Extragalactic Distance Determinations Research Articles

Exploring the Maximum Magnitude versus Rate of Decline Relation for Novae in M31

The results of a two-decade-long R-band photometric survey of novae in M31 are presented. From these data, R-band light curves have been determined for 180 novae with data sufficient for estimating the peak brightness and subsequent rate of decline. The data show a weak correlation of peak brightness with fade rate consistent with the well-known maximum magnitude versus rate of decline (MMRD) relation. As generally appreciated for Galactic novae, the large scatter in the MMRD relation precludes its use in determining distances to individual novae. The novae at maximum light are distributed with standard deviation σ = 0.89 mag about a mean R-band absolute magnitude given by 〈M R 〉 = −7.57 ± 0.07. The overall M31 luminosity distribution is in excellent agreement with that found for Galactic novae suggesting that the nova populations in M31 and the Galaxy are quite similar. The notion that all novae can be characterized by a standard luminosity 15 days after maximum light (M 15) is also explored. Surprisingly, the distribution of M 15 values is characterized by a standard deviation only slightly smaller than that for novae at maximum light and thus offers little promise for precise extragalactic distance determinations. A dozen faint and fast novae that are likely to be previously unidentified recurrent novae have been identified from their position in the MMRD plot and in the M 15 distribution.

A theoretical framework for BL Her stars. II. New period-luminosity relations in Gaia passbands

In the era of the Hubble tension, it is crucial to obtain a precise calibration of the period-luminosity ($PL$) relations of classical pulsators. Type II Cepheids (T2Cs; often exhibiting negligible or weak metallicity dependence on $PL$ relations) used in combination with RR Lyraes and the tip of the red giant branch may prove useful as an alternative to classical Cepheids for the determination of extragalactic distances. We present new theoretical $PL$ and period-Wesenheit ($PW$) relations for a fine grid of convective BL Her (the shortest period T2Cs) models computed using mesa-rsp in the $Gaia$ passbands and we compare our results with the empirical relations from $Gaia$ DR3. Our goal is to study the effect of metallicity and convection parameters on the theoretical $PL$ and $PW$ relations. We used the state-of-the-art 1D non-linear radial stellar pulsation tool mesa-rsp to compute models of BL Her stars over a wide range of input parameters:\ metallicity ($-2.0\; dex Fe/H dex $), stellar mass ($0.5M_ odot -0.8M_ odot $), stellar luminosity ($50L_ odot -300L_ odot $), and effective temperature (across the full extent of the instability strip; in steps of 50K). We used the Fourier decomposition technique to analyse the light curves obtained from mesa-rsp and $Gaia$ DR3 and then compared the theoretical and empirical $PL$ and $PW$ relations in the $Gaia$ passbands. The BL Her stars in the All Sky region exhibit statistically different $PL$ slopes compared to the theoretical $PL$ slopes computed using the four sets of convection parameters. We find the empirical $PL$ and $PW$ slopes from BL Her stars in the Magellanic Clouds to be statistically consistent with theoretical relations computed using the different convection parameter sets in the $Gaia$ passbands. There is a negligible effect coming from the metallicity on the $PL$ relations in the individual $Gaia$ passbands. However, there is a small but significant negative coefficient of metallicity in the $PWZ$ relations for the BL Her models using the four sets of convection parameters. This could be attributed to the increased sensitivity of bolometric corrections to metallicities at wavelengths shorter than the $V$ band. Our BL Her models also suggest a dependence of the mass-luminosity relation on metallicity. We found the observed Fourier parameter space to be covered well by our models. Higher mass models ($> 0.6\ odot $) may be needed to reliably model the observed light curves of BL Her stars in the All-Sky region. We also found the theoretical light curve structures (especially the Fourier amplitude parameters) to be affected by the choice of convection parameters.

Prospects for X-Ray and FUV Observations to Provide Insight Into the “Cepheid Mass Problem”

The classical Cepheid Leavitt Law (Period-Luminosity relation) has been known for 100 years, and used as in extragalactic distance determination for nearly as long. However, Cepheids still present us with surprises. Recent results about X-ray behavior is just one example. Around minimum radius the pulsation wave from the envelope creates a disruption in the photosphere and chromosphere. X-ray activity, on the other hand remains constant at a low level at this phase. Just after maximum radius, however, X-ray flux increases sharply (four fold in the case of $\delta$ Cep). We summarize here the observational program to explore parameters involved and theoretical investigations searching for a basic understanding of this upper atmosphere phenomena.

Impact of binary interaction on the evolution of blue supergiants

A large fraction of massive stars evolve in interacting binary systems, which dramatically modifies the outcome of stellar evolution. We investigated the properties of blue supergiants in binary systems and whether they are suitable for extragalactic distance determinations using the flux-weighted gravity luminosity relationship (FGLR). This is a relationship between the absolute bolometric magnitude Mbol and the spectroscopically determined flux-weighted gravity gF = g/T4eff, where g is the surface gravity and Teff is the effective temperature. We computed a grid of binary stellar evolution models with MESA and use the v2.1 BPASS models to examine whether they are compatible with the relatively small scatter shown by the observed relationship. Our models have initial primary masses of 9–30 M⊙, initial orbital periods of 10–2511 days, mass ratio q = 0.9, and metallicity Z = 0.02. We find that the majority of primary stars that produce blue supergiant stages are consistent with the observed FGLR, with a small offset towards brighter bolometric magnitudes. In between 1%–24% of cases, binary evolution may produce blue supergiants after a mass transfer episode, that lie below the observed FGLR. A very small number of such stars have been found in extragalactic FGLR studies, suggesting that they may have evolved through binary interaction. Some models with shorter periods could resemble blue hypergiants and luminous blue variables. We used CMFGEN radiative transfer models to investigate the effects of unresolved secondaries on diagnostics for Teff and g, and the biases on the determination of interstellar reddening and Mbol. We find that the effects are small and within the observed scatter, but could lead to a small overestimate of the luminosity, of Teff and of g for extreme cases. We conclude that the observed FGLR can, in principle, be well reproduced by close binary evolution models. We outline directions for future work, including rotation and binary population synthesis techniques.

Thermonuclear supernovae and cosmology⋆

Bright and homogeneous, thermonuclear, or type Ia, supernovae (SNeIa) are our best extragalactic distance indicators. Since the 60s, SNeIa have been used as cosmological tools, initially, to estimate the current expansion rate of the Universe, the Hubble constant. Decades ago SNeIa were discovered by chance, in many cases by amateurs. Advances in the instrumentation, techniques and new observational strategies allowed in the 80s to discover SNe in scheduled surveys. Moreover, through calibration relations, a high precision in extragalactic distance determinations was achieved, allowing SNIa observations to reveal the dynamics of the Universe. The Nobel prize in Physics in 2011 was awarded to the leaders of two independent teams “for the discovery of the accelerating expansion of the Universe through observations of distant supernovae”. This is a brief and incomplete story of SNeIa as cosmological tools. In the Madrasah of Granada (Spain), built in 1349 by the Nasrid monarch Yosuf the 1st, Astronomy was one of the disciplines included in the studies. On the Madrasah walls, a calligraphic decoration reads: “make study shine like stars”. It is a good motto for our 4th Azarquiel School of Astronomy.

LMC Blue Supergiant Stars and the Calibration of the Flux-weighted Gravity–Luminosity Relationship

Abstract High-quality spectra of 90 blue supergiant stars in the Large Magellanic Cloud are analyzed with respect to effective temperature, gravity, metallicity, reddening, extinction, and extinction law. An average metallicity, based on Fe and Mg abundances, relative to the Sun of [Z] = −0.35 ± 0.09 dex is obtained. The reddening distribution peaks at = 0.08 mag, but significantly larger values are also encountered. A wide distribution of the ratio of extinction to reddening is found ranging from = 2 to 6. The results are used to investigate the blue supergiant relationship between flux-weighted gravity, g f ≡ g/ , and absolute bolometric magnitude M bol. The existence of a tight relationship, the Flux-weighted Gravity–Luminosity Relationship (FGLR), is confirmed. However, in contrast to previous work, the observations reveal that the FGLR is divided into two parts with a different slope. For flux-weighted gravities larger than 1.30 dex, the slope is similar to that found in previous work, but the relationship becomes significantly steeper for smaller values of the flux-weighted gravity. A new calibration of the FGLR for extragalactic distance determinations is provided.

Distances to galaxies from the brightest stars in the Universe

Blue Supergiants (BSGs) are the brightest stars in the universe at visual light with absolute magnitudes up to M V =−10 mag. They are ideal stellar objects for the determination of extragalactic distances, in particular, because the perennial uncertainties troubling most of the other stellar distance indicators, interstellar extinction and metallicity, do not affect them. The quantitative spectral analysis of low resolution spectra of individual BSGs provides accurate stellar parameters and chemical composition, which are then used to determine accurate reddening and extinction from photometry for each individual object. Accurate distances can be determined from stellar gravities and effective temperatures using the “Flux Weighted Gravity–Luminosity Relationship (FGLR)”.Most recent results of the quantitative spectral analysis of BSGs in galaxies within and beyond the Local Group based on medium and low resolution spectra obtained with the ESO VLT and the Keck telescopes on Mauna Kea are presented and distances obtained with the FGLR-method are discussed together with the effects of patchy extinction and abundance gradients in galaxies. BSG metallicities and metallicity gradients are compared with results from strong-line H ii region studies and the consequences for the empirical calibration of the metallicity dependence of the Cepheid period–luminosity relationship are pointed out. The perspectives of future work are discussed, the use of the giant ground-based telescopes of the next generation such as the TMT on Mauna Kea and the E-ELT and the tremendous value of the GAIA mission to allow for the ultimate calibration of the FGLR using galactic BSGs.

Calibrating the Cepheid period-luminosity relation from the infrared surface brightness technique

We determine Period-Luminosity relations for Milky Way Cepheids in the optical and near-IR bands. These relations can be used directly as reference for extra-galactic distance determination to Cepheid populations with solar metallicity, and they form the basis for a direct comparison with relations obtained in exactly the same manner for stars in the Magellanic Clouds, presented in an accompanying paper. In that paper we show that the metallicity effect is very small and consistent with a null effect, particularly in the near-IR bands, and we combine here all 111 Cepheids from the Milky Way, the LMC and SMC to form a best relation. We employ the near-IR surface brightness (IRSB) method to determine direct distances to the individual Cepheids after we have recalibrated the projection factor using the recent parallax measurements to ten Galactic Cepheids and the constraint that Cepheid distances to the LMC should be independent of pulsation period. We confirm our earlier finding that the projection factor for converting radial velocity to pulsational velocity depends quite steeply on pulsation period, p=1.550-0.186*log(P) in disagrement with recent theoretical predictions. We delineate the Cepheid PL relation using 111 Cepheids with direct distances from the IRSB analysis. The relations are by construction in agreement with the recent HST parallax distances to Cepheids and slopes are in excellent agreement with the slopes of apparent magnitudes versus period observed in the LMC.

CONCERNING THE SLOPE OF THE CEPHEID PERIOD-LUMINOSITY RELATION

We discuss the impact of possible differences in the slope of the Cepheid Period-Luminosity relation on the determination of extragalactic distances in the context of recent studies that suggest changes in this slope. We show that the Wesenheit function W = V - R x ((V-I), widely used for the determination of Cepheid distances, is expected to be highly insensitive to changes in the slope of the underlying (monochromatic) Period-Luminosity (PL) relations. This occurs because the reddening trajectories in the color-magnitude plane are closely parallel to lines of constant period. As a result W-based Period-Luminosity relations have extremely low residual dispersion, which is because differential (and total line-of-sight) reddening is eliminated in the definition of W and the residual scatter due to a star's intrinsic color/position within the Cepheid is also largely insensitive to W. Basic equations are presented and graphically illustrated, showing the insensitivity of W to changes in the monochromatic PL relations.

On a systematic bias in surface brightness fluctuations based distances due to gravitational microlensing

The effect of gravitational microlensing on the determination of extragalactic distances using the surface brightness fluctuations (SBF) technique is considered and a method to calculate SBF amplitudes in the presence of microlensing is presented. With a simple approximation for the magnification power spectrum at low optical depth, the correction to the SBF-based luminosity distance is calculated. The results suggest the effect can be safely neglected at present but may become important for SBF-based Hubble diagrams at luminosity distances of about 1 Gpc and beyond.

Kinematic Evidence for Different Planetary Nebula Populations in the Elliptical Galaxy NGC 4697

We have analyzed the magnitudes, kinematics, and positions of a complete sample of 320 planetary nebulae (PNs) in the elliptical galaxy NGC 4697. We show the following. (1) The PNs in NGC 4697 do not constitute a single population that is a fair tracer of the distribution of all stars. The radial velocity distributions, mean velocities, and dispersions of bright and faint subsamples differ with high statistical confidence. (2) Using the combined data for PNs brighter than 26.2, we have identified a subpopulation of PNs that is azimuthally unmixed and kinematically peculiar, and thus neither traces the distribution of all stars nor can be in dynamical equilibrium with the galaxy potential. (3) The planetary nebula luminosity functions (PNLFs) of two kinematic subsamples in NGC 4697 differ with 99.7% confidence, ruling out a universal PNLF. We estimate that the inferred secondary PN population introduces an uncertainty in the bright cutoff magnitude of ∼0.15 mag for this galaxy. We argue that this secondary PN distribution may be associated with a younger, ≳1 Gyr old stellar population, perhaps formed in tidal structures that have now fallen back onto the galaxy, as has previously been suggested for the X-ray point sources in this galaxy, or coming from a more recent merger/accretion with a red galaxy. The use of PNs for extragalactic distance determinations is not necessarily compromised, but their use as dynamical tracers of dark halos will require deep observations and careful analysis of large PN samples.

RR Lyrae-based calibration of the Globular Cluster Luminosity Function

We test whether the peak absolute magnitude Mv(TO) of the Globular Cluster Luminosity Function (GCLF) can be used for reliable extragalactic distance determinations. Starting with the luminosity function of the Galactic Globular Clusters listed in Harris catalog, we determine Mv(TO) either using current calibrations of the absolute magnitude Mv(RR) of RR Lyrae stars as a function of the cluster metal content [Fe/H] and adopting selected cluster samples. We show that the peak magnitude is slightly affected by the adopted Mv(RR)-[Fe/H] relation, while it depends on the criteria to select the cluster sample. As for the GCLFs in other external galaxies, using Surface Brightness Fluctuations (SBF) measurements we give evidence that the luminosity functions of the blue (metal-poor) Globular Clusters peak at the same luminosity within ~0.2 mag, whereas for the red (metal-rich) samples the agreement is within ~0.5 mag even accounting for the theoretical metallicity correction expected for clusters with similar ages and mass distributions. Then, using the SBF absolute magnitudes provided by a Cepheid distance scale calibrated on a fiducial distance to LMC (m(LMC)=18.50 mag), we show that the Mv(TO) value of the metal-poor clusters in external galaxies(-7.67+/-0.23 mag) is in excellent agreement with the value of both Galactic (-7.66+/-0.11 mag) and M31 (-7.65+/-0.19 mag)ones.

A New Extragalactic Distance Determination Method Using the Flux-weighted Gravity of Late B and Early A Supergiants

Stellar evolution calculations predict the flux-weighted gravity g/Teff^4 and absolute bolometric magnitude of blue supergiants to be strongly correlated. We use medium resolution multi-object spectroscopy of late B and early A supergiants in two spiral galaxies, NGC 300 and NGC 3621, to demonstrate the existence of such a relationship, which proves to be surprisingly tight. An analysis of high resolution spectra of blue supergiants in Local Group galaxies confirms this detection. We discuss the application of the relationship for extragalactic distance determinations and conservatively conclude that once properly calibrated it has the potential to allow for measurements of distance moduli out to 30.5 mag with an accuracy of 0.1 mag or better.

Long‐Baseline Interferometric Observations of Cepheids

We present observations of the Galactic Cepheids η Aql and ζ Gem. Our observations are able to resolve the diameter changes associated with pulsation. This allows us to determine the distance to the Cepheids independent of photometric observations. We determine a distance to η Aql of 320 ± 32 pc and a distance to ζ Gem of 362 ± 38 pc. These observations allow us to calibrate surface brightness relations for use in extragalactic distance determination. They also provide a measurement of the mean diameter of these Cepheids, which is useful in constructing structural models of this class of star.

The Wind Momentum – Luminosity Relationship of Blue Supergiants

AbstractThe prediction of the Wind Momentum - Luminosity Relationship (WLR) based on the theory of radiation driven winds is verified by quantitative spectroscopy of winds of A-, B- and O-supergiants. The relationship depends on spectral type. New stellar wind calculations are presented reproducing the observed spectral type dependence. The impact of spectral variability on the WLR is investigated by an analysis of some hundred spectra of the luminous A0Ia-supergiant HD92207 obtained within the Heidelberg Spectral Variability Survey and found to be small.Finally, the WLR is discussed as a tool for the determination of extragalactic distances. Recent results obtained for the Galaxy, M31 and M33 are presented. The potential of the method is discussed with the conclusion that it may allow independent distance moduli to be obtained with an accuracy of ten percent out to the Virgo and Fornax clusters of galaxies.

The Hubble Space Telescope Key Project to Measure the Hubble Constant

A Joint Discussion on the extragalactic distance scale and the Hubble constant took place fifteen years ago, at the 1982 XVIIIth General Assembly of the IAU, held in Patras, Greece. At that time, the newest applications of infrared photometers to Tully-Fisher measurements (Aaronson 1983) and Cepheid distances (Madore 1983) were reported. CCDs were just coming into use and had not yet been applied to extragalactic distance determinations; all of the extragalactic Cepheid distances were based on photographic Argelander (eye-estimated) photometry (Tammann and Sandage 1983 and references therein). No Cepheid distances to type Ia supernova-host galaxies were available.

Mass‐Loss Rates and Stellar Wind Momenta of A‐Supergiants in M31: First Results from the Keck HIRES Spectrograph

High-quality Keck HIRES echelle spectra of two A-supergiants in M31, designated 41-3654 (spectral type A2 Ia-O) and 41-3712 (A3 Ia-O), at 10.2 kpc galactocentric distance are analyzed by means of NLTE unified model atmospheres to determine the properties of their stellar winds, in particular the wind momenta. We obtain mass-loss rates of 1.9 × 10-6 and 1.1 × 10-6 M☉ yr-1 for 41-3654 and 41-3712, respectively, with an accuracy of 15% from the fit of the Hα profiles. The terminal velocities are 200 ± 25 km s-1. In addition, the exponents of the wind velocity fields are determined (β = 2 and 3, respectively) and microturbulent velocities of the order of 20 km s-1 are found. The wind momenta of the two targets are in excellent agreement with the wind momentum-luminosity relation (WLR) for galactic A- and B-supergiants. We discuss the potential of the WLR for extragalactic distance determinations and conclude that it may allow independent distance moduli to be obtained with an accuracy of 10%.

The Planetary Nebula Luminosity Function (PNLF) of Our Galaxy Compared to those of other Galaxies

Nowadays it is possible to detect planetary nebulae, and measure their [O III] λ5007 fluxes, in many galaxies. Given this information it is relatively straightforward to build the [O III] λ5007 PNLF for any galaxy, because we can always assume all its PNs to be essentially at the same distance from us.Of course the situation is much more difficult for PNs in the solar neighborhood. We have two problems here: (1) the individual PN distances are poorly known, except for ∼ 25 objects; (2) in the literature there is no agreement on which are the 25 PNs with reliable distances. Clearly it was a wise decision to calibrate the PNLF method of extragalactic distance determinations using the distance to M 31 (Ciardullo et al. 1989, Jacoby et al. 1992). In these short notes I review if it may be possible to build a PNLF for our Galaxy (the answer is: yes, probably more than one) and discuss if it would be worth the trouble (the answer is: yes, it would) and what can be done to achieve that elusive goal.

Model atmospheres for SNe II during early stages

The photospheres of type II supernovae during the coasting phase ( ~ 1 week to 1 month after outburst) are characterized by moderate temperatures (Teff ~ 7...12 × 10^3K) , large radii (R ~ 10^13...10^15cm) , very low densities (p ~ 10^-13... 10^-16 gcm-3) and high expansions velocities (up to ~ 30000 km-1 in the outer layers). These properties lead to large geometrical extensions (i.e. the photons can travel a large fraction of the radius without being absorbed) and to electron scattering as the main source of opacity. Therefore these photospheres are very different from those of stars in hydrostatic equilibrium. In this review we first describe the input physics for models and essential numerical aspects of the model construction. In particular we stress the central role of an adequate treatment of the radiative transfer equation which should simultaneously take into account the sphericity, a high ratio of scattering to absorption, and relativistic effects. Subsequently we discuss details of the emergent spectra and their relevance for parameter determinations. Finally, model spectra are compared with observations of the bright supernovae SN 1979C and SN 1980 K, which seem to be more average examples of type II supernovae than SN 1987A, and possibilities for using these objects for extragalactic distance determinations are investigated.

BRIGHT LONG-PERIOD VARIABLES IN THE DIRECTION OF THE MAGELLANIC CLOUDS : FOREGROUND STARS OR SUPERGIANTS ?

ABSTRACT Radial velocities and infrared photometry have been obtained for seven bright long-period variables in the direction of the Magellanic Clouds. Five stars with periods shorter than 250 days were found to be Cloud members. They are probably core-helium burning supergiants of about 15 times the solar mass; there is also a possibility that they are overtone pulsators on the upper asymptotic branch with masses in the 7-9 solar mass range. It had previously been suggested that the bright short-period (100-250 days) LPVs might be foreground Mira variables of low mass in the Galactic halo. The supergiant long-period variables in the Magellanic Clouds exhibit a distinct period-luminosity relation which should be useful for the purpose of extra-Galactic distance determination.