What is the cepheid period luminosity relation

Similarly the Nardetto et al. The third relation uses the slope of the p -factor relation from Nardetto et al. The last column corresponds to the relation derived in Paper I which we have adopted here, which yields LMC Cepheid distance moduli which are totally independent of their pulsation period. This is borne out in Fig.

It is evident that with the adopted p -factor relation there is no significant correlation between pulsational period and derived distance to the LMC Cepheids. The best fitting line from the data is overplotted in black, and the best fitting line to the Milky Way sample of Paper I is overplotted with a dashed line in red.

Overplotted is the linear regression fit solid line as well as the corresponding Milky Way relation dashed line. In Table 6 the period-luminosity relations we obtain for the LMC in the different photometric bands are given in the form:. In the table the corresponding relations for the Milky Way sample determined in Paper I are given for comparison. These relations are based on Cepheid distances calculated with exactly the same precepts as in this paper, using the same p -factor relation and IRSB calibration so we can perform a direct comparison of the relations.

The dispersions of the Milky Way and LMC samples around the ridge line PL relations given in Table 6 are very similar for all the bands, and we note that there is not a big difference in the dispersion as a function of photometric band. The fact that the dispersion can be reduced so much by adopting a common distance to all the stars suggests that the observed dispersion in the PL relations is dominated by errors in the distance moduli rather than intrinsic dispersion in the luminosities or reddening errors and the standard error on the individual distance moduli is about 0.

Barnes et al. On average these errors should be multiplied by a factor of 3. In fact the error estimates for the distance moduli presented in Table 3 have a mean value of 0. The slopes of the relations are in excellent agreement in the case of the near-infrared J and K bands. Since the slopes of the PL relations for both LMC and Milky Way Cepheids are very well constrained from our samples, we conclude that our results present strong evidence that the slope of the Cepheid PL relation, particularly in the near-infrared J and K bands, is identical for the solar metallicity Milky Way and more metal-poor LMC samples.

The universality of the PL relation slopes appears to be confirmed in this metallicity range. Table 6 Period-luminosity relations for the LMC in the various optical and near-infrared bands as determined from a linear regression to the absolute magnitudes from the IRSB analysis. We can further extend the metallicity baseline by including the 5 SMC Cepheids in the sample. Given the low number of Cepheids and the narrow range of periods for these stars, we cannot constrain the slope of the PL relation at this metallicty, but we can constrain the zero point offset.

In Fig. Considering the excellent agreement between the LMC and the Milky Way from Table 6 this further supports the universality of the zero point of the K -band relation. We can quantify any offsets in the PL relation magnitude zero points as a function of metallicity by comparing the zero point offset for each of the three samples with the reference PL relations determined in Paper I on the basis of all available Cepheids. For each band and sample we computed the mean magnitude offsets, tabulated them in Table 7 and plotted them as a function of metallicity in Fig.

For each band we have fit the weighted least square regression line to the magnitude offset as a function of metallicity. The resulting metallicity effect slopes have been tabulated in Table 7. We estimate the error on the slopes to be of the order 0. From Fig. For extra-galactic distance determination most Cepheid samples will have metallicities in the range from LMC to solar and the zero-point offsets in this range is clearly very small in all the bands.

The full lines show the weighted linear regression fit to the data. It can be seen that especially in the limited but for extragalactic distance determination most important metallicity range from LMC to solar abundance, the zero point offsets are in general indistinguishable from zero. The only bands for which we have excellent agreement between the PL relation slopes are the J and K bands, and the zero-point offsets in both of these bands are small so they each form an excellent basis for a standard candle.

We note that we have assumed a simple linear metallicity dependence, but it is of course entirely possible that the dependence, if present, has a more complex functional form. We emphasize that the metallicity effect on both the slopes and zero points discussed here is entirely independent of the choice of the p -factor relation , whereas the absolute values of the slopes and zero points as well as the resulting LMC and SMC distances do depend on the adopted p -factor relation.

In the near-infrared we use the relations from Persson et al. In the optical we can compare to the relations from the OGLE project Udalski and we similarly find very good agreement. The fact that we reproduce the slopes of the PL relations in the LMC so well strongly supports our empirical calibration of the p -factor used with the IRSB method and confirms our earlier results Gieren et al. The LMC distance modulus of It is thus in good agreement with most recent results, as would be expected considering that we see Paper I have calibrated the IRSB method to match the distances to nine Milky Way Cepheids with direct parallaxes from Benedict et al.

Work is underway to determine the distance to this binary from orbital analysis. This result is in good agreement with the findings by Gieren et al. The reason for this difference was the inappropriate p -factor relation used in the earlier work for determining the Milky Way PL relations. Note that in the present work the choice of the p -factor relation has no bearing on the difference in slope between the Milky Way and LMC PL relations as we are now applying the method to both samples of Cepheids, this was not possible previously as the necessary data for the LMC stars was not yet available.

Sandage also argued that there is a significant difference in slope between the Milky Way and LMC PL relations in the optical bands, the Milky Way relation being steeper. As we show in Paper I the revised IRSB distances are, apart from a small zero point offset, in very good agreement with the latest results on open cluster Cepheids from Turner and does not exhibit a period dependence.

We do not support the conclusion of a strong effect of metallicity on the slope of optical V,I Cepheid PL relations as reached, for example, by Tammann et al. In Table 7 we summarized the PL relation zero point variation as a function of metallicity.

Clearly the effects in the near-IR are small and even in the V band the effect appears to be small, albeit with the opposite sign as for the other bands. This result is slightly at odds with the findings of Bono et al. At the same time we do agree with them that the PL relation slopes are less affected in the J and K -bands and more affected in the optical V and I bands and we also agree on the most likely sign of the effect namely that metal-rich PL relations are shallower than metal-poor ones.

Disregarding the subtle effects of differences in the slopes of the period-colour relations, these results are comparable to the offset of 0. The emerging conclusion based on our data and analysis is that for accurate distance measurements to galaxies the K -band Cepheid PL relation is the best suited tool: it is metallicity-independent both regarding the slope and the zero point, it is very insensitive to reddening, and it has a smaller intrinsic dispersion than any optical PL relation.

It is likely, as indicated in recent work from Spitzer data, that mid-infrared Cepheid PL relations are even superior to their near-infrared relations because of their even lower sensitivity to reddening, and lower intrinsic dispersions Madore et al. Yet, their dependence on metallicity has still to be investigated and they cannot be exploited from the ground making them exceedingly expensive to use. The IRSB analysis yields individual distances from which we calculate absolute magnitudes in optical and near-infrared bands.

These magnitudes define tight period-luminosity relations in the V,I,J,K bands and in the Wesenheit indices. If we restrict ourselves only to the metallicity range between solar and LMC, our results are consistent with universal PL relations in both slope and zero point in the near-infrared J and K bands. Masses for the T2Cs were estimated by Bono et al. In the case of ACs, pulsation models have been considered by various authors to find masses in the range 1.

Luminosities and effective temperatures were derived and are given in the Appendix in GJ The resulting Hertzsprung-Russell diagram was compared in a qualitative way to modern evolutionary tracks.

We confirmed the results of Kamath et al. The light curves of more than systems were investigated to look for the light-travel time LTT effect or light-time effect LITE Irwin in so-called observed minus calculated O—C diagrams. Twenty possible new binaries and about 40 stars that show a significant period change were identified.

Previous work concentrated almost exclusively on deriving the PL relation in the NIR bands or using the Wesenheit index; the main aim of this paper is to use the stellar luminosity as parameter and in that way study the properties of these stars in a more fundamental way. In addition, we derive estimates of the masses of these stars, based on theoretical pulsation models of RRL and CCs. In Sect. The most prominent outliers are indicated with their identifier. Table 1 , in addition, includes other, both observational and theoretical, determinations of the Wesenheit PL relation from the literature.

The Wesenheit PL relation does not seem to depend on metallicity. The derived relations are also in agreement with those listed in the literature, although this is not so surprising as they are all based on the same OGLE-III data and only differ in details. The agreement with theoretical models is good for the BLH. The comparison with observations requires an adopted distance to the LMC and an assumed metallicity for the models.

Some outliers are indicated with their identifier. Stars with an IR excess according to GJ17 are indicated by a green plus sign. Stars that show eclipsing or ellipsoidal variations according to OGLE are indicated by a blue cross. Table 1 Wesenheit and bolometric period-luminosity relations. Figure 2 shows the bolometric version of the PL relation, using the luminosities derived in GJ The bottom part of Table 1 gives the corresponding fits to the PL relation.

What is immediately noticeable is that the scatter in the bolometric PL relations is significantly larger than in the corresponding Wesenheit relations. There could be several reasons for this.

First, the Wesenheit relations are based on two intensity-mean magnitudes, while the luminosities are derived based on a fit to the entire SED that is based on non-contemporaneous photometry. Second, if there are issues related to blending or binarity then certain combinations of the parameters involved may still yield a Wesenheit index that is close to the mean relation, but the fitting of the entire SED more likely yields deviant results.

This source is not listed in the 1st Gaia data release Gaia Collaboration Time-series photometry in V, I is available from Berdnikov , from which we derived the mean magnitudes.

In Fig. Breitfelder et al. Pilecki et al. The derived radius and effective temperature Breitfelder et al. In fact, Matsunaga et al. Stars in the SMC are plotted in red. The error in M bol is smaller than the plot symbol. Some outliers are plotted with their identifier.

Figure 3 shows the PR relation based on the derived effective temperatures and luminosities in GJ The resulting radii with error bars are given in Table 3. Contrary to the PL relations, where the dusty RVT stars deviated significantly and were excluded, this is not the case here.

Table 2 Period-radius relations. Specifically they present period-mass-radius-metallicity PMRZ relations for fundamental and first-overtone pulsators their Eqs. We find 1 for FU pulsators, and 2 for FO pulsators. These relations are plotted in Fig. The theoretical relation lies above the observed relation. The slope agrees within the error bar with the observed relation for BLH see Table 2 , but the zero point is slightly larger.

The international team of astronomers discovered many new cepheids in the 18 galaxies they studied. In the giant spiral M81, for instance they found 32 Cepheids to add to only two that had been found previously using ground-based telescopes.

Using the HST they made 22 twenty-minute exposures of each of two fields in M 81containing the Cepheids. Once the data from these was reduced they were able to calculate a distance to M 81 of 3. This value was based on the results of the Cepheid studies which were then combined with other techniques such as observations of Type Ia supernovae, Type II supernovae, the Tully-Fisher relation and the surface brightness of galaxies.

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