Black Hole Mass Determination Research Articles

Orientation and quasar black hole mass estimation

We have constructed a sample of 386 radio-loud quasars with z < 0.75 from the Sloan Digital Sky Survey in order to investigate orientation effects on black hole mass estimates. Orientation is estimated using radio core dominance measurements based on FIRST survey maps. Black hole masses are estimated from virial-based scaling relationships using H-beta, and compared to the stellar velocity dispersion (sigma_*), predicted using the Full Width at Half Maximum (FWHM) of [O III] 5007, which tracks mass via the M-sigma_* relation. We find that the FWHM of Hbeta correlates significantly with radio core dominance and biases black hole mass determinations that use it, but that this is not the case for sigma_* based on [O III] 5007. The ratio of black hole masses predicted using orientation-biased and unbiased estimates, which can be determined for radio-quiet as well as radio-loud quasars, is significantly correlated with radio core dominance. Although there is significant scatter, this mass ratio calculated in this way may in fact serve as an orientation estimator. We additionally note the existence of a small population radio core-dominated quasars with extremely broad H-beta emission lines that we hypothesise may represent recent black hole mergers.

Constraints on the broad line region from regularized linear inversion: velocity–delay maps for five nearby active galactic nuclei

Reverberation mapping probes the structure of the broad emission-line region (BLR) in active galactic nuclei (AGN). The kinematics of the BLR gas can be used to measure the mass of the central supermassive black hole. The main uncertainty affecting black hole mass determinations is the structure of the BLR. We present a new method for reverberation mapping based on regularized linear inversion (RLI) that includes modelling of the AGN continuum light curves. This enables fast calculation of velocity-resolved response maps to constrain BLR structure. RLI allows for negative response, such as when some areas of the BLR respond in inverse proportion to a change in ionizing continuum luminosity. We present time delays, integrated response functions, and velocity-delay maps for the $\rm{H}\,\beta$ broad emission line in five nearby AGN, as well as for $\rm{H}\,\alpha$ and $\rm{H}\,\gamma$ in Arp 151, using data from the Lick AGN Monitoring Project 2008. We find indications of prompt response in three of the objects (Arp 151, NGC 5548 and SBS 1116+583A) with additional prompt response in the red wing of $\rm{H}\,\beta$. In SBS 1116+583A we find evidence for a multimodal broad prompt response followed by a second narrow response at 10 days. We find no clear indications of negative response. The results are complementary to, and consistent with, other methods such as cross correlation, maximum entropy and dynamical modelling. Regularized linear inversion with continuum light curve modelling provides a fast, complementary method for velocity-resolved reverberation mapping and is suitable for use on large datasets.

The AGN Black Hole Mass Database

The AGN Black Hole Mass Database is a compilation of all published spectroscopic reverberation-mapping studies of active galaxies. We have created a public Web interface where users may get the most up-to-date black hole masses from reverberation mapping for any particular active galactic nucleus (AGN), as well as obtain the individual measurements upon which the masses are based and the appropriate references. While the database currently focuses on the measurements necessary for black hole mass determinations, we also plan to expand it in the future to include additional useful information, such as host-galaxy characteristics. New reverberation mapping results will also be incorporated into the database as they are published in peer-refereed journals.

THE MASS OF THE CENTRAL BLACK HOLE IN THE NEARBY SEYFERT GALAXY NGC 5273

We present the results of a reverberation-mapping program targeting NGC5273, a nearby early-type galaxy with a broad-lined active galactic nucleus. Over the course of the monitoring program, NGC5273 showed strong variability that allowed us to measure time delays in the responses of the broad optical recombination lines to changes in the continuum flux. A weighted average of these measurements results in a black hole mass determination of $M_{\rm BH} = (4.7 \pm 1.6) \times 10^6$ M$_{\odot}$. An estimate of the size of the black hole sphere of influence in NGC5273 puts it just at the limit of the resolution achievable with current ground-based large aperture telescopes. NGC5273 is therefore an important future target for a black hole mass determination from stellar dynamical modeling, especially because it is the only nearby early-type galaxy hosting an AGN with a reverberation-based mass, allowing the best comparison for the masses determined from these two techniques.

Constraining black hole masses in low-accreting active galactic nuclei using X-ray spectra

In a recent work we demonstrated that a novel X-ray scaling method, originally introduced for Galactic black holes (GBHs), can be reliably extended to estimate the mass of supermassive black holes accreting at a moderate to high level. Here we investigate the limits of applicability of this method to low-accreting active galactic nuclei, using a control sample with good-quality X-ray data and dynamically measured mass. For low-accreting AGNs, because the basic assumption that the photon index positively correlates with the accretion rate no longer holds the X-ray scaling method cannot be used. Nevertheless, the inverse correlation in the Gamma-Lx/LEdd diagram, found in several low-accreting black holes and confirmed by this sample, can be used to constrain black hole mass within a factor of ~10 from the dynamically determined values. We provide a simple recipe to determine black hole mass using solely X-ray spectral data, which can be used as a sanity check for black hole mass determination based on indirect optical methods.

BLACK HOLE MASS DETERMINATION IN THE X-RAY BINARY 4U 1630-47: SCALING OF SPECTRAL AND VARIABILITY CHARACTERISTICS

We present the results of a comprehensive investigation on the evolution of spectral and timing properties of the Galactic black hole candidate 4U 1630--47 during its spectral transitions. In particular, we show how a scaling of the correlation of the photon index of the Comptonized spectral component Gamma with low frequency of quasi-periodic oscillations (QPO), nu_L and mass accretion rate, $\dot M$ can be applied to the black hole mass and the inclination angle estimates. We analyze the transition episodes observed with the {\it Rossi} X-ray Timing Explorer (RXTE) and BeppoSAX satellites. We find that the broadband X-ray energy spectra of 4U~1630--47 during all spectral states can be modeled by a combination of a thermal component, a Comptonized component and a red-skewed iron line component. We also establish that Gamma monotonically increases during transition from the low-hard state to the high-soft state and then saturates for high mass accretion rates. The index saturation levels vary for different transition episodes. Correlations of Gamma versus nu_L also shows saturation at Gamma ~ 3. Gamma-Mdot and Gamma-nu_L correlations with their index saturation revealed in 4U~1630--47 are similar to those established in a number of other BHCs and can be considered as an observational evidence for the presence of a black hole in these sources. The scaling technique, which relies on XTE J1550--564, GRO 1655-40 and H 1743-322 as reference sources, allows us to evaluate a black hole mass in 4U~1630--47 yielding M_{BH}~10+/- 0.1 solar masses, and to constrain the inclination angle of i< 70 degrees.

Analysis of X-ray spectral variability and black hole mass determination of the NLS1 galaxy Mrk 766

We present an XMM-Newton time-resolved spectral analysis of the NLS1 galaxy Mrk 766. We analyse eight available observations of the EPIC-pn camera taken between May 2000 and June 2005 to investigate the X-ray spectral variability as produced by changes in the mass accretion rate. The 0.2-10 keV spectra are extracted in time bins longer than 3 ks to accurately trace the variations of the best fit parameters of our adopted Comptonisation spectral model. We test a bulk-motion Comptonisation (BMC) model which is in general applicable to any physical system powered by accretion onto a compact object, and assumes that soft seed photons are efficiently up-scattered via inverse Compton scattering in a hot and dense electron corona. The Comptonised spectrum has a characteristic power-law shape, whose slope was found to increase for large values of the normalisation of the seed component, that is proportional to the mass accretion rate (in Eddington units). Our baseline spectral model also includes a warm absorber lying on the line of sight and radiation reprocessing from the accretion disk or from outflowing matter in proximity of the central compact object. Our study reveals that the normalisation-slope correlation, observed in Galactic Black Hole sources (GBHs), also holds for Mrk 766: variations of the photon index in the range Gamma~1.9-2.4 are indeed likely to be related to the variations of m-dot, as observed in X-ray binary systems. We finally applied a scaling technique based on the observed correlation to estimate the BH mass in Mrk 766. This technique is commonly and successfully applied to measure masses of GBHs, and this is the first time it is applied in detail to estimate the BH mass in an AGN. We obtain a value of M_{BH}=1.26^{+1.00}_{-0.77}x10^6 M_{sun} that is in very good agreement with that estimated by the reverberation mapping

Elliptical galaxies with rapidly decreasing velocity dispersion profiles: nmagic models and dark halo parameter estimates for NGC 4494

NGC 4494 is one of several intermediate-luminosity elliptical galaxies inferred to have an unusually diffuse dark matter halo. We use the chi^2-made-to-measure particle code NMAGIC to construct axisymmetric models of NGC 4494 from photometric and various kinematic data. The extended kinematics include light spectra in multiple slitlets out to 3.5 R_e, and hundreds of planetary nebulae velocities out to ~7 R_e, thus allowing us to probe the dark matter content and orbital structure in the halo. We use Monte Carlo simulations to estimate confidence boundaries for the halo parameters, given our data and modelling set-up. We find that the true potential of the dark matter halo is recovered within Delta G (merit function)<26 (Delta chi^2<59) at 70% confidence level (C.L.), and within Delta G<32 (Delta chi^2<70) at 90% C.L.. These numbers are much larger than the usually assumed Delta chi^2=2.3 (4.6) for 70% (90%) C.L. for two free parameters, perhaps case-dependent, but calling into question the general validity of the standard assumptions used for halo and black hole mass determinations. The best-fitting models for NGC 4494 have a dark matter fraction of about 0.6\pm0.1 at 5R_e (70% C.L.), and are embedded in a dark matter halo with circular velocity ~200 km/s. The total circular velocity curve (CVC) is approximately flat at v_c=220 km/s outside ~0.5R_e. The orbital anisotropy of the stars is moderately radial. These results are independent of the assumed inclination of the galaxy, and edge-on models are preferred. Comparing with the halos of NGC 3379 and NGC 4697, whose velocity dispersion profiles also decrease rapidly from the center outwards, the outer CVCs and dark matter halos are quite similar. NGC 4494 shows a particularly high dark matter fraction inside ~3R_e, and a strong concentration of baryons in the center.

Short time-scale AGN X-ray variability with EXOSAT: black hole mass and normalized variability amplitude

Abstract The old EXOSAT medium energy measurements of high-frequency (HF) active galactic nuclei (AGN) power spectral normalization are re-examined in the light of accurate black hole mass determinations which were not available when these data were first published by Green et al. It is found that the normalized variability amplitude (NVA), measured directly from the power spectrum, is proportional to Mβ, where β ∼ −0.54 ± 0.08. As NVA is the square root of the power, these observations show that the normalization of the HF power spectrum for this sample of AGN varies very close to inversely with black hole mass. Almost the same value of β is obtained whether the quasar 3C 273 is included in the sample or not, suggesting that the same process that drives X-ray variability in Seyfert galaxies applies also to 3C 273. These observations support the work of Gierliński et al. who show that an almost exactly linear anticorrelation is required if the normalizations of the HF power spectra of AGN and X-ray binary systems are to scale similarly. These observations are also consistent with a number of studies showing that the short time-scale variance of AGN X-ray light curves varies approximately inversely with mass.

Supermassive Black Holes and Their Relationships with Their Host Galaxies

We review how the masses of black holes in active galactic nuclei are measured and outline the current limitations and uncertainties. Masses have been measured directly by emission-line reverberation for nearly 50 relatively nearby AGNs, but uncertainties due to the unknown geometry and projection effects limit the accuracy of these masses to ∼ 0.3 dex. Reverberation studies show that there is a very tight relationship between the broad-line region radius and the AGN luminosity, with an intrinsic scatter of ∼ 0.1 dex, which shows (1) that the largest source of systematic uncertainty in the black hole mass determinations is how the velocity field of the broad-line region is characterized, not the size of the broad-line region, and (2) that the size of the broad-line region can be estimated to fairly high accuracy from the AGN luminosity alone, thus providing a powerful indirect method of estimating black hole masses in even distant AGNs.

IS THERE A BLACK HOLE IN NGC 4382?

We present HST STIS observations of the galaxy NGC 4382 (M85) and axisymmetric models of the galaxy to determine mass-to-light ration (M/L, V-band) and central black hole mass (M_BH). We find M/L = 3.74 +/- 0.1 (solar units) and M_BH = 1.3 (+5.2, -1.2) \times 10^7 M_sun at an assumed distance of 17.9 Mpc, consistent with no black hole. The upper limit, M_BH < 9.6 \times 10^7 M_sun (2{\sigma}) or M_BH < 1.4 \times 10^8 M_sun (3{\sigma}) is consistent with the current M-{\sigma} relation, which predicts M_BH = 8.8 \times 10^7 M_sun at {\sigma}_e = 182 km/s, but low for the current M-L relation, which predicts M_BH = 7.8 \times 10^8 M_sun at L_V = 8.9 \times 10^10 L_sun,V. HST images show the nucleus to be double, suggesting the presence of a nuclear eccentric stellar disk, in analogy to the Tremaine disk in M31. This conclusion is supported by the HST velocity dispersion profile. Despite the presence of this non-axisymmetric feature and evidence of a recent merger, we conclude that the reliability of our black hole mass determination is not hindered. The inferred low black hole mass may explain the lack of nuclear activity.

THE LICK AGN MONITORING PROJECT: THEMBH-σ*RELATION FOR REVERBERATION-MAPPED ACTIVE GALAXIES

(Abridged) To investigate the black hole mass (MBH) vs. stellar velocity dispersion relation of active galaxies, we measured the velocity dispersions of a sample of local Seyfert 1 galaxies, for which we have recently determined MBH using reverberation mapping. For most objects, velocity dispersions were measured from high S/N ratio optical spectra centered on the Ca II triplet region (~8500 A), obtained at the Keck, Palomar, and Lick Observatories. For two objects, in which the Ca II triplet region was contaminated by nuclear emission, the measurement was based on high-quality H-band spectra obtained with the OSIRIS at the Keck-II Telescope. Combining our new measurements with data from the literature, we assemble a sample of 24 active galaxies with stellar velocity dispersions and reverberation-based MBH measurements in the range of black hole mass 10^6<MBH/M_sun<10^9. We use this sample to obtain reverberation mapping constraints on the slope and intrinsic scatter of the M-sigma relation of active galaxies. Assuming a constant virial coefficient f for the reverberation mapping black hole masses, we find a slope b=3.55+-0.60 and the intrinsic scatter sigma_int=0.43+-0.08 dex in the relation log (MBH/M_sun) = a + b log (sigma/200 km/s), which are consistent with those found for quiescent galaxies. We derive an updated value of the virial coefficient f by finding the value which places the reverberation masses in best agreement with the M-sigma relation of quiescent galaxies; using the quiescent M-sigma relation determined by Gultekin et al. we find log f=0.72^{+0.09-0.10} with an intrinsic scatter of 0.44+-0.07 dex. The uncertainty of the virial coefficient remains one of the main sources of the uncertainty in black hole mass determinations using reverberation mapping, and therefore also in single-epoch spectroscopic estimates of MBH in active galaxies.

DETERMINATION OF BLACK HOLE MASSES IN GALACTIC BLACK HOLE BINARIES USING SCALING OF SPECTRAL AND VARIABILITY CHARACTERISTICS

We present a study of correlations between X-ray spectral and timing properties observed from a number of Galactic Black Hole (BH) binaries during hard-soft state spectral evolution. We analyze 17 transition episodes from 8 BH sources observed with RXTE. Our scaling technique for BH mass determination uses a correlation between spectral index and quasi-periodic oscillation (QPO) frequency. In addition, we use a correlation between index and the normalization of the disk "seed" component to cross-check the BH mass determination and estimate the distance to the source. While the index-QPO correlations for two given sources contain information on the ratio of the BH masses in those sources, the index-normalization correlations depend on the ratio of the BH masses and the distance square ratio. In fact, the index-normalization correlation also discloses the index-mass accretion rate saturation effect given that the normalization of disk "seed" photon supply is proportional to the disk mass accretion rate. We present arguments that this observationally established index saturation effect is a signature of the bulk motion (converging) flow onto black hole which was early predicted by the dynamical Comptonization theory. We use GRO J1655-40 as a primary reference source for which the BH mass, distance and inclination angle are evaluated by dynamical measurements with unprecedented precision among other Galactic BH sources. We apply our scaling technique to determine BH masses and distances forCygnus X-1, GX 339-4, 4U 1543-47, XTE J1550-564, XTE J1650-500, H 1743-322 and XTE J1859-226. Good agreement of our results for sources with known values of BH masses and distance provides an independent verification for our scaling technique.

RADIATION PRESSURE FORCE AND BLACK HOLE MASS DETERMINATION IN LOW-REDSHIFT TYPE-I AND TYPE-II ACTIVE GALACTIC NUCLEI

The distributions of L(oiii 5007), black hole (BH) mass and L/L(Edd) in two large samples of type-I and type-II active galactic nuclei (AGNs) are compared in order to test the suggestion that radiation pressure force is affecting the gas velocity in the broad line region and hence the BH mass determination. The samples are drawn from the SDSS archive and are modified to represent the same parent distribution at 0.1 < z < 0.2. BH masses in type-I sources are calculated in two different ways, one using a simple virial mass assumption and the other by taking into account the effect of radiation pressure force on the gas. The simple virial mass estimate results in good agreement with the sigma*-based BH mass and L/L(Edd) estimates in type-II sources. In contrast, there is a clear disagreement in the L/L(Edd) distributions when radiation pressure-based estimates are used. This indicates that radiation pressure force is not important in 0.1 < z < 0.2 AGNs with L(5100)=10^{42.8-44.8} erg/s. This has important implications to the physics of the gas producing the broad emission lines in AGNs, in particular the existence of extremely large (about 10^24 cm^(-2)) column density clouds.

NLS1 galaxies and estimation of their central black hole masses from the X-ray excess variance method

Black hole mass determination in active galaxies is a key issue in understanding various luminosity states. In the present paper we try to generalise the mass determination method based on the X-ray excess variance, successfully used for typical broad line Seyfert 1 galaxies (BLS1) to Narrow Line Seyfert 1 (NLS1) galaxies. NLS1 galaxies differ from BLS1 with respect to several properties. They are generally more variable in 2-10 keV energy band so the natural expectation is the need to use a different scaling coefficient between the mass and the variance in these two types of sources. However, we find that such a simple approach is not enough. Although for majority of the 21 NLS1 galaxies in our sample a single scaling coefficient (larger by a factor 20) provided us with a satisfactory method of mass determination, in a small subset of NLS1 galaxies this approach failed. Variability of those objects appeared to be at the intermediate level between NLS1 and BLS1 galaxies. These exceptional NLS1 galaxies have much harder soft X-ray spectra than majority of NLS1 galaxies. We thus postulate that the division of Seyfert 1 galaxies into BLS1 and NLS1 according to the widths of the Hbeta line is less generic than according to the soft X-ray slope.

A STELLAR DYNAMICAL MEASUREMENT OF THE BLACK HOLE MASS IN THE MASER GALAXY NGC 4258

We determine the mass of the black hole at the center of the spiral galaxy NGC 4258 by constructing axisymmetric dynamical models of the galaxy. These models are constrained by high spatial resolution imaging and long-slit spectroscopy of the nuclear region obtained with the {\em Hubble Space Telescope}, complemented by ground-based observations extending to larger radii. Our best mass estimate is $\MBH = (3.3 \pm 0.2) \times 10^7 \MSun $ for a distance of 7.28 Mpc (statistical errors only). This is within 15% of $ (3.82\pm 0.01) \times 10^7 \MSun$, the mass determined from the kinematics of water masers (rescaled to the same distance) assuming they are in Keplerian rotation in a warped disk. The construction of accurate dynamical models of NGC 4258 is somewhat compromised by an unresolved active nucleus and color gradients, the latter caused by variations in the stellar population and/or obscuring dust. These problems are not present in the $\sim 30$ other black hole mass determinations from stellar dynamics that have been published by us and other groups; thus, the relatively close agreement between the stellar dynamical mass and the maser mass in NGC 4258 enhances our confidence in the black hole masses determined in other galaxies from stellar dynamics using similar methods and data of comparable quality.

Emission‐Line Gas Kinematics in the Vicinity of the Supermassive Black Holes in Nearby Radio Galaxies

We describe our characterization of the kinematics of the emission-line gas in the nuclear regions of a complete sample of 21 nearby radio galaxies. We obtained data using the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope. We show that the point-to-point variations are largest perpendicular to the disks and in nuclei where the organized motion is less pronounced, suggesting that motions are present from gas that has not settled into smooth rotation. We show that the velocity dispersion is not distributed as a function of inclination, and so likely arises from isotropic random motions in the gas. We find that the difference in mean velocities on either side of the nucleus does not vanish as the disks become face-on, suggesting there may be bulk motions of the gas disks. We show that the gas velocity dispersions are closely related to the stellar velocity dispersions, which has implications for black hole fueling and growth mechanisms. We show that significant motions digressing from a smooth thin disk configuration are ubiquitous, and even in those cases where the velocity profile of the emission-line gas appears smooth and uncomplicated there may be dynamical components of the system that are not explained by a thin Keplerian disk model, suggesting caution in the use of gas disk kinematics for the determination of black hole masses.

Supermassive black holes from OASIS and SAURON integral-field kinematics

AbstractSupermassive black holes are a key element in our understanding of how galaxies form. Most of the progress in this very active field of research is based on just ~30 determination of black hole masses, accumulated over the past decade. We illustrate how integral-field spectroscopy, and in particular our OASIS modeling effort can help improve the current situation.

Determination of Black Hole Mass in Cygnus X‐1 by Scaling of Spectral Index–QPO Frequency Correlation

It is well established that timing and spectral properties of Galactic Black Hole (BH) X-ray binaries (XRB) are strongly correlated. In particular, it has been shown that low frequency Quasi-Periodic Oscillation (QPO) frequency - photon index correlation curves have a specific pattern. In a number of sources the shape of the index-low frequency QPO correlations are self-similar with a position offset in the QPO frequency-Gamma plane. Titarchuk & Fiorito presented strong theoretical and observational arguments that the QPO frequency values in this QPO frequency-Gamma correlation should be inversely proportional to M_{BH}. A simple translation of the correlation for a given source along the frequency axis leads to the observed correlation for another source. As a result of this translation one can obtain a scaling factor which is simply a BH mass ratio for these particular sources. This property of the correlations offers a fundamentally new method for BH mass determination in XRBs. Here we use the observed QPO-index correlations observed in three BH sources: GRO J1655-40, GRS 1915+105 and Cyg X-1. The BH mass of (6.3 +/- 0.5) M_Sun in GRO J1655-40 is obtained using optical observations. RXTE observations during the recent 2005 outburst yielded sufficient data to establish the correlation pattern during both rise and decay of the event. We use GRO J1655-40 as a standard reference source to measure the BH mass in Cyg X-1. We also revisit the GRS 1915+105 data as a further test of our scaling method. We infer the value of BH mass of (15.6 +/- 1.5) M_Sun in this source which is consistent with the previous BH mass estimate in GRS 1915 of (13.3 +/- 4) M_Sun. We obtain the BH mass in Cyg X-1 in the range (8.7 +/- 0.8) M_Sun.

Line and continuum variability of two intermediate-redshift, high-luminosity quasars

Context. It has been shown that the luminosity of active galactic nuclei and the size of their broad line region obey a simple relation of the type R-BLR = aL(gamma), from faint Seyfert nuclei to bright quasars, allowing single-epoch determination of the central black hole mass M-BH = bL(gamma) Delta(2) H-beta from their luminosity L and width of H-beta emission line. Adopting this mass determination for cosmological studies requires the extrapolation to high redshift and luminosity of a relation whose calibration relies so far on reverberation mapping measurements performed for L less than or similar to 1046 erg s(-1) and redshift z less than or similar to 0.4. Aims. We initiated a campaign for the spectrophotometric monitoring of a few luminous, intermediate redshift quasars whose apparent magnitude, V < 15.7, allows observations with a 1.8 m telescope, aimed at proving that emission lines vary and respond to continuum variations even for luminosities less than or similar to 1047 erg s(-1), and determining eventually their MBH from reverberation mapping. Methods. We have repeatedly performed simultaneous spectrophotometric observations of quasars and reference stars to determine relative variability of continuum and emission lines. We describe the observations and methods of analysis. Results. For the quasars PG 1634+ 706 and PG 1247+ 268 we obtain light-curves respectively for CIII](lambda lambda 1909 angstrom), MgII(lambda lambda 2798 angstrom) and for CIV(lambda lambda 1549 angstrom), CIII](lambda lambda 1909 angstrom) emission lines with the relevant continua. During 3.2 years of observation, in the former case no continuum variability was detected and the evidence for line variability is marginal, while in the latter case both continuum and line variability are detected with high significance and the line variations appear correlated with continuum variations. Conclusions. The detection of the emission line variability in a quasar with L similar to 10(47) erg s(-1) encourages the continuation of the monitoring campaign which should provide a black hole mass estimate in another 5-6 years, constraining the mass-luminosity relation in a poorly explored range of luminosity.