through the inner Lagrange point, L1 (a) More massive star B evolves more quickly, it becomes a red giant and loses mass through L1 point; after a while it becomes the White Dwarf star (b) Main Sequence star A gains the mass and becomes more massive; after a while it loses its mass to WD satellite Mass transfer in a close binary system can significantly alter stellar masses and affect their evolution This process in more details Start Nothing remains after WD explosion… Companion star ejecting End Fixed limiting mass of the White Dwarf (~1.4 solar) together with known physical description of thermonuclear reactions of Carbon & Oxygen nuclear burning, suggest the similarity of SN Ia properties used to derive the distances to SNe host galaxies SN Ia : ~45%, explodes in spiral, irregular and elliptical galaxies SN II + SN Ib/c : ~55%, explodes only in spiral and irregular (star-forming ) galaxies, and most luminous (SN Ib/c) – in the regions of current star formation populated with youngest massive stars NGC 6946 (~3·1010 LSun) is the champion, with its 6 SN (!) registered from 1917 SN rate for Milky Way is supposed to be ~1 SN/100 years, but the last observed SN exploded in 1604 - selection effects due to strong interstellar extinction or not ? NGC 2770 with its two SN (2008) Supernova taxonomy SN Ia spectral features α-elements: 20Ne 24Mg 28Si 32S 40Ca… Primary nuclides, formed from He A.Filippenko “Optical spectra of Supernovae” (ARA&A V.35, P.309, 1997) Comparison of Ia, II, Ic, Ib spectra after 1 week from maximum Ia & Ic: no H, no He Deeper lines in SN Ia Ia II Ic Ib A.Filippenko (1997): expansion velocity for SN Ia vs time (from spectral data) > 10000 km/s Total kinetic energy output ~ 1051 ergs (a) To explain SN Ia events among both old and young populations (b) To explain the absence of Hydrogen in their spectra (c) To explain widely accepted idea of the homogeneity of the SN Ia class -------------------------------------------------Accretion rate is key parameter: small rate ! Qualitative SN Ia light curve 56Ni + 56Co 56Fe decay rate Early decay heating explains the luminosity rise 1043 Optical light curve . 1042 0 20 40 t (days after peak) Decay produces gamma-rays 60 A.Hirschmann et al. (2007) for different detonation models: a lot of radioactive 56Ni C.Travaglio et al. “Nucleosynthesis in multidimensional SN Ia explosions” (A&A V.425, P.1029, 2004): Element yields (mass-to-Fe fraction/the same for Sun); Fe = 1. Ni in excess ! The results from two different models From C.Travaglio et al. (2004) Stable isotopes masses in MSun Most abundant are underlined C, O, Mg, Si, S, Ca, Cr, Mn, Fe, Ni are most abundant elements We all and all things around us have borne in Supernovae explosions ! Real physical picture of the SN Ia ignition is very complex, with non-trivial topology of the ignition fronts, explaining the differences between models proposed. But a number of numerical simulations in 3D have been performed in the last decade Two main models of the burning front spread (from C.Travaglio et al., 2004): Central ignition Floating Bubble model (with a small number of primary ignition centers) Central ignition front snapshots after T = 0, 0.2, 1 0.4 and 0.6 s 3 2 4 Floating bubbles front snapshots after 1 T = 0, 0.1, 0.14 and 0.2s 3 2 4 The adequate physical model of the SN Ia explosion is yet to be created Individual Supernovae light-curves differ in peak luminosity by the factor of about 6-10 How can we use SN Ia as the “standard candles”? (a) Correct photometric data for interstellar extinction in host galaxy and inside the Milky Way (b) For high-z SNe, calculate K-correction due to redshift of the energy distribution (c) Calculate “stretching” factor and fit SN Ia light curve by the template Some SN Ia explode in galactic halos and often are not greatly affected by the extinction in host galaxies, whereas most SN Ia infound in Riess et al., 1998 star-forming galaxies are embedded into dusty spiral arms Except for a small group of very rapidly fading supernovae (fainter), at maximum light, SNe Ia are supposed to have a relatively small scatter in their intrinsic colors, Δ(B-V)Max ~ 0.2, near <BV>Max≈0.05m, that depend on the rate of lightcurve decline and is used to crudely estimate the extinction Energy redistribution to larger wavelength in the spectra of high-z SNe is adjusted by calculations of K-corrections to the apparent magnitude in ith band: mi (z) = mi (z=0) + Ki (z), where Si(λ) is ith bandpass curve, and (1+z)=λ/λ0 accounts for the shift to red and of the increase of Δλ wavelength interval z effect to passbands (shifting and stretching) z=0.2 z=0.5 SNe energy distribution shifts to the red, as if filter passband was shifted to the blue (in rest λ) R passband shift for z = 0.2, 0.5 is shown, as compared to standard Johnson B & V color bands: R(z = 0.2) is bluer than V, R(z = 0.5) looks like B ! Supernovae light curves differ from each other by the (a) rate of the brightness decline, (b) the peak luminosity and (c) color at maximum light The diversity of their light curves can be fitted by single light curve “template” that can be “stretched” by time axis and shifted by magnitude axis M.Philips relation (ApJ V.413, L105, 1993): Dimmer SN Ia – faster brightness decline Dimmer SN Ia – redder color at maximum light Philips relation (maximum brightness vs rate of the decline) is continuously adjusted by new data on SN Ia, derived from multicolor observations K.Krisciunas et al. (AJ V.125, P.166, 2003) SN 2001el in NGC 1448 host galaxy (~18 kpc) One of the best studied SN Ia in multicolor (UBVRIJHK), from 12d before to 142d after maximum, to check the theory K.Krisciunas et al. (2003) Optical and NIR light curves of SN In JHK, maximum earlier than in 2001el (shifted optics vertically) -6 -5 -4 -2 B-V -1 Max +1 +2 SN Ia bolometric light curve: ~2·1043 erg/s of radiative energy flux near maximum light Total energy output > 1051 ergs SN 1998bu A.Riess et al (AJ V.116, P.1009, 1998): Empirical SN Ia light curves Δ=MMax-<M> is the magnitude difference at the maximum light between SN Ia and the “fiducial” light curve (template) Data for 2 SN Ia are shown A.Riess et al. (AJ V.607, P.665, 2004) SNe with z > 1 from HST as compared to low-z SN Ia: composite light curves Low-z and high-z SN Ia seem to be similar in the light-curve shapes: the same explosion physics ? All SN Ia are not the same! Correlations: slowbright, blue-bright Manage us to use light-curve “templates” and different templatefitting techniques Peak brightness Colour Index (CI) Light curve width (stretch) B mB MB ( s 1) CI Corrected distance modulus Corrected absolute magnitude of the observed SN Ia as: MFit = MT - α·(s-1) + β·ΔCI, where stretch factor (light curve “width”) s = Δm15T /Δm15, CI - Color Index, ΔCI = CI - CIT, (“T” for template curve) Δm15 – magnitude decay after 15 days (the faster is SNe, the more magnitude decay) (a) For slower SN, s > 1, MFit < MT, SN brighter and distance modulus larger (b) For redder SN, ΔCI > 0, MFit > MT, SN dimmer and distance modulus lower Why expect β~4 ? Color problem: RB = AB/E(B-V) =AV+1, β factor at CI is due to so RB ≈ 4.1 for “mean” extinction law in MW Extinction inside host galaxy and Milky Way Intrinsic properties of SN Ia (colors) β (at B-V color) from SN observations ~2 instead of ~4 we could expect from “standard” extinction curve in the MW SN Ia distances, RB To~ be2sure is in not seen anywhere in the MW! we have to solve the problem The reasons: “Strange” dust changed by the SN explosion? Dust evolution with z? Cannot discriminate an intrinsic Color-Luminosity relation from extinction? Advanced light curve fitting methods: (a) MLCS (Multicolor Light-Curve Shape) – A.Riess et al. (PhD Thesis, Harvard University, 1996; ApJ V.116, P.1009, 1998) (b) CMAGIC (Color-MAGnitude Intercept Calibration) – L.Wang et al. (ApJ V.590, P.944, 2003) – enables to estimate extinction as well (c) SALT (Spectral Adaptive Light-curve Template) – J.Guy et al. (A&A V.443, P.781, 2005) K.Krisciunas et al. (2006) In NIR, SN Ia are more alike to the “standard candles” – max (JHK) are nearly constant (except for fastest SN), with rms scatter ~0.14m, distance error ~7% from individual SN Seems to be very perspective Are SN Ia really “standard candles”? Some people doubt in homogeneity of supernovae SN Ia sample and even consider SN II type as possible “standard candles” candidate More extensive calculations of SN explosions are needed and new rich SN statistics, with spectral and multicolor photometric data, to answer all questions D.Branch & G.Tammann (1992) emphasized the observational homogenity of SN Ia: The intrinsic dispersion in absolute magnitudes, MB and MV, after correction for extinction by intervening interstellar dust in our Galaxy and the supernova parent galaxies, was estimated to be no more than 0.25m, which corresponds to a dispersion of only 13% in distance when SN Ia are used as standard candles. This luminosity homogeneity, together with the extremely high luminosity of SN Ia (~1010 LSun) that makes them detectable across the universe, make SN Ia extremely attractive as distance indicators for cosmology As distance indicators SNe Ia are invaluable. They provided the first evidence of an acceleration of the cosmic expansion and are currently the best objects to determine the dynamics of the universe. However, we need to understand these explosions better to raise confidence in the claims. The normalisations applied so far are entirely empirical and the different methods in use are not consistent with each other. Also, as long as we have the uncertainties on progenitor system, explosion mechanism and radiation transport, which ultimately provide the observable light, questions remain about the distances derived from supernovae beyond a redshift of about 0.2 SN Ia luminosity can depend on the metallicity (age) of early-type galaxy (J.Gallagher et al., ApJ V.685, P.752, 2008): from 29 galaxies SNe Dimmer in more metalrich (perhaps older) galaxies ΔM From J.Tonry et al. (ApJ V.594, P.1, 2003) Estimated apparent magnitudes at the maximum light for high-z SN Ia Extrapolated in () Accessible to observations with large telescopes G.Altavilla et al. “Cepheid calibration of Type Ia supernovae and the Hubble constant” (MNRAS V.349, P.1344, 2004) Cepheid distances to 9 SN Ia host galaxies Cepheids P-L relation was used, consistent with LMC distance ~50 kpc (m-M)0≈18.50m, in agreement with the HST Key Project Distances to 96 SN Ia have been calculated and local Hubble constant estimated as 68-74 km/s/Mpc G.Altavilla et al. (2004) List of SN Ia and Cepheid host galaxies (only 9!) used to calibrate SN Ia luminosities SN Ia zero-point under different assumptions lies in the range MB ≈ -19.60…-19.40m C.Ngeow & S.Kanbur “The Hubble Constant from Type Ia Supernova Calibrated with the Linear and Non-Linear Cepheid Period-Luminosity Relations” (ApJ V.642, P.29, 2006) Cepheid distances to 4 SN Ia host galaxies with 142 Cepheids in total Cepheid P-L (linear and nonlinear) have been used based on LMC Cepheids, with LMC distance also as (m-M)0≈18.50m Galaxies distances ~16 Mpc Supernovae for cosmology: state of art Estimating ΩM, ΩΛ and w (equation of state parameter) (ΩM = ΩB + ΩDM) (a) SN Ia Magnitude describes the expansion of light sphere with respect to comoving coordinates (b) SN Ia Redshift reflects the expansion of comoving coordinates Comparison of the apparent distance modulus with RedShift (z) can set the limits to the cosmological model and constants involved Hubble diagram for different pairs (ΩM,ΩΛ) Best-fit flat solution: (ΩM, ΩΛ) ≈ (0.28, 0.72) 0 0.2 0.4 0.6 0.8 1.0 z For the first time cosmological constant Λ have been estimated at high confidence level, giving rise to Dark Energy (or vacuum energy) with its unique property of universal repulsion (or antigravitation), in contrast to gravitational attraction known before Dark Energy became newest field of interest for cosmologists and cosmo-micro-physicists Now it turned clear that baryonic matter (ordinary matter) make only 4-5% of all energy density in the Universe, whereas Dark Energy greatly dominates Best-fit confidence regions (68%, 90%) Note that lines of constant Universe age are nearly parallel to contour lines: Age ~ 14.9 Gyr (for flat model) and the fate of the Universe Our future depends on how the Universe has expanded in the past SELESAI