On the mass accretion rate and infrared excess in Herbig Ae/Be Stars

TL;DR

This study utilizes Gaia data to accurately determine stellar parameters of Herbig Ae/Be stars, revealing how their mass accretion rates decay over time and differ between star types, with implications for disk evolution.

Contribution

First comprehensive analysis combining Gaia data with H-alpha flux to estimate mass accretion rates and disk dissipation timescales in Herbig Ae/Be stars.

Findings

Mass accretion rate decays exponentially with age.

Estimated disk dissipation timescale of 1.9 Myr.

Differences in disk structure between Herbig Be and Herbig Ae stars.

Abstract

The present study makes use of the unprecedented capability of the Gaia mission to obtain the stellar parameters such as distance, age, and mass of HAeBe stars. The accuracy of Gaia DR2 astrometry is demonstrated from the comparison of the Gaia DR2 distances of 131 HAeBe stars with the previously estimated values from the literature. This is one of the initial studies to estimate the age and mass of a confirmed sample of HAeBe stars using both the photometry and distance from the Gaia mission. Mass accretion rates are calculated from $H\alpha$ line flux measurements of 106 HAeBe stars. Since we used distances and the stellar masses derived from the Gaia DR2 data in the calculation of mass accretion rate, our estimates are more accurate than previous studies. The mass accretion rate is found to decay exponentially with age, from which we estimated a disk dissipation timescale of $1.9\pm 0.1$ Myr. Mass accretion rate and stellar mass exhibits a power law relation of the form, $\dot{M}_{acc}$ $\propto$ $M_{*}^{2.8\pm0.2}$. From the distinct distribution in the values of the infrared spectral index, $n_{2-4.6}$, we suggest the possibility of difference in the disk structure between Herbig Be and Herbig Ae stars.

Tables

Table 1. Table 1: Table consists of the stellar parameters for our sample of 131 HAeBe stars. The colums in the table include object name, distance, age (our work), age ( Vioque et al., 2018 -V18), mass (our work) and mass (V18). Our estimates of age and mass are derived using Gaia CMD.

Object	Distance (pc)	Age (Myr)	V18 Age (Myr)	Mass (M$\odot$)	V18 Mass (M$\odot$)
51 Oph	${123}_{-4}^{+5}$	${1.02}_{-0.02}^{+0.02}$	${1.22}_{-0.57}^{+0.29}$	$4_{-0.02}^{+0.03}$	${3.35}_{-0.22}^{+0.79}$
AB Aur	${162}_{-2}^{+2}$	${3.92}_{-0.01}^{+0.02}$	$4_{-1.5}^{+1.4}$	${2.34}_{-0.01}^{+0.01}$	${2.15}_{-0.21}^{+0.36}$
AK Sco	${140}_{-1}^{+1}$	${6.94}_{-2.41}^{+2.91}$	${8.4}_{-0.4}^{+1.7}$	${1.62}_{-0.17}^{+0.19}$	${1.401}_{-0.07}^{+0.07}$
AS 220	${220}_{-7}^{+7}$	–	${18.5}_{-1.4}^{+1.5}$	–	${1.513}_{-0.076}^{+0.076}\ast$
AS 442	${843}_{-21}^{+22}$	${0.26}_{-0.02}^{+0.02}$	${0.84}_{-0.19}^{+0.19}$	${6.9}_{-0.2}^{+0.22}$	${3.89}_{-0.26}^{+0.35}$
AS 443	${826}_{-19}^{+20}$	${0.13}_{-0.01}^{+0.01}$	${1.13}_{-0.37}^{+0.91}$	${11.2}_{-0.09}^{+0.1}$	${3.5}_{-0.64}^{+0.48}$
AS 505	${855}_{-21}^{+23}$	${0.28}_{-0.01}^{+0.01}$	${0.188}_{-0.065}^{+0.095}$*	${5.8}_{-0.02}^{+0.02}$	${6.8}_{-0.9}^{+1}$
BD+40 4124	${893}_{-24}^{+26}$	<0.1	${0.1}_{-0.07}^{+0.11}$	${10.77}_{-0.14}^{+0.14}$	${9.1}_{-1.8}^{+3.9}$
BD+46 3471	${759}_{-16}^{+17}$	${0.86}_{-0.01}^{+0.01}$	${1.25}_{-0.73}^{+0.64}$	${4.2}_{-0.01}^{+0.02}$	${3.3}_{-0.4}^{+1.1}$
BD+61 154	${561}_{-9}^{+9}$	${0.17}_{-0.01}^{+0.01}$	${1.89}_{-0.78}^{+0.49}$	${9.5}_{-0.17}^{+0.27}$	${2.94}_{-0.23}^{+0.59}$
BD+65 1637	${874}_{-19}^{+20}$	${0.3}_{-0.01}^{+0.01}$	${0.41}_{-0.13}^{+0.15}$	${6.42}_{-0.02}^{+0.02}$	${5.31}_{-0.48}^{+0.69}$
BF Ori	${385}_{-8}^{+8}$	${5.08}_{-0.36}^{+0.38}$	${6.38}_{-0.46}^{+0.32}$	${2.11}_{-0.03}^{+0.35}$	${1.807}_{-0.09}^{+0.09}$
BH Cep	${371}_{-3}^{+3}$	${12.73}_{-0.21}^{+0.21}$	${10.6}_{-3.1}^{+3}$	${1.57}_{-0.01}^{+0.01}$	${1.37}_{-0.1}^{+0.15}$
BO Cep	${332}_{-2}^{+2}$	${8.66}_{-0.43}^{+1.88}$	${17.1}_{-2.4}^{+0.9}$	${1.49}_{-0.05}^{+0.07}$	${1.215}_{-0.061}^{+0.061}$*
CD-42 11721	${1634}_{-137}^{+164}$	<0.1	${0.023}_{-0.012}^{+0.026}$*	${10.38}_{-0.13}^{+0.13}$	${20}_{-5}^{+7}$
CPD-61 3587B	${2672}_{-248}^{+303}$	<0.1	–	${13.3}_{-0.5}^{+0.2}$	–
CQ Tau	${162}_{-2}^{+2}$	${10.82}_{-1.87}^{+2.49}$	${8.9}_{-2.5}^{+2.8}$	${1.65}_{-0.15}^{+0.05}$	${1.47}_{-0.11}^{+0.19}$
DG Cir	${821}_{-28}^{+30}$	${0.25}_{-0.06}^{+0.06}$	$4_{-3}^{+16}$	${6.94}_{-0.68}^{+1.12}$	${2.3}_{-0.65}^{+0.6}$
DX Cha	${108}_{-1}^{+1}$	${3.52}_{-1.02}^{+0.02}$	${5.48}_{-0.4}^{+0.27}$	${2.48}_{-0.01}^{+0.01}$	${1.849}_{-0.092}^{+0.092}$*
HBC 334	${1774}_{-98}^{+109}$	${2.32}_{-0.05}^{+0.05}$	${3.71}_{-0.19}^{+0.49}$	${2.94}_{-0.03}^{+0.02}$	${2.1}_{-1.1}^{+4.3}$
HD 100453	${104}_{-0}^{+0}$	${12.88}_{-0.03}^{+0.02}$	${6.53}_{-0.49}^{+0.45}$	${1.61}_{-0.01}^{+0.01}$	${1.251}_{-0.063}^{+0.063}$*
HD 100546	${110}_{-1}^{+1}$	${5.08}_{-0.08}^{+0.06}$	${5.5}_{-0.8}^{+1.4}$	${2.49}_{-0.02}^{+0.02}$	${2.05}_{-0.12}^{+0.1}$
HD 101412	${407}_{-5}^{+5}$	${3.48}_{-0.02}^{+0.02}$	${4.37}_{-0.32}^{+0.22}$	${2.51}_{-0.01}^{+0.08}$	${2.1}_{-0.11}^{+0.11}$
HD 114981	${699}_{-29}^{+32}$	${0.23}_{-0.01}^{+0.01}$	${0.277}_{-0.068}^{+0.053}$*	${7.07}_{-0.07}^{+0.07}$	${6.09}_{-0.34}^{+0.59}$
HD 130437	${1662}_{-95}^{+107}$	<0.1	${0.046}_{-0.026}^{+0.077}$*	${20.45}_{-0.2}^{+0.21}$	${13.4}_{-3.8}^{+4.6}$
HD 132947	${378}_{-8}^{+8}$	–	${4.05}_{-0.2}^{+0.32}$	–	${2.22}_{-0.11}^{+0.11}$
HD 135344B	${135}_{-1}^{+1}$	${8.93}_{-0.03}^{+0.04}$	${8.93}_{-0.91}^{+0.45}$	${1.52}_{-0.01}^{+0.01}$	${1.432}_{-0.072}^{+0.072}$*
HD 139614	${134}_{-1}^{+1}$	${14.1}_{-0.03}^{+0.03}$	${14.5}_{-3.6}^{+1.4}$	${2.35}_{-0.01}^{+0.01}$	${1.481}_{-0.074}^{+0.074}$*
HD 141569	${110}_{-1}^{+1}$	${7.2}_{-0.02}^{+0.02}$	$9_{-1}^{+11}$	${2.14}_{-0.01}^{+0.01}$	${1.86}_{-0.093}^{+0.093}$*
HD 141926	${1345}_{-78}^{+88}$	<0.1	${0.023}_{-0.005}^{+0.007}$*	>25	${19.5}_{-2.2}^{+2.4}$
HD 142527	${157}_{-1}^{+1}$	${2.96}_{-0.02}^{+0.02}$	${6.6}_{-1.5}^{+0.3}$	${2.4}_{-0.01}^{+0.01}$	${1.61}_{-0.08}^{+0.12}$
HD 142666	${148}_{-1}^{+1}$	${7.27}_{-0.07}^{+0.08}$	${9.33}_{-0.47}^{+0.77}$	${1.82}_{-0.01}^{+0.01}$	${1.493}_{-0.075}^{+0.075}$*
HD 144432	${155}_{-1}^{+1}$	${7.24}_{-0.02}^{+0.02}$	${4.98}_{-0.55}^{+0.25}$	${1.81}_{-0.01}^{+0.01}$	${1.386}_{-0.069}^{+0.069}$*
HD 145718	${152}_{-2}^{+2}$	${5.7}_{-0.13}^{+0.17}$	${9.8}_{-0.5}^{+2.8}$	${2.09}_{-0.04}^{+0.17}$	${1.605}_{-0.08}^{+0.08}$
HD 150193A	${150}_{-2}^{+2}$	${4.55}_{-0.03}^{+0.03}$	${5.48}_{-0.27}^{+0.44}$	${2.2}_{-0.01}^{+0.01}$	${1.891}_{-0.095}^{+0.095}$*
HD 163296	${101}_{-1}^{+1}$	${6.52}_{-0.25}^{+0.26}$	${7.6}_{-1.2}^{+1.1}$	${2.1}_{-0.02}^{+0.02}$	${1.833}_{-0.092}^{+0.092}$*
HD 179218	${264}_{-3}^{+3}$	${2.24}_{-0.01}^{+0.01}$	${1.66}_{-0.26}^{+0.54}$	${2.95}_{-0.01}^{+0.01}$	${2.98}_{-0.3}^{+0.18}$
HD 190073	${872}_{-49}^{+55}$	${0.26}_{-0.01}^{+0.01}$	${0.22}_{-0.07}^{+0.11}$	${5.99}_{-0.05}^{+0.06}$	${5.89}_{-0.76}^{+0.8}$
HD 200775	${357}_{-6}^{+6}$	${0.11}_{-0.01}^{+0.01}$	${0.41}_{-0.2}^{+0.15}$	${9.41}_{-0.06}^{+0.07}$	${5.3}_{-0.5}^{+1.3}$
HD 216629	${790}_{-17}^{+18}$	${0.11}_{-0.01}^{+0.01}$	${0.07}_{-0.033}^{+0.044}$*	${8.22}_{-0.02}^{+0.02}$	${9.8}_{-1.3}^{+2.7}$
HD 244314	${427}_{-11}^{+11}$	${7.93}_{-0.06}^{+0.05}$	${7.43}_{-0.54}^{+0.37}$	${1.77}_{-0.01}^{+0.01}$	${1.691}_{-0.085}^{+0.093}$*
HD 244604	${417}_{-11}^{+11}$	–	${4.89}_{-0.52}^{+0.24}$	–	${1.98}_{-0.1}^{+0.1}$
HD 245185	${427}_{-19}^{+21}$	${5.54}_{-0.14}^{+0.22}$	$8_{-3}^{+12}$	${2.2}_{-0.01}^{+0.01}$	${1.92}_{-0.1}^{+0.18}$
HD 250550	${704}_{-47}^{+54}$	${1.7}_{-0.05}^{+0.05}$	${2.56}_{-0.67}^{+0.43}$	${3.26}_{-0.03}^{+0.04}$	${2.6}_{-0.14}^{+0.3}$
HD 259431	${712}_{-23}^{+25}$	${0.25}_{-0.01}^{+0.01}$	${0.42}_{-0.28}^{+0.53}$	${6.28}_{-0.02}^{+0.04}$	${5.2}_{-1.3}^{+1.8}$
HD 287823	${356}_{-7}^{+7}$	${6.04}_{-0.05}^{+0.05}$	${7.43}_{-0.37}^{+0.37}$	${2.27}_{-0.01}^{+0.01}$	${1.704}_{-0.085}^{+0.085}$*
HD 290409	${451}_{-16}^{+17}$	–	$7_{-2}^{+13}$	–	${1.9}_{-0.09}^{+0.18}$
HD 290500	${434}_{-13}^{+13}$	${8.36}_{-0.09}^{+0.17}$	${10.4}_{-3.3}^{+9.3}$	${2.04}_{-0.05}^{+0.05}$	${1.383}_{-0.069}^{+0.082}$*
HD 290764	${394}_{-10}^{+10}$	${6.4}_{-0.05}^{+0.06}$	${6.9}_{-1.4}^{+0.5}$	${1.88}_{-0.01}^{+0.01}$	${1.69}_{-0.08}^{+0.13}$
HD 290770	${396}_{-11}^{+12}$	${4.3}_{-0.09}^{+0.11}$	${4.59}_{-0.54}^{+0.49}$	${2.39}_{-0.02}^{+0.02}$	${2.22}_{-0.11}^{+0.11}$
HD 305298	${5905}_{-829}^{+1119}$	<0.1	${0.04}_{-0.01}^{+0.31}$	${17.76}_{-0.48}^{+0.46}$	${17.7}_{-2}^{+2.1}$
HD 31648	${161}_{-2}^{+2}$	${5.65}_{-0.02}^{+0.02}$	${6.2}_{-1.1}^{+0.3}$	${2.06}_{-0.01}^{+0.01}$	${1.78}_{-0.09}^{+0.13}$
HD 35187	${162}_{-3}^{+3}$	${5.99}_{-0.94}^{+0.25}$	$5_{-2}^{+15}$	${2.02}_{-0.12}^{+0.32}$	${2.1}_{-0.25}^{+0.25}$
HD 35929	${384}_{-8}^{+8}$	${1.16}_{-0.01}^{+0.01}$	${1.46}_{-0.17}^{+0.07}$	${3.48}_{-0.01}^{+0.01}$	${2.92}_{-0.15}^{+0.15}$
HD 36112	${160}_{-2}^{+2}$	$8_{-0.04}^{+0.03}$	${8.3}_{-1.4}^{+0.4}$	${1.78}_{-0.01}^{+0.01}$	${1.56}_{-0.08}^{+0.11}$
HD 37258	${360}_{-13}^{+13}$	${7.1}_{-0.03}^{+0.62}$	$8_{-2}^{+12}$	${1.93}_{-0.1}^{+0.05}$	${1.88}_{-0.11}^{+0.14}$
HD 37357	${796}_{-175}^{+297}$	${0.97}_{-0.11}^{+0.13}$	${1.69}_{-0.93}^{+0.87}$	${3.92}_{-0.16}^{+0.18}$	$3_{-0.4}^{+1}$
HD 37490	${320}_{-35}^{+45}$	${0.1}_{-0.01}^{+0.01}$	${0.1}_{-0.07}^{+0.11}$	${9.16}_{-0.23}^{+0.29}$	${8.6}_{-1.6}^{+3.9}$
HD 37806	${423}_{-10}^{+11}$	${1.65}_{-0.02}^{+0.02}$	${1.56}_{-0.6}^{+0.64}$	${3.28}_{-0.02}^{+0.02}$	${3.11}_{-0.33}^{+0.55}$
HD 38120	${402}_{-13}^{+14}$	${2.62}_{-0.1}^{+0.1}$	$3_{-1}^{+14}$	${2.96}_{-0.07}^{+0.07}$	${2.37}_{-0.24}^{+0.43}$
HD 53367	${131}_{-13}^{+16}$	–	–	–	–
HD 59319	${660}_{-21}^{+22}$	${1.12}_{-0.02}^{+0.02}$	${0.96}_{-0.2}^{+0.24}$	${3.93}_{-0.02}^{+0.02}$	${3.81}_{-0.26}^{+0.31}$
HD 68695	${392}_{-6}^{+6}$	${7.3}_{-0.06}^{+0.05}$	${7.6}_{-1.2}^{+1.1}$	${2.08}_{-0.01}^{+0.01}$	${1.833}_{-0.092}^{+0.092}$*
HD 72106	${2552}_{-1256}^{+2141}$	<0.1	${2.1}_{-1.5}^{+2.6}$	${9.06}_{-0.73}^{+0.81}$	${2.7}_{-0.7}^{+1.5}$
HD 76534	${895}_{-29}^{+31}$	${0.27}_{-0.01}^{+0.01}$	${0.171}_{-0.028}^{+0.023}$*	${6.31}_{-0.05}^{+0.05}$	${7.46}_{-0.37}^{+0.51}$
HD 85567	${1002}_{-28}^{+30}$	<0.1	${0.217}_{-0.051}^{+0.045}$*	${11.4}_{-0.1}^{+0.1}$	${6.32}_{-0.39}^{+0.53}$
HD 87403	${2038}_{-170}^{+203}$	${0.19}_{-0.01}^{+0.01}$	${0.28}_{-0.08}^{+0.11}$	${6.72}_{-0.08}^{+0.08}$	${5.51}_{-0.53}^{+0.65}$
HD 94509	${1857}_{-112}^{+127}$	–	${0.28}_{-0.12}^{+0.17}$	–	${5.7}_{-0.8}^{+1.1}$
HD 95881	${1148}_{-42}^{+46}$	${0.16}_{-0.01}^{+0.01}$	${0.28}_{-0.07}^{+0.05}$	${7.06}_{-0.04}^{+0.04}$	${5.5}_{-0.27}^{+0.5}$
HD 96042	${4007}_{-497}^{+649}$	<0.1	${0.019}_{-0.005}^{+0.008}$	${20.09}_{-0.46}^{+0.49}$	${20.7}_{-2.9}^{+3.9}$
HD 97048	${184}_{-1}^{+1}$	${3.48}_{-0.02}^{+0.01}$	${4.4}_{-0.3}^{+1.1}$	${2.52}_{-0.01}^{+0.01}$	${2.25}_{-0.13}^{+0.11}$
HD 98922	${678}_{-15}^{+16}$	${0.15}_{-0.01}^{+0.01}$	${0.204}_{-0.038}^{+0.01}$*	${7.42}_{-0.04}^{+0.02}$	${6.17}_{-0.31}^{+0.37}$
Hen 3-1191	${1959}_{-247}^{+327}$	${0.38}_{-0.02}^{+0.03}$	${0.23}_{-0.11}^{+0.37}$	${4.96}_{-0.1}^{+0.1}$	${8.1}_{-0.4}^{+2.1}$
IP Per	${305}_{-7}^{+8}$	${11.3}_{-0.25}^{+0.24}$	${12}_{-3.3}^{+8}$	${1.74}_{-0.01}^{+0.01}$	${1.56}_{-0.12}^{+0.11}$
LkHA 167	${1176}_{-114}^{+141}$	${0.19}_{-0.01}^{+0.01}$	${18.5}_{-1.4}^{+1.5}$	${6.18}_{-0.11}^{+0.1}$	${1.513}_{-0.076}^{+0.076}$*
LkHA 208	${676}_{-86}^{+115}$	${4.17}_{-0.22}^{+0.23}$	$9_{-5}^{+11}$	${2.28}_{-0.05}^{+0.04}$	${1.56}_{-0.14}^{+0.47}$
LkHA 218	${1104}_{-43}^{+46}$	${2.02}_{-0.04}^{+0.04}$	$5_{-1}^{+15}$	${3.01}_{-0.02}^{+0.02}$	${2.12}_{-0.12}^{+0.19}$
LkHA 220	${1162}_{-51}^{+56}$	${1.57}_{-0.05}^{+0.05}$	${2.04}_{-0.15}^{+0.34}$	${3.54}_{-0.05}^{+0.06}$	${3.02}_{-0.15}^{+0.15}$
LkHA 224	${1253}_{-180}^{+249}$	${0.29}_{-0.06}^{+0.07}$	${1.2}_{-0.6}^{+1.1}$	${5.52}_{-0.12}^{+0.28}$	${2.85}_{-0.55}^{+0.72}$
LkHA 234	${901}_{-18}^{+19}$	${0.32}_{-0.04}^{+0.04}$	${1.63}_{-0.6}^{+0.75}$	${6.38}_{-0.3}^{+0.38}$	${3.18}_{-0.39}^{+0.51}$
LkHA 25	${868}_{-89}^{+112}$	–	$6_{-1}^{+14}$	–	${2.3}_{-0.11}^{+0.13}$
LkHA 257	${777}_{-10}^{+10}$	${7.39}_{-0.03}^{+0.03}$	${3.6}_{-1.1}^{+1.1}$	${1.82}_{-0.01}^{+0.01}$	${3.08}_{-0.15}^{+0.15}$
LkHA 259	${743}_{-18}^{+19}$	${1.24}_{-0.02}^{+0.02}$	${6.4}_{-0.9}^{+1.6}$	${3.43}_{-0.02}^{+0.02}$	${1.7}_{-0.13}^{+0.1}$
LkHa 339	${839}_{-18}^{+19}$	${2.37}_{-0.04}^{+0.03}$	${2.54}_{-0.16}^{+0.23}$	$3_{-0.03}^{+0.03}$	${2.59}_{-0.13}^{+0.13}$
MWC 1080	${1336}_{-154}^{+199}$	–	${0.04}_{-0.02}^{+0.45}$	–	${16.1}_{-4.2}^{+6.3}$
MWC297	${372}_{-12}^{+12}$	–	${0.027}_{-0.006}^{+0.006}$*	–	${16.9}_{-1.2}^{+1.9}$
PDS 124	${843}_{-33}^{+36}$	${4.98}_{-0.07}^{+0.06}$	$6_{-1}^{+14}$	${2.16}_{-0.01}^{+0.01}$	${2.07}_{-0.12}^{+0.1}$
PDS 130	${1278}_{-33}^{+34}$	${2.02}_{--0.04}^{+0.02}$	${3.48}_{-0.26}^{+0.27}$	${3.12}_{-0.01}^{+0.01}$	${2.33}_{-0.12}^{+0.12}$
PDS 133	${1437}_{-48}^{+51}$	${4.88}_{-0.43}^{+0.4}$	$3_{-1}^{+14}$	${2.01}_{-0.04}^{+0.06}$	${2.93}_{-0.44}^{+0.45}$
PDS 134	${2802}_{-242}^{+291}$	${0.37}_{-0.02}^{+0.02}$	${0.73}_{-0.21}^{+0.22}$	${5.62}_{-0.04}^{+0.04}$	${4.28}_{-0.38}^{+0.52}$
PDS 144S	${149}_{-3}^{+3}$	–	–	–	–
PDS 174	${393}_{-6}^{+6}$	${3.11}_{-0.05}^{+0.04}$	$2_{-1}^{+18}$	${2.69}_{-0.02}^{+0.02}$	${2.71}_{-0.23}^{+0.36}$
PDS 24	${1099}_{-23}^{+23}$	${6.41}_{-0.14}^{+0.06}$	${10}_{-4}^{+10}$	${2.22}_{-0.02}^{+0.02}$	${1.95}_{-0.1}^{+0.1}$
PDS 241	${5259}_{-1057}^{+1535}$	<0.1	${0.078}_{-0.028}^{+0.036}$*	${23.01}_{-0.94}^{+0.95}$	${11.1}_{-1.3}^{+2.3}$
PDS 27	${3262}_{-428}^{+570}$	<0.1	${0.042}_{-0.027}^{+0.072}$*	>25	${12.2}_{-3.4}^{+5.5}$
PDS 281	${914}_{-25}^{+27}$	<0.1	–	${10.06}_{-0.04}^{+0.06}$	–
PDS 286	${1838}_{-111}^{+126}$	–	${0.011}_{-0.001}^{+0.006}$*	–	${31.2}_{-5.5}^{+4.5}$
PDS 33	${931}_{-23}^{+24}$	${7.16}_{-0.17}^{+0.16}$	${10.7}_{-3.9}^{+9.3}$	${2.04}_{-0.01}^{+0.01}$	${1.85}_{-0.093}^{+0.093}$*
PDS 344	${2360}_{-89}^{+96}$	${2.38}_{-0.03}^{+0.04}$	${1.8}_{-0.2}^{+8.4}$	${2.89}_{-0.02}^{+0.02}$	${3.48}_{-0.23}^{+0.17}$
PDS 361S	${3378}_{-318}^{+389}$	${0.19}_{-0.01}^{+0.01}$	${0.6}_{-0.3}^{+3.8}$	${7.81}_{-0.11}^{+0.11}$	$5_{-0.7}^{+1}$
PDS 37	${2260}_{-264}^{+342}$	–	${0.06}_{-0.03}^{+0.1}$	–	${10.9}_{-3}^{+4.5}$
PDS 415N	${144}_{-3}^{+3}$	–	${13.1}_{-4.5}^{+5.4}$	–	${1.21}_{-0.09}^{+0.16}$
PDS 431	${1787}_{-82}^{+90}$	${1.59}_{-0.03}^{+0.03}$	${2.77}_{-0.73}^{+0.45}$	${3.46}_{-0.02}^{+0.03}$	${2.52}_{-0.15}^{+0.27}$
PDS 69	${689}_{-18}^{+19}$	${0.95}_{-0.01}^{+0.02}$	${0.8}_{-0.3}^{+5.6}$	${3.96}_{-0.02}^{+0.02}$	${4.18}_{-0.51}^{+0.73}$
R CrA	${96}_{-6}^{+7}$	–	–	–	–
RR Tau	${763}_{-26}^{+28}$	${1.7}_{-0.64}^{+0.2}$	${1.98}_{-0.69}^{+0.4}$	${3.28}_{-0.14}^{+1.23}$	${2.82}_{-0.19}^{+0.46}$
SV Cep	${341}_{-2}^{+2}$	${4.6}_{-0.04}^{+0.24}$	$6_{-1}^{+13}$	${2.48}_{-0.02}^{+0.11}$	${1.55}_{-0.077}^{+0.077}$*
T Ori	${403}_{-7}^{+7}$	${4.64}_{-0.34}^{+0.36}$	${4.15}_{-0.67}^{+0.56}$	${2.18}_{-0.06}^{+0.06}$	${2.11}_{-0.11}^{+0.14}$
TY CrA	${136}_{-3}^{+3}$	${5.39}_{-0.05}^{+0.04}$	$6_{-2}^{+14}$	${2.09}_{-0.01}^{+0.02}$	${2.06}_{-0.19}^{+0.22}$
TYC 8581-2002-1	${549}_{-7}^{+7}$	${3.36}_{-0.04}^{+0.02}$	$8_{-1}^{+12}$	${2.99}_{-0.05}^{+0.05}$	${1.88}_{-0.094}^{+0.094}$*
TYC 8593-2802-1	${1570}_{-74}^{+81}$	${3.23}_{-0.06}^{+0.06}$	${1.75}_{-0.35}^{+0.63}$	${2.43}_{-0.02}^{+0.02}$	${2.99}_{-0.31}^{+0.27}$
UX Ori	${322}_{-5}^{+5}$	${8.22}_{-0.26}^{+0.27}$	${11.4}_{-2.7}^{+8.6}$	${1.74}_{-0.02}^{+0.05}$	${1.612}_{-0.081}^{+0.091}$*
UY Ori	${353}_{-10}^{+11}$	–	–	–	–
V1012 Ori	${383}_{-7}^{+8}$	–	${8.5}_{-0.9}^{+1.1}$	–	${1.3}_{-0.065}^{+0.065}$*
V1028 Cen	${997}_{-218}^{+379}$	${2.28}_{-0.25}^{+0.26}$	${2.4}_{-1.1}^{+8.5}$	${2.93}_{-0.11}^{+0.13}$	$3_{-0.15}^{+0.6}$
V1308 Ori	${5523}_{-1168}^{+1730}$	–	${0.018}_{-0.008}^{+0.019}$*	–	${23}_{-7}^{+11}$
V1366 Ori	${309}_{-5}^{+5}$	–	${6.5}_{-0.6}^{+2.4}$	–	${1.45}_{-0.072}^{+0.072}$*
V1787 Ori	${387}_{-8}^{+8}$	${0.57}_{-0.02}^{+0.02}$	${7.4}_{-1.1}^{+0.6}$	${2.04}_{-0.02}^{+0.03}$	${1.659}_{-0.083}^{+0.094}$*
V346 Ori	${363}_{-6}^{+6}$	${8.23}_{-0.17}^{+0.17}$	${9.33}_{-0.47}^{+0.47}$	${1.89}_{-0.01}^{+0.01}$	${1.572}_{-0.079}^{+0.079}$*
V350 Ori	${389}_{-18}^{+19}$	${9.96}_{-1.5}^{+1.29}$	${12.2}_{-4.7}^{+7.8}$	${1.8}_{-0.06}^{+0.08}$	${1.706}_{-0.085}^{+0.094}$*
V380 Ori	${486}_{-36}^{+42}$	${0.51}_{-0.02}^{+0.02}$	$2_{-0.8}^{+1}$	${5.04}_{-0.05}^{+0.08}$	${2.82}_{-0.38}^{+0.59}$
V599 Ori	${406}_{-7}^{+7}$	${0.36}_{-0.05}^{+0.05}$	${4.29}_{-0.54}^{+0.42}$	${2.17}_{-0.15}^{+0.15}$	${2.03}_{-0.1}^{+0.1}$
V699 Mon	${703}_{-22}^{+23}$	${0.53}_{-0.01}^{+0.02}$	${0.96}_{-0.3}^{+0.44}$	${4.99}_{-0.04}^{+0.03}$	$4_{-0.48}^{+0.49}$
V791 Mon	${872}_{-28}^{+30}$	${0.92}_{-0.02}^{+0.01}$	$1_{-0.3}^{+3.1}$	${4.28}_{-0.04}^{+0.04}$	${3.94}_{-0.45}^{+0.51}$
V856 Sco	${160}_{-2}^{+2}$	${3.88}_{-1.22}^{+0.66}$	–	${2.22}_{-0.07}^{+0.24}$	–
V892 Tau	${117}_{-2}^{+2}$	–	–	–	–
VV Ser	${415}_{-8}^{+8}$	${0.9}_{-0.37}^{+0.12}$	${2.8}_{-0.2}^{+8.1}$	${4.37}_{-0.36}^{+1.35}$	${2.89}_{-0.14}^{+0.14}$
VX Cas	${529}_{-10}^{+11}$	–	$9_{-4}^{+11}$	–	${1.88}_{-0.09}^{+0.18}$
WW Vul	${497}_{-9}^{+9}$	${3.3}_{-0.06}^{+0.06}$	${5.08}_{-0.71}^{+0.84}$	${2.58}_{-0.03}^{+0.04}$	${1.95}_{-0.1}^{+0.11}$
XY Per	${456}_{-18}^{+19}$	${1.56}_{-0.05}^{+0.04}$	${1.95}_{-0.44}^{+0.43}$	${3.31}_{-0.04}^{+0.03}$	${2.82}_{-0.2}^{+0.29}$
Z CMa	${253}_{-61}^{+118}$	–	${0.8}_{-0.59}^{+0.83}$	–	${3.8}_{-0.8}^{+2}$

Equations

$$\frac{A_G}{A_V}=0.831,\frac{A_{G_{BP}}}{A_V}=1.032,\frac{A_{G_{RP}}}{A_V}=0.678$$

$$\frac{A_G}{A_V}=0.831,\frac{A_{G_{BP}}}{A_V}=1.028,\frac{A_{G_{RP}}}{A_V}=0.672$$

$$\frac{A_G}{A_V}=0.831,\frac{A_{G_{BP}}}{A_V}=1.028,\frac{A_{G_{RP}}}{A_V}=0.672,$$

$$L_{H\alpha }=4\pi d^2{F}_{H\alpha }$$

$$log\frac{L_{acc}}{L_{\odot }}=2.09(\pm 0.06)+1.00(\pm 0.05)\times log\frac{L_{H\alpha }}{L_{\odot }}$$

$$L_{acc}=\frac{G{M}_{\ast }{\dot{M}}_{acc}}{R_{\ast }}(1-\frac{R_{\ast }}{R_i})$$

$$R_{*}=\bigg{(}\frac{L_{*}}{4\pi\sigma T_{eff}^{4}}\bigg{)}^{1/2}$$

$${\dot{M}}_{acc}(t)={\dot{M}}_{acc}(0)e^{-t/\tau }$$

$${\dot{M}}_{acc}=constant\times t^{-\eta }.$$

$$n_{{\lambda }_1-{\lambda }_2}=\frac{log(\frac{{\lambda }_2{F}_{{\lambda }_2}}{{\lambda }_1{F}_{{\lambda }_1}})}{log(\frac{{\lambda }_2}{{\lambda }_1})}$$

$$\bigg{|}\frac{Vioque~{}estimate~{}-~{}Our~{}estimate}{Our~{}estimate}\bigg{|}\times 100$$

Full text

stars: pre-main sequence — protoplanetary disks — emission line — accretion

††journal: AJ

\useunder

\ul

1 Introduction

Herbig Ae/Be stars are intermediate-mass pre-main sequence (PMS) stars with masses between 2 and 10 M$\odot$. They are often used to understand the missing link in the star formation sequence connecting T Tauri stars and massive young stellar objects (e.g. Herbig, 1960; Waters & Waelkens, 1998; Oudmaijer et al., 2017). Herbig Ae/Be stars (hereafter HAeBe) show emission lines in their spectrum and exhibit infrared excess (known as IR excess) in the continuum, suggestive of hot and/or cool dust in the circumstellar medium (CSM) (Hillenbrand et al., 1992; Malfait et al., 1998). The emission lines such as H$\alpha$ are formed in the CSM and are used for understanding the mass accretion process in HAeBe stars (eg. Hamann & Persson, 1992; Vieira et al., 2003; Manoj et al., 2006; Mendigutía et al., 2011a, b).

Understanding the accretion of material from the CSM is important to study the PMS evolution because it can provide vital information about the formation and evolution of planets around the stars (Muzerolle et al., 2003; Beltrán & de Wit, 2016). It is proposed that Herbig Ae (HAe) and Herbig Be (HBe) stars may show considerable differences in disc morphology and mode of accretion (Vink et al., 2002; Alonso-Albi et al., 2009; Vioque et al., 2018). However, in order to establish these results, we need to have precise distance measurements. This is due to the fact that the precision of stellar parameters such as age, mass, log(g) etc., strongly depend on precise distance measurements. One of the pioneering missions which provided accurate distances of nearby astronomical objects was the Hipparcos mission. Based on the distance measurements of nearby HAeBe stars from the Hipparcos mission (ESA, 1997), van den Ancker et al. (1998) derived the astrophysical parameters of a sample of 44 HAeBe stars and found that 65% of HAeBe stars show photometric variability. It may be noted that Hipparcos provided reliable distance values for stars within 1 kpc to the Sun (de Zeeuw et al., 1999). The Gaia mission is designed to provide high-quality astrometry and photometry of 1.3 billion stars (Gaia Collaboration et al., 2016a, b). With the second data release of Gaia (named as Gaia DR2) (Gaia Collaboration et al., 2018a), it is possible to get parallax measurements of stars with uncertainties limited to 0.04 mas, for sources brighter than G = 14 mag (Luri et al., 2018). From precise distance measurements, it is possible to derive the relations connecting the IR excess and mass accretion rates ($\dot{M}_{acc}$) with the stellar parameters of HAeBe stars. This can be used to understand whether magnetospheric or disc accretion plays a major role in HAeBe stars.

In this work, we estimate the stellar parameters of a well-studied sample of HAeBe stars, thereby understanding the mass accretion process in pre-main sequence stars. We present the sample of HAeBe stars used for this study in Sect. 2. The results of this study are presented in Sect. 3, wherein we discuss the procedure associated with distance and extinction measurements. Also, we estimate the mass and age of HAeBe stars and discuss mass accretion in HAeBe stars. Recently, Vioque et al. (2018) estimated stellar parameters of HAeBe stars using distance measurements from Gaia DR2. They based their analysis on the derived quantities such as luminosity and temperature, which can introduce additional errors in the estimation of mass and age of HAeBe stars. Instead, in the present study, we based the analysis on Gaia color-magnitude diagram. The main results are summarized in Sect. 4.

2 Data Inventory

A sample of 142 stars is taken from Mathew et al. (2018), which is a carefully selected, well-studied sample of HAeBe stars from The et al. (1994), Manoj et al. (2006) and Fairlamb et al. (2015). Mathew et al. (2018) discussed various mechanisms for the formation of Oi emission lines in HAeBe stars and found that Lyman beta fluorescence is the dominant excitation mechanism. This is the second work in the series, studying about the $\dot{M}_{acc}$ and IR excess in HAeBe stars. Here we re-estimate the relations connecting the $\dot{M}_{acc}$ with the stellar parameters such as age and mass in the context of the Gaia DR2 release. These new estimates will be used for our future work to explore the possibility of using Oi 8446 Å emission line as an accretion indicator in HAeBe stars (Mathew et al. in prep.).

The coordinates, proper motions and $V$ magnitudes of the 142 stars are taken from the literature. RA and Dec of these stars are converted from J2000 to J2015.5 epoch using their proper motion. A query for a Gaia DR2 match for these stars was then performed around the converted coordinates with a search radius of 10 arcsec via the Mikulski Archive for Space Telescopes (MAST)111https://archive.stsci.edu/. If a match was not found, then the search radius was increased up to 30 arcsec. This procedure returned 354 Gaia DR2 rows for 142 stars. For 60 stars, only one Gaia DR2 match was returned. For the remaining 82 stars with multiple entries, those which had $\mid$G$-$V$\mid$ mag $>$ 3.5 were removed. For the remaining multiple entries, the Gaia DR2 row with the closest positional match was selected for which $\mid$G$-$V$\mid$ mag $\leq$ 2. Thus we got the Gaia DR2 parallax and magnitudes for all stars in the sample. After avoiding 11 sources, where 6 showed no parallax data and 5 had negative parallax, we finalized our sample of HAeBe stars to 131. These stars are found in the distance range of 0.09$-$6 kpc, with a range in Gaia G band magnitude from 4.4 to 14.5 mag.

3 Results

3.1 Comparison of the Gaia DR2 distances with previous estimates

The uncertainty in the distance determination of stars is mitigated to a considerable extent due to the precision of the Gaia mission. Although Gaia DR2 provides accurate positions and parallax measurements via a rigorous astrometric reduction technique, the estimation of distance by simple inversion of Gaia parallax does entail certain inherent problems. The distance obtained through such a method is acceptable only when the parallax measurements are fairly precise, i.e., when the signal to noise ratio (SNR) of the parallax measurement is preferably high (SNR$\geq$5). In cases where fractional parallax uncertainty is high, the probability distribution for the distance inferred from inverted parallax becomes strongly asymmetric and non-Gaussian in nature. Furthermore, the distance thus estimated will be nonphysical if the concerned parallax measurement is negative, owing to the large measurement noise or due to the star moving opposite to the direction of the true parallactic motion. To tackle this problem, Bailer-Jones et al. (2018) applied a probabilistic approach to estimate distances to 1.3 billion stars having Gaia DR2 data. They adopted the distance likelihood (inferred from Gaia parallax) and a distance prior (an exponentially decreasing space density prior that is based on a Galaxy model) approach. The distance estimates and corresponding uncertainties thus determined are purely geometric and devoid of any underlying assumptions. Hence, for the present study, we use the distance estimates from Bailer-Jones et al. (2018), which are listed in LABEL:tab:Table1.

We compared the distance estimated from the Gaia DR2 with the values listed in the literature. Manoj et al. (2006) compiled the distances of HAeBe stars from various studies and provided the best estimate of distance for each star. This is supplemented with the distance information from the Gaia DR1 (Gaia Collaboration et al., 2016b) and those given in Fairlamb et al. (2015). The extreme values of distance from these compilations are included in Figure 1 along with the Gaia DR2 estimates. It can be seen from the figure that distance estimate from the Gaia DR2 is more accurate (with minimal error) than previous estimates.

3.2 Extinction Calculation

The extinction in all the photometric bands, G, GBP and GRP, are listed in the Gaia archive. But this extinction and reddening values are limited to a small number of objects. The extinction calculation is done by an automated algorithm, which is explained in detail in Evans et al. (2018). Also, they have listed the caveats involved in the automated way of estimating extinction values. For this work, we have independently estimated the extinction values from the extinction curve of McClure (2009). From the curve we calculated \bigg{[}\displaystyle\frac{\mbox{A_{G}}}{\mbox{A_{V}}}\bigg{]},\bigg{[}\displaystyle\frac{\mbox{A_{G_{BP}}}}{\mbox{A_{V}}}\bigg{]} and \bigg{[}\displaystyle\frac{\mbox{A_{G_{RP}}}}{\mbox{A_{V}}}\bigg{]}.

The AV values for our sample of HAeBe stars are taken from Fairlamb et al. (2015), Chen et al. (2016) and Mathew et al. (2018). Hernández et al. (2004) suggested using high values of total-to-selective extinction (RV = 5) for estimating the extinction values of HAeBe stars. This is suggestive of grain growth in the disk of HAeBe stars (Gorti & Bhatt, 1993; Manoj et al., 2006). For the present work, we adopted RV = 5 while calculating the extinction (AV) values. This method was followed while calculating the AV values of HAeBe stars in Mathew et al. (2018). Hence, for this analysis, we included the AV values of HAeBe stars which are listed in Mathew et al. (2018). For remaining stars, AV values are taken from Fairlamb et al. (2015) and Chen et al. (2016), which are re-estimated for RV = 5. It may be noted that Hernández et al. (2004) pointed out that the age and luminosity of HAeBe stars better match with that of PMS stars when RV = 5 is employed. The AV values estimated for all the HAeBe stars will be used for correcting the Gaia photometry for extinction.

The mean wavelength values in the Gaia passbands and Johnson $V$ band are taken from Jordi et al. (2010). The \bigg{[}\displaystyle\frac{\mbox{A_{G}}}{\mbox{A_{V}}}\bigg{]},\bigg{[}\displaystyle\frac{\mbox{A_{G_{BP}}}}{\mbox{A_{V}}}\bigg{]} and \bigg{[}\displaystyle\frac{\mbox{A_{G_{RP}}}}{\mbox{A_{V}}}\bigg{]} values for different ranges of AV are calculated using McClure (2009), which are listed below.

For $A_{V}$ $\leq$ 2.5

[TABLE]

For 2.5 $<$ $A_{V}$ $<$ 7.5

[TABLE]

For 7.5 $\leq$ $A_{V}$

[TABLE]

Using these relations we estimated $A_{G}$, $A_{G_{BP}}$ and $A_{G_{RP}}$ from the known values of AV. This is further used to correct the Gaia magnitudes, which will be used for this work.

3.3 Age and mass of HAeBe stars

In addition to precise astrometric measurements, the Gaia DR2 lists three broad-band photometric magnitudes, G, GBP and GRP, extinction in G band (AG) and reddening (E(GBP $-$ GRP)) values. This provides the possibility to construct a color-magnitude diagram (CMD) exclusively from Gaia magnitudes (Gaia Collaboration et al., 2018b). We identified that the G-band filter in Gaia is very wide (720 $nm$) and hence can introduce uncertainty in G magnitude measurements. Hence for the present work, we use GBP and GRP magnitudes for constructing the CMD. The observed Gaia GBP and GRP are corrected for extinction using the method discussed in Sect. 3.2. Further, making use of the distance estimates (see LABEL:tab:Table1), we estimated the absolute GRP magnitude (M${}_{G_{RP}}$), which will be used for the CMD analysis. Usually, the construction of the CMD with non-homogeneous datasets belonging to different epochs can introduce systematic errors in the estimation of stellar parameters. The use of Gaia astrometry and photometry for the CMD analysis alleviate this issue. Also, we derived the age and mass of HAeBe stars from the observed CMD rather than from a theoretical Hertzsprung-Russell (HR) diagram. Luminosity calculation for stars in the HR diagram involves the conversion of V magnitude to luminosity using bolometric corrections. Such a conversion will provide substantial errors in mass and age estimates. In addition, the effective temperature of the star (Teff) is identified using a calibration table which introduces degeneracy in Teff for relatively nearer spectral types.

The age and mass of the HAeBe stars are estimated by plotting the Modules for Experiments in Stellar Astrophysics (MESA) isochrones and evolutionary tracks (MIST)222http://waps.cfa.harvard.edu/MIST (Choi et al., 2016; Dotter, 2016) in the Gaia CMD. The MIST is an initiative supported by NSF, NASA and Packard Foundation which builds stellar evolutionary models with different ages, masses, and metallicities. The updated models in the MIST archive included isochrones and evolutionary tracks for the Gaia DR2 data. We know that HAeBe stars have a range of rotation rates but we adopted the isochrones corresponding to (V/Vcrit) = 0.4, since that is the only model available in the MIST database for a rotating system. Also, we adopted the metallicity \bigg{[}\displaystyle\frac{\mbox{Fe}}{\mbox{H}}\bigg{]} = 0 (corresponding to solar metallicity; Z$\odot$ = 0.0152) for estimating the age and mass of HAeBe stars.

The Gaia CMD for our sample of 131 HAeBe stars is shown in Figure 2 & Figure 3. From Figure 2, we estimated the ages of 110 HAeBe stars by over-plotting MIST isochrones. They are found to be in the range of 0.1 to 15 Myr. From Figure 3, it can be seen that the mass range of our sample of HAeBe stars is 1.4 to 25 M$\odot$. The masses are identified from the coincidence of the data points with the grid of MIST evolutionary tracks. The estimated ages and masses of the HAeBe stars from this work are compared with that in Vioque et al. (2018) and are listed in LABEL:tab:Table1. We found that 21 stars from our sample are placed below the main sequence and hence the parameters could not be estimated. Since these stars are catalogued as HAeBe stars, they may be properly positioned in the pre-main sequence location in previous studies. HAeBe stars are known to show photometric variability (van den Ancker et al., 1998). The stars which are found below the main sequence in Figure 2 & Figure 3 may show photometric variability. Also, some stars are positioned in the evolved region of the evolutionary track. Further studies are needed to evaluate the nature of these candidates.

3.4 Mass accretion rates of HAeBe stars

The mass accretion process during the pre-main sequence phase represents one of the important mechanisms associated with star formation. In T Tauri stars, mass accretion is through a process known as magnetospheric accretion (MA) in which the magnetosphere of the host star truncates the circumstellar disk at a few stellar radii and the material from the disk fall on to the star at free-fall velocities along the magnetic field lines, which in turn create shocks at the surface of the star. The hot (104 K) emission from the post-shock gas appear as excess in the UV continuum of T Tauri stars (e.g. Calvet & Gullbring, 1998; Gullbring et al., 1998; Hartmann et al., 1998; Bouvier et al., 2007). The MA accretion model may not be a viable mode of accretion in HAeBe stars since there are no convincing signatures of a magnetic field in these systems (Alecian et al., 2013). Although many studies suggest disk accretion as the possible mechanism in Herbig Be stars, a consensus is yet to be obtained whether MA accretion can account for mass accretion in low mass HAeBe stars (Muzerolle et al., 2004). For the present work, we employed magnetospheric accretion formalism while calculating the $\dot{M}_{acc}$ in HAeBe stars.

The H$\alpha$ line flux values of 102 HAeBe stars are taken from Mathew et al. (2018), Fairlamb et al. (2017) and Mendigutía et al. (2011b). In addition, we took the H$\alpha$ equivalent width (EW) for four stars from Boehm & Catala (1995), Baines et al. (2006), Borges Fernandes et al. (2007) and Vieira et al. (2011). The EW is converted to line flux from the $R$ band magnitude using the method mentioned in Mathew et al. (2018). Hence, for the present analysis, we will be using the H$\alpha$ line flux (FHα) values of 106 HAeBe stars. The H$\alpha$ line flux is converted to luminosity (LHα) using the equation,

[TABLE]

where $d$ is the distance in pc. The accretion luminosity (Lacc) is calculated using the empirical relation given in Fairlamb et al. (2017), which is reproduced below.

[TABLE]

The ($\dot{M}_{acc}$) can be derived from the Lacc using the relation,

[TABLE]

where $M_{*}$ is the mass of HAeBe stars, estimated in Sect. 3.3 and given in LABEL:tab:Table1; $R_{i}$ is the disk truncation radius. For T Tauri stars, $R_{i}$ is assumed to be 5 R∗ (Gullbring et al., 1998; Costigan et al., 2014). HAeBe stars are fast rotators and therefore have a smaller co-rotation radius. The disk truncation radius, $R_{i}$, should be smaller than the co-rotation radius (Shu et al., 1994). Thus in this work, we adopt disk truncation radius, $R_{i}$ = 2.5 R∗ (Muzerolle et al., 2004; Mendigutía et al., 2011a; Fairlamb et al., 2015). The stellar radius $R_{*}$ for the 106 HAeBe stars are calculated using the equation,

[TABLE]

where $L_{*}$ is the bolometric luminosity of the star, which is calculated from the $V$ magnitude, bolometric correction and Gaia distance. Using the calibration table listed in Pecaut & Mamajek (2013), we identified Teff and bolometric correction corresponding to the spectral type of the HAeBe star. The $V$ magnitudes of 101 HAeBe stars are compiled from AAVSO Photometric All Sky Survey (APASS; Henden et al., 2016) and Tycho-2 (Høg et al., 2000) catalogues. The remaining 5 stars which had no $V$ magnitude listed in both the catalogues are taken from the following references $-$ Herbst & Shevchenko (1999), Getman et al. (2008), Fresneau & Osborn (2009) and Girard et al. (2011).

3.5 Correlation analysis of mass accretion rates with stellar parameters

The relationship between the $\dot{M}_{acc}$ and the stellar parameters such as age and mass are analyzed in some of the studies (e.g. Mendigutía et al., 2011a, 2015; Fairlamb et al., 2017). However, in the context of precise mass and age estimates using Gaia DR2, we re-assessed the relations between $\dot{M}_{acc}$ and the stellar parameters using the largest sample of 106 HAeBe stars to date. Figure Figure 4 illustrates the correlation between the $log(\dot{M}_{acc})$ and age of HAeBe stars. It can be seen that $log(\dot{M}_{acc})$ decays exponentially with the age of HAeBe stars. This trend is discussed in the studies of Manoj et al. (2006) and Mendigutía et al. (2012). From the rate of decline of accretion rate, it is possible to estimate the disk dissipation timescale, $\tau$, using the relation,

[TABLE]

where $t$ is the age of HAeBe stars. By fitting the relation to the set of data points, we obtained the disc dissipation time scale, $\tau$ = $1.9\pm 0.1$ Myr. This value is near to that given in Mendigutía et al. (2012), which is $\tau$ = $1.3^{+1.0}_{-0.5}$ Myr. It may be noted that $\tau$ for T Tauri stars is 2$-$4 Myr (Fedele et al., 2010; Takagi et al., 2014). We find a lower $\tau$ value for HAeBe stars indicating that the disk dissipation timescale is shorter for intermediate mass young stars compared to their lower mass counterparts.

Further, another parameter used in the literature for calculating the rate of decline of accretion rate with age in young stellar objects (YSOs) is the power law index, $\eta$ (Hartmann et al., 1998; Mendigutía et al., 2012; Fairlamb et al., 2015). The relation which connects $\dot{M}_{acc}$ with age of the star can also be considered as a power law distribution of the form,

[TABLE]

From the best fit to the distribution of the data points in Figure Figure 4, we obtained $\eta$ = $1.2\pm 0.1$. This value is on the lower end when compared to the estimates of Mendigutía et al. (2012) and Fairlamb et al. (2015), which are $1.8^{+1.3}_{-0.7}$ and $1.92\pm 0.09$, respectively. This could be because of the increased number of high mass HBe stars in our sample.

In Figure 5 we plotted the correlation between $\dot{M}_{acc}$ and stellar mass. Our sample of HAeBe stars cover a broader range in spectral type/mass and $\dot{M}_{acc}$ ($\sim$ $10^{-3}$ $-$ $10^{-7}$ $M_{\odot}$ yr*-1*), when compared to the sample of stars given in Mendigutía et al. (2011a). This is because our sample contains high mass candidates with mass $>$ 6 $M_{\odot}$, whereas those listed in Mendigutía et al. (2011a) are with mass $<$ 6 $M_{\odot}$. The best fit for our sample of HAeBe stars in Figure 5 provides the relation $\dot{M}_{acc}$ $\propto$ $M_{*}^{2.8{\pm 0.2}}$. Mendigutía et al. (2011a) did a similar study and obtained a steep power law relation, $\dot{M}_{acc}$ $\propto$ $M_{*}^{5}$. The reason for a steeper power law relation might be due to the unavailability of massive HAeBe stars in their sample. The Pearson correlation coefficient for our fit is 0.81 for a sample size of 106 stars. Incidentally, Fairlamb et al. (2015) obtained the relation between stellar mass and accretion rate as $\dot{M}_{acc}$ $\propto$ $M_{*}^{3.72\pm 0.27}$, which comes close to our estimate. It may be noted that the mass dependence of accretion rate in T Tauri stars is lower than the value calculated for HAeBe stars, i.e., $\dot{M}_{acc}$ $\propto$ $M_{*}^{2}$ (Muzerolle et al., 2005; Natta et al., 2006).

The best fit and the confidence limits for Figures 4(a), 4(b) and 5 are determined using the Monte Carlo method to account for the associated uncertainties in age, mass and $\dot{M}_{acc}$. For this purpose, 100,000 samples for age, mass and $\dot{M}_{acc}$ were created. The values for these samples were randomly drawn from a Gaussian distribution having a mean equal to the actual measured value in each case and a standard deviation equal to the associated uncertainty. The best fit is then estimated for each of the resulting data set. The fit parameters obtained for all 100,000 datasets results in a normal distribution, the mean of which, along with its 3 $\sigma$ confidence limits, is taken as the final best fit.

3.6 Quantifying IR excess using spectral index

IR excess in the Spectral Energy Distribution (SED) is one of the important criterion used in identifying YSOs. It provides a better understanding of the composition of gas and dust in the disk of a PMS star. Lada & Wilking (1984) differentiated YSOs into different classes from the shape of their SEDs in the IR region. Lada (1987) quantified the classification scheme using the slope in the IR region of the SED, which are known as Lada indices. The YSOs can be classified as Class 0, Class I, Class II and Class III, based on the steepness of the indices at various wavelength intervals (Lada, 1987; Andre et al., 1993). The estimation and analysis of Lada indices are very important in studying the evolution of HAeBe stars as it gives an idea about the evolution of the CSM. The equation defining the spectral index (Lada, 1987; Wilking, 1989; Greene et al., 1994) is expressed as,

[TABLE]

For our analysis we consider the spectral index, $n_{2-4.6}$, which is the ratio of the flux values at 2MASS (Skrutskie et al., 2006) $K_{s}$-band (i.e., $\lambda_{1}$ = 2.159 $\mu$m) and WISE (Cutri et al., 2013) W2-band (i.e., $\lambda_{2}$ = 4.6 $\mu$m). The age estimates are available only for 110 stars. However, the spectral index is not calculated for the HAeBe stars CPD-61 3587B and LkHA 224 due to the unavailability of WISE magnitudes. Hence, a sample of 108 stars is used for this analysis.

A plot between spectral index ($n_{2-4.6}$) and age of HAeBe stars is shown in Figure 6. No clear trend is evident in the variation of $n_{2-4.6}$ with respect to age in Figure 6. However, when we categorize the HAeBe stars in various mass bins, a tentative trend seems to emerge. For HAeBe stars with mass less than 2 $M_{\odot}$, the $n_{2-4.6}$ value is around -1. For stars in the mass range 2$-$7 $M_{\odot}$, there is a scatter in the distribution of $n_{2-4.6}$ values, with majority of the data points around $n_{2-4.6}$ = -1. The majority of massive stars (mass $>$ 7 $M_{*}$) are showing IR index from 0.5 to -3, where the negative index is more prominent in these high mass candidates. This agrees with the study of Alonso-Albi et al. (2009) where they suggested that in high mass HBe stars disk dispersal is faster and disk masses are 5$-$10 times lesser than low mass counterparts. They explained this observation by suggesting that photoevaporation mechanism due to the UV radiation disperses the gas content in the disk, after which only a thin dusty disk containing large grains remain. The caveat in our study is the upper bound in age quoted for massive HBe stars.

3.7 Comparison with Vioque et al. (2018)

Calculation of stellar parameters from the theoretical HR diagram involves the use of derived variables such as bolometric luminosity (Lbol) and effective temperature (Teff). The estimation of these quantities from magnitude and color/spectral type involves approximations and comparison with standard calibration tables, which add more errors into the calculation of age and mass. Our analysis is based on the Gaia CMD rather than a theoretical HR diagram. Using a uniform photometric system combined with precise distances can give accurate estimation of age and mass of PMS stars. Thus, combining the refined stellar distances and the most consistent photometric measurements from the Gaia DR2, along with the help of synthetic photometry isochrones and evolutionary tracks from the MIST, accurate stellar ages and masses are estimated in this work. In comparison, Vioque et al. (2018) adopted the theoretical HR diagram for the analysis of age and mass. The differences between our analysis with that of Vioque et al. (2018) are listed below.

• •

We used the photometry and distances from the Gaia for the estimation of age and mass of HAeBe stars. Vioque et al. (2018) used only the Gaia distances for the same.

• •

Vioque et al. (2018) used the distance estimation method outlined in Bailer-Jones et al. (2018) and the calculated distances have high error bars than the values listed in the catalogue released by Bailer-Jones et al. (2018). We used the distances listed in the catalog of Bailer-Jones et al. (2018). For example, the distance of star DG Cir from Bailer-Jones et al. (2018) is $821^{+30}_{-28}$ pc. For the same star Vioque et al. (2018) estimated a distance of $833^{+52}_{-43}$ pc.

• •

We used RV = 5 for the AV calculation of HAeBe stars whereas Vioque et al. (2018) used RV = 3.1. This is because Hernández et al. (2004) showed that total to selective extinction RV = 5 better reproduces the stellar parameters of HAeBe stars. Also, it is understood that the photometric variability and high value of reddening in HAeBe stars are not due to the interstellar medium, but due to dust particles with large grain size in the CSM (see Gorti & Bhatt, 1993; Manoj et al., 2006).

• •

For a statistical comparison of stellar parameters with Vioque et al. (2018), we also estimated ages and masses of HAeBe stars with RV = 3.1. The median of the fractional difference between our ages with RV = 3.1 and Vioque et al. (2018) ages is calculated to be within 19%. The fractional difference is defined as,

[TABLE]

For masses, the fractional difference is found to be within 8%. The difference in age and mass could be due to our use of the Gaia CMD and the MIST models whereas Vioque et al. (2018) used the HR diagram and the PARSEC models (Bressan et al., 2012). This comparison is extended to our actual estimates of age and mass for RV = 5. The median of the fractional difference of age and mass between our work (RV = 5) and Vioque et al. (2018) is within 31% and 17% respectively.

• •

Vioque et al. (2018) used the H$\alpha$ EW for correlation studies with age and mass of HAeBe stars. However, for our analysis, we used the H$\alpha$ line flux, from which the $\dot{M}_{acc}$ is calculated, which is used for the correlation analysis with age and mass of HAeBe stars. It may be noted that Mendigutía et al. (2012) have reported that the H$\alpha$ EW may not give a clear idea about the gas content of the disk. They suggested estimating $\dot{M}_{acc}$ from the H$\alpha$ line flux to study the gas content of the disk, which we employed in this work.

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Vioque et al. (2018) used the continuum flux distribution from 1.24 $\mu m$ to 22 $\mu m$ for the analysis of IR excess in HAeBe stars. This includes the flux measurement from the WISE W4 photometric band, which is not very reliable as the images of many HAeBe stars are not registered in W4 band. Hence, we restricted the analysis to WISE W2 band, which provides better photometry with good SNR and is free of artifacts.

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Vioque et al. (2018) found that there is a break in IR excess with mass. We also arrived at a similar conclusion. However, they suggested considerably low IR excess for massive HAeBe stars whereas we see a considerable range in IR excess values in this work (see Figure 6).

4 Summary

The present study made use of the unprecedented capability of the Gaia mission to derive the stellar parameters such as age and mass of HAeBe stars. Using the stellar parameters and the compiled $H\alpha$ flux, the $\dot{M}_{acc}$ for the sample is estimated. Also, we investigated the capability of the IR spectral index as a better method in quantifying the IR excess. The main results of this study are summarized below.

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Better accuracy of the Gaia DR2 astrometry is confirmed from the comparison of the Gaia DR2 distances with the previously estimated values from the literature. We adopted the distance values compiled in Bailer-Jones et al. (2018), which are the best distance estimates to date with minimal errors, for the sample of HAeBe stars used for this study.

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Age and mass of 110 HAeBe stars are estimated using the Gaia CMD, with the aid of MIST isochrones and evolutionary tracks. In our knowledge, no studies were done till now which calculated the age and mass of a confirmed sample of HAeBe stars using both the photometry and distance from the Gaia mission. Since we employed Gaia CMD for estimating the age and mass of HAeBe stars, we avoided considerable errors when these quantities are estimated from theoretical HR diagram.

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Mass accretion rates are calculated from the $H\alpha$ line flux measurements of 106 HAeBe stars, which is the largest sample to date. Since we had used distances and the stellar masses derived from Gaia DR2 data in the calculation of $\dot{M}_{acc}$, our estimates can be more accurate than previous studies.

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The disk dissipation time scale derived for our sample of HAeBe stars is $1.9\pm 0.1$ Myr, which is consistent with the previous estimate (Mendigutía et al., 2012).

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We found that mass accretion rate is related to the mass of HAeBe stars in the form of the relation, $\dot{M}_{acc}$ $\propto$ $M_{*}^{2.8\pm 0.2}$.

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We calculated the spectral index ($n_{2-4.6}$) in quantifying the IR excess in HAeBe stars. A correlation between the spectral index and age suggested a distinction between the disk of HAe and HBe stars. Massive HBe stars with ages $<$0.1 Myr show diverse values of the infrared spectral index, ranging from 0.5 to $-$3, with the negative index being more prominent. The possibility of photoevaporation resulting in the dissipation of gas content in the disk and thereby forming a thin disk and the formation difference between HBe and HAe stars needs to be explored from further studies.

We would like to thank the anonymous referee for providing helpful comments and suggestions that improved the paper. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC; https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular, the institutions participating in the Gaia Multilateral Agreement. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Also, we made use of the VizieR catalog access tool, CDS, Strasbourg, France.